Posts Tagged ‘infinity’

Infinity Police and the Ontological Disconnect

Sunday, July 13th, 2008 by Terence Witt

Cultures usually have subjects that are taboo – things that are too repugnant to even discuss in low tones in the privacy of one’s own home. Cannibalism, for whatever reason, does not fall into this category. Far from it; people eating people is a staple of the movie industry, from low-budget zombie movies (always a favorite) to blockbusters where an elderly, avuncular man easily overpowers much younger (and one would think agile) opponents and well, eats some of them. Horrific subjects, such as the ‘cides’ (genocide, patricide, suicide, and of course the all-time favorite homicide) are more often entertainment than taboo. Indeed, certain daytime series have created an industry based on incest and adultery.

Then there’s infinity. I realized two things, as I was recently defending my interpretation of infinity for the 782nd time. First, that writing a book might not be the best way to present new concepts, and second, that infinity was, for whatever reason, sacred mathematical ground that I had despoiled by, well, thinking about it in a new way. Talking about cannibalism is not taboo, you see, but discussing the physical implications of infinity is simply not done. But across that hallowed ground I had trodden, and now found myself in trouble with the infinity police.

The infinity police are just one of many branches of thought police that have arisen in the past few hundred years to ensure that we think about things in the proper way. These include the quantum reality, black hole and big bang police, among others. The good news about thought police is that they can’t issue citations; the bad news is they always seem to show up just when you’re trying to start a productive conversation. The thought police are certain, with an absolute certainty born of their deeply suppressed fear of nonconformity, that questioning the way in which science or mathematics is done is simply unthinkable. This is because, of course, it requires thinking. Progress has nothing to do with it. The thought police are ready and able to enforce any given perspective, for decade after decade, even if it directly impedes new development. Especially if it impedes new development. Because you see, new development means that the old development was well, missing something.

So there I was, my dialog parked by the side of the road, making my case to a young infinity policeman who was trying to peer into my mind with his vacant, unwavering stare. I told him how I used infinite magnitudes all the time, large and small, in calculus, and it worked each and every time I did it! I told him that the two poles of the Riemann sphere were zero and infinity, and that their product was 1! He continued to stare, but I could see the anger rising in his cheeks. The source of the anger was obvious; he didn’t like what I was saying (at all), but he couldn’t arrest me for it either.

Ontological disconnect

Our mathematical systems are built on axioms, which are used to prove theorems and allow us to perform certain operations. Our number systems begin with empty sets and end with multidimensional geometries, to which we can apply topology, differential geometry, and all sorts of other neat mathematics. So we’ve got this thought construct called math, and we use it to make sure that our bridges stay up and our planes stay in the air. The infinity police don’t get upset when engineers borrow calculus, because the only things they see when they peer over our shoulders are finite quantities.

But here’s the rub. The thought construct called math is full of all sorts of rules and regulations, but it cannot, by its own design, contain a rule that says it is ok to use it on reality or that it actually conforms to reality. Math is a bridge, built on thin air, with no clear destination, and it certainly never arrives at reality. Indeed, pure mathematicians, the artists of this thought project, often look down on applied mathematicians the way that scientists might sometimes denigrate engineers.

Along comes null physics. Here we postulate the apocryphal heresy that the best way to understand reality is to start with reality. Perhaps, just perhaps, the reason why math works to describe reality is because math is the thin shadow that reality leaves in the human mind. So we rummage through its tool box, looking for mathematical widgets that have proven useful in keeping our bridges up and our planes in the sky. Head and shoulders above all of the rest of these tools stands calculus. This isn’t because of our associative or transitive axioms or even math itself. It is because the universe is a compositional thing, and when you do an integral in calculus, and add an infinite number of infinitely small differentials, you get a valid result because that is the way the universe is built.

What the infinity police fail to understand, as they glower at that (inf) symbol, is that infinity is everywhere. Every single piece of our universe has an infinite aspect, even finite pieces. Finiteness has infinite resolution, as in 2.033230… kg, because it is the result of infinite composition. So go ahead infinity police, try to write me a ticket. You have no jurisdiction in reality.

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