
Math ∩ Programming - bigblind
http://jeremykun.com/
======
j2kun
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...](http://jeremykun.com/2011/06/26/teaching-mathematics-graph-
theory/)

[2]: [http://jeremykun.com/2014/05/26/learning-to-love-complex-
num...](http://jeremykun.com/2014/05/26/learning-to-love-complex-numbers/)

[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.

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RaitoBezarius
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!

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Kluny
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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alfonsodev
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-...](http://jeremykun.com/2013/02/08/why-there-is-no-hitchhikers-
guide-to-mathematics-for-programmers/). Which I'd recommend to read as entry
point to this website if you feel intimidated by maths. Nice to find it again
:)

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turbohz
Previous discussion:
[https://news.ycombinator.com/item?id=11129375](https://news.ycombinator.com/item?id=11129375)

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

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greydius
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
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.

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misiti3780
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.

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qrendel
@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_correspon...](https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence)

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j2kun
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.

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iheatu
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!!!!

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derjames
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.

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zardo
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.

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ergl
> 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_componen...](https://en.wikipedia.org/wiki/Multilinear_principal_component_analysis)

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shasta
> 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 ...

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jfoutz
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.

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shasta
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.

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jfoutz
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.

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ph0rque
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](https://en.wikipedia.org/wiki/Stirling%27s_approximation))

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madcaptenor
Not exactly "proportional", because you have that pesky e in the denominator.
But that's the right idea. Basically, to get n! you're multiplying together n
things that are sort of n-ish, so you'd expect n! ~ n^n. (When the numbers get
really big, like in statistical mechanics, I've seen the approximation log n!
~ n log n.) The next step is to figure that you're multiplying together n
things that are on average n/2, so n! ~ (n/2)^n. But then it really turns out
that you should have been using a geometric average (since you're
multiplying), not an arithmetic one, so n! must be smaller yet. (I don't know
a way to get (n/e)^n without doing an integral, though.)

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ph0rque
Right, proportional in the sense that for both n! and n^n, the fastest-growing
component is ~n^n. (I was curious in the context of which grew faster for
larger values of n in the big O notation).

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bpchaps
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. :)

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eterm
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.

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alfonsodev
If you use safari or firefox, reader view is available for the articles.

[https://support.mozilla.org/en-US/kb/firefox-reader-view-
clu...](https://support.mozilla.org/en-US/kb/firefox-reader-view-clutter-free-
web-pages)

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montibbalt
The reading view in Edge (and metro IE fwiw) works as well

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cosinetau
Math ∩ Programming = Math.

Just sayin'. :P

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ebola1717
That would imply Math is a subset of Programming, when in fact it's pretty
clearly a strict superset of Programming.

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jonsterling
Unless you are a Russian / Markovian constructivist!

