The number of the fish

Today seems to be a day for playing with numbers.

Several months ago, I described a memorable occasion when The Bean was looking at a picture of his uncle, and solemnly pronounced "Shish" (fish). This verdict was repeated often enough over the ensuing weeks that I was sure he really meant something by it; but what he meant, I had no idea. I really didn't think his uncle looked any more like a fish than most men do in their wedding photos.

This week, it all became clear. The pronouncement was a prophecy. The Bean's uncle and his wife have just bought a house, whose number, spookily enough, is 153: the "number of the fish".

153 is a remarkable number. In much the same way that 42 fascinates fans of the Hitch Hiker's Guide to the Galaxy, 153 fascinated the Pythagoreans, a group of ancient Greek mathematical mystics. Here are some of the unusual things about it:

• 153 is the sum of the cubes of its own digits: 1x1x1 + 5x5x5 + 3x3x3 = 153. In fact, if you start with any number that divides by three and repeatedly replace it by the sum of the cubes of its digits in this way, you eventually end up with 153.
  
• 153 is a triangle number. If you make a triangle of red balls like the ones on a snooker table, but have seventeen rows of them rather than just five, then there are 153 balls. And it happens that the prime factors of 153 (the prime numbers which, when multiplied together, give 153) are 17, 3, and 3.
  
• 153 is the sum of the first five factorials: 1 + 2x1 + 3x2x1 + 4x3x2x1 + 5x4x3x2x1 = 153.
  

But the reason it's called the number of the fish is because of the so-called vesica piscis, or "bladder of the fish": two intersecting circles of equal size, with the centre of each one lying on the circumference of the other, so that a vertical fish-like shape is formed. The Pythagoreans worked out that the ratio of the width of this figure to its height is almost exactly (to within one part in 7,000) 265 to 153, or 5x53 to 153. In fact, the precise value is the square root of three. Not only self-acknowledged trimorphs such as your author but trinitarian mystics in general may find it interesting how the number three occurs repeatedly in all these formulae.

According to Robert Price (The Incredible Shrinking Son of Man, page 158; why couldn't he have mentioned it five pages earlier?), there is a story from Iamblichus (Life of Pythagoras, 8) in which Pythagoras, a strict vegetarian, comes across a group fishermen hauling in a large catch. He asks them if they will throw them back if he can tell them the exact number of them. They agree; he correctly names the number; and the fish are returned alive to the water. This story has uncanny similarities to the (much later) account in the last chapter of John's gospel where Jesus, after his resurrection, comes across the disciples, who had been fishing all night but caught nothing. He tells them to put the net down on the right side of the boat. They do so, and immediately haul in a large catch.

The strange thing is that it is John, not Iamblichus, who tells us that there were 153 fish, a detail which adds nothing to the plot of John's story but which would have been understood as a clear Pythagorean reference to educated people of those times. I wonder whether all this may have something to do, either as cause or as consequence, with the choice of the fish symbol for Jesus among the early Christians.

I wish the The Bean's uncle and aunt all the joys of the Fish in their new home -- especially as before the year is out there will be three of them living there. And while we're on the subject of numbers, I hope another of The Bean's pronouncements, repeated several times recently, doesn't come true for them, at least not unless they really want it to: "One, two, three -- nine!".