Continuing with my occasional posts on baralbion‘s philosophical questions, I have chosen this one today:
The universe is infinitely large. So matter can also be infinitely small. Things are large or small only in relation to ourselves.
The first two sentences bother me. This is because infinity is a difficult concept and yet the layman bandies it about as though it were the simplest thing imaginable. Even mathematicians (who know far more about this sort of thing than you or I) fight shy of infinity. They don’t like it. For one thing it doesn’t mean what it is popularly taken to mean and it doesn’t behave as it is popularly thought to behave.
You cannot get a handle on infinity. It is not a number. One divided by infinity is not zero and one divided by zero is not infinity. Such beliefs are the myths of ignorance. The universe is not infinitely large and there is no such thing as infinitely small matter. If there is matter, then it has a size and therefore it is not infinitely small. Even if the universe were infinitely large (which it isn’t), it wouldn’t be a necessary conclusion from this that it contained infinitely small matter.
Some scientists believe that the universe is quantized. That means that everything ultimately consists of units that cannot be further divided. Even space. Even time. That would mean, for example, that you cannot divide a unit of space into smaller and smaller parts and carry on like that for forever. You would eventually come to the smallest unit of space and you wouldn’t be able to divide it. Likewise with time: there would be the smallest unit of time, the chronon, and you couldn’t have less time than that. You could say “Wait half a chronon,” but no one would actually be able to do that. They would have to wait a whole chronon.
The third quoted sentence is more interesting. It reminds me that a very clever man called Chuang Tzu wrote a book in about 350 BC in which he talked about how things are large or small according to how you look at them. Or he may have done. The collection of texts called The Inner Chapters in English may have been written by a single author and he may have been called Chuang Tzu or Chuang Chou. Either way, he was a very bright fellow, philosophically in advance of his time. In fact, the Chinese language of his day didn’t have the terms he needed in order to express his ideas. Yes, he was that clever.
Chuang or Chou loves to point out how apparently useless things survive because no one bothers with them. Be useless and live long, is his timeless advice. We relate things to our own needs. A gourd that is so big that it sags and is therefore useless for storing things is called “too big” and discarded but if you cut it in half and use the half as a boat it is no longer “too big”. A deformed dwarf is called “useless” and is apparently the unluckiest man alive until you realize that he never gets drafted into the army, he receives free food handouts, lives without working and no one ever bothers him. To a giant bird, flying round the world is nothing; to a tiny bird, flying to the next tree is a great journey.
We measure everything by ourselves and this makes us stupid. But this is just a habit. We can be a bit cleverer than that if we follow Chuang Tzu’s example. We will never be quite a clever as Chuang but we can go some of the way along his path.
Is there any connection between Chuang Tzu and infinity? Well, in one of his writings, Chuang refutes an argument by showing that if we accept it, it leads to infinite regress, thus proving that the argument cannot stand. So Chuang apparently had a concept of infinity even though there was no word in Chinese then for “infinity” or for “infinite regress”. He had to get his point across by other means. Being a skillful writer (his work is considered a literary gem, quite apart from its philosophical value) he managed this though not without difficulty. Chuang Tzu knew what he was talking about in this as in the other themes he tackles and his writings remain a timeless classic.