
Mathematics and Computation - altro
https://www.math.ias.edu/avi/book
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garganzol
I would also mention that LISP is a highly enlightening instrument that
connects math (lambda calculus) with programming (Turing).

Once you get LISP you will never separate math and programming again. Two
slightly different facets of the very same computational thing.

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TheRealPomax
If you never separate those two again, you will have lost the ability to
reason about programming at the various levels of abstraction... which would
be a net loss, not a net win.

~~~
chongli
Could you expand on this? I’m not quite sure what you mean. Are you suggesting
that there are levels of abstraction in programming that can’t be modelled
mathematically?

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AnimalMuppet
Let's say I'm working on a user interface. Thinking of it in terms of lambda
calculus instead of user interaction is... let's call it sub-optimal, _even
though the code can be thought of in terms of lambda calculus._

Now, you can come up with some metrics to mathematically analyze certain
aspects of the user interaction. I don't think that's what garganzol was
talking about, though.

~~~
chongli
_you can come up with some metrics to mathematically analyze certain aspects
of the user interaction_

And we have done that! Fitts’ law [1] gives us a very good way of quantifying
certain aspects of user interface design. I can’t tell you how many UIs I’ve
used (lost count) that have ignored this very basic principle and as a result
they’re extremely frustrating to use.

In any case, it may not be what garganzol was talking about, but it did
resemble a comment I’ve seen made many times. In the vast majority of cases
I’ve seen, people who claim that math is inapplicable to some problem are
completely unaware of a rich and storied field of mathematics dedicated to
that topic.

[1]
[https://en.wikipedia.org/wiki/Fitts%27s_law](https://en.wikipedia.org/wiki/Fitts%27s_law)

~~~
AnimalMuppet
Sure. But like TheRealPomax said, that's a different level of abstraction. If
you need to be thinking in terms of Fitts' Law, and you're thinking of your
code in terms of lambda calculus-level math, you're going to have a rough
time.

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rory_isAdonk
Loving reading this, thanks altro.

Motivation gained to do a MSc in Statistics.

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altro
There are so many beautiful books, notes, blogs on theoretical computer
science...Keep reading ;)

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petulla
Share some!

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dpflan
Check out altro’s other submissions, quite a few PDFs.

>
> [https://news.ycombinator.com/submitted?id=altro](https://news.ycombinator.com/submitted?id=altro)

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zozbot234
Tl;dr: an excellent book on computational complexity theory.

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deyouz
Thanks a lot!

