F=ma

On Christmas Day 1642, a baby boy was born to a well-off Lincolnshire family in Woolsthorpe Manor. His childhood was somewhat chaotic; his father had died before he was born, and his mother remarried (to a stepfather he came to acutely dislike) when he was three. He was later to run away from school, discovered he hated the farming alternative and returned to become the school’s top pupil. He was also to later attend Trinity College Cambridge; oh, and became arguably the greatest scientist and mathematician of all time. His name was Isaac Newton.

Newton started off in a small way, developing binomial theorem; a technique used to expand powers of polynomials, which is a kind of fundamental technique used pretty much everywhere in modern science and mathematics; the advanced mathematical equivalent of knowing that 2 x 4 = 8. Oh, and did I mention that he was still a student at this point? Taking a break from his Cambridge career for a couple of years due to the minor inconvenience of the Great Plague, he whiled away the hours inventing calculus, which he finalised upon his return to Cambridge. Calculus is the collective name for differentiating and integrating, which allows one to find out the rate at which something is occurring, the gradient of a graph and the area under it algebraically; plus enabling us to reverse all of the above processes. This makes it sound like rather a neat and useful gimmick, but belies the fact that it allows us to mathematically describe everything from water flowing through a pipe to how aeroplanes fly (the Euler equations mentioned in my aerodynamics posts come from advanced calculus), and the discovery of it alone would have been enough to warrant Newton’s place in the history books. OK, and Leibniz who discovered pretty much the same thing at roughly the same time, but he got there later than Newton. So there.

However, discovering the most important mathematical tool to modern scientists and engineers was clearly not enough to occupy Newton’s prodigious mind during his downtime, so he also turned his attention to optics, aka the behaviour of light. He began by discovering that white light was comprised of all colours, revolutionising all contemporary scientific understanding of light itself by suggesting that coloured objects did not create their own colour, but reflected only certain portions of already coloured light. He combined this with discovering diffraction; that light shone through glass or another transparent material at an angle will bend. This then lead him to explain how telescopes worked, why the existing designs (based around refracting light through a lens) were flawed, and to design an entirely new type of telescope (the reflecting telescope) that is used in all modern astronomical equipment, allowing us to study, look at and map the universe like never before. Oh, and he also took the time to theorise the existence of photons (he called them corpuscles), which wouldn’t be discovered for another 250 years.

When that got boring, Newton turned his attention to a subject that he had first fiddled around with during his calculus time: gravity. Nowadays gravity is a concept taught to every schoolchild, but in Newton’s day the idea that objects fall to earth was barely even considered. Aristotle’s theories dictated that every object ‘wanted’ to be in a state of stillness on the ground unless disturbed, and Newton was the first person to make a serious challenge to that theory in nearly two millennia (whether an apple tree was involved in his discovery is heavily disputed). Not only did he and colleague Robert Hooke define the force of gravity, but they also discovered the inverse-square law for its behaviour (aka if you multiply the distance you are away from a planet by 2, then you will decrease the gravitational force on you by 2 squared, or 4) and turned it into an equation (F=-GMm/r^2). This single equation would explain Kepler’s work on celestial mechanics, accurately predict the orbit of the ****ing planets (predictions based, just to remind you, on the thoughts of one bloke on earth with little technology more advanced than a pen and paper) and form the basis of his subsequent book: “Philosophiæ Naturalis Principia Mathematica”.

Principia, as it is commonly known, is probably the single most important piece of scientific writing ever written. Not only does it set down all Newton’s gravitational theories and explore their consequences (in minute detail; the book in its original Latin is bigger than a pair of good-sized bricks), but he later defines the concepts of mass, momentum and force properly for the first time; indeed, his definitions survive to this day and have yet to be improved upon.  He also set down his three laws of motion: velocity is constant unless a force acts upon an object, the acceleration of an object is proportional to the force acting on it and the object’s mass (summarised in the title of this post) and action and reaction are equal and opposite. These three laws not only tore two thousand years of scientific theory to shreds, but nowadays underlie everything we understand about object mechanics; indeed, no flaw was found in Newton’s equations until relativity was discovered 250 years later, which only really applies to objects travelling at around 100,000 kilometres per second or greater; not something Newton was ever likely to come across.

Isaac Newton’s life outside science was no less successful; he was something of an amateur alchemist and when he was appointed Master of the Royal Mint (a post he held for 30 years until his death; there is speculation his alchemical meddling may have resulted in mercury poisoning) he used those skills to great affect in assessing coinage, in an effort to fight Britain’s massive forgery problem. He was successful in this endeavour and later became the first man to put Britain onto the gold, rather than silver, standard, reflecting his knowledge of the superior chemical qualities of the latter metal (see another previous post). He is still considered by many to be the greatest genius who ever lived, and I can see where those people are coming from.

However, the reason I find Newton especially interesting concerns his private life. Newton was a notoriously hard man to get along with; he never married, almost certainly died a virgin and is reported to have only laughed once in his life (when somebody asked him what was the point in studying Euclid. The joke is somewhat highbrow, I’ll admit). His was a lonely existence, largely friendless, and he lived, basically for his work (he has been posthumously diagnosed with everything from bipolar disorder to Asperger’s syndrome). In an age when we are used to such charismatic scientists as Richard Feynman and Stephen Hawking, Newton’s cut-off, isolated existence with only his prodigious intellect for company seems especially alien. That the approach was effective is most certainly not in doubt; every one of his scientific discoveries would alone be enough to place him in science’s hall of fame, and to have done all of them puts him head and shoulders above all of his compatriots. In many ways, Newton’s story is one of the price of success. Was Isaac Newton a successful man? Undoubtedly, in almost every field he turned his hand to. Was he a happy man? We don’t know, but it would appear not. Given the choice between success and happiness, where would you fall?

Money- what the &*$!?

Money is a funny old thing- the cornerstone of our way of existence, the bedrock of modern-day life, and the cause of, and solution to, 99% of all life’s problems. But… well, why? When you think about it, money doesn’t actually mean anything- it is an arbitrary creation brought in for convenience’s sake, and yet it as an entity has spiralled into so much more than a mere tool. Now how on earth did that happen?

Before about two and a half thousand (ish) years ago, money just about not exist. To the best of my knowledge, coinage only became commonplace in Europe with the rise of the Roman Empire- indeed, when they left Britain in the 5th century AD, much of the country went back to simply bartering- trading goods and services for other goods and services. This began to change as time went on however, and by the time of William the Conqueror’s invasion, the monetary system was firmly established across Europe. Coins were a far more efficient system than bartering- trading stuff for one another is a highly subjective process, and it can be hard to get a sense of value and to what extent you were being ripped off. By giving everything a fixed, arbitrary value (ie a price), everything suddenly had a value relative to one another. More importantly, this allowed for goods and services to be traded for the potential to buy more goods and services of equal value in coin form, rather than the things themselves, which was both easier and more efficient (there was now no risk of carrying a lampshade to the supermarket to exchange for a pint of milk, because a wallet is far easier to carry). The idea of money representing the potential to buy things can be seen by anyone looking on a British note, where it reads “I promise to pay the bearer on demand the sum of…” however many pounds (this is in fact a callback to the days when banks stuck to the gold standard, when you could theoretically walk into the Bank of England and ask for five pound’s worth of gold for your fiver).

However, with coins representing potential to buy things, they instantly took on a value of their own, and here things start to get confusing. Because, when money itself takes on a value, it instantly becomes a commodity just like any other- just as people trade in gold bullion, oil and bits of companies, so people trade with money itself. And this… actually, I’ve got ahead of myself- let me take a step backward.

The input of human effort can be used to increase the value of various bits of the world we live in. For example- a heap of planks may be bought for £50 from a sawmill, but once you have gone home and spent 6 hours swearing at a hammer, you may now have a bench or something worth £500 or more. The materials themselves have not changed, but since a bench is more useful, better looking, and is better appreciated by people than a few planks, people set more value by it. Because more value is set by it, so it is worth more money.

This, at a base level, is how the economic system works- human effort is used to turn raw materials, which we don’t want, into products, which we do. Because people want these products, they pay money for them, and because they need this money to pay for them, they get a job. Because they are providing human effort to their boss (which itself has a value for its ability to raise the value of raw materials), their boss pays them the money they need. The boss gets the money he uses to pay his employees from selling things to people, which makes money because the human effort put in to make his final product raises the value of his final product above that of the raw materials he bought in order to make it- and thus we are back at the beginning of the cycle.

If we study this process, we can see that the only way the boss can make any money out of it is if the value of his final product (F) is greater than the value of its raw materials (M) plus however much he pays his employees for the effort they input (E)- ie, F>M+E. However, pretty much by definition, F should equal M+E- thereby the only way he can make money is by paying his workers less than their human effort is actually worth in the context of the product (A communist would seize on this as evidence of corporations exploiting the masses, but I refuse to go into this argument here- it is far too messy). This is the only way that any money actually gets produced in an economy, and the result is inflation. If inflation did not exist, then the only way anyone could make any money would be by spending less- but this automatically means that somebody else will not be getting your money, and so will be losing some. Thus inflation is vital to ensure that everybody in an economy gains money, and although this does lead to the gentle devaluation of currency, it allows the human race to stay one step ahead of a potential vicious cycle of decline- and inflation can only be generated by an economy manufacturing things.

But why do we need our level of money to continually rise? Well, imagine you have a steak worth £5 (It’s just an example, don’t judge me on my figures). When you eat that steak, something of value £5 has been turned into the contents of your gut, and ultimately into what comes out the other end- which is clearly worth a lot less than the steak. Thus, the human race consuming resources  reduces the overall value of planet earth, just as making stuff increases it. Nature in fact has an inbuilt system to prevent this from turning into a cycle of endless decline- reproduction. If the cow you ate your steak from had had a calf, then nature has ensured that your consumption of the steak has not, in the long run, decreased the overall steak value of the world due to the steak potential existing in the calf (I’ve just realised I’m making all these terms up on the fly- my apologies). I could go into the whole energy from calf <- energy from grass <- energy from sun <- universe in general etc. thing here, but this is extrapolating the economic problem somewhat. However, suffice it to say that ensuring our overall monetary value continues to rise via inflation is our version, from an economic perspective, of reproduction, balancing out our consumption of finite resources in terms of value.

Phew- this is getting longer than I anticipated. My apologies once again for it turning into a semi-coherent ramble, I only hope you could follow it. There is still quite a lot more to get through, so I think I’ll try to wind this all up on Wednesday (after another Six Nations post Monday- COME ON ENGLAND!). If you have been able to follow all of that then congratulations- you now understand core economics. If you haven’t then also congratulations- you are sufficiently normal to not understand my way of thinking.