The Equivalency of Mathematics and Logic
My point here, David, is that quantum mechanics may be looking at - and mixing up - two (or more) different levels of physicality - the structure of objects, and the separately existing structure of the physical thoughts which refer to them (whether or not the objects actually exist).
I'd like to propose an argument that figuring out a math problem and writing a letter are expedited by the same core mental processes. The argument is based on the concept of physical ideas.
The concept of physical ideas is based on two assumptions: (1) The Big Bang (or some other "starting time or times" vitalized by energy) is valid; and (2) E=MCC. Then:
1) The Big Bang created a Universe of energy;
2) Each thing that exists in the Universe is composed of energy;
3) Ideas exist in the Universe, and are composed of energy;
4) Energy can be viewed as matter;
5) Ideas can be viewed as matter;
6) Ideas are defined in terms of other ideas;
7) A Geometry of Ideas follows.
This establishes an interlocking structure of physical ideas. And what are these "ideas"? Since they are composed of energy, ideas are physical particles arranged in unique designs - designs mandated by the power relationships - energy relationships, understood in mathematical terms - among the particles composing the ideas. (The ideas themselves are the relationships among the particles I am not a logician, but to me the "sense" of the argument is clear: 1) we live in a physical universe; 2) the ideas that exist in this universe are also physical; 3) these ideas (like Plato's Ideals) exist independently of an observer.
If we add one more element to this picture - an equivalency between logic and mathematics - then we can establish that mathematics and poetry are products of the same mental processes.
We can take the easy road for that: the Merriam-Webster dictionary states:
Logic - "The fundamental principles and the connection of circuit elements for arithmetical computation in a computer."
In other words, logical circuits produce results indistinguishable from mathematical results.
Physical ideas, as described here, are particles arranged in unique designs mandated by the mathematical relationships among the particles composing the ideas. Increasing the number of particles is equivalent to joining more ideas together. Since the joining of particles is governed by forces measurable by mathematics, and insofar as mathematics is a subset of logic (or vice-versa ! ), then this joining is what we call logical thinking.
This is more than just playing with words. If we can prove that ideas have a physical aspect then we can bring down the barriers between the physical and social sciences - because energy relationships will be the common denominator to every knowledge discipline. If ideas can be proven not to have a physical existence, then no harm done - we are just back where we started.
Physical ideas, as described here, are particles arranged in unique designs mandated by themathematical relationships among the particles composing the ideas. Increasing the number of particles is equivaIent to joining more ideas together. Since the joining of particles is governed by forces measurable by mathematics, and insofar as mathematics is a subset of logic (or vice- versa ! ), then this joining is what we call logical thinking.
This is more than just playing with words. If we can prove that ideas have a physical aspect then we can bring down the barriers between the physical and social sciences - because energy relationships will be the common denominator to every knowledge discipline. If ideas can be proven not to have a physical existence, then no harm done - we are just back where we started.
If there existed an algorithm that assigned values to idea quantities - for example, Red=4 bits, Green=4 bits, Blue=4 bits - then all the colors of the rainbow, each equivalent to a different idea, could be represented in an XYZ bit deep binary universe.
This simple demonstration could be the basis for other simulations in which opposites are given values and intermediate ideas are derived. Tall-Medium-Short, Hot-Cool-Cold, etc. The real challenge would come when contexts are mixed and an actual "thinking" algorithm is produced.
I don't pretend to have this all figured out. But it certainly seems doable at a theoretical level. And it can be done in simulation.