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Notes on notation and thought (github.com)
130 points by ingve on July 22, 2016 | hide | past | web | favorite | 17 comments



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.


I have to imagine that attempting long-division or creating log tables or transcendental function tables would have been quite the formidable task in roman numerals. Notation matters.


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



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.


This copy[1] has md5 of 6d62f3c0a63242a318ddd691d3974cd2.

[1]: http://uberty.org/wp-content/uploads/2016/02/Dr_Catarina_Dut...


Why do you share the md5sum of your copy?


So others can confirm that they got the same thing.


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.


Thanks. I love this subject. Any other recommendations not on the list? Favorites on the list?


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.


… 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.


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.


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


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.


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.


Nice post.




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