About mathematical cognition in TGD Universe

When one ponders about consciousness, one sooner or later realizes that the emergence of mathematical consciousness has meant an enormous evolutionary leap. Something completely exceptional seems to have occurred when the apple fell down about 540 years ago. Of course, also the emergence of our species was this kind of event?

This raises questions. What really happens in this kind of giant leaps of mathematical consciousness or cognitive consciousness in general. Is our species even in principle able to answer this kind of questions?

What does being or becoming conscious of a mathematical concept mean? Could one see this kind of event as an emergence of a new reflective level of consciousness? But how to describe this kind of hierarchy of levels of consciousness? What kind of phenomenon, bringing in mind phase transition, took place when humankind became conscious of differential and integral calculus, number theory, algebra, logic? Or did already the emergence of our civilization lead to this even?

One can imagine a more modest goal. What could be the physical correlates of these kinds of cognition. The easy solution of the problem would be that deterministic computations are conscious and one can formally regard any time deterministic time evolution as a computer program. This hypothesis does not however explain anything and is untestable.

Even the understanding of how the basic notions and algorithms are realized consciously at the level of cognitive consciousness seems very difficult in the framework of the recent day physics which has hitherto refused to say anything about conscious experience. Is the existing view of physics enough to meet the challenge?

These challenges look formidable but one can try! Maybe one could say at least something about cognition and mathematical cognition?

1. What are the physical correlates of cognition? Cognition is discrete and finite and cognition represents. Could one identify cognitive representations as a discretization of the sensory world. TGD leads to a number theoretic vision about physics dual to the geometric vision and provides a theory of cognition.

p-Adic topologies seems to be very natural candidates for the topology of cognition. p-Adic number fields fusing together with reals to what is called adele. One can also defined entire hierarchy of adeles induced by algebraic extensions of rationals. There is also a second adele-like structure defined by the union of the p-adic number fields. Two p-adic number fields are glued together at interfaces formed by numbers, which have an expansion in powers of an integer divisible by both primes.

See the article About mathematical cognition in the TGD Universe .

For a summary of earlier postings see Latest progress in TGD.

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.