We can count parts, this being Part 1

Just before Christmas 2020, we lost the writer John le Carré. Not in the literal sense of being misplaced in a dead letterbox, euphemistically lost. Brits (and I assume other nationalities too) thrive on the euphemism: we have scores of them to replace words and subjects which within polite or sensitive company require are deemed unsuitable. Le Carré could have kicked the bucket; shuffled off this mortal coil; been called home; or gone to the pavilion for the last time. He’s brown bread at nearly 90: a good innings. For many of those years he carried with aplomb the spy novel genre as his bat. He came to the crease after the great openers of Joseph Conrad and W. Somerset Maugham. Alongside Eric Ambler, Graham Greene and Len Deighton, he formed a formidable top order and with his passing we are now in the capable middle order hands of Mick Herron and Charles Cumming. Stumped?

Cricket is England (and Wales). Apparently, the good Lord gave the English test match cricket so that we could experience eternity before we arrived at the Pearly Gates. Le Carré’s spy novels were likewise quintessentially England and the English. That’s a tenuous link between le Carré and cricket. I’ve read many obituaries and his memoir and could uncover whether le Carré enjoyed the sound of leather upon willow. So upon appeal, I get to bat on. You can have plenty of fun writing with English (I hope you appreciated the cricketing idioms and terms - count them if you like) and if you excel at writing, you may even slip (still there with the cricket terms) a new word or two into the common vernacular. Mr. le Carré added a few espionage terms to the already rich English language:

to come in from the cold - after a period of isolation to be welcomed back into the community again.

honey trap - whereby an attractive (usually female) person is used to lure another (usually male) into revealing sensitive or secret information.

Perhaps his most lasting addition to the language is mole.

Thanks to the generosity of the good people at the Oxford English Dictionary, the full definition of the word ‘mole’ can be viewed online. No more the solitary meaning of talpa europaea. The rarely seen mammal with spade like paws, adapted to work well in its below ground environment. Digging tunnels to find its food of preference worms, it simultaneously aerates the soil, thus improving soil quality. This enables more plants to grow and more insects to thrive. It also improves soil drainage, reducing flooding and local puddling. A wonderful environmentally helpful animal, which I have been lucky enough to see twice. Alas, both times they had already become worm food.

At secondary school, I was introduced to chemical moles and the eighteenth century Italian chemist, Amedeo Avogadro. The chemical mole derives, strangely, from the German molekül shortened to mol. I guess German was the lingua franca of the eighteenth century chemistry world. Our friends at the Bureau International des Poids et Mesures give us a definition of the mole as being:

The mole is the SI (International System of Units) unit of amount of substance. One mole contains exactly 6.02214076 x 10²³ elementary entities. This number is the fixed numerical value of the Avogadro constant when expressed in the unit mol⁻¹ and is called the Avogadro number. The amount of substance of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles.

Clear as water, right? I may not be the best person to embellish what this means, as I had a somewhat sticky wicket with my chemistry exams. What I recollect is for a mass of a chemical substance (i.e. good old H₂O), you can determine how many molecules (i.e. the number of hydrogen atoms and oxygen atoms) are contained within that mass using Avogadro’s law and constant.

By way of example (Disclaimer: Please, feel free to dispute all the calculations and numbers within this post. I’ve checked them to the best of my capabilities and they are ball-park. I am merely bowling out big numbers and small sizes to embellish a point. Nothing more, nothing less):

Two metric tablespoons of water (30ml) contain approximately 1,002,798,750,000,000,000,000,000 molecules:
Atomic mass of Hydrogen is 1.008g/mol
Atomic mass of Oxygen is 16g/mol
Atomic mass of H₂O is 18.016g/mol
Number of moles in 30ml (assuming normal temperatures and pressures, 30ml of water is 30g) of water = 30 x 1/18.016 = 1.6651865 moles
If 1 mole contains 6.02214076 x 10²³ elementary entities then 30ml/30g of water contains:
1.6651865 x (6.02214076 x 10²³) = 1,002,798,750,000,000,000,000,000 molecules.

In researching this post, the foregoing has thrown up many questions that I must find answers for at some stage. However, for this post, let’s just say that 1,002,798,750,000,000,000,000,000 (or 1.00279875 x 10²⁴) is a big number and molecules of water are small. But exactly how big and how small?

The following is a crude table of volumes (in km³) and assumes, amongst many other things to make it easy, that all the objects below, except for the Milky Way, are perfect spheres.

Water molecule 2.991627 x 10⁻³⁸
Virus 1.022654 x 10⁻³⁰
Grain of sand 4.597231 x 10⁻¹⁸
Football 5.547487 x 10⁻¹²
Earth 1.087800 x 10¹²
Sun 1.412270 x 10¹⁸
Flat Milky Way 6.700000 x 10⁵¹

From these figures, you can appreciate just how small molecules are. In the space of one grain of sand, 153,669,926,097,070,256,419 molecules of water can be fitted. But only 1,206,702 grains of sand will fill a football. Counting at 1 grain per second for 8 hours each day, it would take 41 days to fill that football with sand. However, at the same rate, there have not been enough seconds in our universe’s life to have filled that grain of sand with water molecules. Current thought has our universe celebrating its 13.8 billion years’ birthday a little later this year (15th October if you want to send a card). That grain of sand would only be 0.1% full and would require another 14,618,524,172,095 years to be filled.

Running between the wickets of microscopic and macroscopic, enormous numbers can be encountered. You’d only need about 1.3 million Earths to fill the Sun. Approximately 4,744,150,682,950,400,000,000,000,000,000,000 Suns are required to fill the Milky Way. Even though the Milky Way could accommodate such a number, in reality it only contains 100,000,000,000 or so stars. There’s plenty of ‘nothing’ out there. The Milky Way is but one galaxy of the universe. There are many, many more. About 2,000,000,000,000 of them fill our universe. Want to hit your wicket yet? If not, then consider the multiverse as your ultimate boundary?

We can count the small. We can count the medium. We can also count the large. We can count the birds and the bees. We count runs, wickets, centuries and caps. We count books, authors, and words. We count Counts.

Admittedly, some of those counts are best guesses and use assumptions. As a species we like to count things; we like to compare things; we like to understand the relationships between all of this. Quantify then qualify. We enjoy putting things in compartments and studying them each and every way. Then we dig in deeper.

However, for all the advances and accuracies we have made with our ability to count, we still cannot count age, height or width. We can’t count hydrogen, oxygen, rain or water. Knowledge, gratitude and wisdom. No way to count that. Nonsense? No, can’t count that nor hope nor beauty. We can’t even count pronunciation. As for espionage? Yes, you guessed it: impossible to count… or is it?