What can you say about *infinity*? Well, the word has a pretty lengthy Wikipedia page, so clearly the answer is "a lot."

Which makes sense, since if there's one thing we know about infinity, it's this: infinity is freaking *big*.

Or at least, limitless. I suppose something could be infinitely small -- getting smaller and smaller without limit. But this would mean that it's a freaking *big* bit of small.

God supposedly is infinite.

Infinitely loving, infinitely knowing, infinitely powerful. Heck, God probably has an infinite number of positive qualities, being so infinite. This is assuming that God exists.

We also have to assume infinity exists.

Reading the "A Window on Infinity" chapter in physicist David Deutsch's *The Beginning of Infinity* book, I learned that there's some disagreement about whether infinity is really real, or just conceptually real.

There is a philosophy of mathematics called *finitism*, the doctrine that only finite abstract entities exist. So, for instance, there are infinitely many natural numbers, but finitists insist that that is just a manner of speaking.

They say that the literal truth is only that there is a finite rule for generating each natural number (or more precisely, each numeral) from the previous one, and nothing literally infinite is involved.

I don't feel qualified to comment on the dispute between finitists and infinitists. The whole notion of infinity blows my mind when I ponder it. So it's tough for me to say anything coherent about a word -- *infinity* -- which seems utterly divorced from what I experience in everyday life.

Limits. Discrete numbers of things. Boundaries. Horizons.

Still...

I love the notion of infinity. I want the finitists to be wrong. I get a thrill up my psyche's spine when I try to envision something that isn't really a *some*, nor a *thing*, having no limit.

I haven't finished reading Deutsch's "A Window on Infinity" chapter. But here's my favorite mind-blowing passage so far.

In mathematics, infinity is studied via infinite sets (meaning sets with infinitely many numbers). The defining property of an infinite set is that some part of it has as many elements as the whole thing.

Whoa. Wow.

Every part of an infinite set is just as infinite'y as the whole thing. As soon as this idea entered my mind, it seemed *super significant* to me. Problem is, I can't say why. I get a feeling along the lines of "universe in a grain of sand."

However, with infinity seemingly there's no boundary that could define a universe, or a grain. Seemingly. I'm not mathematically astute enough to know if this is true.

Realizing that most readers of his book would be as math-challenged as I am, Deutsch helpfully recounts a thought experiment by mathematician David Hilbert. Here's a sample of what goes on in the experiment.

He [Hilbert] imagined a hotel with infinitely many rooms: *Infinity Hotel*. The rooms are numbered with natural numbers, starting with 1 and ending with -- what?

The last room number is not infinity. First of all, there is no last room. The idea that any numbered set of rooms has a highest numbered member is the first intuition from everyday life that we have to drop.

Second, in any finite hotel whose rooms are numbered from 1, there would be a room whose number equalled the total number of rooms, and other rooms whose numbers were close to that: if there were ten rooms, one of them would be room number ten, and there would be a room number nine as well.

But in Infinity Hotel, where the number of rooms is infinity, *all* the rooms have numbers infinitely far below infinity.

Whoa. Wow.

That last sentence seems really, really, *really* significant to me. Why, it could be the key to understanding *everything*. Or, nothing. Which doesn't take anything away from the sentence's significance.

After all, nothing is as close to infinity as everything is. I think. Can't be sure. Time to stop blogging and have a glass of wine. That will bring me closer to understanding what infinity is all about.

Of course, that new understanding distance still will be infinitely far below infinity. So I might as well watch TV while drinking the glass of wine.

Reading a holy book. Sitting at the feet of a holy person. Meditating or praying in a holy fashion. Doing any or all of those things would still leave me infinitely far below infinity.

Remember, in the Infinity Hotel *all* the rooms have numbers infinitely below infinity.

yip, its another very interesting question. Tho science often takes very large, or small, numbers to be approximately equal to infinity, conceptually there's a gulf of difference.

If the big bang theory is correct, then the universe is limited and has an edge, albeit massive and continually expanding, and time also has its limit.

From a scientific emperical viewpoint, we are also limited not only by our measurement technology but more fundamentally by the laws of the universe. If the speed of light is a cap, then it would seem impossible to know about anything beyond the observable universe, which might in itself be a small part of the overall universe. If there are other universes or membranes, we also cannot know anything of these. At the quantum scale, again there appear to be discrete quantum energy levels and scales, which also indicate a discrete reality with finite possibilities, rather than a continuous reality with infinite possibilities.

It is possible that the universe is eternal and infinite, but then one would have to ask why is the universe apparently constrained by a specific set of natural laws at all, rather than being completely random with infinite possibilies and events taking place at every instant?

Posted by: George | September 21, 2011 at 08:41 AM

"...why is the universe apparently constrained by a specific set of natural laws at all, rather than being completely random with infinite possibilies and events taking place at every instant?"

The apparent constraint is supposed by the finite mind. It could be there is no constraint at all, but that in order to explain eternity and infinitude, conceptuality imposes constraints.

Posted by: cc | September 21, 2011 at 02:04 PM

Darshan Singh, when asked about a certain

number of souls being marked to be saved,

said that couldn't be, because a percentage

of infinity, is still infinity.

What he didn't realize is, he had debunked

Kirpal's statement of a percentage being

marked.

The Guru always ends up with his foot

in his mouth, every time he uses logic.

Logic is the great taskmaster of the Guru.

Logic thrashes the Guru for life.

Which is why the Guru is an infinite

fountain of inuendo.

Posted by: Mike Williams | September 21, 2011 at 03:40 PM

cc,

agree, that's what i was getting at, but even if our mind's are finite, which they almost certainly are - the fact that natural laws exist at all, as opposed to a completely chaotic universe with infinite possibilities, would seem to suggest against the infinite?

Posted by: George | September 21, 2011 at 05:22 PM

What we call "laws" are persistent conditions that create a context for less persistent conditions to operate in.

Posted by: cc | September 22, 2011 at 09:15 AM