I once thought that mathematical geometry worked by a kind of detail crunching.
If a line is just a systematic set of infinite number of points checking whether two lines intersect would just be a "simple" operation to check whether they contain a point in common. Take points from one line and check whether it is a part of the other line. Doing this with literally infinite number of points would amount to a supertask. So you could only do so to an arbitrary precision but not exactly.
However a very simple math problem like "find the intersection of lines y=2x and y=3x+5" can be done exactly in a finite small number of symbol operations. And actually the description of the infinite number of points on the first line can be done by a very finite expression of "y=2x". There are also an infinite number of such lines but finding each of their intersection doesn't include attending them pair by pair. The procedure of solving the descriptions as a equation pair can be expressed in a expression more meta and "more finite".
So instead of just a big fleet of lowest level comparisons what really happens is a tiny amount of work on different levels. If one would count each symbol manipulation as a single number crunching operation the supertask of point comparisons would seem to be the most demanding. However using multiple levels of symbols means supporting a wider array of symbol manipulation operations.
So while I appears that I compare infinite numbers of points when I am doing simple geometry, it's just that I am bypassing one kind of calculations limits by using another kind of calculation.
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?