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Mathematical Girls - Gödel's Incompleteness Theorems
| Alt Names: |  Mathematical Girls: Gödel's Incompleteness Theorems Suugaku Girl - Godel no Fukanzensei Teiri 数学少女-哥德尔不完备定理 数学ガール ゲーデルの不完全性定理 |
| Author: | Yuuki Hiroshi |
| Artist: | Matsuzaki Miyuki |
| Genres: |  Harem Romance School Life |
| Type: | Manga (Japanese) |
| Status: | Complete |
| Description: | "I" (Boku) love mathematics. Just after the high school entrance ceremony, "I" meet a beautiful girl: Miruka. Miruka is a mathematical genius. She gives me many math problems; she shows me many elegant solutions. Miruka and I spend a long time discussing math in the school library. One year later, I meet another mathematical girl: Tetra. Tetra is one year younger than me, and asks me to teach her math. While I teach her, she begins to understand math and to love its elegance gradually. In this third volume (series), we talk about logic puzzles, Peano arithmetic, epsilon-delta, Cantor's diagonal argument, Hilbert's program and Gödel's Incompleteness Theorems. Sequel of http://bato.to/comic/_/comics/suugaku-girl-r1550 |
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113 Comments
I hope they talk about conditional probability because it takes a long time for me to wrap my head around it
I wouldn't say bashing numbers on a calculator and solving numerical integrals/classical physics probs all day is fun
Its not bullshit because the Game or puzzle isnt designed to be competition.
this is a variant upon a prisoner's hat puzzle, where the prisoners were given a problem and if any one of them can solve with the information present, the WHOLE group goes free but if anyone got wrong then the WHOLE group is punished, so there is no incentive for the prisoners to fight or guess but actually to coperate.
The goal of the puzzle then is not to say who will solve it first, but logically whehter it is possible for the group to derive information from other members given the constraints and arrive at a solution to the puzzle, so the question is really more :"is it possible for the group to solve the puzzle?"
This is Game theory, where u really have to layout carefully the conditions of the game to logically arrive at a conclusion, which makes it very mathemathical. Its a model so if the assumptions are unrealistic thats not a problem since u can adjust the model with different assumpstions and get those outcomes.
It's exactly not a psychological question because they're NOT trying to screw each other over. This is a cooperative game, and there are certainly variants with lives on the line involving prisoners communicating limited bits of information until together they discover information that was not available to any of them previously. They're fighting the male character, not each other.
There are also variants of these information games with countably many people in one or both directions (or even transfinitely). You're the one trying to find psychology where there is no room for such nonsense.
Do you know the theory of Goedel coding? We can start from there.
Not true. That's when the real fun begins.
This series is some kind of beautiful fantasy.
I found most explanations here somewhat over the top. The comic strip was spot on, though. The key phrase was:
I can't say I agree with that. I know high school program varies wildly across countries, but math for common courses where I live include only calculations involving numbers through all areas without calculus. No abstract algebra, no logic, no theorem proving. So, so, so boring.
I don't know the specifics of the argumentation of Godel's and Tarski's theorems so I hope this series will shed some light on the most heartbreaking theorem of Math. That's the closest to drama it will ever get.
There's a joke based on this type of logic problem (and it's easier to understand):
This logic problem typically assumes that all the participants are perfect logicians and that they all know this; that's the only reason why someone answering "I don't know" tells you anything. If the participants acted like normal people, then it would fall apart, as you pointed out. Here not everyone was a perfect logician, but it worked out because the math girl (who is) went second.
Right, anyone still mystified, let me try to explain.
Person one sees 2 bunny ears. She can't definitely say her own ears are bunny or cat because of it. So she says "I don't know."
Person two sees 2 bunny ears and knows person one said "I don't know." Now then, IF she saw person three having cat ears, then she knows that she herself has bunny ears because that's the only way "I don't know" can come from person one along with cat ears on person three. But she sees bunny ears so she doesn't know for sure if her own ears are cat or bunny.
Person three then has all the above info. She knows that if person two saw cat ears on her, she would be able to answer. But person two did not see cat ears on her. Ergo, she knows she's a bunny. That's the only way 2 "I don't knows" can occur.
Well here's my quick explanation of this.
"Stepped on a cat" OHGOD IT IS ALL COMING BACK TO ME...
To anyone who doesn't know the reference, it is quite a simple song that is easy to play on a piano:
https://www.youtube.com/watch?v=ggREiS1JMxc
me reading this when the math involved
maid: Math is fun, teach us more!
yeah, enjoy the math while it is still fun. once u graduate from highschool, u also graduate from fun math
It's not bullshit. The solution applies to the 3 person case exactly and is not meant to be general. They are each trying to give the most accurate answer based on the information they have and are not in competition with each other, so there is no incentive to lie, pass or guess. This isn't Liar Game.
The point as others have said is that the last person to answer can use the fact that the others could not answer to deduce her ears, which is pretty surprising.
The logic is that its a bullshit question.
1. It assumes there are multiple participants in the first place. (If theres only 1 participant, the whole test is just a random guessing game since you don't get any "hints")
2. The rules/conditions are bullshit. (By simply seeing 2 bunny ears on the other participants heads, the -best- answer would have been to guess cat ears since doing so would have a 2-1 chance of being right.)
2b. But since they can all say "Pass" (so to speak) it turns into a psych/mental game, which is further bullshit since they're all on the same wavelength and aren't trying to screw each other over. (If a group of Chess players agree to always force a stalemate against each other; they aren't genius Chessmasters , they're just cheating the game/system.)
3. It assumes said participants don't/won't guess. (If anyone randomly guessed in the first round, the whole quiz would have exploded in their faces)
The quiz isn't really a math question at all, its a psych question. If there was money or (because this is a manga) their LIVES on the line (dundundun!), the quiz would have been about them trying to screw each other over.
Im gonna try as best i can as im not very good at laying these things out
hope that helps
Let's have 3 people whose name are Cindy, Wendy and John. Let's have each of them guess what ears they are wearing.
1. Let's have Cindy answer first: she looks at Wendy and John. Then she says that ''I don't know.'', from that John and Wendy can deduct that they aren't both wearing cat ears, because if they both had cat ears on them, then Cindy would have known that she is wearing bunny ears as there are only 2 cat ears in the box. That means that there is at least 1 bunny ears on either Wendy or John. The choices would be that 1 bunny ear and 1 cat ear OR 2 bunny ears.
2. Then let's have Wendy answer second. She looks at John and answers ''I don't know.''. If John had cat ears, Wendy would have immediately known that she had bunny ears, because there can't be 2 cat ears on both of them. Because Wendy said that she didn't know, that must have meant that John had bunny ears, because if he had cat ears, Wendy would have known the answer.
The point of the quiz is that unless the first person to answer knows absolutely what he/she is wearing based from observing the other two, only the last person to answer the quiz can make a logical deduction based on the answers of those who answered before ^^
The unstated part of the question is that you are not allowed to be wrong when answering, and the sequential answering method also creates another layer. Person A opens eyes and sees two bunnies, so remaining is two kittens and a bunny ergo not a 100% correct guess. Person B is in the same boat, only having the fact that person A couldn't answer as an added clue. From C's standpoint, seeing two bunnies and knowing that A & B couldn't answer, they can answer bunny because if they had kitten B could have answered bunny once she saw C with kitten and A with no answer.
It's roughly something like that.
Okay, i need someone to explain me the logic behind the answer to the quiz, lol
If i remember correctly author of this series (and the rest of suugaku girl) is also author of math books. I hope he won't stupidify those topics too much.
Ooooh, the sequel to Suugaku girl! Thanks scanlators!
It's a sequel to the sequel of that series. When we started doing it we only had raws for this, hence we picked this up. If we're still interested after finishing this series we might do the first sequel.
Blindly followed.
The day the word "mathematics" appears in a manga's title...