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…

Advertisements

NUMBERS

One of the most endlessly charming parts of the human experience is our capacity to see something we can’t describe and just make something up in order to do so, never mind whether it makes any sense in the long run or not. Countless examples have been demonstrated over the years, but the mother lode of such situations has to be humanity’s invention of counting.

Numbers do not, in and of themselves, exist- they are simply a construct designed by our brains to help us get around the awe-inspiring concept of the relative amounts of things. However, this hasn’t prevented this ‘neat little tool’ spiralling out of control to form the vast field that is mathematics. Once merely a diverting pastime designed to help us get more use out of our counting tools, maths (I’m British, live with the spelling) first tentatively applied itself to shapes and geometry before experimenting with trigonometry, storming onwards to algebra, turning calculus into a total mess about four nanoseconds after its discovery of something useful, before just throwing it all together into a melting point of cross-genre mayhem that eventually ended up as a field that it as close as STEM (science, technology, engineering and mathematics) gets to art, in that it has no discernible purpose other than for the sake of its own existence.

This is not to say that mathematics is not a useful field, far from it. The study of different ways of counting lead to the discovery of binary arithmetic and enabled the birth of modern computing, huge chunks of astronomy and classical scientific experiments were and are reliant on the application of geometric and trigonometric principles, mathematical modelling has allowed us to predict behaviour ranging from economics & statistics to the weather (albeit with varying degrees of accuracy) and just about every aspect of modern science and engineering is grounded in the brute logic that is core mathematics. But… well, perhaps the best way to explain where the modern science of maths has lead over the last century is to study the story of i.

One of the most basic functions we are able to perform to a number is to multiply it by something- a special case, when we multiply it by itself, is ‘squaring’ it (since a number ‘squared’ is equal to the area of a square with side lengths of that number). Naturally, there is a way of reversing this function, known as finding the square root of a number (ie square rooting the square of a number will yield the original number). However, convention dictates that a negative number squared makes a positive one, and hence there is no number squared that makes a negative and there is no such thing as the square root of a negative number, such as -1. So far, all I have done is use a very basic application of logic, something a five-year old could understand, to explain a fact about ‘real’ numbers, but maths decided that it didn’t want to not be able to square root a negative number, so had to find a way round that problem. The solution? Invent an entirely new type of number, based on the quantity i (which equals the square root of -1), with its own totally arbitrary and made up way of fitting  on a number line, and which can in no way exist in real life.

Admittedly, i has turned out to be useful. When considering electromagnetic forces, quantum physicists generally assign the electrical and magnetic components real and imaginary quantities in order to identify said different components, but its main purpose was only ever to satisfy the OCD nature of mathematicians by filling a hole in their theorems. Since then, it has just become another toy in the mathematician’s arsenal, something for them to play with, slip into inappropriate situations to try and solve abstract and largely irrelevant problems, and with which they can push the field of maths in ever more ridiculous directions.

A good example of the way mathematics has started to lose any semblance of its grip on reality concerns the most famous problem in the whole of the mathematical world- Fermat’s last theorem. Pythagoras famously used the fact that, in certain cases, a squared plus b squared equals c squared as a way of solving some basic problems of geometry, but it was never known as to whether a cubed plus b cubed could ever equal c cubed if a, b and c were whole numbers. This was also true for all other powers of a, b and c greater than 2, but in 1637 the brilliant French mathematician Pierre de Fermat claimed, in a scrawled note inside his copy of Diohantus’ Arithmetica, to have a proof for this fact ‘that is too large for this margin to contain’. This statement ensured the immortality of the puzzle, but its eventual solution (not found until 1995, leading most independent observers to conclude that Fermat must have made a mistake somewhere in his ‘marvellous proof’) took one man, Andrew Wiles, around a decade to complete. His proof involved showing that the terms involved in the theorem could be expressed in the form of an incredibly weird equation that doesn’t exist in the real world, and that all equations of this type had a counterpart equation of an equally irrelevant type. However, since the ‘Fermat equation’ was too weird to exist in the other format, it could not logically be true.

To a mathematician, this was the holy grail; not only did it finally lay to rest an ages-old riddle, but it linked two hitherto unrelated branches of algebraic mathematics by way of proving what is (now it’s been solved) known as the Taniyama-Shimura theorem. To anyone interested in the real world, this exercise made no contribution to it whatsoever- apart from satisfying a few nerds, nobody’s life was made easier by the solution, it didn’t solve any real-world problem, and it did not make the world a tangibly better place. In this respect then, it was a total waste of time.

However, despite everything I’ve just said, I’m not going to decide that all modern day mathematics is a waste of time; very few human activities ever are. Mathematics is many things; among them ridiculous, confusing, full of contradictions and potential slip-ups and, in a field whose age of winning a major prize is younger than in any other STEM field, apparently full of those likely to belittle you out of future success should you enter the world of serious academia. But, for some people, maths is just what makes the world makes sense, and at its heart that was all it was ever created to do. And if some people want their life to be all about the little symbols that make the world make sense, then well done to the world for making a place for them.

Oh, and there’s a theory doing the rounds of cosmology nowadays that reality is nothing more than a mathematical construct. Who knows in what obscure branch of reverse logarithmic integrals we’ll find answers about that one…

Icky stuff

OK guys, time for another multi-part series (always a good fallback when I’m short of ideas). Actually, this one started out as just an idea for a single post about homosexuality, but when thinking about how much background stuff I’d have to stick in for the argument to make sense, I thought I might as well dedicate an entire post to background and see what I could do with it from there. So, here comes said background: an entire post on the subject of sex.

The biological history of sex must really start by considering the history of biological reproduction. Reproduction is a vital part of the experience of life for all species, a necessary feature for something to be classified ‘life’, and among some thinkers is their only reason for existence in the first place. In order to be successful by any measure, a species must exist; in order to exist, those of the species who die must be replaced, and in order for this to occur, the species must reproduce. The earliest form of reproduction, occurring amongst the earliest single-celled life forms, was binary fission, a basic form of asexual reproduction whereby the internal structure of the organism is replicated, and it then splits in two to create two organisms with identical genetic makeup. This is an efficient way of expanding a population size very quickly, but it has its flaws. For one thing, it does not create any variation in the genetics of a population, meaning what kills one stands a very good chance of destroying the entire population; all genetic diversity is dependent on random mutations. For another, it is only really suitable for single-celled organisms such as bacteria, as trying to split up a multi-celled organism once all the data has been replicated is a complicated geometric task. Other organisms have tried other methods of reproducing asexually, such as budding in yeast, but about 1 billion years ago an incredibly strange piece of genetic mutation must have taken place, possibly among several different organisms at once. Nobody knows exactly what happened, but one type of organism began requiring the genetic data from two, rather than one, different creatures, and thus was sexual reproduction, both metaphorically and literally, born.

Just about every complex organism alive on Earth today now uses this system in one form or another (although some can reproduce asexually as well, or self-fertilise), and it’s easy to see why. It may be a more complicated system, far harder to execute, but by naturally varying the genetic makeup of a species it makes the species as a whole far more resistant to external factors such as disease- natural selection being demonstrated at its finest. Perhaps is most basic form is that adopted by aquatic animals such as most fish and lobster- both will simply spray their eggs and sperm into the water (usually as a group at roughly the same time and place to increase the chance of conception) and leave them to mix and fertilise one another. The zygotes are then left to grow into adults of their own accord- a lot are of course lost to predators, representing a huge loss in terms of inputted energy, but the sheer number of fertilised eggs still produces a healthy population. It is interesting to note that this most basic of reproductive methods, performed in a similar matter by plants, is performed by such complex animals as fish (although their place on the evolutionary ladder is both confusing and uncertain), whilst supposedly more ‘basic’ animals such as molluscs have some of the weirdest and most elaborate courtship and mating rituals on earth (seriously, YouTube ‘snail mating’. That shit’s weird)

Over time, the process of mating and breeding in the animal kingdom has grown more and more complicated. Exactly why the male testes & penis and the female vagina developed in the way they did is unclear from an evolutionary perspective, but since most animals appear to use a broadly similar system (males have an appendage, females have a depository) we can presume this was just how it started off and things haven’t changed much since. Most vertebrates and insects have distinct sexes and mate via internal fertilisation of a female’s eggs, in many cases by several different males to enhance genetic diversity. However, many species also take the approach that ensuring they care for their offspring for some portion of their development is a worthwhile trade-off in terms of energy when compared to the advantages of giving them the best possible chance in life. This care generally (but not always, perhaps most notably in seahorses) is the role of the mother, males having usually buggered off after mating to leave mother & baby well alone, and the general ‘attitude’ of such an approach gives a species, especially females, a vested interest in ensuring their baby is as well-prepared as possible. This manifests itself in the process of a female choosing her partner prior to mating. Natural selection dictates that females who pick characteristics in males that result in successful offspring, good at surviving, are more likely to pass on their genes and the same attraction towards those characteristics, so over time these traits become ‘attractive’ to all females of a species. These traits tend to be strength-related, since strong creatures are generally better at competing for food and such, hence the fact that most pre-mating procedures involve a fight or physical contest of some sort between males to allow them to take their pick of available females. This is also why strong, muscular men are considered attractive to women among the human race, even though these people may not always be the most suitable to father their children for various reasons (although one could counter this by saying that they are more likely to produce children capable of surviving the coming zombie apocalypse). Sexual selection on the other hand is to blame for the fact that sex is so enjoyable- members of a species who enjoy sex are more likely to perform it more often, making them more likely to conceive and thus pass on their genes, hence the massive hit of endorphins our bodies experience both during and post sexual activity.

Broadly speaking then, we come to the ‘sex situation’ we have now- we mate by sticking penises in vaginas to allow sperm and egg to meet, and women generally tend to pick men who they find ‘attractive’ because it is traditionally an evolutionary advantage, as is the fact that we find sex as a whole fun. Clearly, however, the whole situation is a good deal more complicated than just this… but what is a multi parter for otherwise?