A Short History of Blurriness

I am short sighted; have been since I was about eight. It was glasses for a few years, but then it started to get bad and taking it off for rugby matches ceased to be a feasible strategy if I wanted to be able to catch the ball. So the contact lenses came in, firstly only for match days and subsequently the whole time. Nowadays, quite a lot of my mates are completely unaware that I wake up each morning to a blurry vision of my ceiling, which I guess is a tribute to the general awesomeness of modern technology

The reasons for poor vision concern the mechanics of the eye; eyes consist of (among other things) a lens made from some squishy substance that means its shape can change, and the retina, a patch of light-sensitive cells at the back of the eye. The aim is to bend light, emanating from a source, so that it all focuses onto one point right on the retina. The extent to which this bending must occur depends how far away the source is. How much the light is bent depends on the thickness of the lens- if it is thicker, the light is bent to a greater degree, which is preferable if the object is close to you, and vice-versa for objects further away. Your body is able to control the thickness of the lens thanks to a couple of suspensory ligaments running around the top and bottom of the eye, which pull at the lens to stretch it out. If they pull harder, then the lens gets thinner and light is bent less, allowing us to focus on far away objects. The degree to which these ligaments pull is controlled by the ciliary muscle; when the ciliary muscle pulls, the ligaments slacken, and vice-versa. If the lens was kept at this thickness, then light coming from a source close to us would not be focused onto the retina, and instead of a nice, clean, crisp picture then we would instead see a blurry image. All this, it should be pointed out, is working on the scale of fractions of millimetres, and it’s all a very finely-tuned balance.

In the majority of people, this is no problem at all- their eye muscles work fine and keep the lens at the thickness it needs to be. However, amongst the short-sighted, the ciliary muscle is too big and so cannot relax to the extent that it can in a normal eye. This means that the suspensory ligaments do not have quite the range that they should, and are unable to pull really hard to get the lens out to its thinnest setting. When viewing objects up close, this is no problem at all; the light needs to be bent a lot and it all lines up nicely over the retina, producing a lovely, clear image. However, once objects get further away, try as the ligaments might, they just can’t get the lens thin enough to do its job properly. The end result is that light from faraway objects is bent too much, focusing it onto a point just in front of the retina rather than actually on it, and resulting in a blurry image. In some ways, it’s quite an amusing paradox; the need to wear glasses, so often stereotypically associated with nerdery and physical weakness, comes about as a result of a muscle being too big.

In long-sighted people, the situation is reversed; the ciliary muscle is too small, and is unable to exert the required force to make the lens sufficiently thick to see close-up objects. This causes light to be focused behind the eye, resulting in the same kind of blurriness and requiring the person concerned to wear reading glasses or similar for dealing with nearby objects.

And whilst we’re on the subject of reading glasses, let us pause and consider glasses and contact lenses in general. In many ways, glasses were humankind’s first tentative step into the field of biomechanics, and I am occasionally amazed that they have been around long enough for us to take them for granted so. Somehow, I find it endlessly amazing that, by looking through some special glass, I can suddenly see things properly; it all feels suspiciously like witchcraft, even if it takes only simple science and geometry to understand. It’s a commonly known fact that light, when passing through glass, slows down and bends.  If we mess around looking at the geometry of the problem and apply that to light passing through a convex or concave shape, we arrive at an interesting conclusion- that a convex lens causes light to ‘turn inwards’, focusing initially parallel rays of light onto a point, and that a concave lens will do the reverse, causing light waves to spread out.

As we have seen, our eye has a convex lens built into it already to focus light onto the retina but we have already seen how this system can fail if all the finely-tuned controls are out of sorts. However, if we place another lens in front of our ‘broken’ lens, we can correct the flaws in it; if, for example, our original lens is too thick and bends light too much (as in short-sighted people), then by putting a concave lens in front of it we can bend the incoming light outwards, necessitating the light to be bent by a greater degree by the eye’s lens and allowing it to do its job properly. This, in effect, causes the light rays to be set at such an angle that it acts as if the object were positioned closer to the eye (my apologies if that sentence made no sense whatsoever), and a similar system using convex lenses can be utilised by long-sighted people. This is the principle upon which both glasses and contact lenses operate.

Then there’s laser eye surgery, in which the surgeon cuts open the eye, fires a laser at the cornea (the bit of the eye containing the lens and all the other refracting equipment) in order to reshape it, and then re-seals it. Now, if you will excuse me, I have to go and huddle under my duvet as a direct result of that image…

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?