In a not-so-recent post, I mentioned a letter I wrote to Philosophy Now challenging a throwaway remark by Raymond Tallis in his regular column called Tallis in Wonderland. As I said in that post, I have a lot of respect for Tallis but we disagree on what physics means. Like a lot of 20th Century philosophers, he challenges the very idea of mathematically determined natural laws. George Lakoff (a linguist) is another who comes to mind, though I’m reluctant to put Tallis and Lakoff in the same philosophical box. I expect Tallis has more respect for science and philosophy in general, than Lakoff has. But both of them, I believe, would see our ‘discovery’ of natural laws as ‘projections’ and their mathematical representation as metaphorical.
There is an aspect of this that would seem to support their point of view, and that’s the fact that our discoveries are never complete. We can always find circumstances where the laws don’t apply or new laws are required. The most obvious examples are Einstein’s general theory of relativity replacing Newton’s universal theory of gravity, and quantum mechanics replacing Newtonian mechanics.
I’ve discussed these before, but I’ll repeat myself because it’s important to understand why and how these differences arise. One of the conditions that Einstein set himself when he created his new theory of gravity was that it reduced to Newton’s theory when relativistic effects were negligible. This feat is quite astounding when one considers that the mathematics, involved in both theories, appear, on the surface, to have little in common.
In respect to quantum mechanics, I contend that it is distinct from classical physics and the mathematics reflects that. I should point out that no one else agrees with this view (to my knowledge) except Freeman Dyson.
Newtonian mechanics has other limitations as well. In regard to predicting the orbits of the planets, it quickly becomes apparent that as one increases the number of bodies the predictions become more impossible over longer periods of time, and this has nothing to do with relativity. As Jeremy Lent pointed out in The Patterning Instinct, Newtonian classical physics doesn’t really work for the real world, long term, and has been largely replaced by chaos theory. Newton’s, Einstein’s and Schrodinger’s equations are all ‘linear’, whereas nature appears to be persistently non-linear. This means that the Universe is unpredictable and I’ve discussed this in some detail elsewhere.
Nature obeys different rules at different levels. The curious thing is that we always believe that we’ve just about discovered everything there is to know, then we discover a whole new layer of reality. The Universe is worlds within worlds. Our comprehension of those worlds is largely dependent on our knowledge of mathematics.
Some people (like Gregory Chaitin and Stephen Wolfram) even think that there is something akin to computer code underpinning the entire Universe, but I don’t. Computers can’t deal with chaotic non-linear phenomena because one needs to calculate to infinity to get the initial conditions that determine the phenomenon’s ultimate fate. That’s why even the location of the solar system’s planets are not mathematically guaranteed.
Below is a draft of the letter I wrote to Philosophy Now in response to Raymond Tallis’s scepticism about natural laws. It’s not the one I sent.
Quantities actually exist in the real world, in nature, and they come in specific ratios and relationships to each other; hence the 'natural laws'. They are not fictions, we did not make them up, they are not products of our imaginations.
Having said that, the wave function in quantum mechanics is a product of Schrodinger's imagination, and some people argue that it is a fiction. Nevertheless, it forms the basis of QED (quantum electrodynamics) which is the most successful empirically verified scientific theory to date, so they may actually be real; it's debatable. Einstein's field equations, based on tensors, are also arguably a product of his imagination, but, according to Einstein's own admission, the mathematics determined his conclusion that space-time is curved, not the other way round. Also his famous equation,
E= mc2, is mathematically derived from his special theory of relativity and was later confirmed by experimental evidence. So sometimes, in physics, the map is discovered before the terrain.
The last line is a direct reference to Tallis’s own throwaway line that mathematical physicists tend to ‘confuse the map for the terrain’.