Eric Baum was a fellow physics student both at Harvard and Princeton, completing his Ph.D. in the early 1980s on a topic in quantum gravity. During his years as a physics postdoc he came up with an argument for why the cosmological constant is so small that is sometimes referred to as the “Hawking-Baum” argument. He finally left physics, joining NEC Research in Princeton to work in cognitive science.

Eric has a new book out from MIT Press called “What Is Thought”, and you can read a review by Witten on the Amazon web-site. There’s also a web-site for the book.

His point of view on cognitive science is very much that of a physicist, emphasizing the way the brain encodes a very compact understanding of how the world works that has been made possible by the huge amount of computation and experiment that has taken place during the evolution of the human organism. One thing that most impressed me about the book is the underlying theme that he refers to as his version of Occam’s razor and summarizes as follows:

“mind is a complex but still compact program that captures and exploits the underlying compact structure of the world.”

To understand something about the world is to capture its features in a compact subroutine that allows one to effectively interact with it. This is clearly related to what theoretical physicists mean when they discuss the “beauty” or “elegance” of the fundamental equations and concepts that they are exploiting. So, if you have an interest in cognitive science, and enough interest in physics to be reading this weblog, I recommend heartily that you find yourself a copy of Eric’s book.

My comment involved a different kind of “compactness”, not the compactness of the supposed extra dimensions. A description of nature is a “compact” one if it can be expressed simply in terms of a small number of fundamental objects or ideas. A small number of simple equations, if you like. String theory is a very complex business and its proponents hope that it can be reduced to some simple principle or equation, but there is no evidence that this is the case.

Peter,

http://www.tech.port.ac.uk/staffweb/seahras/images/compact.jpg

“The are several different ways in which one can “roll-up” a non compact manifold, like the one on the left, into a compact space, like the other surfaces”

http://www.tech.port.ac.uk/staffweb/seahras/neat_physics/extra_dimensions/fifth.htm

I looked at number 2 of your response here and what you thought of string theory as not having this compaction principle?

What is your response to the above?

I guess I think of the mathematical formalisms of theoretical physics as more powerful extensions of the sort of understanding of the world built into our minds that Eric is writing about. As we try and improve them, the criteria should be:

1. Do they agree with the real world, as our minds have managed to understand it?

2. Are they compact, since to understand something new seems to mean to find a compact representation of it.?

For the three theories you mention, there’s still no compact form of them that agrees with the world. String theory is in the middle of desperately trying to get agreement with the world by abandoning the requirement of compactness, and adopting a huge, nearly infinitely complex theory.

“To understand something about the world is to capture its features in a compact subroutine that allows one to effectively interact with it. This is clearly related to what theoretical physicists mean when they discuss the “beauty” or “elegance” of the fundamental equations and concepts that they are exploiting. So, if you have an interest in cognitive science, and enough interest in physics to be reading this weblog, I recommend heartily that you find yourself a copy of Eric’s book.”

As I mentioned on another site, I find the need here to understand how such mathematical discriptions are born in mind to demonstrate the natural expressions that emerge from describing that nature.

This has been the quest as far as I understood it, from a student perspective. If one looks to Penrose or Smolin, there is always this need to explain the world from a basis of logical undertanding. So it first startsfrom a philospohcal discussion and then moves from this basis of logic, into the forms and requirments of the new math?

Examples here would have been Twistor Theory, Loop Quantum Gravity, or String Theory.

What are your thoughts here?