I don't disagree with anything in this post. An interesting footnote on that Newton quote is that some reserachers have speculated it may have contained a veiled slight to Robert Hooke, Newton's great rival in the Royal society, who was a very short hunchback. Who knows? But research has shown Newton experienced intense vitriol toward all rivals, going so far as to excoriate Leibnitz's reputation even after his death in an official Royal society review which he authored psuedonymically under the guise of an independent panel.
The present thread came out swinging with an overview of the average condition of mankind throughout history and how the curve suddenly exploded upward when science became the dominant methodology of uncovering physical consistencies we basically call truth. Those events have more connection than do the Yankees were dominant during prohibition.
It was more an artist's rendition of history, not so analytical. Ask Picasso what history is, he will paint you a strange picture with much misery and conflict and ignorance. Let us call it standard of living. Indeed it is a lower standard to use an outhouse instead of an indoor commode, to steer a horse-drawn buggy instead of a car, to be put to servitude as a child instead of receivng a mandatory education, to use leeches, animal horns and chants instead of pharmaceutical medicines.
The institutionalizing of science as the leader "forward" was only possible once the philosophy of science had duked it out socially with religion and come to a Mexican standoff with a compromise of dualism.
Everything from satellites to computers to mandatory mass education, came about (not coincidentally) only when we refused to let religion dictate physical truth to us anymore. The dualism many abhor was necessary to confine the truths of religion to an abstract region of the soul and out of the way of advancement.
For thousands of years brilliant individuals made life easier for many, tiny isolated step by step. The screw of Archimedes certainly improved things. Uncle Ben's bifocals and lightning rods did too. They were experimentalists, abstact thinkers and tinkers.
The unleashing of the techologies made possible through catalogued science and the growth of math exploded our comforts and awareness upward. We know so much more than the man of 1860 about the bigger picture, not to mention the man of 1060. To William the conquerer or Charlamagne a decent modern eleven year old would be a mathematical genius and treated as such, perhaps considered a wizard, able to divide troops or grain shipments at his whim and multiply from either memory or technique without an abacus.
Math is not a fictional story, never gets its facts wrong, never has to correct itself. The propositions of mathematics seem true whether anyone is there to form them or not. I do not think something else was true before they were formed. The forest had as many trees after someone counted them as it did before, so to speak.This gives numbers an eternal quality. Our simple number line marking off the whole numbers with all their infinite properties cannot and never could be different from what it is now. The relations of numbers do not change and shift around within an axiomatic system. To say that mathematics is foundational to the universe seems like it could be an understatement. In the system of integers an+bn never equals cn, end of story. It can be proven beyond any dispute from reasonable men. Hardcore proof.
Science is different. How do you prove that the boiling point of water averages 212° at sea level? You do experiments and keep a record, a history, a story of your results. Only repeatability and predictability prove such scientific facts. To work backwards starting with air composition, atmospheric pressure, water density et al is unbelievably difficult. The same thing that makes math true is what science leans on, for math is always repeatable within a system and always predictable. That's what a theorem is.
No amount of experiment would suffice to prove to a mathematician that the prime numbers are infinite in number. That there are no additional Brownian pairs up to two billion factorial has been numerically shown, but no one considers it a proof. *Factorials grow faster than powers. It would take more universes than there are stars in this universe to contain two billion factorial atomic particles. By 1022, 22! (twenty-two factorial) has already outpaced the powers and will accelerate its lead. It will eventually outpace any base.
It was scientific truth in overwhelming abundance that finally overhthrew the grip of superstition enough to proceed. Religion originated out of superstition the way language originated in grunts and squeals. Religion is completely superstition supported in so-called phenomena that cannot be numerically defined and are therefore not scientifically approachable so far as we know. Good riddance. That is its stubborn domain. But should that domain in the future prove to be scientifally approachable through the ingenuity of some domain-busting abstract thinker, science will have to annex more of religion's mysterious territory by force. Only that which can be numerically defined can exist. That is just the universe we live in and the only kind possible. Because we have not yet learned to numerically define spirits and souls and the like does not mean those things do not exist, and if they do exist, that they only started to exist once we defined them. Before a proper law can be formulated I believe all its principles are operant. This seems only reasonable to me. Newton only caged the operant dynamics of falling objects in an inverse square law because that is the law that was operant. Otherwise he couldn't do it. Numerically defined.
It sounds like a big tautology, and it is. The universe is all tautology, all its operant principles a snap to spot and connect if you only know the correct theory. We are embedded in a tautology so complex that we can only unfold its obvious nature slowly and a step at a time. Sometimes we take a big step. That is how I see the structure of the universe and very existence.
But since there are infinitely many emergent properties to unfold, we can never know them all or get to the end of it, so there will always be mystery and the unknown, which could turn out to be anything except numerically unapproachable. There will always be fictional literature and poetry of some type, there will always be music and visual arts of some type. Ingenius writers will find a way to composee believable mysteries even in a future when it seems like Big Brother would know everything. I own up to these Platonic beliefs. I did not always hold them. I had to come to them the old fashioned way—in an armchair.
Since art is not lost but continually unfolds even more interestingly in a universe which is nonetheless fated to be a tautology of mathematics if it ever could fully reveal itself, I am only too happy to own up to my Platonic sympathies regarding the primacy of number in the structure of existence. Even for non existence we have a number—zero.
Human imagination does not lose any quality with these admissions, once they are understood correctly, but imagination gains.



Reply With Quote