Hacker News: szany

New comment by szany in "Functional Programming, Abstraction, and Names"

szany — Sat, 21 May 2016 00:38:35 +0000

This is a bit defeatist. Parsing the definition in your head is only the first level of understanding you can have about a mathematical structure. You don't really understand something until you can reinvent it (and in particular give a plausible answer to "why these axioms and not others?")

For example, to motivate groups, you could introduce the concept of a symmetry as a mapping from an object to itself that doesn't change its properties, introduce the idea of an isomorphism as a mapping with an inverse (where f and g being inverse means they compose to identity maps), put them together and postulate that a reasonable formalization of a symmetry is an automorphism (isomorphism from an object to itself), note that isomorphisms are closed under composition, and arrive at the definition of a group by considering sets of symmetries closed under finite composition (thinking of identity maps as the composition of 0 morphisms).

I'm sure there's a similarly conceptual way to motivate monads in functional programming. Hyland and Power have papers on algebraic theories of "effectful" operations and how they give rise to (finitary) monads, as one starting point.

New comment by szany in "A collaborative residency program in mathematical biology and deep learning"

szany — Fri, 31 Jul 2015 08:12:33 +0000

Part of starting this was finding a place and moving in.

New comment by szany in "A collaborative residency program in mathematical biology and deep learning"

szany — Thu, 30 Jul 2015 19:40:37 +0000

This isn't full-time — one of the goals is explicitly "to complement rather than conflict with the tenure of a full-time position elsewhere".

New comment by szany in "A collaborative residency program in mathematical biology and deep learning"

szany — Thu, 30 Jul 2015 19:09:44 +0000

Thanks for raising that question. Actually the house was rented for the purpose of hosting the program, not the other way around.

Of course we're trying not to operate at a loss, but we're willing to accept that if necessary to accomplish the stated goals.

A collaborative residency program in mathematical biology and deep learning

szany — Thu, 30 Jul 2015 17:19:33 +0000

Article URL: http://topos.house/cfp

Comments URL: https://news.ycombinator.com/item?id=9976440

Points: 52

# Comments: 11

New comment by szany in "Relation Between Type Theory, Category Theory and Logic"

szany — Sat, 11 Jul 2015 07:08:09 +0000

Most true statements are uninteresting.

New comment by szany in "Relation Between Type Theory, Category Theory and Logic"

szany — Sat, 11 Jul 2015 06:21:03 +0000

See also Bob Harper's blog for a more leisurely exposition:

https://existentialtype.wordpress.com/2011/03/27/the-holy-tr...

Unifying Structured Recursion Schemes

szany — Fri, 21 Mar 2014 08:28:59 +0000

Article URL: http://www.youtube.com/watch?v=9EGYSb9vov8

Comments URL: https://news.ycombinator.com/item?id=7441226

Points: 1

# Comments: 0

New comment by szany in "Never Be Intimidated"

szany — Wed, 19 Feb 2014 03:43:33 +0000

What makes ambition/creativity/drive/perspective/attitude/inspiration any more intrinsic than intelligence/knowledge?

New comment by szany in "15-819 Homotopy Type Theory"

szany — Sun, 12 Jan 2014 02:19:58 +0000

It's a foundation of mathematics whose native objects are structures fundamental to higher mathematics (∞-groupoids, which are more or less equivalent to topological spaces up to homotopy), rather than awkward encodings (ZFC "sets", which are tree-like things), and where everything is automatically invariant with respect to abstract notions of equivalence (think isomorphism vs. equality).

The point is that it makes it much more realistic to check complicated math using computers, which will become more important as math inevitably gets more complicated.

Oh, and it happens to be a functional programming language. Which says something about functional programming.

New comment by szany in "What I Wish I Knew When Learning Haskell"

szany — Sun, 08 Dec 2013 05:25:14 +0000

  SET : Group
  MAN : Lie Group
  TOP : Topological Group
  GRP : Objects

The last line should really be "GRP : Abelian Group"

See http://en.wikipedia.org/wiki/Eckmann-Hilton_argument

New comment by szany in "Student Entrepreneurs: If Peter Thiel Calls, Hang Up"

szany — Sun, 06 Oct 2013 18:59:35 +0000

This is good advice, because the right sort of person to be a Thiel fellow would read this and scoff anyway.

New comment by szany in "Mio: A High-Performance Multicore IO Manager for GHC [pdf]"

szany — Mon, 12 Aug 2013 11:13:05 +0000

“Programming languages are not arbitrary. They are manifestations of deep invariants of human thought, i.e. they are grounded in logic.” —Bob Harper

Logic ~ Type theory ~ Functional programming

New comment by szany in "Ask HN: Best Haskell projects and gists to learn from"

szany — Sun, 28 Jul 2013 21:34:29 +0000

http://www.haskellforall.com/

New comment by szany in "What Is the Most Surprising Result in Mathematics?"

szany — Sat, 06 Jul 2013 21:18:21 +0000

Constructivist answer: they don't.

New comment by szany in "The Extensible Web Manifesto"

szany — Mon, 10 Jun 2013 15:16:29 +0000

Alan Kay has been calling for this for a long time now.

New comment by szany in "As Math Grows More Complex, Will Computers Reign?"

szany — Tue, 05 Mar 2013 11:26:47 +0000

Essentially the same way we reason about infinite mathematical structures in our heads: we define infinite structures by a finite system of generators and prove things by induction. The computer verifies that your inductive proof is correct.

New comment by szany in "As Math Grows More Complex, Will Computers Reign?"

szany — Tue, 05 Mar 2013 11:22:51 +0000

There was a mention of dependent types.

New comment by szany in "Commentary on Grothendieck-Serre correspondence"

szany — Sun, 06 Jan 2013 20:34:07 +0000

In the fall of 1958, Zariski invited Grothendieck to visit Harvard. He was pleased to go, but made clear to Zariski that he refused to sign the pledge not to work to overthrow the American government which was necessary at that time to obtain a visa. Zariski warned him that he might ﬁnd himself in prison; Grothendieck, perhaps mindful of the impressive amount of French mathematics done in prisons (think of Galois, Weil, Leray...) responded that that would be ﬁne, as long as he could have books and students could visit.

New comment by szany in "Why Facebook Makes Us Depressed "

szany — Sat, 29 Dec 2012 20:52:50 +0000

I'm sat here, in my dressing gown. My fingers are greasy from eating crisps all morning. My back aches because I spent all night playing a stupid video game. The gin hangover isn't helping either. My week off work has been a wash out. I didn't write any code, I didn't cook anything other than pizza, and I'm beginning to smell of used dish water.

Is Facebook really to blame here?