tag:blogger.com,1999:blog-21067129960789876992021-07-30T00:39:51.885+08:00觀楓日誌Blog with all sorts of random stuffs tracking my life.Forretriohttp://www.blogger.com/profile/18048483702091533151noreply@blogger.comBlogger790125tag:blogger.com,1999:blog-2106712996078987699.post-30810498228965405672021-07-29T01:47:00.001+08:002021-07-30T00:39:17.070+08:00奧運/麥兜/臘鴨<div style="text-align: left;"><div><div style="text-align: left;"><i>年少，練了六套腳法 </i><i>可惜我依然未覺夠用。</i></div><div style="text-align: left;"><i>年晚，又培育了珊珊！</i><i>可惜我依然未覺......</i><i>但我依然未覺......</i></div><div style="text-align: left;"><i><br /></i></div><div style="text-align: left;"><i>尋晚，食了六個餐包 </i><i>可惜我依然覺得仍未十分飽。</i></div><div style="text-align: left;"><i>尋晚，夢見下塌包山！</i><i>可嘆是我只含住個包，無－－力－－挽－－。</i></div></div><div style="text-align: left;"><br /></div><div style="text-align: left;">－－麥兜故事《黎根之歌》</div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><div>1996年亞特蘭大奧運，風后李麗珊在滑浪風帆項目奪得金牌。你還記得嗎？</div><div><br /></div><div>很抱歉，那時候的我還小，對奧運這種世界大事仍然一無所知。</div><div><br /></div><div>我關注奧運最多的應該是2004雅典奧運，到了2008我已經沒在看電視了；2012我的印象僅停留在那流傳千古的開幕式(還有牛下女車神)，2016那屆不值一提。</div><div><br /></div><div>然後是2020東京奧運。我的主要感想是：你他媽別擋著我們辦同人展，而且一擋還擋了快兩年。我知道這不完全是日本的責任，但從結果來看的確就是這樣。當然如果要說甚麼奧運的政治經濟效應，甚麼東升西降、甚麼建蚊子館或者社區活化都是我感興趣的內容，只是這些跟我本人關係不大，這些最終都只會化為知識而不是回憶。</div><div><br /></div><div>我對珊珊奪金的印象只有一個，就是那句「香港運動員不是垃圾」，連同臘鴨一起封印在麥兜故事這部可以完美代表那個特殊時空下本土文化的神作裡面。誰又會想到這個沒法保證精英運動員生計的文化砂漠可以養出奧運金牌得主呢？</div><div><br /></div><div>這面金牌引出了各方勢力前來沾光，但感觸最深的肯定還是香港人。正如馬勒當拿率阿根廷在兵敗福克蘭後踩著死敵捧走世界盃，又或者1966年大英帝國瀕臨瓦解之時奪得世界盃(2021其實也差不多，可惜被一頓謎之操作搞沒了)一樣，體育往往可以成為國民最好的慰藉。香港兩次奪金對應「回歸」與「二次回歸」兩個風雨飄搖之際可能只是巧合，卻讓奪金這事更別具意義。</div><div><br /></div><div>感謝張家朗和一眾其他參加東奧的香港運動員。希望大家要堅持，不要放棄。</div><div><br /></div><div>2021.7.29</div><div><br /></div><div><br /></div></div><div style="text-align: center;"><iframe allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" frameborder="0" height="315" src="https://www.youtube.com/embed/UcOqdibdFCI" title="YouTube video player" width="560"></iframe></div>Forretriohttp://www.blogger.com/profile/18048483702091533151noreply@blogger.com0tag:blogger.com,1999:blog-2106712996078987699.post-26921710626729643102021-07-25T02:55:00.005+08:002021-07-29T00:43:59.715+08:00Thoughts on IMO2021 Q2<div>IMO 2021 is finally over. As usual I skimmed through the question and focus on the inequality problem where I usually perform the best. It was Q2 this year, but it is not an average Q2.</div><div><br /></div><div>It turned out to be as hard as Q3 (mean score 0.375 against Q3's 0.372, but Q2 gives out more partial scores and more zeros), both harder than this year's Q6 (mean 0.481). Possibly one of the most controversial Q2 in IMO history. What makes it so interesting? Here are my thoughts.</div><div><br /></div><div>First let us look at the question.</div><div><br /></div><div><b>Problem (IMO2021 Q2).</b> Show that </div><div>$\sum _{i,j} \sqrt{|x_i-x_j|} \leq \sum _{i,j} \sqrt{|x_i+x_j|}$</div><div>for all real numbers $x_1,...,x_n$.</div><div><br /></div><div>If you have already spent time onto this problem, here is the solution. This is similar to the solution mentioned by TheUltimate123 in the <a href="https://artofproblemsolving.com/community/c6h2625850p22697952">AoPS thread</a>.</div><div><br /></div><div><u>Claim 1.</u> The case $n = 0,1$ is trivial.</div><div><br /></div><div><u>Claim 2.</u> LHS is invariant upon shifting all $x_i$ by a constant (let us simply call that "shifting" for the rest of the solution)</div><div><br /></div><div><u>Claim 3.</u> If $x_k = 0$ for some $k$ then the $x_i$-related terms on both sides are the same which is</div><div>$2\sum _{i\neq k} \sqrt{|x_i|}$. Therefore we now WLOG assume that all terms are non-zero.</div><div><br /></div><div><u>Claim 4.</u> If $x_k+x_l=0$ for some $k\neq l$ then the $x_k$ or $x_l$-related terms on both sides are also the same, which is $2\sqrt{2|x_k|} + \sum _{i\neq k,l}(\sqrt{|x_i-x_k|}+\sqrt{|x_i+x_k|})$. </div><div><br /></div><div><u>Claim 5.</u> RHS is not minimal upon shifting unless $x_k+x_l=0$ for some $k,l$.</div><div><br /></div><div>Proof: Jensen gives that </div><div>$\sqrt{|x+y+\varepsilon|} + \sqrt{|x+y-\varepsilon|} \leq 2\sqrt{|x+y|}$</div><div>for $x+y\neq 0$ and $\varepsilon \leq |x+y|$. </div><div>Summing over all $x_i$ gives</div><div>$\sum _{i,j} (\sqrt{|x_i+x_j+\varepsilon|} + \sqrt{|x_i+x_j-\varepsilon|}) \leq 2\sqrt{|x_i+x_j|}$.</div><div>for sufficiently small $\varepsilon$. Therefore a shift of either $\varepsilon /2$ or $-\varepsilon /2$ would give a smaller RHS while having LHS fixed.</div><div><br /></div><div>Note that $x_k+x_l\neq 0$ is required to maintain convexity of $\sqrt{|x+y|}$.</div><div><br /></div><div>Therefore the induction is completed. If $x_k=0$ for some $k$ then we reduce to the $n-1$ case by claim 3. Otherwise shift until $x_k+x_l=0$ for some $k,l$, then reduce to the $n-2$ case by claim 4.</div><div><br /></div><div>The above also gives the equality case in full. Firstly adding arbitrarily many zero terms does not affect the sum. If we assume non-zero terms then the only instance where RHS decreases is by shifting, so in order to obtain equality the terms must be canceled pair by pair without the need of shifting. We therefore conclude that equality holds if and only if the terms are symmetric along zero.</div><div><br /></div><div>*</div><div><br /></div><div>There are alternative solutions using completely different approaches like the use of integral to prove the more generalized case $E|X+Y|^{1/2} \geq E|X-Y|^{1/2}$ for random variables $X,Y$. Even more fascinating, one used the integral</div><div>$\sqrt{|a+b|}-\sqrt{|a-b|} = \frac{1}{\sqrt{2\pi}}\int ^{\infty}_0 x^{-3/2}(\cos (a-b)x-\cos (a+b)x)dx$</div><div>$= \frac{1}{\sqrt{2\pi}}\int ^{\infty}_0 2 x^{-3/2} \sin ax \sin bx dx$. </div><div><br /></div><div>It is also note worthy that the original problem uses the exponential $\alpha = 1/2$. The statement holds for all $\alpha \in (0,2]$. Convexity works all the way up to $\alpha = 1$ but college techniques is absolutely necessary for higher $\alpha$. One approach is to use linear algebra and binomial theorem for non-integer exponents(notice that when $\alpha = 2$ it simply reduces to prove that $4\sum x_i x_j \geq 0$ which is obvious. But then for $\alpha \in (1,2)$ you can also write $|x_i-x_j|^{\alpha} = (x_i^2+x_j^2-2x_ix_j)^{\alpha /2}$, then you may expand and compare both sides using positive-definiteness), and the other is a generalization of that integral identity (with the help of gamma function).</div><div><br /></div><div>You might have noticed something here already: the abundance of calculus solutions, the clear generalization to something famous and common in undergraduate maths, and the flexibility in exponential (cf. most $a,b,c$ type inequalities that you saw in 2000s-2010s IMOs), all suggests that this is a very good question for undergraduate contests.</div><div><br /></div><div>However if we consider IMO to be the pool of the most talented math students in the world (even better than those participating undergraduate contests on average), why is this a hard problem to them? And why did they perform poorly at the end?</div><div><br /></div><div>I figured out the solution almost immediately, like within 15 minutes, and the flow of thoughts is as follows: the shift is clear immediately. Then I tried to solve the case $n=2$, which is not easy already. By using the parametrization $x_2 = rx_1$, it is found that the equality is tight if $r=-1$. Putting back to the inequality with $x_1$ and $x_2$, it can be found that when $x_1=-x_2$ the terms on both sides are equal. The cancellation trick is soon found to be working with larger $n$. We now know that induction may work as long as we can reduce to these cases. (I missed the case $x_k=0$ when I first solved the question, so I didn't get a 7 in that sense...)</div><div><br /></div><div>By reducing to these case, we must show that shifting to these case gives a smaller RHS, and this is what we need to prove. We applied Jensen and showed that we can always get smaller as long as $x_k+x_l \neq 0$ so we are done.</div><div><br /></div><div>...or not?</div><div><br /></div><div>You might have spotted the problem already. <b>The hard bit of the question is the indirect relation between the fact that you can shift to reduce RHS and the goal that you can shift to a smaller RHS that $x_k+x_l=0$.</b></div><div><br /></div><div>It goes through only if you have a calculus sense, or else it could trap you forever.</div><div><br /></div><div>For starter let us consider to shift by the maximum possible distance $\pm\min |x_i+x_j|/2 = \pm t$ so that we reached a singular point (where $x_k+x_l=0$...). The problem is: we only know that a either a shift of $+t$ or $-t$ gives a smaller RHS but not necessarily both. If you shift to the point where $x_k+x_l=0$ you are not guaranteed a smaller RHS.</div><div><br /></div><div>Or, if you shift little by little to reduce RHS, can you guarantee that you end up with a singular point?</div><div><br /></div><div>These are never a problem if you know calculus argument, and they can only be understood via calculus argument.</div><div><br /></div><div>From a global point of view, the sum is definitely increasing with large enough shifts. Since the sum is also bounded below and is continuous, there must be a global minimum. Since the minimum does not occur at the smooth part it must be at one of the singular point. We can shift directly to that point to complete the induction.</div><div><br /></div><div>To shift gradually you may argue that the derivative between two singular points do not change signs so one of the two neighboring singular point must be a local minimum [or even weaker, a local minimum with respect to the closed interval bounded by the two singular points]. Alternatively, since we know that $(\sqrt{x})' = 1/(2\sqrt{x})$ which rockets as $x\to 0$, we argue that the derivative of $\sqrt{|x_k+x_l|}$ overwhelms all other terms as we shift $x_k+x_l\to 0$, so that must incur a minimum [hence even singular point is a local minimum]. </div><div><br /></div><div>And how can you argue that by "elementary means"? Probably not, unless the official solution suggests something spectacular.</div><div><br /></div><div>If you check everything else in the solution they are pretty standard. induction of course, simple special case ($x_k=0$) and a more complicated special case ($x_k+x_l=0$), substitution [in fact, instead of a shift, we may apply the substitution $x_i = y_i+t$ to achieve the same] to hold one side invariant, Jensen on convex functions --- these are all standard tricks in IMO. It is the final link that completes the solution, is hard to realize and that link is, regrettably unavoidable.</div><div><br /></div><div>It is a beautiful and insightful inequality. Again quoting someone in the thread -- the beauty of this problem is that $n=2$ provides everything you need: minimal condition and the shifting. (Although to be fair, $n=2$ hides the technical problem as described above, and you will only meet that at $n\geq 3$.) It simply requires Jensen (or even just elementary comparison because it is just square root) in a two line calculation. We do not need 30 lines of machinery like other IMO inequalities did.</div><div><br /></div><div>We can continue the list and praise the problem in many more different ways. The only criticism is that the problem unfortunately does not belong to IMO.</div><div><br /></div><div>*</div><div><br /></div><div>I last wrote about IMO problems in 2006, before this blog opened. I wrote that in my previous blog, a site that is long abolished (at least I do not have to worry about Blogger closing soon...yet).</div><div><br /></div><div>I was of course, too immature to understand what happened -- I copied someone else's solution and put it on my blog. For whatever reason that post received tons of comments out of nowhere: recalling that discussion now I believe that those people are truly qualified to do these IMO problems. It is still a mystery up to now how did they found my post (out of a blog that never talked about advanced mathematics otherwise) and open a contextful discussion there, but this is the beauty of Internet in the 2000s.</div><div><br /></div><div>Without running into a nostalgic loop, let me finish with that particular IMO problem that I discussed back in 2006. That problem was 2001 Q2 -- another Q2, another inequality, and another problem that allows elegant solution using Jensen's inequality. </div><div><br /></div><div><b>Problem (IMO2001 Q2).</b> Prove that for all positive real $a,b,c$ the inequality $\sum _{cyc} \frac{a}{\sqrt{a^2+8bc}} \geq 1$ holds.</div>Forretriohttp://www.blogger.com/profile/18048483702091533151noreply@blogger.com0tag:blogger.com,1999:blog-2106712996078987699.post-73200236360754579922021-07-23T02:04:00.001+08:002021-07-23T12:26:54.675+08:00被青梅竹馬抓來(略) (2)：別人十年磨一劍，你一年磨一劍已經非常快了<div style="text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-1b0mYuNQOuA/YPmwJmPFNfI/AAAAAAAABu4/PCwj8hkMuakenJn7vqg6yIRExcM9hqh-ACLcBGAsYHQ/s1200/90422792_p0_master1200.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="914" height="400" src="https://1.bp.blogspot.com/-1b0mYuNQOuA/YPmwJmPFNfI/AAAAAAAABu4/PCwj8hkMuakenJn7vqg6yIRExcM9hqh-ACLcBGAsYHQ/w305-h400/90422792_p0_master1200.jpg" width="305" /></a></div><div style="text-align: center;"><i><span style="font-size: xx-small;">"優雅な午後"</span></i></div><div style="text-align: center;"><span style="font-size: xx-small;"><span face="Arial, sans-serif" style="background-color: white;">Character design: <a href="https://www.plurk.com/kuonyuu" style="color: #3d81ee; text-decoration-line: none;">@kuonyuu</a>, Illust: <span style="color: #3d81ee;"><a href="https://twitter.com/mixyu_tea">@</a></span></span><span style="text-align: left;"><span face="Arial, sans-serif" style="color: #0000ee;"><a href="https://twitter.com/mixyu_tea">茶桜みゅ</a></span></span><span face="Arial, sans-serif" style="background-color: white; text-align: left;"> commissioned by forretrio. <a href="https://www.pixiv.net/artworks/90422792">Pixiv</a></span></span></div><div style="text-align: center;"><span style="font-family: arial; font-size: xx-small;">Editing and re-posting are prohibited // 無断転載、無断使用禁止です</span></div><div><br /></div><div><br /></div><div><br /></div><div><span style="font-size: large;">帝都的上層社會由一張張緊密的關係網組成。從冒險者協會到銀行工會到各種商會，帝都充斥著交流情報的地方。只要你在那個圈子裡，今天誰跟誰約會，或者昨天誰跟誰吃飯其實都不難打聽到。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">最近在校園出盡風頭的白髮青年無疑是大家最近感興趣的對象。雖然他登場的時候沒多少人認得出他來，但只要在場有一個人認識他，那在賽後想調查他一點都不困難。身為以前的學生，完全沒人能把他認出來才奇怪。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">從比試到正式上課隔了數天的時間，足以讓他的背景在學生之間廣為流傳。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">庫里斯，二十三歲，出身自某小城市的男爵家。以平民的身份入學並且成功進入魔法科。實戰非常優異，在冒險相關的課題上經常展現極強的個人戰力。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">在入學大半年後因為與高階貴族衝突並對其集團發起挑戰，並以一人之力將對方全數碾壓，第二天隨即退學在帝都中消失。這些年一直在外面作為冒險者活躍著，以接受委託的形式在不同隊伍中遊走，不知為何沒有加入任何隊伍的打算。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">主力當然是風屬性，但其他屬性也有一定適性且戰鬥風格多變，可以勝任隊伍中不同角色。委託中較少發揮其多面手的能力，有隊伍曾形容將某位置空出來讓他頂上的話很容易對其產生依賴。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">最近不知道為何推掉所有委託孤身一人回到帝都，並回到校園成為教師。在帝都在冒險者體系以外人脈不多。唯一比較相熟的是當年的同班同學，目前擔任宰相副手一職的伯爵之女。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">這些經歷不禁讓一些人覺得這傢伙該不會是討厭貴族的人，畢竟這個班上超過一半跟當年被教訓的學生一樣都是貴族。不過有認真跟他交手的學生多半還是對他抱有期待，因為那天的比試實在太震撼了。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">至少伊雅娜是這樣想的。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">慘敗給她將來老師的一幕深深地烙在她的腦海中。她一直在想怎樣打才可以對他構成威脅，但她在腦裡每模擬一次戰鬥，得出的結果就使她更絕望。她的結論是，她要快上整整一倍才能突破他的防御，這對她來說實在不太可能。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">至於他最後的提點，她把這句話原封不動地丟給了她的父親。父親的回應是，是對也是錯。對的是，全力催出來的電光劍在面對很強的對手時，蓄力的空窗期的確會對她不利；錯的是她的劍足以擊破大部分對手，把電光劍的威力催出來就能發揮最大優勢。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">這個很強的對手到底是多強？她這樣問道。她父親想了想後表示：帝都就算算上冒險者，能兼具魔法戰力的劍士不到十位。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">她沒有告訴父親的是，這人似乎不是會魔法的劍士，而是會揮劍的法師。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">父親還說，他有興趣見一下這位年輕人。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">她父親是誰？一代劍術宗師，每年無數人拜其門而不得入，而今天父親居然開口說想見他？</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">想到自己接下來會接受這種人指導，她對之後的課就更期待了……</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">*</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">今天是上課的第一天。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">魔法科以外的新生雖然都想跟新老師見上一面，不過所有新生都要到所屬教室報到，要見面只能等下課以後了。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">庫里斯已經跟其他教師寒喧過了。一些老牌的教師雖然沒有教過魔法科的學生，跟他們相處的經驗卻也不少。在他們看來，庫里斯再強也只是一介武夫，就算在實戰上可以讓小姐少爺們服氣，日常相處也還是一大問題。他自己可不這樣想，有最強腹黑軍師指點的他才不會搞砸呢。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「大家早安～歡迎來到國立魔法學園，也歡迎大家成為魔法科的一分子。再次自我介紹一次，我是庫里斯，將會擔任魔法科的導師一職。特長是風魔法－－嗯，相信在座各位已經充分理解這一點了吧？」台下立刻傳來殺人般的目光。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">教室門口突然傳來「咚」的一聲，一個水桶從天而降。奇怪的是沒有半點水飛濺出來，但那沉重的聲響怎樣也不像空水桶。在教室後排的幾位男學生目睹這一幕，同時發出了小小的歡呼聲和嘆氣聲。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「哎呀，真是危險～」庫里斯從講台上跳下來，水桶在他的操控下飛到他的面前：「我看看……裡面裝的居然是冰？這樣砸到頭肯定要進醫院呢。老師我可以接受水桶，但是冰桶有點過份了喔，克萊伊同學。」他特地把水桶裡面展示給同學看，只見裡面的水已經結成一整塊冰。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">被點名的克萊伊滿臉通紅，在同學熱切的眼光中站了起來：「老……老師怎能憑空污人清白呢，我怎樣看都不像會這樣陷害老師啊。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「嘛，老師的確不知道誰把水桶放上去，不過我看到你嘗試用魔法把水桶推下來呢。這樣遠距離操作其實很顯眼，我建議你下次準備好觸發性的魔法陣喔。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">只見庫里斯在水桶底部抹了一把，然後讓水桶浮在高處：「這樣－－」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">他伸出手臂掃過水桶下方時冰桶一百八十度翻轉，一桶水立刻傾瀉而下：「想要查出是誰搞的鬼就比較困難了哦。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">把水無聲無息的變成冰再變回去當然是他的小把戲。學生們滿是疑惑的眼神讓他非常滿意：「今天是你們第一天上課也是我第一天教書，我就先說說我的教學方針好了。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「在此之前，我希望你們想一下－－你們來到這裡，是希望得到甚麼呢？既然你們進入了魔法科，那就代表你們的能力已經遠超常人，甚至已經可以成為即戰力了。這樣的話為甚麼要浪費三年在這裡再聽一次你們以前很可能已經聽過的知識呢？」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「如果你們是貴族的話，在這裡就讀就只是一個過程而已。身為貴族擁有一定的魔法能力就足夠了，過份強大只會讓人懼怕。你們大部分人畢業都會接過家業，在帝都舒適地生活著，這樣魔法再好又有甚麼用呢？」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「對於平民入學的你們，我要恭喜你們：進入魔法科代表通往帝都頂層的大門已經為你們躺開，你們是受益最大的一群。不過你們也可以想一下，進了這裡就一定要從事魔法相關的職業嗎？很多人都覺得身為魔法師可以當冒險者發大財，可是你們知道正是因為魔法師的折損率是冒險者之間最高的一群所以才這麼值錢的嗎？」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「我沒有要勸大家別當冒險者的意思，相反我很樂意以過來人的身份幫助你們。不過我想你們既然有能力進入這個班級，自然也有餘裕考慮標準課程以外的興趣－－你們應該不會只對冒險有興趣吧？」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「我的想法是讓你們花時間找出你們希望學習的東西，然後由我或者其他人來指導。我會花三分一的時間講解標準課程內容裡面比較有用的東西，剩下的就作為課題交給你們了。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「至於另外三分二的時間就是個別指導的時間了。唔－－具體時間要怎樣分配主要還是看你們的興趣在哪個方面。對魔法或者戰鬥有興趣的話可以一起去地下城冒險；就算是鍊金術或者商業這些東西我也可以找我朋友幫忙。當然你們想要找我過招的話只要別偷襲，我隨時都歡迎哦。畢竟－－」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「為師我，不討厭打架呢。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">*</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">第一天的課就這樣結束了。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">雖然有不少人留了下來想要發問，但他們看到公主殿下與她的侍衛也留了下來以後便識趣把機會讓出來。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「庫里斯老師你好。」公主殿下首先打了個招呼她的名字是菲莉，是帝國正室的次公主。本人是頭腦派，體質一般所以成為了唯一一個沒有參加跟老師對戰的魔法科學生。不過她也繼承了優秀的血統，可以使出強力的水跟光魔法。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「菲莉公主您好，」他稍鞠一躬：「雖然公主您沒有參與比試，不過我早就聽說過您是一位優秀的光魔法師。有機會讓我指導您是我的榮幸才對。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「老師過獎了。聽說老師作為冒險者十分活躍，這些實戰經驗對我們學生來說是非常寶貴的呢。不過－－」她稍微頓了一下：「我只是有一丁點擔心，那件事會影響老師你與貴族的關係嗎？」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">他對公主殿下知曉自己的過去並不感意外：「算是年少輕狂吧……不過都是過去的事了呢。如果公主殿下再打聽一下的話應該就知道有人擔保我不會再胡亂出手我才得以回來喔。我可以保證在這個班級每一個都是我的學生，絕對不會因為他們的背景而有所偏袒。如果這方面我有甚麼不足的話就有勞公主殿下指點了－－這樣可以嗎？」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「嗯。」她不置可否地點了下頭然後呼喚伊雅娜道：「其實今天想找老師你的是她才對。伊雅娜～你有東西想問吧？」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">伊雅娜走上前問道：「老師你好，我想問一下關於那天你對電光劍的評價。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「嗯？」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「我問過父親，他也認同你的看法。不過他也說了只有對上很強的對手時才有犧牲威力而加強隱蔽性和速度的價值。即便是這樣，老師也會建議我這樣朝這個方向鍛練嗎？」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「非常好的問題呢。這樣說好了，對你來說電光劍到底是常規招式，還是保命的底牌呢？」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「嗯……算是底牌？我的魔力本來就沒法一直在劍上附魔，上次我也是最後才把這招掏出來。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「作為底牌的招式沒有一擊必殺的能力就沒有意義了。在高階的戰鬥中，所有常規套路都是為了那一兩招殺著而準備的。你想一想，作為殺著到底是可能打不到高階對手的超強力攻擊，還是稍弱一點但是很穩的攻擊更好呢？」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「老師的意思是，對上一般的對手不用全力的電光劍也能贏，所以練習加速版電光劍應付高手更好嗎？」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「這個思考方向沒錯，不過讓我來選的話我覺得兩招同樣重要。全力的電光劍並不是一無用處－－跟不上那速度但擁有優秀防御能力的人和魔物多的是，那招作為破防非常實用。反正底牌又沒人規定只能有一張，都一起練就好了嘛。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「……」伊雅娜同學有點無言。他是把底牌招式當成甚麼了，以為這是回家練一個星期就能熟練地使出來的招式嗎？為了讓魔法效力與她往前突刺的動作同步，她花了半年多的時間才算小成，期間魔力失控電到自己等意外更是不計其數。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「要我說的話，你甚至可以考慮再加練一招－－將輸出的魔力壓制到可以在格劍時隨時使出來的程度。我保證這招由主修物理劍術的妳使出來的話絕對能嚇到對手的。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「老師……你是不是忘記了一件事……」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「嗯？怎樣了？」庫里斯擺出燦爛的笑容。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">她努力地解釋著自己練不來的原因：「輸送的魔力不同的話，電光在劍上面爆發所需要的時間也會不同。我是通過大量練習才讓身體記住這個時間差的，實在沒辦法隨意改變輸入的魔力。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">庫里斯眼睛一亮：「你這不就把問題給自己找出來了嘛！還記得我上課時說過甚麼嗎？</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">我不喜歡指定你們要學習的課題，因為你們既然能進到這裡來，課本上的知識肯定不會是問題，那些你們回家自己看就可以了。我來這裡是希望幫你們找到自己所需要的東西，對吧？</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">現在你所以欠缺的第一件東西已經找到了，那就是跟低輸出兼容的電光劍使用方法。下一步就是找出解決的方法吧？」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「咳唔，所以你這個學期的第一個課題已經決定好了－－」他清了一下喉嚨道：「我希望你花點時間研究一下在劍上附魔的不同方法。在你對兵器附魔有一定了解以後我們再來討論吧。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">不用想太多，我沒說你要收集其他流派秘傳招式的原理。仔細想想看，日常生活中在物體上施加魔法不是很常見的一件事嗎？你把魔力灌在水壼中使水煮沸，跟把魔力灌在劍上使其帶電而且變輕的分別在哪裡呢？你往這個方向想就好了。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「好……好吧。」伊雅娜並不相信老師真的可以幫她練出電光劍的變種，但是作為學習的課題的話還是可以接受。圖書館應該有相關的書籍吧？</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">……才怪。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">老師對她提出了各種奇怪的問題，比如電流是從劍的中央發出來還是只留在表面啦，還者用不同材質的劍有沒有分別之類的。她沒料到每次當她以為自己完成了這個課題以老師總能拋出更多的問題難倒她。她更沒料到的是，這些問題併到一起居然把電光劍的時間差問題解決了－－不過這已經是她入學一年後快一年的事了。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「別人十年磨一劍，你一年磨一劍已經非常快了呢！」老師帶著一貫的笑容這樣應道。當下她真的想一拳灌在老師的帥臉上，不過她覺得這一拳打在風盾上使她骨折的機會更大，所以她才忍住沒有出手。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">這不過是，魔法科的同學們對他們鬼畜老師的認識的開始而已。</span></div><div><span style="font-size: large;"><br /></span></div><div><span face="Arial, sans-serif" style="background-color: white; font-size: large;">=============</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">有聽過科科班嗎？就是那個意思啦。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">魔劍士或者更一般的魔武雙修在這個世界觀下絕無僅有，原因有二：擁有魔法師資質的人在社會中本來就是鳳毛麟角的存在，有能力魔武雙修的人大概跟有能力練棒球二刀流的人一樣多。另一個原因就是物理上的限制：要使出魔法配合物理武器的攻勢其實十分困難，在大部分時間還不如專注於物理和魔法攻擊其中之一。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">比如火焰劍。在劍與劍的碰撞中火焰劍並沒有甚麼優勢，就算成功砍到對方這一瞬間的高溫也不一定帶來決定性的傷害。火焰劍對劍本身的負擔也很大，數十秒的高溫足以使劍的結構永久受損。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">比較合理的做法是使用物理武器同時分別使出魔法，而非把魔法附到物理攻擊之上。庫里斯就是這方面的專家。</span></div></div>Forretriohttp://www.blogger.com/profile/18048483702091533151noreply@blogger.com0tag:blogger.com,1999:blog-2106712996078987699.post-9839094968569149142021-07-04T03:20:00.005+08:002021-07-04T03:20:32.606+08:0004/07/2021: Game optimization patterns<div>Two notable events in the world of competitive gaming.</div><div><br /></div><div>Rolling has been a viable style in classic Tetris and we found Cheez breezing through loads of world records. The way he broke the 100 line speedrun so casually when the previously newly set record was made upon multiple extreme optimization is simply spectacular. Rolling allows one to input above 20Hz edging close to the hardware limit (30Hz for the on-off cycle). The problem now is about consistency and flexibility, and we will know more in upcoming CTM and of course CTWC.</div><div><br /></div><div>The SMB1 Any% record has been broken once again, this time entering the last possible second at 4:54. The human sum of best is merely a few frames slower than TAS. This is probably the closest against TAS in gaming history after dragster. </div><div><br /></div><div>They represent the frontline of game optimization: it reaches the realm where inputs are almost impossible to humans, which is a mechanical problem rather than a software problem. This matches the spiral theory where software and mechanical optimizations take the role in turns. </div><div><br /></div><div>Fortunately we also developed more tools during the years using science. Taking SMB1 as an example, in early days people experimented different tricks and do whatever is the fastest. We knew that there are shortcuts (e.g. 4-2 clips) but we didn't know how that worked but to take that as pure luck. As time passed, we started to use TAS first to get a route that works. We then refine that to "humanly possible" tricks -- after that it's speedrunners' job to execute those "humanly possible" tricks. And how refining works? Well the science of NES games and SMB1 itself is very well established, so people can calculate all the subpixels bit by bit for the possible route. If we take subpixels as a chaotic parameter as affected by the dynamics of the character, we may perform exhaustive searches around the possible routes until we found one that works for players. </div><div><br /></div><div>Since I mentioned the science behind speedrunning, I should mention the Youtuber that does a great job on the matter. In fact, everything I wrote above is just a set up for one of my favourite comment that mentions 4 great youtubers, three of which make videos that I would watch at highest priority. Here is the comment from <a href="https://www.youtube.com/watch?v=Y5KWOHlP8eQ">this video</a>...</div><div><br /></div><div><i>Remember people:</i></div><div><i>* <a href="https://www.youtube.com/channel/UCtUbO6rBht0daVIOGML3c8w">Summoning Salt</a> for History</i></div><div><i>* <a href="https://www.youtube.com/user/BismuthWasTaken">Bismuth</a> for Science</i></div><div><i>* <a href="https://www.youtube.com/channel/UC3mixv9nJPCzHYXXorIbx5w">FlibidyDibidy</a> for Technology</i></div><div><i>* <a href="https://www.youtube.com/user/karljobst">Karl Jobst</a> for Social Sciences</i></div>Forretriohttp://www.blogger.com/profile/18048483702091533151noreply@blogger.com0tag:blogger.com,1999:blog-2106712996078987699.post-73568461929601055432021-07-02T01:21:00.003+08:002021-07-02T01:21:45.888+08:00TWEWY the Animation: Beat week and general thoughts<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-E6VVOy5unHM/YN34w3htxqI/AAAAAAAABuI/3HcQw6iASzwNW08xWq861hrV86PS0aF5gCLcBGAsYHQ/s662/%2560LOBK027%2560Z1YZU%2540COZK%257B%25249M.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="504" data-original-width="662" src="https://1.bp.blogspot.com/-E6VVOy5unHM/YN34w3htxqI/AAAAAAAABuI/3HcQw6iASzwNW08xWq861hrV86PS0aF5gCLcBGAsYHQ/s320/%2560LOBK027%2560Z1YZU%2540COZK%257B%25249M.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;">Joshua the smol character in TWEWY.</div><div style="text-align: left;"><br /></div><div style="text-align: left;"><br /></div><div style="text-align: left;">I expected Beat's week to last 4 episodes where the last episode can be spared for something else. It turns out that they spent 4.5 episodes on the week. This is not a bad choice as spending a complete episode decoding (unless Vivy ep.12.5 just trying to reiterate from another POV) will surely scare the pure anime audiences away. </div><div><br /></div><div>At the same time, problem arises: there is not enough time to decode everything that is necessary to give a full story. Well that even happened in the original game: the secret reports contained a vast amount of information yet they are not enough to tell the full story that an average player/reader could understand. What they did in the anime is actually a wise move -- instead of covering everything essential, they highlighted the difference between OG and the anime which is considered the "true storyline" that leads to neo. There are already too many unanswered questions throughout the episodes and it is a waste of effort to answer them all in 12 minutes -- just leave them to neo instead.</div><div><br /></div><div>I think I have criticized enough about the choice of pins (and their effect) and monsters so I do not plan to do that in detail again here. That is again disappointing in ep.8-12 as we observe loads of week 1 monsters and more boring (and wrong) presentation of pin psychs. So instead I would highlight the differences between OG and the anime here. Some of them are quite influential and some are not (and probably also true in OG just not explicitly shown), but most of them are worth mentioning.</div><div><br /></div><div>Episode 8:</div><div>- Reapers had their eyes hidden in OG, but as shown in the anime although they still their consciousness (for now), they are probably under partial control of the pin already.</div><div>- I said that I don't want to criticize the choice of pins anymore but here's something that I actually appreciate. They used a few Pegaso pins in the late episodes but I couldn't recognize them easily. The only thing that I noticed is the Pegaso icon on the pin -- but then when I stared at the pin list, every Pegaso pin has the same logo on it! This is a funny little observation from me.</div><div>- We can see Kitaniji's hand timer in the anime which the time running out -- this is not explicitly shown in OG although he said something like that.</div><div><br /></div><div>Episode 9:</div><div>- Makoto finally appeared! Well there is none other than him who can do a better job to distribute the red skull badges.</div><div><br /></div><div>Episode 10: </div><div>- Eiji's truck appeared in the anime, but it is clear that the Shibuya sheeps didn't care anymore. They were already under unification of consciousness.</div><div>- Starting from the last episode it feels like the battle lags quite a lot which is surely disappointing.</div><div>- But Sho's teleportation is so cool! I wish that is shown in the week 2 final fight because every OG player would agree how painful it was to hit him in that fight...</div><div><br /></div><div>Episode 11: </div><div>- Konishi has the potential to do ASMR on YouTube.</div><div>- Kind of interesting to see that Shibuya river is not linear -- where do the other branches lead to?</div><div>- The battle is horribly simplified and even more it's not happening in the Dead God's pad. If you do not plan to show the fight there, why putting that in previous cutscenes and also in OP?</div><div>- In OG the formation of the special space created in the Konishi fight was explained and that the pact were explicitly sent back to ambient space before the fight concludes. Instead in the anime the space simply crumbled without further explanation. The same problem happened in the Sho fight already.</div><div>- Shiki reappeared but Joshua didn't as in OG. This is actually making sense because it is said that their return was due to the return of the entry fee. Shiki's part of the entry fee, but Joshua isn't. It is possible that he just showed up randomly after playing enough Tin Pins (see secret reports week 3) and try to get into the team. </div><div>- Sho was not found dead under garbage heap. Instead he was able to talk to Neku in the anime. In fact if you think really carefully almost all characters were erased at the spot after being found severely injured, and Sho was the only exception. That could be a hint that he's not dead even in OG.</div><div>- They combined the two fights (Kitaniji phase 1 and berserk Shiki) into one. Other than my complain that it didn't happen in the pad, it's sad that the badge cutting scene was not replicated in the anime.</div><div>- Golden chain psych...that is not in the game, and no pins were specified there. The Mr.Mew ball is utterly nonsense but still made me smiled right there.</div><div>- It's still a mystery what happened when Kitaniji trapped Shiki, Beat and Joshua and try to drain energy from them. Nice to see that to be removed in the anime.</div><div><br /></div><div>Episode 12:</div><div>- First of all, there was no indication that day 6 was gone. Were they still in day 6 or in day 7? If it's day 7 it would be cool to see the "LAST DAY" as shown in OG title.</div><div>- In OG the ultimate fusion pin just somehow appeared for you to finish the boss. In the anime this is due to the combination of power also from Shiki and Beat. But the representation is quite similar: the quintuple laser beams with a big cross.</div><div>- A door appeared when after the final fight -- the same door when Kitaniji was defeated in the pad in OG. Behind the door is a graffiti room that we have never seen before.</div><div>- Josh should have banged right after Neku's final words, just as in OG...</div><div>- Tin pin bro (and Makoto) appeared as cameo. Naomi's team as well as the 777 band are also revived.</div><div>- Half the face of RG Shiki, will she appear in neo?</div><div>- Mr.H tried to take an extra sip from the canned coffee after flipping it to confirm nothing's left</div><div>- Beat raised the question "why are they able to use such psych" and Neku guessed it's Mr.H's support. In some sense this is correct because that's in fact upon "imagination" according to OG secret report.</div><div>- Josh revealed that the player pin given to Neku is special and not the ordinary one. That explained why Kitaniji couldn't destroy that particular pin and shout "so that's why...!". He thought he couldn't gain control over Neku because Neku got an extra player pin, but it's in fact a special player pin that cannot be destroyed by him.</div><div>- It's a shame that the anime did not end with the OG ending song "A Lullaby for You"...it's such a fantastic song. I know something's wrong with the artist but still it's worthy to be put here.</div><div><br /></div><div>As you can see most reactions came from the last 2 episode as the 2 episodes contain the core information of the story. Regarding the conversation at the end there are a few things that are worth mentioning:</div><div>- The golden key pin was an actual master key pin in OG (also in secret report), but here it become the pin that allowed them to do the final attack. We know that the harmonizer pin/fusion pin setting was abolished in the anime where the pact just use the fusion attack somehow, but are there any further implication about that?</div><div>- Mr. H explained about his graffiti. This may not be obvious but the exact same's in secret report 12.</div><div>- Joshua said that composers cannot be defeated by reapers even in RG. According to secret reports this is because the frequency of the repeaers are also lowered in RG that composer being vulnerable to reapers is invalid. However Mr. H somehow thought that Sho can do that with with the help of Taboo sigil?</div><div><br /></div><div>The largest difference between the anime and the OG is perhaps the treatment on Rhyme. As much as the treatment being a lot less cruel it also leaves loads of extra question or even potential conflicts with the OG setting.</div><div>- In what form does Rhyme exist in UG in week 3? As some sort of energy (or soul -- see explanation from secret reports), something summoned upon psychs/pins (as in OG), noise a creature form? </div><div>- Human beings if not repeats are not supposed to be in UG during the game. In what way Rhyme was allowed to stay with the team without any problems?</div><div>- Rhyme probably did not turn into pin in the anime, but if we do not know the nature of existence of Rhyme, how do we now the nature of reincarnation that "composers can do"? Of course what Beat refereed to is to revive Rhyme as a human, but this is not necessarily what others meant.</div><div>- The most interesting thing about Rhyme is how she managed to damage Konishi. As mush as that being a reasonable answer, it is also extraordinarily funny.</div><div><br /></div><div>*</div><div><br /></div><div>It is not hard to find games that has a similar setup/plot as TWEWY: teen based; "game" or more generally being tagged into unexpected events; confined in a specialized area in Tokyo; the growth of character along the story: Shin Megami Tensei (SMT), Persona or even Trip in Akiba. </div><div><br /></div><div>Comparing with these games, the story in TWEWY looks incredibly shallow. This is kind of an inherited problem due to the nature of the 7 days game where everything has to be done quick. The story maker had taken that into consideration and made reasonable stories for the three weeks. Shiki week is kind of relaxing so they can spare the time to reveal the background of Shiki and allowing more interactions. Joshua from Neku's point of view is a complete enigma and hence doesn't need much story. Beat's week is more of a decode and the big story unfolding, so the attention is shifted to the overworld as well as Rhyme. That part of the story is shallow but fitted into the game properly. </div><div><br /></div><div>What I wanted to know more is the big story behind. It's ok for me not to dig into the discussion of angels, vibes or anything that is of "higher existence", but what happened around UG and RG should be explained clearly at the end.</div><div><br /></div><div>For example, it was said that Neku changed (in a desirable way) so that Shibuya is saved, but how? One may argue that Neku's personality changed positively given the social norm, but these are never objective. Why was Shibuya considered boring that needs to be destroyed? Such judgement could not be made just by looking at Neku or people around him -- unless this is commonly observed in Shibuya. There are many dreading regions in a city around the world, so why Shibuya? Is it about the imagination (which, was never properly defined other than its literal meaning) declining in Shibuya? That is never addressed in the story unfortunately. In the worst case scenario everything was set up just because Joshua wanted to without any reason, then the whole thing is no more than a child's play...</div><div><br /></div><div>At the end of the day, TWEWY is still my favourite game by a long shot. The anime may not be the best reiteration of the game, but it is good to have that as a refresher or teaser before we meet NEO. I have already order the game and is ready to stream my gameplay (for the first time). Hopefully I will see you there in 25 days :)</div>Forretriohttp://www.blogger.com/profile/18048483702091533151noreply@blogger.com0tag:blogger.com,1999:blog-2106712996078987699.post-28631087620788189062021-06-19T19:00:00.001+08:002021-06-19T19:00:09.091+08:00FEH VG predictor continued: wave pattern and early estimation<div style="text-align: left;">Building a model for VG is something that I wanted to do for a long time. In the <a href="https://www.forretr.io/2021/06/some-optimization-on-feh-vg-predictors.html">previous article</a> I wrote about the basics of a VG model and the article concluded with the chart below:</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-Q7yl2Qjsgjs/YMJTOi_yq9I/AAAAAAAABs0/Mtjjbofxr18z5N0Mcwizy0D9KhE3WJbnACPcBGAYYCw/s625/5TPPLEM%257E3AA%2524%2528HD_Z%257E%255DX1%255D5.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="379" data-original-width="625" height="243" src="https://1.bp.blogspot.com/-Q7yl2Qjsgjs/YMJTOi_yq9I/AAAAAAAABs0/Mtjjbofxr18z5N0Mcwizy0D9KhE3WJbnACPcBGAYYCw/w400-h243/5TPPLEM%257E3AA%2524%2528HD_Z%257E%255DX1%255D5.png" width="400" /></a></div><div><br /></div><div>The perfect wave in the first 12 hours caught my eyes -- is that a coincidence or is that a general phenomenon? The aim of this article is to look into further patterns that help us to build the model. Before we start recall the terms that I used in the previous article -- please refer to the previous article for further details.</div><div><br /></div><div>- Three examples all extracted from VG June 2021. Please refer to <a href="https://www.forretr.io/2021/06/some-optimization-on-feh-vg-predictors.html">the previous article</a> for further details. You can extract the raw data from the <a href="http://ramtieger.sakura.ne.jp/p/game/feh/Touhyou/">Japanese predictor</a> made by @rammtiger_n. </div><div><br /></div><div>Example 1: Final (Popularity ratio >4)</div><div>Example 2: Quarterfinal 4 (Popularity ratio 1~2)</div><div>Example 3: Semifinal 2 (Popularity ratio close to 1)</div><div><br /></div><div>- Parameter $k$: the parameter so that the accumulated score is of order $O(t^{2+k})$, or that the team's activity is of order $O(t^{1+k})$. To be more precise, for team i (i = 1,2) define $c_i(t)$ to be the constant factor which scales upon team size, and switch between three values according to the state of the hour, and $f_i(t)$ is the corresponding hour multiplier (which can either be $1.05+0.05t$ or $3.2+0.2t$). Ignoring intraday variation we assume that the team activity $A_i(t)$ is approximated by $c_i(t) f_i(t)^{1+k}$.</div><div><br /></div><div>One should note that this parameter for the two teams are not necessarily the same, but they are close enough for most of the time. Let us assume that parameter $k$ is uniform across the two teams first.</div><div><br /></div><div>*</div><div><br /></div><div>The chart showed at the beginning is what happened in example 3. The curves are easily spotted because it is a perfect ping-pong where activity of the two teams are almost equal. At the same time when a team is in the excited state the other must be in the post-excitement state as it is exhausted due to bonus multiplier at the previous hour. As a result we find two perfect curves with alternating dots, one for the activity at excited state, another one for the activity at post-excitement state.</div><div><br /></div><div>We do not have a perfect ping-pong most of the time, so are there any ways to extract such trend if it exists? One approach is to assign a factor to the three states: we may assume that the normalized activity in the excited state is 10 times the normal activity and 100 times of the post-excitement activity. Although we can explain this by the fact that flags comes in a multiplier of 100, such ratio is still affected by the parameter $k$, which we do not want to fix. </div><div><br /></div><div>There is a smarter way to get around this: observe that the state of the two teams are almost always excited + post-excitement or normal + normal. On rare occasions it could be normal + excited or normal + post-excitement but they always cancel out. Therefore we can simply take the (geometric) average of the (normalized) activity to retrieve the trend!</div><div><br /></div><div>Mathematically, we first guessed that the parameter to be $k_0$. We then normalize the activity by considering $A_i(t)/(f_i(t))^{1+k_0}$. By taking the geometric mean we have that</div><div>$GM = (c_1(t)c_2(t))^{1/2}(f_1(t)f_2(t))^{(k-k_0)/2}$.</div><div>If we are either in the excited + post-excitement or normal + normal states, then $\sqrt{c_1(t)c_2(t)} = c_S$ is a constant. Since $f_1(t)f_2(t)$ is always $\Theta (t^2)$, we know that the geometric mean is constant (or regressed to be constant) if and only if $k=k_0$, i.e., if the estimated parameter $k_0$ meets the true parameter. We take log GM instead of GM to even out the impact of normal + excited states against normal + post-excitement states.</div><div><br /></div><div>As a demonstration we calculate the log-geometric mean team activity for example 1 we get the following chart (with the guess of $k=1$):</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-HbYIFaRfYEY/YML3zjoxcJI/AAAAAAAABs4/n_qvB_XB0uUL7JdcMMjxXngiu5v2cIrPgCLcBGAsYHQ/s363/1.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="235" data-original-width="363" height="259" src="https://1.bp.blogspot.com/-HbYIFaRfYEY/YML3zjoxcJI/AAAAAAAABs4/n_qvB_XB0uUL7JdcMMjxXngiu5v2cIrPgCLcBGAsYHQ/w400-h259/1.PNG" width="400" /></a></div><div><br /></div><div>We can see a downward trend starting from hour number 8, indicating that $k=1$ is an overestimate here. </div><div><br /></div><div>Again we retrieved the same early wavy pattern as in the first chart. It has a simple explanation: in FEH there are quests to clear. You need to clear these simple quests to get the (maximum number of) flags. The quests are mostly "clear VG with red/blue/green/colorless unit", but they require you to enter VG actually. On the other hand, you start the event with zero vote so you cannot do these quests right away. Most people do these quests with votes almost fully restored, which is exactly 4-8 hours into the event. </div><div><br /></div><div>Now we can estimate $k$ by removing the first 4 hours as outliers and search for $k_0$ such that the linear regression returns a zero slope. Since the regressed slope is strictly decreasing with $k_0$ we can always find such $k_0$.</div><div><br /></div><div>If we apply that on example 1 we estimate $k$ to be 0.85: </div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-7nK4snd11w0/YML4DR_M_jI/AAAAAAAABtA/EhWYh_kLciMfwmjkk3ulePSXhFZeCbgOQCLcBGAsYHQ/s305/2.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="192" data-original-width="305" height="252" src="https://1.bp.blogspot.com/-7nK4snd11w0/YML4DR_M_jI/AAAAAAAABtA/EhWYh_kLciMfwmjkk3ulePSXhFZeCbgOQCLcBGAsYHQ/w400-h252/2.PNG" width="400" /></a></div><div><br /></div><div>And if we apply that on example 2 we estimate $k$ to be 1.17:</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-MQnXcXhd6OQ/YML4NOmv-RI/AAAAAAAABtE/QV7NtCrajvMjxXtd9jdOJo5t5y3CudX3gCLcBGAsYHQ/s303/3.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="206" data-original-width="303" height="272" src="https://1.bp.blogspot.com/-MQnXcXhd6OQ/YML4NOmv-RI/AAAAAAAABtE/QV7NtCrajvMjxXtd9jdOJo5t5y3CudX3gCLcBGAsYHQ/w400-h272/3.PNG" width="400" /></a></div><div><br /></div><div>The wavy pattern seems to be very consistent among all situations: we always observe two peaks, one at hour number 4 (which corresponds to 8 hours into the event since we removed the first four) and another one at hour number 12 (16 hours into the game). We may interpret these as the activity peak from players in different part of the world. Computationally the peak and troughs helps us greatly in the sense that we can do the same linear regression using the first two peaks and troughs, i.e., the data of the first 20 hours, and the result is highly correlated to the estimate using all 44 hours of data.</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-rVeiBZic0OQ/YML4eMgnBvI/AAAAAAAABtQ/FBJHQKd47_QBoj8ErqZjb0tuLManQ8t-wCLcBGAsYHQ/s446/4.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="446" data-original-width="313" height="400" src="https://1.bp.blogspot.com/-rVeiBZic0OQ/YML4eMgnBvI/AAAAAAAABtQ/FBJHQKd47_QBoj8ErqZjb0tuLManQ8t-wCLcBGAsYHQ/w281-h400/4.PNG" width="281" /></a></div><div><br /></div><div>Example 1: $k$ estimated to be 0.8 with the data of hour number 5~20 vs 0.8 on global data</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-8YwxaWJQUCA/YML4srGfzcI/AAAAAAAABtU/P0aeeNqe9JEibFUPhI4tN9ha3o27ObG5gCLcBGAsYHQ/s441/5.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="441" data-original-width="304" height="400" src="https://1.bp.blogspot.com/-8YwxaWJQUCA/YML4srGfzcI/AAAAAAAABtU/P0aeeNqe9JEibFUPhI4tN9ha3o27ObG5gCLcBGAsYHQ/w276-h400/5.PNG" width="276" /></a></div><div><br /></div><div>Example 2: $k$ estimated to be 0.92 with the data of hour number 5~20 vs 0.92 on global data</div><div><br /></div><div>It seems that such estimation is always an underestimate due to (out-of-correlation) increased activity at the far end, but we can always add a little bit to our estimate. </div><div><br /></div><div>*</div><div><br /></div><div>So, what can we do with the predictor now? This is a purposed way of creating a prediction:</div><div><br /></div><div>- Use the early data to estimate the constant factor for teams' activity with $k_0=1$</div><div>- Predict by combining team activity and states guessing</div><div>- Analyze team composition by wave decomposition at hour number 20 and modify $c_i(t)$ accordingly</div><div>- Update $k_0$ by linear regression every time before iterating through the prediction after hour number 12 or 20</div><div>- ???</div><div>- Feathers!</div><div><br /></div><div>As much as the above being a big and serious discussion, I still prefer participating the event in a simple way by guessing frequency of the bonus hours linearly. A 99% accurate predictor? Sure but no thanks if I am the one to write the codes. Not to mention that it is actually quite hard to measure the error in a dynamic system and we just can't tell in a mathematically rigorously way that how accurate our predictor could be...</div><div><br /></div><div><a href="https://docs.google.com/spreadsheets/d/1U4lUQLiI0woW1dxxr4TFCCjS9G0dHy3WNE8h54ERa6M/edit?usp=sharing">You can find the raw data that I used here</a>. </div><div><br /></div><div>The charts were not properly imported onto google drive, but you can plot them easily. Column L-N are time-normalized difference and bonus boundaries with $k=1$. Column T is the log-geometric mean of team activities. You can change $k$ as you like at W4 and W5, but the $k$ for the two teams are by default equal. The three labels are SF2, F and QF4 which correspond to examples 3, 1 and 2 respectively.</div>Forretriohttp://www.blogger.com/profile/18048483702091533151noreply@blogger.com0tag:blogger.com,1999:blog-2106712996078987699.post-26848746621617422652021-06-11T02:03:00.015+08:002021-06-12T21:31:20.710+08:00Some optimization on the FEH VG predictors<div>Voting Gauntlets in FEH is always controversial in many ways. In terms of outcome some hates to see popular characters always triumph over ordinary characters while the rest complains how the result is unpredictable and favors the chasing side by so much. In terms of reward some players are unhappy about the lack of rewards -- well actually 12 orbs is a lot, but the feathers are also very friendly to new players (and even me back in the days). In terms of difficulty, some found that playing with 3 random characters is quite fun, but some say they have terrible luck and facing 3 fallen Edgelord is bullshit.</div><div><br /></div><div>But today I want to talk about mathematics and not the game mode itself. How can we predict the outcome given the first few/12/24 hours of data? Certainly there are a few attempts already: on Reddit there are a few predictors on the West and also one from Japan. I found that the interface of the Japan predictor is pretty nice, despite that the prediction is sometimes off. </div><div><br /></div><div>In the past <a href="https://www.forretr.io/2017/09/cooperative-games-and-feh-voting-event.html">I have talked about VG in the sense of a multiplayer game</a> -- in the game theory sense, but this article is doing the complete opposite. We assume that the reaction is fixed under some unknown parameters, and the goal is to build a model out of that.</div><div><br /></div><div>I do not plan to build a predictor by myself. It takes lots of time and does not benefit one so much ingame: in terms of ranks it makes no difference if the bonus hour shifts as everyone has the same bonus time. You can almost always get the highest reward by not missing the bonus hours in the last 20-24 hours, which can be done using VG bots. The prediction for the last few games where final result matters, can be predicted fairly accurately by most models anyway. </div><div><br /></div><div>The reason I wanted to write this is because there are a few things that I spotted that are relevant but they were not accounted in existing models, so it serves more as an investigation.</div><div><br /></div><div>For starters, these are what you need to know: (FEH and negligible details are cropped, just to give a sufficient model here)</div><div>- Two teams undergo a head-to-head battle over 44 hours.</div><div>- Every player has a voting gauge which recovers by 1 vote per hour and is capped by 8. </div><div>- Every player has 2000 flags which they can spend over the battles. One may spend a maximum of 100 flags per vote that they applied. With N flags applied the score is multiplied by N. For example if one spends 8 votes with 800 flags then the score is multiplied by 800. If no flags were spent the multiplier is 1 per vote.</div><div>- There are two multipliers: the normal multiplier starts from 1.1x and increase by 0.05x per hour. The bonus multiplier starts from 3.4x and increase by 0.2x per hour.</div><div>- The score is updated every hour. If a team is 1% more than the other, bonus multiplier will be triggered for the weaker team during the hour. </div><div>- The team with higher score at the end wins.</div><div><br /></div><div><b><u>Score normalization</u></b></div><div><br /></div><div>First of all, we know that the score is not growing linearly and we need a way to normalize them for a time-invariant comparison. A clear choice would be the direct score ratio between the two teams. This is a very intuitive choice which also hooks with the bonus trigger, but the accumulated score certainly affects the velocity of this indicator over time.</div><div><br /></div><div>Another choice is to divide the score by the multiplier, whether it's the ordinary or bonus multiplier does not matter too much because that is just a constant scaling (almost). The problem is that player's VG activity isn't constant either: higher multipliers are expected at the end so they prefer to spend flags towards the end. With flags around the score obtained by not spending flag is basically negligible. We need to capture when people spend flags.</div><div><br /></div><div>With everything being non-linear it is so hard to decide the right exponent, so I decided to look at the accumulated score instead. It is natural to assume that players' activity is non-decreasing in general, then their points gained per hour, after enlarged by the linearly growing multiplier, is at least linear. As a result, the accumulated points are at least quadratic, i.e., $\Omega (t^2)$. </div><div><br /></div><div>Assume that the players' activity -- or the teams' activity as a whole, is of order $O(t^{1+k})$ then the accumulated score will be of order $O(t^{2+k})$. It is not hard to find that the accumulated score is indeed at the order $O(t^{2+k})$ for some small $k$ -- so let us just divide everything by $t^2$ before we look into the parameter $k$. </div><div><br /></div><div>Here are the two typical examples taken from VG 2021 June.</div><div><br /></div><div>Example 1: VG final (F!Corrin vs Klein)</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-1QmkmsydKaY/YMJNNOXTaUI/AAAAAAAABsE/kgzBU_nw5VMVqCUb3KGx9PkvgHb-cQc_wCLcBGAsYHQ/s653/%257B%25607DFYM6%2540PA4BN%2540YZ2CE0D3.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="653" data-original-width="598" height="400" src="https://1.bp.blogspot.com/-1QmkmsydKaY/YMJNNOXTaUI/AAAAAAAABsE/kgzBU_nw5VMVqCUb3KGx9PkvgHb-cQc_wCLcBGAsYHQ/w366-h400/%257B%25607DFYM6%2540PA4BN%2540YZ2CE0D3.png" width="366" /></a></div><div><br /></div><div>Example 2: VG quarterfinal 4</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-vdoRZHyCeA8/YMJNSUN3wyI/AAAAAAAABsI/msmSKYcXLCUD7gO-fi71b7dYGLhAzD0XACLcBGAsYHQ/s626/R%25603%2525708%25257G_8O2LVYV7U%257BZ4.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="626" data-original-width="591" height="400" src="https://1.bp.blogspot.com/-vdoRZHyCeA8/YMJNSUN3wyI/AAAAAAAABsI/msmSKYcXLCUD7gO-fi71b7dYGLhAzD0XACLcBGAsYHQ/w378-h400/R%25603%2525708%25257G_8O2LVYV7U%257BZ4.png" width="378" /></a></div><br /><div><br /></div><div>These are two typical matches in VG: example 1 is when the popularity of one clearly overwhelms the other, while example 2 happens when a team is of significantly higher popularly but not as extreme as example 1.</div><div><br /></div><div>All the charts are time-normalized by $t^2$ where $t$ is the average of the two multipliers.</div><div><br /></div><div>In the first chart, the orange and yellow line indicates the time-normalized boundary for bonus multipliers, while the blue line shows the normalized score difference. The second chart indicates the normalized score activity of the first team (a positive score difference means that the first team is leading). </div><div><br /></div><div>We expect the normalized player activity should be of order $O(t^{k-1})$, and from here we can estimate $k$. The spikes are when bonus multiplier happens.</div><div><br /></div><div>We can see that the parameter $k$ clearly varies in different situation. We can assume that $k$ is close to 1 in example 1 while $k$ is clearly much smaller than 1 in example 2. In fact, $k=0.2$ is a pretty good estimate. The $k$ value can also be verified by checking the growth rate of the bonus boundary curve.</div><div><br /></div><div>We can explain the correlation by how player anticipate the battle towards the end instead of casually spending their flags in the middle. Very interestingly the parameter $k$ seems to be independent of the ratio of player base size: the dominant a team is, the more bonus hours the opposite team will get. So in theory if the parameter is decided by the frequency of bonus hours, then the parameter for the two teams should be different, but that is not the case here. If we plot the activity of both teams on the same chart for example 1, we can see that the parameter for the two teams are more or less equal.</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-26Ylj0_hW5o/YMJNXCt3YJI/AAAAAAAABsU/bohTf5MAYFwVG1f0Ts_ltpgW-S6v7QJPgCLcBGAsYHQ/s568/DCZYIZ1XRRCMT%257DO_7TBQLMW.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="388" data-original-width="568" height="274" src="https://1.bp.blogspot.com/-26Ylj0_hW5o/YMJNXCt3YJI/AAAAAAAABsU/bohTf5MAYFwVG1f0Ts_ltpgW-S6v7QJPgCLcBGAsYHQ/w400-h274/DCZYIZ1XRRCMT%257DO_7TBQLMW.png" width="400" /></a></div><br /><div><br /></div><div>Calculating the parameter $k$ would be extremely helpful because we can then get a normalized data. (And we will cover that in the sequel of this article!)</div><div><br /></div><div><b><u>The three states of players</u></b></div><div><br /></div><div><div>With the above graph we see that the activity of the players divide into three categories, or three states that we call.</div><div><br /></div><div>A team is in an excited state if it receives a long-waited bonus hour, or a bonus hours that shoots them to the leading position. The activity clearly spikes for this hour.</div><div><br /></div><div>A team is in a post-excitement state if the bonus hour in excited state shoots them into leading position with bonus triggered on the opponent then the team enters the post-excitement state where activity is abnormally low because they run out of votes and flags.</div><div><br /></div><div>A team is in a normal state otherwise. There are more fluctuation within this state depending on the score situation. </div></div><div><br /></div><div>We can plot the same for example 2 which is a lot more chaotic, but the activity is still clearly divided into the three states as described.</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-K_CRYYBhTX8/YMJQ6P3feAI/AAAAAAAABso/HicrPepHPRwXEOt7tnDy_s9i7Bw9SIlUgCLcBGAsYHQ/s571/0%2525LLG9Q0A%2529%2524%2528M%2540%25245%2529R%255D%257B%2524RK.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="388" data-original-width="571" height="271" src="https://1.bp.blogspot.com/-K_CRYYBhTX8/YMJQ6P3feAI/AAAAAAAABso/HicrPepHPRwXEOt7tnDy_s9i7Bw9SIlUgCLcBGAsYHQ/w400-h271/0%2525LLG9Q0A%2529%2524%2528M%2540%25245%2529R%255D%257B%2524RK.png" width="400" /></a></div><div><br /></div><div>The pattern shows that most players aren't playing to optimize the chance to win as a team. Rushing to overtake the opponent early has little to no effect on the final result but looks good in a team sport, while the increased activity when a team enters bonus multiplier is natural as it maximizes score gain (for those who urgently need to spend flags).</div><div><br /></div><div>I am actually quite surprised that this was not taken into account by most predictors, as it plays an important role at the end where people react to the hourly updated results vigorously. For example the JP predictor predicted a constant downward ping-pong at the end for example 1 (i.e., bonus for second team for 1 hour + no bonus for both teams for 1 hour alternately and these two together results in favor of the second team), but the reaction from the second team at hour 42 should be much more violent as it sends the team into leading position -- and of course the first team hit them back with 10x the power. This is the nature of VG predictor: players react to score but not team result.</div><div><br /></div><div><b><u>Daily variation on player activity</u></b></div><div><br /></div><div>Clearly players do not stay awake 24/7 for these shitty reward (well even if orbs are worth its monetary cost that is merely a burger meal, so it's not worth the time to stay awake overnight), so they stop playing when they are asleep. But people over the world situates in different time zone and they sleep over different time. More importantly, the taste from different part of the world seems to be different. As a result, we may observe higher activity from one team during daytime then higher activity from the other team during nighttime (which could then be daytime for that part of the world).</div><div><br /></div><div>Assuming that the main division would be Japanese (or Asian) players vs the West, we can divide the players into 3 groups: time-invariant players, Asian players and Western players. We estimate the portion of the three and how supportive they are to each team. This is taken as a scaling factor when we predict the future outcomes. </div><div><br /></div><div>And how do we do that? Well this is simple linear algebra -- these three groups of players can be modelled into 3 kinds of waves: constant, sine and cosine waves, orthogonal to each other. We can then apply orthogonal projection to estimate the portion from each of the three. </div><div><br /></div><div>*</div><div><br /></div><div>I really believe that the three factors together with what we already have around, builds a very accurate VG predictor, but surely no one would waste the time doing that.</div><div><br /></div><div>To conclude this article let me show the graph plotted for the same VG but semifinal 2, which is ping-pong all the way. I stacked (apology for the poor stacking) the two graphs together so that you can observe the interaction more clearly. Since it's a perfect ping-pong first the first 20 hours or so, you can see that the activities alternates from excited and post-excitement states but not the normal state. Although the waving pattern in the first 20 hours which in fact, also occurred in the first two examples, seems to raise more questions from here...</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-Q7yl2Qjsgjs/YMJTOi_yq9I/AAAAAAAABsw/VYSuuINeJRUoS0bSzcrC1wibumWN8bOjACLcBGAsYHQ/s625/5TPPLEM%257E3AA%2524%2528HD_Z%257E%255DX1%255D5.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="379" data-original-width="625" height="243" src="https://1.bp.blogspot.com/-Q7yl2Qjsgjs/YMJTOi_yq9I/AAAAAAAABsw/VYSuuINeJRUoS0bSzcrC1wibumWN8bOjACLcBGAsYHQ/w400-h243/5TPPLEM%257E3AA%2524%2528HD_Z%257E%255DX1%255D5.png" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">(To be continued)</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><i>Acknowledgements</i>: raw data extracted from the <a href="http://ramtieger.sakura.ne.jp/p/game/feh/Touhyou/">Japanese predictor</a> by @rammtiger_n</div>Forretriohttp://www.blogger.com/profile/18048483702091533151noreply@blogger.com0tag:blogger.com,1999:blog-2106712996078987699.post-59598764817460505232021-06-02T21:27:00.002+08:002021-06-04T00:57:17.665+08:00夢醒<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-g2APGm9rUWA/YLeG-NcFzJI/AAAAAAAABrA/JysElJiOqGMKjUbwQJhKWMwE7tb4SGq5ACLcBGAsYHQ/s509/%2540OHIO%25240VI%2560%255B%257B7F%257DMD%257EA%2528A%25601.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="303" data-original-width="509" src="https://1.bp.blogspot.com/-g2APGm9rUWA/YLeG-NcFzJI/AAAAAAAABrA/JysElJiOqGMKjUbwQJhKWMwE7tb4SGq5ACLcBGAsYHQ/s320/%2540OHIO%25240VI%2560%255B%257B7F%257DMD%257EA%2528A%25601.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: x-small;">The pride of London. Captured from ChelseaTV.</span></div><br /><div><br /></div><div>九年前，一個偏僻的小鎮上。</div><div><br /></div><div>那裡的網絡居然還是ADSL而且每個月只有20GB限制。早就把流量吃光的我只好去客廳把星期天早上的電視機霸佔起來。</div><div><br /></div><div>我跪在電視前，距離之近甚至可以感受到屏幕的靜電。</div><div><br /></div><div>從加時賽開始就跪在那，大腦在拜仁獲得十二碼時早已當機了吧，回過神來兩隊已經打完一百二十分鐘要互射十二碼決勝負了。</div><div><br /></div><div>不知為何，就算馬達射失第一個十二碼我也沒有那種會像莫斯科雨夜那樣飲恨的感覺。隨後大衛雷斯的爆射右上角、林伯特特地改掉習慣正上方射進、艾殊利高爾右中貼網側射進也印證了這一點。</div><div><br /></div><div>杜奧巴不負眾望打進致勝十二碼的一刻，他第一時間找到施治相擁而哭，筋疲力盡的車路士球員紛紛跪地流淚。然後同一時間我竟然也哭了，趴倒在電視機前放聲哭泣－－在此之前我似乎從而因為體育而流淚。零八零九那兩場看完臉一黑就回去睡了，啊頂多就以後把那裁判拿出來鞭，當時在那邊哭又有甚麼用呢？</div><div><br /></div><div>房子的主人的小孩問道：為甚麼要哭呢？你所愛的球隊不是贏了嗎？我仍然在那邊流淚沒法回答。小孩看看我又看看其他大人，一臉不解地跑開了，真是奇怪的少年。</div><div><br /></div><div>對啊，為甚麼呢？</div><div><br /></div><div>如果要我回答的話，流淚是屬於勝利者的專利。很多人未必會認同這一看法，但我相信至少對車路士這種性格的球隊來說沒錯。球賽可以輸，學費也可以交，唯獨魂不可以丟。只有在勝利那一刻你的努力付出才化為事實，那時候你想怎樣都可以，包括流下喜悅的淚水。</div><div><br /></div><div>所以九年後的歐冠決賽，我又哭了。</div><div><br /></div><div>車路士在九年前那個歐冠之後開始迷失，連兩年對上大巴黎先勝後敗後完是在歐冠賽場上失魂落魄；去年球隊更是吃到轉會禁令，在無人可買的情況下保四岌岌可危。但這時候林伯特，那個九年前對巴塞次回合在上半場結束前搶斷美斯然後向拉米雷斯長傳助攻的林伯特－－站了出來，以教練的身份帶領一幫青年軍保住了第四。在疫情肆虐下轉會禁令忽然使車路士成為受益的一方，最終由杜曹接手將這幫青年軍帶向歐洲之巔。</div><div><br /></div><div>當年的淚水反映的是十六強開始的各種打不死，外加零八零九兩場飲恨的結果；這次流的淚更多是這些年來的低迷而忽然在短時間的連續巧合下奪下冠軍的落差。兩者雖然性質不同，曲折程度其實難分高下。</div><div><br /></div><div>與上次奪冠異曲同工的還有球隊立足於歐冠的防守。比起上次的力挽狂瀾這次更多是波瀾不驚：淘汰賽七場只失兩球，一球是次回合領先兩球第九十四分鐘失的倒鉤世界波，另一球則是領先被追平的不落地側身窩利。兩球都是靠個人能力與運氣射進的高難度入球(也入選本季歐冠最佳進球)，而且對局面幾乎無實質性損傷。整個賽事僅失四球為史上最少，單是這項數據就能讓我這種防守控十分滿足。</div><div><br /></div><div>要數兩次奪冠相近之處根本數不完。比如兩隊都充滿了剛進隊不久，沒大賽經驗也沒被寄予厚望的新兵；又或者兩次都是剋死西班牙球隊上位(上次小組賽最後一輪生死戰三比零斬落黃色潛艇)等等……但不變的是，車路士還是那支堅忍的鐵血球隊。只要這點不變，我就會繼續支持下去。</div><div><br /></div><div>喔不過雖然球隊我十分支持，但是Nike的球衣很醜，我支持不下去。如果要我選一個球員印在背面的話……我應該會選11號吧？他值得如同我們對托利斯一樣的喜愛。</div>Forretriohttp://www.blogger.com/profile/18048483702091533151noreply@blogger.com0tag:blogger.com,1999:blog-2106712996078987699.post-12253885041658278822021-05-27T20:39:00.009+08:002021-05-29T12:21:13.731+08:0027/5/2021: Thoughts on nos techniques<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-XtXONhNp-D4/YK-Sg8KuhtI/AAAAAAAABqQ/rN97822KxbI7jdQFDcTL6blqrbzce3PzACPcBGAYYCw/s600/Ew0dEL0UcAAxP2e.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="600" height="266" src="https://1.bp.blogspot.com/-XtXONhNp-D4/YK-Sg8KuhtI/AAAAAAAABqQ/rN97822KxbI7jdQFDcTL6blqrbzce3PzACPcBGAYYCw/w400-h266/Ew0dEL0UcAAxP2e.jpg" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;">My second S on real lv.3. Stamina maps are my favourite.</div><div style="text-align: left;"><br /></div><div style="text-align: left;"><br /></div><div style="text-align: left;">Today I realized that my e-amusement album on facebook was gone. I knew that the e-amusement app removed its linkage with facebook but the album should still be there, but that isn't the case anymore. It took me sometime to retrieve all my DDR/beatsream captures, but they are worth the time. I guess it's also a good time to take record of my MUG progress.</div><div><br /></div><div>Since the lockdown I have been playing ring fit or doing exercises at home a lot more, so I simply play DDR less and less frequent. Playing 18 is no longer a regular thing to me again, although Konami didn't produce enough sensible 18s in the past year...び is pure shit in my view.</div><div><br /></div><div>So I basically play Nos all the time, and the progress is clear. By the end of Op.2 my recital grade was 5300, it was then 5500 by the end of 2019, and now my grade is 5760. In other words, I can obtain S rank consistently across level 11 by the end of 2019, but I can S consistently across level 12.5 and a few 13.0 right now.</div><div><br /></div><div>What's hard to me right now are basically nonsense streams (like True Blue) or hardcore trills (like Appassionata 3rd movement, Etude Op. 25-11 "Winter Wind" or the Ballade No.1 in G minor). It takes time for me to recall my piano muscle memory...but what's interesting to me is how me or other nos player play maps at 12.5-13.0, start to differ from other MUGs. We need to deal with streams that are practically impossible to hit in a discrete way, so we need some other approaches, and the choice would be to sweep or to play like a pianist?</div><div><br /></div><div>There are other MUGs in the arcade where you can sweep the keys instead of hitting independent to be count as a hit. Chunithm is the prime example but people also do that sometimes in jubeat, but the technique is widely adopted in Chunithm while restricted to a small group of players for jubeat. Why?</div><div><br /></div><div>Chunithm encourages sweeping in nature: a flat input device and sliding notes exist for sweeping already, so sweeping ordinary notes is just something natural to them. The notes are usually 4 keys wide and the timing is loose -- that makes sweeping much easier. </div><div><br /></div><div>On the other hand, jubeat consists of a 4x4 pad, so sweeping for longer streams implies a change in direction during the sweep, and to keep a consistent pace during the sweep is definitely hard. The streams are not for sweeping most of the time where notes appear alternately on the left and right half: sweeping anything more broken than 2-7-10-15 would be extremely hard. At top level (the only instance where sweeping could be relevant) people always go for the hard mode, so positioning plus timing would be too demanding for this technique.</div><div><br /></div><div>Nos interestingly situates between the two. Its panel is linear (although not flat) and sweeping is easy. There are also maps where sweeping is clearly desired (e.g. </div><div>ピアノ体操第一). The timing is not as loose as Chunithm but a lot easier than jubeat on hard mode. On the other hand, sweeping is quite hard when the notes are not spaced apart enough (like Etude 10-4), and bad sweeping causes a bunch of good or misses. As a result, both sweeping or piano style are equally popular among high end players. We can even see both styles at KAC final level. </div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-M1kkPTEk7Ko/YK-SgyWSD0I/AAAAAAAABqc/PUp7zQ5TpxwdhGCvuBgC5VH599-zjRQ7wCPcBGAYYCw/s600/E119UDBVcAchPH1.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="600" height="266" src="https://1.bp.blogspot.com/-M1kkPTEk7Ko/YK-SgyWSD0I/AAAAAAAABqc/PUp7zQ5TpxwdhGCvuBgC5VH599-zjRQ7wCPcBGAYYCw/w400-h266/E119UDBVcAchPH1.jpg" width="400" /></a></div><div><br /></div><div>I have been on piano style since the beginning, but sweeping really helps me to master many level 12.5 maps especially on the left hand. Typical examples include 蒼氷のフラグメント and Moonstone. For バルベリア・タンゴ I have been trying to trill in the pianistic way but it's simply too hard on the left hand. I gave up and swept with one finger instead...and that's an instant S. I felt like I have fallen somehow...</div><div><br /></div><div>I still think for more complicated streams the pianistic style would trump against sweeping, but to do that smoothly would require much more practice to me or anyone else. Maybe if I play like now (every Thursday for the new songs basically) for another year I will be able to S half of the real level 3...?</div>Forretriohttp://www.blogger.com/profile/18048483702091533151noreply@blogger.com0tag:blogger.com,1999:blog-2106712996078987699.post-33683224222031057662021-05-23T21:15:00.008+08:002021-05-29T12:22:25.743+08:00TWEWY the Animation: Joshua week impression<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/--O91iLcfXhM/YKpU5Do_qjI/AAAAAAAABp0/zvP4bfGKS6gLWqJ3goAZpyjAl4SG7xBGwCLcBGAsYHQ/s911/E2AqMQAVcAQBnyT.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="554" data-original-width="911" src="https://1.bp.blogspot.com/--O91iLcfXhM/YKpU5Do_qjI/AAAAAAAABp0/zvP4bfGKS6gLWqJ3goAZpyjAl4SG7xBGwCLcBGAsYHQ/s320/E2AqMQAVcAQBnyT.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;">Among all of Josh's smol faces, his T-pose still impresses me the most.</div><div style="text-align: left;"><br /></div><div style="text-align: left;"><br /></div><div style="text-align: left;">Week 2 occupied 4 episodes instead of 3 or even 3.5 episodes. This is making sense because we see the most developments and basically all characters in the week. Considering the nature of week 3 which is more like a team solo that part it should be easily covered in 3 episodes (with one episode solely for the final fights), unless they want to introduce more NEO hypes (which they did also this week).</div><div><br /></div><div>Again I will focus on the difference between OG (the original DS game) and the anime. It is apparent at this point that covering the story with like, half the detail is already impossible (when you also want to display the fights). One particular example this week is that Sho's math meme is really weird in contrast to what we saw in the OG dialogues because it's simply coming out of nowhere. The story focused on interactions among people and their feelings which is so delicate that most dialogues are relevant to the main plot. As such the producer have already done a satisfactory job to cover what should have been covered. My critics are again mainly on how the anime could have been closer to OG in terms of game mechanics.</div><div><br /></div><div>Let's start again with pins and monsters.</div><div><br /></div><div>On Ep.4, they finally got the monsters right: Carcinofolk appears on W2D1. Neku used Burning Melon here which is effective against crabs, but not much use against the rhinos. Instead of a fire sphere bouncing on the screen it was shown as ordinary fireballs only. He also used Pop Pendulum against kangaroos, which of course failed because this pin is too damn slow to hit them. I always preferred JoM slashing attacks as it stuns the enemy, and I have no idea why they never used those pins.</div><div><br /></div><div>Nothing too much about Ep.5, but they have once used the ordinary Pyrokinesis pin again. Starter pin should not be used at this stage anymore! And since your Burning Melon was shown as fireball last episode, the Pyrokinesis pin can easily be replaced by some other random fire pin anyhow. Oh and taboo noises firing cannons...</div><div><br /></div><div>On Ep.6 the game started with Garage Wolf and Doom Metal Drake...the former only appears on week 1 and the latter only on W3D7. This is just inappropriate. They finally used Frozen Cool instead of the Ice- pins, but this is the unevolved pin (cf. Blizzard Cool) so we should see one icicle instead of three. Swift Storm, Swift End is another new pin introduced and it seems like they really like Dragon Coulture. The other new pin introduced was Crackle Pop Barrier, which was shown as a weak barrier instead of time-limited invincibility. Joshua also exhibits his levitation + angel beam ability on day 6 (instead of day 5 in OG) this episode...his attack is always my favourite.</div><div><br /></div><div>Ep.7 started with the scramble crossing mini-boss fight. In the anime Neku faced Jungle Boomer and Grindcore Minks, but there were two red minks instead of the red-gold duo! There were Mosh Grizzly around which is also untrue to OG as it should have been Wall of Grizzly (black wolf) instead. In the boss fight Neku also (explicitly) used the starter pin Thunderbolt pin for the first time...again why? Storm Warning and the Spider series are similar but much better. Thunderbolt-type attacks are effective against Sho since he evade attacks so swiftly though.</div><div><br /></div><div>*Edit: it seems like Superfine beam were used in Ep.7 but I couldn't recall any attach like that...anyway.</div><div><br /></div><div><b><u>Other OG related</u></b></div><div><br /></div><div>Sho's missions started with [Game I(/II/III)] which is the same as OG. I now realized it looks like [Maths I/II/III] for Japanese's high school maths curriculum, but I am not sure if there are any relation between the two. The stupid 30+74 was also modified into sqrt(10816). </div><div><br /></div><div>Even before the anime we already know that many regions are renamed into their reality name as SE got the consent from the property owners. We saw the Tsutaya O-East last time, and this time it's Shibu Q-front (instead of Q-head). Then later in Ep.7 Pork City was renamed to Mark City. Back in 2008 I have not visited Shibuya so I wouldn't have react to Mark City even if that was the name in OG, but since now I have been there many time and also that the Mark City was shown explicitly (Pork City was never shown in OG -- you just enter a mall from Dogenzaka) I immediately understand the way the game describe Pork/Mark City as "where emotion gathers" -- for those who don't know, Mark City is a large complex above the Tokyu-Tokyo Metro Shibuya station...and one of the shopping malls loaded with top restaurants in Shibuya.</div><div><br /></div><div>At a point Mr.H helped Joshua and Neku by adding new functions to their phones. This is making less sense on smartphones as they have a much more compact designs comparing to phones in the 00's. That reminds me of the time when there were shops specializing in amending the hardware of phones and GBAs adding weird functions on it.</div><div><br /></div><div>In OG we never saw the movement of characters other than the protagonist team. Apparently the reapers can fly. Another difference in Ep.6 is that Joshua explicitly mentioning the isolated UG area, in particular the existence of Shinjuku UG.</div><div><br /></div><div>A map was shown when Joshua talked about route 5 and that is the exact same map in OG and I loved that. </div><div><br /></div><div>The mission on day 7 was not issued by Sho but by the conductor himself. In OG this is reckoned by the way the mission was written. The mission started with "Game 7" instead of "Game IV/VII", but this was not delivered in the anime which is slightly disappointing. </div><div><br /></div><div>The representation as in Ep.7 clearly deviates from OG more than the previous episodes. Firstly we have spider noises that never appeared in OG, then we have imaginary space appearing much earlier than Sho's fight (and visually it is so different -- I wonder now how Konishi's fight would be). The fight is a bit weird though, Joshua and Neku never managed to hit Sho effectively at least on screen but the fusion attack somehow did the job...</div><div><br /></div><div><b><u>Impressions</u></b></div><div><br /></div><div>- Shiki's emotion was close to the OG emotions most of the time, but Joshua's smug-ness is much clearer in the anime than in OG. He simply has so many different smol faces in the four episodes.</div><div>- Tin Pin's gone. Natural choice but I hope it will at least be in NEO.</div><div>- Mr. H calling Neku correctly in anime.</div><div>- Joshua talking about they need to attack the taboo noises to deal effective damage: a possible reference to puck relay.</div><div>- The N---d Prey shown on Ep.6 after Neku's flashback</div><div><br /></div><div>*</div><div><br /></div><div>I can hardly say the anime met my full satisfaction so far, but I will rate it a 9/10 regardless. Let's see what would happen on the Beat week!</div>Forretriohttp://www.blogger.com/profile/18048483702091533151noreply@blogger.com0tag:blogger.com,1999:blog-2106712996078987699.post-36546836096246742882021-05-14T09:31:00.006+08:002021-07-16T20:46:47.806+08:00After Dark 4.0 in Win 10: screensaver being reset to "None"<p><a href="https://www.forretr.io/2017/01/after-dark-40-in-windows-710.html">Installing After Dark 4.0 in Win 7/10</a></p><div style="text-align: left;">On my new computer (win 10 of course) I frequently encounter the following problem: the screensaver, after a while, resets to "None" (no screensaver) in the screensaver setting. You can explicitly go to the setting and set the AD screensaver again, but that is a waste of time. </div><div style="text-align: left;"><br /></div><div style="text-align: left;">After some investigating I found that this is again something that is lost in compatibility mode.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">If you go to HKEY_CURRENT_USER/Control Panel/Desktop, you will see the default path for the current screensaver. If your screensaver was reset to "None", then the path is likely</div><div style="text-align: left;"><br /></div><div style="text-align: left;">C:\WINDOWS\system32\AFTERD~1.SCR</div><div style="text-align: left;"><br /></div><div style="text-align: left;">but it turns out that the screensaver was installed in SysWOW64!</div><div style="text-align: left;"><br /></div><div style="text-align: left;">The simplest solution is then to copy the .scr file also into system32, and that worked immediately for me without further efforts required.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">Edit (16/7/2021): I found that leaving the screensaver in SysWOW64 causes all sorts of weird stuffs: the screensaver automatically triggers when you move the mouse to the right-top corner (while Windows does not have hot corners by default), and the screensaver triggers somehow when you are typing password in the lock screen blocking you from logging on. Just make sure the screensaver only stays in System32 and everything will be fine.</div>Forretriohttp://www.blogger.com/profile/18048483702091533151noreply@blogger.com0tag:blogger.com,1999:blog-2106712996078987699.post-69805903965655725942021-05-07T12:33:00.007+08:002021-06-02T21:27:20.168+08:0007/05/2021: Chelsea's road to Istanbul<div style="text-align: left;">There are quite some aftermaths since ESL collapsed: protests at Old Trafford, and Chelsea allowing fans representatives to join some board meetings. But none of them matches Chelsea's competitive achievement just a few hours ago.</div><div><br /></div><div>That is, a magnificent performance outclassing Real Madrid over two legs which wins them a ticket to the Champions League final in Istanbul -- somewhere we could have been to 16 years ago if not the phantom goal from Liverpool.</div><div><br /></div><div>I couldn't help but to shed tears with semifinal scenes flashing through my head...</div><div><br /></div><div>In 2008 Ivanovic scored two headers out of nowhere marking the beginning of his era in Chelsea; and of course the 4-4 is one of the most entertaining match ever.</div><div><br /></div><div>In 2009 that was the night of fucking disgrace which I don't want to talk about that ever again. But the 1-1 game is absolutely filled with quality: Essien scored a stunner and so did Iniesta. The Barca team went on and become one of the strongest team in history (despite multiple controversies).</div><div><br /></div><div>And 2012? I can still recite every single quote and every goalgasm from Neville for the two miraculous goals.</div><div><br /></div><div>The semifinals are never boring, and so was today's game. Real Madrid's midfield were so exhausted and they simply failed to pressurize Jorginho -- who always play like a master whenever unmarked. </div><div><br /></div><div>Kante was of course the star above all, he was too good on both ends of the field. It was his change in tempo that created the first goal. His contribution to the second goal is even more direct: a clear interception before sending to Pulisic who fed Mount. He is almost flawless in the tie. He even won all aerial challenges which is amazing considering he is just 5'7!</div><div><br /></div><div>The other players should receive their deserved praise too. Mendy's two crucial saves saved Chelsea in the first half; AZP playing the best he possibly can with his declining physicality; Rudiger who is solid as rock...it is truly a team effort. </div><div><br /></div><div>I don't blame Hazard for being sloppy in the game. He did he part, just that he simply lost his bursting power he had back in the days. He was thoroughly neutralized under the effort of Christensen and AZP, and the rest of Real's midfield were even less creative. Tuchel once again showed his tactical geniusness, and Zidine meanwhile, showed that his team is so awful under 3-back against top teams.</div><div><br /></div><div>Back in the days I fell into love with Chelsea because of Mourinho and his 1-0ism. I thoroughly believe in 1-0ism works in sports in particular football (I like 1-0ism in baseball too, though I have to admit it may not be the best way there). Being good defensively however sometimes implies the lack of sparks on the other end and the lack of consistency to win against lower teams. We have seen enough of that from Chelsea during these years.</div><div><br /></div><div>Some like Abramovich of course prefer the complete opposite: he wanted beautiful football. He bought many good attackers but most of them didn't perform as expected. On the other hand, coaches/managers that played attacking football -- like Ancelotti's team with 103 seasonal goals in 2009-10, AVB's high pressing team in 2011-12 and Sarri's Sarriball in 2018-19 -- never reached the same level of success in terms of European performance.</div><div><br /></div><div>At a point we thought that it is impossible to play beautiful and solid football at the same time. But now with Chelsea and City's performance this year we see a glimpse of hope that this is actually possible. The key of playing solid and beautiful football simultaneously is not all about stacking world class players (like PSG). It's being able to run, to play physically, and to execute tactics thoroughly. This is the common feature we observed in both the City vs PSG and Chelsea vs Real Madrid ties. These are the two teams that overwhelmed their opponents in all aspects, and they deserve the spots in Istanbul.</div><div><br /></div><div>To be honest I expect a dull display in the final because the two teams will probably play very conservatively, but that does not mean it is dull tactically, it is the right tactics adopted by both teams that prevent the talents from making comfortable decisions. This may not be a match that is enjoyed the most by general public, but I certainly have very high expectation on it.</div><div><br /></div><div>Most of Chelsea's players actually never played in the Champions League semifinal let alone final, but that's not something we should worry. There were numerous players in the 2012 Chelsea team who just joined. Cahill even just joined the club during the winter transfer window! The newcomers in 2021 -- Werner, Havertz, Chilwell and Silva -- have shown their quality and we should be faithful that they can do it again on May 29.</div>Forretriohttp://www.blogger.com/profile/18048483702091533151noreply@blogger.com0tag:blogger.com,1999:blog-2106712996078987699.post-60306974339741264592021-04-30T12:15:00.000+08:002021-04-30T12:15:47.802+08:00被青梅竹馬抓來當教魔法的我想要教出最強學生(仮)(1)：感覺進了火坑但擅長的不是水屬性可以怎辦<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-Tyxd6kt1fUQ/YItwh4Pom9I/AAAAAAAABok/NYmorz3BDkohFx6Jw7hfWQemCL664VNgACLcBGAsYHQ/s1200/89333396_p0_master1200.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1200" height="400" src="https://1.bp.blogspot.com/-Tyxd6kt1fUQ/YItwh4Pom9I/AAAAAAAABok/NYmorz3BDkohFx6Jw7hfWQemCL664VNgACLcBGAsYHQ/w400-h400/89333396_p0_master1200.jpg" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: x-small;"><i><u>"Wizard in the magic sunset"</u></i> </span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: x-small;">Character design: <a href="https://www.plurk.com/kuonyuu">@kuonyuu</a>, Illust: <a href="https://twitter.com/mihayuuno">@</a></span><span style="text-align: left;"><span style="font-size: x-small;"><a href="https://twitter.com/mihayuuno">mihayuuno</a> commissioned by forretrio. </span></span><a href="https://www.pixiv.net/artworks/89333396" style="font-size: small;">Pixiv</a></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: left;"><span style="font-size: x-small;">Editing and re-posting are prohibited // </span></span><span style="text-align: left;"><span style="font-size: x-small;">無断転載・自作発言禁止</span></span></div><div style="text-align: left;"><br /></div><div style="text-align: left;"><br /></div><div style="text-align: left;"><span style="font-size: large;">帝都，國立魔法學園。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">這裡是國家直屬培養人材的地方，進來就讀的不是貴族就是經過嚴格挑選的有能者。雖然傳授的內容以魔法為主，但也有培養冒險者、士官或者商人的課程。對於貴族來說，魔法是權力階級的一部分，因此學習魔法是必要的；這個學園聚集了同齡層中最頂尖的人物，因此也是絕佳的社交舞台。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">學生進入學園以後會被分配到不同的班級，每個班級都各自有特化的教學內容。當中最特別的是魔法科：擅長魔法的人多出身於貴族世家，因此大家都搶著希望進入這個班級，慢慢地魔法科成了每一屆最強學生聚集的地方。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">與學生的來源正好相反，這邊的教師幾乎都憑自己的實力取得教席。他們有成名已久的學者、也有離開前線的冒險者；就算偶有一兩個貴族成為教師，他們多半也是名聲在外，只因各種原因不得已回到王都而選擇在此工作。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">這個差異造就了一個有趣的傳統：新來的教師必須與他所執教的第一個班級進行對戰。班級可以派出一位領袖應戰，亦可以派出數人甚至整班一起上也是允許的。按常理說教師們要擊敗學生們應該不會太難，但單純打贏是不夠的，只有展示自己的看家本領才會讓學生們心服口服。沒法降服學生們的新人教師雖然不至於被立刻辭退，但教師學生的上下關係逆轉以後想好好教書根本是不可能的事，這些教師多半不到一兩年就會主動離去。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">教師所面對的班級也是有講究的。新人教師剛進來教的大多都是低年級的班級，與學生對戰也相對較易。有些倒楣鬼一進來就要面對高年級的學生，他們被刁難的機會就大得多了。在此之上要挑戰魔法科的難度就更大了。那些學生當中不少已有相當的實戰經驗，一起上的話即使是教師也不太好對付。當然執教魔法科可以近水樓台更方便接觸到未來的大人物，這個肥差幾乎肯定輪不到新人教師的。上一次出現新人教師執教魔法科已是快十五年前的事，而那位老師只待了兩個月便連夜逃了出去，連私人物品都沒有帶走。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">過去幾年，這個職位都由某位前宮庭首席魔法師擔任。也只有他可以壓得住那些擁有極強魔力的貴族學生。沒想到今年這位魔法師身體不適教下去了，校方只好找一個替代人選。但是指定一位新人教師來教這個決定，讓大部分人吃了一驚，也有人暗中開賭盤來賭這位可憐蟲到底可以撐多久。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">*</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">此時此刻，這位新人教師正在競技場裡履行學園的傳統。作為多年來第一個挑戰魔法科的新人，前來觀戰的人填滿了大半個看台。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">預期中的刀光劍影或者火球亂飛並沒有出現。只見一個巨型的龍捲風將整個賽場覆蓋起來，甚至連觀眾席上都能感受到強風。龍捲風將場上的塵土都捲起來，所以大家除了一兩道閃光以外甚麼也沒看到。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">過了好一會暴風終於散去，大家看到的只有倒滿一地的學生們。仍然站立在場上的只有一男一女。少女是跟隨公主入學的貼身侍衛，她本人也是劍術大家的名門之後。只見她身上的校服被強風割出了一堆口子，雖然看起來並沒有受到甚麼傷害，實際上她光是站著就用盡全力了。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">在她不遠處的是一位白髮青年，正一臉輕鬆地看著她。青年穿的不是校服而是整齊的襯衫外加一件長披風，身上半個傷口也沒有，顯然他就是這次新來的教師。不過他看起來也只比學生們年長個六七歲，光是以這個年紀進入學園成為教師已經是不得了的成就。更讓人驚嘆的是他看起來要創下成功挑戰魔法科的紀錄了。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">場邊的學生都沒看過他，畢竟他已經消失在王都好一段時間了。只有在這所學園裡混了好一段時間的教師才記得，眼前青年的戰鬥風格與多年前一位同樣是白髮的學生非常相似。那時他在同一地方同樣以壓倒性的風魔法將一整個貴族集團吹飛，那一役使他得到了「青色惡魔」的外號。其實說青色不太準確，青年所使的風魔法特別之處正是不帶任何顏色，就這麼隱藏在空氣之中隨時發動致命一擊。不過在那場戰鬥以後第二天他就從學園裡消失了，多年來再沒有在王都出現過。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「為甚麼要把我留在場上？」少女擺出生氣的樣子問道。一方面她在風暴裡目睹了青年出手的瞬間，她很清楚如果青年在那個時候朝她攻擊的話她是肯定會像其他同學們那樣倒下的。另一方面，她雙腿似乎還不怎樣聽使喚，拖一下時間她才有反攻的希望。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">青年完全沒有要攻上來的意思，他悠悠說道：「唔……雖然是來教魔法的但是我比較喜歡近戰呢。雖然有點抱歉但是我沒信心單靠近戰打你們全班，所以我只好先解決一部分學生囉。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">這算是甚麼借口啊！還說一部分，明明都只剩我一個了！少女揉了一下自的大腿，麻痺的感覺正在消退：「那為甚麼是我留下來？」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「因為你劍術很強吧？沒記住學生們的資料可是教師失格的呢。家中劍術流派第四代傳人、十三歲時隨行魔物討伐隊擔任前衛、一年前成為公主殿下的貼身侍衛。我沒說錯吧？伊．雅．娜．同．學？」青年一字一字將少女的名字唸出來，似乎從少女閃過驚訝的眼神中獲得了一絲愉悅。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「……」少女也沒有回應他。既然自己被盯上了肯定要跟他打一場，那還是等自己多恢復一點比較好。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">先前倒下的學生一些已經爬了起來，他們剛才只是在地上動彈不得而已。看到少女與青年一對一的架勢也不好參與其中，他們彼此攙扶著退到場邊。不論是場上的其他同學還是場外的觀眾都屏息靜待二人的對決。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">少女感覺自己的腿恢復得差不多了，便深呼吸了一下道：「這樣的話我要上了－－」說罷便衝了上去，連影子都看不到便在青年面前揮出一劍。她家的流派強調唯快不破，不論是對上人還是魔物也可以將趁對手不備而攻其弱點。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">青年身上沒有帶武器，只見他輕輕往旁邊閃便躲過了第一劍。他踏著輕逸的步伐一直閃躲著，少女的攻擊不是落空了就是落在最後一刻出現的魔力盾上。「唔。每一擊都簡潔有力也瞄準了要害，這樣可以在討伐隊當隨行也不奇怪呢。這樣下去在十年內就會成為家主了吧，到時你還會一直待在公主殿下身邊嗎？」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">少女的心情有點複雜。他給予自己的評價十分高，但自己的攻擊完全沒有命中對方。觀眾們或許看不出來，但少女很清楚眼前的青年並不是單靠速度閃過她的劍。她感覺到自己身邊的空氣並沒有依遁正常的空氣力學而流動，也不是單純變得黏滯，而是在關鍵的地方妨礙著她施力。手臂每一次揮動都會出現一點點的偏差，對追求精度的她來說是個大麻煩。她知道自己這樣下去早晚會力盡而敗，不如現在賭一把。空氣流動被干擾了嗎？只要減少旋轉而沿著肢體的軸向攻擊就好。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「吃我這招！－－」少女改揮為刺，手臂直直地向前刺去。之前一直沒用魔法的她此刻將雷電魔法附在劍上，雷電到最後一刻都可以改變攻擊的目標，如果說她有辦法對青年造成傷害的話應該就是這招了吧。附魔的一劍比之前的攻勢都更快更狠。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">青年露出讚賞的眼神：「這劍不錯，可惜還是差了一點－－」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">沒人看得清發生了甚麼事。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">少女雷霆萬鈞的一劍落在了青年的右側。就像格檔了她那一劍一樣，青年的戴著手套的右手貼著少女持劍的右手指著她的咽喉。在外人看來青年的劍指直取少女要害是不失武德而勝，但實際上少女感到自己脖子正被甚麼鋒利的東西抵著，要讓她血濺當場只在青年的一念之間。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">她苦笑了一下，隨即丟下佩劍高舉雙手投降：「我輸了……」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">青年把右手收回來道：「這一剌的氣勢是很不錯，但是蓄魔力的動作有點太顯眼了。減少魔力輸出取個平衡會比較好喔。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">他環視一周後放大聲音向全場喊話，平靜而不容反駁：「這裡應該很多人都不認識我，所以請容我再次自我介紹一次。我的名字是庫里斯，算是你們的學長，直到上星期都在外面當冒險者。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">我將會擔任魔法科的導師一職。只要你們想學的話不論是格鬥、魔法還是冒險技巧也好，我身上所有的都可以傳授你們。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">前提是－－你們跟得上的話。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">學生們此時隱約有一種預感，眼前這位老師比以前他們所遇過的都要鬼畜。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">*</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">學園教師宿舍。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">為了安置來自來自五湖四海的教師們，學園設置了教師專用的宿舍。教師宿舍位置甚至比學生宿舍更接近校園，設計上更豪華也配置了學生宿舍沒有的管家與女僕，這些一切都是為了讓教師們更方便在校園裡做事。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">庫里斯在競技場大展拳腳後便回到了宿舍，在路上不論是學生還是其他人都對他投以奇異的目光。他雖然感覺到了但也沒有想太多，與自己相關的流言在開學以後就會消停了吧，他這樣想著。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">他在自己房間前正想開門，卻感覺到有人已經在裡面了。這個時間不可能是來清潔的女僕，那就只能是她了吧？</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">輕輕地推門進去，只見一名女性坐在落地窗邊正在品著茶。夕陽打在她的金色長髮上更顯出她高貴的氣場。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「我說啊……大小姐你不要擅自闖進來喝我的茶好嗎？這些茶都是我找遍全國收回來的珍品，有錢都買不到耶。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">金髮女性也沒有轉過來望他，只是輕啜了一口茶道：「……這個品牌的茶以香氣見長，不過只要存放超過九個月就會變得與一般紅茶無異。我看現在你這罐已經放半年了吧？」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">庫里斯看了一眼桌面上的茶罐，的確是他半年前順手買下的。那是經煙熏的鳥龍茶，喝下去會有像花香般的回甘。他感嘆了一下，自己算是十分好茶，但是眼光還是遠不如眼前這位受過嚴格貴族教育的大小姐毒辣。女性彷彿知道他心中所想，輕輕說道：「沒甚麼大不了的，這個品牌雖然不在王都，但王都一直都有商人在進貨。以我所知有賣這個品牌的茶的店舖就有三家，我家裡也進了一些。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">他把椅子搬到女性所坐沙發的對面道：「嗯……所以呢？你過來就只是為了消耗我所剩無幾的茶葉嗎？」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「我只是來看一下你有沒有辦法搞定那幫學生而已，看過試煉之後我就安心了。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「難道你覺得我打不過他們嗎？還在讀書時我就能單挑一整班了，現在要贏根本毫無難度吧。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「立場不同，要採取的打法也不同。你這次做得很好，在他們心中留下了強大的形象又不至於讓他們害怕或厭惡你。要是你下狠手打傷他們的話麻煩才大呢。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「雖然我是冒險者，但出手輕重我還是懂的。我過來是真的希望可以好好教書，不但因為是妳讓我過來，也是為了給別人還一個人情。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「你的意思是說，我的邀請份量不夠嗎？」女性把茶杯放下，俏冷的臉龐露出了戲虐的笑容。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">他連忙擺手否認：「不敢不敢……您一句話我就得人頭落地了吧。大小姐您還有別的事儘管吩附，我押上我冒險者的名聲也必定為你赴湯蹈火的。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「呵呵，你這幾年也混得不錯嘛。幾個在邊疆活躍的大公會都搶著指名要你，不知道如果我把你的使用權賣給他們的話可以值多少錢呢。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「……還請您高抬貴手，我一定會安份地在這裡教書的。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「嗯，你明白就好。雖然你有點鬼畜，但我相信你不會隨便坑學生的。我只是來提醒你一下，這一屆學生的實力和身份非比尋常，除了我以外還有很多人在背後關注你。萬一出了甚麼事的話，我可沒有百分百的信心可以把你保住。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「那我現在辭職還來得及嗎？」原來是屎缺啊。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「你可以像以前的教師那樣落跑啊，不過我保証以後不會有半個公會雇用你而已，最差的狀況是冒險者的身份被註銷吧？」她平淡地描述著可怕的後果。當初把庫里斯弄出王都當冒險者的人是她，他毫不懷疑只要她一聲令下，自己所累積的一切瞬間就會灰飛煙滅。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「呃……」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「不想死的話，我建議你盡快跟學生們混熟。這樣你才有辦法駕馭那堆小怪物。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「謝謝你的好意，我會用自己的辦法把跟他們打好關係的。先從公主殿下的侍衛入手也是我事先計劃好的。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「好吧，你加油。那麼我也差不多該回去了，晚上我還要回去宰相府接見其他客人。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「啊……」似乎自己與她的距離變得更遙遠了：「現在做到甚麼位置了？」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「算是副手吧。每天都從早忙到晚，至少當冒險者可以給自己放假呢。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「我們的進行任務的時候的生活也不是大小姐能忍受的，算是彼此彼此吧。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">金髮女性沒有把話題接下去，而是站起來告別：「順帶一提，這裡不少茶都放好一段時間了，我建議你盡快把庫存清掉。實在喝不完的話可以邀請同學過來進行茶會，你的品味要得到他們的認可不是太大的問題。大部分你的收藏我認識的商會都有，你有需要的話寫信過來我可以幫你訂購。不過事先聲明，透過我買茶是沒有折扣的。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「嗯，我到時會聯絡你的。還有－－」他頓了一下問道：「改天我可以約你出來吃頓飯嗎？」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">她報以淡淡的微笑：「可以。不過先等你安頓下來，把學生們搞定再說吧。另外你最好先複習一下王都有甚麼好吃的，畢竟你已經好久沒在王都尋找美食了呢。」說罷她便轉身離去，在外面已經等候多時的傭人適時為她打開了門。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">啊……奇怪？庫里斯明明記得自己回宿舍的時候沒看到有人守在外面的。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「嘛，算了」他伸了個懶腰，心念一轉一股風便把門關上。與她的重逢來得比自己預料中來得早，不過至少她接受了自己的邀請，那麼以後再相處的時間肯定不會少吧。把目光投向辦公桌上那疊厚厚的資料，他自言自語說道：「現在該想想怎樣料理我可愛的學生們了－－」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">=============</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">諸君，我熱愛教學。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">我喜歡讓別人感受到解題的樂趣，我喜歡看著自己的學生在考試取得好成績並走出自己的道路。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">那感覺就像……勇者育成一樣。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">只是這世界上不只有勇者，也有那些萬年F級天天泡在酒館裡做一天混三天的冒險者。教學也是一樣，世界上有會自動讀書的勤奮學生，天天上課混日子的不良學生也不是沒有。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">所謂不良學生不一定代表他們學習能能力不好。他們有些只是沒找到適合他們的學習方法，有些是成長環境問題，有些則是沒有得到合適的資源。以這類背景為題材的作品其實不少，比如暗殺教室、高分少女DASH和一年A班的怪物都在此列。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">當中暗殺教室對我的影響很深，先不說這部作品劇情完整、音樂好聽、人際互動豐滿之類的好處，殺老師應該是作為老師的完美模範了吧？我對那種聖母裝到底的老師並沒有太大興趣，與其要用裝的不如將自己真實的一面融入到教學中。當然現實要在實體學校這樣做畢竟會有社會壓力，這點從補習名師的風格中就能看出來。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">所以老師一定要「拯救」學生才能成就有趣的作品嗎？那也未必。只要合適的老師遇上合適的學生就能擦出火花：像東大特訓班那幾個學生就遠不能稱得上笨，帶他們考進東大同樣是一段勵志的故事(至於後來我也把學生送進了東大又是另一段故事了)。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">至於我呢？要感受到解題的樂趣並不限於甚麼高深題目，就算是讓小孩發現可以從1+1=2變成10+10=20也是十分有趣的事情。不過我也喜歡用更高角度去理解整個理論的脈絡。這個方法在大學比較常用，中學的話對學生的要求難免會比較高。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">我經常掛在嘴邊的一句：中學程度的考試，你只要把30年試卷做好做透要拿A根本不是難事(除了某幾個特別難的考試，比如香港高考……)。但是對於讀書能力出色的學生，真的會甘於背課本和背試題嗎？其實別的學生可以找不到讀書方法和找不到良師，難道好學生就不會發生這個問題嗎？如果給他們配上好的導師加上任性的資源不就能帶他們一起飛了嗎？</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">－－以上，就是我想寫的故事。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">當初這是我一時興起做人設時產生的角色，上面也沒打算續寫下去，怎料開了個頭就停不下來了。我對魔幻世界的想象有一大部分源自於科學角度的理解，簡單說就是熱力學定律消失不見，但牛頓不會從棺材裡爬出來的世界。在這種前提下社會會怎樣發展，又或者冷兵器和魔法之間又會怎樣取捨之類的問題，我說不定能在寫作中找到答案。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">這部真的不保証會填坑就是，沒填就當是短篇。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">喔對了，最後我還是要安利一下我的茶。文中提到的茶是Mariage Freres的Roi Soleil－－實際上不是鳥龍而是中國茶種，但那種香氣與中式濃茶的回甘有相輔相成的效果，絕對值得一試。不過話說回來，如果異世界沒中國，那我要怎樣形容中國茶呢？異世界也沒大吉嶺，那大吉嶺茶也不能叫了吧？我又不想一直捏造地名，總不能叫C國茶或者甚麼比比魯茶吧？</span></div>Forretriohttp://www.blogger.com/profile/18048483702091533151noreply@blogger.com0tag:blogger.com,1999:blog-2106712996078987699.post-89614984532574979902021-04-28T23:03:00.001+08:002021-04-29T11:53:24.854+08:00TWEWY the Animation: Shiki week impression<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-Kyldbb1kGQg/YIl4-p7jSSI/AAAAAAAABoI/lG-AXym6yGoODRSJbLaf_4qa-gnMUjrvQCLcBGAsYHQ/s1113/%255B%2525UB%257DUNN_ASD%2560XV6W%257D9%257ETET.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="618" data-original-width="1113" src="https://1.bp.blogspot.com/-Kyldbb1kGQg/YIl4-p7jSSI/AAAAAAAABoI/lG-AXym6yGoODRSJbLaf_4qa-gnMUjrvQCLcBGAsYHQ/s320/%255B%2525UB%257DUNN_ASD%2560XV6W%257D9%257ETET.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><i>Probably the most iconic shot of the week.</i></div><div style="text-align: left;"><br /></div><div style="text-align: left;">Anime this season are exceptionally good in general. There are so much that I want to talk about, but if I have to talk about one particular of them then it must be The World Ends With You the Animation.</div><div><br /></div><div>The animation is a successful reiteration of the 2008 game with some modern twists, but it also keeps features from the original game like the character's postures and of course the music. I do not intend to analyze in detail the difference between the game and the anime. Instead, this is a collection of my live reaction based on my game experience.</div><div><br /></div><div>Probably not spoiler alert because I mainly refer to the game content of the same progress, but I will refer a lot to game data like pin code, pin evolution, droppings and so on -- check the <a href="https://twewy.fandom.com/wiki/The_World_Ends_with_You_Wiki">wiki pages</a> if you are not sure.</div><div><br /></div><div>Let us start from Episode 1-3 aka the Shiki week.</div><div><br /></div><div><b><u>Pins</u></b></div><div><br /></div><div>That's something that I concern the most since I remember the pins too well and that's the unique system in the game. I wished that the game uses pins in the order of gameplay -- some pins are much more accessible in the early game, so they should be introduced earlier. </div><div><br /></div><div>Neku started with the 6 basic pins, but it was the Pyrokinesis pin that was used mainly. That's a natural choice but it appeared for too many times. They used Thunderbolt as well, but I feel like it'll be more impressive to use the other 4 as well. Shockwave might clash visually with Shiki's psych, but Force Rounds and Psychokinesis would be cool to display. Cure Drink as an immediate potion also expand the versatility of the pins (to whom never played the game).</div><div><br /></div><div>In early days, players are almost guaranteed to come across to D+B pins and probably D+B pins only. It's unfortunate that they decided to display the pins in a random order. Changing Murasame into a jumping psych is ok, but one only obtains the pin from 33N (Hard Corehog) on Shiki day 5 -- so you can't have that on day 1!</div><div><br /></div><div>Similar problem occurred on episode 2: Fiery Spirit, Spirited Fire is a pretty powerful pin and it's only obtainable from 13NU (Alterna Wolf) that is not around before week 2. </div><div><br /></div><div>Then on episode 3 Neku activated Ice Risers but it was visually showed as Blizzard Cool. Both of them are available by the end of week 1 so they should really display Blizzard Cool instead. </div><div><br /></div><div>D+B pins is really one of the best brand of pins to use against the first GM fight because they are mostly psychs that works regardless of distance. 001/002 (Ice Blow/Risers) surely works with a simply flick, but 003/004 (Frozen/Blizzard Cool) is even better: when the icicles are halfway out the enemy is dealt with constant damage. Even better the boss can't move so it's free damage and combo all the way. The Sexy- pins (006-8) are also effective against the boss. These are all the pins that I used when I first played the game.</div><div><br /></div><div>Oh they also used Sweet Talk Tether, another wonderful pin against static opponents. Although obtaining the pin is less obvious in game: it's either from 35E that does not appear during week 1 in the original game, only on W1D7 in the final remix (so the pin choice for the anime was decided when they made final remix? Though that's kind of hard to believe), or to evolve from Love Me Tether which is a pig drop on day 6.</div><div><br /></div><div><b><u>Impressions</u></b></div><div><br /></div><div>- Calling as an OP substitute is a natural choice. All fans would love that. Aaaaand we just get another remix of Twister.</div><div><br /></div><div>- A-East was renamed probably because it was purchased by Tsutaya after the original game.</div><div><br /></div><div>- The 1-3 bat boss was defeated by a 4-man collab, which is of course different from the original game. But relating to what we saw from the Neo trailer, I guess this will be the norm in Neo?</div><div><br /></div><div>- They simplified the imprint system. I wish I could do the same instead of hissing around for the meme keywords.</div><div><br /></div><div>- New fish noises?</div><div><br /></div><div>- They mentioned that the noises will grow stronger over time. This wasn't in the original game. Instead it's closer to the mechanics in the 3 new days. Maybe something similar in Neo?</div><div><br /></div><div>And that's all. Stay tuned for my impression on week 2 contents!</div>Forretriohttp://www.blogger.com/profile/18048483702091533151noreply@blogger.com0tag:blogger.com,1999:blog-2106712996078987699.post-68378441891110048692021-04-27T02:28:00.006+08:002021-05-05T12:35:17.598+08:00Two problems on cubic functions<div style="text-align: left;"><b><u>Problem 1.</u></b> Find the number of integer solutions to the equation </div><div>$m^3+n^3+30mn = 10^3$ with $mn \geq 0$.</div><div><br /></div><div>I was given the above question today which is a pity because I've been drafting questions for some other contests. Questions like the above is definitely something I would consider.</div><div><br /></div><div>At first glance recall the identity $(m+n)^3 = m^3 + n^3 + 3mn(m+n)$, so if $m+n = 10$ then the equation becomes $(m+n)^3 = 10^3$, and that gives 11 solutions $(10,0),...,(1,9), (0,10)$. This is however not all the solutions -- and that's why the question is not an easy one.</div><div><br /></div><div>Now consider a more general factorization where $m+n = k$. Then the equation becomes</div><div>$k^3 + (30-3k)mn = 10^3$</div><div>$10^3 - k^3 = (10-k)(10^2+10k+k^2) = 3(10-k)mn$.</div><div><br /></div><div>If $k\neq 10$ then we expand $k$ to obtain</div><div>$10^2 + 10(m+n) + (m+n)^2 = 3mn$</div><div>$m^2-mn+n^2-10m-10n+10^2 = 0$</div><div>$(m+10)^2+(n+10)^2-(m+10)(n+10) = 0$.</div><div><br /></div><div>Since $LHS \geq 0$ we have the only extra solution $m = n = -10$, and there are 12 solutions in total.</div><div><br /></div><div>*</div><div><br /></div><div>When we see cubic equations in contests we know it's going to be nasty. Here is another one, from an university entrance exam in the late seventies or early eighties.</div><div><br /></div><div><b><u>Problem 2.</u></b> Sketch the graph of $x^3+y^3-3xy = 0$.</div><div><br /></div><div>I recommend you to plot the graph using Wolframalpha because otherwise who in the world could sketch this by mathematically analyzing the function $x^3+y^3-3xy$?</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-fFoHsNG8atA/YIcE4l_YXoI/AAAAAAAABn8/bY-1cnoMwjY2Ew-A1Grh0JfHVEcrpf0KACLcBGAsYHQ/s492/98%25293%257BV%257B%2540E6XB%257E%2525P%2528LSEC6RI.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="469" data-original-width="492" src="https://1.bp.blogspot.com/-fFoHsNG8atA/YIcE4l_YXoI/AAAAAAAABn8/bY-1cnoMwjY2Ew-A1Grh0JfHVEcrpf0KACLcBGAsYHQ/s320/98%25293%257BV%257B%2540E6XB%257E%2525P%2528LSEC6RI.png" width="320" /></a></div><br /><div><br /></div><div>Notice that the curve has an asymptote $y=-1-x$ (notice that $x^3+y^3-3xy = -1$ when $x+y=-1$, like what we did in problem 1, but mathematically showing the asymptote falls to the category of algebraic geometry, where you calculate the tangent at infinity. See <a href="https://math.stackexchange.com/questions/474860/how-to-find-asymptotes-of-implicit-function">this post for example</a>). So we start with a change in coordinates $(x,y) = ((X+Y)/2, (X-Y)/2)$ (by the way why a multiple of 2 not $\sqrt{2}$ which gives an orthogonal transformation? Well 2 is easier to calculate with but more importantly, it cancels the coefficient of $X^3$) which rotates the asymptote into a vertical line. The new transformed equation is then $X^3-3X^2+3XY^2+3Y^2 = X^2(X-3)+3Y^2(1+X)=0$, so the graph becomes the plot of </div><div>$Y = \pm \sqrt{ \frac{-X^2(X-3)}{3(1+X)}}$ , (1)</div><div>which has domain (-1,3] and a vertical asymptote at $X = -1$ as expected. The roots of the function are of course $X = 0,3$, and the extrema (of the positive bit) is $\sqrt{2\sqrt{3}-3}$ at $X = \sqrt{3}$ (high school calculus by looking at the function $\frac{-X^2(X-3)}{3(1+X)}$). Finally, since the curve is smooth everywhere, you know that the cross at the origin are actually two smooth and symmetric curves and that should be enough to sketch the graph. (Even better, using implicit differentiation and (1) you know that </div><div>$(\frac{dY}{dX})^2 = \frac{X^2(2-X)^2}{4Y^2(1+X)^2} = \frac{3(2-X)^2(1+X)}{4(1+X)^2(3-X)} = 1$ at the origin. Therefore the two tangents at the origin are of slope $\pm 1$.)</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-XyWgIyWKHrY/YIu7GtWIhOI/AAAAAAAABos/__6ueYuym_IpwGcMQ4xVZEqsYNUMv6aFwCLcBGAsYHQ/s450/%255DQPDX84V%2524TNAPS9%252897ILMEP.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="450" data-original-width="382" height="320" src="https://1.bp.blogspot.com/-XyWgIyWKHrY/YIu7GtWIhOI/AAAAAAAABos/__6ueYuym_IpwGcMQ4xVZEqsYNUMv6aFwCLcBGAsYHQ/s320/%255DQPDX84V%2524TNAPS9%252897ILMEP.png" /></a></div><br /><div>This curve is pretty famous in fact -- its name is <a href="https://en.wikipedia.org/wiki/Folium_of_Descartes">the Folium of Descartes</a>. This is just another example that people always get their ideas for exam questions from the old stuffs regardless of the time.</div><div><br /></div><div>This is the beauty of the old entrance exams: you get questions too analytic and too open-ended for high school or college Olympiad but too hard under modern high school or college curriculum. These are questions that we do not meet everyday, but I guarantee that a large portion of them are fun to play with.</div>Forretriohttp://www.blogger.com/profile/18048483702091533151noreply@blogger.com0tag:blogger.com,1999:blog-2106712996078987699.post-69847772160560189232021-04-22T16:54:00.021+08:002021-04-22T21:52:36.255+08:00Thoughts on ESL (3): the future and other observations<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-V3jBtm9IdCo/YIF3NPLCmmI/AAAAAAAABnE/Dw6u1YxCWXcRM2oxwhIeCRdKY3YqtN9pwCLcBGAsYHQ/s867/9MLAR8X%257EJBO0%25299V%252543FD%2524T8.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="867" data-original-width="751" height="320" src="https://1.bp.blogspot.com/-V3jBtm9IdCo/YIF3NPLCmmI/AAAAAAAABnE/Dw6u1YxCWXcRM2oxwhIeCRdKY3YqtN9pwCLcBGAsYHQ/s320/9MLAR8X%257EJBO0%25299V%252543FD%2524T8.png" /></a></div><div style="text-align: left;"><i>That was 2016, the first year of the Yokohama era. Torres was long gone. I had many other possible choices especially Ivanovic and Hazard, but I chose Torres without any hesitation. The reason is simple: Champions League is the highest platform and the CL semi-final is the best tie in the world. Torres scored the critical goal in the best tie in the world, in 2012. </i></div><div style="text-align: left;"><br /></div><div style="text-align: left;">*</div><div style="text-align: left;"><br /></div><div style="text-align: left;">The ESL did not appear just because of American capitals. UEFA and their cups have to take a big part of the blame. In fact, this is not the first time that the big clubs came together and tried to form a group out of the FIFA/UEFA framework and that was the G14 scandal 20 years ago. Only this time they came together in the form of a new football league overriding CL, hence a much sharper conflict.</div><div><br /></div><div>UEFA has been known to be fully corrupted. Platini's attempt to "promote beautiful football" by suppressing Barca's opponents is by far the most iconic scandal. Their Nations League and the expanded CL were made to raise more money without bear the responsibility of taking care of those really exhausted players. They are unfair on the matter of financial fair play (FFP) and they never make clear about their financial situation. Perez made a good quote out of that: "I know the salary of LeBron James, but I have no idea about the salary of the UEFA president."</div><div><br /></div><div>For owners of the big clubs though, whether players were forced to play 70 games per season or were treated unfairly on the pitch is of secondary concern. Their ultimate goal is to squeeze more money out of the club, and this is a common goal among the 12 clubs joining ESL -- and this is their only common goal.</div><div><br /></div><div>The big clubs of course do have different considerations. United, Arsenals, Liverpool and Milan who are owned by American capitals together with Perez's Real Madrid, is trying to introduce the American model into football (just listen to FP's talk about shortening match duration and so on). Clubs like Barca, Juventus, Chelsea (and City) takes it as a leverage against UEFA. Clubs like Atletico, Spurs and Arsenal are not the best among the big names, so they feared to miss out the chance to earn big in ESL. With different motivation behind, it's hard to expect them to unite strongly against the expected pressure around the globe.</div><div><br /></div><div>When we say that everyone involved in football (except the owners) opposed the idea of ESL, we also have to admit that sometimes the opposition of football fans (plus pundits and coaches and players...) does not mean much to the higher ups. Arsenal, United and Newcastle fans have been shouting Kroenke, Glazer and Ashley out for years and oh they are still leeching the club. They are not leaving because fans wanted them to leave (probably not this time though). </div><div><br /></div><div>Just look at big6's reaction against FA, EPL, ECA and UEFA's condemnation. It was expected that ESL will not be liked by most people. What they did not expect is that the fan's violent reaction triggered strong responses from the governments: Tories and Labours united in UK and Macaron standing for PSG's decision. City's legal team might be better than UEFA's, but they are nothing against government's policy. Once Boris Johnson mentioned working visa everything is over -- that is out of legal action's reach. Considering how hard is getting a working visa for a footballer in UK after Brexit, there are so many ways to stop foreign players to play for ESL in UK. For those who shorted United shares when BJ stood out and talked about ESL congratulations you know football (and stocks market) really well (that should have been 10% profits in two days!).</div><div><br /></div><div>And the future. What is good for the industry and the teams? Clearly the CL expansion is a big no and that should be retreated. This is however technically hard as it just went through as a response to ESL. I think there are alternatives even if we have to adopt 36 teams in CL -- for example just put them into 9 groups of 4, and 4 worst runner-ups will have to compete for the two final seats in the last 16. They really need to control number of matches played by the teams strictly.</div><div><br /></div><div>UEFA already promised to increase the CL bonus. Some even says they paid the English clubs secretly to lure them to withdraw from the ESL. This is great to the teams, but it also implies that UEFA actually hid their profit from the participating clubs. They need to be more transparent financially.</div><div><br /></div><div>And 50+1? I know many agreed with the idea and praised the German League especially Bayern, but honestly I don't agree. Competitively it is not so great inside the league and all other teams are like served Bayern to be the giant representative. They are not even close to their successes in Europe like back in 2012-15. Teams other than Bayern failed to do well in both the domestic league and the European cups. Even with EPL's commercial success I heavily doubt if the League is good enough to breed 6 big teams under the 50+1 system. Implementation of the system is technically hard too. 50+1 means fans need to buy the shares from the current owners -- and that would be billions of dollars under current market value. The league must go on without interruption -- you can't really stop City or other teams from playing the just because she's not turning into 50+1 quick enough. There are also comments on Reddit suggesting the use of shares of different classes (with different voting rights) but bare in mind that it still costs unrealistic amount of money and, shares of different classes is still not a thing in Europe (soon in London, but whether or not that applies to unlisted company is another thing).</div><div><br /></div><div>*</div><div><br /></div><div>Finally below are some random observations. It is always interesting to read the event from other perspectives.</div><div><br /></div><div>- UK government's reaction is certainly a consequence of reaction from fans plus the rest of football industry, but it is also the tradition of Britain protecting their soft power seriously. Football is one of the most important icon of England, and it would be a shame if that turns into the American style. It is an easy decision for the government to take.</div><div><br /></div><div>- Some suggested that the EPL teams withdrew too early. They could have waited for negotiation with UEFA before and look for concession -- because this is what some teams wanted in the first hand -- if possible. I actually agree but the immediate reaction all over the world made that impossible. Look at the protests at Stamford Bridge: if the big6 didn't retreat that night, without any doubt we will see violent protests in front of (inside) the Spurs' stadium on Wednesday.</div><div><br /></div><div>- Conspiracy theory: what we saw is American capitals entering football market trying to turn that into the American way for more profit. But what about American capitals trying to ruin football so that they can promote their American sports?</div><div><br /></div><div>- When you look into online forums, the reaction from English based communities and Chinese based communities are completely different. Watching people grudging against UEFA so much that they wanted ESL anyhow even to the point of associating UEFA with supremacy theories is...just funny.</div><div><br /></div><div>- FP did make a correct point of teenagers having more diversified entertainment and less are watching football. That is correct but can be salvaged by different means. Football in the past 30 or 50 years was promoted in the traditional way: local communities and traditional media like radio and TV. These are pretty much past tense and clubs/FAs/UEFAs need other ways to promote football in 2021. On reddit people gave a great example: chess. Being such an ancient and complicated game, chess received much better attention in recent years via streaming and also Netflix's movie. On the traditional sports side F1 is also doing great by promoting their sport online. I wonder why can't they do the same for football -- or that they are not willing to invest for greater good?</div><div><br /></div><div>- There are comparisons between the ESL scandal (which survived for 2 days flat) and the hundred days revolution in China (~1910). Of course they are not totally the same (for example the difference in stakeholders that opposes the changes), but this is quite insightful actually. One lesson for FP: stop talking so idealistically and anger more people. </div><div><br /></div><div>And...that's about it. I never thought I would rant that much (5000 words) but that's possibly because I never write about football other than the matches themselves. Thanks for reading and I hope to write about football again when Chelsea lifts the CL this year, if that ever happens...</div>Forretriohttp://www.blogger.com/profile/18048483702091533151noreply@blogger.com0tag:blogger.com,1999:blog-2106712996078987699.post-53672846241368466982021-04-22T11:52:00.003+08:002021-04-22T11:52:42.230+08:00Thoughts on ESL (2): consequences and why we shouldn't<div style="text-align: left;">Perhaps it's not a bad idea to adopt a new business model of football after all, so the question is, why is ESL bad for football? My answer has been partially covered in the first part, that it breaks down the pyramid model and shrinks the industry scale massively, but let us go into the details.</div><div><br /></div><div>First of all we need to make clear of what games they will be playing with ESL. Currently top division leagues are playing 38 games a season. In England the two cups would be another 2 to 12 games, and European cups would be 6 to 15 more games (most will get 8 in extra). That means top teams are currently playing up to 65 games a year. That is a tremendous amount and people are complaining about injury problems with frequent and intensive games. What if we take ESL into consideration?</div><div><br /></div><div>According to the news, the 20 teams are divided into two group with round-robin inside the group then some extra play-offs. That would be 20 games in minimum which is damn lot! If they are playing domestic leagues and cups as well then they must play at least 70 games, about 10 more than average. Considering how condensed the fixtures are in the second half of a season, fitting 70 games means they are already playing 2 games per week since early season. That is absolutely impractical and excessive injuries will consume the top players fast.</div><div><br /></div><div>While the rest of the teams are certainly opposing EPL all together with the attitude of the FA, the fans, the coaches and the government, it is unlikely that the big teams will still play in their original leagues. Assuming that the big teams will now play the ESL and perhaps some domestic cups, what do we expect from here?</div><div><br /></div><div>It is clear that the top domestic leagues take the greatest impact since the big teams are the icon of the leagues. The commercial value could drop vastly without them. On the other hand the leagues may have to promote extra teams from the lower divisions and that may temporally lower the match quality.</div><div><br /></div><div>A slight unexpected drop in TV revenue could cause great trouble to some teams in the top flight, especially in La Liga (Spain) and Serie A (Italy). They are struggling financially in general even before 2019 to the point of having difficulty of paying the salary weekly on time. In 2020 they took another heavy hit and some of them had to negotiate with the players for plans to cut the salary so that the club wouldn't go bankrupt straightaway. It is foreseeable that these clubs with even less revenue received will not be as competitive as of now. They may cut cost, sell their profitable players and reduce investment on the youths. That is detrimental to the whole industry. The worst case scenario would be simultaneous financial problems from multiple teams in the league to the point that games cannot be held properly. The league will be severely dragged at the point as huge compensation may need to be made. Imagine what happens with Leeds and many other teams with financial troubles -- to dive into third divisions or lower -- happening on multiple top division teams? That's would be the middle layer of the pyramid crumbling.</div><div><br /></div><div>And what happens to the bottom of the pyramid? With top flight clubs now restricted to 12, 15 or 20 clubs only it will be much harder to become a "top flight player" as opposed to nearly 100 teams in the top 5 domestic leagues in Europe. It will be much less profitable to play in the domestic leagues even if you play for the new top teams in those leagues. As a result the industry receives less new blood in general lowering the quality of players in the long term. </div><div><br /></div><div>The ESL clubs are also cutting their connection with their local fans, and that ruins the local football culture. Sometimes it's even hard to find a substitute. </div><div>Doing that in London is easy: Crystal Palace, West Ham, Fulham or even QPR (not for Chelsea fans) are some alternatives, but what about fans in Manchester? Which team are they going to support other than the Manchester duos? Like FC United? For people that enjoyed football and share the history with their club for 20, 40 years or multiple generations, clubs joining ESL would be the heartbreaking moment for them and they will never come back again, so as their children. 10 or 20 years later, where are you going to obtain good players like now? Smaller clubs certainly won't become minor clubs because they have their own history and local fans. Not way that they can get enough funding like the NCAA model. That is the bottom of the pyramid turning into sand. By the time when we raise our eyes and look at the top, ESL is no more than a castle in the sky, if not already sunk.</div><div><br /></div><div>I am also skeptical about the expected sales of ESL. Remember the four American leagues are making so much money not only because they are commercially successful, but also because they are from America, one of the wealthiest countries that invests so heavily on entertainment. The 12 clubs are promised 3.5 billion euros "welcome bonus" from the ESL, when distributed could be as much as what they can earn by winning CL. That is however not free money -- this is by pawning the broadcasting rights. The sales revenue will be in theory promising but one never knows. How much can you sell it for when people are opposing the idea so much? For example if you look at the EPL, a big portion of EPL revenue comes from local broadcasting and not overseas: the ridiculous pricing from Skysports or iTV has been complained years over years but that was withstood by the people because it is their local teams. Overseas permits over America and Asia worth less comparing to Europe and the same phenomenon holds for CL. Whoever broadcasts the games are also under the pressure from the people -- in fact, DANZ and Amazon, declined the rumor/deal very early on. What happens if you failed to create enough revenue to pay back the "welcome bonus"? Well, good luck dealing with American capitals.</div><div><br /></div><div>Some people say that the financial situation of the big clubs (Barca and the Italian trio) are bad enough and they urgently need a source of funds right now, so they had no choice but joined ESL. In theory the welcome bonus could have helped them to survive this pandemic crisis and after that they can rely on the great success of ESL, but is it worth to bet on something that may not return well but will absolutely ruin the industry in long term? Having financial problems is not the end of the club -- at the worst case they will take a dive, but they are backed by the fans who will support them till they return into glory.</div><div><br /></div><div>When the ESL teams cut off their association with domestic leagues, their connection with domestic cups are also much weaker. Cups play an important role in the football ecosystem and it is bad to have teams that plays even more negatively on the cup matches. Cup matches is magical in the world of football because it is so unpredictable. It is the stage of smaller teams doing their best to knock out the giants. The unpredictability comes from the fact that these matchups are rare and tactical prediction works less often. If Chelsea plays against Luton town 3 times in a row, I can tell for sure starting from the fourth time and so on Chelsea will beat the shit out of Luton Town every single time (no offence to Luton Town). But the first encounter? Luton Town has a small but realistic chance to pull something out there. </div><div><br /></div><div>I always say that the CL semi-final is the most entertaining games in the world, and that is again due to rare encounter but also this is the highest stage before the final with only the strong teams around. It would be boring to see Bayern vs PSG many times in the League, but having that in a quarter-final knockout is another level of thriller. Strategies for knockout ties are completely different from league encounters as they bare a greater consequence. Without CL this may not happen again.</div><div><br /></div><div>Domestic cup games is an important part of the ecosystem. For the FA Cup, TV revenues and ticket sales are split between the two teams in every leg. Whenever a small team gets to play against a giant team (in an away game) then they get to sell thousands of tickets in a big stadium. The extra one million or so may not help the top teams a lot, but it could be more than the yearly income of some third division teams. The extra money could be used to acquire better players and improve the infrastructures. Despite the dream of playing against the big names, money is also a big motivation for smaller teams to play the best in cup games. It would be a disgrace if the ESL teams still decide to participate these cups but to play even more negatively with more benched players starting the game (and still win), what is then the point for smaller teams to do their best? They may just surrender right away since they have already pocketed the money and they will lose anyway. The lost in competitiveness is the last thing we want to see in football.</div><div><br /></div><div>As of now ESL is basically dead, but its impact is far from over. The potential punishments from the leagues and UEFA are still pending, and the ESL does indeed signal an alert about the football industry. In the last part I want to talk about some possible aftermath as well as all sorts of random observations.</div>Forretriohttp://www.blogger.com/profile/18048483702091533151noreply@blogger.com0tag:blogger.com,1999:blog-2106712996078987699.post-60822301728363029722021-04-21T05:57:00.002+08:002021-04-21T05:57:28.398+08:00Thoughts on ESL (1): the European football model<div style="text-align: left;">It was 6:30 a.m. and I was preparing for a late sleep. I know it will be Chelsea vs Brighton in 30 minutes, but I don't really care. Semi-final in 7 years? It's nothing comparing with what Chelsea, along with 11 other clubs, planning for something that could potentially destroy football as the most popular sport in the world. I rolled on the bed scrolling over Reddit, Skysports, BBC and all other new sources and forums and simply failed to sleep. I have so much to talk about the European Super League (ESL) --- I failed to squeeze out the time to talk about that, but maybe it is a good time right now.</div><div><br /></div><div>As I am writing we have received some good news -- Chelsea and City are leaving. Ed Woodward resigned. Altetico and Barca are there to leave. We will see more in the coming days, but I will try to cover my thoughts about ESL in general.</div><div><br /></div><div>The American sport model is something that I never appreciate with because competitiveness has to give way to entertainment and commercial consideration. When we say sport we mean competition. Entertainment comes from players doing the best to win, not by placing cheerleading girls or MC warming up the games. Wrestling, boxing and MMA is merely a comical joke trying to make up stories among players. </div><div><br /></div><div>The four American leagues -- are closed on their own with all the smaller leagues withering. Recently we observe a reform of the baseball minor leagues (MiLB) shutting down a number of teams. They were down so easily because minor teams are simply not sustainable in the American model. They hang on the poor little money from the Major and squeeze the most out of their players -- overnight bus trips to the field, salary lower than most normal office workers, and of course no pay during the off-season. Taking a step back the NCAA model is not even sustainable without the help of the colleges and the government. All we see is a greedy league sucking the blood from the youth ladders for their money and glory. There is no need to doubt the players' professionalism, but what can you do when those sports are designed to entertain in ways other than pure competition? (There is no room for cheating and violent plays though -- they shouldn't be part of the game and should not be counted into competitiveness.)</div><div><br /></div><div>Close leagues and the drafting system making things even worse because team can benefit from intentionally play bad/not playing the their best. We have seen that happening in MLB over and over again: Rays, Cardinals, Marlins...and even the Cubs team that broke the curse and won WS! Why is it possible for a team to benefit from being bad? There are similar operations in the world of football as well. Arsenal with her owner Kronke is one of the best example: the investment is calculated to be just enough to keep their commercial value while making consultant company that "gives advices" about the players' market (which doesn't seem to be helpful after all). But the borderline is they must perform up to a certain level (top 4 and CL spot, or top 6 with EL spot) -- that's why EPL is always fun to watch on teams around such ranks. </div><div><br /></div><div>Of course I watch baseball, but that is more of a substitution when football's off-season. I enjoy the number and science behind baseball, and I appreciate how off-speed pitches work. But at the end of the day I never feel the same passion from baseball as from football. Football is the culture, identity and religion of those who love it. (Another reason I prefer football than baseball is that baseball is discrete in nature and too easy to quantify -- sports lose part of their sacred or romantic mask with numbers, but that's a topic for another day).</div><div><br /></div><div>Football in Europe takes the pyramid model instead. The pyramid means that lower teams provide variety and base numbers, while the top teams provide attractiveness and money which part of those will be transferred down the pyramid.</div><div><br /></div><div>For example lower teams are not under the upper teams (slightly different in Spain but that does not happen in the top division so we will overlook that), but they are still motivated to breed good players. For the sake of their team result for sure, but good players also bring important revenues by selling them to higher teams. Often there are clauses that the original team gets a small portion of the transfer fee if the player is sold again -- which is often to an even bigger team -- which brings more money to the lower teams.</div><div><br /></div><div>Instead of a single closed league, there are multiple divisions of leagues within a country, divided just like a pyramid. That pushes teams to do well to be rewarded, and at the bottom-line fight to survive. There are also continental and domestic cups that reward teams who performed well over a short period of time. Top leagues like the Premier League (EPL) sells the most because it is quite famous even overseas but not the lower leagues, but they have been funding and supporting the lower leagues significantly (although that's part of the agreement on 1991). Lower leagues even without the money from EPL are also live with esteem: ticket sales, broadcasting revenue (especially they do well in cup matches) are already good enough for them. </div><div><br /></div><div>It's just a free market with some protection, and it is way healthier than the American model. The whole industry is sustainable and everyone's happy by getting their bit out of it. The difference in sports model perfectly reflects the difference between American capitalism and European capitalism. It may be hard to tell which capitalism is better, but in the world of Football or sports industry, the European way is much preferred.</div><div><br /></div><div>To be continued --- I shall cover the football aspect of ESL in the second half, after having some good sleep. That's 10 a.m. here after the 0-0 game against Brighton...</div>Forretriohttp://www.blogger.com/profile/18048483702091533151noreply@blogger.com0tag:blogger.com,1999:blog-2106712996078987699.post-18406217237620968702021-04-09T00:55:00.004+08:002021-04-10T19:39:58.618+08:0008/04/2021: Neo The World Ends with You revealed<div style="text-align: center;"><iframe allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" frameborder="0" height="315" src="https://www.youtube.com/embed/4Qr_sWBjCyU" title="YouTube video player" width="560"></iframe></div><div><br /></div><div>There aren't many things that could catch my attention immediately and motivates me to address on my blog that is three entries in four days, but the following is one of them: the true remake of the best RPG game in the DS era, The World Ends With You (TWEWY) is finally getting a true remake this summer! The game that I have awaited for finally is finally here 13 years after the debut, along with the animation that will be on air in the coming 24 hours.</div><div><div><br /></div><div>Final remix works as a memory freshener but merely amazes players simply because Switch is not DS, and many features tailored for DS were gone. This is just a porting attempt that wasn't very successful.</div><div><br /></div><div>I am not fully prepared to write something about TWEWY in full length, at least not before we are a few episodes into the animation. But there are sooooooo many things that I would be hyped for the game:</div><div><br /></div><div>- Story: The original 3 weeks + another days + secret report wasn't complete. And neither did the extra days from the final remix. But it is a good time to let go and enter a new chapter, and we can leave the details to the animation or novels if necessary. I look forward to a completely new story but also with reference to the old world.</div><div><br /></div><div>- Artwork: TWEWY perfected their art expression (some complained the skinny skeleton but I don't mind really). The characters, the items and the pins all reflected the taste of Shibuya in 2008. I know Shibuya so well that I can surf freely there without getting lost on my first arrival to Tokyo. The caption in fashion with extreme variation is the key element of TWEWY that is uncontested in the DS era, and I would say it even trumps the Persona series.</div><div><br /></div><div>In the Neo trailer Rindo and other characters are clearly dressed in the 2021 fashion. We also see a revamped Shibuya yet familiar. I look forward to the art elements in the game very much.</div><div><br /></div><div>- Combat system: historically unique is what I would describe the original combat system. Two screen sharing the same HP bar with a completely separate input system that is controlled by a single player. Without the help of game breaking items, beating the post-game contents is a supreme but very interesting challenge. Final remix is a pain to play not just because this is stupidly ported into switch, and even all the stylus related psych's are not working as smooth as in the original version. </div><div><br /></div><div>In the Neo trailer, we saw a completely redesigned system so hypes are there. We also observe multiple characters on the screen so there might be another form of multi-controls. There are also discussions on Reddit finding that it is possible for the characters to be binded to a few pins. It makes sense just to consider Neku was the only one who mastered so many pins in the original game, but I still regard the variety of pins to be a great selling point of the game. We will see how that works out.</div><div><br /></div><div>And, the 3D fighting scene. Who doesn't love Genshin-like fights?</div><div><br /></div><div>Music: No more words are needed I guess, TWEWY contains some of the best game soundtracks around. Twister, Someday, Calling or not -- just bring it on. That is the part that I never worried about.</div><div><br /></div><div>Misc: there are many features in the original game that was not even properly handled in the Switch version. Tin Pin is one of them. We need more multiplayer content, as it fits the current trend anyway.</div><div><br /></div><div>...and yes, what about more Radian and So Zetta Slow noises?</div></div><div><br /></div><div>*</div><div><br /></div><div>Update after the second trailer: </div><div><br /></div>
<div style="text-align: center;"><iframe allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" frameborder="0" height="315" src="https://www.youtube.com/embed/xSVYX1FLMGQ" title="YouTube video player" width="560"></iframe></div><div><br /></div><div>It's been a thrilling day. Having hundreds of TWEWY fans hyping the same trailer in the same chatroom is simply unreal. Everyone is shouting about what they found in the trailer with the slightest references to the original game. Pin style, Tsugumi references, Minimimoto....and of course Neku.</div><div><br /></div><div>WELCOME BACK, Neku. We look forward to your performance.</div><div><br /></div><div>I really like the deluxe package but all I want is Mr. Mew plushie and the artbook. It is a bit unfortunate that the artbook is not included in the NA version but we will see. It is also good to know that they are releasing all regional versions on the same day so that I won't need to buy the Japanese version first before going back to the English version. But maybe I will again, because it's TWEWY...</div>Forretriohttp://www.blogger.com/profile/18048483702091533151noreply@blogger.com0tag:blogger.com,1999:blog-2106712996078987699.post-54413869965506129852021-04-07T12:40:00.007+08:002021-04-07T12:40:48.577+08:0007/04/2021: 約稿相關<div style="text-align: left;"> Pixiv跟Skeb的約稿功能太爛了吧，完全沒有方法找到特定繪師。</div><div><br /></div><div>Pixiv拿著一大個數據庫能做的事情很多：最簡單就是讓繪師在約稿系統中幫自己上tag，然後有一個按繪師發表過的作品中過濾合適的tag自動加上去。tag功能是最基本的，畫畫的領域太廣，沒法篩選繪師的話想找到合適的繪師只能碰運氣。</div><div><br /></div><div>Skeb的話有相關的回答效率/交稿效率的統計也可用作過濾之用。</div><div><br /></div><div>比較有爭議的應該是對希望金額的過濾吧？對用家來說十分方便，卻有一點不尊重繪師+促進壓價之嫌。</div><div><br /></div><div>嘛，最近發了一堆委託，新的作品很快會登場(？)。夢十夜還需要一些靈感就是。</div>Forretriohttp://www.blogger.com/profile/18048483702091533151noreply@blogger.com0tag:blogger.com,1999:blog-2106712996078987699.post-58031091980012595482021-04-05T14:53:00.002+08:002021-04-07T23:54:18.603+08:00r/second: the Reddit April Fool 2021<div style="text-align: left;">Every year on the first of April, Reddit hosts a "social experiment" which is nothing more than a time limited inspiring minigame. One of the greatest example is the <a href="https://www.reddit.com/r/place/">r/place</a> which is truly impactful as a precious snapshot of the Internet on April 2017.</div><div><br /></div><div>Many abandoned the tradition of making something funny for the day on 2020, but fortunately Reddit held on and again delivering something simple but funny this year. Introducing the <a href="https://www.reddit.com/r/Second/">r/second</a>. </div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-oonFNKFlDUg/YGqb_zT2MII/AAAAAAAABmQ/ZtV8SKTTo9sjj4OtzPS6NLhgtorgYLgvgCLcBGAsYHQ/s1067/L%2525FDC%2525LM1K3F4_4QM0KAGJD.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="297" data-original-width="1067" height="111" src="https://1.bp.blogspot.com/-oonFNKFlDUg/YGqb_zT2MII/AAAAAAAABmQ/ZtV8SKTTo9sjj4OtzPS6NLhgtorgYLgvgCLcBGAsYHQ/w400-h111/L%2525FDC%2525LM1K3F4_4QM0KAGJD.png" width="400" /></a></div><div><br /></div><div>This is a simple game: each round consists of three pictures sampled online including memes, vintage games, among us mates or even simple words. People would vote for one of the three, but only the one ranked the second would be considered victorious. </div><div><br /></div><div>There are 3 phases in total. Mid-term results are revealed during the two transitions, giving hints on which one to vote for. That of course comes with a penalty. </div><div><br /></div><div>Those who voted in the first phase gets +9 for a correct answer and -3 for an incorrect answer.</div><div>Those who voted in the second phase gets +6/-2.</div><div>Those who voted in the third phase gets +3/-1.</div><div><br /></div><div>Unlike those redditors who eat chalks and murmur about tendies (you pretend that you don't but actually you do, especially those with diamond hands), you actually smelled a way to score effectively. What would you do?</div><div><br /></div><div>The correct answer is: you should find a time machine and travel back to 96 hours ago, because the event has already ended. But let's assume that it hasn't, how can we perform well in this event?</div><div><br /></div><div>Assume the following. </div><div><br /></div><div>1) The three images are indistinguishable. </div><div>2) The population's strategy remains constant.</div><div><br /></div><div>The first one is actually reasonable even to those who knows memes well because of the dynamics. Even if you can tell which is more popular, comparing the three is a completely different story.</div><div><br /></div><div>A quick glance at the leaderboard reveals that top players score around 4.7 points per win. Points gained per game is actually a hidden stat, but assuming that he only goes for phase two then he has been correct for about 80% of the times. That says, his average point <i><b>per game participated</b></i> is around 3.7. Can we get close to this number?</div><div><br /></div><div><u>Attempt 1: Blind guessing</u></div><div><br /></div><div>Well if you decided to vote every time on phase 1, then according to the assumption the only thing you can do is to guess blindly. That gives a 33% correct rate and an average of 1 per game. Not bad, but we can definitely do better.</div><div><br /></div><div><u>Attempt 2: Blind guessing, no middle</u></div><div><br /></div><div>Someone took record of the first 500 games and found that the middle come second at only 20% of the times in contrast to 40% for left and right. If we guess blindly without middle the correct rate is raised to 40% and the average point per game would be 1.8, still far away from optimal.</div><div><br /></div><div>Don't forget that skipping a particular round is actually a viable option, but only when you are not guessing on phase one because guessing on phase one this round or next round are indifferent according to our assumption. But what if we start to take mid-term results into consideration?</div><div><br /></div><div>We shall note that the target average score implies that guessing on phase three is inefficient, so we now consider strategy on phase two.</div><div><br /></div><div>We observe that when mid-term are released, people vote for both the first and second. They vote for second of course for free win, but they also vote for the first in hope that the second would overshoot. One certain thing is that no one is voting the third unless the three are close.</div><div><br /></div><div><u>Attempt 3: Guessing first or second randomly</u></div><div><br /></div><div>That gives a correct rate of almost 50% and an average of 2 per game. Can we do even better?</div><div><br /></div><div>We assumed that the population's reaction to mid-terms is consistent. This is actually in line with the observation. We may therefore apply kernel estimates to create a map $f(x_1,x_2) = p$ meaning that when the mid-term reveals that the first has $x_1$ of the votes and the second has $x_2$ of votes then there is a chance $p$ for the first to win (i.e. for the first to come second at the end). </div><div><br /></div><div>Note that it is the percentage difference that matters: dynamics from a 45%-40%-15% distribution should be almost the same as a 40%-35%-25% distribution. So we may compress the data into a single parameter distribution: $f(x_1-x_2) = p$ when the percentage difference is $x_1-x_2$ then there is a chance $p$ for the first to win. </div><div><br /></div><div><u>Attempt 4: KDE prediction + skips</u></div><div><br /></div><div>Although I never traced the numbers seriously, it can be observed that when the first leads by a large margin (say 10%), the second is almost certain to win despite everyone voting for it after mid-term. We expect the function about is quite close to 0 or 1 at the tails. We can then maximize the integral</div><div><br /></div><div>$R(I) = \left ( \int_I g_X(x) \right )^{-1}\int _I g_X(x)(6\max(f(x), (1-f(x)))-2\min (f(x), (1-f(x))))dx $</div><div><br /></div><div>by choosing the interval $I$ properly. The above may simplify into </div><div><div><br /></div><div>$R(I) = 2 + 4 \left ( \int_I g_X(x) \right )^{-1}\int _I g_X(x) |1-2f(x)| dx = 2+4E(|1-2X| \mid X\in I) \geq 2$, </div></div><div><br /></div><div>where $g_X$ is the probability density for the parameter $x_1-x_2$. Since $R(I)\geq 2$, this strategy is strictly better than attempt 3, and this is a strong indicator that the mid-term results are extremely useful. If we smoothen $f$ and $g_X$ so that it is differentiable (in the computational sense) then this is just a simple exercise of calculus.</div><div><br /></div><div>There is a problem though. If we take $I$ a very slim set then we win almost every time but voting may only happen for every 5 or 10 games, but top players win 55% out of all games! That means they probably have voted for at least 75% of the available games (not taking sleeping time into account even). </div><div><br /></div><div>Instead one may want to maximize the score gained per game, whether you skipped or not. This is simply the maximization of score! Since the expectation is always positive for any approaches mentioned above, what you should do in this case is to participate all games and always vote in phase two. When $f(x)$ is close to 1 or 0, vote for the indicated one, and otherwise vote randomly between first and second. (Or if you trust your function $f$, always follow the indicator, since your correct rate should always be above 50%.) </div><div><br /></div><div>Unfortunately I never collected the mid-terms and I don't notice anyone else who did. All that was left is the final result of the rounds, which do not help too much. Yet I believe this approach will be good enough for us to match the top rankers.</div><div><br /></div><div>One last note: the mid-terms are not fixed snapshots. You actually get to see the votes in live for a few seconds. I do not think that helps much however as the dynamics largely depend on percentage difference of the round, hence nothing significant can be extracted out there. </div><div><br /></div><div>*</div><div><br /></div><div>Let's be honest -- there are many more valuable things we may do if we had the chance to travel back to 1/4. r/second is no match against r/place after all. This is merely a little game that expires so fast. One better thing to do on 1/4 would be watching Your lie in April in my opinion. Yes?</div>Forretriohttp://www.blogger.com/profile/18048483702091533151noreply@blogger.com0tag:blogger.com,1999:blog-2106712996078987699.post-5598839444065555692021-03-30T10:42:00.008+08:002021-03-30T10:42:53.202+08:0030/3/2021 遊戲meta的三兩事<div style="text-align: left;"><div>不知道算不算日記……來說一下meta好了。</div><div><br /></div><div>遊戲只要含有PVP元素，那就總會有人研究更好/更有效率的打法，也就是所謂的meta。meta作為字根就是-後的意思，就是指在遊戲之外對遊戲的理解。</div><div><br /></div><div>meta的平衡在遊戲設計中十分重要。meta太過單一的話所有頂端玩家都會用同一打法，這樣遊戲會變得枯燥乏味；meta多的話對遊戲多樣性來說肯定是好事，但要開發出多套meta又談何容易呢？只有最強最穩定的打法才會被當成meta，如果想要有幾套meta存在的話唯有讓這些打法產生相生相剋的效果才行。</div><div><br /></div><div>屬性系統當然是一個方便的解決辦法。寵物小精靈的對戰中單對單的相剋非常明顯，就算是隊伍之間的比試當中，Uber Tier裡面也沒有誰一定可以橫掃同級其他精靈。最好的例子應該是2014大師賽的帕奇利茲，明明單隻只是幾乎沒人用的廢物，在隊際賽中跟其他精靈配搭卻可以出奇制勝。</div><div><br /></div><div>很多遊戲當然沒有屬性系統，要維持meta的多樣性就更難了。「一代補丁一代神」就是最常見的現象：為了解決當下最流行的meta而引入一個新的機制去剋制，結果新機制成了取代舊有meta成為新meta。火炎紋章英雄最近為了解決比翼琳的再動大軍而弄了個擋駕的技能，結果重甲大復活重新成為meta－－至於我這週差50點才到38階那又是另一個故事了。</div><div><br /></div><div>不過現代問題有現代解決辦法。我在想……機器學習(ML)應該可以很好地預測非即時戰鬥類的遊戲meta吧？在投下新技能/角色以前用帶有新技能的trained model跟用舊有技能練出來的trained model對戰，如果可以打敗現行meta之餘對上其他打法沒有太明顯的優勢那就說明這個技能有創造平衡的潛力，如果新技能只是一通亂殺的話那只是用新meta取代舊meta的騙錢技倆而已。</div><div><br /></div><div>也不是說騙錢技倆不應該用啦，人家做遊戲就是要賺錢的。你看IS現在一直用新技能蓋舊技能，舊角完全丟一邊不管不還是一堆人在舔嘛？立繪香一點，再多放兩個四維+5技能就一堆人抽下去了。</div><div><br /></div><div>其實玩家思維領先於開發者很正常，因為玩家會絞盡心思去改進成績，但開發者還有一堆別的要兼顧。這點跟八十年代的港英政府很像，不過這點以後再談。新科技的出現讓開發者追上來出現了一點可能，前提是要他們肯砸錢下去。可能嗎？不太樂觀，連龍頭大佬暴雪都一副半死不活的樣子，其他小廠又哪來的資源請data analyst呢？</div><div><br /></div><div>至於那個被擱置三年的ACGN萌戰2.0，在我們研究出meta之前，首先要找人把它寫出來……</div></div>Forretriohttp://www.blogger.com/profile/18048483702091533151noreply@blogger.com0tag:blogger.com,1999:blog-2106712996078987699.post-76307709010218328292021-03-17T22:43:00.008+08:002021-03-27T08:22:14.470+08:00夢．十夜 (6.5) Interlude<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-GR-rDB9I_28/YFIRFhg01UI/AAAAAAAABlY/HAhZAWjmidk0Yk3o1BXsiVo6U-u8sT8PgCLcBGAsYHQ/s252/%257B4PF37Z7%2524N%2560GU%2524O9P%25607OF0F.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="184" data-original-width="252" src="https://1.bp.blogspot.com/-GR-rDB9I_28/YFIRFhg01UI/AAAAAAAABlY/HAhZAWjmidk0Yk3o1BXsiVo6U-u8sT8PgCLcBGAsYHQ/s0/%257B4PF37Z7%2524N%2560GU%2524O9P%25607OF0F.png" /></a></div><div style="text-align: left;"><br /></div><div style="text-align: left;"><br /></div><div style="text-align: left;"><span style="font-size: large;">銀髮少女發了一個夢，那是她小時候生日會的回憶。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">生於衣食無憂的家庭裡，每年辦生日會慶祝是必須的。對於大人來說那是社交的場合，對小孩來說玩樂一下也不要緊。只有身為主角的她一邊應付著那些大人帶著小孩過來的祝賀，一邊依從父親的教誨把小孩們的長相名字記下來，他們都是以後可以交的朋友。對她來說應付社交不是問題，但她更願意回到的被窩裡看小說或者美美的睡一覺。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">有一堆小孩圍繞在鋼琴前輪流演著古典曲目。她雖然也會彈琴，但是在那些三四歲開始每天練兩三小時的人面前自己實在無需獻醜；有一些小孩則在大廳的角落裡玩起了桌遊，但對局已經開始了她也不好跳下去。剩下的小孩都正在被大人拖著到處應酬，除了一位正坐在電腦前不知道在幹甚麼。那台電腦本來是拿出來播放音樂的，不過那位小孩肯定在弄其他東西。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">出於好奇心她貼了上去問道：「你在幹甚麼呀？」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">被發現偷玩電腦的他閃過一絲尷尬。他老實回答：「啊……我試了一下感覺這裡上網很快，我就順手把網遊載下來了。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">在那個大部分人還在ADSL甚至撥號上網的時代，光纖提供的速度可是一般人不能想像的。那個快2GB的網遊安裝包居然二十分鐘就載好了。她一邊看著他把遊戲安裝起來一邊問道：「為甚麼要玩網遊呢？我平時都玩Flash小遊戲比較多呢。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「因為好玩嘛！你等下就知道了，而且網遊可以累積進度，可以一直看著角色成長呢！」他孜孜不倦地介紹著遊戲內容：遊戲好像叫甚麼古龍同萌傳Online，是由古龍筆下的武俠小說改編而成。她古龍沒看多少，金庸的倒是因為動畫化而看了一些。按他的說法這個遊戲被做成網遊以前就出過幾個單機遊戲了，可是家裡從來都不會給她買單機遊戲，她也根本沒玩過多少單機遊戲－－GBA模擬器例外，她玩牧場物語可多了。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">他麻利地弄了個新帳號然後登入。遊戲剛開始玩家便看到江楓被憐星邀月逼上絕路的一幕。「我們是要救他嗎？」她好奇問道。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「呃……江楓應該已經沒救了。故事的主角是他的後代呢，不過我們要先打通新手劇情才能看到。喏，在地圖上點一下角色就會跑過去，點怪物就能攻擊了。你試試看吧！」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">在地圖上奔跑是她玩Flash和GBA模擬器從未有過的體驗。眼前2.5D地圖上的角色比Flash的平面視角和GBA的320*240像素更為生動。她在屬於新手村的流星沙灘上把一隻又一隻貝殼和龍蝦敲成經驗值，快速的升級與新撿來的武器讓她的角色快速成長。剛好她又撞見被圍攻的小boss龍蝦王，沒被boss狙擊的她可以偷偷地刀下去，而尾刀幸運地被她撿去了。她不但拿到了稀有物品龍蝦冠，經驗值也一口氣漲到可以脫離新手村的範圍。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「我現在可以繼續看劇情了嗎？」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「可以哦！不過你要先挑選一個主門派，完成轉職才可以繼續喔。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「那個……門派怎樣挑啊？」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">他打開遊戲官網把三個主門派惡人谷、移花宮跟天外天展示出來。少女心發作的她立刻就選了移花宮。當劇情繼續推進，花無缺的大頭正要顯示在屏幕上時，老爸卻不適時地喊她過去切蛋糕－－</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">*</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">少女看了下一片漆黑的天花板，每次這個夢都讓她回憶起當初進坑以後發生的事情。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">夢境每次都在切蛋糕時結束。那天後面發生的事對他來說不重要，她也沒有在夢中回憶過。後來她從老爸口中得知他父親是老爸的大學死黨，現在在不知道甚麼地方當教授。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">那個新辦的帳號理所當然的成為了她的所有物，古龍同萌傳Online也成為她玩電腦時唯一會打的遊戲。但很快她便發現了一個問題：遊戲實在太肝了。那個年代的網遊經驗值不是二次方在長就是三次方在長，高等打低等的經驗值還會被扣掉一大截。明明從1等升到10等只要兩小時，升到20等卻需要兩三天，到50等沒三個月根本不用想。對她這種每天頂多能玩半小時一小時的人來說戰力根本不可能跟上。把等級推高除了玩得更爽以外也能解鎖更多劇情，對她來說就像追連續劇一樣停不下來。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">雖然自己沒有時間，但是對她來說錢能解決的問題就不叫問題。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">首先是包月制的雙倍經驗，然後是每日登入都能領到的30分鐘雙倍經驗卷；在商城花點小錢抽一些強力裝備，在組隊時稍微給一些甜頭對方也不會介意你整天在那邊掛機。到了後來與其到處找隊友還不如乾脆成立公會收集人材和資源，每次活動都算好物品價格與打獵策略，務求將更多的資源收到自己手中。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">她只不過是想用自己的零花錢堆一個小小的城堡而已。回過頭來自己卻已經成為一個小有名氣的公會會長，還有兩個得力的副手忠實地按著她的欲望把公會發展起來。只要她有空登入遊戲隨時都可以拿著練好的帳號跟大家起衝副本。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">至於後來隨著武俠網遊的衰落他們轉移到其他遊戲再到終戰幻想上，那是後話了。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">*</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">她再次緩緩睡去。同一時間電腦上的After Dark剪刀石頭布的螢幕保護程式消失不見，Skype的視窗傳來了幾行新訊息。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">是那個肥宅傳來的。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「您要他們的資料已經出來了。我在aoisora2的留言版上找到他們網聚的討論，他們都在同一城市沒錯。雖然大部分ID在遊戲以外都搜不出甚麼來，但是那個甚麼alex應該是做生意的。我找到一家公司的負責人名字跟他差不多，公司的業務動態跟alex的活動時間也相常吻合。我覺得要在現實中找到他們的話這個是個很不錯的突破口。」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「好消息是，您也居然跟他們住在同一城市耶！」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「這樣的話由您親自出馬應該沒問題吧？」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">「……洛雪大人？」</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">=========</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">關於她的故事，上面只是一半。另一半關於她性格的故事以後再補上吧？當初給她設計的外型與最近炎上過的天使<ruby><rb>烏頭</rb><rp>(</rp><rt>うと</rt><rp>)</rp></ruby>不謀而合，性格也有點像？演技派，可以成為舞會的大小姐也可以成為腹黑JK這樣(？</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">以前的社交模式還是以論壇/BBS為主，遊戲相關的社交還是以這些論壇為媒介。直到2004前後作為分界點，MMORPG的出現使得電子娛樂與社交可以真正合一。當然同期或者稍早一點也有Discuz!插件和江湖遊戲等社交平台娛樂化的嘗試就是。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">也就是說，在這個時間點以前要以網上娛樂的人際互動為題材執筆的話可以選擇的題材十分有限。總不能寫以前他們怎樣拼speedrun紀錄吧？看<a href="https://www.youtube.com/channel/UCtUbO6rBht0daVIOGML3c8w">Summoning Salt</a>和<a href="https://www.youtube.com/user/BismuthWasTaken">bismuth</a>的影片就知道在那個時候紀錄和攻略心得都是用電郵或者頂多論壇傳遞的，與今天有一整個完整網站加上審查員的制度完全不同。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">儘管如此，屬於那個年代的網絡回憶有趣的還是不少。只是我大概只能在小說以外的地方去講這些東西了。隨便舉兩個例(記得先開flash)：本地的話當年<a href="http://web.archive.org/web/20020605111205/http://www.smallcampus.net/">小校園</a>是開放註冊的，裡面的學會版面其實有不少小學生看不懂的東西；<a href="http://web.archive.org/web/20030405173058/http://www.iyellowbus.com/">黃巴士</a>作為香港的數碼藝術先驅，架設的網站雖然好看也是flash的先行者，但保安系統實在太差勁－－可以換禮品的積分居然可以透過F5反複登入而取得！</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">同一年代外國的網絡世界同樣精彩。日本的先不說，在英美的科網熱潮雖然已經爆破，但那些公司或經營模式並沒有立刻倒掉，大部分都撐了好幾年，甚至有苟活到現在的(比如neopets)，當年的網絡世界就因為這些注資而得以百花齊放。在商業角度來看它們不怎樣成功，對我們說卻是好玩就夠了。我比較有印象的應該是<a href="https://web.archive.org/web/20040615215427/http://alfy.com/arcade/Adventure/pang/index.asp">Alfy</a>跟<a href="https://www.battleon.com">Adventure Quest</a>(到現在還沒倒也是神奇)吧。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">當年網絡世界的另一個特色是大量的個人網頁－－那是一個free hosting滿地跑的時代。懶人可以直接用blogger、Xanga和各種奇怪的動態留言版，但更多人都愛用Frontpage express或者Dreamweaver寫自己的網頁。單說香港的geocities網頁數已經是世界前幾名，到現在去<a href="https://www.oocities.org/">oocities</a>能找到的遺跡也有不少。當年的網站都有一頁連結，專門放好友網站的banner，在社交平台還沒大一統的時代一個個小圈子就是這樣撐起來的。放到現代的話有點像噗浪？</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">所以說，我想寫的東西真的很多。不過發夢的話繼續打遊戲就好了。</span></div><div><span style="font-size: large;"><br /></span></div><div><span style="font-size: large;">順便一提，把網絡現象當背景的小說我大推M.S.Zenky的閉鎖密室系列喔。這個(偽)偵探系列中每一本都對應了不同網絡現象，比如第一本是病毒、第二本則是網絡文學這樣。實體書由鮮鮮出版，不過鮮鮮墳頭草已經跟人一樣高了。想看這本的話去<a href="https://mszenky1022.pixnet.net/blog/">Z大的網站</a>看就好囉。</span></div>Forretriohttp://www.blogger.com/profile/18048483702091533151noreply@blogger.com0tag:blogger.com,1999:blog-2106712996078987699.post-31198742608154418882021-02-26T21:35:00.001+08:002021-02-26T21:52:40.537+08:0026/2/2021: Ebony & Ivory from Beatstream to Nos<p> </p><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-xV59ipLF6yM/YDjvwXxkaVI/AAAAAAAABkk/BH97h4DpG2cuDAcuPRi7Ot-7be5Dd0S7wCLcBGAsYHQ/s600/EvENJg-UcAQ91rO.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="600" height="266" src="https://1.bp.blogspot.com/-xV59ipLF6yM/YDjvwXxkaVI/AAAAAAAABkk/BH97h4DpG2cuDAcuPRi7Ot-7be5Dd0S7wCLcBGAsYHQ/w400-h266/EvENJg-UcAQ91rO.jpg" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;">An easy level 12, disappointingly easy. I got 98% on the second day.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">I hate difficulty locks in MUGs by a lot. Games like Nostalgia, Chunithm and DDR partially, have an unlock system where higher difficulty unlocks only when one completes a lower difficulty with good enough scores. This is a complete waste of time because a large portion of advanced players simply do not touch the lower difficulties. Among these Beatstream had the most notorious system among all -- the nightmare difficulty only unlocks when the player completes a course with accuracy up to 95%-99%.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">As a result I never got the chance to try the <a href="https://www.youtube.com/watch?v=lxyJDcfrJFU">nightmare difficulty of Ebony & Ivory</a> till the last play that was available to me via multiplayer game with my friend, and it plays as exciting as watching that on screen. It has one of the most iconic streams in Beatstream that is uncontested till the end of service. It's a nice song too, another great piece of work my long time favourite OSTER project.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Unfortunately the design of Beatstream is really incompatible with extreme maps. At note density as high as those top maps in Reflec Beat it looks really bad on Beatstream. This is apparent when they pushed Lv.神 on KAC which looked really unappetizing. As a result Beatstream had its service terminated on 31/7/2017. Still I am still waiting for its revival on mobile device as it is apparently one of the Konmai MUG that is more compatible with tablets (right after Reflec Beat). </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Beatstream machines were transformed into Nostalgia machine since then. It's properly designed and is connected to my beloved piano based songs. I have spent around 1000 credits since its introduction -- but I still miss Beatstream time to time. And with Ebony & Ivory became available I am triggered so write this diary as a record just in case I cannot retrieve my score screenshot anymore (I am pretty sure I have a screenshot on my Beatstream score for Ebony & Ivory but I failed to find that somehow).</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Oh and something about the Nos map: the lack of Real difficulty is really disappointing, cause I have been waiting for that for a long time! The expert map yields 1009 combo whereas the nightmare difficulty from Beatstream contains 991 combo where most notes are single notes. This song is perfect for a real lv.3 I am not joking...</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-NKwlOzuLO1c/YDj9CsspQpI/AAAAAAAABks/gEjO4FvvbSUDjg0itKDMvgKKvrgH1l-xwCLcBGAsYHQ/s256/setting_emblem.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="256" data-original-width="256" src="https://1.bp.blogspot.com/-NKwlOzuLO1c/YDj9CsspQpI/AAAAAAAABks/gEjO4FvvbSUDjg0itKDMvgKKvrgH1l-xwCLcBGAsYHQ/s0/setting_emblem.png" /></a></div><div class="separator" style="clear: both; text-align: center;">My Jubeat emblem, since 2017 and never changed</div><br /><div class="separator" style="clear: both; text-align: left;"><br /></div><p></p>Forretriohttp://www.blogger.com/profile/18048483702091533151noreply@blogger.com0tag:blogger.com,1999:blog-2106712996078987699.post-59675175613859355112021-02-20T11:43:00.003+08:002021-02-20T23:22:22.407+08:00The bullshit "equity math"<div style="text-align: left;"><i>“You are a slow learner, Winston."</i></div><div><i>"How can I help it? How can I help but see what is in front of my eyes? Two and two are four."</i></div><div><i>"Sometimes, Winston. Sometimes they are five. Sometimes they are three. Sometimes they are all of them at once. You must try harder. It is not easy to become sane.”</i></div><div>-- George Orwell, 1984</div><div><br /></div><div>*</div><div><br /></div><div>Recently schools in Oregon <a href="https://content.govdelivery.com/accounts/ORED/bulletins/2bfbb9b?fbclid=IwAR3U8iS7fCD-g0NArQh74qlRa5IVFiTXoithZA89kMvmD0DETmzcV9DuQdg">are sent toolkits</a> about teaching maths in "proper" way and to "eliminate white supremacy". I usually don't care about lefty nonsenses but this time they went too far and touched my beloved mathematics. It went so far that I can't stop myself writing a defend against it.</div><div><br /></div><div>Macroscopically this is just another batch of money wasted onto the "political correctness" industry, where you will only find in the States. Their way of philosophy and action are quite similar to that those from the cultural revolution in China in the sixties. Even back then when rocket scientist Qian Xuesen had to lie about agricultural production, their revised mathematics curriculum is still mathematical in context, only with a political twist in it. You get questions like "in accord to instructions from Chairman Mao we seized X acres of land yesterday and Y square meters of land today. How much land did we recover from the damned landlord in total?", and yet they are still doing proper mathematics.</div><div><br /></div><div>We need to stop the horrible wave of decontextualization, in all possible fields. It's not just only for mathematics or science, but also in history, literature, social science and so on. Today as an math educator I feel like I should break the myth of the so called equity maths.</div><div><br /></div><div>First of all, what is mathematics? Well this is a very complicated question with diversed answers. According to Wikipedia mathematics can be treated as a symbolic logic or its dual pair as operation of a formal language (the logical or mechanical one, not the linguistic one). Or if you like constructivism then there is also one definition for intuitionists. However if we lower the bar and ask the same question for primary/secondary school level mathematics, then it will for sure be the operation based on Peano axioms on integers, which is then extended to the rational (or real) number system. From such aspect the logic induced is consistent and unique. For every question you ask within the logic they is one and only one answer. If a quadratic equation has two roots then you don't call another root be "an alternative" to your first root. The answer is to include both roots. Giving only one of them is mathematically wrong.</div><div><br /></div><div>For the rest of the article I want to focus on the part of solving questions within the mathematical logic. That means questions that can be completely described in propositional logic. A famous example is in Laudau's book "A Course of Pure Mathematics", where he wrote in the preface that he expects the deduction of "2+2=4" to be:</div><div><br /></div><div style="text-align: center;">2+2 = (1+1)+(1+1) = ((1+1)+1)+1 = (2+1)+1 = 3+1 = 4</div><div><br /></div><div>which uses the definition that 1,2,3,4 are right next to each other on the sequence of positive integers and the axiom of associativity. Similarly arithmetic calculations are within mathematical logic. High school algebra are also within mathematical logic using statements like "for all x if x^2-1 = 0 then x = 1 or -1". Geometry is a bit tricky, but we can also form a first-order logic using Euclid's axioms (with parallel postulate) and so on. I stress that this is just to give a more concise definition of the part to be taught in the subject of mathematics to be discussed in the following, but not the axiomatic approach that should be taught. For kids 2+2=4 just because "two steps after two" is four and that's it, but the problem itself can be described as in mathematical logic, that it is within scope of our discussion.</div><div><br /></div><div>The truth of a proof for a question in mathematical logic, is purely objective. This is due to the uniqueness and consistency in the logic. In a more practical level when we assess student's work, logical errors are one of the two types of mistakes (or imperfections) from students' work. The other type of mistakes would be stylish problems (presentation, key steps being skipped etc.) which are subjective. That does not change the fact that the logic or rather the core knowledge of the subject is objective. Relativism does not apply in mathematics or other sciences.</div><div><br /></div><div>With precise definitions, a grading scheme can also be objective by exhausting possibilities. While grading remains objective under proper settings, this is by no means an attempt to promote quantity over quality -- it is just a statistic showing the estimated understanding of the students. Grades can be used solely for the purpose of improving teaching quality. This is just one of the many standardization for the sake of efficiency, which we shall cover again later. </div><div><br /></div><div>The goal of solving a question within the mathematical logic is of course to complete the deduction. Focusing on intermediate steps does not mean the final answer is not important. In fact, the answers obtained in previous questions are often step stones for a consequent question. In such sense the answer is of no less importance than the middle step. Getting the right answer, is of course a major goal in a maths class. (And right here means correct(ortho-), and does not imply that political or social rightness is of the same correctness. Such discussion is a pure waste of everyone's time and resources.)</div><div><br /></div><div>One very important consideration when you teach someone mathematics is called mathematical maturity. Roughly speaking, it is your exposure to different levels and fields in mathematics so that you can understand a new topic quickly without spending 10 minutes on every definition. Due to the correctness and uniqueness of mathematics it is always possible to introduce someone a highly sophisticated tool and he can do mechanics out of it without sufficient maturity as long as he can follow the logic. However his lack in maturity means that the process will take exponentially longer, and that is a waste of time. When I was year 1 in university I joined a open courseware site and took a course in functional analysis. Yes I can understand every word about the Arzela-Ascoli theorem, but I had truly zero idea what it was doing. This is because I simply did not have enough exposure in function spaces as well as point-set topology that I couldn't visualize what is going on (unlike now I can casually use that a few times in a single article).</div><div><br /></div><div>For primary and secondary school level mathematical maturity applies as well. At a lower level this is almost equivalent to arithmetic fluency which is gained by repeated practices on calculation, hence the teaching sequence is almost linear. At high school level there are various topics that are indeed taught in sequence. While they may or may not be taught independently, these are designed in the way that previous topics would boost the exposure and maturity of the students to equip better against the next topic. </div><div><br /></div><div>Topic sequencing, alongside with many other existing standards and practices, are based on years of professional experience (bottom-up) and research (top-down). They do not come for whatever supremacy theories, but rather efficiency in teaching (and learning). We focus on formalism and mathematical rigorousness because these are the core of mathematical maturity and the key to master those topics. We grade the assignment as to reflect the portion of question that students are able to tackle. We standardize tests because that gives us an objective, scientific and reliable way to understand the progress of the students. And yes we need objectivity, just because this is how the world works.</div><div><br /></div><div>Talking about efficiency, there are always idealistic imaginations on how education could be at its best: teachers tailoring materials for every students, personalizing feedbacks and updating goals constantly; school preparing the best peer environment and passive resources (e.g. library) for them. Is this possible? Yes and it exists -- in the few top high schools over the world, particularly in the States and Scandinavia (note that top secondary schools in western Europe and Asia took completely approaches). They mimicked what Euclid or Socrates did in the ancient times with the best possible teachers and resources around. That comes with a cost though: the tuition fee would be up to hundreds of thousand dollars if not millions per year, and this is open to the only half-hundred geniuses every year. </div><div><br /></div><div>Taking a step back, there are new AI technologies which automates some of the assessing steps freeing more time for the teachers to work on more inspirational stuffs. In China they took a step further by monitoring students' reaction during class as part of the assessment -- I am against such measure though, as it hinders the students' privacy.</div><div><br /></div><div>But now...we are talking about reforms of public schools, and most of them won't have the resources to take any of these measures. Sadly this is the fact as supported by the highly valued private education sector both at the institutional level and also the individual level. Over the past 30 years, teachers have spent more and more time on out-of-the-classroom matters. It is almost impossible to squeeze out more time to boost the quality of teaching. Unless significantly more resources are being put into the sector, what we observe nowadays is basically the equilibrium point of public school teaching. </div><div><br /></div><div>I believe most math teachers are in the classroom to teach mathematics, and I expect most students are there to learn mathematics (at least, not politics). We separated the curriculum into various subjects that teaching and learning are specialized. What we do in the classroom can be evaluated, but only in the context of mathematics. We do not need the interference from dumb politicians and their fanatics. </div><div><br /></div><div>I tried to write the article without real criticism on the reform. But since I mentioned the cultural revolution at the beginning, I shall <a href="https://thejewishvoice.com/2021/02/across-america-leftists-dumb-education-down-declaring-math-as-racist-abandoning-reading-writing-for-black-power-ideology/">quote from Andrea Widburg</a> something that I also observed from that horrifying cultural revolution: 'the only way to achieve the left’s beloved “equity” is to lower the standards or abolish them entirely'. Think about a world where hospitals were run by youngsters without medical knowledge, and bridges build by "engineers" who had no idea about civil engineering. As scary as it sound that really happened in China, just 50 years ago. Would you like to see the same in the western world?</div><div><br /></div>Forretriohttp://www.blogger.com/profile/18048483702091533151noreply@blogger.com0