I conjecture: The concept of infinity could not exist in a finite universe.
“I am incapable of conceiving infinity, and yet I do not accept finity.”
Simone de Beauvoir
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Pure philosophy? It might be. It’s probably not provable in any scientific manner; but it’s certainly conjecturable. So let’s discuss the implications, as many of the Millennium Conjectures to come herein presume the universe—or multiverse, if you please—to be infinite in some shape or form. As most religions require a belief in god as a given, my worldview based on science needs to take a stand on infinity.
As best as can be determined, the ancient Greeks seem to have invented the mathematical concept of infinity. (Okay—with the possible exceptions of baseball, hot dogs, apple pie and Chevrolet—what didn’t the ancient Greeks think of first?) So the question begs, did we humans discover infinity or did we invent it? It’s certainly conceivable that we could have invented it, at least in the mathematical sense. Let’s look briefly at two other possible dimensions of infinity—time and space. Of course, Einstein asserted that time and space are a single four-dimensional continuum, but let’s separate the two for the purposes of this metaphysical discussion.
The Possibility of Infinite Time
In 1949, using Einstein’s equations of general relativity, Kurt Gödel provided a proof that a certain type of rotating universe would be static and spatially finite, but temporally infinite in a rather unnerving form: it would contain closed time loops that would permit time-travel into the past. While evident that it did not exactly describe our universe, which is indeed expanding, Einstein himself admitted it raised disturbing questions about the nature of time in our universe. Gödel later expressed a philosophical argument that this proof suggests that time in our own universe does not exist, either as Einstein described it or as we intuitively experience it.^{1}
More recently, philosopher-scientist Julian Barbour has taken complete issue with Einstein suggesting that time is an illusion created by change–that it in fact does not exist at all. He asserts that time does not flow, but is a series of distinct, static and timeless instants that we experience as “flowing” time.^{2 } David Deutsch, took this once step further in his book The Fabric of Reality, when he asserted that time not only does not flow, but each instant we experience represents an alternate universe, each deterministic. He essentially argues that our consciousness moves from alternate universe to alternate universe and that it is this which is the source of perceived in-determinism and free will. [For now, don’t worry about the “many worlds” interpretation of quantum mechanics if you don’t understand it. I’ll provide some simple primers on these concepts in “asides” between the main posts.]
So let’s leave it at this: nobody really knows for sure exactly what time is, or if it even exists in anything like the form in which we experience it. So let’s move on. Next up is a discussion of space as a possible “infinite” dimension of reality. And don’t worry–there will be some intervening silliness if only for comic relief.
Notes:
- Gödel universe, The Encyclopedia of Science (online)
- Barbour, Julian, The End of Time: The Next Revolution in Physics (1999) Oxford University Press p.9
- Deutsch, David, The Fabric of Reality (1997) Penguin Books, Chapter 11, Time: the First Quantum Concept, pp. 259-288.
When I sat through a three-hour algebra class, I finally understood the concept of infinity. No matter where I look on the Periodic Table the element of surprise is never where I expect it to be.
It wouldn’t be a surprise if you expected it!
An extremely well explained conjecture. A simplistic explanation I like is: “ Zero and infinity are two sides of the same coin — equal and opposite, yin and yang. Multiply zero by anything and you get zero. Multiply infinity by anything and you get infinity.”
Thanks Marty; and I am not even done with this conjecture yet–two more posts to come!