- make 2 objects that holds an array, initialize one to [true], the other to [false]
- each timestep, self-replicate the most recently made objects twice each, and append true, false to the array
- after N timesteps, every possible set of values for the boolean variables will be in memory
- if the object detects it has the correct length to do the check, then check it and update a global variable
- after you check every case in a single timestep (click of the js engine) because I used self-replicating objects, terminate the program
I consider this to be quite useful from a practical point of view, since I can now decide the answer to any problem in the family NP-complete in P time. I thought maybe mathematicians would also find it useful so I am sharing it on this site. This discovery resulted from thinking about the theoretical physics of energy in the human nervous system, and the massive computational power of cell self-replication, and has led to a number of math questions I now have, of which this is the most pressing
My understanding is that the regular theory of computation cannot be applied to this code sample. So I made up a new theory of computation where its exactly the same except Turing machine’s have a magic axiomatic self replication property.
I asked this question on Math Overflow now closed and was told it was off topic and does not involve research mathematics, so I am posting it here instead
I was told this is a non-physical model of computation in a subsequent discussion with one of the users on that site who was actually extremely helpful and made a number of very insightful comments. But this is physical, it’s exactly what the human nervous system does.
Question: What theory of computation should we use to describe the computational power of the human nervous system?
I was told my algorithm cannot possibly be O(N) because there are too many atoms in the universe and this algorithm would break cryptography. I found that to be a little silly since how come the human body doesn’t fall apart but our cells self-replicate?
I was told this would violate the church-turing thesis based on energy arguments, but again, according to the theoretical physics of the human nervous system, cell self-replication really does lead to an exponential increase in energy.