
Kindergarten Quantum Mechanics - ColinWright
https://arxiv.org/abs/quant-ph/0510032
======
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](https://twitter.com/coecke/status/1285531026270367744)
[2] [https://arxiv.org/abs/0908.1787](https://arxiv.org/abs/0908.1787)

------
supernova87a
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 essentially the whole vector
space structure, but in fact we need none of this, and we will show that in
any picture calculus we always have..."

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

------
082349872349872
Kindergarten Quantum Mechanics: if you ask mom for something, she will say
"yes" or "no" (even if she wasn't sure before you asked). Asking her again
won't change her answer. At this point, to try to get a different answer to
the same question, you have to ask dad.

------
mgraczyk
Does this paper describes an early form of Coecke's ZX calculus? What is the
relationship between the two systems?

[https://zxcalculus.com/](https://zxcalculus.com/)

~~~
mathgenius
Yes, very closely related. ZX is a specific set of tensors within this
diagrammatic framework.

------
mncharity
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.

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

------
Kednicma
"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](http://math.ucr.edu/home/baez/rosetta.pdf)

[1] [https://arxiv.org/abs/quant-ph/0404040](https://arxiv.org/abs/quant-
ph/0404040)

~~~
Fishysoup
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.

~~~
mncharity
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.

~~~
Kednicma
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 deep and permanent generalization of Gödel,
Tarski, Turing, et al. on incompleteness and undecideability.

Starting in the 60s and continuing to the present, there's been a theme of
exploring category theory as a prime foundation for maths. There's been
complete foundations like the Elementary Theory of the Category of Categories
(ETCC) [3], and also much smaller but pointed presentations that focus on just
simplifying set theory. I like [4] in particular.

On a deeper level, in terms of structure and philosophy, the entire existence
of homotopy type theory (HoTT) relies on categorical presentations and memes.
HoTT is, more than any other type theory, an investigation into what
equivalence means, and it dovetails wonderfully with 2-category theory and the
understanding that algebraic laws can be transformed into transformations.

[0]
[https://en.wikipedia.org/wiki/Formal_criteria_for_adjoint_fu...](https://en.wikipedia.org/wiki/Formal_criteria_for_adjoint_functors)

[1]
[https://en.wikipedia.org/wiki/Yoneda_lemma](https://en.wikipedia.org/wiki/Yoneda_lemma)

[2]
[http://tac.mta.ca/tac/reprints/articles/15/tr15.pdf](http://tac.mta.ca/tac/reprints/articles/15/tr15.pdf)

[3] [https://ncatlab.org/nlab/show/ETCC](https://ncatlab.org/nlab/show/ETCC)

[4] [https://arxiv.org/abs/1212.6543](https://arxiv.org/abs/1212.6543)

~~~
spekcular
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).

~~~
Kednicma
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](http://boole.stanford.edu/pub/yon.pdf)

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

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

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

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

~~~
spekcular
I read the links you provided (except [0], which I do not have time for at the
moment). I do not think Awodey and McLarty come across as well as you think
they do, and I do not think Friedman misunderstands anything.

Moreover, you omit some of Friedman's best postings on this topic. The
challenge is to show what advantages this proposed theory has over the
standard foundations, or to demonstrate some interesting problem or conceptual
issue that it resolves. I did not see any serious replies to this.

(Incidentally, the same challenge is my reply to the other comment to my
previous post, about the ZX-calculus.)

Here's an analogy. Why do mathematicians consider groups interesting, but
general Moufang loops not interesting? I propose the answer is that the
additional generality provided by Moufang loops doesn't aid in addressing any
interesting questions external to their theory. On the other hand, the utility
of the group concept is obvious to anyone who studies a subject with
connections to algebra.

This reasoning is roughly why the vast majority of mathematicians don't give
two hoots about category theory, beyond picking up the few tricks like
Yoneda's lemma that are actually useful. You can – as certain members of the
category theory community have shown – take any mathematical concept, consider
some generalization, and play various definition pushing games. But that's
pointless without a good motivation (e.g. a concrete problem).

The previous two paragraphs concern "actual" mathematics, but similar remarks
apply to foundations of mathematics. Friedman is pointing out that we already
have a perfectly good foundational theory of mathematics and asking what gain
we get by introducing categorical concepts.

~~~
Kednicma
In ten words or less: Sets are just 0-categories [7][8]. With more words: Set
theory is just 0-category theory. This is obvious today, but two decades ago,
Friedman couldn't just go to nCat [0] and educate himself.

Friedman repeatedly demonstrates [1][2] that he isn't interested in grokking
_why_ category theory is even a thing; he doesn't see e.g. Pratt's careful
explanation that category theory is motivated by studying (natural)
transformations. Simpson comes across as a spoiled brat [3] and Friedman comes
across as a narcissist who needs to fuel himself by being the bastion of FOM
[4]. Seriously, in [5], he has the audacity to simultaneously claim that
Lawvere's foundations are the same as Friedman's set-theoretic foundations,
_and also_ to ask what a Lawvere theory/sketch is! Unbelievably rude.

I read the entire three-month slapfight again, just to double-check that I
hadn't mis-remembered the general outline. Simpson wastes message after
message being wrong about Boolean algebras vs. Boolean rings (they're the same
picture) and doesn't understand how categorical dualities like Stone duality
lead to equivalences. At no point do either of them manage to fully grok a
2-category or how ETCC could be a practical foundations. Tragesser says it
well in [5] when he analogizes the entire affair to the sheep and their shop
[6], going around and around and always changing the framing but never
actually getting to the philosophical meat of the inquiry.

[0]
[https://ncatlab.org/nlab/show/periodic+table](https://ncatlab.org/nlab/show/periodic+table)

[1]
[https://cs.nyu.edu/pipermail/fom/1998-February/001182.html](https://cs.nyu.edu/pipermail/fom/1998-February/001182.html)

[2]
[https://cs.nyu.edu/pipermail/fom/1998-March/001303.html](https://cs.nyu.edu/pipermail/fom/1998-March/001303.html)

[3]
[https://cs.nyu.edu/pipermail/fom/1998-February/001228.html](https://cs.nyu.edu/pipermail/fom/1998-February/001228.html)

[4]
[https://cs.nyu.edu/pipermail/fom/1998-February/001234.html](https://cs.nyu.edu/pipermail/fom/1998-February/001234.html)

[5]
[https://cs.nyu.edu/pipermail/fom/1998-February/001210.html](https://cs.nyu.edu/pipermail/fom/1998-February/001210.html)

[6] Edit: I can link directly to the text!
[https://en.wikisource.org/wiki/Through_the_Looking-
Glass,_an...](https://en.wikisource.org/wiki/Through_the_Looking-
Glass,_and_What_Alice_Found_There/Chapter_V)

[7]
[https://ncatlab.org/nlab/show/0-category](https://ncatlab.org/nlab/show/0-category)

[8]
[https://ncatlab.org/nlab/show/negative%20thinking](https://ncatlab.org/nlab/show/negative%20thinking)

~~~
spekcular
Again, what I see is Friedman and Simpson asking for fairly specific and
concrete things, and those things not being provided.

More to the point, what I asked for in my previous comment has also not been
provided! What does the knowledge that Sets are "just 0-categories" buy me in
concrete terms? Does it facilitate the proof of any theorems in set theory?

------
mncharity
From [0] 2018: "In [1] we present an entirely diagrammatic presentation of
quantum the-ory with applications in quantum foundations and quantum
information.This was the result of many years of work by many, and started of
as acategory-theoretic axiomatisation motivated by computer science as well
asaxiomatic physics. However, I have always felt that the diagrammatic pre-
sentation is of great use in its own right, be it to bridge disciplines,
makequantum theory more easy to grasp, or, for educational purposes, in [2]
wemade the bolt claim that using diagrams high-school kids could even out-
perform their teachers, or university students. Now, we will put this claimto
the test. To do so, we have written two tutorials [3,4], covering exactlythe
same material, but one only using diagrams, while the other containsthe
standard Hilbert space presentation. There are corresponding sets ofexamples
too."

[0] Quantum Theory for Kids
[https://repositorio.usp.br/directbitstream/95d90813-2c2f-4cc...](https://repositorio.usp.br/directbitstream/95d90813-2c2f-4cc6-b513-6a8c9bf5082c/2890851.pdf#page=141)
[1] Picturing Quantum Processes
[https://doi.org/10.1017/9781316219317](https://doi.org/10.1017/9781316219317)
; slides
[https://www.cs.ox.ac.uk/ss2014/programme/Bob.pdf](https://www.cs.ox.ac.uk/ss2014/programme/Bob.pdf)
; talk
[https://www.youtube.com/watch?v=7Fvjpjhimic](https://www.youtube.com/watch?v=7Fvjpjhimic)
[2] Quantum Picturalism
[https://arxiv.org/abs/0908.1787](https://arxiv.org/abs/0908.1787) [3] Quantum
theory in Pictures ... "Top Secret"... I didn't quickly find.

A recent talk:
[https://www.youtube.com/watch?v=AOLoyx6EHq8](https://www.youtube.com/watch?v=AOLoyx6EHq8)

------
taliesinb
If you want to see the author riff on density matrices, check out this recent
video:
[https://youtu.be/wP_Jsxn7BA4?t=1020](https://youtu.be/wP_Jsxn7BA4?t=1020)

And by riff I mean with an actual electric guitar

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

~~~
mathgenius
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.

------
Koshkin
Yeah, kids are bosons...

