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Have you heard the one about the group of prison inmates who puzzled
a visitor to their grim penitentiary? ‘Thirty-nine,’ shouted one, and the
rest rolled around in laughter. ‘Fourteen,’ said another, and more guffaws
ensued.

A guard explained that these bored long-termers had simply assigned
numbers to their favourite jokes, as an easy way to entertain each other
and pass the time. But the now-enlightened visitor noticed that one prisoner,
although he shouted ‘forty-three and ‘seven’ with gusto, never got a laugh.
‘Oh,’ said the guard, ‘that’s old Gus. He just doesn’t know how to tell
a joke.’

I suspect those prisoners were ex-scientists (possibly sent up the river
on charges of insufficient publication, compounded by felonious overhead
mismanagement) since only people with intense quantitative training could
get joy or any other emotional frisson out of numbers. Oh, there are a few
exceptions – our ages and waist sizes probably carry emotional baggage for
most of us, scientist or not. But I’m thinking of numbers with strong associations
distant from such direct connections. If these don’t exactly create a mood,
they at least generate a striking non-numerical mental image, or unexpectedly
mine a rich lode of memories or knowledge.

I first really noticed this feature of my own internal landscape one
day, when I idly glanced at an auto licence plate showing the sequence 488.
Instantly, the picture of a sizzling blue light ray snapped into mind, like
the very best special effect from Star Wars. From where did this spring?
It’s simple. I use lasers in my research, and know that 488 is the wavelength
in nanometres of the bright blue line emitted by one of the more powerful
sources, an argon ion laser.

Once I noticed this, I realised how certain numbers – on licence plates,
credit cards, in my work – bring strong imagery or ideas along with them.
The host of laser numbers is especially vivid; 514, also from an argon ion
laser, is a beautiful emerald green that the Wizard of Oz would love; 613,
from a helium neon laser, a torchy red-orange. But 337 carries no image.
More exactly, it’s invisible; expressed in micrometres as the main line
from a hydrogen cyanide laser, it lies far, far out in the infrared, well
past where the human eye responds.

Other numbers lack the sheer visual presence of the colourful laser
line set, and don’t even carry physical units like nanometres, but impress
through their compelling logic. Anyone who deals much with computers learns
the powers of 2, even the bigger ones, such as 1024, 2 to the 10th power.

These potent numbers are also so innocently charming in the ultimately
simple binary code they represent, that like a favoured child, the apple
of my eye who always draws attention, I always notice when they pop up in
ordinary life. Because they’re easy to remember, they’re good codes for,
say, a bicycle lock – at least if other fanciers of the binary are not in
sight.

Then there are the honoured loons of numbers which have been around
long enough to grow intricate and layered histories. One group is the irrationals:
pi of course; e, the base of natural logarithms; and the length-to-width
ratio (1 + 5)/2, the aesthetically pleasing proportion of the golden rectangle.
The stories of their discovery, the puzzlement over their unending digits,
the searches to find good approximations or to add yet more thousands of
digits, create a kind of awe. These numbers and others, such as various
infinite enumerations, carry a vaguely mystical tinge of elusive higher
truth. Perhaps akin to Platonic ideal forms, they may be as close as some
scientists ever get to the spiritual.

Generating amazement rather than awe are what might be called the ‘isn’t
it a small universe’ numbers of coincidence. To take these seriously is
to risk the madness of numerology; still it rings in my mind that 13.6 is
both mercury’s density (in grams per millilitre, at 0 °C), and hydrogen’s
ionisation energy (in electronvolts); and that the Earth’s mass in kilograms
is very nearly ten times Avogadro’s number. These also produce the unscientific
but seductive thought: ‘Is there really – somehow – a connection?’

This is all very well, but I’m begging the question: do people, even
scientists, ever actually laugh at numbers? Unlike the prisoners in the
pen, the answer is probably ‘No’ for single integers or decimal numbers,
no matter how deftly delivered by a raconteur of numerals; but ‘Yes’, for
numerical comparisons conveying the basic comic elements of exaggeration
and surprise. Absurdly magnified overstatement, restrained understatement
and catastrophe, ridiculously heightened contrast, are all funny.

I would laugh if someone said, ‘The distance to Alpha Centauri is 4.3
light years, 2 inches,’ and I have snickered at Arthur Stanley Eddington’s
statement, ‘I believe there are 15, 747, 724, 136, 275, 002, 577, 605, 653,
961, 181, 555, 468, 044, 717, 914, 527, 116, 709, 366, 231, 425, 076, 185,
631, 296 protons in the Universe and the same number of electrons.’ The
mind-bending disparity between light years and inches is what makes the
first statement laughable; Eddington’s sublime chutzpah in giving an enormous,
untestable theoretical result down to the very last proton in the Universe
is the tickler in the second. (If an actual count showed Eddington to be
off by just a couple of protons, would he still get full credit? I’d certainly
vote to give it, on the grounds of ‘close enough’.)

Nevertheless, at my next physics conference, I’ll try for a laugh like
Gus at the penitentiary; by shouting out the right number in the right way.
Logical and scientific, I’ll begin with positive integers, move on to zero
and negative integers, then rational numbers, irrational, complex, on to
the highest reaches of numberdom. If none of these work, I’ll revert to
the old gags, say number 73: ‘An American physicist, a French biochemist,
and a British chemist are sitting on the stage in Stockholm, waiting for
their Nobel prizes, when suddenly the American says . . .’ But you know
the rest.

Sidney Perkowitz is Charles Howard Candler Professor of Physics at Emory
University, Atlanta, Georgia.