Huh?   A Model of Space, Infinity and Flow

Working Draft  Copyright (c) 2005 - 2007 Jim Imboden

Chapter 1  Models, Theories and Reality

Slowly I began to formulate what I still consider the fundamental fact about learning: anything is easy if you can assimilate it into your collection of models. If you can’t, anything can be painfully difficult. . . What an individual can learn, and how he learns it, depends on what models he has available.

Seymour Papert, Mindstorms: Children, Computers, and Powerful Ideas

To most people Models and Theories are seen pretty much the same thing, and while they may visualize them as somewhat different there is a great deal of fuzziness and overlap between them.  Scientists and physicists see them as two distinct things all relating to the same phenomenon.  The best description I’ve seen is in Roger Penrose’s book, “The Road to Reality”.   He views it to look like:

Reality is what we see and observe, it is the physical world.  The scientists and physicists try to understand this physical world and how it works, but the deeper they investigate the more complicated it gets.  To deal with the complexities they build mental images to explain their observations.  When building these mental images the scientists are bound by only one rule, the image must fit within the realm of the mathematical world.  Fortunately the mathematical world has a vast collection of tools to select from and the scientist only needs to select the tools to complete the mental image.

You should now be thinking: “What if the scientist selects the wrong tool (formula)”?  With the vast array of mathematical tools available it certainly can happen.  The scientist selects what they think the best tool is; it is their theory, the tool or tools they select will best describe what they have observed.

For the scientist, after selecting and building the model, mentally or otherwise, they test it.  If the tests show that they can duplicate what is observed then their theory could be considered correct.  Of course the acceptance of the theory is not automatic and it may take many tests by many people to validate it.

The correctness of theories over time can change.  A scientist may come along and build a new model, using different formulas and thoughts.  If this new theory proves to predict behaviors more accurately than the older theory then this new theory will replace the old one.   If the new theories ability to predict is the same as the old then the simplest one should become the accepted theory.

There will be times when what is observed cannot be modeled.  In Roger Penrose’s drawing Fig. 1.1 the Platonic mathematical portion does not exist, leaving the scientist with a mystery.  The scientists can still develop theories, but the mental images are non-existent.  To build the Platonic Mathematical Model the scientists need to find an arrangement of formulas to match the observations or develop a new formula.  This work focuses on a new formula.

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