Q: Why is mathematics so effective as a tool in describing parts of the physical world?
A: Mathematics is not a random collection of facts. It was created by the minds of individuals. Though it pleases us to imagine that we can think any kind of thought, that is an illusion. Our "idea space" is highly constrained by the process that created the thinking engine.
Our distant ancestors used their proto-minds as images of certain relevant parts of the external so they could anticipate better or faster and generally be more effective at passing on genes. An early example of this might have been an oozing toward or away from a higher concentration of a chemical in the water. An impulse like this, by its survival, contains information about the world.
As these impulses accumulated a "negotiator" would be highly advantageous, to "break ties" and avoid paralysis. The collection of impulses and negotiators, together, would be the proto-mind. The proto-mind itself could be thought of as a genetically encoded memory of past contact with the external, with properties assembled by random mutation but selected for over eons by ability to confer advantage.
The genes that created the proto-mind were "survivor genes," selected over eons precisely because they increased the fidelity of the mirror they generate to parts of the external.
Billions of years of evolution created better and better internal models of parts of the external and added individual memories - an enormous advance that would allow for (evanescent) improvement of the model during the lifetime of an individual. Volition, or a means to probe the boundaries of increasingly sophisticated models would benefit individuals with memory if done cautiously. Both of these might come through changes to the "tie-breaker" mechanism.
A means to transmit useful memories among related individuals would also be selected for if it should ever arise. Curiosity or even outright recklessness in probing the boundaries of the growing model would benefit the genes if there were a means of transmitting memories of the outcome among related individuals.
We could go on with this, and it is a long way from the ruminations found above to consciousness and self-awareness, but we need to get back to the question:
Q: Can you list the implicit assumptions in the question and in your answer with which people might take issue?
A: Not on one page. Not on many pages. But it works for me!
