MODELS

Models are essential for humans in order to understand the universe around us. A model seeks to represent empirical objects, phenomena, and physical processes in a logical and objective way. Scientific theories, laws, postulates, and ideas are a way of generating abstract, conceptual, graphical and/or mathematical tools to use to predict and understand future patterns. A model can be a scaled version of the real thing, a verbal description, a picture, contrasts, or more importantly these days, a mathematical formalization of physics.

It is really important to understand that all models are inherently false.

Models serve a very important purpose. No one would argue that Newton's Philosophiæ Naturalis Principia Mathematica is not one of the greatest works of human intelligence, but they will tell you that it is fundamentally incorrect. Newton's model of the universe still has value, and is still taught in the universities because of its facility to predict motion and force, and its easy visualization.

When my son was in the eighth grade, he had a science project to build a model of the Boron atom. He asked me for my help (BIG mistake). We made a model with each electron on a straight wire at the correct respective n-distance from the nucleus to depict its electron shell energy. Further we color-coded each electron to correspond to the shell configuration. We then graphed a simple scale for shell size to each other.

He received a poor grade because he didn't show the electrons on a ring circling the nucleus (this was 1998, so the knowledge that electrons do not 'circle' the nucleus was only 80 years old, give or take a moron or two). I was incensed, and went in to explain the rationale to the teacher. He told me that Alex received a bad grade because he did not show the electrons on a fixed ring circling the nucleus. I explained the energy scales, configuration patterns, overlap detail, and then he asked me where the rings were shown, and I gave up.

Electrons circling the boron atom nucleus in the Bohr model.

Ask anyone you meet to draw an atom, and the Bohr model of the atom is the most likely picture you will get. It is easy to understand, it predicts the behavior fairly well, and no one can see an atom anyway (these things are very small, probably operate in extra dimensions, and they act funny). The point is, the model that we all carry in our head of an atom is wrong, and misleading. Probably looks more like the following, if you could see it.

Boron Atom Dramatization

First of all, if I scale the electron cloud of a boron atom up to the size of the next graphic, and I show the nucleus and electrons as white dots, this is what you would see;

Atom mass shown in white.

If you actually see any white, clean your screen, it is just dust.

That is why mathematical models are so important. Most things that we want to study now are just too small to see. We are learning about them by their behavior when they interact with other things. Mathematics gives us a tool to use to predict an outcome, and then test it by observing experimental behaviors. Einstein said, "As far as the laws of mathematics refer to reality, they are not certain, as far as they are certain, they do not refer to reality."