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Math ∩ Programming

jeremykun.com

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Re: Math ∩ Programming

#21

Post by arielb1 »

jfoutz wrote: post #14
shasta wrote: post #12

Earlier quoted context omitted.

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! factorial wins. The problem is worse than exponentiation.

But if you have r=sqrt(n) that works out fine.

Re: Math ∩ Programming

#22

Post by [deleted] »

shasta wrote: post #5

> 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 ...

[deleted]

Re: Math ∩ Programming

#23

Post by klekticist »

j2kun wrote: post #10

I'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…

List of ideas:

* I'd agree that first and foremost, I'd change the line width. I've always found the blog a bit difficult to read on the site because of the number of words per line. The site seems to be responsive - maybe just change the width of the articles?

* It might be worth having the landing page have something other than "featured articles" right at the top. Since the content of your site is so diverse, it might help to have some pointers as to how to navigate the site up front.

* On the navigation sidebar, maybe have a "New Here?" or a "Getting Started" link.

Just some ideas. I've been reading your blog for many years, btw. It even inspired me to start my own!

Re: Math ∩ Programming

#24

Post by j2kun »

greydius wrote: post #20

I'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.

This has been on my todo list for a long time :(

Also, sadly, my rate of progress toward this goal has averaged at around one blog post per year. But hopefully in the coming months (after defending my thesis) I'll have more time to dedicate to blogging.

Re: Math ∩ Programming

#25

Post by zardo »

derjames wrote: post #17

QUOTE: > Like in a non-dimensional number?. For example the Reynolds number in fluid flow.

No, the meaning dimension there is different. In the Reynolds number it's a ratio of measures where the units cancel.

Here we're talking about mapping data into a high dimensional space, then trying to project that down to the minimum dimension space that can preserve the relevant information.

In the example we don't have any reason to even think all our dimensions are orthogonal, we're assigning a new dimension for each word, but we know there is a lot of overlap in word meaning.

Re: Math ∩ Programming

#26

Post by j2kun »

shasta wrote: post #5

> 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 ...

You're right. Amended.

Re: Math ∩ Programming

#27

Post by ph0rque »

jfoutz wrote: post #14
shasta wrote: post #12

Earlier quoted context omitted.

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! factorial wins. The problem is worse than exponentiation.

At some point, I wondered if n! is proportional to n^n.

Turns out, it is:

n! ~= (2 * pi * n)^1/2 * (n/e)^n

(https://en.wikipedia.org/wiki/Stirling%27s_approximation)

Re: Math ∩ Programming

#28

Post by turbohz »

alfonsodev wrote: post #2

I 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 :)

Previous discussion: https://news.ycombinator.com/item?id=11129375

Re: Math ∩ Programming

#29

Post by Kluny »

RaitoBezarius wrote: post #19
j2kun wrote: post #10

I'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!

Same here! I've had the Math ∩ Programming blog open in a tab on my computer for probably 3 weeks now, trying to get around to reading it. Having it delivered once or twice a week in a logical order would be amazing, and worth paying for.
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