6 ms·

Math ∩ Programming

236 points by bigblind 11y ago

alfonsodev 11y ago
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-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 :)
- woodcut 11y ago
  Thanks for this. It's an enjoyable read!
- turbohz 11y ago
  Previous discussion: https://news.ycombinator.com/item?id=11129375 https://news.ycombinator.com/item?id=11129375
eterm 11y ago
I 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.
- alfonsodev 11y ago
  If you use safari or firefox, reader view is available for the articles. https://support.mozilla.org/en-US/kb/firefox-reader-view-clutter-free-web-pages https://support.mozilla.org/en-US/kb/firefox-reader-view-clu...
  - montibbalt 11y ago
    The reading view in Edge (and metro IE fwiw) works as well
- lukeschlather 11y ago
  I just zoomed in until the left-hand panel disappeared. Annoying, but the font is too small anyway.
noobie 11y ago
Jeremy is actually a HN user, soon enough he will be summoned. Kudos to you sir if you are reading this!
shasta 11y ago
> 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 ...
- goblinking 11y ago
  but it looks sorta mathy, I better upvote even if the guy has no clue whatsoever!
- jfoutz 11y ago
  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.
  - shasta 11y ago
    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.
    - jfoutz 11y ago
      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.
      - arielb1 11y ago
        But if you have r=sqrt(n) that works out fine.
j2kun 11y ago
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-theory/ http://jeremykun.com/2011/06/26/teaching-mathematics-graph-t... [2]: http://jeremykun.com/2014/05/26/learning-to-love-complex-numbers/ http://jeremykun.com/2014/05/26/learning-to-love-complex-num... [3]: http://jeremykun.com/2013/05/11/bezier-curves-and-picasso/ http://jeremykun.com/2013/05/11/bezier-curves-and-picasso/ [4]: http://jeremykun.com/program-gallery/ http://jeremykun.com/program-gallery/ edit: updated font size & article width. I'm considering changing the theme completely.
- jilljennV 11y ago
  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/ 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.
- RaitoBezarius 11y ago
  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!
  - Kluny 11y ago
    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.
- klekticist 11y ago
  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!
deleted 11y ago
[deleted]
misiti3780 11y ago
i 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.
derjames 11y ago
QUOTE: << Is it possible to condense high-dimensional data into smaller dimensions and retain the important geometric properties of the data? >> Like in a non-dimensional number?. For example the Reynolds number in fluid flow.
- zardo 11y ago
  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.
  - ergl 11y ago
    > 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. Isn't this what M/PCA is all about? https://en.wikipedia.org/wiki/Principal_component_analysis https://en.wikipedia.org/wiki/Principal_component_analysis and https://en.wikipedia.org/wiki/Multilinear_principal_component_analysis https://en.wikipedia.org/wiki/Multilinear_principal_componen...
greydius 11y ago
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.
- j2kun 11y ago
  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.
cosinetau 11y ago
Math ∩ Programming = Math. Just sayin'. :P
- ebola1717 11y ago
  That would imply Math is a subset of Programming, when in fact it's pretty clearly a strict superset of Programming.
  - jonsterling 11y ago
    Unless you are a Russian / Markovian constructivist!
iheatu 11y ago
This website is doubtlessly one of the best introductions to higher math available online. I've gained a lot by both finding and reading the website posts. A weekly email with some sort of order would be great and I would sign up immediately. Keep it up!!!!
bpchaps 11y ago
This is really, really awesome. I have a long train ride coming up, so I just put together a quick wget script to get all the pages for when I have zero internet. :)
qrendel 11y ago
@j2kun: Just curious, any chance you'd do an explainer on the Curry-Howard equivalence[1] sometime? Forgive me if you already have, but a search didn't turn anything up. Seems pretty relevant to math ∩ programming and also of interest to a lot of generalists. [1] https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspon...
- j2kun 11y ago
  I think I have a mildly different opinion about the correspondence than most other people on the internet. That's mostly why I have decided to write about other things. But then again maybe that's a good reason to write about it.

236 points by bigblind 11y ago

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-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 :)

woodcut 11y ago
Thanks for this. It's an enjoyable read!
turbohz 11y ago
Previous discussion: https://news.ycombinator.com/item?id=11129375 https://news.ycombinator.com/item?id=11129375

eterm 11y ago

I 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.

alfonsodev 11y ago
If you use safari or firefox, reader view is available for the articles. https://support.mozilla.org/en-US/kb/firefox-reader-view-clutter-free-web-pages https://support.mozilla.org/en-US/kb/firefox-reader-view-clu...
- montibbalt 11y ago
  The reading view in Edge (and metro IE fwiw) works as well
lukeschlather 11y ago
I just zoomed in until the left-hand panel disappeared. Annoying, but the font is too small anyway.

noobie 11y ago

Jeremy is actually a HN user, soon enough he will be summoned. Kudos to you sir if you are reading this!

shasta 11y ago

> 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 ...

goblinking 11y ago
but it looks sorta mathy, I better upvote even if the guy has no clue whatsoever!
jfoutz 11y ago
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.
- shasta 11y ago
  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.
  - jfoutz 11y ago
    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.
    - arielb1 11y ago
      But if you have r=sqrt(n) that works out fine.

j2kun 11y ago

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-theory/ http://jeremykun.com/2011/06/26/teaching-mathematics-graph-t... [2]: http://jeremykun.com/2014/05/26/learning-to-love-complex-numbers/ http://jeremykun.com/2014/05/26/learning-to-love-complex-num... [3]: http://jeremykun.com/2013/05/11/bezier-curves-and-picasso/ http://jeremykun.com/2013/05/11/bezier-curves-and-picasso/ [4]: http://jeremykun.com/program-gallery/ http://jeremykun.com/program-gallery/ edit: updated font size & article width. I'm considering changing the theme completely.

jilljennV 11y ago
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/ 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.
RaitoBezarius 11y ago
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!
- Kluny 11y ago
  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.
klekticist 11y ago
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!

deleted 11y ago

[deleted]

misiti3780 11y ago

i 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.

derjames 11y ago

QUOTE: << Is it possible to condense high-dimensional data into smaller dimensions and retain the important geometric properties of the data? >> Like in a non-dimensional number?. For example the Reynolds number in fluid flow.

zardo 11y ago
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.
- ergl 11y ago
  > 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. Isn't this what M/PCA is all about? https://en.wikipedia.org/wiki/Principal_component_analysis https://en.wikipedia.org/wiki/Principal_component_analysis and https://en.wikipedia.org/wiki/Multilinear_principal_component_analysis https://en.wikipedia.org/wiki/Multilinear_principal_componen...

greydius 11y ago

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.

j2kun 11y ago
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.

cosinetau 11y ago

Math ∩ Programming = Math. Just sayin'. :P

ebola1717 11y ago
That would imply Math is a subset of Programming, when in fact it's pretty clearly a strict superset of Programming.
- jonsterling 11y ago
  Unless you are a Russian / Markovian constructivist!

iheatu 11y ago

This website is doubtlessly one of the best introductions to higher math available online. I've gained a lot by both finding and reading the website posts. A weekly email with some sort of order would be great and I would sign up immediately. Keep it up!!!!

bpchaps 11y ago

This is really, really awesome. I have a long train ride coming up, so I just put together a quick wget script to get all the pages for when I have zero internet. :)

qrendel 11y ago

@j2kun: Just curious, any chance you'd do an explainer on the Curry-Howard equivalence[1] sometime? Forgive me if you already have, but a search didn't turn anything up. Seems pretty relevant to math ∩ programming and also of interest to a lot of generalists. [1] https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspon...

j2kun 11y ago
I think I have a mildly different opinion about the correspondence than most other people on the internet. That's mostly why I have decided to write about other things. But then again maybe that's a good reason to write about it.