
Notes on notation and thought - ingve
https://github.com/hypotext/notation
======
rdtsc
Very cool. I like this kind of stuff.

One of the links there is about Dirac's notation. When I was doing Quantum
Computing in school, professor started us with matrices and vectors. We were
familiar with those and we could multiply them and do basic operations.

Then one homework they assigned us a more complex quantum circuit to solve.
And it was quite painful because matrices had gotten bigger. However there was
a method to his madness, because after they introduced Dirac notation. The
power of a better notation because obvious to us. It is like programming in C
doing some text procecessing or some command line scripts, then someone
showing you Python.

Programming is notation in a way. So knowing different paradigms and
frameworks is important as some might allow for a very concise representation
of the problem.

There was a link here on HN about using Prolog to represent and work with a
type system, and it was just very elegant how it worked.

Object oriented design, (which we like to hate today it seems), was seen as a
powerful way to represent entities so it became useful. Then design patterns
came about, that is also a notation ("Wow there Jim, looks like you've go a
singleton, wrapping a factory with an observer flyweight..."). I joke, but it
did (still does?) help talk about architecture.

Functional programming is the same way -- learning it teaches you to think in
a different way. When state is mutated it is not just s.add_foo(foo) but looks
like new_s = add_foo(s, foo). That seems trivial and silly, but it changes how
you think about data and state. Or I remember when closured "clicked" for me
and I realized how similar they are to class instances when they capture their
environment.

Or say thinking how your language approaches concurrency -- is it based on
actors and messages, threads, callbacks (maybe with a reactor loop), promises,
transactional memory, and so on. Those are notations to solve "concurrent
things" in a way. Some might be a lot more efficient at representing the
problem than others. But if you never know about it or used it before, it will
be hard to convince yourself of it usefullness.

~~~
GavinMcG
If you or someone could track down the Prolog/Type System post, I'd be
interested!

~~~
Avshalom
[https://news.ycombinator.com/item?id=12108041](https://news.ycombinator.com/item?id=12108041)

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gue5t
Try "Formal Languages in Logic: A Philosophical and Cognitive Analysis" by
Catarina Dutilh Novaes. It's maybe the best work I've read in this field, and
I've read most of what's on the github list.

My copy has md5sum 6d62f3c0a63242a318ddd691d3974cd2, sha1sum
17aee5d2ceeabf947ea07e6ef55196b337a8f999, and sha256sum
f2d56ac1e3cd0fa479a4fc0c03f94d338663e6ed29799a2544b5b9b159643a05.

~~~
kovek
Why do you share the md5sum of your copy?

~~~
Etheryte
So others can confirm that they got the same thing.

~~~
kovek
I understand that md5sums help you know you got the same copy. Why not share
his resource directly instead? Also, what if someone gets the same resource
"Formal Languages in Logic: A Philosophical and Cognitive Analysis" under a
different md5sum (for example, the format or edition is different)? It seemed
somewhat useless in this case.

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ColinWright
Wow! Amazed to see that my interview, talk, and comments are (currently)
number one on the list.

I'm sure that will change, but it briefly gave me the warm fuzzies.

~~~
Smaug123
… You're the same person that does the juggling talk! I never made that
connection. Great talk and very interesting - I saw it a couple of years ago
at St John's College, Cambridge.

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mathgenius
There's a story here involving a unification of the Dirac notation and
Einstein notation, into tensor networks. I think Penrose started this. And
this mathematics also connects to knot theory. John Baez writes well about
these things, also Bob Coecke.

~~~
hypotext
I'd love to read a source on this! Sounds like it'd be a good addition to the
repo.

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jonnybgood
Nice. Should add some Wittgenstein. Particularly, his Philosophical
Investigations. PI has been highly influential to mathematicians such as
Timothy Gowers on how they "see" mathematical objects and by extension
notation.

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apricot
Very interesting. I found several books, papers and stories that I had enjoyed
very much, but I never realized that they all shared a common subject.

I look forward to reading the ones on the list I didn't know about.

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aj7
Nice post.

