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Kindergarten Quantum Mechanics

arxiv.org

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Re: Kindergarten Quantum Mechanics

#21

Post by anonytrary »

Fishysoup wrote: post #12
themonoid wrote: post #10

Earlier quoted context omitted.

Just in case you are serious about having a messiah complex, I am prone to having a messiah complex, thanks to schizoaffective disorder. It took me a while to figure out which medications actually help me, without too many unpleasant side effects, but I am very grateful to have discovered the cocktail that works for me now.

i'm glad to hear you've found something that helps you. I was joking about the messiah complex, though it is something my therapist has made the occasional joke about too when i get over-ambitious about things i wanna do (he did specify i don't seem to actually have it, though - just good old-fashioned depression).

> just good old-fashioned depression

So you're normal (half joking). Humor is a good medication for depression, and at least you can joke about it.

Re: Kindergarten Quantum Mechanics

#22

Post by GoblinSlayer »

T-A wrote: post #20
minkowski wrote: post #17

Earlier quoted context omitted.

This is rather uncharitable. Category theory is an essential part of the vocabulary of 20th-century mathematics. Large swaths of algebra, topology, geometry, and logic are fairly inextricably formulated in this language. Similarly, it seems irreplaceable for certain parts of programming language theory (arguably due to its connection to mathematical logic). There's certainly a community trying to bring a category-the…

I think parent meant big wins in physics, where the search started well over a decade ago. See e.g. the dates of the references here: https://en.wikipedia.org/wiki/Categorical_quantum_mechanics#...

QM is just linear algebra, no need to turn it into Haskell.

Re: Kindergarten Quantum Mechanics

#23

Post by tokai »

supernova87a wrote: post #14

Kindergarten? They just took bra/kets, Feynman diagrams and substituted block-looking shapes. The underlying logic is hardly changed to kindergarten level. The kid better have a masters in physics to follow this. "...i.e. we need to conjugate the first Hilbert space (although this gives an isomorphic copy). In the above argument establishing the bijection we used the matrix representation of Hilbert spaces and hence…

I don't know if you are joking, but the text is not aimed at kindergarteners regardless of the title.

Re: Kindergarten Quantum Mechanics

#24

Post by spekcular »

Kednicma wrote: post #19
mncharity wrote: post #13

Earlier quoted context omitted.

Just a cautionary note - category theory has seemingly been at "There's tremendous potential here! We just need to find a big win to make that clear to everyone else..." for quite a few years now.

I'm obliged, I suppose, to list off a few big wins. From the 50s and 60s, we have classic theorems which use abstract nonsense to generalize big statements about entire classes of objects, like Freyd's adjoint functor theorem [0], Yoneda's lemma [1], and Lawvere's fixed-point theorem [2]. Yoneda's lemma is the slogan that "an object is equivalent to the arrows coming/leaving it", but formal. Lawvere's theorem is a de…

Those aren't really "big wins" though. To most mathematicians, generalizations and abstraction are only interesting insofar as they are useful, and I don't see any results there someone working in mainstream mathematics would or should care about. (Obviously the Yoneda lemma is used in algebraic topology and geometry, but that's the odd one out on your list, and you don't really need categorical language to state the interesting examples.)

Also, EETC/HoTT are basically junk, as explained in detail by Harvey Friedman in various postings on the foundations of math mailing list. We already have a perfectly good foundation for mathematics and EETC/HoTT don't improve on it in any way (and in fact are worse in many respects).

Re: Kindergarten Quantum Mechanics

#25

Post by zrkrlc »

mncharity wrote: post #11

As meta, I suggest most everyone is vastly underestimating the magnitude of potentially transformative improvement being left on the table by current science education. But that's a discussion for another time.

Imagine putting all of science on a common (diagrammatic) footing, implemented down to the level of types so you can immediately perform calculations...mouthwatering.

Re: Kindergarten Quantum Mechanics

#26

Post by mathgenius »

Apparently there is an actual experiment on six-year-olds taking place [1,2]:

"Experiment. Consider ten children of ages between six and ten and consider ten high-school teachers of physics and mathematics. The high-school teachers of physics and mathematics will have all the time they require to refresh their quantum mechanics background, and also to update it with regard to recent developments in quantum information. The children on the other hand will have quantum theory explained in terms of the graphical formalism. Both teams will be given a certain set of questions, for the children formulated in diagrammatic language, and for the teachers in the usual quantum mechanical formalism. Whoever solves the most problems and solves them in the fastest time wins. If the diagrammatic language is much more intuitive, it should in principle be possible for the children to win."

[1] https://twitter.com/coecke/status/1285531026270367744 [2] https://arxiv.org/abs/0908.1787

Re: Kindergarten Quantum Mechanics

#28

Post by mathgenius »

tmabraham wrote: post #15

I have only skimmed this paper, but the diagrams look somewhat similar to Penrose graphical notation. Is there any connection there?

Yes, they are pretty much the same thing. There are some particular quantum-y elements though, such as the cup & cap. In general relativity these would (i think?) correspond to index raising and lowering operators.

Re: Kindergarten Quantum Mechanics

#29

Post by mathgenius »

Fishysoup wrote: post #6
Kednicma wrote: post #5

"Of course we do not expect you to know about category theory, nor do we want to encourage you here to do so." Ugh. Well, I can encourage you to do so, with some Baez [0][1]. [0] http://math.ucr.edu/home/baez/rosetta.pdf [1] https://arxiv.org/abs/quant-ph/0404040

Man everyone seems to be talking about category theory lately and I still have no idea what it is except some general sense in which different types of mathematical objects can operate on each other (which is probably wrong). Looks like I should probably actually put the effort in and learn about it.

It helps if you get interested before putting the effort in.... Check out this breezy youtube from superstar Tai-Danae Bradley:

https://www.youtube.com/watch?v=wiadG3ywJIs

Re: Kindergarten Quantum Mechanics

#30

Post by Kednicma »

spekcular wrote: post #24
Kednicma wrote: post #19

Earlier quoted context omitted.

I'm obliged, I suppose, to list off a few big wins. From the 50s and 60s, we have classic theorems which use abstract nonsense to generalize big statements about entire classes of objects, like Freyd's adjoint functor theorem [0], Yoneda's lemma [1], and Lawvere's fixed-point theorem [2]. Yoneda's lemma is the slogan that "an object is equivalent to the arrows coming/leaving it", but formal. Lawvere's theorem is a de…

Those aren't really "big wins" though. To most mathematicians, generalizations and abstraction are only interesting insofar as they are useful, and I don't see any results there someone working in mainstream mathematics would or should care about. (Obviously the Yoneda lemma is used in algebraic topology and geometry, but that's the odd one out on your list, and you don't really need categorical language to state the…

Friedman and Simpson are, unfortunately, dinosaurs who don't grok categorical concepts. This became clear on the FOM list when Pratt and other abstract algebraists who know category theory but do not depend on it were able to pry apart the problem. Friedman and Simpson deny that certain mathematical objects exist and are equivalent to each other, and while I won't begrudge them their nearsight due to spending so much time with weak/reverse maths, I won't excuse the mistakes.

I had to go find a blow-by-blow of the drama because it's good. Simpson cannot imagine topoi which don't implement standard set theory [3]. Friedman demonstrates a total misunderstanding of sets vs. categories [4]. McLarty and Feferman claim that categorical FOM make sense once one is used to categories [1]. Finally, the truth is laid bare: Friedman and Simpson simply don't agree with us on whether categorical logic is philosophically valid [2].

For more on this perspective, check out Pratt's take on Yoneda's lemma [0].

(An interesting aside: Simpson is an Objectivist who hates postmodernism! I wonder if this is part of what causes them to reject topos theory, where there are many different logics and collections, with a single barren plain Boolean set theory?)

[0] http://boole.stanford.edu/pub/yon.pdf

[1] https://cs.nyu.edu/pipermail/fom/1998-March/001309.html

[2] https://cs.nyu.edu/pipermail/fom/1998-March/001467.html

[3] https://cs.nyu.edu/pipermail/fom/1998-January/000782.html

[4] https://cs.nyu.edu/pipermail/fom/1998-January/000835.html

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