3 ms·

Yes, that is what I mean. Why is there a disconnect between the complexity of the compact description and the naive description? Why are simple expressions not

by wyager 10y ago

Yes, that is what I mean. Why is there a disconnect between the complexity of the compact description and the naive description? Why are simple expressions not simple in all "natural" representations? This is not addressable with the contrived example of "you can create an encoding scheme that reduces an arbitrarily complex description to an arbitrarily short identifier". After all, this is not a constructed compression scheme. Why does nature expand simple expressions to these particular complicated forms?

schoen 10y ago
> Why are simple expressions not simple in all "natural" representations? Another example might be the primes, which have a very simple description and very subtle structure in their distribution.
- qubex 10y ago
  I don't really agree that the primes “have a very simple definition” in that the notion of ‘primeness’ is one of satisfiability and no constructive algorithm is known to exist.
  - Chinjut 10y ago
    I'm not sure what you're getting at here. Is it not relevant that there is a simple algorithm to enumerate the primes, or, even more so, determine whether a given value is prime?
    - spacehome 10y ago
      Of course it's relevant. qubex is just confused.
  - jerf 10y ago
    I'm not sure what you mean by not having a constructive algorithm to produce primes. The Sieve of Eratosthenes will output any given prime, with the primes coming out in order, given enough time. There may not be an efficient algorithm, but for most definitions of "information" that won't matter. The sequence of all primes is both so richly structured we've probably only scratched the surface and almost entirely bereft of information.
    - qubex 10y ago
      Yup you're right and I'm wrong.
gerbilly 10y ago
> Why are simple expressions not simple in all "natural" representations? I think because that simple description describes a non-linear iterative process that feeds back on itself.
lmm 10y ago
> This is not addressable with the contrived example of "you can create an encoding scheme that reduces an arbitrarily complex description to an arbitrarily short identifier". After all, this is not a constructed compression scheme. Why does nature expand simple expressions to these particular complicated forms? If not these particular forms then it would be some others. That fractals exist is pretty-much the fact that pseudo-random number generators exist: you plug in a small amount of input and it generates noise. The fact that it looks like something is more a sign of the overactive human facility for pattern recognition than anything else. (Also I suspect it would look a lot less like a burning ship if we hadn't been told it was a burning ship)

by wyager 10y ago

schoen 10y ago

> Why are simple expressions not simple in all "natural" representations? Another example might be the primes, which have a very simple description and very subtle structure in their distribution.

qubex 10y ago
I don't really agree that the primes “have a very simple definition” in that the notion of ‘primeness’ is one of satisfiability and no constructive algorithm is known to exist.
- Chinjut 10y ago
  I'm not sure what you're getting at here. Is it not relevant that there is a simple algorithm to enumerate the primes, or, even more so, determine whether a given value is prime?
  - spacehome 10y ago
    Of course it's relevant. qubex is just confused.
- jerf 10y ago
  I'm not sure what you mean by not having a constructive algorithm to produce primes. The Sieve of Eratosthenes will output any given prime, with the primes coming out in order, given enough time. There may not be an efficient algorithm, but for most definitions of "information" that won't matter. The sequence of all primes is both so richly structured we've probably only scratched the surface and almost entirely bereft of information.
  - qubex 10y ago
    Yup you're right and I'm wrong.

gerbilly 10y ago

> Why are simple expressions not simple in all "natural" representations? I think because that simple description describes a non-linear iterative process that feeds back on itself.

lmm 10y ago

> This is not addressable with the contrived example of "you can create an encoding scheme that reduces an arbitrarily complex description to an arbitrarily short identifier". After all, this is not a constructed compression scheme. Why does nature expand simple expressions to these particular complicated forms? If not these particular forms then it would be some others. That fractals exist is pretty-much the fact that pseudo-random number generators exist: you plug in a small amount of input and it generates noise. The fact that it looks like something is more a sign of the overactive human facility for pattern recognition than anything else. (Also I suspect it would look a lot less like a burning ship if we hadn't been told it was a burning ship)