If the brain is like a computer, how do humans even solve the halting problem? Maybe it's because humans feel anxiety at the unproductive passing of time while computers will just do what they're doing forever.
Write a program that, for a positive integer, runs the Collatz process on it (if even: halve it; if odd, multiply by three and add one; repeat).
If the process results in a 1, move on to the next number and repeat.
If the process produces a number it produced previously, halt. (Worried you’ll need unbounded state for this part? Use tortoise+hare, it’s fine).
This program halts if and only if the Collatz conjecture is false.
Now, the Collatz conjecture might not be unprovable. But for now no human can tell you whether or not that program halts.
I ended up using it to compare single core performance on any windows machine, because the timestamped logging was deterministic. Rewrote it in python and still use it these days.
For example, it’s trivial to write a program that searches by brute force for a cycle that would disprove the Collatz conjecture, and halts if it finds one. No human knows whether that program will halt.
IMO, in biological systems the explore vs exploit tradeoff is pretty analogous to the halting problem. There doesn’t seem to be an optimal general “solution” to it.
Once an organism is very familiar with its environment it’ll approximate near-optimal trade offs, which would suggest it’s just using heuristics.
That’s a common misconception. The brain is not like a computer. The brain can’t store and execute programs.
Can't it? The brain is absolutely capable of emulating a turing complete system such as running a program.
I mean, sure you can reason about a portion of code on your screen but there is no way you could emulate anything without some visual support.
There is no way your short term memory could store the program and the variables. The human brain can barely remember 5 to 10 words for several seconds and you have no control on your long term memory.
So yes your brain can somehow emulate a computer if you give him a pen, a sheet of paper paper, time, and a lot of sugar. But that’s not because it’s functioning like a computer but rather because you learnt how a computer work.