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One Two Three Infinity Facts and Speculations of Science

All right. One, Two, Three Infinity: Facts and Speculations of Science, George Gamow. All right, Mr. George Gamow.

All right. Playing with numbers, space, time, and Einstein, micro cosmos, macro cosmos, and then a whole bunch of illustrations. Whole bunch of them. Big numbers. No, let’s see what he’s talking about. My eyes are kind of funny.

How high can you count? A gazillion. Boom. Just did it. Count as high as possible. Infinity. All right. “There’s a story about two Hungarian aristocrats who decided to play a game in which one who calls the largest number wins. ‘Well,’ said one of them, ‘You name your number first.’ After a few minutes of hard mental work, the second aristocrat finally named the largest number he could think of. ‘Three,’ he said. Now it was the turn of the first one to do the thinking. But after a quarter of an hour, he finally gave up. ‘You’ve won,’ he agreed.

“Of course, these two Hungarian aristocrats did not represent a very high degree of intelligence, and this story is probably just a malicious slander. But such a conversation might actually have taken place if the two men had been not Hungarians, not Hottentots. We have indeed on the authority of African explorers that many Hottentot tribes did not have in their vocabulary the name for numbers larger than three. Ask a native down there how many sons he has or how many enemies he has slain. And if the number is more than three, he will answer, ‘Many.’

“Thus in the Hottentot country in the art of counting fierce words would have been beaten by an American child of kindergarten age who could boast the ability to count up to 10. Nowadays, we’re quite accustomed to the idea that we can write as big a number as we please, whether it is to represent war expenditures, incense or stellar distances in inches by simply setting down a significant number of zeros on the right side of some figure. You can put in zeros until your hand gets tired. And before you know it, you will have a number larger than the following number of atoms in the universe, which identically is a lot.”

That, and that’s what I meant. Nowadays, what’s the largest number you can think of? Infinity. All right, going on and on and on. But this is interesting. “This arithmetic wasn’t known in ancient times. In fact, it was invented less than 2000 years ago by some unknown Indian mathematicians before his great discovery. And this was a great discovery. Although we usually do not realize it, numbers were written by using a specific symbol for each of what we now call decimal units and repeating this symbol as many times as there were units. For example, the number 8,073 was written in ancient Japanese.”

How? What are you even… Okay. Makes sense. So you have, look, you have eight of these, seven of these, three of these. You have eight of these, seven of these, three of these, two of these. Whereas, a clerk in Caesar’s office would have represented it in this form. So remember, this is what Egyptians and this is the Romans. So obviously, Roman numerals, we still use Roman numerals. Think of the Super Bowl.

Well, and think about it. Okay. What he’s saying right here, the only way that you would have been able to write one million is to take the thousand and write that down. Or what is it? A thousand M’s in succession, and then that would have been a million, because a thousand times a thousand is a million. Right?

Psammites or Sand Reckoner, Archimedes says, “There are some who think that the number of sand grains is infinite in multitude. And I mean, by saying not only that which exists about [inaudible 00:06:59], and the rest is Sicily, but all the grains of sand which may be found in all the regions of the earth, whether inhabited or uninhabited. Again, there are some who, without regarding the number as infinite, yet think that no number can be named which is great enough to exceed that, which would designate the number of the earth’s grains of sand.

“And it is clear that those who hold this view, if they imagine a mass made up of sand and other respects as large as the mass of the earth, including in it all the seas and all the hollows of the earth filled up in the height of the highest mountain, would be still more certain that no number could be expressed which would be greater than that needed to represent the grains of sand that’s accumulated. But I will try to show that of the numbers named by me, some exceed not only the numbers of grains of sand, which would make a mass equal in size of the earth, fill in a way to describe, but even equal to the mass of the universe.”

All right. So the way that he did this is kind of the way we do it today. He begins with the largest number that existed in ancient Greek arithmetic, a myriad or a 10,000. Then he introduced a new number, a myriad myriad, a hundred million, which he called an octate or a unit of a second class octate, octates, or 10 to the 16th is called a unit of the third class, octate, octate, octate. A unit of the fourth class of writing of large numbers may seem too trivial a matter to which to devote several pages of a book, but in the time of Archimedes, the finding of a way to write big numbers was a great discovery and important step in the forward to science and mathematics.”

I’m very interested. I am very interested. That is super interesting. And it keeps going on and on and one, playing with the big numbers. I’m glad I found this. I never would’ve thought about that. But if you think about where we came from, that’s true. We talked about writing in a different book this morning. We’re talking about numbers now. Man, just think a thousand years from now, all the things that they’re doing, they’re going to look back at us and be like, “Man, those were ancient people.” You know what I’m saying?

They only used 10% of their brain? Right? Because back here, it seems like they’re only using maybe 5%, maybe 1%, right? They didn’t know how to write. They didn’t know how to read. They didn’t know how to create. They didn’t know how to do large numbers. So let’s say 3% of their brain. So we’re studying off of people like 3% of their brain.

Imagine some of the top smartest people nowadays use 15, maybe 10%. Right? So in 2000 years, hopefully it doesn’t take that long, and people are using 80% of their brain, they’re going to look back at us and just think of us as the Neanderthals. Does that make sense?