Alex's Adventures in Numberland - Alex Bellos [46]
It is worth taking a breath to consider the view. There are an estimated 1080 atoms in the universe. If we take the smallest measurable unit of time – known as Planck time, which is a second divided into 1043 parts – then there have been about 1060 units of Planck time since the Big Bang. If we multiply the number of atoms in the universe by the number of Planck times since the Big Bang – which gives us the number of unique positions of every particle since time began – we are still only on 10140, which is way, way smaller than 10421. The Buddha’s big number has no practical application – at least not for counting things that exist.
Not only was the Buddha able to fathom the impossibly large, he was also proficient in the realm of the impossibly tiny, explaining how many atoms there were in the yojana, an ancient unit of length around 10km. A yojana, he said, was equivalent to:
Four krosha, each of which was the length of
One thousand arcs, each of which was the length of
Four cubits, each of which was the length of
Two spans, each of which was the length of
Twelve phalanges of fingers, each of which was the length of
Seven grains of barley, each of which was the length of
Seven mustard seeds, each of which was the length of
Seven poppy seeds, each of which was the length of
Seven particles of dust stirred up by a cow, each of which was the length of
Seven specks of dust disturbed by a ram, each of which was the length of
Seven specks of dust stirred up by a hare, each of which was the length of
Seven specks of dust carried away by the wind, each of which was the length of
Seven tiny specks of dust, each of which was the length of
Seven minute specks of dust, each of which was the length of
Seven particles of the first atoms.
This was, in fact, a pretty good estimate. Just say that a finger is 4cm long. The Buddha’s ‘first atoms’ are, therefore, 4cm divided by seven ten times, which is 0.04m×7–10 or 0.0000000001416m, which is more or less the size of a carbon atom.
The Buddha was by no means the only ancient Indian interested in the incredibly large and the unfeasibly small. Sanskrit literature is full of astronomically high numbers. Followers of Jainism, a sister religion to Hinduism, defined a raju as the distance covered by a god in six months if he covers 100,000 yojana in each blink of his eye. A palya was the amount of time it takes to empty a giant yojana-sized cube filled with the wool of newborn lambs if one strand is removed every century. The obsession with high (and low) numbers was metaphysical i nature, a way of groping towards the infinite and of grappling with life’s big existential questions.
Before Arabic numerals became an international lingua franca, humans had many other ways of writing down numbers. The first number symbols that emerged in the West were notches, cuneiform bird tracks and hieroglyphics. When languages developed their own alphabets, cultures began to use letters to represent numbers. The Jews used the Hebrew aleph () to mean one, bet () to be two and so on. The tenth letter, yod (), was ten, after which each letter went up in tens, and on reaching 100 went up in hundreds. The twenty-second and final letter of the Hebrew alphabet, tav (), was 400. Using letters for numbers was confusing and also encouraged a numerological approach to counting. Gematria, for example, was the practice of adding up the numbers of the letters in Hebrew words to find a value and using this number for speculations and divinations.
The Greeks used a similar system, with alpha () being one, beta (ß) being two, and so on to the twenty-seventh letter of their alphabet, sampi (), which was 900. Greek mathematical culture, the most advanced in the classical