One day Aristotle went on a cruise with Pythias his 10 year old daughter. He was getting bored, so he turned to her and said, “Let’s talk. I’ve heard that the trip will seem to go by quicker, if you strike up a conversation with a fellow passenger.” Pythias was laying out trying to get a tan, but she sat up and said to her father, “What would you like to talk about?” Aristotle said, ‘I am not sure, but do you have any thoughts about atomism?” “OK”, she said. “I always find that to be an interesting topic. But first, let me ask you a question. A cow, a deer and a horse all eat grass, but the cow turns out a flat patty, while the deer excretes little pellets and the horse produces a clump of dried grass. Why do you suppose that is?” Aristotle thinks this over for a while and then he said, “Hmmm, I have no idea.” Pythias then replied, “Do you really feel qualified to discuss atomism when you don’t even seem to know shit?”
People have always enjoyed getting together to discuss things and the ancient Greek philosophers did a lot of discussing, with part of their conversations concerning the physical world and its composition. One of the on-going debates had to do with sand. The question posed was, into how small of pieces can you divide a grain of sand? The prevailing thought at the time, pushed by Aristotle, was that the grain of sand could be divided indefinitely, that you could always get a smaller particle by dividing a larger one and there was no limit to how small the resulting particle could be.
One day, Aristotle was walking on the beach thinking seriously about some of the great problems of existence, believing that he was getting close to solving everything. While pondering this serious problem, he saw another man on the beach who was doing something very intensely, so intensely that even Aristotle could not ignore him. Normally Aristotle would have ignored this man, but it peaked his curiosity observing what the man was doing, continuously going to the ocean, coming back, going to the ocean again, and coming back again and again. Anyway Aristotle stopped and asked the strange man, “Hey, what are you up to?” The man said, “Don’t disturb me, I am doing something very important,” and went on about his business.
Aristotle became even more curious and asked again, “What are you doing?” The man said, “Please stop disturbing me, I told you that it is something very important.” Aristotle said, “What is this important thing?” The man showed Aristotle a little hole that he had dug in the sand, and he said, “I am emptying the ocean into this hole.” Aristotle looked at this man and laughed really hard when he saw that this man had a tablespoon in his hand. Aristotle said, “That is ridiculous! You must be insane. Do you know how vast this ocean is? How can you ever empty this ocean into this little hole? Why are you using a tablespoon, as you should at least have a bucket, then you might have a better chance. Please give this up this madness.”
The man looked at Aristotle, threw the his spoon down and said, “My job is already done.” Aristotle said, “What do you mean? You did not empty the ocean and even your hole is not full of water yet. How can you say your job is done?” The strange older man was Heraclitus of Ephesus. Heraclitus stood up and said, “I am trying to empty the ocean into this hole with a tablespoon and you are telling me it’s ridiculous, it’s madness, so I should give it up. What are you trying to do? Do you know how vast this existence is? It can contain a billion oceans like this and more, and you are trying to empty it into the small hole of your head.” Heraclitus then exclaimed, “Can’t you see the underlying connection between opposites. Health and disease, good and evil, hot and cold, and everything that is an opposite has a relation to something else. Thus a single substance may be perceived in varied ways, as seawater is both harmful (for human beings) and beneficial (for fishes). Understanding the relation that opposites have to each other enables us to overcome the chaotic and divergent nature of the world. The world exists as a coherent system in which a change in one direction is ultimately balanced by a corresponding change in another. Between all things there is a hidden connection, so that those that are apparently tending to be pulled apart are actually being brought together. History is a child building a sandcastle by the sea, and that child is the whole majesty of man’s power in the world.”
The Roman numeral for 1,000 is represented by the capital letter M and any number with a bar over it, is equivalent to that number times 1,000, thus since X = 10 then X̄ = 10,000. The ancient Greeks originally had a number system like the Romans, but in the 4th century BC, they started using the same system. In Greece the number ten thousand was called a myriad and it stems from the Greek word murios meaning countless. Archimedes proposed a number system that used powers of a myriad (base 100,000,000) and it was capable of expressing extremely high numbers. He wrote a work called The Sand Reckoner in which he set out to determine an upper bound for the number of grains of sand that fit into the universe. In order to do this, he had to estimate the size of the universe according to the contemporary model, and invent a way to talk about extremely large numbers.
Archimedes argued, “There are some, like King Gelon tyrant of Gela and Syracuse in Sicily, who think that the number of the sand particles is infinite in multitude; and I mean by the sand not only that which exists about Syracuse and the rest of Sicily, but also that which is found in every region whether inhabited or uninhabited. Again there are some who, without regarding it as infinite, yet think that no number has been named which is great enough to exceed its multitude. And it is clear that they who hold this view, if they imagined a mass made up of sand in other respects as large as the mass of the Earth, including in it all the seas and the hollows of the Earth filled up to a height equal to that of the highest of the mountains, would be many times further still from recognizing that any number could be expressed which exceeded the multitude of the sand so taken.”
Archimedes was trying to prove that numbers could be greater in magnitude than all the grains of sand, and he said, “There is Aristarchus of Samos who made a hypotheses, in which the premises lead to the result that the universe is many times greater than that now so called. His hypotheses are that the fixed stars and the Sun remain unmoved, that the Earth revolves about the Sun in the circumference of a circle, the Sun lying in the middle of the orbit, and that the sphere of the fixed stars, situated about the same center as the Sun, is so great that the circle in which he supposes the Earth to revolve bears such a proportion to the distance of the fixed stars as the center of the sphere bears to its surface. Now it is easy to see that this is impossible; for, since the centre of the sphere has no magnitude, we cannot conceive it to bear any ratio whatever to the surface of the sphere. We must however take Aristarchus to mean that since we conceive the Earth to be, as it were, the centre of the universe, the ratio which the Earth bears to what we describe as the ‘universe’ is the same as the ratio which the sphere containing the circle in which he supposes the Earth to revolve bears to the sphere of the fixed stars.
For Aristarchus adapts the proofs of his results to a hypothesis of this kind, and in particular he appears to suppose the magnitude of the sphere in which he represents the Earth as moving to be equal to what we call the universe. I say then that, even if a sphere were made up of the sand, as great as Aristarchus supposes the sphere of the fixed stars to be, I shall still prove that, of the numbers named in the Principles (a lost work of Archimedes), some exceed in multitude the number of the sand which is equal in magnitude to the sphere referred to, provided that the following assumptions be made.”
Written for Ray NotBradbury Cool Writing Prompt ‘The End Of Infinity’.