Tal, a conversation with an alien (12 page)

W
hat do you mean?

I mean like a ratio
, one third of infinity, or one fourth or one tenth of infinity.

Since infinity is infinitely bigger,
I am not sure.

If we have 25%
of something, it is the same as saying one fourth, mathematically written 1 over 4.  If we want to know what part of infinity my number is, we need to put it over infinity. So my number, as it relates to infinity would be written mathematically as Supergoogolplex Extreme over infinity.  And in math we know that any real number, any actual number, no matter how large over infinity has a limit of zero, which mathematicians typically treat simply as zero. The Supergoogolplex Extreme, as large as it is, would be, in the vastness of an infinity of numbers, nothing.

But how can it equal nothing, it is a
real number, it is a part, even if a small part, of infinity.

You make a good point.
To be completely accurate, this number is actually called an infinitesimal. An infinitesimal is smaller than any actual number, just as infinity is bigger than any actual number. So compared to infinity, my Supergoogolplex Extreme is too small to be measured, too small to have any actual value. Thus your known universe, in the scope of the infinite multiverse is also too small to be measured, it is basically, nothing. I will show you another way of looking at the situation. Let's try to mathematically remove the Supergoogleplex Extreme from infinity. Do you know what number you get?  You will still get infinity. In mathematics, infinity minus any finite number is still infinity. Thus if you remove your known universe, or even a massive Supergoogolplex universe from the infinite multiverse, what you will be left with is still an infinite multiverse. If you tear one patch out of an infinite quilt, you still have an infinite quilt. If you tear out a million patches, you will still have an infinite quilt.

This is confusing.

Yes because you still think that infinity is
a really large thing. Infinity doesn't act like a giant number. Unlike a googol, if I take infinity, times two, I do not get twice as much of infinity, I still have, infinity. If I add infinity to infinity, I still have infinity, not something twice as big as infinity. If I take any countable amount of stuff, no matter how large, out of infinity, I still get infinity.

Perhaps
Infinity is unfathomable to finite creatures. 

Not really,
great mathematicians like George Cantor and Kurt Gödel made major insights into its nature. They transcended the traditional ways of thinking to gleam real insights into infinity, and these days mathematicians rely heavily on the use of infinity and infinitesimals in their equations to solve real world engineering problems. The main thing I want you to understand is that when dealing with an infinite universe, simply adding another dimension to it does not make it too big, or even bigger at all, it is still infinite. This is why we laugh at Charlie Brown when he protests that our infinite 3D universe is too big, while his infinite 2D universe is just big enough. Though his infinite 2D universe is bigger than we can possibly imagine, adding another dimension does not confuse us. So now, if I tell you that in an infinite universe there are also infinite variations, can you comprehend it?

I am not sure
. Logically I understand it, psychologically not so much.

It will take time, but
you believe in logic and mathematics, and as you accept your logical understanding, it will become more natural to you. It will become something that you can feel is true, and this leads us back to whether I can know if the multiverse is infinite. Here is the concept that is really important to understand when dealing with infinities. You cannot imagine or comprehend infinity in the same way you comprehend finite concepts; by putting parts together or breaking them apart. No matter how much finite stuff you have, you will never reach infinite stuff. No matter how much finite knowledge you have, you cannot reach infinite knowledge. So when dealing with an infinite concept, like an infinite universe, or an infinite God, you cannot fully understand it by combining finite parts. Nor can you prove or disprove such a thing by breaking it down into smaller parts, as its parts themselves, are infinite. I can tell you that the universe behaves as if it is infinite, in that there is nothing in its nature that would point to any limit. But do you understand that unless I had infinite knowledge, I could not truly know if the universe was infinite?

Indra and the Ants

It is very complicated.

You don'
t need to understand it all, but try to understand that your notion of the multiverse being too big is a mental projection of your mind. The multiverse is infinite, therefore it cannot be too big. Freed from a conception of a limited universe, does it not seem even more beautiful that there is not just one world, but all possible worlds? In fact, since you now understand that mathematically, one infinity is just as good as many, you don't even have to believe in the multiverse at all. If you just believe that your single universe is infinite in size, or eternal in time, you still will get infinite parallel worlds, within your single universe. 

How?

If you allow that either space or time is infinite, the universe is already much vaster than anything you have actually imagined. It is so vast a thing, that it will allow for infinite variation and infinite repetition.

Repetition?

Even if you exist only in your traditional single world, where things only happen one way, since it is of infinite size, there are actually copies of you, scattered throughout the universe. Though of course those copies would think of you as a copy. If the world is infinitely large, then there is an infinite amount of galaxies and an infinite amount of stars. There will be somewhere in the universe of galaxies, planets just like Earth. There will be people living on these planets, and on some of these planets there will be a person just like yourself. Again, if you think of your universe as an infinite patchwork quilt, with your observable universe as a patch; then somewhere there will be other patches in the quilt just like, or very similar to your own.

So
out there in the universe there are billions of me's, but I can't see them.

Correct. D
ue to the very limited range that you can observe, the chance of a copy of you existing in your known universe is small. Yet in a universe that is infinite, you are everywhere.

This is
hard for me to believe, but I guess I did not understand the result of a limitless universe. Perhaps the universe is not infinite after all?

As you come to terms with the concept of an infinite universe, you will have some very strange and challenging insights, but that is
good, you just need to, as they say, "go with the flow." But I will indulge you. Let's imagine that the universe is not infinite, and it does stop somewhere. However, it is eternal, never ending in time. Again, in an eternal universe, even if finite in size, somewhere in time, copies of you exist.

Wouldn't a world that is limited i
n space also be limited in time? It could not be eternal.

There are m
any types of eternal universes. One well-known type of universe that your scientists believe is possible is the rebirthing, or cyclical universe. This type of universe is written about in Hindu texts thousands of years old. In a cyclical universe, we have a universe that starts with a big bang, expands and then at some point contracts back onto itself, and then starts all over again. Like an infinite series of Big Bangs. As it develops, due to quantum uncertainty, this universe will cycle through many copies and slight variations of itself. Within the scope of such a universe, you exist now just as you have an infinite amount of times before, and will again. There is a well-known Hindu story called 'Indra and the Ants' that illustrates this concept. In the story, the god Indra, the creator of the universe, builds a massive castle and brags about how powerful and great he is. He is king and creator of the universe after all. Vishnu, the all mighty God, in the guise of a boy tells Indra "Don't be so brazen, I have seen many Indras come and go, you are not that special, you are just one of many Indras." Vishnu looks down at a line of ants walking on the floor of Indra's castle and says, "All of these ants were Indras once."  Indra is the master of one universe; Vishnu is the master of all universes. He is not bound by any local time, he is able to observe the Indras of all times, of all universes.

Monkeys

--Perhaps I was looking a bit overwhelmed, because he then said,

L
et me try to explain this to you in a more basic way that you might be familiar with. Have you heard of the thought experiment called the infinite monkey theorem?

Yes, it
states that because of the simple possibility of chance, if you make a bunch of monkeys type on a typewriter, sooner or later, some monkey will write 'Hamlet' or 'War and Peace', from just pure chance.

Yes that
's right, now let's imagine a universe full of these monkeys writing on typewriters.

If we line up an infinite amount of monkeys and have them all start typing, somewhere in the universe of infinite monkeys there will be monkeys who type 'War and Peace' without making a single mistake. Similarly, if we have just one monkey, an immortal monkey, who types forever, eventually he will also type 'War and Peace' most likely after many mistakes. So no matter how unlikely, if the universe is large enough or old enough, you will get a monkey to type 'War and Peace'. In the multiverse, you would not need an army of monkey's or an immortal one. One very lucky monkey will type 'War and Peace', and will do it right on the first try. He will type it perfectly in some very unlikely universe variation within the multiverse. Even more amusingly, somewhere in the multiverse there will be versions of 'War and Peace' typed with a few random words added, which will be judged even better than the original!

That would be one smart monkey.

How excited the humans of that dimension would be to find such an amazing monkey. They would breed him in hopes of creating a new race of literary geniuses. And how sad it will be, when they realize that his children are complete idiots.

Very funny. So there are copies of me somewhere in the universe, it is just
unlikely I would ever meet them? 

Yes, in fact it would be
very unlikely, even with billions and billions of galaxies out there, that you would ever meet anyone even remotely similar.

But theoretically, it is
possible to see a version of me nearby, in this universe.

Correct.

Sounds like another interesting science fiction plot.

Yes. Imagine
a time in the future. Humans on Earth send an astronaut to explore a nearby star system that looks very similar to your own. When the astronaut gets there, he sees a solar system just like Earth's, and within it, a planet just like Earth. When he lands, he is shocked to find that everything seems to him to be exactly like Earth, including the people. He is even greeted by people who look just like his wife and children. The planet is an exact duplicate. It evolved in exactly the same manner as your own planet. 

There was some movie along those lines I think.

Perhaps, but I doubt it really gives duplicate worlds justice. If it is truly a duplicate world, our astronaut is in trouble. Because unfortunately for him, the inhabitants of that world also sent an astronaut at the very same moment, to explore your solar system. The people of that world will think that your astronaut is actually the astronaut that they themselves had recently sent out. Since your astronaut's spaceship and appearance are exact copies of the astronaut they sent out, they assume his spaceship had a guidance malfunction and brought him back home. When your astronaut insists that everyone is just a copy of the inhabitants of the real Earth, they think he has gone mad with space sickness. Your astronaut demands to be sent home, but The United States of America of their planet, refuses to fund another failed mission to distant stars, especially if it is flown by a lunatic. Thus your astronaut is forced stay on in his new home, with his new wife, and new kids, living out the rest of his life with what he calls, doppelgangers.

Quite a sto
ry.

Yes, hi
ghly improbable, but possible. This may be fantasy, but I hope you understand now that your bias against a multiverse of infinite possibility is a product of faulty logic and the limits of your imagination, not an actual physical or mathematical limit. Your imagination can grow to understand the consequences of infinity. Once it does, the idea that there is an infinite dimension of universes out there will not surpass you.

Now you are talking of feeling
or imagining infinity, not just logically understanding it.

Yes, logical
understanding is good. It can inform how you feel or imagine a concept.  You felt that the universe could not be so vast as to have billions of copies of yourself, yet now you understand that it can. Now you will start to expand your feeling of how vast the universe is, and that will, in time, change your concept of the universe itself. 

I
understand what you are saying, that the universe is vast and the possibilities endless. But what about that feeling of uniqueness; with so much stuff, copies, variations, dimensions, what does it mean for us, do we like our mathematical equivalents just get smaller and smaller, like that infinitesimal? Are we basically meaningless?