Elegant but over-rated?
How high can physics fly?
Mathematics and physics are much weaker systems than they appear to be.
Most of us find Maths hard. Strange symbols, strange concepts, strange algebraic manipulations. Hard because they are in our heads, and we cannot touch and taste them. It is a kind of ideal world, perhaps heavenly; many of the ancient Greeks thought it really existed. Plato, particularly, thought there was such an ideal world, somewhere, perhaps among the gods, with real graspable objects – an ideal circle, an ideal atom, ideal numbers, ideal values. He thought our circles in this world are only reflections or shadows of these perfect or archetypal forms.
Maths is the ideal discipline? Groan. Probably most of us think that if this is meant to be an ideal, we’d prefer to abolish maths. Please give us what we can touch, handle and taste!
How powerful and useful are these ideals?
Beauvais cathedral in France suffered two collapses (13th and 16th centuries) in its building quest to be the tallest in Europe. The masons only used experience and intuition. If the builders had been able to use modern engineering mathematics to calculate stresses in buildings, the original Beauvais Cathedral would still be standing today.
The first half a dozen people attempting to fly, attached feathered wings to arms, or constructed simple machines. They failed, and crippled or killed their inventors. Physics knows now that their attempts would never have worked and today we can design a successful hang glider, and huge transport planes because we understand the physics ideals much, much better.
WWII physicists working on the first atom bombs used complex modern physics to calculate the exact structure they should have. I have worked on the same software for a different purpose and know how difficult this was. We’ll never forget the explosions above Hiroshima and Nagasaki and how alarmingly successful the physics is!
As we develop maths and physics and logic, more and more we find past centuries’ understanding of maths and physics was rough, and sometimes wrong. Modern equations are better, in fact often amazingly better. Does this all mean that the physics and mathematics shows there is some realm of perfection out there? And we are nearly there? Rather, it shows the opposite – physics and maths theories are constantly changing and improving. This could well go on for ever.
It is so tempting to think that this ideal world of abstractions is almost a heavenly realm. The horrible probability is that we are making our little knowledge into a final picture of God. “God is the perfect triangle, God is the perfect mathematical equation.” Ugh! When God speaks to us he completely overwhelms our limited ideals. Thomas Aquinas in the Middle Ages worked out over many years a remarkable logical and philosophical system to describe God and how he interacted with the world. Then he had an actual experience of God and said his entire previous work amounted to “straw.”
The ancient Greeks thought that circles were such a perfect form, that all reality must be made of circles. The orbits of planets round the sun obviously had to be circles, and if observation showed otherwise the observation was wrong. But the idea of circles was wrong – we now know that planetary orbits are ellipses. The lesson of history is that our ideas of ultimate abstract and beautiful principles although very seductive and very powerful, are only approximations. As of 2023, the astronomical observations say that the universe seems a bit asymmetric; a beauty with a slightly warped nose.
Sometimes the maths is better than our eyes. Perhaps we see this in the famous riposte of Einstein who said that if any scientific observations contradicted his principles of Relativity, he was sorry, but the observations would be wrong! So far he has been proved right; his principles are correct. But the future? Who knows.
Our array of principles from modern Maths, Physics and Philosophy is amazing, even beautiful and very useful, but does not talk to us as people. But God does.