
Making math more Lego-like - jonbaer
http://news.harvard.edu/gazette/story/2017/03/making-math-more-lego-like/
======
kmill
Related work:

* Penrose graphical notation. [https://en.wikipedia.org/wiki/Penrose_graphical_notation](https://en.wikipedia.org/wiki/Penrose_graphical_notation)

* Trace diagrams. [https://en.wikipedia.org/wiki/Trace_diagram](https://en.wikipedia.org/wiki/Trace_diagram)

* Trace diagrams for Hopf algebras. [http://tmp.esoteri.casa/hopf.pdf](http://tmp.esoteri.casa/hopf.pdf)

* Frobenius algebras. [http://math.ucr.edu/home/baez/week299.html](http://math.ucr.edu/home/baez/week299.html)

* Temperley-Lieb algebras. [https://en.wikipedia.org/wiki/Temperley%E2%80%93Lieb_algebra](https://en.wikipedia.org/wiki/Temperley%E2%80%93Lieb_algebra)

* Planar algebras. [https://math.berkeley.edu/~vfr/VANDERBILT/pl21.pdf](https://math.berkeley.edu/~vfr/VANDERBILT/pl21.pdf)

* String diagrams for 2-categories. [https://en.wikipedia.org/wiki/String_diagram](https://en.wikipedia.org/wiki/String_diagram)

* Diagrammatic algebras in general. [http://mathoverflow.net/questions/168888/who-invented-diagra...](http://mathoverflow.net/questions/168888/who-invented-diagrammatic-algebra)

* Begriffsschrift. [https://i.ytimg.com/vi/KFYvF3t1xUM/hqdefault.jpg](https://i.ytimg.com/vi/KFYvF3t1xUM/hqdefault.jpg)

* Existential graphs. [https://en.wikipedia.org/wiki/Existential_graph](https://en.wikipedia.org/wiki/Existential_graph)

* Laws of Form by Spencer-Brown. [https://en.wikipedia.org/wiki/Laws_of_Form](https://en.wikipedia.org/wiki/Laws_of_Form)

* Opetopes. [http://mat.uab.es/~kock/cat/zoom/scan.jpg](http://mat.uab.es/~kock/cat/zoom/scan.jpg)

~~~
trustthispost
There's a history from the introduction of Tensor networks by Penrose to the
3D tensor networks, the quon language:
[https://dl.dropboxusercontent.com/u/78485948/PNAS-2017-Biamo...](https://dl.dropboxusercontent.com/u/78485948/PNAS-2017-Biamonte-1700736114.pdf)

~~~
trustthispost
This gives more of a physical development, and frames the context of the lego-
like language in the cross-disciplinary field of quantum information

------
gravypod
Why do this rather then define an abstract, human-evaluatable, programming
language? Give it some S-expr syntax and make more things implicit and you're
golden.

Making strange squigles on a page doesn't help. Making strange greek symbols
on the page doesn't help. Writing functions, "unit tests", building on
abstractions, and creating "libraries" do help. We all know this because it
works well in CS. Why would this not work well in physics?

Ditch the alphabet soup (and yes, even the 5th centry Greek alphabet soupe).
Abstract common ideas into "functions". Write human-provable "test-cases". Add
documentation. Use logically derived variable names (even if they're 5-10
characters). Formalize the definitions and syntax of this language and it's
abilities. You'd be golden.

Phi shouldn't mean 30 things depending on the field you're in.

Am I wrong? Is this not possible? Is there a reason as to why math and logic
can't be expressed as an abstract programing language? Is there a reason why
it wouldn't be better to have a completely standard way as to how to define
all of your algorithms and logical assertions?

I could be wrong but no one has provided information as to why what we do is
better. Nor does this look much better (what kmill has linked).

~~~
andrepd
I have absolutely no idea what you're trying to say.

What do you mean with all that? Maybe I'm being obtuse but you're just saying
random words and terms from programming. How on earth is that applicable to
physics? I have absolutely no idea what you're trying to propose.

~~~
traverseda
Well, not OP, but that was all very understandable to me, and resonated. I'll
try to explain some specific points.

>Why do this rather then define an abstract, human-evaluatable, programming
language?

The syntax of math is bad for a number of reasons. Making it some big 3D thing
isn't going to make that syntax more reasonable.

Math is a language that could learn a lot from programming languages, even if
you don't plan on running it on a computer and dealing with all that hassle.

>Making strange squigles on a page doesn't help. Making strange greek symbols
on the page doesn't help. >Ditch the alphabet soup (and yes, even the 5th
centry Greek alphabet soupe)

Math is optimized for paper. This makes it a lot less accessible these days.
All these custom glyphs are a damn weird idea. Naming your variables "a"
wouldn't be accepted in any other languages.

>Abstract common ideas into "functions".

Once you've abandoned the idea of single-letter variable names, it becomes
easier to abstract common mathematical ideas into functions and build a great
big library of those functions.

> Use logically derived variable names (even if they're 5-10 characters).

Naming your variables "a" wouldn't be accepted in any other languages, and
from the outside looks like a pretty silly idea.

>Phi shouldn't mean 30 things depending on the field you're in.

Choose more descriptive variable names.

------
ballenf
Isn't it ironic that the article had not a single picture of said picture
models? (You can't count the rough chalkboard sketches as 3D model, imo.) The
actual linked paper does, of course.

~~~
aviggiano
I was also impressed by the fact that the news title talks about 3D lego
models but has no images whatsoever

------
deepnet
Quons: A 3D Language for Quantum Information Liu, Wozniakowski, & Jaffe
[https://www.arxiv.org/abs/1612.02630](https://www.arxiv.org/abs/1612.02630)

Holographic Software for Quantum Networks Jaffe, Liu, & Wozniakowski
[https://arxiv.org/abs/1605.00127](https://arxiv.org/abs/1605.00127)

~~~
trustthispost
Here, you'll find discussion on the development of the picture-language and
some application, i.e., topological design of protocols (by Jaffe, Liu, and
Wozniakowski):
[https://arxiv.org/abs/1611.06447](https://arxiv.org/abs/1611.06447)

------
elchief
> It turns out one picture is worth 1,000 symbols

Says article with ~750 words and one useless picture

------
egonschiele
This sounds incredibly cool, but how can I see an example of the images? A
simple search for "Quon examples" yielded nothing.

~~~
dongslol
The paper has a few:
[http://www.pnas.org/content/early/2017/02/03/1621345114.full](http://www.pnas.org/content/early/2017/02/03/1621345114.full)

------
trustthispost
If you want an intermediary between the linked Lego story and the quon paper
in PNAS, then check out the commentary (in PNAS):
[https://dl.dropboxusercontent.com/u/78485948/PNAS-2017-Biamo...](https://dl.dropboxusercontent.com/u/78485948/PNAS-2017-Biamonte-1700736114.pdf)

------
minimaxir
In deep learning, layer manipulation in Keras is often compared to Legos, as
you can mix-and-match connections between layers and stack them pretty easily
with minimal code adjustments. It makes iteration/experimentation extremely
easy.

~~~
nathancahill
I generally keep memes off of HN*, but this one always cracks me up:
[http://i.imgur.com/GYdvtAW.jpg](http://i.imgur.com/GYdvtAW.jpg)

[so I'll delete it if it gets downvoted]

------
billforsternz
I would have expected "making math more legos like" (US English) or "making
maths more lego like" (British English). Instead we have a hybrid version.

~~~
psquid
it's US english, they're referring to Lego the product as a whole, rather than
individual Lego pieces (the meaning ends up basically the same, but the
distinction does change the grammar)

~~~
billforsternz
I see. My impression is that in US film and television "legos" is used almost
exclusively. But it's not like I've been taking notes or anything, and I could
well be wrong.

------
mrcactu5
all these wonderful graphic languages exist. now it's time to put them into
practice!

------
mattxxx
Cool.

------
mehaveaccount
University magazines are a terrible place to learn about new research because
they are effectively trying to sell the research at their university as great
whether it is really great or not. Looking at the arxiv link they linked I was
underwhelmed compared to the title. It is not a new lego-like language for
"mathematics", it's some definitions in a very particular subfield in
mathematics. An accomplishment within that subfield to be sure, but not
anything relevant to the wider math community and certainly not Hacker News.

~~~
Amygaz
My personal experience with Harvard is they are the best at over-exaggeration.
Also very good at branding "been done before, but not at Harvard" research as
brand new and revolutionary. Others do it too, but HU masters this.

------
chris_chan_
A wise man once told me visual image speak louder than words. Yes, this sounds
incredibly awesome.

