szany
Re:Functional Programming, Abstraction, and Names
on Friday May 20, 2016 @08:38PM (#11742584)
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.
Re:A collaborative residency program in mathematical biology and deep ...
on Friday July 31, 2015 @04:12AM (#9980544)
Part of starting this was finding a place and moving in.
Re:A collaborative residency program in mathematical biology and deep ...
on Thursday July 30, 2015 @03:40PM (#9977440)
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".
Re:A collaborative residency program in mathematical biology and deep ...
on Thursday July 30, 2015 @03:09PM (#9977238)
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.
Re:Relation Between Type Theory, Category Theory and Logic
on Saturday July 11, 2015 @03:08AM (#9868867)
Most true statements are uninteresting.
Re:Relation Between Type Theory, Category Theory and Logic
on Saturday July 11, 2015 @02:21AM (#9868770)
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
Re:Never Be Intimidated
on Tuesday February 18, 2014 @10:43PM (#7261666)
What makes ambition/creativity/drive/perspective/attitude/inspiration any more intrinsic than intelligence/knowledge?
Re:15-819 Homotopy Type Theory
on Saturday January 11, 2014 @09:19PM (#7044846)
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.
Re:What I Wish I Knew When Learning Haskell
on Sunday December 08, 2013 @12:25AM (#6869053)
SET : Group
MAN : Lie Group
TOP : Topological Group
GRP : Objects
Re:Student Entrepreneurs: If Peter Thiel Calls, Hang Up
on Sunday October 06, 2013 @02:59PM (#6505018)
This is good advice, because the right sort of person to be a Thiel fellow would read this and scoff anyway.
Re:Mio: A High-Performance Multicore IO Manager for GHC [pdf]
on Monday August 12, 2013 @07:13AM (#6198622)
“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
Re:Ask HN: Best Haskell projects and gists to learn from
on Sunday July 28, 2013 @05:34PM (#6118174)
Re:What Is the Most Surprising Result in Mathematics?
on Saturday July 06, 2013 @05:18PM (#6000114)
Constructivist answer: they don't.
Re:The Extensible Web Manifesto
on Monday June 10, 2013 @11:16AM (#5854963)
Alan Kay has been calling for this for a long time now.
Re:As Math Grows More Complex, Will Computers Reign?
on Tuesday March 05, 2013 @06:26AM (#5323934)
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.
Re:As Math Grows More Complex, Will Computers Reign?
on Tuesday March 05, 2013 @06:22AM (#5323927)
There was a mention of dependent types.
Re:Commentary on Grothendieck-Serre correspondence
on Sunday January 06, 2013 @03:34PM (#5017609)
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.
Re:Why Facebook Makes Us Depressed
on Saturday December 29, 2012 @03:52PM (#4983415)
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?
Re:Ask HN: I lost my will to program. How can I get it back?
on Monday December 17, 2012 @09:21AM (#4932313)
What language are you programming in? Try a language like Haskell or ML. It might just be that you have taste.
Re:The Mathematical Hacker
on Thursday December 13, 2012 @08:37PM (#4919135)
Programming is math, in the same way that accounting is.
If you read the link that's not what it says.
Doing programming all day will not make you a mathematician.
Sad truth. For now!
Re:The Mathematical Hacker
on Thursday December 13, 2012 @10:30AM (#4916068)
There's also the simple fact that programming literally is math.
Re:Just Finish Everything
on Sunday December 09, 2012 @06:49AM (#4894513)
This is stupid. Perseverance ≠ finishing everything. Not every project is worthy of being finished.
Canadian scientists create a functioning virtual brain
Re:Hugepic - a web app for showing massive pictures
on Sunday November 04, 2012 @04:19AM (#4739336)
Someone should upload the zebrafish image to this.
http://v.jcb-dataviewer.glencoesoftware.com/webclient/img_de...
Re:Hey, C Is a Functional Language Too
on Friday November 02, 2012 @07:01AM (#4732033)
In fact it's purely functional!
http://conal.net/blog/posts/the-c-language-is-purely-functio...
Re:Topology: The Secret Ingredient In The Latest Theory of Everything
on Monday October 08, 2012 @10:59AM (#4627117)
In the past, topology was little more than an amusing diversion for mathematicians doodling about the difference between donuts and dumplings.
...what?
Re:Peter Thiel gives new class of students $100K to forgo college
on Wednesday June 13, 2012 @11:24AM (#4106398)
Honestly, it feels like putting kids in a zoo and seeing what happens. It's a spectacle, and I'm sure some enjoy it, but it looks somewhat exploitative (like some aspects of Hollywood :).
Sadly I think you're right about this: http://www.youtube.com/watch?v=aRk7uP5S9VQ
(I'm one from the previous class.)