Jan 03 2007
When Scientific Models End
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
Finally I have managed to describe what I want to say about how science works. The concept of a model, that can be manipulated by some tools, and that there are similarities (isomorphism if you want to be pompous) between the model and the way the real world works. I have also explained, though probably not very clearly the problem that logic, the tools science uses to manipulate its models, cannot be proved to be consistent – though no inconsistencies have ever been found.
The next problem is that of what exactly the similarities (isomorphism) to the real world mean, and can we rely on them. Something almost every school child is taught are Newton’s Laws of Mechanics. These describe a model of, say, a tennis ball being struck by a tennis racquet. When you look at a real tennis ball, being hit by a real tennis racquet, then the results are the same. If the model ball goes 106 meters, then the real world ball does too. At least, it does when you make sure your model includes all other factors that apply in the real world, like air.
For a long time, this was fine, and everyone thought that it would always be fine. This is called the problem of induction. It works as follows: “We have compared our model to the real world on many previous occasions, and it was always similar. So it will always be similar.†This is a bit of a leap of faith. We do not know the future, and so we don’t know that the next time we test it it will still work. In reality we assume that it will work, and the first time we find a case that it doesn’t work in, we have to modify our model.
Newton’s Laws of Mechanics, as it turns out, did not work for all time. They only worked until we were able to look at things moving very fast. Then Newton’s model starts to give answers that do not match what we see in the real world. But we can use a more complex model – one that Einstein created called Special Relativity, which still gives the right answers.
The same problem might be there for every single scientific theory we have. They might well only agree with the real world for a range of situations, those that we are able to recreate and then examine. There is even the (probably very remote) chance that they only work agree with the real world on dates before tomorrow…..
Most of this is purely academic though - unless it turns out that the models are only of any use before a certain date. We have spent a lot of time recreating scenarios in the real world, and checking to see if the models agree. Those that don’t are forgotten.
Hi Laurie
I just thought I’d prod you with the phrase “evolutionary epistemology” courtesy of Popper.
Well worth reading up on if you are thinking about thinking about science.
Interestingly, for me, it does a good job of describing the range authority that the scientific method itself is limited to; that being the range of all models that are, in principle, falsifiable.
To quote Pauli: “This isn’t right. This isn’t even wrong.”
Nice site btw.
Cheers
Pete
Pete,
Thanks for the reference, I will look it up and have a read up on it. You are most certainly right that only models that are falsifiable are of any value, something which I intend to write a bit about in a future post. Though most of my ideas for developing this theme currently lie in a slightly different direction. For anyone else, some of Poppers works can be found on Amazon
[...] 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. [...]