The guy in figure 24 is a French mathematician called Étienne Ghys and somewhat known to the public for his commitment to the popularisation of mathematics. I guess he would love this sort of things. I wonder if this picture that chosen randomly on the internet or if this is some kind of homage.
Fundamental limits presuming one has arbitrarily high (but finite) quantities of time and space with which the computations can be performed. Given in real world computation we will never have either, the fundamental limits of real-world computation are a lot less (even infinitely less) than those given by Gödel's work.
Also, demonstrations of the theoretical limits of computation (Gödel, Turing, etc) often make the assumption that we only have finite (even if arbitrarily large) resources, and that true contradictions (dialetheias) are disallowed. If we give up either (or both) of those of two assumptions, we can compute beyond those limits. It may be objected that computations beyond those limits are not physically realisable; but, almost all computations within those limits are not physically realisable either, so how much significance does that objection actually have?
If some thing is impossible with arbitrarily large finite resources, it is still impossible with "practically large" finite resources ! That's why Turing / Gödel results really tell something fundamental about computing/proving; it tells everyone that they do not need to spend time solving an unsolvable problem on computers "as we know them".
But if you prove that something is possible in a your own magic computing framework, it remains practically useless until you implement it in the real world (an example of such a situation is the framework of "quantum computer" trying to solve prime factorization).