[cjfd]

I am sorry to be this blunt but this is really utter and complete nonsense. The phrase that the mandelbrot set can't be represented in a lookup table is as such true but that is because nothing that you do with finite precision numbers can represent the mandelbrot set because it essentially is an inifinte object. The function f(x) = x^2 + c as an RNN can also not compute the mandelbrot set if the numbers it uses are of finite precision. That is exactly the same limitation that the lookup table also faces so there is no fundamental difference between the two.

[Legend2440]

We can give them both infinite precision, you still can't build a lookup table of the mandelbrot set.

The mandelbrot set is essentially a map of the halting behavior of a specific program. You can't know whether or not the program will halt for a given input, and so cannot build the lookup table. Programs are stronger than input-output mappings.

[ben_w]

Infinity is really hard to reason about, are you sure about that?

(For all I know you're a PhD in transfinites, your profile says nothing).

[somewhereoutth]

Infinity (of the various kinds) is well understood (see Cantor etc).

The Halting Problem is a central result in computer science, again well understood (especially here I would think!)

Their comment is correct.

[imtringued]

I see you are a fan of flying disembodied brains, but this time without a universe surrounding the brain.