A Brilliant Science Moment, Brought to You By Zeno of Elea
Posted: Tue Oct 02, 2018 3:57 am
Thanks to so many Mormon scholars and apologists who smash up and cripple scientific thinking in their musings, I have taken it to heart to not let myself be swayed by their inchoate thinking and scrofulous undergraduate assumptions, which means off to the science stacks for me.
I just finished a truly inspiring book by David Deutsch (shall I sing of his accomplishments in honor-toned accolades? Yes, I shall. This man was educated at both Cambridge and Oxford, is a fellow of the royal Society and a professor of physics at the University of Oxford. He is a member of the Center of Quantum Computation, and an expert at the theory of parallel universes. He is the recipient of the Paul Dirac Prize at the Institute of Physics. In other words, anything this man says about science, is bound to upset Mormons, so I read him)
One particular moment in his The Beginning of Infinity, Penguin Books, 2011, that captured my attention (other than the other 487 pages) was his discussion of Zeno of Alea. I quote thusly starting at page 182.
I just finished a truly inspiring book by David Deutsch (shall I sing of his accomplishments in honor-toned accolades? Yes, I shall. This man was educated at both Cambridge and Oxford, is a fellow of the royal Society and a professor of physics at the University of Oxford. He is a member of the Center of Quantum Computation, and an expert at the theory of parallel universes. He is the recipient of the Paul Dirac Prize at the Institute of Physics. In other words, anything this man says about science, is bound to upset Mormons, so I read him)
One particular moment in his The Beginning of Infinity, Penguin Books, 2011, that captured my attention (other than the other 487 pages) was his discussion of Zeno of Alea. I quote thusly starting at page 182.
"Only the laws of physics determine what is finite in nature. Failure to realize this has often caused confusion. The paradoxes of Zeno of Elea, such as that of Achilles and the tortoise, were early examples. Zeno managed to conclude that, in a race against a tortoise, Achilles will never overtake the tortoise if it has a head start - because, by the time Achilles reaches the point where the tortoise began, the tortoise will have moved on a little. By the time he reaches that new point, it will have moved a little further, and so on ad infinitum. Thus the 'catching-up' procedure requires Achilles to perform an infinite number of catching-up steps in a finite time, which as a finite being he presumably cannot do.
Do you see what Zeno did there? He just presumed that the mathematical notion that happens to be called 'infinity' faithfully captures the distinction between finite and infinite that is relevant to that physical situation. That is simply false. If he is complaining that the mathematical notion of infinity does not make sense, then we can refer him to Cantor, who showed that it does. If he is complaining that the physical event of Achilles overtaking the tortoise does not make sense, then he is complaining that the laws of physics are inconsistent - but they are not. But if he is complaining that there is something inconsistent about motion because one could not experience each point along a continuous path, then he is simply confusing two different things that both happen to be called 'infinity.' There is nothing more to all his paradoxes than that mistake.
What Achilles can or cannot do is not deducible from mathematics. It depends only on what the relevant laws of physics say. If they say that he will overtake the tortoise in a given time, then overtake it he will. If that happens to involve an infinite number of steps of the form 'move to a particular location', then an infinite number of such steps will happen. If it involves his passing through an uncountable infinity of points, then that is what he does. But nothing physically infinite has happened.
Thus the laws of physics determine the distinction not only between rare and common, probable and improbable, fine-tuned or not, but even between finite and infinite. Just as the same set of universes can be packed with astrophysicists when measured under one set of laws of physics but have almost none when measured under another, so exactly the same sequence of events can be finite or infinite depending on what the laws of physics are.
Zeno's mistake has been made with various other mathematical abstractions too. In general terms, the mistake is to confuse an abstract attribute with a physical one of the same name. Since it is possible to prove theorems about the mathematical attribute, which have the status of absolutely necessary truths, one is then misled into assuming that one possesses a priori knowledge about what the laws of physics must say about the physical attribute."