[and] + [be] -- infinity
The concept of infinity is a persistent logical conundrum. There are basically two ways to visualize it — as a line or as a circle.
The West thinks of infinity as a line. When we think we have reached the end of the line, we can always go a little further. Infinity is a process that always has a next step, something that recedes beyond our view. For example, Euclid IX.20 states that “prime numbers are more than any assigned multitude of prime numbers”. Today we would simply say that there are an infinite number of primes, but Euclid was a little more careful in his phrasing. He makes it clear that infinity is not something that we can grasp and hold on to.
The East thinks of infinity as a circle. The ancient symbol of the ouroboros, a serpent eating its own tail, illustrates this concept. Although the ouroboros is infinite, it is at the same time limited. A serpent can be picked up and manipulated even though it has no beginning or end. The ouroboros may have been the inspiration for our modern symbol of infinity, the sideways 8. After inventing a discrete symbol for infinity, mathematicians began to treat it as if it were as “solid” as any other number. On the whole, this has been an unfortunate development because infinity is certainly *not* the same as any other number. This logical error has created a huge amount of confusion, especially in 20th century mathematics.
The linear view of infinity has also influenced the West’s concept of linear time. Judeo-Christian thought holds that the universe had a definite beginning and will have a definite end. Conversely, the circular viewpoint perfectly coincides with the East’s doctrines of “God within”, reincarnation, and cyclical time.
The line and the circle are both fundamental cognitive structures. By emphasizing one over the other, two radically different cultures emerge.