[deleted]
Math ∩ Programming
11–20 of 40 posts
Re: Math ∩ Programming
#12> A consequence is that, if you’re trying to cluster data points by looking at points within a fixed distance r of one point, you’ll have to make r exponentially large in the dimension. That does not follow ...
His point is the volume of the unit sphere is tiny. The "volume" of the unit 20-cube is 1. The volume of a 20-sphere is just 0.0258. 100-cube, volume is 1. 100-sphere, 2.36e-40 If your algorithm works well for "nearby" meaning 1, i can just keep adding dimensions till you find nothing. If "nearby" on the other hand is related to the number of dimensions, you're going to have to grow the "nearby" value exponentially.
You've made the same error as the OP. The volume of a unit n-dimensional sphere decreases exponentially in n. But that doesn't mean you need to increase r exponentially to compensate - in the volume formula, the r also has an exponent of n. The distance between opposite corners of a unit cube in n-dimensional space is root(n). That's hardly exponential.
Re: Math ∩ Programming
#13i love this guy's blog posts - not only is he clearly a very smart talented mathematician - he explains concepts in a way that is very easy to understand. I wish i would have found this website when i was getting my master in math. some of the signal processing stuff would have helped a lot.
Re: Math ∩ Programming
#14Earlier quoted context omitted.
His point is the volume of the unit sphere is tiny. The "volume" of the unit 20-cube is 1. The volume of a 20-sphere is just 0.0258. 100-cube, volume is 1. 100-sphere, 2.36e-40 If your algorithm works well for "nearby" meaning 1, i can just keep adding dimensions till you find nothing. If "nearby" on the other hand is related to the number of dimensions, you're going to have to grow the "nearby" value exponentially.
You've made the same error as the OP. The volume of a unit n-dimensional sphere decreases exponentially in n. But that doesn't mean you need to increase r exponentially to compensate - in the volume formula, the r also has an exponent of n. The distance between opposite corners of a unit cube in n-dimensional space is root(n). That's hardly exponential.
Huh. I always thought n! grew faster than c^n which would be even worse than exponential. Maybe enough cancels out to make it simpler than it appears.
edit
Actually, for even dimensions it's pretty clear. n = dimension/2
pi^n / n!
Re: Math ∩ Programming
#15I know it's a HN cliche to complain about form over the message, but I find this impossible to read without first removing the entire left-hand panels (and ::before p-elements) which re-grab my eye every line-break.
If you use safari or firefox, reader view is available for the articles. https://support.mozilla.org/en-US/kb/firefox-reader-view-clu...
The reading view in Edge (and metro IE fwiw) works as well
Re: Math ∩ Programming
#16I found this blog time ago in Google, searching with terms "mathematics for programmers" I arrived to the article : Why there is no Hitchhiker’s Guide to Mathematics for Programmers http://jeremykun.com/2013/02/08/why-there-is-no-hitchhikers-... . Which I'd recommend to read as entry point to this website if you feel intimidated by maths. Nice to find it again :)
Thanks for this. It's an enjoyable read!
Re: Math ∩ Programming
#17QUOTE: >
Like in a non-dimensional number?. For example the Reynolds number in fluid flow.
Re: Math ∩ Programming
#18I'd like to find a way to reorganize Math ∩ Programming eventually. As alfonsodev points out, it's a bit hard to find stuff for newer and less mathy readers, though there is a handful of articles aimed at them. [1,2,3,4] As other users point out, they don't like the layout. Suggestions? [1]: http://jeremykun.com/2011/06/26/teaching-mathematics-graph-t... [2]: http://jeremykun.com/2014/05/26/learning-to-love-complex-n…
First of all, I'd be curious to plug Algolia on this blog :)
Then, maybe you should have less words per line. http://digerateur.xyz/2015/11/18/tri-bulle-ation/ is a good example.
Also, I'd love to see Jupyter notebooks made out of the coding material you cover. But maybe that's only me.
Re: Math ∩ Programming
#19I'd like to find a way to reorganize Math ∩ Programming eventually. As alfonsodev points out, it's a bit hard to find stuff for newer and less mathy readers, though there is a handful of articles aimed at them. [1,2,3,4] As other users point out, they don't like the layout. Suggestions? [1]: http://jeremykun.com/2011/06/26/teaching-mathematics-graph-t... [2]: http://jeremykun.com/2014/05/26/learning-to-love-complex-n…
It would be interesting to have a kind of "course" (emailed to subscribers) to discover your blog.
Something like "Every day, a chunk of Math ∩ Programming in your inbox", I would personally be interested at least!
Re: Math ∩ Programming
#20I'm looking forward to the persistent homology posts. It's a really interesting subject with a lot of potential, but I don't feel that the existing textbooks do a good job explaining the computations.