Dec 26 2006
An Orrery - All of science in a clockwork model
Table of contents for The Limits of Science
- An Orrery - All of science in a clockwork model
- When Scientific Models End
- Believe Data, not Models.
- Sometimes Models Make Reality
An orrery is a mechanical device. It has a big sphere – representing the Sun, at its centre. Connected to a clockwork mechanism are arms that rotate about the “Sunâ€Â, at the end of each arm is a smaller globe, representing one of the planets. You can wind the mechanism’s cogs backwards to see the positions of the planets relative to each another in the past, and you can wind it forward to see the future alignments.
Regardless of how well it is designed or built, an orrery will have two problems. It’s not consistent, and it might be fundamentally wrong. As a mechanical device it suffers from wear and tear. Each time you set it up, and then wind it forward one “dayâ€Â, you get a different answer. The cogs will have worn down; turning a different amount, imperceptibly small bits of the teeth will have been smoothed down. The first time you get one configuration of the planets, the next time you set up the device to show you the same configuration, you will get a slightly different answer. What use is a model that doesn’t consistently give the same answer when asked the same question?
We can ignore that though, the small changes in answer are insignificant really, they are small and irrelevant. But there is potentially a bigger problem - the arms could be the wrong length, maybe on of the arms goes in the wrong direction. More realistically, they would not change in speed when two planets get nearer each other, or they might move in a circle rather than an eclipse. Even when it works as intended, it might be an imperfect recreation of the solar system.
Old fashioned as this may seem, it perfectly describes the way all “rigorous†science works. For anything we wish to explain, we construct a form of orrery: a model. We can wind it forwards or backwards to tell us the past, or the future. Today we don’t build a physical model. We build a conceptual model. A model made up of ideas. It doesn’t use cogs, or gears, but it uses predicates, axioms and theorems – the tools of logic. Scientists build conceptual models, using logic, of everything they try to explain.
These conceptual models suffer from the same two big question marks as the real orrery: Those of consistency and accuracy. That is to say, do they always give the same answer to the same question, and does the answer they give actually tell you the right, real world, answer?
[...] I recently wrote about what a scientific model is, and what are the limits of using models. Briefly, you can’t prove that the language used (logic) is consistent, and you can’t prove that the model really maps onto the world. [...]