5 ms·

That was actually implemented in a paper: https://fermatslibrary.com/s/drawing-an-elephant-with-four-complex-parameters https://fermatslibrary.com/s/drawing-an

That was actually implemented in a paper: https://fermatslibrary.com/s/drawing-an-elephant-with-four-complex-parameters https://fermatslibrary.com/s/drawing-an-elephant-with-four-c...

canjobear 6y ago
You can do it with one parameter http://colala.berkeley.edu/papers/piantadosi2018one.pdf http://colala.berkeley.edu/papers/piantadosi2018one.pdf
- contravariant 6y ago
  Using complex parameters, clever.
- TeMPOraL 6y ago
  If you try hard enough, you can do anything computable with a single integer parameter - if your model is a Turing machine, and the parameter encodes a program. It's perhaps less clever or cool than the hack above (by virtue of us being used to Turing machines), but serves as a friendly reminder that you can encode a lot of information in a long enough number.
  - lisper 6y ago
    The real lesson here is that "number of parameters" is not a useful measure of information content. The only useful measure of information content is information entropy, which is the logarithm of the number of distinguishable states. The base of the logarithm is arbitrary, but by modern convention is invariably taken to be 2. The resulting unit is the bit.
    - deepnotderp 6y ago
      This is not true. Consider the two sequences: 1 2 3 4 5 6 And 6 4 6 3 8 2 Do these sequences really have equivalent entropy? Welcome to algorithmic information theory :)
      - lisper 6y ago
        Your example is vacuous. You cannot determine the information content of a sequence of numbers in isolation. You can only determine information content of a system with respect to a model that tells you how to use the state of the system to distinguish between a number of possible states. The information content of the system is the log of the number of possible states from which the state of the system allows you to select one. Yes, algorithmic information theory is a thing. But neither it nor your example refute what I said (because what I said is in fact true).
      - Dylan16807 6y ago
        If they're that short, they basically do, to be honest.
    - Dylan16807 6y ago
      Number of parameters is fine when you're not trying to be sneaky with ridiculously precise constants. And it's more expressive in certain ways than a raw bit count. For general use you can impose reasonable limits, so that one parameter can't go overboard with bits. Something like a precision cap of one part per thousand and no going over a trillion.
- dekhn 6y ago
  every possible story, image, or really anything anywhere is just an index into PI.

That was actually implemented in a paper: https://fermatslibrary.com/s/drawing-an-elephant-with-four-complex-parameters https://fermatslibrary.com/s/drawing-an-elephant-with-four-c...

canjobear 6y ago

You can do it with one parameter http://colala.berkeley.edu/papers/piantadosi2018one.pdf http://colala.berkeley.edu/papers/piantadosi2018one.pdf

contravariant 6y ago
Using complex parameters, clever.
TeMPOraL 6y ago
If you try hard enough, you can do anything computable with a single integer parameter - if your model is a Turing machine, and the parameter encodes a program. It's perhaps less clever or cool than the hack above (by virtue of us being used to Turing machines), but serves as a friendly reminder that you can encode a lot of information in a long enough number.
- lisper 6y ago
  The real lesson here is that "number of parameters" is not a useful measure of information content. The only useful measure of information content is information entropy, which is the logarithm of the number of distinguishable states. The base of the logarithm is arbitrary, but by modern convention is invariably taken to be 2. The resulting unit is the bit.
  - deepnotderp 6y ago
    This is not true. Consider the two sequences: 1 2 3 4 5 6 And 6 4 6 3 8 2 Do these sequences really have equivalent entropy? Welcome to algorithmic information theory :)
    - lisper 6y ago
      Your example is vacuous. You cannot determine the information content of a sequence of numbers in isolation. You can only determine information content of a system with respect to a model that tells you how to use the state of the system to distinguish between a number of possible states. The information content of the system is the log of the number of possible states from which the state of the system allows you to select one. Yes, algorithmic information theory is a thing. But neither it nor your example refute what I said (because what I said is in fact true).
    - Dylan16807 6y ago
      If they're that short, they basically do, to be honest.
  - Dylan16807 6y ago
    Number of parameters is fine when you're not trying to be sneaky with ridiculously precise constants. And it's more expressive in certain ways than a raw bit count. For general use you can impose reasonable limits, so that one parameter can't go overboard with bits. Something like a precision cap of one part per thousand and no going over a trillion.
dekhn 6y ago
every possible story, image, or really anything anywhere is just an index into PI.