[wwweston]

> But can you prove that human beings can solve them? > Tessellation of the infinite plane? Please demonstrate a person that can solve this

Penrose himself would seem to be a demonstration that there is at least one person, IIRC.

Is your argument that uncomputable really just means no guaranteed success, and that just because some human can get a solution to an uncomputable problem doesn't mean that it isn't following a set of algorithms?

[theaiguy]

You misunderstand the result Penrose has shown. There are plenty of aperiodic tessellations of the plane that can be computationally generated. The issue is whether a computer can, in all cases, determine if a set of shapes can tile aperiodically.

I don't understand the second bit. But, no. Computability has very specific definition. Getting a solution to an uncomputable problem isn't generally hard. It is trivial to create a program that will solve the halting problem for an infinite class of cases. The issue is that such solutions can be shown not to be general over all cases.