
From Philosophy to Program Size (2003) - pizza
https://arxiv.org/abs/math/0303352
======
abelhabel
I found this interesting.

"if a physical law can be as complicated as the experimental data that it
explains, then there is always a law, and the notion of “law” becomes
meaningless! Understanding is compression! A theory as complicated as the data
it explains is NO theory"...

Then saying that program -> computing -> output has to follow from small to
large in size, ie the program is the algorithmic information and the output is
the data it explains.

Looking at modern day web development we are seeing the opposite, where the
program is many times bigger than it's output, suggesting to me that the
modern frameworks do not come from any sound theory.

~~~
naasking
> Looking at modern day web development we are seeing the opposite, where the
> program is many times bigger than it's output

You're seriously underestimating the size of output in a web browser. Consider
that the CSS, JS and HTML describe the position of every pixel and its motion
on the screen.

~~~
dmreedy
Not just the size of a given output, but the space of possible outputs. I am
also of the opinion that webdev is bloated and miserable, but it is still a
massive compression of the information it represents.

~~~
titzer
I don't really buy that acres of whitespace and gradients really describe much
information.

Considered at the boundary of your awareness--in that you are mostly unaware
of all the pixels on the page, then absolutely not true. A typical news
article might be a few KB of text but MBs and MBs of images that you never
look at.

~~~
dmreedy
I'm talking about Shannon Information specifically. In which case, acres of
whitespace and gradients very much _are_ information. Calling them
"whitespace" and "gradients" is a significant act of compression in and of
itself.

~~~
titzer
I understand your argument, but even then I don't think it's quite right;
there is lots of room to improve on the size of a webpage vs its rendered
pixels on the screen, even with the fancy fonts and gradients and animations.
I still don't believe it's really megabytes. Have you seen 4k demo contests,
btw?
[https://www.youtube.com/watch?v=0w_xEUoK79o](https://www.youtube.com/watch?v=0w_xEUoK79o)

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rimher
One of the most fascinating things I discovered when studying Computer Science
is the deep connection that exists between CS and Philosophy in general.

When CS was born, it wasn't by 'accident' or because some 'genius' invented
it. There were some impressively intelligent people out there, that
contributed in a very meaningful way. Philosophy paved the road to get there
though, and it's always strange to discover how it has done so through the
ages.

~~~
chadgeidel
Interesting, I'd love to hear more. Can you recommend any books or papers
exploring this topic?

~~~
dmreedy
If you're interested in more about this particular subject, I think Gleick
does a pretty good job of providing a 'road through history' on the subject of
the representation/computation duality in "The Information".

If you're keen on the broader problems of philosophy that will sound
strikingly familiar to anyone who has studied a bit of computer science,
Bertrand Russell's "Problems in Philosophy" is a tidy little dip into the
fundamental problems philosophers have wrestled with throughout history, and
the various tools they've invented to solve them (including logic,
mathematics, and by extension, computer science)

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dmreedy
For those who find this interesting, Chaitin's work is a subset of (or
complement to) Kolmogorov's work on complexity theory; fundamentally, the
unification of computation and representation under Shannon-style Information.
It collapses so many superficially different ideas about representation and
function as to be spooky. Or beautiful.

~~~
westoncb
Is there some work of his in particular that you'd recommend? I remember
coming across a pop-sci thing he'd written that seemed interesting, but I was
ultimately turned off by cheesy graphic design kind of things.

Just re-located it. It was called "Meta Math!: The Quest for Omega"

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Bodell
This is great I just got into a long conversation about this with a friend,
because of comments in another recent post about "Mapping Mathematics." A
specific comment had refereed to the information in the video about Godel as
being false. Specifically they did not like the video claiming that Godel's
incompleteness had impacted the way in which we view maths 'usefulness' all be
it an over-simplification Godel's work definitely had a vast impact on the
philosophical way that we view information, math, and science and does
certainly beg some questions about the limits of mathematics).

Being as I am currently in the middle of reading 'Meta Math' by Chaitin,
(because of his recommendations in that book) 'NKS' by Wolfram, and 'Number:
The Language of Science' by Datzig. I am glad to see this on the front page in
an era where we have so many 'science loving philosophy deniers' out there.
I'm assuming this being here at all is not a coincidence and that OP was maybe
thinking something similar, but I could be wrong.

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diego898
If you enjoy this, I can recommend the excellent "Why Philosophers Should Care
About Computational Complexity"[1] by Scott Aaronson

[1]
[http://www.scottaaronson.com/papers/philos.pdf](http://www.scottaaronson.com/papers/philos.pdf)

~~~
pizza
100% agreed! Also he did a cool lecture on the computational complexity
constraints of simulation - using a thought experiment concerning Newcomb's
paradox!

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bootsz
Very interesting topic. I also just generally enjoyed the liberal use of
exclamation points throughout.

"These are Irreducible Mathematical Truths!!! No rational justification is
possible!"

Imagine just shouting that at someone who you're having an argument with

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equalunique
"N-bit theory to prove that an N-bit program"

Am I the only one who thought of Curry-Howard correspondence?

