I am a very special person. My body contains about a million atoms that once resided in the body of Christ. Also, every time I take a breath I inhale a molecule of the air that Christ exhaled as he died. I am tempted to sit back and wait for the tour buses to arrive at UCC laden with pilgrims.
But we are having a parking problem here so let me explain quickly that each of you is just as generously endowed as I am with atoms and molecules from the body of Christ. This is a consequence of two things: the nature of huge numbers, and the constant exchange of the fabric of our bodies with the fabric of the universe.
It is difficult to get a feeling for the meaning of very large or very small numbers. We can only intuitively grasp the meaning of numbers between 10,000 and one-thousandth. You could count to 10,000 in three hours and one-thousandth of an inch is about the thickness of a human hair. Most of physics deals with numbers outside this range, and the meaning of such numbers can only be conveyed by familiar word-pictures.
The material world is made of matter, and matter contains 92 different elements. The smallest part of an element that can exist is the atom. Atoms exist either independently or, more commonly, joined with other atoms to form compounds. The smallest part of a compound that can exist is a molecule. Atoms and molecules are extremely tiny and there are lots of them even in small bits of matter.
Each atom has a tiny mass, measured in atomic mass units (a.m.u.), e.g. the mass of the hydrogen atom is 1 a.m.u. and the mass of the oxygen atom is 16 a.m.u. The mass of a molecule (molecular weight) is the sum of the masses of the atoms in the molecule. For example, the molecular weight of water (H 2O) is 18 a.m.u.
The molecular weight expressed in grams is a mole of that compound. A mole of water is 18 grams (about a tablespoon full). A mole represents an amount detectable by our senses in the everyday world.
Count Amadeo Avogadro of Turin introduced a very useful concept in 1811: a mole of any compound contains the Avogadro Number of molecules. This number is impossibly large by human standards: 6.02 x (10 to the power of 23). 10 to the power of 23 means 10 multiplied by itself 22 times. If we fully wrote out the Avogadro Number it is 602 followed by 21 zeros. This could also be described in words as six hundred and two thousand million million million. But this is of little help in conveying a mental picture of the actual size of the number.
The theorem of Caesar's Last Breath helps us understand the immensity of the Avogadro Number. It states that every breath you take contains, on average, a molecule of the air that Julius Caesar (or indeed Christ, or Genghis Khan) exhaled as he died.
A breath of air is a small volume of air but it contains an enormous number of molecules, about one-tenth of the Avogadro Number. Also, the atmosphere of the Earth contains about one-tenth of the Avogadro Number of lungfulls of air. Therefore, assuming that Caesar's last breath mixed evenly into the Earth's atmosphere, each breath that we inhale contains, on average, one molecule of Caesar's last breath.
Avogadro's Number is unimaginably large, but it is just as difficult to get an intuitive grasp for numbers that are much smaller. The human body contains over one trillion cells, i.e. 1,000 billion cells.
How do you get a feel for a trillion? The physicist Hans Christian von Bayer explains it as follows. Picture a book of 1,000 pages with a photograph on each page. Now picture a very long train, each carriage filled with passengers each of whom has a copy of the book. The train is so long that, travelling at full speed, it takes six hours to pass a telegraph pole.
Imagine that this train made a six-hour trip once every day for a year and that each time it did so, each passenger on the train looked at every page of his/her book. At the end of the year one trillion photographs would have been examined.
For something to be grasped intuitively it must be accessible to the human senses. Billions and trillions are not accessible and therefore to get a sense of them they must be reduced to pictures anchored in common human experience such as breathing and riding on trains.
Complex relationships (e.g., exponential relationships) between variables are even more difficult to visualise than huge numbers. We come across exponential relationships, for example, when we consider compound interest or population growth. Unlike linear growth, which remains steady with time, rate of growth in an exponential relationship increases with time, thereby producing explosive results.
ONE of the best illustrations of exponential growth is an old Indian legend. Sissa Ben Dahir invented chess for King Shirham. The king was so pleased that he decided to give Sissa a present and asked him what he would like.
A game of chess is played on a board with 64 squares. Sissa said: "Your Highness, give me a grain of wheat to place on the first square, two grains to place on the second square, four grains to place on the third square, eight grains for the fourth square, and so on until all the squares are covered."
The astonished king said: "If that is all you wish, you poor fool, then let it be so." Shirham ordered wheat from his stores, and soon got a great surprise. By the 40th square, a million million grains were called for. The kingdom's entire wheat supply was completely exhausted well before the last square was reached. To comply fully with Sissa's request would require 2 to the power of 64 grains, sufficient to cover the surface of the Earth to a depth of one inch.
William Reville is a senior lecturer in biochemistry and director of microscopy at UCC