2 ms·
> All the observed complexities can be regarded as partial descriptions of a simple fundamental reality: the Universe’s wavefunction. As an analogy, a perfect s
by tromp 3y ago
> All the observed complexities can be regarded as partial descriptions of a simple fundamental reality: the Universe’s wavefunction. As an analogy, a perfect sphere can be cut into many chunks with complicated shapes, yet they can be put back together to form a simple sphere.
As another analogy, the 100-bit lambda calculus term
(λ 1 1) (λ (λ λ λ 1 (2 (λ λ λ 3 1 (2 (λ 2)))) (3 (λ 4 (λ 4 (2 1))))) (1 1)) (λ 1)
is a binary tree containing all (infinitely many) closed lambda terms at its leaves. Thus including representations of all possible data and all programs.
- dd1988 3y agoFascinating - familiar with basic lambda calculus, but trying to wrap my head around this. Can you link to anything that explains more about how this works?
- tromp 3y agoA more readable form of the program is given at [1]. The tree contains all combinators built up from the single point basis A = λxλyλz. x z (y (λ_.z)), which is encoded as bit 0 (left branch), while bit 1 (right branch) encodes prefix application. [1] https://github.com/tromp/AIT/blob/master/ait/allA.lam https://github.com/tromp/AIT/blob/master/ait/allA.lam