Thursday, 28 December 2023

Thoughts on CTWC2023 finals


CTWC2023 has been over for some time. If you follow the tourney or even my blog posts covering it each year, you'd know it's held somewhere at the bottom of November. Could be a bit later but definitely not after Christmas.

And I completely missed it, only noticing something else which I will also cover here that YouTube started pushing CTWC clips to me. I received zero pushes on CTWC23 clips at all. Yes, zero.

YouTube is of course partially for the blame cause YouTube must have known my interest on CTWC. But then...is it also because the hit rate on classic tetris that is dropping that YouTube decided not to push? But before getting into that let us talk about the tournament itself.

Sadly I don't have time to watch all match ups one by one -- I kind of treasure the time in 2020 where lock down gave me enough time to really go through every single ones. I ended up watching the finals only, so this is my brief thoughts on the finals instead of the whole tourney. Sidnev and Fractals are good representatives of the top circle so my conclusion may apply to those (single digit number of) top players, but not to the larger base like all CTWC finalists.

Very close match between the two. It is very hard for me to tell the difference in style -- the grip may differ but they way they controlled the pieces are too similar. Some luck kicked in and Fractal ended up with a reverse sweep. That requires unparalleled precision but also heart of steel. Good sportsmanship between the two but it had been tradition among the top classic tetris players circles anyway.

...and that's all. Giving further comments is even harder than doing that on the 22 finals where there is at least one unforgettable game that you can talk about. All 5 games in the finals are basically smooth all the way up to Lv.29 then kill screen (or second transition if you like) hits where a roll of dice decides the winner. One may wonder why would it be a roll of dice when the sequence is identical for the two. That is because placement difference is chaotic so eventually the boards would be totally different. Some configurations are weak to a particular sequence and that's the moment that kills.

But wait! Even when you find yourself in trouble due to bad sequence there is still room for rebounce right? Unfortunately we have the Lv.39 hard cap this time. Sounds irrelevant but a hard cap means pure survival is no longer the primal goal in the play. Or rather, a strategy that is relative safe for one to stay at Lv.29 speed over a prolonged period is no longer desirable. Instead you take a high risk high reward route where you would probably die somewhere between Lv.29 and 39 but gives a higher average score (assuming the hard cap at Lv.39) -- if you can't score enough you lose either way hitting the cap or not, so it's better to be aggressive from the beginning.

Last year I said the meta was optimization up to Lv.29 then survive, partly because the cap wasn't there but also because rollers are not super comfortable with Lv.29 speed...yet. This year they got themselves enough space to optimize under such hostile condition, and this is probably what most top players did in recent months.

As the style homogenizes, what is left is basically consistency (ideal input vs actual input), mentality (concentration etc.) and tiniest bit of efficiency. Sure if you count the stats over a bigger sample like the accumulated masters heads to heads you will be able to see the difference among the top players, but in a first to 3 this is just a roll of dice where the better side has a slightly better chance of winning (not to mention lower rounds are just first to 2 sets). (Kind of reminds me about a math question that I just analyzed not long ago -- Simon Marais 2023 B2. I am not going to cover the math here to check my entry if you want to have a look at it.)

This is not by means undermining the credibility of the tournament. A winner is still a winner and I truly believe that every player deserves their final ranking in this tournament. The point is the fun is gone. The commentaries on how close the scores are and how close to top out their players had been are enthralling, but it becomes repetitive soon after some games. The commentators are doing their jobs well, but the game is losing its value to be spectated. 

It might be unfair to compare views count on a fresh video but it is surely dropping, and they might be the reason that they weren't pushed in the first place. It could be a death spiral -- less attention means less new blood, which means less attention in turns. Granted the game has been low key for 20+ years before the current community bought it back, but the spiral is still something one wants to avoid. 

What is the future of the competition, if you ask me? 

There is no reverting in skill and meta progression. Players have proven themselves that Lv.29 speed is no longer a hurdle in general. From this point the remaining progression would be to find the sweet spot balancing aggression and average performance. On the non-capped track the game is even 'cleared' -- Blue Scuti, a very young new comer to the game reaching semifinals this year, survived up to Lv.157 in a game where the game crashes due to memory overflow. Such ending could be viewed as a 'game clear' in the same way as donkey kong or pac-man. I considered the game 'solved' in the sense that all remaining milestones are reachable given enough tries/luck. 

(I am quite surprised that the color shifts didn't cause too much trouble to Blue Scuti though. Other than the really dark blocks at Lv.157 which Blue Scuti almost topped out there are a few more notorious color combinations like dark green and blue at 146 or black and white at 148 but he breezed through the levels fine. Maybe players have practiced enough for that? They recall me of TGM invisible blocks too...)

Classic Tetris will remain as a competitive sport fine despite the lost in visible progression/meta shifts that makes it less appealing. New variations is essential if we want to revitalize the game, but each change will bend it further away from the original game. If it's too far away from NES Tetris people will just as well play modern interpretations like Tetris Effect, so the issue is pretty delicate here.

With top players really comfortable up to Lv.29, I think it will be fine to start from Lv.19 speed just to spare time for later stages. The new Lv.19 phase could last more than 100 lines, somewhere between 100 and 230, but this is up to debate. The time spared can be spent at Lv.29 speed -- actually I prefer a longer Lv.29 speed section like up to Lv.49 considering how quick players topped out with their current aggression. 

Also perhaps a change in game format? Just like how chess is categorized into classic, rapid and blitz we can create multiple rule sets for classic Tetris matches as well. For example the 'uncapped' with no extra cap after Lv.29, a 'rapid' as described above that starts from Lv.19 to Lv.49, or 'first to million' where players optimize to reach million as quick as possible. Some requires slight tweaks to the game but not beyond where modifications have already taken place. The rest are merely change of rules but not changing the game itself. The common theme is to force players into diversified strategy or optimization bias. I expect a much more interesting game in that way. I called a change last year and I would do the same here, and hopefully the drop at anticipation if any, would alert the organizers to evaluate what's going on.

I still look forward to CTWC next year, and if you are interested in the game it's definitely worth a peek into the fantastic world of classic Tetris. It's never too late!

Friday, 15 December 2023

15/12/2023: 完結撒花

很久沒寫日記,來說說最近的輕小說和音遊。

首先是跨時代的無敵大坑9S終於要出續篇完本了!!13、14兩卷明年9/2同時發售!!當初出12卷試讀再到正式出版時我還是不抱期望,畢竟都荒廢這麼多年。出一本後再躺平這事已經有大量前輩示範過了,比如涼宮春日(本來要開個安倍的玩笑,不過死者為大還是算了)。上一次有這種終於完結的感覺大概要數到零之使魔……不過畢竟山口老師是一直寫到不行為止,跟直接躺平的葉山老師不同(望)。如果有一天緋彈的亞莉亞終於完結的話我也會有類似感覺吧?

9S吸引人之處正是其描繪的科幻世界。以峰島遺產為中心、遠超人類水平的科技看上去有趣多變的同時也不會因為破綻過多使讀者無法投入的問題。當中我記憶最深的是可以複製對方記憶的「瑪門」其實是互相複製記憶,在這個前提下其實有方法保留自己人格;還有可以使用極高溫和極低溫作攻擊手段的矽基生物「撒旦」,以及人類找出來的對應手段。七原罪裡面每個人(?)各具特色,但最有吸引力的果然是用高科技的兩人。甚至乎我覺得自己寫"被青梅竹馬抓來(略)"時對各種手段的運用理解都有受9S影響。

另一本被腰斬但感覺未完結的作品是片山憲太郎的紅Kure-nai。面對沒有高科技(只有黑科技)但同樣令人絕望的反派boss,我們看到的是主角一步一腳印的成長,最後以合理的方法把事情解決。與9S相同的是對反派形象的建立,不論是切彥還是絕奈都帶有可愛的一面。之所以說感覺未完結當然就是指裡十三家還沒全數登場這件事,但看看事隔六年寫出來的裂空之姬……嗯,感覺找不到以前的筆觸了呢。至少肯定的是在被期待的舊作裡面這本絕對有和9S並列的空間,看PTT底下帖文大家的反應就知道了。

講完日本輕小說在這裡捎一句華文輕小說好了,就一句。就是那個我在這個blog裡面編了張考卷那本……沒想到妳也逃到外國了哈,希望妳以後也能寫出一樣精彩的作品。

*

然後是關於音遊的碎碎念。

DDR沒啥好說的,弄個低能活動只想白嫖玩家那幾個代幣。三道的錢打四首歌真當大家是白痴?啊抱歉我還真看到有人上釣而且不少……Flare Gauge跟encore extra stage有點像不過把判定難度分成三六九等的話至少普羅大眾可以喝點湯。不過對我這種低acc玩家來說沒甚麼分別就是,反正用上flare gauge要解鎖18怎樣也打不過,解鎖低等級的譜面可以但沒甚麼意義。想想我連Snow Garland Fairy ESP都沒興趣去解了,你還叫我去打活動?Konmai你還是去騙那些會掏錢買GP的人吧,有本事你就把歌曲一直鎖住,這樣我也省去刷Lv18全通的功夫。

在一個沒有nos機台而DDR機台極爛的環境裡我本來打jubeat為主,原因是覺得在日本打了這麼多的中二,回去海外版要重頭打起很痛苦,而且累積起來的角色技能也不能用。那為甚麼我打了一陣子jubeat以後還是投向中二的懷抱呢?首先jubeat機台經過十幾年摧殘又沒專人維修已經很破了,我甚至可以打出單位數的GREAT下出現200MISS以上被關門的慘況。這種情況下怎能怪人家貪新厭舊跑去玩中二呢?

另一個jubeat的問題是我的jubility已經上不去,這個問題我一年前已經提過。事實上我的jubility從clan到現在beyond Ave都沒動過。其實除了間距問題以外更麻煩的是那個30+30的制度,也就是jubility來是最高分的30首自選和30首pick up譜面的總和,而pick up池就是當下版本的新增曲目。pick up池裡面的曲目他媽的少,而且多半都要通過漫長的遊玩來解鎖。Ave我也累積200道以上,pick up池裡卻只有20首不到根本沒法填滿pick up分數,還是你覺得我應該把Advanced打一打把分數算進去呢?每次改版後pick up池裡面的10.6~10.9稀缺到玩家再強也暫時拿不到金名,那jubility的鑑別度又在哪裡呢?我就遇過幾次紫(Violet)名一上來就隨手在10.6 10.7打個99+的。當然你可以說jubility根本從頭到尾都只是騙錢的機制,這樣說我也可以接受。

抱怨了jubeat那麼多來說說中二的rating。jubeat和中二在分數上的設計很接近,都不會苛刻扣GREAT(中二-Justice)的分數,只扣再低一級判定Good(中二-Attack)的分數。但在rating上jubeat對GREAT的分數扣很大,中二直接用分數算rating則沒有這個問題。我在中二的Justice率都在6-10%,這樣算的話一個中二1005000在jubeat上可能只有92%左右,對應Lv10.0的話一首就是115分。比起我在jubeat的成績好一點但也沒好到哪去--當然這是現況。

在中二分數容許一堆Justice的情況下能否在高等級譜面拿到同樣分數取決於你能不能看懂譜面然後採用正確的打法而非每一個音符都打得很準。在這方面我的潛力明顯還有提升的空間:本來看不懂的Jade Star現在已經可以FC,蒼穹舞楽在yt看過譜面後回去就打了個接近1000000的分數。現在15.6的我要再上大概就只能開始讀14.6 14.7的譜面了吧?能不能有朝一日摸到16.0的大門,我十分期待。



Monday, 27 November 2023

古早遊戲BGM巡遊(6): Csikos Post

在遊戲裡使用古典樂remix作為配樂可謂屢見不鮮,一個遠古的例子是任天堂俄羅斯方塊C模式的音樂實際上來自巴哈的BWV 814 Minuett。那麼,如果要你選一首古典樂配樂的代表作的話你又會選哪首呢?

我會選Csikos Post。說英文可能還不夠明確,但如果我叫它郵遞馬車呢?還是不懂?那如果我叫它熱血行進曲呢?


嚴格來說,熱血行進曲只是遊戲名字,而這個BGM在遊戲中依然被叫作跟郵遞馬車差不多的東西(馬車馬のように),但這不影響它成為遊戲的代表配曲之一。

非常具張力的一首樂曲而且長度適中,很適合放在遊戲裡作配樂使用。最特別的是其原曲作者並不怎樣出名也沒有別的代表作:比如給愛麗絲你會叫給愛麗絲或者貝多芬的給愛麗絲,叫不出來像上面的BMV 814你至少也會叫巴哈那首;可這首郵遞馬車作曲家叫不出名字,曲名也不容易叫出來,於是命名權就落到將其發揚光大的遊戲裡。

但這首音樂被使用的廣泛程度絕對不限於熱血高校。遠的有耀西曲奇(Yoshi's cookie/類似瑪莉醫生的spin off)或GBC哈姆太郎,近的則有NDS右腦爽解2012瑪莉奧x索尼克奧運會等。其在音遊上的版本就更多了:pop'nReflec BeatO2JamDDR Mario MixNostalgia都有自己的版本,但我最愛的還是PIU的Banya版本

對於那些太年輕(與熱血系列的紅白-超任年代相比)的香港觀眾來說,接觸這首樂曲的契機更可能是麥兜故事的「一二三四五六七」:



顯然一二三四五六七的選曲本身和MV都以熱血系列為靈感就是。當時還沒有聽過熱血系列的我看到這MV第一眼就已經在想,不知道這遊戲有沒有被實裝出來呢?答案應該是有,在某一時空黃巴士網站遊戲頁面裡的一個Flash小遊戲,現在已經石沉大海。

最後說一下為甚麼會選這首以及為甚麼在BGM巡遊出現。那是因為右腦爽解(Quickspot)是我喜愛的遊戲之一,遊戲中所有BGM其實都來自古典樂,郵遞馬車就是其中一首。這遊戲半年前也出了個switch版本,但我覺得新版在計分上過於複雜,各項目花樣也過多,還不如兩個NDS版來得單純。不過至少它是一個switch上的好玩小遊戲就是了,在廁所殺時間一流,有興趣的朋友可以玩玩看。

不過……過幾天……洛克人EXE冷飯就要出來了……(*本文完成於9/4/2023。)

上面介紹了十幾隻基於郵遞馬車的遊戲BGM,但其實還有漏網之魚:更詳盡的列表在這裡。不知道你又聽過多少呢?

Saturday, 18 November 2023

Simon Marais 23B4 revisited + comments on official solution

(SM2023, B4) Let $n$ be a non-square number. 

(a) Find all pairs of natural numbers $(a,b)$ so that $r^a+\sqrt{n}, r^b+\sqrt{n}$ are both rational for some positive real $r$.
(b) Find all pairs of natural numbers $(a,b)$ so that $r^a+\sqrt{n}, r^b+\sqrt{n}$ are both rational for some real $r$. This is an open question currently.


When I first drafted my quick comment I simply omitted this question because a Q4 is a Q4 and has to be respected, so I only left one or two sentences there. Later on I found this one of interest so I dived in and wrote a simple answer. But then some gap in the solution had been lingering in my mind, and unsurprisingly I missed out something important so the answer is not fully correct. But I feel like I am close to the answer since the math behind is nothing overly complicated.

Below is my later attempt. There is a gap still, not recommended for readers.

****

Obviously, every $a=b$ pair is a solution because you can easily make up $r = (n-\sqrt{n})^{1/a}$. Next, if $(a,b)$ is a solution then so as its multiples $(ka,kb)$ because you can take $r' = r^{1/k}$. 

As a result we can now assume that $a,b$ are coprime. As $r^a, r^b \in \mathbb{Q}[\sqrt{n}]$, we know that $r\in \mathbb{Q}[\sqrt{n}]$ as well. I think this is well known -- but in case that is not, think about Euclidean algorithm (recall that a field is Euclidean...or even simpler the algorithm where you find gcd) that you can divide each other until you reach $r^1 = r$. 

Now write $r= p-q\sqrt{n}$ for some positive rational $p,q$ (the proofs are similar for different sign combination. Like you can write $r = p+q\sqrt{n}$ can the argument below proceeds the same). If you still remember your linear algebra lesson you can solve the recurrence by writing $p_k-q_k \sqrt{n} = (p-q\sqrt{n})^k$ for rational $(p_k), (q_k)$. For $v_k = (p_k,q_k)^t$, we have $v_k = A^{k}v_0$ where $A = \begin{bmatrix}p & nq\\ q & p\end{bmatrix}$.

The general formula for $p_k,q_k$ can be easily obtained by either method of eigenvectors or if you know how expand binomial powers. Anyway we have: 
$p_k = \frac{1}{2}((p+q\sqrt{n})^k+(p-q\sqrt{n})^k)$
$q_k = \frac{1}{2\sqrt{n}}((p+q\sqrt{n})^k-(p-q\sqrt{n})^k)$.
Notice that the formula is the same for $(p+q\sqrt{n})^k$. For negative $p,q$ the sign just alternates. 

Clearly $q_k$ is an alternating almost exponential series. More precisely we expect $q_{2k}-1 \approx q(p+q\sqrt{n})^{2k-2}$ and $q_{2k}\approx 2pq(p+q\sqrt{n})^{2k-2}$. The two subsequences are surely strictly monotonic and would not give us any non-trivial answer. The difficult task is however to find $k,k'$ so that $q_{2k} = q_{2k'-1}$.

A few approaches are there: first you may want to show that $q_n$ may not even be an integer if $p,q$ are (non-integral) fractions past a certain $k$. Secondly you may consider something even stronger that $q_k$ can't be 1 for largr $k$ because exponential sequences are either diverging or goes to zero, but the problem is you can always make very marginal case where $(p+q\sqrt{n})$ is very close to 1 (e.g. using continued fractions) so that the 'rate of divergence' is not properly bounded.

The problem for us is (1) we can't calculate terms manually for anything past $k=4$ -- even that is nasty enough as you can see below, and (2) what is the meaning of (b) being unsolved? Most arguments, if we assume that $r\in \mathbb{Q}[\sqrt{n}]$, does not really care about its positivity. In fact, we care if $(p-q\sqrt{n})$ being negative or not more so $(1-2\sqrt{2})^k$ is easier to handle than $(1+2\sqrt{2})^k$!

My approach is basically the observation that the last $k$ where $q_k$ can easily be made as an integer when $p,q\notin \mathbb{Z}$ is $q_4$ with where $(\frac{1}{2} + \frac{3}{2}\sqrt{3}) = \frac{223}{4} + 21\sqrt{3}$. One suspects that for larger $k$ the expansion looks like $q_k = kp^{k-1}q + cnp^{k-3}q^3 + c'n^2q^5(...)$, where the $n^2$ is causing problems when we want to solve integrality or doing mod checks. But at the end the approach does not distinguish between (a) and (b). Now I am really confused...and I see nothing wrong in the Euclidean argument too. 

Still, let us try to check the lower $q_k$'s:

$q_1 = q$
$q_2 = 2pq$
$q_3 = 3p^2q + nq^3$
$q_4 = 4pq(p^2+nq^2)$

As claimed, $q_1\neq q_3$ and $q_2\neq q_4$ so we only need to solve the 12,14,23,34 pairs.

$q_1=q_2=1$: this is easy with $p = \frac{1}{2}$ and $q=1$. Possibly a solution that students would have noticed without going through all these hassle.

$q_2=q_3=1$: Substitution gives the quintic equation $8p^4 - 4p^3 + n = 0$ with discriminant $256n^2(512n-27)$. By checking $(512n-27)$ mod 8 we know this is a non-square so that gives no rational solution.

$q_1=q_4=1$: Substitution gives the equation $4p(p^2+n)-1 = 4p^3 + 4np-1 = 0$. Surely one real root but the discriminant of a cubic equation doesn't tell much about rationality. Instead we convert $p$ into a fraction $p = \frac{s}{t}$ so $4p(p^2+n)$ becomes $\frac{4s(s^2+nt^2)}{t^3}$ for some $(s,t)=1$ but then we require $t^2\mid s^2$ which is absurd.

$q_3=q_4=1$: this is of course the hardest...but the technique never changes. From $q_3=1$ we obtain $q = (4p-1)/8p^3$. Substitution into $q_4=1$ gives a horrible degree 9 equation 
$3p^2((4p-1)/(8p^3)) + n((4p-1)/(8p^3))^3$
$ = (n(4p-1)^3 - 3\times 64p^2 + 3\times 256p^3)/512p^9 = 1$. 
Looks horrible but all we need is to take mod $p^2$ which eliminates the last two terms. Since $(p,4p-1)=1$ that forces $n$ to be non-square-free, hence the contradiction. So $(a,b) = (k,k)$ or $(k,2k)$ are all the possible pairs.

Other than discriminant checking, the main trick is to force a term to be multiple of $p^2$ (or anything else) if you want the sum to be a multiple of $n^2$ and so does the rest of the terms, then we can apply the square-free assumption. I believe this can be applied for higher $q_k$'s because we can check higher powers of $p$ against the $n^2$ factor. But clearly (b) being open does not support that.

So, basically the sure answers are in forms of $(a,b) = (k,k)$ or $(k,2k)$. But are there more? I don't know.

The more I think about this question the more I like it with so many different scattered technique that were used. This is the type of question we would like to see more. I would not hide the fact that my first attempt is a miserable fail as I overlooked a large part of it. I wrote that we look at $A^2$ again we know from there that the denominator would sure to stack up every 2 steps, but what about consecutive terms $q_k$ and $q_{k+1}$? I stared at what I wrote before I finally realized what should be corrected...but nope I am probably not getting 7 this time.

Just food for thought...what if we are now in $\mathbb{Q}[\sqrt{-n}]$, or that $(a,b)$ are simply integers instead? 

--------------------(NEW 08/12/2023)---------------------------

The solution is out and below is my answer-checking...

A1. No surprise, but their solution 3 is neat. If you skipped that while reading the solution you should go and have a check.

A2. The idea is right but I got the lower bound wrong for not considering $S$ to be set of all possible convex functions, but that is still easy.

A3. Completely wrong...hmmm I totally missed the 'unequal size' condition. Instead I took the sets $A_i$ in the way that $A_i$'s are not pairwise subsets and supsets. The correct version of A3 is much easier. Still I appreciate they put all the details unlike me (especially A2 and A3).

A4. As expected but their approach of finding the 'crtical point' is more elegant than calculus bashing.

B1-B3 are all as expected. But they spent more words on B2 that I would have thought. At this point I think all Simon Marais contestants should learn generating functions before they come -- such question appears almost every year!

B4. Here is the big thing -- I say that I can't see how should I tweak the solution to accustom the condition that distinguishes (a) and (b). How about scrapping the whole approach? It is now clear that my approach is more for (b) the open problem. (a) is much easier. I also missed that fact that for $(a,b) = (1,2)$ we actually got a negative solution so that does not count in (a) but in (b)...

No surprise in C1-C3 again, though C3 should deserve only a one-line solution if any.

Monday, 13 November 2023

Rains and returning period

Auckland's 1-in-200 years flood was given the name Anniversary Weekend flood 2023 on wiki...or simply just the Anniversary flood. The scars are still visible around, and recently a review has just been concluded from the Metservice side. The conclusion is that their rain prediction is poor.

Um...thank you.

I think most Aucklanders aren't surprised as the forecast tends to underestimate rains heavily all the time, where longer forecasts on precipitation are merely better than flip of a coin. We used to read radar directly because we can pinpoint the location of interest and is more accurate in general. We can at least tell whether a region is going to rain in an hour while the forecast can't!

When I wrote about the flood earlier this year, I said it's not a good time to talk about the 1-in-N-years thing because it's not the right time to do so. I think we are in the position to do it now especially when a comparable event happened later this year: the torrential rainfall over Hong Kong on early September 2023: record breaking 158mm in one hour, 800mm+ widely over the Island over 12-24 hours. A rare city wide flood that immediately recalls what happened over Auckland some times ago. It ended up being described as a 1-in-500-years event but was taken as excuse to inability of the government.

There are too many things we can talk about the two storms here like crisis management or building standards but I just want to focus on the numerical and scientific bits here as below.

Auckland's major flood on 27 January was caused by atmospheric river dragged near NZ by remnants of Tropical Depression 06F and blocked or forced stationary by a nearby anticyclone/high. At the same time, Hong Kong's flood was caused by the remnants of Typhoon Hanna (11W), stuck in a saddle field right above Hong Kong so that rain bands kept sweeping in.

The similarity is clear: both floods were caused by remnants of tropical systems that are stuck so that the affecting period is prolonged. But then it seems like this is the only recipe for such rainfall: normal lows can't be that powerful so it must be something related to tropical systems; mature systems (e.g. typhoons) are primarily driven by higher atmospheric features and seldom stuck like that so it has to be as weak as depressions or lows as remnants of the previous systems. Even so we need that to get stuck over an extended period (e.g. 12h) and provide enough water vapor to the system for that to work. Without considering other more extreme events like volcanic eruption/nuclear winters etc, is there any other possible way to produce such rainfall?

I suspect that the long tail on rainfall distribution over considerable period of time -- is not normal, because it is only produced under a specific combination of meteorological events. The distribution is composed of some 'common raining events', then events like what caused the above floods that is responsible for part of the tail, then more extreme event for the rest of the tail. Just think of adding three unequal Poisson (not saying these distribution is Poisson of course) distributions together and what would you get? Of course these are more speculation than anything, but that should allow us to get into what causes these rainfall outliers.

The next thing we should think about is the returning period which is the most talked about. If the distribution is not even normal how can we calculate the returning period? Another problem is, even with the returning period on our hands how should we set standards using that? 

The 1-in-500-years claim of the Hong Kong flood is based on the peak 1 hour rainfall 158.1mm which exceeds the 500 years mark (~155mm) on the 1hr rainfall returning period table. Auckland's 1-in-200-years flood is based on NIWA's claim but I can't find any numerical evidence supporting that. They were referring to the specific flood on 27 Jan so it might be 24hrs cumulative rainfall (or least 12, considering this is how long it lasted). Of course the flood is record breaking in all timeframes like the monthly precipitation of 539mm easily exceeding any of the months in the last 170 years. 

It is clear that the officials picked 200 and 500 respectively because this is the greatest that can be interpreted out of the numbers so that it sounds as serious as possible. But to those who want to use the returning period for risk management what's the proper timeframe to look at?

Unlike water level for dams where the returning period is duration independent, drainage capacity isn't and could have very different implication over different timeframe. A 1-in-200-years 2mins rainfall may sounds scary but is nothing to the drainage. The returning period of monthly rainfall is also pretty useless for drainage system because all you care is whether or not you can handle the spike. If the 538mm rainfall is distributed evenly then we will receive ~0.7mm of precipitation per hour nonstop for a month. Bad to have in the summer but no big harm at all.

Now suppose we take 1hr and 12hr rainfall into consideration more than anything else. Does it make the returning period a reliable indicator? On one side you say yes because it covers flash floods that are  immediately visible as well as the whole raining period that the system is designed to withstand. But consider this: a typhoon just swept through Hong Kong exactly a week before the flood that introduces significant amount of trash into the drainage which of course weakens its capability to drain. Should we take the two as independent event? If not, is it necessary to take returning period of longer timeframe back into consideration? Same thing happened to Auckland as a subtropical low hit Auckland 4 days after bringing more precipitation, then there came Gabrielle early February that again broke the still sagged SH1.

The lesson here is that the returning period is a highly on-paper number, easily manipulated by the data interpreter, highly confusing to the public and hard to use as a reliable reference. The bottom line is that it's something that you can always calculate and compare...but that's it. 

Oh and before I conclude it's unfair not to say something for the forecast institutes. Precipitation forecasting is a very complicated task even in 2023: it is very random in locality and intensity. The difference between rain and no rain could just be hundreds of meters apart, and there is no point to forecast upon such precision. Even if we can tell if it's going to rain or not, the cloud may develop or dissipate at any moment. This is particularly true in case of heavy rains. Just look at the radar -- the chances of actual heavy rain is much higher than finding signals of "heavy rains" on the chart! These are true limitations of technology up to now and are things that can't improve overnight. Still I am grateful that they are thinking to improve. Let us hope that floods like that don't ever happen again.

Friday, 20 October 2023

Simon Marais 2023

Another year, another set of Simon Marais problems. Let's go! *Last edited 24/10/23 -- I added my comment on B4 which turned out nicely.

A1. Simple. The coordinates of the final point can be calculated as limit of geometric series.

A2. Quite confusing that you might waste time thinking about plane partitioning problem (aka cake cutting problem), but it's much simpler. The function $g(n)$ must be of the form of piecewisely glued $f_i(x)$. Since $f_i$'s are linear functions (or affine they call not to be confused with linear in the operator sense) it is easier to interpret convexity with positive second derivative almost everywhere. 

That is, whenever we switch from $f_i$ to $f_j$, the slope value must have gone higher for the sake of convexity. In the ideal case we can have linear functions $f_i$ with increasing slopes so that the $n-1$ intersection points between $f_i$ and $f_{i+1}$ has a natural increasing order. And to construct such example is easy: just take tangent lines from a parabola (because we are taking about positive second derivative). 

The last thing we need to show is that in such case we can skip one of the linear function and the rest could retain such structure. More precisely, suppose $f_i,f_{i+1}, f_{i+2}$ are in increasing slope. Let $(x_i,f_i(x_i))$ and $(x_{i+1}, f_{i+1}(x_{i+1}))$ be the intersection points of $f_i,f_{i+1}$ and $f_{i+1}, f_{i+2}$ respectively. Then the intersection between $f_i$ and $f_{i+2}$ is $(x,f_i(x))$ where $x\in (x_i,x_{i+1})$. This is clear because everything is continuous and almost everywhere differentiable.

The weird thing is that the question asks for smallest possible value as well...isn't it 1 unless I didn't read properly?

A3. Instinctive guess: the smallest $2k$ (or $2k+1$) such that $C(2k,k) \geq n$ (or $C(2k+1,k)$). Why? Try to look at the poset $(n,\geq)$. If you choose an element then everything above AND below it would be banned, so it's a really powerful restriction. The best choice is to choose everything from the same level. That says, we can already fit $C(2k,k)$ sets with a total of $2k$ elements. The only thing that is left to show is that we can't make $C(2k,k)+1$ such sets.

What I am thinking is much stronger: given $A_1,...,A_n$ using $k$ elements and suppose that $C(k,r)\geq n$ for some $r$. Then there exists valid sets $A'_1,...,A'_n$ so that each $A'_i$ is either a subset or superset of $A_i$, each of size $r$. Is it really possible? Probably takes pages to prove.

A4. The focus is the function $f_n(x) = \frac{(n^2+1)x^2}{x^3+n^2}$. We want to split the sequence into two parts: $n=0,1$ and the rest because the function behaves more steadily for $n\geq 2$. 

The first two iterations are simple: $a_1 = a_0^{-1}$ and $a_2 = 2a_1^2(a_1^3+1)^{-1}$, so we get $a_2 = 2a_0(1+a_0^3)^{-1}$. What's so special about this formula? Well, we claim that if $a_2>1$ then the sequence diverges. If the above claim is true then the rest is easy: $x^3-2x+1=0$ has two positive roots: $\phi -1$ and $1$, so that is the range of divergence!

The proof of the claim is also about bashing the function $f$ like $f_n(x)$ peaks at $x_n = (2n^2)^{1/3}$ and $f'_n(x)>1$ between 1 and halfway to $x_n$...complicated, but not hard.

But then I figured out the significance of $a_2$ and the perturbation $\phi -1$ only using computers but participants have to do it by hand! As for difficulty of A4 it somehow makes sense but it's a bit sad to see questions like this being the 'boss' of a paper.

B1. We have seen questions of similar style for many, many times in this competition: simple question with simple solution, worded in an abstract way to confuse people. In my words it would be like "find largest possible $|| \sum v_i||/2$". Do you understand now?

B2. Notice that the whole schedule is decided before tournament. For example the first 2-bracket is always player 1 (ranked 1st) vs 2 (let's call that 1v2). The first 4-bracket (first 2 rounds) is always 1v2, 3v4 and the winner of 1v2 plays the winner of 3v4. The same goes for 8-bracket, 16-bracket and so on. The thing is, if the expected rank of winner of the first 4-bracket is $r$, then the expected rank of the winner of the second 4-bracket is $r+4$. Since the winner of the first 4-bracket is always ranked higher than that from the second 4-bracket, we can calculate the expected rank for the winner of the first 8-bracket as well. Similar calculation repeats till the 8th round aka the final.

I don't mind repeating the calculation 8 times for 1/8 of total credits in a college math competition. But it's not fun.

B3. An intuitively true statement in linear algebra. 

WLOG assume that $A,B$ have basis $e_1,...,e_n$ and $e_{n+1},...,e_{2n}$ respectively. Since $A,B$ share no non-trivial intersection, $(e_j)$ is a basis for the whole space. For a basis $v_1,...,v_n$ for $C$, we can write $v_i = \sum a_{ij}e_j$ for each $i$. Now we look at the rank of the matrix $M = (a_{ij})_{i,j=1,...n}$ and similarly $N = (a_{ij})_{i=1,...,n, j=n+1,...,2n}$. If $M$ does not have full rank, that means a linear combination of $c_i$ is in $B$ causing contradiction. Similarly $N$ must have full rank as well. That is, we can take $c_i$'s component in $A$ as the basis for $A$ and the same for $B$. Call that $a_i$ and $b_i$ respectively then we have $a_i+b_i=c_i$ for each $i$, hence the linear dependence.

Linear algebra is just that elegant.

B4. (EDIT 24/10/23) Ok I am back to solve B4 when my friend pings me back for discussion.

Obviously, every $a=b$ pair is a solution because you can easily make up $r = (n-\sqrt{n})^{1/a}$. Next, if $(a,b)$ is a solution then so as its multiples $(ka,kb)$ because you can take $r' = r^{1/k}$. 

As a result we can now assume that $a,b$ are coprime. As $r^a, r^b \in \mathbb{Q}[\sqrt{n}]$, we know that $r\in \mathbb{Q}[\sqrt{n}]$ as well. I think this is well known -- but in case that is not, think about Euclidean algorithm (recall that a field is Euclidean...or even simpler the algorithm where you find gcd) that you can divide each other until you reach $r^1 = r$. 

For the rest see my updated post.

C1. Cover most cup by adjusting the modulo offset. No quick way to solution but to check 30 combinations...or 15.

C2. Quite disgusting in my view...but not super hard. The following should be clear once you draw the diagram:


Here red and blue are not the underlying colors but for easier reading. For odd $2n+1$, you can along the axis draw consecutive triangles, exactly half of it colored blue and half red. Above those triangles are parallelograms with slopes 1 and $(k-1)/(k+1)$ (below the diagonal line, reflect to the other side for similar result), covering both colors half each.

And for even $n$, I think similar argument gives a no but I didn't write down concretely.

C3. EXCUSE ME WHAT? 

Well I know most unis do not put inequalities in standard materials but this is an insult to those with competitive exposure.

Rewrite sequence as product so that we minimize $\sum x_i$ where $\prod x_i = 2$. AM-GM gives the answer $n2^{1/n}$ and it suffices to take the limit. Write $2^{1/n} = e^{\log (2)/n} = 1 + \log (2) /n + \log ^2(2)/(2n^2) + ...$ we clearly sees that $n2^{1/n}-n \to \log 2$.

Easiest of all.

C4. Hmmm chess and game theory, gonna skip this one unless I want my puzzle rating falls further tonight.

*

If they are not going to change their way of drafting questions it does not make sense for me to criticize from the perspective of comparing against Putnam and other major competitions. Instead I shall compare this year's problems to that from the previous years.

Q1 is what I called the "7 points to everyone" or "free points so that they come back next year" question. That's fine. All three of them serves as an appropriate free question this year.

Q2 is the warm up question. B2 is perhaps a bit too straightforward but A2 and C2 brings abstractness to quite a level. In terms of difficulty they are consistent with previous Q2s.

Q3 is the real deal usually involving very long but reasonable (cf. Q4 being overly fancy) answers. I think A3 is up to that level (or slightly lower than if we go back to the graph problems few years ago). B3 is clearly not at Q3 level and C3 is a joke.

Q4 is the really hard question. A4 is nice (the "non open question Q4 being easier"), B4 looks very niche and C4 is crazy. All three are typical.

In overall it's quite consistent against past tests all in terms of scope, difficulty, and problems that are completely messed up, although I don't have full confident on my solutions for those Q3 and 4s that I have solved given how shockingly short it is. Surely this won't be the Pacific Putnam in another 50 years, but we can at least expect a few nice problems every year.

See you in 2024.

Friday, 13 October 2023

夢.十夜 (9) Fatigue


事情已經很清楚了。

卡羅跟Yuki早就認識,Yuki的打法想法都是他帶出來的。不知為何他們後來變得疏遠,後來我才變成被看上那位。

自己對這個遊戲的喜愛出於尋找打法的樂趣沒錯,但經過這事件後我甚至對自己的熱情產生懷疑。繼續玩下去的動力是甚麼?真的只是為了尋找不同活動的打法嗎?但活動再多總有重複的一天。是沉沒成本嗎?至少我一分錢沒課過,退一步說這也只是打了幾個月的手遊。還是那群可愛的隊友?還是……他?

軍團決戰活動我當然沒有參加,我甚至懶登入也懶的做,反正這遊戲最重要的資源都是在活動打回來或者交易換回來,登入獎勵一點也不重要。甚至熊熊說要把賣卡的報酬轉過來也沒能把我拉上線。

後來Alex借了我一張他幸運抽出來的活動七星,那是碰巧抽出來的。說是要給我重振一下對遊戲的興趣,卻沒想到這張卡不但沒有令我提起回坑的欲望,反而出現反效果。

這張七星對應的是現在的爬塔活動妖精之森(The Elder Tree),顧名思義這就是一直爬塔闖關的活動。每一層都有隨機生成的怪物或寶箱,每十層和百層都有對應的中BOSS和大BOSS。此外還有一些特殊規則比如收集一些碎片通往隱藏樓層有不同的掉落和分數加成等,但其實核心玩法就是訓練活動那樣。跟訓練活動一樣每爬一層都會消耗若干體力,不同的是這裡打輸了的話玩家會掉到下一層,怪物會保持殘血而重試的時候可以呼叫好友支援。

如果是過去的我,大概會執著於找出極大化利用隱藏樓層的效率吧。那些碎片是隨機掉落的,但開啟特殊樓層的時機是自己決定。只要事先準備好攻略用的卡片物資加上隨時候命支援的好友,在隱藏樓層拿到成倍以上的分數並不難。

但七星活動卡在手就如同從山腳爬到山頂一樣,看到的東西可謂截然不同。

打BOSS得到的分數跟你的輸出能力和重試次數有關。活動卡片在活動裡面的火力會得到加成,本來就很強的七星卡片在加成下變成極為誇張的戰力。拿著這張卡配上其他還可以的角色不說平推所有樓層,但可以無腦打過去肯定沒問題。

分數來源的部分已經解決了,那麼刷分的效率呢?

爬塔的速度當然會被你手上隊伍的輸出能力、按手機的手速和網絡延遲等影響,但最主要的因素還是你能負擔的體力消耗。每五分鐘回復一點的體力,在活動裡咻一下就不見了,你的手速根本不會影響刷分效率。於是要刷分數最重要的變成你願意消耗的多少瓶體力藥水的問題。這時候拿著七星活動卡的價值就來了:它除了作為戰力加成會帶來額外分數,在結算時分數還會按比例加成。簡單來說,拿著七星活動卡的刷分效率完全是所有其他玩家、甚至包括那些拿著五六星活動卡的玩家所不能比擬的。

簡單來說,活動變成了持有七星活動卡的玩家對第一檔排位的競拍。當然不是一口氣拍完那種,而是競爭者們一直把分數堆上去,覺得不划算的自然會慢慢掉隊。情況有點像選舉活動一樣,但是單幹的話整件事變得更為可控。

我拿著之前拿到的獎勵卡片通通變賣存下來的八百瓶體力藥水開始刷,策略跟選舉活動幾乎一樣:一開始全力衝剌,算出一檔分數線的推進速度後就知道每天刷多久可以把自己留在安全範圍以內,最後數小時則一直監察著分數榜以防身後玩家集體暴動。結果也沒有任何意外,不過明明前五十就有一檔獎勵我卻硬生生排到了第八。果然在這方面的控制上我還是遠不如Yuki。

排名靠前也有好處就是。爬塔活動除了最終排名獎勵以外在完成指定周回次數時也會發放對應獎勵。這次完成主塔十遍合共一千層的獎勵是六星卡「草藥獵人」瑪喬(Marjoram)。這張miso老師的作品除了一貫的自帶小故事外還帶一點活動分數加成。雖然這個加成完全比不上抽出來的活動六七星,但是在較低的檔次還是可以達成降維打擊。這種獎勵先到先得,在活動中期開始有人刷出來的時候可說是非常搶手。這次我沒再豫疑,迅速丟給了熊熊而賣出了450瓶藥水的高價。到了活動快要結束時其價值已經掉到150瓶藥水不到,僅僅比爛大街六星高了一點點,算是miso系列的附加價值。

但這一切都不是重點。

重點是在活動七星的加持下,整個活動變成了可以無腦刷下去就能贏的遊戲。不只這樣,這活動同時也是無課玩家絕對贏不了的遊戲。縱然有複雜的遊戲機制掩護,這仍然是赤裸的P2W(Pay to Win)活動。

試想想,無課玩家可以靠自己之前肝下來的資源刷出同樣的成績嗎?假設完全不用活動加成卡片,單靠無限體力藥水刷的話看似沒問題。但實際上刷分效率大降之下不單是藥水消耗大增,連刷分所需要的時間都倍升。本來拿著七星活動卡平均一天要刷十三四小時,現在算下來直接超過了二十四小時,也就是物理學上的不可能。

那活動一開始就高價砸一張七星活動卡可行嗎?先不說這次市場上根本沒有人放售,即使有也是把活動回報算進去的離譜高價--參照過去活動的叫價加上這次瑪喬的價值,沒兩千瓶藥水怎樣也說不過去。再加上打活動本身的花費,那是個即使從開服開始無課玩也難以賺到的數字--大概只有熊熊之流能賺的到吧?

一陣難以言喻的空虛感在確保一檔排名那一剎那開始蔓延,好像失去了玩這個手遊的意義一樣。熊熊賣瑪喬的錢我沒有拿回來,她已經幫了我實在太多了。我提早把活動七星還給了Alex,他憑著這張卡的加成在低檔排名裡遇神殺神,最終收獲了個不錯的排名。一併發給他的還有在活動裡雜七雜八的爬塔獎勵和我預算之內用剩下的藥水。雖然加起來都不及一張瑪喬值錢,但也算我能力內的報答了。

這個遊戲的本質其實從來都沒有變,每個活動其實都是這樣:競技場活動早就被當成給土豪派福利的活動,像訓練活動那些強度無上限的活動也是天然地把沒有活動加成的玩家排除在第一檔甚至第二檔獎勵以外。投票活動理論上是隨機分組所以大致上公平沒錯,但很明顯這種活動就不是主菜,都是墊檔期用的。營運甚至懶得推出活動卡包,活動獎勵當然也比較低。

自己之所以改變了想法是因為這次自己忽然被賦予站在獵食者一方的權利而已。從高位看下去以前的自己在那邊用自己的策略去戰鬥也好、沉迷在與隊友合作的快感中也好、還是完全躺平也好,自己在遊戲裡依舊是獵物的事實都不會改變。那些心靈雞湯常常告訴我們甚麼「旅程不在於最後的寶藏,而是在旅途中交到的朋友」。可是……我和我的朋友們都是獵物啊。

自活動結束以來我幾乎沒再上過線。熊熊再次把賣掉瑪喬換到的體力藥水傳過來然後對我說就算暫時不想接收也好,至少也上線按個取消交易讓她方便周轉云云。我沒有回話,只是默默上去按了個取消便再次消失,熊熊大概猜到我的想法也沒有再糾纏。

逆戰幻想被封印了在手機深處。

*

自從自己沒再碰手遊以後自己的空閒時間忽然憑空多了一大截。

不過想想也是。先不算高強度刷活動的日子,平時5分鐘可以刷一次的素材關卡光是點擊進入關卡、擺放角式、確認獎勵之類的動作加起來耗時也在十秒以上,這樣一天下來就快一個小時了。

那多出來的時間可以做甚麼呢?

不想去機廳,也不想去平常一直去的咖啡廳,簡單來說就是不想接觸到會讓自己想起有關手遊的東西。但如果真的很想喝點東西呢?這次我挑了一家開張不久的,方便一個人自己喝的店。

咖啡廳以黑色為基調將店面分割成一個個小空間,每個空間裡都以黑色金屬椅搭配木製桌子,這種對比予人一種頗為自在的感覺。縱使店裡坐了不少兩人以上的顧客,坐在獨立空間裡面我也能毫不在意地享受自己獨處的時間。店裡播放的音樂是鋼琴版的Speak Softly, Love,原曲的那種厚重感被爵士節奏重構成一首輕快的小曲。不過能認出這首的顧客應該不多,大概是店主或者店員的口味吧?

眼前的飲品是冰咖啡的變奏Shakerato。把濃縮咖啡和冰塊放進調酒器裡混合達成快速降溫效果,變成一杯沒被冰水稀釋而且也不會冷到完全失去咖啡香氣的飲品。雖然經典做法是用馬丁尼酒杯上桌,但我倒覺得這裡的窄身酒杯可以有效地將香氣長時間鎖在杯子裡,對我這種偏好慢慢喝的人來說再適合不過。飲品裡還加了點蜂蜜,與本身是花香味的咖啡十分合得來。本來還在想要不要點個甜點,現在看來專注在這杯咖啡止已經足夠。

我一邊一小口一小口地品著咖啡,一邊百無聊賴地在手機上滑著。如果不玩逆戰幻想,那我還可以玩甚麼呢?把Play Store裡面的營收排行榜拉出來看,逆戰幻想排在第五名。除它以外榜上並沒有太多社交式網遊,更多的是靠著社交平台傳播但本身沒有社交功能的小遊戲。比如某個把三消糖果的闖關遊戲,只要在facebook上求助就能收到體力的設計深得中年大叔大嬸的喜愛,輕鬆讓他們真的很需要過關時掏出錢包買那些貴死人的道具。又比如那個推銀機,單是可以不用錢在家裡玩這點已經吸引無數玩家,然而他們不知道的是他們所看的廣告已經讓開發者賺得盆滿砵滿了。

小遊戲和大型網遊,有點像個人電腦上面flash遊戲和網遊之間的分化。不過近年來網遊的取向似乎出現了一點變化,那就是營運希望從虛擬物品市場裡分一杯羹。新出爐的網遊要不把交易限制在官方的市場裡面並收取一定的抽成,要不直接弄個綁定系統讓玩家沒法把綁定裝備賣出去等等。一個細思極恐的想法在心裡浮現:將來即使我投入到其他遊戲上,是否都沒法體驗到交易市場的樂趣?

這時從咖啡廳門口傳來店員的聲音,中斷了我的思考:「客人不好意思,裡面已經沒有單獨位子了,能否請您在外面稍等一會呢?」

「沒事,我進來找朋友。」一把不能再熟悉的聲音從後響起。接著是一陣從遠到近的腳步聲,然後一隻手輕輕地搭在肩膀上:「小紅對不起,我來晚了。」卡羅一派輕鬆地說道。店員看我沒有反應便放下餐單隨他拉開椅子座下,他很快就點了自己想的東西。我沒有抬頭望他,只是死死盯著自己的咖啡,怕自己會被他像雷伊一般的眼神勾去。

「真是~好久沒見了呢。」

「好幾次問你是不是在跟著我你都說只是碰巧,這次被抓了吧。」

「真的沒有啦,你要聽聽看我的推理嗎?」

我喝了一小口咖啡,本來快要爆發的心境一個不慎就被清爽的味道加上積在水面上的香氣壓了下來:「嗯。」

「我想你應該暫時不會去那些『我們』平時會去那個咖啡廳和機廳了吧。」他特別強調了我們兩個字:「機廳附近就這麼一家,所以我就從咖啡廳裡下手。從你對茶和其他飲料的喜好來看,你應該比較看重飲品的香氣。正好這家開張不久的店其實還有本店而我剛好去過,他們常設三四種豆供客人挑選這點我印象蠻深刻的。我在想說不定你會過來,於是就來碰碰運氣囉。怎樣?」

「……勉強說得通吧。我不介意你坐我對面,安靜吃完就滾吧。」

「不要這麼冷淡嘛,難得再會讓我請個客不是理所當然嗎?」

「謝謝,一杯咖啡我還是喝得起的。」

「真是……」他雙手枕在桌子上向前滑,那張臭帥臉還是出現在我的視野之內:「難道你完全不對我和她的過去感興趣嗎?那天當你得知我們是舊交以後你幾乎立即就跑掉了,總覺得你誤會了甚麼,所以我才一直想找你解釋一下。」

「哈?為甚麼我要對你們的私事感興趣?!?」

少年也沒理我,直接把故事講下去。

…………
………
……

最初是難以置信,但至少細節合理,他也是有問必答。

「所以說我們真的不是你想關係。只要你能相信這一點,今天我就不枉此行了。」他一口氣把故事說完連忙拿起已經送到桌上的expresso猛灌一口,然後拿叉子把另外點的巴斯克芝士蛋糕割了一塊下來,叉子指向我道:「要不要試一口?」

芝士蛋糕裡面鬆軟到快要塌掉的流心和外面的焦糖形成強烈的對比,光用看的就十分誘人。但此刻的我還在思考卡羅剛才的自白而無視了他遞過來的誘惑。他歎了口氣把這個叉住蛋糕的叉子放在一旁,用了隻新的叉子切下另一塊蛋糕放進口中:「真可惜呢,蛋糕附帶的藍莓乳酪味道非常鮮明(sharp),應該跟你的shakerato十分相襯呀。」

「……就一塊,我自己來。」他居然剛好在我喝咖啡的時候開始描述蛋糕的口感,實在太可惡,我搶在他之前把叉子搶過來把蛋糕放入嘴裡。清爽的芝士加和藍莓乳酪的確十分相襯,不過乳類香味終究十分容易蓋過咖啡的花蜜香,我十分慶幸剛才沒追加甜點。

「當然,說沒有的話你也不會相信--我是代表他們來問候你,看看我們有沒有能幫的上的地方。」他看準我在心情高點之際拋出這個敏感的話題。

「也沒有,單純開始覺得厭倦罷了。作為一個雙子,貪新厭舊也是十分正常的吧?」

「可是,我覺得你是被上次的活動養大了胃口?」

「啊哈哈怎會呢。那些活動獎勵我都還給Alex和熊熊了,我頂多就是個代打的。」

「我可是從他們口中聽到你硬要把活動紅利送給他們呢。或都說,你覺得再多的計謀在強大的課金力量前都不值一提吧?」

「……」

「應該就是這樣沒錯了。這也難怪你,難得找到喜愛一款遊戲的切入點卻被告知自己的努力其實毫無價值,這樣的打擊很大吧?」

我小聲「嗯」了一下,他繼續道:「告訴你一個秘密好了:熊熊現實中也是個小富婆,其買賣手段早就在現實裡練出來了。這樣數的話加上Alex和我~群組裡面能負擔重課的人絕對不少。重點是課金的成本沒有你想像中高,以一美金對一個體力藥水的公價算好了。把錢砸進遊戲裡面直接買藥水換卡片,拿這些卡片閉著眼打個很爛的排名出來。這樣應該也就虧幾百個藥水而已,如果是你這種精算型玩家這樣操作下去至少平手小賺起跳吧?幾百個藥水對一般人來說可能掉一層皮但絕對不會傷筋動骨,那為何大家不搶著砸錢下去過過手癮呢?」

「因為……大家都知道市場很小,一起上的話就變成大家都無利可圖了?」

「其實不用想太多。在我看來,要不要課金在於你怎樣看待這個遊戲而已。當初你覺得策略可以改變命運,於是拼命參加活動將所有東西精算到極致,這是你熱愛這遊戲的原因;後來你又覺得再多的策略也比不過金錢之力,改變命運之類的通通都是騙人,於是一瞬間失去所有興趣甚至變得抗拒,這也是十分自然的事。你應該問自己的是,這真的是你想法的全部嗎?」

他把剩下一小塊蛋糕的盤子挪開,在手機上打開遊戲比划著然後向我展示:「比如看看這個,還記得這張卡嗎?」

--「惡夢」吸血鬼。由遊戲主催之一、擔任過FF美術的繪師繪製。復古的畫風除了色色元素以外該有的威嚴和氣勢都有了。

「這是當初『萬聖Parade』裡面更高檔次的獎勵卡吧?」

「嗯沒錯,這張卡片是當時小雨托你的福衝進一千名拿到的獎勵。你來看看卡片的簡介?」

在那瘋狂的盛宴之後
回到主人身邊 等待第二朝的到來
「以血為證,展現我的忠誠」--

「開頭的句子跟人狼(Werewolf)一樣?」

「嗯,」他打開瀏覽器給我看:「你再看看同一張卡其他語言的版本。」

中文服的翻譯是:
以血相連的羈絆
以血為生的永生--
「血的誓言,血的契約」

日本服的則是:
祭典之後 百年之約即將完成
在血池之中 等待第二朝的到來
「以血為證,展現我的忠誠」--

韓國服的是……嗯,看不懂。

「有沒有發現,每個版本都有一點差異呢?但如果你把卡片附上的故事打開就能發現,其實幾個版本都沒有錯。大概是不同地區的譯者選取了故事裡不同重點放進簡介裡面,就像寵物小精靈(Pokemon)不同版本對精靈也有不一樣的簡介互補。只要交叉檢查一下,就算不看故事也能大概知道其詳細背景,這也算是收集卡片的的樂趣之一吧。」

他的叉子叉進最後一塊蛋糕裡指過來:「那麼你--玩這個遊戲真正的原因是甚麼呢?」

***

靈魂一問。

應該會有不少人包括我回答看著數字在長就能滿足之類的答案,也難怪掛機類遊戲會在這十年迅速崛起。當然不少人會說對角色的投入很重要(又稱婆力),最近連續兩個手遊編劇作死導致要整個回爐甚至收掉就證明以此為取向的手遊要滿足玩家是多麼的不容易(?)。那麼,各位的答案又是甚麼呢?

卡羅和Yuki兩人過往的一段被省略掉是有意而為,但部分答案已經在某個章節裡揭示過了。剩下的讓它成為我個人的回憶吧,當然如果將來時機成熟我不介意補上一點。又或者有人覺得主人翁好像暈爛……不過對手是乙女向男主的話好像也沒辦法呢。

是說我偷偷作了個微妙的改變,就是把遊戲名字給正名了。

首先一個倒了的遊戲(連遊戲公司都改行了)實在沒甚麼好忌諱的,當然我不認為裡面有甚麼冒犯性的內容。對整個遊戲的評價我留到整篇收尾再講,但我想起坂口博信講到FF當初命名問題的報導:當初的FF本來是想叫Fighting Fantasy,後來因為商標問題而只能改成Final Fantasy卻造就一代經典。這個遊戲的中文名字逆戰幻想直譯自日文,好端端地硬要改成終戰也太奇怪了。

故事講到這裡,剩下的就非常簡單了,就是以一個華麗的煙火作為這個難得可以完本的創作來收個尾。感想當然是留到完本再說,但我感覺這個日子已經不遠了。就現實的軌跡來看,公會戰張力過高導致玩家興致燃燒殆盡的情況真的很明顯:競爭最大的時候正是前面場數最多、規則最原始的時候,後面就算如何迎合玩家作出改變也無濟於事,公會戰變成聊勝於無的活動。投入前幾次公會戰的我自然也是殆盡的一員,但我覺得我玩這個遊戲的初衷一直都沒改變,也希望各位可以帶著類似的想法投入一個遊戲。

有關爬塔活動我還想補充三點:

第一、「草藥獵人」瑪喬(Marjoram)這張卡,其實是我私心加進這個活動裡的卡片。在現實中它屬於「Mandragora March!」的活動卡片,這個是「萬聖Parade」外另一個帶我進坑和認識miso老師的訓練活動。不過章節所限我已經沒地方寫這個活動了,所以決定以這個形式把這張卡插進來。

第二是關於活動七星卡片的價值問題。按道理說,在市場均衡的情況下我們應該可以期望在活動剛開始時活動七星的價格應該可以估算為活動回報加上勞力成本減去藥水成本,但實際上七星活動卡片的價格一直偏高且不限於這個活動。為甚麼呢?其實只要把上面式子逐項拆出來看就不難得出答案。

首先是勞力成本,這是由願意刷榜的玩家設定的,酬勞不夠的話請自己來謝謝。但其實消耗藥水的量和活動回報這兩點人與人的差異可以很大。消耗量取決於玩家其他卡片的強度和刷分效率;而活動回報正如正文所述,除了視乎把獎品脫手的能力以外也看你刷分的效率。刷得快的玩家早拿到周回報酬,回報自然更高--但不是每個人都願意每天長時間地刷分的。在2023的今天在一些有工作室長駐的超人氣手遊裡或許會發生,在這裡卻決不可能。

上面聽上去好像一個會使卡片價值因風險產生折扣(discount),但事實正恰好相反有一個加成(premium)。因為賣方不是隨機賣給其中一位刷榜玩家是賣給能付出最高價錢的玩家。那些玩家的刷分能力應該在平均以上,這張對他們來說這張卡的價值也在我們用平均值去算的期望以上也就不奇怪了。

最後說到那些刷榜玩家我想起一個類似的例子:偶像大師星光舞台(Im@s Cinderella Girl Starlight Stage)。不知是哪個喪心病狂發明了打音遊刷分的活動,而且稱號之類的獎勵只限前三甚麼的,於是激起了玩家之間慘烈的競爭……前幾名幾乎是七天二十四小時刷分,刷分的歌曲難度高但準確度不能掉。這種刷分法連Osu分數榜的觸手(望)都甘拜下風好嗎?最後他們通通筋膜炎入院就是。

回到這個爬塔活動的話,每天中等強度刷個十三四個小時一共刷七天就好。那種不停按來縮短待機時間的高強度刷法的話甚至十到十一小時就夠,而且按鍵的位置閉著眼也能摸對,比起CGSS那種活動可謂十分仁慈了吧?

咳咳。

現在你知道為何勞動有價了吧。

Wednesday, 20 September 2023

DDR diary: the BOOSTED mind

How silly was I. Here are the evidences:

June 12 -- passed Bitter Chocolate Strike CSP 2.25x. "Now with the crappy 2nd gen cab I can only do BPM 350 boost."
June 24 -- "I suddenly find BPM360 boost too slow and BPM300 intolerable."
August 30 -- Passed perditus†paradisus CSP 2.75x with an exhilarating 6:1 fast-slow ratio, a score of 550k. Lowest ever passing score.


Early September -- Every play ended up with notes overwhelmingly hit too fast. Change in offset (this is nice to have btw) helps nothing.

What happened?

Well, a closer inspection on the captures reveals the answer that took me too long to figure out: the damn boost is gone when I played perditus†paradisus. I has been using the default option since July till recently, and I played so bad in the period (not over) that I almost give up on playing any further.

In Bitter Chocolate Strike the speed was 2.25x BOOST, an effective speed of ~BPM560, slow but not intolerably slow even in the usual (i.e. good white cab) standard. And perditus†paradisus? Without BOOST would be BPM470 but if boosted would be close to 700, doable on white cab in the past (or rather, very comfortable for these hard songs), but very susceptible on this shitty cab.

Going back to what I said, I felt BPM350 BOOST comfortable in this cab, which is effectively BPM525, so BPM470 is rather slow in such standard. Together with the fact that my brain is so used with the BOOST flow that ended up with the historically low passing score. (Another possibility is that I changed my sneakers and perditus†paradisus was played in the first credit with the new sneakers, but the thickness of the new pair is similar to the old one so I don't think it's too much of a problem. As a contrast it took me months to get used with my last pair of sneakers.)

I finally realized and corrected such error last week and the result is clear. I started getting A+~AA- consistently across warm up levels (i.e. 13-15). So I started experimenting about the optimized setup seriously this time:

- Speed: BOOST is a must, now I say firmly say that. The problem is that I don't bother the extra cost for premium and BPM350 BOOST is too narrow of a range to get without the 0.25x multiplier. I found BPM380 (e.g. 御千手メディテーション or Possession) barely doable and BPM400 BOOST too much.

- Note colors: the sole reason I can't use higher BPM is the existence of unreadable blue arrows, so I really want the note option to minimize that. I tried NOTE again but then the deep blue arrows are simply impossible to read (to the point I almost failed a lv13 just by that and the most recent mystery is how did I passed 18s like Glitch Angel with that). RAINBOW is acceptable but the occasional purple-ish blue notes are still mildly annoying, and VIVID is similar. I will settle with FLAT for now, something I never would have imagined in the past.

To test if it worked I tried Fascination Eternal Love Mix ESP at 1.0x BOOST, which is BPM400 BOOST:


This is not too bad -- on a mild/bad/tiring day I might get similar result on a proper white cab. BPM400 boost is manageable with 1/1 notes at the beginning, but the double steps in the middle starts becoming hard and the last section is very hard to read given the speed and note option. The song is a clear indication the what works and what doesn't. The only thing yet to be verified is whether or not I played perditus†paradisus too nervously that I treated it more like BPM190 and hit notes too fast. To address that I should think about trying 18s again...

Monday, 4 September 2023

古早遊戲BGM巡遊(5): 藏海村

最近我在把我的Youtube收藏清單從頭到尾聽一次,看看我以前都在聽甚麼東西。隨便舉例的話列表上在100、200、300和400位附近的分別是陳慧琳的星期五檔案、四月是你的謊言古典音樂集、beatstream的地方創生☆チクワクティクス和The Best of Brahms。第一千位呢?是One Winged Angel的交響樂版。即使這列表已經累積了十年以上的曲目,有些規律喜好還是始終如一:古典和遊戲音樂。

又比如今天主角,新絕代雙嬌Online的藏海村BGM。


有關新絕代雙嬌/武林同萌傳Online的東西相信我在這裡提過無數次,為何我偏要挑選這首呢?該不會我以為打到藏海村就到此為止了嗎?--這倒沒有,正常小學生再廢再沒時間也能兩三個月內推到這裡。

從個人角度來看,我好像對這種曠野民族風的音樂特別有感?不算Sun of Son也有Babylonia跟喜多郎的Dance Of Sarasvati(也就是尋找他鄉的故事主題曲)。也許是極度適應發達城市的我的情意結?也對啦,在Mt Cook躺在芒草上仰望著星空聽著這類音樂也十分應景。

從遊戲角度來看藏海村玩家擺脫新手期的轉折點,而非九秀山莊。後者雖是第一個新手副本的位置,但說穿了只要穿過Lv.12的樹海就能抵達。這裡只是走出門派據點後的第一個中轉站而已。藏海村呢?你需要穿過三四個難度遞升的地圖,也會接觸到第一張怪物都會主動攻擊玩家的地圖。在重重困難下終於抵達藏海村的玩家可說是完成了遊戲第一個挑戰:學會裝上合適的裝備,在戰鬥中能適時使用技能和補血的玩家,終於不再是新手了。

藏海村是遊戲向玩家展示一個更廣闊世界的要點。這裡是玩家第一次接觸坐騎,第一次接觸副門派,也是三四個支線劇情的開展之處。這裡還是通往大城市成都的最後一個據點,也就是說,藏海村是最後一個新人玩家聚集之處,過了這裡你就要面對五湖四海的妖魔鬼怪了。就是這麼一個地方,怎能教人不印象深刻?

作為武俠風online其BGM當然是古風為主,比如我出身的惡人谷、輕快的水上杭州和悠長的龍虎山等。

但非純古風的關卡BGM也有一堆,比如雲夢湖底會令我想到JR的發車BGM water crown;塞外沙漠的波斯風則令人想起1987倚天屠龍記的熊熊聖火;八門八窟則以現代鼓聲將以笛子為主的旋律帶來強烈的動感。當然還有最輕快的新手流星村啦!

每一首BGM都跟其地區特色相襯,這已經是非常難得了。在台灣這邊實在不容易找到在這方面可以與新絕代相提並論的網遊--把外國一狗票網遊拉進來比的話那當然是另一回事了。甚麼RO、甚麼楓之谷,這我們以後有機會再說…………

Saturday, 19 August 2023

Formal framework of ordinal mate in infinite chess

It's quite rare for me to talk about a particular youtube video on twitter, let alone on this blog. The previous exception is Alan Becker's animation series which makes sense considering the long time nostalgia. But from a creator of 2 videos?



I guess I just can't refuse the combination of chess and maths.

Chess is my recent hobby, entering around the world championship 23'. I don't really play 10 min games on toilet tub like others, but at least I am doing the puzzles every day now rated close to 2000. And needless to say, math is my lifelong hobby (or occupation).

Ordinal is always an abstract idea and often comes with even more with its abstract applications except for the Riemannian hotel I guess. But the above video is quite a concrete realisation of what ω is. 

Let us examine the phrase "mate in ω" carefully. Consider the setup as shown in 3:02 of the video.

First, is it a mate-in-X? Yes, one side has a winning strategy in finite moves no matter what, and it's not a draw. Yes, finite moves -- this is the most fascinating concept in the whole thing, where you can create an ω with apparently finite stuffs. 

Next we would like to find X. Clearly X is larger than any natural numbers given those infinite board setups, so ω is a potential candidate. Is it ω+1, ω+2 or any aω+b? This is the first tricky bit in the whole argument. The steps we need to checkmate is a cardinal, a number. The cardinality of those infiniteness is are equal (cue Hilbert here), so we can't really say this is ω+1 and that is ω because that setup takes 1 more steps to checkmate.

Below is the framework I would suggest:

Definition 1. A setup is Mω (mate in ω) if each possible opponent move results in a mate in k where k is a positive integer, but the supremum of such k's does not exist in natural numbers.

The extension of the clock to ordinals is simply a min-max thing. For example let us think about the finite case so that we can extend it to the transfinite one. What does it mean by a setup of M6? That means for each opponent move the best you can move is to keep it at most M5 (with is at least one opponent move that makes it M5). Now in the transfinite case it would be the following:

Definition 2. A setup is Mγ if there is a corresponding self move for every opponent move such that the best self move results in a mate number γ' that is less than γ, and that supremum of all such (γ'+1) is γ.

Together with the fact that a setup has a mating clock only if the game can be won finitely, the above covers all setups with a clock by transfinite induction (unless you doesn't believe in ZFC...).

Theorem. The mating clock as in Definition 2 is well-defined for all setup that is winning. In other words, any setup is either a draw or a mate for either side.

Proof: Suppose not. Then there is a setup that is not a draw but without a mating clock. By Definition 2 that setup has an opponent move that no self move would render a new setup with well-defined mating clock. That creates an infinite descent, contradicting the fact that a winning setup is finite.

Ok we are now done with the abstract bullshit. What's more important is whether the definition fits the intuition? Like how we judge the clock in the video? The answer is a clear yes. When the clock is of non-zero constant term, the opponent's move is just a regular one: the best your opponent can do is to retain the clock. But when the clock value is a limit ordinal (with no predecessor), it is then the time for the opponent to make the 'announcement' -- which drops the limit ordinal to something lower. 

A Mω setup is clearly what we would expect intuitively: the opponent move is the announcement of Mk for k being finite.

A M(ω+1) is the setup that is one move away from Mω. The best the opponent can do is a move that keeps the board at M(ω+1) so that the self move would turn it to Mω.

A M(2ω) setup is where the opponent makes the announcement to turn it to M(ω+k) before it renders down to Mω, then to Mk.

And M(ω^2)? It is where the opponent makes the announcement to turn it into M(aω+b) (note that ω^2 is the supremum of all aω as well as of all aω+b). It's straightforward to verify that the setup at 6:58 exactly does that.

There is a separate problem though. Is there really a setup with mating clock Mγ for every γ? There are setups that are Mω and M(ω^2) respectively. Adding a constant is straightforward. How about M(2ω)? That is easy: add another double column of pawns from the example of Mω on 5:24. 

Before even thinking about larger ordinals common seen in logic problems like $\varepsilon _0$, the video already addressed that M(ω^3) is a problem. Is that so? My guess is that it's probably the case due to planarity (or that the chess board is 2-dimensional) and the fact that chess pieces can only move in a finite set of inclination (45 degrees for bishop, 90 for rook, and 63.4 for knights). Even if M(ω^3) is possible, there should be a concrete value k so that setup of M(ω^k) does not exist, for some small k like 4 or 5.

When I first tried to create the framework for the clock I made multiple approaches to the problem. How do we define the clock value? Mω is always obvious, but the intuition is a definition that identifies M(2ω) and M(ω^2) clearly.

I have thought of measuring the asymptotic of possible mating sequences, before realizing that one may put infinitely many garbage to disrupt the mating sequence. In that way we cannot get the constant coefficient right too, but the constant should be clear defined just like above -- regular move required before the ω-announcement. 

At the end the framework is so simple and elegant. What's more surprising is how close is it to how ordinals are built canonically. In other words, the way the mating clock is built in the exactly same way as how ordinals are constructed. How can you not love this analogy?

*

Before we conclude for today I just want to say the comment section is also treasury. Allow me to pick a few:

- Never realized how important the 50 moves rule is
- I want to flip the board but I can't on an infinite board
- Mathematicians finding how an infinite hotel ran out of rooms but here we are finding how a rook on infinite board ran out of checks

But the most interesting one is the one asking if we have an algorithm finding these ordinal mating value? Thinking again that we can put infinitely many garbage around I don't really have much hope...it should barely be on the horizon of being decidable if not undecidable (just my guess). Of course, another comment ask if infinite chess simulates logic gates as well. In that case, well, the halting problem will be what decides the complexity of this question.

Update (2024/1): they actually made a new video showing examples of M(ω^3) and M(ω^4)! They even claimed that M(ω^ω) or anything countably higher is possible! The examples are convincing, but the other claim requires some extra thoughts...

Tuesday, 8 August 2023

夢.十夜 (X6) Fair

晚上八時,香港會展。

又一年的書展在剛結束,大夥們一陣衝鋒陷陣,總算是把東西都裝到運貨板上。三小時前還好好的展場裡現在只剩滿地的紙和紙皮,少年終於被獲准放行。就算在吹冷氣的空間裡面,經過一陣勞動的少年已經氣喘吁吁,身上的襯衫也已被染濕。誰叫他習慣在十五度的天氣下也這樣穿呢。這裡的夏天--不、看溫度的話從三月他就開始該喊熱了--對他來說每一刻都是個折磨。那個該死的濕度每次都讓他不由自主地想到那首不知道在唱甚麼的<<相對濕度>>:

♪~一點一點增加濕度 滴汗是特別訊號
 很心急想找出路 但是並未做到
 似聽到看到海嘯 不需三秒便由旱土 改變做瀑布

從三樓下去一樓的電梯就在那面巨型天幕玻璃旁邊,從這裡可以看到整個維港西面。會展身處港島的突出部,這個角度剛好可以同時看見左邊的中環沿岸和右邊尖沙嘴海港城一帶,當然還有正面的海中心。甚麼摩天輪、甚麼中環海濱長廊,在他看來風景還不如這裡。

一樓跟三樓一樣,充滿了推著起重推車來來往往的工人們。誰也沒留意到電梯和大玻璃之間站著個少女,束腰洋裝打扮的她比數年前更具魅力。此刻的她正玩著手機,完全沒注意到少年從她背後的電梯緩緩下降。發現少女的他趕快把額汗的瀑布擦掉順便拉一下身上的恤衫,打算繞到另一邊穿過電梯正下方從暗角處出現給她一個驚喜。

♪~あゝ 君よ
星となりて愚かしきを憂うのだろう--

鈴聲不合時宜地從少年的手機響起。手機被他調到震動模式,唯獨起床鬧鐘和少女來電都會響起這一首La prière的君よ。本來只是因為開頭的漸進音階作成鬧鐘鈴聲應該不錯,後來又覺得藍月なくる那個穿透的聲線十分醒神,聽著聽著就成了他的指定鈴聲。至於因為少女來電而響起這首歌,在這部手機上是第一次。

電梯下方的少年探出頭來,少女已笑吟吟地望著他。

「妳今天就像後面的兩岸景色一樣美麗。」

「我該讚你跟以前一樣有趣嗎?」

「換個字眼比較好,風度翩翩甚麼的我都接受哦。」

「你看你現在滿身大汗的樣子還說甚麼甚麼風度。」少女掩嘴而笑,他也只能尷尬一笑回應:「先休息一下吧,我在這裡根本沒有人理會安全得很。」

「嗯。」他跟少女一樣背靠電梯看著外面的景色。金紫荊廣場還是充滿著遊客,但是再往外看總感覺兩岸的燈飾變少了。是環保問題嗎?還是現在不需要用這種傳統方式打廣告?

「我想要的書都買到了嗎?」少女忽然發聲。

「嗯。」他卸下背包拿出好幾本書來:「你要的簽名版我都拿到了,本來沒簽名的我也要到簽名了。」

少女接過貓封面的小說第一時間掀開封面,發現的確是簽名後滿意問道:「那你有機會跟他們聊天嗎?」

「很可惜沒有呢。我當時在對面的攤檔拿著一本George Orwell的Why I write中譯本一邊看一邊偷瞄作者到底有空了沒,一直到纏住作者的粉絲都離開再等作者回去休息室喝了口水出來我才撲過去找他,沒想到不到三五分鐘又有讀者找上門來了。只能說他的粉絲累積得越來越多了啊。」

「Why I Write你也看?不愧是Orwell的粉絲。不過這種東西回家看就好了嘛。」

「Why I Write其實很短,中文版還收錄了他幾篇其他散文。我看到裡面有政治與英語[Politics and the English Language]才打開來看的。機會難得,我想看看中文版怎樣翻譯那些例句。」

「嗯~」少女對歐威爾明顯不感興趣:「難得有機會跟作者聊天卻被其他讀者打斷,你該不會站在那邊等下去吧。」

「才沒有。我的行程緊湊得很還要去找一堆只在最後一天現身的人,只能後約他們吃飯了吧?到時你還有哪本想要簽名一併給我。」

她揮舞著手上略舊橙色封面的小說:「不用了,簽名就是要在特別的時空才有紀念價值嘛。說起來,」她又指著她身下夾在她和電梯中間的大紙袋:「這是慰勞你的。」

他早就瞄到那袋東西,紙袋上的品牌很明顯不是來自出版商,也不會是補習班、教育軟件、宗教團體、文具商、棋院……等會理所當然出現在書展的公司。但他還是決定裝傻:「不會是鋼筆墨水吧?我有看到他們大減價,但日元貶這麼多算起來還是不划算,而且自從我改由網上改卷以後就沒怎樣用鋼筆了……」

「笨蛋,那有人用這麼大一個紙袋裝墨水的。」她從紙袋中抽出一小袋東西,那是一袋炸雞皮:「是上面的零食展啦。」

到這裡少年才猛然想起其實五樓其實另外有個零食展同時進行,說不定不少進場客都是為了零食才進來。說來也是,以前能擺滿一三五七四個展館的書展現在兩個都擺不滿,今時今日還有誰要讀書呢?只有他是個例外,幾天都抽不出時間上去看。

他接過那一包炸雞皮,包裝上的雞皮跟某上校炸雞的雞皮很像:「不會要在這裡打開來吃吧?可是出去的話外面太熱我一刻都不想待呢。」其實聽說為了遷就零食展,那個長久以來不准外帶飲食的規矩放鬆了一點。

她直接從紙袋裡抽出另一包炸雞皮打開,算是對少年問題的回應。

咔嚓咔嚓。雞皮香脆,但是雞油香味不足,像一塊比較厚的炸粉。二人就這樣看著窗外的維港景色把手上的零食消滅掉。電梯後面運輸工人們的聲音沒有停過,誰也沒空理會這對吃炸物發出嚴重噪音的狗男女。

「你在偷笑甚麼?」少女突然轉過去問他。

「沒……只是在回味這幾天下來各種互動而已。感覺掛上了參展者的牌子就像RPG裡換了個職業一樣,跟NPC的對話都會變得不同呢。出書的成本、找靈感的玄學……實在太多新東西了。」

他開始把不同作者的話題逐個介紹,反正手上還有零食她也樂得一邊吃一邊聽。不過吃到一半她的喉嚨就開始在抗議,她有預感今晚非來點涼茶不可了。

「對了,我記得亞士厘道有間不錯的日式餐廳。我們要不要去試試?」少年的邀請把她從夏枯草還是廿四味的訣擇中拉了回來。

「好啊。坐地鐵去?」她從紙袋裡拿出個膠袋把二人剩下的炸雞皮塞回去,然後拿出消毒紙巾一人一張。膠袋是買罐裝咖啡時拿的,現在要收一塊。

少年露出厭惡神色:「會展站是近但兩層單面的設計太糟糕了,人流的動線和指示都沒規劃好。我都不只一次不小心坐錯方向直接過海到紅磡。而且去尖沙嘴的話要到金鐘站轉車怎樣想都很奇怪。」

「那就只能……」

「船。」提到天星小輪時他的表情跟提到會展站時完全相反:「晚上吹吹海風會涼快一點,地理上也方便很多。」

對他來說,坐船其實是每年逛展不可或缺的一部分。提著戰利品站在圍欄旁邊,那短短十分鐘(大概沒有)的路程裡總是能反思到甚麼。又或者更直接地他只是想在船上輕唱一曲而已:

♪~夜渡欄河再倚 北風我迎頭再遇
動盪如這海 城在兩岸凝神對視

七月的香港當然沒甚麼寒冷的北風。可是在彼岸的家那邊,現在可是冬天啊。

*

旅居生活點滴,重返十幾年沒去過的活動意義重大。感謝所有抽空跟我說過話的人。

上面沒提過但我覺得最有趣的一件事是我買了某書的重制版,回家想想把這書的原版(~2009)翻出來時卻找到一模一樣的重制版--原來這本書在2018重制時我已托人買了一本,這次買的是重制版二刷。這本書又是哪本呢?在這個博客上找2018書展前後的帖文不難找到。

這次特別挑了幾首背景時空完全不同的樂曲。但其實我看見兩岸燈火的時候想唱的是這一首:

♪~幸せ幸せよ 嬉しい気持ちが止まらない
雨よ雨よもっと降れ
早く建てよ私のため
建てよ 進め 高い塔を
建てよ 進め 高い塔を--

2023.8.8
快將熱死之人

Thursday, 27 July 2023

Enshittification of Reddit round 3: the place

We know from insiders and outsiders that Reddit management has always been a mess. But it's not necessary that every single move they make is stupid.

r/place is definitely a great idea on their perspective. Not well executed but also not bad, even pretty good in fact considering their standard in the beginning of the blackout. 

Reddit has been quite successful with their April fools. Some of the better recent ones are the button (2015), the imposter (2020), the second (2021 which I found it interesting mathematically), and of course the place (2017, 2022).

Both April fools r/place were a successful snapshot of various community hanging around Reddit. The 2022 one were welcomed and even more successful with the extended canvas got properly filled with daily active user pushed to the peak. Some may say this is such a successful event and as internet trend changes so fast these days it makes sense to make that an annual event right?

I think u/spez thought so, at least after all the attempts he tried to fought against those uncooperative mods. 

r/place was relaunched a few days ago without any warning with the tagline "right place, wrong time". Nice slogan, but people won't forget what was taken away by Spez. Many protest words were put on the canvas in multiple languages, and the most impressive one is probably the guillotine on reddit head marked spez, on a fitting French flag. This is just part of the story, though.

I lost interest after day 1, but a few conclusions hold throughout in my opinion. Let us go through one by one.

1) Dropping activity

The management may have wanted to take this as an advertisement on how attractive Reddit has been that within a single call everyone would be back. Sorry that didn't happen.

In the 2022 event, 160 millions pixels were placed in 3.5 days, but looking at the official count this year  numbers aren't even close, and this is before taking bots into account.

There is now a site that tracks Reddit activity including new post and comment counts, subs status and so on(which I forgot the website). Number wise the post and comment count remained largely unchanged since the blackout, but the owner of the site also warned that such statistics is deceptive as most posts and comments are in fact, meaningless trash in funky awkward subs. Services monitoring network flow shows that Reddit's receiving less attention since the blackout, and the ad-spaces are now filled with Reddit's own promotion. But we will never know these numbers accurately, and Reddit will always neglect such claims.

And now r/place has put things under sunlight, and it becomes the latest stone cold proof that this site is in fact not in a proper state.

2) Dwindling communities

Together with the dropping pixel count (and probably true participating user count) is the dropping of smaller communities. After the blackouts many subs were forced to reopen/unprivate/un-nsfw and so on. Some ended up archived, some had their mods replaced with the sub losing steam, some decided to let weeds grow on the sub, and some decided to move the whole community away (to lemmy or discord).

This is clearly seen on the earlier days of r/place 2023 when the number of participating niche communities is low. It only improved in later days with bigger canvas, where large communities locked their piece of land and started to help smaller communities as well as opening colour block for others to use.

Looking at Reddark, almost 2000 out of ~9000 subs are still private, and some are still John Oliver'd. If you were an investor of the Reddit IPO would you be convinced about Reddit's latest attempt of redemption?

3) Flags

National flags are always a big part of the canvas in 2017 and 2022, but this time it's even more obvious. It's not surprising that Germany, the US and France are top 3 on the global leader board considering how fast Germany and France are taking over new territories (insert WWII memes here). Turkey took fourth place, but they only managed to make a single proper flag (or a few) perhaps because a moon and a star are damn hard to draw. Canada, placed tenth, will absolutely agree(but credits to them coz they made a proper flag at the end). 

Why did flags flourish even more this time? A clear reason is that with less communities around, national identity does the best to bind users together.

4) Large ambitious communities are prepared

Together with nationalists are members of a few large non-reddit based communities (i.e. with a theme of an external entity which is well run so that the fondness is not affected by the blackout), they are prepared to make the best out of r/place whenever it's coming. 2023 July is an unexpected time, but they easily powered up the machine and dominated the canvas.

Germany has a discord server coordinating over 40k users, France are more or less similar. Osu! and Touhou fans are...simply everywhere like Finland snipers. The latter even collaborated to make a bad apple animation over the course. To accomplish that undisrupted requires tremendous effort and manpower needless to say.

But something is quite worrying about that if r/place are to be held again anytime in the future. If these communities decides to play in their own terms, are there any survival space for the rest?

When people realized team effort is overwhelming over a game they eventually team up to optimize to the point where individual effort are insignificant and the game is not fun anymore. It happens over and over again not only in r/place -- it's also in gacha games where you see those Chinese "workshops" dominates the game is simply depressing but this is a topic for another 10000 words of discussion (in fact my novel is a partial dedication to this phenomenon).

Oh and as usual there are communities unrelated to reddit trying to leave their mark on the canvas as well. Some random twitch streamers, I reckon.

5) Bots

While large communities are mostly actual active users (claimed to be, although some participants are there using bots too), bot activity is a big part of the game. The most obvious one is the 1337 building right next to Osu! which arrogantly occupied the space, "issuing warning" to anyone who wanted to fight back and highly synchronized and coordinated to the point that is impossible to be human controlled.

Reddit admin claimed that they wanted to fight bots but they refused to take action "because it's hard to distinguish between bots and highly coordinated humans". What?

Yeah you can say that they have accounts created way back in 2017 and 2022. You can say that they can farm pointless posts, comments and Karmas as well. But What about accounts created just these days then? Can you add restriction based on actual activity because not every bot account do the karma farming? Can you restrict API access like you did to the third party apps? Captcha before pixels?Bots can always squeeze through the leaks but the more obstacles you set the less effective they would be.

But Reddit did none of that and let bots do whatever they wanted to. All of that going to the fake number of traffic that would look good for their IPO. But again, such number is pure garbage if you know what's behind.

Reddit admin isn't completely wrong though. Bots are increasingly human-like behaviorally on the Internet. Captcha challenges isn't a challenge for them anymore (instead the system catches bot on other background information). The imposter event further confirms the evolution of bots. Many are in fact quite pessimistic on whether Internet would be a useful place in the future when you are not even interacting with humans. I definitely don't want to see measures like Google's plan to DRM our browsers though.

6) Censorship

Interestingly I thought this is somewhat expected even in 2017 and 2022 but did not become an issue. A probable reason is that more communities means that the canvas is more fragmented, leaving smaller room for that. To be honest finding inappropriate drawings is pretty normal for Reddit as a whole. 

I am fine taking NSFW as a no on this event considering r/place to be a place for all. Although that does not explain some of the most controversial censoring like Ronaldo's piss and Spez's guillotine. The way they censored those problematic figures are also partly why it looked bad when you have a blob of random pixels with no username suddenly splashed on the target.

If you need to censor things please do it in a more low-key way next time, but if there is a next time and of course the best is to let the communities to sort it out...

*

Reddit is not dead, yet. 

There are still a number of active users and communities around. The end product still shows a wide variety of cultures on it. It surely will be an important snapshot to look at when we wonder what the Internet looked like back in 2023.

But that does not change the fact that Reddit is going down the hill one step at a time, behind all those shiny (not really...just merely satisfactory?) fake numbers. Everything going just as the enshittification cycle and we will know the fate of Reddit in coming years.

Also, a big f to spez :).

Friday, 21 July 2023

IMO 2023 quick thoughts

Ok the yearly event to review, IMO 2023. This time it was in Japan, hosted exactly at where comiket is held. This is kind of strange huh?

Q1. Many different approach towards the right idea. My first thought is that prime powers certainly works. Then the next simplest type of numbers to check is of the form $pq$ which...immediately fails with very simple numbers like 6 and 15. When going for 30, the product of 3 distinct primes, you quickly realizes where the problem is, then question solved.

I'm quite shocked by how easy this is due to how approachable the idea is. Here is the approach taken by most as on AoPS: observe that $d_{n-2}|d_n$ to force a chain of divisibility. It is also easy because how easy is it to check the examples and counterexamples, starting from small integers. The question gets an average score of almost 6 (5.85) shows how easy this is.

Q2. Okay geometry...so I am not going to act like smart ass and solve. But frankly this is possibly one of the few geometry questions that I can actually solve at this level. There are too many parallel and perpendicular lines, trivializing angle and similar angle tracing. The extra triangle to construct is also pretty straightforward.

Q3. Very nice looking question. FToA strikes when it comes to solution of polynomials (just like the Vandermonde matrix), so you get ideas of recurring sequence (this is already non-trivial). Solution can proceed from here, details not discussed. After all this is quite a respectable Q3.

Q4. Yes finally, inequality is back! Also not in the traditional way with difficulty stacked because you guys can do AM-GM pretty easily with 3 terms but not with 2022+n terms.

The idea is obvious here. $a_n$ is strictly increasing and also increasing by at least 1 each time. But the number in question is 3034, indicating an increment of 1.5 per term -- or 3 every two terms! It is easy to calculate how much the increment needs to be to achieve an increment of 1, and this is where the pairwise different condition kicks in (which is pretty odd before this step). 

Of course, those inequality gurus already spot the obvious pattern of Cauchy-Schwatz: square roots and reciprocals. This is solvable directly using C-S, or AM-GM, or a combination of two. In overall a suitable and nice looking Q4. 

Q5. Combinatorics question and I skipped, but I saw the word ninja. I saw what you did, Japan ;)

Q6. The moment I saw the condition about 480 degrees and scalene triangles (and it took me some time to realize what's a scalene triangle) I knew immediately this a devilish question. Not only the angle sum condition is absurd, the graph itself is absurd too: $AA_1A_2$ are almost colinear, making the corresponding circumcircle (as well as the other two) incredibly huge. 

The thing I notice is that why two? What happens if we don't have a scalene triangle -- well then the almost colinear points becomes colinear and the problem collapses. From here the radical axis would come to help. Of course, proving two is another difficult thing: you prove one, then prove another, but you also need to prove that the two are distinct. Proving one seems to be the harder part though.

I am of course not qualified to talk about this problem, but quite funny that we find many possible solutions: pure geometry, inversion, coordinate geometry, bary bash and so on. The fact that the problem allows so many solution yet not many solved right (second hardest pure geometry Q6 since 2000), is the beauty of it.

*

The only thing I can say is that geometry is not my cup of tea, but I can feel the beauty of the two questions assigned this year. Yet, I always love to see a Q6 in number theory. The most elegant but lethal problems. 

I am less focused on competitive maths this year, but Simon Marais is again something I will eagerly wait for.

Sunday, 9 July 2023

被青梅竹馬抓來(略) (8):我站的那邊才是正確的一方

Character design: @kuonyuu, Illust: @メリー commissioned by forretrio. Skeb
Editing and re-posting are prohibited // 無断転載、無断使用禁止です

魔法科的課程相當緊湊。

這點光是看入學測試就能略知一二了。每個學科都會設計出對應的測試,報考魔法科以外的科系只需要在該科和魔法能力測試中取得一定成績即可。但報考魔法科的考生要接受所有科系的測試,在每一個非魔法學科都拿到合格加上優異的魔法能力才會被邀請到魔法科的加試裡去。

每一科的測試其實在檢驗考生的基礎能力多於專業知識--學園相信,它有能力把一個有潛力但專業訓練不足的人培育成材。所以測試中只要將基礎能力相關的問題都答對多半就摸到合格線,但這不代表測試裡沒有更艱深的考驗。筆試形式的試卷都很長,在基礎能力相關的問題後面還有一大堆可供作答,越往後試題越難。相對地在考卷裡每進一步對比其他考生都是個巨大優勢。這些問題對魔法科以外的考生來說不重要,但對魔法科考生來說就重要多了。不是每個人都是真正的全能--不如說這要求實在強人所難。所以有個規定是可以將一科的分數折算到不合格的科目上,以這種形式達成全學科合格的要求。

魔法科的加試與前面針對基礎不同,加試旨在找出將其魔法潛力兌換成某種魔法專長的考生。只要是魔法相關的專長都可以,加試以一對一的形式進行,考官是對應專長的魔法科舊生,絕對不會手軟。那些沒有特別專長的考生申報的往往是某種屬性的魔法。正如宮庭魔法師的投票一樣,此類專長往往是最被嚴格審核的那一批。

總而言之,進入魔法科的學生都是大致全能且擁有巨大魔法潛力的人,正是培養成王國下一代精英最佳人選。其他科系的教學都以該科系加上魔法為核心,只有魔法科學生大部分科系都要學一點,再加上比其他科系強度高上許多的魔法教育,課業壓力比其他科系高了一倍不止。你說他們要會一點文科和商業嗎?不少學生將來會繼承領地,這些只是基本功;冒險科呢?先不說不少畢業生會成為冒險者,就算是當領主缺了此類經歷要打仗起來也是事倍功半。

魔法科的學生到了二三年級可以只選修部分其他科系,但一年生只能全部都修一下。同一時間他們花在魔法相關課程的時間也不會少,一年級的魔法課都由庫里斯負責,但到了二三年級時一些專門科目就會交由其他人講授。手握大量課時是他覺得可以大幅改革課綱的原因,也是其他人質疑他計劃的原因:都這麼多東西要教了還想把更多東西塞進去?

不管怎樣,看菜下飯都是最重要的。學生興趣不在此則安排再多也是徙勞。

把艾基爾打發走以後庫里斯繼續批改眼前的作業,這是發給他們探討第二屬性的的第一份作業,正好讓他了解這些學生的想法。

因為是能力全面的學生,每一份寫起來都有模有樣。這種開放式作業比起一般的習題更能反映出學生的個向和習性。那些接受過充分教育的學生,比如說公主殿下,早就知道自己的長處和對應屬性,甚至接受過多屬性的訓練也不意外。他們的回答多半來自小時候接受過的判定,著重於自己如何將兩者配合發揮。一些比較有探究精神的同學比如克萊伊,就做了完整的圖表講解自己自看法。至於那些比較草根的學生回答起來就比較困難:當初他們根本沒有挑選屬性的餘裕,接觸到甚麼就用甚麼了。有接觸過或者換過主修屬性的就老實回答自己試用過後的感覺,但連這種經歷都沒有的學生就只能靠想象了。艾基爾甚麼小法術都能用,比較擅長的是水屬性,但他承認自己更擅長將堪用的法術放到自己的武器庫裡而非打磨單一屬性。如果讓他選一個第二屬性的話會是風屬性。

不少學生選擇了風屬性作為可能的第二屬性,其原因不言而喻。正如布拉德的學生會希望在他身上學會厲害的火魔法一樣,不學點風魔法傍身都不好意思說自己跟著庫里斯混。但很顯然每個學生潛力不同、與風屬性的適性也不同,希望和可以將其變成第二屬性有著頗大的差距。他要做的就是在從這份作業裡找出學生真正的想法並給出適切的建議。

當中一個學生的回答非常特別。他當初的申報屬性是光屬性,在作業中說自己希望鑽研暗屬性作為第二屬性。

學生名字是丹特,背景是來自富商家庭。申報的專長是魔法史,在加試審核中曾出現過爭論這算不算魔法方面的專長。後來在面試中其所表現出對魔法史的理解,尤其理解並模仿現今比較罕見的手法上甚為出色,於是被接納成魔法科學生之一。資料顯示他隨家人四出經商,搜集回來的大量書本成為他打發時間的方法,加上魔法的天賦才成了現在的樣子。

他在作業裡表示自己對兩種看似對立的屬性感到興趣,而且希望透過自己的經驗去捉摸兩種屬性的對立與歷史中這兩種屬性所關連派系的對立之間的關係。他的第一屬性是光,但這並沒有讓他完全使不出暗屬性的法術來,這又是為甚麼呢?

在庫里斯看來這是個成熟得過分的答案,但也是個十分符合丹特專長的答案。但是要為他找個合適的指導者恐怕不恐怕不太容易:該給他找個史學家嗎?還是專長光或暗屬性的專家?顯然兩種屬性都擅長的人在社會中幾乎不存在,因為會同時受到兩個派系的排擠。剛剛因為收到有趣答卷而喜悅的庫里斯又不禁頭痛了起來。

將作業批改好以後他將評語整理一遍,接下來的任務可不能少了這份評語。

*

魔法科專屬教師向來直接向學園長華萊里安負責,他這個菜鳥當然是被最嚴格看管的那一個。聘書上明確地寫上了向學園長定期報告的責任,而今天就是報告的日子。

學園長的辦公室處於圍繞學園中央廣場建築之一的頂樓,與學生會的辦公室隔空對望。學生會那邊他去過一次--他在學園的最後一晚--但學園長的辦公室對他來說是陌生的地方。

只能說不愧是文官系統空降的人物,庫里斯在頂樓沒有看見太多魔法的痕跡,只有一個個文職人員埋首在自己的紙堆裡面工作。其中一員抬頭發現了他,隨即站起來給他帶路。穿過掛滿歷代學園長畫像的走廊,盡頭木門的另一端便是學園長的聖域。職員敲門得到回應後向他點了點頭道:「學園長已經在裡面了,請進去吧。」他點頭致意後推門而入。

華萊里安看上去就是位精明幹練的男性,比庫里斯還要大上十五歲左右。庫里斯可以感覺出他所散發的上位者氣場,與那個在開學派對中作出輕鬆發言的那個學園長完全不同,正是其管理手段的展現。他看上去沒有甚麼特別背景,卻能在貴族氣息濃厚的文官系統中拼殺而出也是其能力的實證。靜韻甚至向他暗示這位學園長就是王室的耳目之一--想想也是,這位置實在太敏感了。

「華萊里安學園長午安。」庫里斯低頭問好。

「庫里斯老師好,請坐吧。」

庫里斯按指示坐下,第一次報告難免有點緊張。定期報告是要報告哪些?對方會在一堆細節上說三道四嗎?還是像個控制狂一樣管著他要教甚麼?

華萊里安顯然看出庫里斯的不安,笑著開口道:「庫里斯老師不用太緊張,你準備了甚麼就講甚麼吧。」

於是他開始作出報告。首先是教學進度:以魔法的本質和適性作為簡介、加上一些概論和方法;本來要在課堂上詳細講的古典元素觀改為指定預習,之後便能快速帶過。接著他將作業的評語整理拿出來,加上自己課外時間接觸學生的經驗而作出對班級整體水平和能力的判斷。他的評價是這批學生是多年來最強的一批,當然他也不忘吹噓班上的公主和幾位高階貴族學生將水準拉高了一截。提到接下來的計劃,在課程以外他提到會跟蓋伊合作進行水準比往年高一點的地下城探索活動。最後他也不忘提起自己的三年大計。這東西早就傳開去了,但他結合自己對班級的粗略認識,認為學生們能應付並從中受益的結論。

華萊里安只是靜靜的聽著,臉上表情和手上的筆一樣沒有動過。在庫里斯講完了以後他將評語整理拿過來認真端詳了一會才開始講話:「不錯,判斷學生的能力作出教學上的調整是老師的本分。」

「但是作為魔法科專屬教師,這還遠遠不夠。」

他看著睜大眼的庫里斯開始說:「我問問你,為甚麼布拉德那老鬼可以這這位置待上這麼久?他可以量產宮庭魔法師和各式火系法師這點跟他是否一定要當魔法科專屬教師並沒有必然關係。真的缺火系法師的話讓他在學園裡專教一個課,再讓他多帶宮庭魔法師學徒就好了。他也不會拉下不臉或者嫌地位變差,光是他那票學生誰敢得罪他?」

「原因很簡單:他總是能站在對的那一邊,他知道對於王國、王室和貴族們來說這個學園的利益在哪裡。這三年對學生來說是在這個縮小版社會裡實踐作為大人所要的社交和政治技巧的機會,是轉成大人以前最重要的階段。但青春期的少年少女年少氣盛很容易出現各種意外,這時候就需要有人替他們擦屁股了。有時是學生會,更多時是老師們,但絕不能是外人。學園內的事學園內解決,這是不成文的規定--傳到外面就是讓家族蒙羞的事情了。在這些事情上布拉德做得相當不錯。作為魔法科專屬教授,他不但負責傳授知識,也負責將利益結構整合到下一世代裡面,這才是布拉德的價值。」

「那為甚麼現在又把他換成白紙一張的你呢?原因也是一樣,但我們這次不需要總是站隊的人。如你所見今年魔法科學生能力好得過分,這個世代好幾位備受矚目的公子千金碰巧都在同一年入學。一個總是會站隊的人和一個白紙一張的人,在立場衝突下誰更能讓大家安心呢?」

「學園長您的意思是我應該……」

「像白紙一張那樣隨他們擺佈?這種人多到數不完也不用麻煩你。從學園裡調一位教師過去不好嗎?你是個聰明人,想想你自己的價值在哪就能明白了。真的不行的話就問別人看看吧。」

「至於你的三年計劃我暫時不會反對,資源上也不是問題。但要不要採用這個計劃,還是按照原本課綱授課對我來說分別不大。你覺得公主殿下這些人會缺專門的指導者嗎?」

庫里斯反駁:「我的確沒能力指點公主殿下的專長,也不覺得我可以找到比王室所能找到更好的指導者。但她是一個例外,其他學生的話我認為學園的確有能力幫上忙才是。」

「也是呢,我聽到的質疑主要是會否影響學業的問題,如果可以證明這一點的話阻力會減少很多。比如說……在接下來的測驗上放上跟以往相若的內容,藉此顯示他們應付學業的能力?地下城探索也是測試學生實戰能力的好機會。」

「我會考慮的。」

華萊里安向後貼著椅背,看起來這次報告已經差不多了:「那就先這樣吧,這次報告是個好的開始。你還有甚麼問題嗎?」

「我可以問一個問題嗎?」

「請說。」

「我在這裡讀書的時候您還沒調任過來,您是兩年前才接過這位置的。可以問一下……您會坐在這裡也是出於一樣的原因嗎?」

他笑道:「也許吧。不過作為學園長特權還是有一點的--在學園裡我站的那一邊就是正確的一邊。明白了嗎?」

「……明白。」

「我期待你的表現。」

*

庫里斯感覺自己腦袋快變成一團漿糊。

布拉德會處理人際關係?那是他從沒聽過的東西。也許自己從來都不在需要幫助之列,包括衝突那一晚。

即使他不怎樣熟悉政治也能感受到華萊里安的確有點手段:一方面他肯定庫里斯的教學,也許諾可以將資源放到三年計劃上;另一方面他不動聲色地將上面的意志投放到庫里斯身上,即使出了甚麼問題也不會追究到他來。文官出身的他就算不太懂這裡的課程也能抓住可以測量的指標--不過以他的能力在學園待上兩年又怎會不清楚魔法科本來在教甚麼呢?

如無意外王室早就知道今年魔法科的特殊性:兩年前安排了心腹空降學園長,今年又把他推上去,這樣的話華萊里安會把上面的意志傳達過來就說得通了。

問題是他今後應該怎樣辦,如果有教學以外的事情要他處理又可以怎辦?現在還沒出現問題大概是一年級生的勢力們仍在掠奪空白的地帶,還不到引起磨擦的時候。又或者以公主為首班級裡已經出現統治階層,可以將事情直接壓下去。但如果這個小圈子不喜歡他呢?他在開學時的確展現了實力,但那跟能否抓住學生的心毫無關係。

他能想到的就兩條路:一是徹底無為而治讓學生們把自己的私事處理掉,二是透過教學取得他們一點點信任看有沒有自己能幫的上的地方……?到時自己想不通就只能找她吧。

對他來說教學才是第一要務,按他理想中風格來的那種。不論是學生們的特殊性、其他教師的質疑還是學園長的壓力都不能妨礙他將自己所知所想的傳承下去……一定。

教師宿舍當然配有員工餐廳,但庫里斯今天已經不想再跟別人交流,所以便著管家將晚餐送過來。

「庫里斯大人,我們收到一封給你的信件。」管家將晚餐從餐車放到餐桌時順便遞上信件。他道謝並接過信件,待管家退出房間後便把它拆開。

這封信是一個商業推銷……或者說一個邀請。

=============

相當簡短的一章,有時這樣也不錯。

其實我一直都沒留意到火紋風花雪月貝老師的來歷跟庫里斯如此的像。要說我開這本故事有受到那遊戲的影響嗎?很難說,說不定有。

進一步看風花雪月的話下一個問題就是,貝老師有甚麼可以教這堆學生的呢(此處不可色色)?用數據看的話我們的主角各種熟練度都和學生們沒兩樣……按現實的話就是一個實戰很強的二十歲傭兵但似乎只有純戰鬥經驗,似乎也沒有太多可以教的。看無雙裡面貝老師比較沒那麼無嘴,會多講一點自己的過去,不過距離一個全面的教師也還有一大段距離(當然另外那對夫妻檔(?)也沒好到哪裡去)。當然打通遊戲的話答案大家都知道:「是愛啊、哈利」(Love, Harry. Love)。

那麼撇除華庫里安(及其上面的旨意)所提到的因素,庫里斯又有甚麼可以教他的學生呢?就明面上的資料至少他受過前一年多的學園教育而且應該相當出色,所以至少應付一年級的課程毫無問題。再往上他只需要專教一部分課程就好,考慮到其實戰鬥經驗和元素專長這點也問題不大。最最最重要的是他可是比貝老師年長一大截,這都是累積經驗的重要時期啊……如果他當年已經可以強到在校內鬧出大風波,現在又可以進化到哪個程度呢?這方面就敬請期待了。

這次附上的委託繪圖一張是來自ashi老師。當時我發了一堆以月光和辦公室為題的委託,出來的效果都差不多是這樣。我想主要是我自己對那個辦公室的想像有了定式,所以看見別人的想像與自己不符所以有落差?當然另一個問題是要畫出那種精細度肯定要加錢就是(心虛)。另一張來自miliL老師,非常有動感的施法動作!學生眼中的他大概就是這樣子的吧。

Character design: @kuonyuu, Illust: @miliL commissioned by forretrio. Pixiv
Editing and re-posting are prohibited // 無断転載、無断使用禁止です