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
Why do I feel like I have read this somewhere before...
Is this a prequel to this series? -> http://vatoto.com/comic/_/comics/suugaku-girl-r1550
GODDAMN MOE CHARA FORCES TO READ THIS.
yeah... i hate math.. but moe.. moe.. moe
Thanks for the clarification about the list of systems, that's my oversight.
The Liar paradox was the one cited by the author, I agree that "system doesn't prove its own consistency" is more relevant, but I think that's too relevant in that it's actually one of the theorems.
1+2=3 is an example of a conclusion from axioms (you do indeed also need 0+0=0, a + b* = (a+* and a* + b = (a+* or something similar), that's the only purpose it's serving there.
I agree; I think we also need s(n+1) = s(n) + 1 to prove this.
I also hope that this manga covers the second inconsistence theorem too, which I personally find a far more interesting result
Sure enough I'm not completely satisfied by the author explanation at the end of the chapter; I know I am nitpicking, and explaining fully probably can't be done in a single page (and withouth equations) but I sure hope he explains more carefully in the next chapters...
To start Gödel incompleteness speaks about first order predicate logic (as I understand it).
The list of axioms need not be finite, but recursive.
The example 1+2=3 is probably nonsense (need more axioms).
But more troubling, the liar paradox is more related to tarski undefinability of truth, than Gödel's incompleteness.
I closer analogy is the statement "this system is consistent" which runs into a different paradox (you may have heard of the story of a teacher announcing he will give a surprise exam in the week,
it cannot be the friday because by then it would not be a surprise, but then it cannot be on thursday, etc. I heard of this analogy from terrence tao's blog, which I recommend).
Ok.
I'm not a mathematical logician, but I know a bit of mathematical logic.
This is a pretty popular subject for nontechnical exposition, and I haven't read chapter 0 yet (I hope that is an easter egg, starting at 0, probably not though), anyway I am a bit skeptical, this is also a subject that is very easy to misrepresent...
So, here is to hoping.
How come? As a mathematical logician, I assure you the mathematics will be sound.
And yeah there's not much to chapter 0. I trust we'll get to the fun in due course.
this offends me >:C
Its sequel of sugaku girl?
but i like artist in sugaku girl
It might turn out neat, though the initial chapter was pretty thin. I'll stick with it for a bit longer and see if it catches my interest.
This might be promising - depending on how the author does his math...
Though... Gödel... they've chosen one hell of a subject.
To conclude I will add one of my favourite quotes as it came to mind when reading the first chapter:
"The book of nature is written in the language of mathematics" - Galileo Galilei (The Assayer)
So this is where Love transcends all, even Math.
Oh yeah, I'm a match teacher so..
yeah !