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?

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What we know and what we understand are two very different things…

If the whole Y2K debacle over a decade ago taught us anything, it was that the vast majority of the population did not understand the little plastic boxes known as computers that were rapidly filling up their homes. Nothing especially wrong or unusual about this- there’s a lot of things that only a few nerds understand properly, an awful lot of other stuff in our life to understand, and in any case the personal computer had only just started to become commonplace. However, over 12 and a half years later, the general understanding of a lot of us does not appear to have increased to any significant degree, and we still remain largely ignorant of these little feats of electronic witchcraft. Oh sure, we can work and operate them (most of us anyway), and we know roughly what they do, but as to exactly how they operate, precisely how they carry out their tasks? Sorry, not a clue.

This is largely understandable, particularly given the value of ‘understand’ that is applicable in computer-based situations. Computers are a rare example of a complex system that an expert is genuinely capable of understanding, in minute detail, every single aspect of the system’s working, both what it does, why it is there, and why it is (or, in some cases, shouldn’t be) constructed to that particular specification. To understand a computer in its entirety, therefore, is an equally complex job, and this is one very good reason why computer nerds tend to be a quite solitary bunch, with quite few links to the rest of us and, indeed, the outside world at large.

One person who does not understand computers very well is me, despite the fact that I have been using them, in one form or another, for as long as I can comfortably remember. Over this summer, however, I had quite a lot of free time on my hands, and part of that time was spent finally relenting to the badgering of a friend and having a go with Linux (Ubuntu if you really want to know) for the first time. Since I like to do my background research before getting stuck into any project, this necessitated quite some research into the hows and whys of its installation, along with which came quite a lot of info as to the hows and practicalities of my computer generally. I thought, then, that I might spend the next couple of posts or so detailing some of what I learned, building up a picture of a computer’s functioning from the ground up, and starting with a bit of a history lesson…

‘Computer’ was originally a job title, the job itself being akin to accountancy without the imagination. A computer was a number-cruncher, a supposedly infallible data processing machine employed to perform a range of jobs ranging from astronomical prediction to calculating interest. The job was a fairly good one, anyone clever enough to land it probably doing well by the standards of his age, but the output wasn’t. The human brain is not built for infallibility and, not infrequently, would make mistakes. Most of these undoubtedly went unnoticed or at least rarely caused significant harm, but the system was nonetheless inefficient. Abacuses, log tables and slide rules all aided arithmetic manipulation to a great degree in their respective fields, but true infallibility was unachievable whilst still reliant on the human mind.

Enter Blaise Pascal, 17th century mathematician and pioneer of probability theory (among other things), who invented the mechanical calculator aged just 19, in 1642. His original design wasn’t much more than a counting machine, a sequence of cogs and wheels so constructed as to able to count and convert between units, tens, hundreds and so on (ie a turn of 4 spaces on the ‘units’ cog whilst a seven was already counted would bring up eleven), as well as being able to work with currency denominations and distances as well. However, it could also subtract, multiply and divide (with some difficulty), and moreover proved an important point- that a mechanical machine could cut out the human error factor and reduce any inaccuracy to one of simply entering the wrong number.

Pascal’s machine was both expensive and complicated, meaning only twenty were ever made, but his was the only working mechanical calculator of the 17th century. Several, of a range of designs, were built during the 18th century as show pieces, but by the 19th the release of Thomas de Colmar’s Arithmometer, after 30 years of development, signified the birth of an industry. It wasn’t a large one, since the machines were still expensive and only of limited use, but de Colmar’s machine was the simplest and most reliable model yet. Around 3,000 mechanical calculators, of various designs and manufacturers, were sold by 1890, but by then the field had been given an unexpected shuffling.

Just two years after de Colmar had first patented his pre-development Arithmometer, an Englishmen by the name of Charles Babbage showed an interesting-looking pile of brass to a few friends and associates- a small assembly of cogs and wheels that he said was merely a precursor to the design of a far larger machine: his difference engine. The mathematical workings of his design were based on Newton polynomials, a fiddly bit of maths that I won’t even pretend to understand, but that could be used to closely approximate logarithmic and trigonometric functions. However, what made the difference engine special was that the original setup of the device, the positions of the various columns and so forth, determined what function the machine performed. This was more than just a simple device for adding up, this was beginning to look like a programmable computer.

Babbage’s machine was not the all-conquering revolutionary design the hype about it might have you believe. Babbage was commissioned to build one by the British government for military purposes, but since Babbage was often brash, once claiming that he could not fathom the idiocy of the mind that would think up a question an MP had just asked him, and prized academia above fiscal matters & practicality, the idea fell through. After investing £17,000 in his machine before realising that he had switched to working on a new and improved design known as the analytical engine, they pulled the plug and the machine never got made. Neither did the analytical engine, which is a crying shame; this was the first true computer design, with two separate inputs for both data and the required program, which could be a lot more complicated than just adding or subtracting, and an integrated memory system. It could even print results on one of three printers, in what could be considered the first human interfacing system (akin to a modern-day monitor), and had ‘control flow systems’ incorporated to ensure the performing of programs occurred in the correct order. We may never know, since it has never been built, whether Babbage’s analytical engine would have worked, but a later model of his difference engine was built for the London Science Museum in 1991, yielding accurate results to 31 decimal places.

…and I appear to have run on a bit further than intended. No matter- my next post will continue this journey down the history of the computer, and we’ll see if I can get onto any actual explanation of how the things work.