4 ms·

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 satis

by extr 7y ago

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.

ardit33 7y ago
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)....
- lonelappde 7y ago
  > But decoding any meaningful information has to be at least in two dimensions.... What does this mean?
  - goldenkey 7y ago
    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.
jodrellblank 7y ago
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.
- lonelappde 7y ago
  Not encoded as, but can be interpreted as. Any precisely specified object can be interpreted as a number.
ShorsHammer 7y ago
The entire Library of Babel is encoded in Pi. https://en.wikipedia.org/wiki/The_Library_of_Babel https://en.wikipedia.org/wiki/The_Library_of_Babel
- kvakil 7y ago
  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 https://en.wikipedia.org/wiki/Normal_number
- deleted 7y ago
  [deleted]
- ConcernedCoder 7y ago
  So cool, you can find anything you search for: https://libraryofbabel.info/bookmark.cgi?concernedcoder0001 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"
  - twic 7y ago
    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?concernedcoder00001:1 https://libraryofbabel.info/bookmark.cgi?concernedcoder00001...
goldenkey 7y ago
Dimensions can always be compressed and uncompressed. Naturals: https://en.wikipedia.org/wiki/Pairing_function https://en.wikipedia.org/wiki/Pairing_function Reals: https://en.wikipedia.org/wiki/Space-filling_curve 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 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 https://en.m.wikipedia.org/wiki/G%C3%B6del_numbering
- deleted 7y ago
  [deleted]
- goldenkey 7y ago
  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 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 https://youtu.be/Szd6RBsWntg
  - saschag 7y ago
    what i was pointing at was that these theories are evolutions of hundreds of years old assumptions of 'predestination'. rooting in ideas of a big absolute clockwork, fortune telling, astrology. they're making promises that they can not prove without breaking the construct to begin with. it's a paradox, sci-fi, distraction from any type of wholesome outcome, claiming wholesome beginnings, claiming "more", breaking it to get there, because/thus lie. the concept is much older than that too. 6000 years or more. it's said that god has a name for every star. implying that there must be an appropriate singular unique identifier, coming from one truthful system, for every thing (that originated from his will). the idea, however, that a numerical system is any more appropriate than the alphabet or any other abstract symbolical representation to express law (logic), is ridiculous. it is obvious that people lie nonetheless, under the covers of 'science', making big promises and the only ones to benefit from them are the ones that sell such ideas, even though unproven. while i believe that there is 'one law', i believe too that it is broken by many and cause for schizms/conflicts and lies. no one truth will explain (justify) all lies. with the exception that they will be identified as a lie from broken origin but can not justify it's shape. from that perspective, no 'master constant' will predict your lottery numbers, stock markets, death nor life, because of the volatility of increasing utter bullshit. the only truthful prediction you can make, as time progresses more, is that mankind will undeniably conclude that the liars lie is the root of all evil and many liars made many victims.

by extr 7y ago

ardit33 7y ago

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)....

lonelappde 7y ago
> But decoding any meaningful information has to be at least in two dimensions.... What does this mean?
- goldenkey 7y ago
  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.

jodrellblank 7y ago

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.

lonelappde 7y ago
Not encoded as, but can be interpreted as. Any precisely specified object can be interpreted as a number.

ShorsHammer 7y ago

The entire Library of Babel is encoded in Pi. https://en.wikipedia.org/wiki/The_Library_of_Babel https://en.wikipedia.org/wiki/The_Library_of_Babel

kvakil 7y ago
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 https://en.wikipedia.org/wiki/Normal_number
deleted 7y ago
[deleted]
ConcernedCoder 7y ago
So cool, you can find anything you search for: https://libraryofbabel.info/bookmark.cgi?concernedcoder0001 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"
- twic 7y ago
  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?concernedcoder00001:1 https://libraryofbabel.info/bookmark.cgi?concernedcoder00001...

goldenkey 7y ago

Dimensions can always be compressed and uncompressed. Naturals: https://en.wikipedia.org/wiki/Pairing_function https://en.wikipedia.org/wiki/Pairing_function Reals: https://en.wikipedia.org/wiki/Space-filling_curve 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 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 https://en.m.wikipedia.org/wiki/G%C3%B6del_numbering

deleted 7y ago
[deleted]
goldenkey 7y ago
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 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 https://youtu.be/Szd6RBsWntg
- saschag 7y ago
  what i was pointing at was that these theories are evolutions of hundreds of years old assumptions of 'predestination'. rooting in ideas of a big absolute clockwork, fortune telling, astrology. they're making promises that they can not prove without breaking the construct to begin with. it's a paradox, sci-fi, distraction from any type of wholesome outcome, claiming wholesome beginnings, claiming "more", breaking it to get there, because/thus lie. the concept is much older than that too. 6000 years or more. it's said that god has a name for every star. implying that there must be an appropriate singular unique identifier, coming from one truthful system, for every thing (that originated from his will). the idea, however, that a numerical system is any more appropriate than the alphabet or any other abstract symbolical representation to express law (logic), is ridiculous. it is obvious that people lie nonetheless, under the covers of 'science', making big promises and the only ones to benefit from them are the ones that sell such ideas, even though unproven. while i believe that there is 'one law', i believe too that it is broken by many and cause for schizms/conflicts and lies. no one truth will explain (justify) all lies. with the exception that they will be identified as a lie from broken origin but can not justify it's shape. from that perspective, no 'master constant' will predict your lottery numbers, stock markets, death nor life, because of the volatility of increasing utter bullshit. the only truthful prediction you can make, as time progresses more, is that mankind will undeniably conclude that the liars lie is the root of all evil and many liars made many victims.