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?

How Quantum Physics Explains Action Films

One of the key ideas used by cosmologists (yes, physics again, sorry) to explain away questions asked by annoying philosophical types is known as the anthropic principle. This has two forms (strong and weak) but the idea remains the same for both; that the reason for a situation being as it is is because, if it wasn’t, we wouldn’t be around to ask that question. For example, one might ask (as Stephen Hawking did in ‘A Brief History of Time’) why the universe is around 10 billion years old, a decidedly awkward question if ever there was one. The anthropic principle provides the simplest answer, stating that since organic life is such a complicated business and that the early universe was such a chaotic, unfriendly place, it is only after this vast amount of time that life forms capable of asking this question have been able to develop.

This answer of ‘because we’re here’ is a wonderfully useful one, albeit one that should be used with caution to avoid not answering valid question, and can be applied to problems that do not concern themselves directly with physics. One example concerns the origin of the human race, as we are all thought to stem from just a few hundred individuals who lived in East Africa’s Rift valley several million years ago. At that time our knowledge of weapons, fighting and general survival was relatively scant, and coming face to face with any large predator would have been a fairly assured death sentence; the prehistoric equivalent of a smart pride of lions, or even some particularly adverse weather one year, could have wiped out a significant proportion of the human race as it stood at that time in just a few months. Despite the advantages of adaptability and brainpower that we have shown since, the odds of natural selection were still stacked against us; why did we arise to become the dominant multicellular life form on this planet?

This question can be answered by listing all the natural advantages we possess as a species and how they enabled us to continue ‘evolving’ far beyond the mere natural order of things; but such an answer still can’t quite account for the large dose of luck that comes into the bargain. The anthropic principle can, however, account for this; the human race was able to overcome the odds because if we hadn’t, then we wouldn’t be around to ask the question. Isn’t logic wonderful?

In fact, one we start to think about our lives and questions of our existence in terms of the anthropic principle, we realise that our existence as individuals is dependent on an awful lot of historical events having happened the way they did. For example, if the Nazis had triumphed during WWII, then perhaps one or more of my grandparents could have been killed, separated from their spouse, or in some way prevented from raising the family that would include my parents. Even tinier events could have impacted the chance of me turning out as me; perhaps a stray photon bouncing off an atom in the atmosphere in a slightly different way could have struck a DNA molecule, causing it to deform the sperm that would otherwise have given me half my genes and meaning it never even made it to the egg that offered up the other half. This is chaos theory in action, but it illustrates a point; for the universe to have ended up the way it has depends on history having played out exactly as it has done.

The classic example of this in quantum physics is the famous ‘Schrodinger’s Cat’ experiment, in which a theoretical cat was put into a box with a special quantum device that had a 50/50 chance of either doing nothing or releasing a toxic gas that would kill the cat. Schrodinger’s point was that, when the cat is put into the box, two universes emerge; one in which the cat is dead, and one in which it is alive. Until we open the box, we cannot known which of these universes we are in, so the cat must be thought of as simultaneously alive and dead.

However, another thought experiment known as the ‘quantum suicide’ experiment takes the cat’s point of view; imagine that the cat is an experimenter, and that he is working alone. Imagine you are that experimenter, and that you had stayed in the box for five iterations of the 50/50 life/death random event. In 31 out of 32 possible futures, you would have been gassed, for at least once the device would have selected the ‘death’ option; but in just one of these 32 alternative futures, you would still be alive. Moreover, if you had since got out of the box and published your results, the existence of those results is solely dependent on you being that lucky one out of 32.

Or, to put it another way, consider a generic action hero, in the classic scene where he runs through the battlefield gunning down enemies whilst other, lesser soldiers fall about him from bullets and explosions. The enemy fire countless shots at him, but try as they might they can never kill him. They try, but he survives and the film reaches its triumphant conclusion.

Now, assuming that these enemies are not deliberately trying to miss him and can at least vaguely use their weapons, if our action hero tried to pull that ‘running through a hail of bullets’ stunt then 999 times out of a thousand he’d be killed. However, if he was killed then the film would not be able to reach its conclusion, since he would be unable to save the heroine/defeat the baddie/deliver a cliched one-liner, and as such the story would be incomplete.  And, with such a crappy story, there’s no way that a film would get made about it; therefore, the action hero must always be one of the lucky ones.

This idea of always triumphing over the odds, of surviving no matter what because, if you didn’t, you wouldn’t be around to tell the tale or even be conscious of the tale, is known as quantum immortality. And whilst it doesn’t mean you’re going to be safe jumping off buildings any time soon, it does at least give yo a way to bore the pants off the next person who claims that action movies are WAAYYYY too unrealistic.

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.

Death post Mk. II

I must begin this post with an apology- the topic of this blog is again going dark. I know that the last time I touched on this is was both a) rubbish and b) weird, but this is something I feel like I need to get off my chest- this is about self-harm and suicide.
I have, in my life, thought of suicide once. And I mean once- I spent most of the rest of that day internally beating myself over the head, each thump made up of a reason as to just why it was such a stupid, horrible idea. But it happened. This was at the very depths of my depression- I was lonely, I was angry, and, worst of all, I had very little idea about how to get out, or exactly what was going on. In hindsight I hadn’t been thinking it through properly, but I’m wandering off-topic.
In Britain, around five and a half thousand people commit suicide every year, although I recently saw another statistic that suggested less than one in seven people with suicidal intent ever go on to kill themselves. The human race has a base instinct for self -preservation, and many people, even though they may question their worth, their value, their purpose, will find it near-impossible to get up the courage to kill themselves. This is in fact a major cause of self-harm; people who want to (to some degree) commit suicide, and may even half-attempt to, but who find themselves unable to go all the way, ending up merely inflicting damage. However this is far from the only reason- two other particularly common ones are an almost self-indulgent sense of revelling in one’s own suffering, similar to what I discussed in last week’s post about depression, and as a kind of plea for help.
I have refrained from calling the latter ‘attention-seeking’, because it demeans the level of pain the sufferer is experiencing. Mental health issues, depression and unhappiness can slaughter a soul (as, again, I have posted previously), and the level to which a human being must descend to contemplate harming themselves, or considering killing themselves, is a truly horrible thing. There may be a tendency among people to classify the above two reasons for self-harm as ‘selfish’ or ‘stupid’, but this is just plain wrong. The ideas themselves are illogical, yes, to a rational, non-depressed brain. To someone who feels that they have no way out and are in a state of despair, it can seem almost natural. If someone, anyone you know, ever self-harms or thinks of doing so, then that is the time to put your life to one side, for it is time to help save another.
Self-harm is one thing- suicide is an entirely different kettle of fish. I have already spoken about the depravity of murder, and its impact, and the impact of suicide is the same if not worse. Suicide deprives families of siblings, parents and children, couples of partners, social circles of friends. It leaves a gap in the world. Then there is the impact for those in the immediate vicinity- the train driver who saw someone jump on the line, the hotel maid who found someone in the bath with slashed wrists, the person who the building-jumper landed next to. The trauma of events like that will live with people for the rest of their lives.
But, this stuff is what potential suicides know- rationally anyway, as this stuff can be very difficult for the soul to comprehend. So, instead of listing more incoherent ramblings, I am going to explain why I have never seriously thought of suicide, and why I live how I do. I hope it can help you too.

Throughout my life, I have always been willing to fight and work as hard as I can to be the best I can be, and live my life to its fullest. Why? Well, because the core tenet of my belief is that life is something with potential- endless potential. No matter how much crap life throws in your face, there is a way for you to battle on through it and make of life what you will, what you can. This is something that many people find hard to believe, or in the case of some who I know, simply refuse to. This is where I draw on my inspiration. People have had to fight far harder, against far steeper odds than me, in the pursuit of goals far loftier and more inaccessible than my own, and they have triumphed. Think Nelson Mandela- born in a Xhosa village in a country where racism was ingrained into the psyche and law, he spent his entire life fighting for his people’s equality. After spending over a quarter of his life in an island prison, he not only served as President for 5 years and won a Nobel Peace Prize, but now is one of the most internationally recognised and respected men on Earth (and incidentally my all-time hero). Think  William Kamkwamba, a Malawian teenager who, after being forced to drop out of school when a famine slashed his family’s income, used knowledge gained from a children’s library book to harness wind power and provide electricity to his village. He is now on a scholarship in South Africa and has delivered speeches to packed audiences across the world. Stephen Hawking was diagnosed with motor neurone disease 50 years ago, a disease that would render him almost totally paralysed, unable to move or speak, and was given just months to live. He is now 70, a giant in the field of theoretical physics, the most advanced science of the modern age, and is publicly acclaimed as one of the most intelligent people on earth. I could go on. No matter how low your life gets, it is never, no matter the situation, impossible to turn things around. That is what keeps me going. That is the mental state that has kept me firmly away from thoughts of suicide

As Thomas Jefferson once wrote, it is an “unalienable truth” that every human is entitled to the rights of “life, liberty, and the pursuit of happiness”. Rights, the first and last especially, that everybody should exercise.

Time is a funny old thing…

Today I am rather short on time- the work I have to do is beginning to mount up despite (and partially because) of a long weekend. To most people this is a perfectly good reason to put up an apologetic cop-out of a post to prevent them having to work on it, but for me, it is a perfectly good excuse for my bloodymindedness to take over, so I thought I might write something about time.
As such a strange and almost abstract concept as it is, time can be viewed from a number of perspectives- the physical sense, the thermodynamic sense, and the human sense are the three obvious ones that spring to mind. To a physicist, time is a dimension much like width and length, and is far from unique- in fact there is a large sector of theoretical physics open to the idea that in the big bang there were many millions of dimensions, only 4 of which (3 spacial and one temporal) opened up into the rest of the universe, the other dimensions only existing on a microscopic, atomic scale (which might explain why the quantum world is so plain weird. Hey- I’m no physicist, and the web can probably tell you more). The really special thing about time compared to spacial dimensions to a physicist (among a long list, that are confusing and difficult to describe), is that it is the only dimension with an obvious direction. People often talk of ‘the arrow of time’, but the idea of any other dimension having an arrow is only a sort of arbitrary point of reference (north & south, up & down are only relative to our own earth and so are merely convenient reference points. This idea of time having an irreversible arrow annoys a lot of physicists as there appears to be little, fundamentally, that means we couldn’t travel in time in the other direction- the theory of relativity, for example, shows how fluid time can be. The idea of time’s direction has a lot to do with thermodynamics, which is where the second perspective of time comes from.
Really I am using the word thermodynamic very loosely, as what I am really thinking of is more to do with the psychological arrow of time. To quickly paraphrase what I mean by thermodynamics, the second law of thermodynamics states that the universe’s level of entropy, or randomness, will always increase or stay the same, never decrease, because a more random, chaotic system is more stable. One way of thinking of this is like a beach- the large swathes of sand can be arranged in a huge number of configurations and still seem the same, but if there are lots of sandcastles over it, there is a lot less randomness. One can seemingly reverse this process by building more sandcastles, making the universe more ordered, but to do this requires energy which, on a universal level, increases the universe’s entropic level. It is for this reason that a smashed pot will always have been preceded, but not followed by, the same pot all in one piece.
The thing is, the psychological and thermodynamic arrows of time point in the same direction, and their link on one another is integral. Our whole view of the passing of time is influenced by the idea of events that have irrevocably ‘happened’ and are ‘over’, hence our eternal fascination with ‘what if’s’. We persistently worry about past mistakes, what could have been, and what things were like, but never can be- hence the popularity of historical stories, ruins, nostalgia and grumbling about teenagers. For a better explanation of the various ‘arrows of time’, try Stephen Hawking’s ‘A Brief History of Time’- it is somewhat out of date now and it is fashionable now to think of it as overly simplistic, but it’s still a good source of a grounding in high-level physics
The final, and to me most interesting, perspective of time I want to talk about is deeply linked to the psychological arrow and our thoughts of the passing of time, but brings its own, uniquely relative, view- the human perspective (notice how it is always people I seem to find the most interesting.) We humans view time in a way that, when thought about, paints a weirdly fluid portrait of the behaviour of time. There is never enough time to work, too much time spent waiting, not enough time spent on holidays or relaxing, too much time spent out of work, too little time spent eating the cake and too much spent washing up. There are the awkward pauses in conversation that seem to drag on for an eternity, especially when they come just after the moment when the entire room goes silent for no accountable reason, enabling everyone to hear the most embarrassing part of your conversation. There are those hours spent doing things you love that you just gobble up, revelling in your own happiness, and the bitter, painful minutes of deep personal pain.
Popular culture and everyday life often mentions or features these weirdly human notions of time being so relative to the scenario- Albert Einstein himself described relativity thus: “When you are talking to a nice girl, an hour seems like a second. When you have your hand on a bar of red-hot iron, a second seems like an hour”. In fact, when you think about it, it is almost as if time appears to be a living thing, at least in the context of our references to it. This, I think anyway, is the nub of the matter- time is something that we encounter, in its more thermodynamic form, every day of our lives, and just like pet owners will tend to anthropomorphise their pets’ facial expressions, so the human race has personified time in general conversation (well, at least in the western world- I cannot speak for anywhere non English-speaking as a certainty). Time is almost one of the family- ever-present, ever-around, ever-referred to, until it becomes as human as a long-lost friend, in its own little way.
Finally, on the subject of time, Mr Douglas Adams: “Time is an illusion; lunchtime doubly so”