# 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?

# Time is an illusion, lunchtime doubly so…

In the dim and distant past, time was, to humankind, a thing and not much more. There was light-time, then there was dark-time, then there was another lot of light-time; during the day we could hunt, fight, eat and try to stay alive, and during the night we could sleep and have sex. However, we also realised that there were some parts of the year with short days and colder night, and others that were warmer, brighter and better for hunting. Being the bright sort, we humans realised that the amount of time it spent in winter, spring, summer and autumn (fall is the WRONG WORD) was about the same each time around, and thought that rather than just waiting for it to warm up every time we could count how long it took for one cycle (or year) so that we could work out when it was going to get warm next year. This enabled us to plan our hunting and farming patterns, and it became recognised that some knowledge of how the year worked was advantageous to a tribe. Eventually, this got so important that people started building monuments to the annual seasonal progression, hence such weird and staggeringly impressive prehistoric engineering achievements as Stonehenge.

However, this basic understanding of the year and the seasons was only one step on the journey, and as we moved from a hunter-gatherer paradigm to more of a civilised existence, we realised the benefits that a complete calendar could offer us, and thus began our still-continuing test to quantify time. Nowadays our understanding of time extends to clocks accurate to the degree of nanoseconds, and an understanding of relativity, but for a long time our greatest quest into the realm of bringing organised time into our lives was the creation of the concept of the wee.

Having seven days of the week is, to begin with, a strange idea; seven is an awkward prime number, and it seems odd that we don’t pick number that is easier to divide and multiply by, like six, eight or even ten, as the basis for our temporal system. Six would seem to make the most sense; most of our months have around 30 days, or 5 six-day weeks, and 365 days a year is only one less than multiple of six, which could surely be some sort of religious symbolism (and there would be an exact multiple on leap years- even better). And it would mean a shorter week, and more time spent on the weekend, which would be really great. But no, we’re stuck with seven, and it’s all the bloody moon’s fault.

Y’see, the sun’s daily cycle is useful for measuring short-term time (night and day), and the earth’s rotation around it provides the crucial yearly change of season. However, the moon’s cycle is 28 days long (fourteen to wax, fourteen to wane, regular as clockwork), providing a nice intermediary time unit with which to divide up the year into a more manageable number of pieces than 365. Thus, we began dividing the year up into ‘moons’ and using them as a convenient reference that we could refer to every night. However, even a moon cycle is a bit long for day-to-day scheduling, and it proved advantageous for our distant ancestors to split it up even further. Unfortunately, 28 is an awkward number to divide into pieces, and its only factors are 1, 2, 4, 7 and 14. An increment of 1 or 2 days is simply too small to be useful, and a 4 day ‘week’ isn’t much better. A 14 day week would hardly be an improvement on 28 for scheduling purposes, so seven is the only number of a practical size for the length of the week. The fact that months are now mostly 30 or 31 days rather than 28 to try and fit the awkward fact that there are 12.36 moon cycles in a year, hasn’t changed matters, so we’re stuck with an awkward 7 day cycle.

However, this wasn’t the end of the issue for the historic time-definers (for want of a better word); there’s not much advantage in defining a seven day week if you can’t then define which day of said week you want the crops to be planted on. Therefore, different days of the week needed names for identification purposes, and since astronomy had already provided our daily, weekly and yearly time structures it made sense to look skyward once again when searching for suitable names. At this time, centuries before the invention of the telescope, we only knew of seven planets, those celestial bodies that could be seen with the naked eye; the sun, the moon (yeah, their definition of ‘planet’ was a bit iffy), Mercury, Venus, Mars, Jupiter and Saturn. It might seem to make sense, with seven planets and seven days of the week, to just name the days after the planets in a random order, but humankind never does things so simply, and the process of picking which day got named after which planet was a complicated one.

In around 1000 BC the Egyptians had decided to divide the daylight into twelve hours (because they knew how to pick a nice, easy-to-divide number), and the Babylonians then took this a stage further by dividing the entire day, including night-time, into 24 hours. The Babylonians were also great astronomers, and had thus discovered the seven visible planets- however, because they were a bit weird, they decided that each planet had its place in a hierarchy, and that this hierarchy was dictated by which planet took the longest to complete its cycle and return to the same point in the sky. This order was, for the record, Saturn (29 years), Jupiter (12 years), Mars (687 days), Sun (365 days), Venus (225 days), Mercury (88 days) and Moon (28 days). So, did they name the days after the planets in this order? Of course not, that would be far too simple; instead, they decided to start naming the hours of the day after the planets (I did say they were a bit weird) in that order, going back to Saturn when they got to the Moon.

However, 24 hours does not divide nicely by seven planets, so the planet after which the first hour of the day was named changed each day. So, the first hour of the first day of the week was named after Saturn, the first hour of the second day after the Sun, and so on. Since the list repeated itself each week, the Babylonians decided to name each day after the planet that the first hour of each day was named, so we got Saturnday, Sunday, Moonday, Marsday, Mercuryday, Jupiterday and Venusday.

Now, you may have noticed that these are not the days of the week we English speakers are exactly used to, and for that we can blame the Vikings. The planetary method for naming the days of the week was brought to Britain by the Romans, and when they left the Britons held on to the names. However, Britain then spent the next 7 centuries getting repeatedly invaded and conquered by various foreigners, and for most of that time it was the Germanic Vikings and Saxons who fought over the country. Both groups worshipped the same gods, those of Norse mythology (so Thor, Odin and so on), and one of the practices they introduced was to replace the names of four days of the week with those of four of their gods; Tyr’sday, Woden’sday (Woden was the Saxon word for Odin), Thor’sday and Frig’sday replaced Marsday, Mercuryday, Jupiterday and Venusday in England, and soon the fluctuating nature of language renamed the days of the week Saturday, Sunday, Monday, Tuesday, Wednesday, Thursday and Friday.

However, the old planetary names remained in the romance languages (the Spanish translations of the days Tuesday to Friday are Mardi, Mercredi, Jeudi and Vendredi), with one small exception. When the Roman Empire went Christian in the fourth century, the ten commandments dictated they remember the Sabbath day; but, to avoid copying the Jews (whose Sabbath was on Saturday), they chose to make Sunday the Sabbath day. It is for this reason that Monday, the first day of the working week after one’s day of rest, became the start of the week, taking over from the Babylonian’s choice of Saturday, but close to Rome they went one stage further and renamed Sunday ‘Deus Dominici’, or Day Of The Lord. The practice didn’t catch on in Britain, thousands of miles from Rome, but the modern day Spanish, French and Italian words for Sunday are domingo, dimanche and domenica respectively, all of which are locally corrupted forms of ‘Deus Dominici’.

This is one of those posts that doesn’t have a natural conclusion, or even much of a point to it. But hey; I didn’t start writing this because I wanted to make a point, but more to share the kind of stuff I find slightly interesting. Sorry if you didn’t.

# SCIENCE!

One book that I always feel like I should understand better than I do (it’s the mechanics concerning light cones that stretch my ability to visualise) is Professor Stephen Hawking’s ‘A Brief History of Time’. The content is roughly what nowadays a Physics or Astronomy student would learn in first year cosmology, but when it was first released the content was close to the cutting edge of modern physics. It is a testament to the great charm of Hawking’s writing, as well as his ability to sell it, that the book has since sold millions of copies, and that Hawking himself is the most famous scientist of our age.

The reason I bring it up now is because of one passage from it that spring to mind the other day (I haven’t read it in over a year, but my brain works like that). In this extract, Hawking claims that some 500 years ago, it would be possible for a (presumably rich, intelligent, well-educated and well-travelled) man to learn everything there was to know about science and technology in his age. This is, when one thinks about it, a rather bold claim, considering the vast scope of what ‘science’ covers- even five centuries ago this would have included medicine, biology, astronomy, alchemy (chemistry not having been really invented), metallurgy and materials, every conceivable branch of engineering from agricultural to mining, and the early frontrunners of physics to name but some. To discover everything would have been quite some task, but I don’t think an entirely impossible one, and Hawking’s point stands: back then, there wasn’t all that much ‘science’ around.

And now look at it. Someone with an especially good memory could perhaps memorise the contents of a year’s worth of New Scientist, or perhaps even a few years of back issues if they were some kind of super-savant with far too much free time on their hands… and they still would have barely scratched the surface. In the last few centuries, and particularly the last hundred or so years, humanity’s collective march of science has been inexorable- we have discovered neurology, psychology, electricity, cosmology, atoms and further subatomic particles, all of modern chemistry, several million new species, the ability to classify species at all, more medicinal and engineering innovations than you could shake a stick at, plastics, composites and carbon nanotubes, palaeontology, relativity, genomes, and even the speed of spontaneous combustion of a burrito (why? well why the f&%\$ not?). Yeah, we’ve come a long way.

The basis for all this change occurred during the scientific revolution of the 16th and 17th centuries. The precise cause of this change somewhat unknown- there was no great upheaval, but more of a general feeling that ‘hey, science is great, let’s do something with it!’. Some would argue that the idea that there was any change in the pace of science itself is untrue, and that the groundwork for this period of advancing scientific knowledge was largely done by Muslim astronomers and mathematicians several centuries earlier. Others may say that the increasing political and social changes that came with the Renaissance not only sent society reeling slightly, rendering it more pliable to new ideas and boundary-pushing, but also changed the way that the rich and noble functioned. Instead of barons, dukes and the nobility simply resting on their laurels and raking in the cash as the feudal system had previously allowed them to, an increasing number of them began to contribute to the arts and sciences, becoming agents of change and, in the cases of some, agents in the advancement of science.

It took a long time for science to gain any real momentum. For many a decade, nobody was ever a professional scientist or even engineer, and would generally study in their spare time. Universities were typically run by monks and populated by the sons of the rich or the younger sons of nobles- they were places where you both lived and learned expensively, but were not the centres of research that they are nowadays. They also contained a huge degree of resistance to the ideas put forward by Aristotle and others that had been rediscovered at the start of the revolution, and as such trying to get one’s new ideas taken seriously was a severe task. As such, just as many scientists were merely people who were interested in a subject and rich and intelligent enough to dabble in it as they were people committed to learning. Then there was the notorious religious problem- whilst the Church had no problem with most scientific endeavours, the rise of astronomy began one long and ceaseless feud between the Pope and physics into the fallibility of the bible, and some, such as Galileo and Copernicus, were actively persecuted by the Church for their new claims. Some were even hanged. But by far the biggest stumbling block was the sheer number of potential students of science- most common people were peasants, who would generally work the land at their lord’s will, and had zero chance of gravitating their life prospects higher than that. So- there was hardly anyone to do it, it was really, really hard to make any progress in and you might get killed for trying. And yet, somehow, science just kept on rolling onwards. A new theory here, an interesting experiment here, the odd interesting conversation between intellectuals, and new stuff kept turning up. No huge amount, but it was enough to keep things ticking over.

But, as the industrial revolution swept Europe, things started to change. As revolutions came and went, the power of the people started to rise, slowly squeezing out the influence and control of aristocrats by sheer weight of numbers. Power moved from the monarchy to the masses, from the Lords to the Commons- those with real control were the entrepreneurs and factory owners, not old men sitting in country houses with steadily shrinking lands that they owned. Society began to become more fluid, and anyone (well, more people than previously, anyway), could become the next big fish by inventing something new. Technology began to become of ever-increasing importance, and as such so did its discovery. Research by experiment was ever-more accessible, and science began to gather speed. During the 20th century things really began to motor- two world wars prompted the search for new technologies to enter an even more frenzied pace, the universal schooling of children was breeding a new generation of thinkers, and the idea of a university as a place of learning and research became more cemented in popular culture. Anyone could think of something new, and in that respect everyone was a scientist.

And this, to me, is the key to the world we live in today- a world in which a dozen or so scientific papers are published every day for branches of science relevant largely for their own sake. But this isn’t the true success story of science. The real success lies in the products and concepts we see every day- the iPhone, the pharmaceuticals, the infrastructure. The development of none of these discovered a new effect, a new material, or enabled us to better understand the way our thyroid gland works, and in that respect they are not science- but they required someone to think a little bit, to perhaps try a different way of doing something, to face a challenge. They pushed us forward one, tiny inexorable step, put a little bit more knowledge into the human race, and that, really, is the secret. There are 7 billion of us on this planet right now. Imagine if every single one contributed just one step forward.