The point was, doesn't this require a lot of number crunching? Big numbers, for what its worth...
Ask such a blind mathematician to calculate an abstruse property of a geometric figure with randomized values down to the, say, 60th decimal place. Will they be able to do it? After all, it's a trivial amount of computation compared to what you imply is going on in their heads when they do the math that so impresses you.
A general counter-example to your post is dreams: in a dream, one usually feels sure of the reality and convincingness of the dream (and when one has cultivated the rare & unusual skill of doubting dreams, then one can do things like lucid dreaming) and yet there's hardly any information or calculation involved. Have you ever tried to read a book in a dream? Has an excellent logical argument been explained to you in a dream and then you tried to remember it when you woke up? I've heard both examples before, and when I was working on lucid dreaming & kept a dream journal, I did both, to no effect.
What's going on is more a case of domain-specific calculating power being hijacked for other things, heuristics, and people looking where the light is.
(Why was research into fractals and chaotic functions delayed until the '50s and later, when the initial results could often be shown to stem from material in the 1800s? It doesn't require much calculating power, Mandelbrot did his weather simulations on a computer much weaker than a wristwatch. Because the calculating power required, unlike geometry say, was not one that fits nicely into the visual cortex or requires extremely few explicit arithmetical calculations.)
From time to time I encounter people who claim that our brains are really slow compared to even an average laptop computer and can't process big numbers.
At the risk of revealing my complete lack of knowledge of neural networks and how the brain works, I want to ask if this is actually true?
It took massive amounts of number crunching to create movies like James Cameron's Avatar. Yet I am able to create more realistic and genuine worlds in front of my minds eye, on the fly. I can even simulate other agents. For example, I can easily simulate sexual intercourse between me and another human. Which includes tactile and olfactory information.
I am further able to run real-time egocentric world-simulations to extrapolate and predict the behavior of physical systems and other agents. You can do that too. Having a discussion or playing football are two examples.
Yet any computer can outperform me at simple calculations.
But it seems to me, maybe naively so, that most of my human abilities involve massive amounts of number crunching that no desktop computer could do.
So what's the difference? Can someone point me to some digestible material that I can read up on to dissolve possible confusions I have with respect to my question?