Literary Discussions

Imagine some enormous hyper-dimensional fork (as in spoon and fork) which has its prongs stuck in our universe. We see those prongs as points, separate entities. If we do something to one prong we measure an instantaneous change at the other prong some great distance away and we jump to the conclusion that an effect can move FASTER than the speed of light.

Human beings feel that they do not COMPREHEND something until they have built a mathematical model which perfectly imitates and predicts the physical observations.  We feel that when we can predict some future event precisely then we understand that event.

When one of the space explorers passed near the rings of Saturn and photographed them up close, scientists were delighted that the composition of the rings was exactly as they predicted.

I suppose it is the field of study called EPISTEMOLOGY which questions how we know anything or understand it.  

Aristotle conjectured that what humans take greatest delight in is MIMETIC (from where we get the word Mime, as in Marcel Marceau ) IMITATION. Aristotle said this in The Poetics. A mathematical model imitates some behavior in the physical world to within some degree of accuracy. Newtonian physics predicted the path of projectiles like cannon balls accurately enough to strike the enemy but not accurately enough to strike the moon.

The mathematician Kurt Godel had almost a religious belief that numbers and objects of mathematics had an actual existence in some ideal, eidetic realm, untouched and uncorrupted by the physical world and attainable only by the mind.  Einstein on the other hand rejected such a notion and saw mathematics as an ad hoc tool to achieve some end.

If you google on a picture of Wittgenstein's grave you will see a little decorative ladder is part of the tombstone. Wittgenstein wrote his Tractatus in which he says on the first page "That of which we cannot speak we must pass over in silence."  Wittgenstein saw the self-referential problem of any language which predicates qualities (or quantities) whether a spoken language or the symbolic language of mathematics. Kurt Godel and Wittgenstein both touched upon the possible inherent weaknesses of mathematics. Those weaknesses suggest that the task of mathematicians will never come to a conclusion, a final age of absolute knowledge which Hegel dreamed of.   

The IBM OS operating system has been described as one of the most complex human creations ever. At any give time it has 1000 bugs. It is like an infinite carpet with bumps and no matter how you work to smooth out all the bumps, they simple reappear elsewhere.

Morris Kline wrote a book entitled something like "The Failure of Mathematics" but I would have to Google and I must post this long post before it disappears.