Church–Turing thesis: the class of turing-computational functions is the same as the class of computationa functions in an intuitive sense
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Digital computer being compared to the human brain must be normalized and/or specified. Eg, 32 bit and 64 bits have different power; supercomputers and desktops , can successfully compute a different set of functions (even regardless of time taken).
Darendra Modhi, lead of IBM's SyNAPSE project, estimates the brain has 38 petaflops of computing power . [1]
TaihuLight, the world's most powerful supercomputer, now has 93 petaflops. [2] They have radically different energy requirements and operate at radically different speeds.
Definition of computational power:
the ability to compute a function.
there is a function that A can compute and B can't => A and B don't have the same computational power. (A also can compute every function that B can compute => A has more computational power than B)
It depends on what you mean by computational power.
xkcd's What If
both are Turing complete
(assuming the brain has acces to external memory like a pen and paper)
Given a fixed (finite) amount of time, both theoretical Turing machine , digital computer, brain can only manipulate a finite amount of data.
Given this, all Turing complete machines != equivalent computational power (per paren'ts definition).
A more accurate model of computational power for modern generation digital computers is the Random-access stored-program machine [1]. Analog, recurrent neural networks may be represented by non-deterministic TM, or something even more complex [2] > different power than RASP.
[1] https://www.wikiwand.com/en/Random_access_stored_program_machine [2] "Expressive Power of Analog Recurrent Neural Networks on Infinite Input Streams" Cabessa et al