spot in the darkness. Some of your scientists have compared it to a patchwork quilt, where your observable universe is one patch in an infinitely large blanket.
All right, our scientists don't know if the universe is infinitely large. But do you know if the universe is infinitely large?
If you truly understood infinity, you would realize tha t I could not know that for certain. I could only be sure if the universe was finite, and to my knowledge it is not.
Why can't you know if it is infinite?
Once you understan d the nature of infinity, you will answer your own question. Understanding infinity is one of the keys to understanding many worlds. Once you have a clear conception of infinity, you will have a much deeper understanding of the world around you.
--He must have seen a lack of confidence in my expression, because he stopped to take a sip of juice and reassured me.
Actually, of the things we have already discussed, this is one of the easier concepts for humans to grasp, at least initially. Infinities can take many forms. Humans are generally familiar with three of these forms: mathematical infinities, imagined infinities and actual physical infinities. Obviously, you can't observe physical infinity, and your ability to imagine infinity is what we are trying to improve. So we are left with mathematical infinity, which for followers of science, is the easiest to comprehend and leads to insights in the understanding of the other types. In math, the set of whole numbers, 1, 2, 3, etcetera is actually an infinite set. No matter how high you count, you can simply add one to create an even larger number. There is no number that serves as the end of the set.
So if numbers are in fact infinite, we deal with pretty small ones.
Indeed you do. Have you heard of a googol?
You mean the search engine?
No, I am referring to the mathematical number.
Yes it is a one with one hundred zero's behind it. And a googolplex is 10 to the googol.
Yes, the googolplex. It is such a massive number; it is bigger than all the elementary particles your scientists know of in the entire universe. A short and simple mathematical representation, for instance a googolplex of atoms, represents more stuff than there is in the entire observable universe. Now, this is a lot of stuff, but is this the largest number you can imagine?
I don't think I can really imagine how much that is, but I can write it.
Actually if you tried to write a googolplex in the traditional way, 1 and then 0's after it, you could spend a billion years doing it, and you would not have even come close to actually writing the number. In fact, there would not be enough room in your observable universe to write this number.
I could forget writing zero's and just write operators, like a googolplex times a million, or a googolplex to the googolplex to the googolplex.
Yes, that is a good way to do it. You could write googolplex to the googolplex to the million times googolplex. And how many of your universes would that number represent?
G oogols of them. I suppose if each googolplex is larger than the known universe, it would be a universe of universes.
Now im agine you wanted to create a number much greater than that; the greatest number ever created by humans. How large a number could you create?
Well I supposed as large as I could think of, or say or write.
I magine you spent the rest of your life saying googolplex to the googolplex to the googolplex like a yogi reciting a mantra. Or you sat down and wrote googolplex to the googolplex all day and night. Let's go further, you could just imagine numbers running through your head, googolplex after googolplex after googolplex, every moment, for the rest of your life.
That would be a massive number.
Yes , after doing this for many, many years, you would certainly believe that you hold the world record for the largest number ever imagined in the history of mankind. Surely just before your death I would visit you, and you
All right, our scientists don't know if the universe is infinitely large. But do you know if the universe is infinitely large?
If you truly understood infinity, you would realize tha t I could not know that for certain. I could only be sure if the universe was finite, and to my knowledge it is not.
Why can't you know if it is infinite?
Once you understan d the nature of infinity, you will answer your own question. Understanding infinity is one of the keys to understanding many worlds. Once you have a clear conception of infinity, you will have a much deeper understanding of the world around you.
--He must have seen a lack of confidence in my expression, because he stopped to take a sip of juice and reassured me.
Actually, of the things we have already discussed, this is one of the easier concepts for humans to grasp, at least initially. Infinities can take many forms. Humans are generally familiar with three of these forms: mathematical infinities, imagined infinities and actual physical infinities. Obviously, you can't observe physical infinity, and your ability to imagine infinity is what we are trying to improve. So we are left with mathematical infinity, which for followers of science, is the easiest to comprehend and leads to insights in the understanding of the other types. In math, the set of whole numbers, 1, 2, 3, etcetera is actually an infinite set. No matter how high you count, you can simply add one to create an even larger number. There is no number that serves as the end of the set.
So if numbers are in fact infinite, we deal with pretty small ones.
Indeed you do. Have you heard of a googol?
You mean the search engine?
No, I am referring to the mathematical number.
Yes it is a one with one hundred zero's behind it. And a googolplex is 10 to the googol.
Yes, the googolplex. It is such a massive number; it is bigger than all the elementary particles your scientists know of in the entire universe. A short and simple mathematical representation, for instance a googolplex of atoms, represents more stuff than there is in the entire observable universe. Now, this is a lot of stuff, but is this the largest number you can imagine?
I don't think I can really imagine how much that is, but I can write it.
Actually if you tried to write a googolplex in the traditional way, 1 and then 0's after it, you could spend a billion years doing it, and you would not have even come close to actually writing the number. In fact, there would not be enough room in your observable universe to write this number.
I could forget writing zero's and just write operators, like a googolplex times a million, or a googolplex to the googolplex to the googolplex.
Yes, that is a good way to do it. You could write googolplex to the googolplex to the million times googolplex. And how many of your universes would that number represent?
G oogols of them. I suppose if each googolplex is larger than the known universe, it would be a universe of universes.
Now im agine you wanted to create a number much greater than that; the greatest number ever created by humans. How large a number could you create?
Well I supposed as large as I could think of, or say or write.
I magine you spent the rest of your life saying googolplex to the googolplex to the googolplex like a yogi reciting a mantra. Or you sat down and wrote googolplex to the googolplex all day and night. Let's go further, you could just imagine numbers running through your head, googolplex after googolplex after googolplex, every moment, for the rest of your life.
That would be a massive number.
Yes , after doing this for many, many years, you would certainly believe that you hold the world record for the largest number ever imagined in the history of mankind. Surely just before your death I would visit you, and you
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