Does the observance of Moore's law mean the reality of super-Turing calculations?

Question

Mathematics

it's all. Although not, wikipedia: Super-Turing Computing , Moore's Law

Answer 1

No. If Moore's law continues to be true, the number of operations performed by the machine per unit of time will increase. But it will remain finite. More precisely, it will become infinite after infinite time, and this does not suit us.

Answer 2

As I understand it, you came to this conclusion from the fact about the convergent series on Wikipedia? More precisely, from the fact that the power is doubled, and the power * time = the number of calculations => with twice the power, the same number of calculations (unsuccessfully, but oh well) can be done in half the time?
There are several problems here. Well, firstly, calculations are not infinitely divisible, and half of a “computation” is the same as zero “computations”. And secondly, the logic itself is wrong. After all, look: today is X, tomorrow the power has doubled - 2X, then 4X. Well, yes, we sum up, we get infinity. But only if we sum up to infinity - and this is infinite time. It is clear that if we take a continuous analogue, nothing will qualitatively change. And your mistake is that you are trying to sum up the series from the inside, but you are doing it wrong, because the inverse to the series \sum_{n=0}^{\inf} \frac{2^n}, which needs to be calculated, not the series \sum_{n=0}^{\inf} \frac{1}{2^n} that you calculate.
That's all if I understood the essence of the error correctly :)

Answer 3

can complete an infinite number of steps in a finite time

I do not think that the number of transistors will somehow affect the fundamentals.