It seems clear that the present quantum mechanics is not in its final form [...] I think it very likely, or at any rate quite possible, that in the long run Einstein will turn out to be correct. 

~Dirac

 

We can also find information embodied in conscious experience. The pattern of color patches in a visual field, for example, can be seen as analogous to that of pixels covering a display screen. Intriguingly, it turns out that we find the same information states embodied in conscious experience and in underlying physical processes in the brain. 

~Chalmers

 

Science

​A complex of coefficients of this type is comparable with a matrix such as occurs in linear algebra. ~Heisenberg

​​

A matrix is an array of values, and the elements of an incoming vector can be operated on by some function to produce an output vector. ~PS Churchland

I was riding the bus one day, working on something completely different, when a thought fell into my lap. 

 

The mathematics of neural nets is the same mathematics found in Heisenberg's formulation of quantum mechanics.

 

Coincidence? Or a clue to something more interesting?

 

Does neural form follow quantum function?

When the solution is simple, God is answering.​​​​ ~Einstein

 

Where is the simplicity underlying the storied complexity of the mind and brain?

 

Over the years, I kept returning to a remark from Helmholtz, who wrote, with the simplicity of genius, that Similar light produces, under like conditions, a like sensation of color.

 

It gradually dawned on me that we can paraphrase this observation and say that the same state vector, acted upon by the same matrix operator(s) produces the same spectrum of colors and sounds and other sensory data.

 

In physics, anything can be expressed as a state vector, so this is quite a general result. Moreover, colors and sounds also behave like vectors. Why is this important?

 

Vectors embody fundamental physical symmetries. These symmetries determine the behavior of all elementary processes in the universe, including those in the brain.

 

That's how it all began to come together for me.

~Brian Flanagan