Hacker Newsnew | past | comments | ask | show | jobs | submitlogin

Wow. I feel like the fact that you can encoding arbitrary information in long numbers is such a far reaching concept in math/computer science, it's really satisfying to see it demonstrated in such an intuitive way.


Dimensions can always be compressed and uncompressed.

Naturals: https://en.wikipedia.org/wiki/Pairing_function

Reals: https://en.wikipedia.org/wiki/Space-filling_curve

The caveat is that a function, like the evolution of the universe, General Relativity, differential equations, would be possibly unwieldy and unaesthetic when written on lower dimensions, and locality might also be lost.

Some techniques try to preserve locality:

https://en.wikipedia.org/wiki/Z-order_curve

The takeaway is that any object, nomatter how complex, can be represented as a single number. That is the basis of Godel Numbering: https://en.m.wikipedia.org/wiki/G%C3%B6del_numbering


Replying to the dead comment by saschag:

Respectfully, your argument just boils down to whether the real numbers actually "exist." And I airquote exist because even that term is loaded.

This HN delved into it: https://news.ycombinator.com/item?id=14080024

It really just boils down to the nature of incompressible infinities.

You may enjoy this video that explores some of the issues with unresolvable infinities:

https://youtu.be/Szd6RBsWntg


The entire Library of Babel is encoded in Pi.

https://en.wikipedia.org/wiki/The_Library_of_Babel


This assumes that pi is a normal number [0], a fact that is widely believed but has not been proven.

[0]: https://en.wikipedia.org/wiki/Normal_number


So cool, you can find anything you search for: https://libraryofbabel.info/bookmark.cgi?concernedcoder0001 about 1/2 way down the page you can find: "concerned coder is a programmer living in the sourthern usa, playing a game called eve online while reading hacker news on a sunday night in january"


Hmm. Other sources suggest that Concerned Coder is a programmer living in the northern USA, playing a game called Eve Online while reading Hacker News on a Sunday night in January:

https://libraryofbabel.info/bookmark.cgi?concernedcoder00001...


you can encode any arbitrary information into a one dimensional value.... eg: a large enough number can encode the whole universe....

But decoding any meaningful information has to be at least in two dimensions....

In two dimensions, you can describe everything.... the other dimensions are not needed (and perhaps just emerging, according to the holographic principle)....


> But decoding any meaningful information has to be at least in two dimensions....

What does this mean?


It's the uncertainty principle and principle of orthogonal observables. Energy vs time for example. You need two dimensions for a comparison. One dimension is static.


1GB of storage is a single number with 2^8billion binary digits.

Everything we do in computers is encoding information in long numbers. Every character is a single number, every file is, every disk image is, every state of RAM, every database, every cache, every piece of source code.


Not encoded as, but can be interpreted as. Any precisely specified object can be interpreted as a number.




Guidelines | FAQ | Lists | API | Security | Legal | Apply to YC | Contact

Search: