Tuesday, May 15, 2007
Heini Halberstam, in the Chapter “Some Unsolved Problems of Higher Arithmetic” [Pages 191-203 in The Encyclopedia of Ignorance, Pergamon Press, Oxford, 1977], writes this:
“Turning to numbers that are the sums of two squares, these are only a littlem ore common than the primes…, and very little indeed is known about their finer distribution. For example, it is almost trivial to see that there is always such a number between n and n + n¼, yet literally nothing better is known…” [Page 201]
And this [ibid]:
“We know that, in a certain precise sense, most numbers are transcendental, yet the problem of deciding whether a given number is transcendental is profoundly difficult.” [Page 201]
Roger Penrose, in the same book, Chapter “Is Nature Complex?” [Page 160] writes:
“Though Nature [sic] is undoubtedly subtle, she is surely not malicious. This, at least, we have on the authority of Einstein…
That Nature can be usefully described, at least to a considerable degree according to the laws of number, has been in evidence for many centuries. But what is not so familiar to those without a mathematical background is that are several different kinds of number, many of which are nevertheless subject to the same arithmetical laws.”
Arithmetic (mathematics), in all its permutations, represents a reality that is as abstract and intangible as the theology of Jesuits. But it has “proofs” which theology does not.
Pi is infinite, and can be (almost) proven to be so. God is infinite, but there is no proof, so far, that can establish that “fact of faith.”
Mathematicians, and their lackeys (which we mean descriptively not pejoratively), including physicists, resort to the “provable” abstractions of arithmetic to resolve issues of physical reality that belie the meta-reality, even though it appears – and we use the word “appears” advisedly – that physicists, cosmologists, and their ilk, are dealing with the meta-reality. (They are not.)
Psychiatry would call the mathematician’s province that place where they (mathematicians) go to escape from the world. It’s not just an escape from the practical reality of life – the vicissitudes of daily living; it’s an escape into a contrived reality that pretends to cope with profound issues affecting mankind.
But what are mankind’s ills that physical laws address? Hunger? Poverty? War? Disease? What?
When theologians tackle the idea of God and/or morality, they are net with opprobrium by scientists, generally.
But when science addresses issues that are not biological, geologic or in ways that are not beneficial to the plight of humankind, such as quantum physics, string theory, and all the other subsets of physics, no one (or rarely anyone) reproaches them, and they win Nobel and other prizes.
We don’t deny that the study of the transcendental ether is important -- some saying that it may even lead to the discovery of God.
But it seems strange that so many scientists, who don’t believe in God or a hereafter, would spend so much time and effort on the curiosities of the Universe which, for them, has bearing on their eventual physical mouldering….unless….unless they, deep down, want to prove that there is a God, or a life after this one, or something more than what we perceive as the human, sensory reality. (But that for another time.)
When one studies the laws of harmony and musical theory itself, the end result may end up being a Beethoven symphony or a Beatle tune.
When one studies art – color, perspective, form, et cetera – one may produce a painting, as that by Monet, Titian, or Hockney.
And if one studies literary manuals, one might even create a work of fiction (or non-fiction) like that of Shakespeare, Gogol ,or Updike.
Those endeavors please the senses, and bring pleasure to an existence which is sometimes fraught with horrors of subtle or unimaginable kinds.
But what about mathematics, sometimes elegant in their construction? What sensory pleasures to they provide?
Yes, they stimulate the mind, so we give them that. And such stimulation can be quite as wonderful as that which one gets by looking at a Van Gogh painting, hearing a Verdi opera, or reading a Eco novel.
But is mathematical stimulation as glorious as sensory stimulation? For some it is, but for the rest of us, it isn’t.
Thus, we see the pursuit of mathematics and physics, not so much as a useful mental endeavor but, rather, as an escape into and from the delectabilities of things mundane, but oh so very delicious mundanities.
And so we’ll address here, some of those delights that assuage the humdrummery of everyday life, and even the stilt of mathematics that afflicts us, and almost everyone else we know….so that we might pursue the ultimate question: Not what does reality consist of but why are we here?