That's the opposite, an example of a computation that is outside of the set of all thoughts.
Notably, such examples wouldn't exist if computation was strictly a subset of thought, but that can be waved away by acknowledging that the brain has finite resources that it does its best to use sparingly. Also, brains definitely run algorithms with staggering numbers of variables, e.g. object recognition from noisy sense data.
Running algorithms doesn’t make something a computer. Lots of things have SoCs in them but aren’t general computers if eg you can’t change the algorithms they do.
And all the results about all computers being equivalent only work if they have access to infinite storage and power. That computation isn’t outside the set of all theoretical thoughts, it’s just outside the set of all ones in actually existing human brains that don’t have access to a pen and paper.
Maybe I was unclear, but I completely agree both that your example does not prove that computation is a superset of thought. I'm looking for an example that would at least suggest the opposite- something humans can think that a computer couldn't compute.
Why does this matter? Both the brain and the workstation have finite amounts of memory, since they have finite masses, and can do random errors when trying to go through a series of steps. It is just the magnitudes that differ regarding these two aspects.
Yes, I can do many such calculations on 10’s of thousands of variables quite easily. Accurately throwing a ball while running for example is a complex activity.
That’s not a program
you’re running on your personal brain-computer, it’s a fixed-function DSP. You can’t reuse it to do other tasks in a way a computer could with such a DSP either - eg you can’t accurately simulate ball throwing in your head.
You learn to throw a ball while running by building on top of many processes that allow you to stand up straight, run, etc. It’s like multiple FPGA operating together rather than a DSP.
As to simulating a ball being thrown, that’s one thing that the brain already does. Visualization is a simulation.
I said "accurately simulating" though - if you're imagining something there's no way to constrain your own imagination to actually be correct.
Like if you're a bad shot you can't install an update to turn into a sniper. Of course, snipers do get to be that good by practicing enough, but I don't know if they visualize the target or do it with conscious math.
Visualization practice is part of many training programs to help people get better at making free throws etc. So it isn’t simply imagination, it’s a useful simulation.
What’s important to realize is people don’t just picture the path a ball takes but also the feel as they make a throw. Predicting the path of a thrown ball to be able to catch it is a another sign of simulation, but combining that with a simulation of how a throw takes place is useful.
Pool is clear example of the brain doing physical simulation. The exact positions are unique, but people learn how to predict what will happen to figure out what’s reasonable to attempt.
