Sunday, 19 January 2014

Truncertainty

As a member of that most exclusive group of objects - "The things which physically exist" - you are imbued with a number of characteristics. First among them is obviously the matter of existing in itself, and that is the gateway to enjoying the other benefits of your membership such as going to the pictures or witnessing crumbs.
                Proud owners of a physical forms (or even leaseholders thereof) generally have predilection for keeping tabs on the characteristic of its position, or, where that physical form or "body" is. They will say "I am in Jamaica",  "I'm in the bath", or "Most of me is in the bath, but some of me has become entwined in the towel rack due to factors beyond my control". Other body owners may even share your interest in the location and engagement of your body, evidenced by exclamations such as "Where are you?", or in more advanced cases: "Why are you in my bathroom and what are you doing with my towel rack?".
                "Where are you?" should be a relatively easy question to answer for most active members and even some distinguished alumni of the things which physically exist. After all, if you can't even point to a space which you are certain that you occupy (generally within arm's reach of your arm) then your existence must be a peculiar thing indeed, and the board of governors may have to review your membership eligibility.
                Another characteristic of this "body" you so proudly wear every day is the speed at which it is travelling. A knowledge of this can be used to determine both where you were some time ago, and where you will be at some point in the future. As such, the value of this quantity is displayed prominently in all  motorcars so that the driver may ignore it in pursuit of important tailgating commitments.
                If you are an electron, this is the stage at which things become a little ropey. Not only can you not reach the pedals or the steering wheel, but if you manage know where you are, then you have no idea how fast you are going and could end up somewhere else entirely in any amount of time. If you are watching your speedometer then you have no idea where you are at the time and will most likely become close friends with a lamp-post, the tail you were so diligently gating, or a discount furniture store. You are a victim of a brutal conspiracy, courtesy of Heisenberg and his unwavering principle of uncertainty.
                As a conspirator, Heisenberg is a fairly eminent chap. He hasn't simply driven a sheet of steel into your car such that your head can be either a) above it looking out of the windscreen, or b) below it looking at the speedometer. He's gone one step further and decided that as soon as you so much as glance at one of them then the other is sabotaged; it is ruined in a fit of quantum mechanical spite - the worst kind of spite. Your knowledge or measurement of one observable  actively precludes the precise measurement of the other. He has either replaced your windscreen with an elaborate kaleidoscope, or glued a random number generator to your speedo. For these reasons, Mr Heisenberg can be inferred to be both a skilled mechanic, and a terrible choice of MOT provider.
                That isn't the only way in which he's been a tinker about people knowing too much about something either. The safeguarding of simultaneous knowledge applies equally to lots of other things, such as the momentum of one object in each of the three spatial dimensions. Should you be so bold, so daring, so ARROGANT as to try and know all three spatial components of your momentum at the same time (god forbid) then you will be mercilessly slapped down. Two components? That's fine. We LIKE knowing two. But all three? You make me sick.
                It's not a question of terrible measurement, it's a fundamental characteristic of the universe we live in, which happens to be a Hilbert Space (this is quite distinct from the crawlspace running behind Mr Hilbert's bath). Defining each observable quantity of a system with an operator and combining them within the mathematical constraints of a Hilbert Space, i.e. reality, causes these relations to fall out of the equations like racial slurs falling out of a UKIP party conference. Some of the operators just don't commute with one another, which means that for two operators A and B, AB does not equal BA, or in other words AB - BA is not 0 (Incidentally, this is not how numbers work, so a reassuring consequence of this observation is that we are not numbers. If this doesn't seem to describe you, then please pause to re-evaluate whether you are a human or the final balance of a weekly shop at Tesco getting rather above its station in terms of literacy.). This very roughly translates to the statement that measuring A first and then B gives you a different answer to measuring B first and then A. This is because knowing one of these things defines the system in such a way that the other thing could be one of a number of values. The value of the second thing is uncertain.
                It's one of those charming eventualities we all cherish, whereby trying to understand reality by plugging something we know into our equations leads to us learning that we don't in fact know what we thought we did. And when we think we do know it?  We not only don't, but actually can't. Or something.

Thursday, 16 January 2014

Trousectomy operations

It is a truth widely acknowledged that humans have a skeleton inside them. They're quite useful in a structural capacity and have received a largely positive reception, with the notable exceptions of devout contortionists and militant mollusc groups (though it is speculated that the motivation of the latter stems from jealousy).
                The skeleton is made of a number of different bones, since early non-articulated prototypes proved impractical when trying to operate heavy machinery or search under the oven for a lost pea. Sadly, the pea retention rate of human skeletons is still far below ideal, but we do keep trying.
Now imagine you have cause to not be sure which of your bones is which. You look at your forearm and think to yourself 'Is that an arm bone in there, or did my skull get the wrong post code?'. Aside from ceasing to be devastatingly stupid, you would need a foolproof method in place if you wished to find out which of a finite number of solutions is the correct one for the (eternal) question "which bone is that?".
                It is a fairly simple thing to determine which of the possible outcomes is the correct one in this case, since the eyes in your face will be able to tell you if your arm is long and thin or if it has a jaw, and from this you could infer whether or not your last surgeon really still knew what he was doing after all that sherry.
                Your spirits buoyed, you step into the cold morning air and BAM. Some bastard has shrunk you to the size of an atom while you weren't looking. Except for your eyes.
Your comparatively huge eyeballs roll around for a bit and settle down conveniently facing you but gosh! You're too small to see, so now how will you work out whether that's a finger bone or a generous portion of your spine attached to your hand. The hand in question is in your ribcage, but we deal with one issue at a time around here.
                Thankfully, all you need to do is consult a group of physicists over a 100 year period and they will find some equations to tell you that at each point around your body there is a good chance of finding a bone, and that bone is a superposition of all the bones in your body. It is all your bones at once and none of them at the same time. By now you should be questioning a) why you asked physicists a question which was clearly medical in nature and b) why you never checked on their progress in the full century you waited. You won't actually get around to asking those questions because you're too small to be heard and you're probably dead. After all, 100 years is a very long time to be alive in the best of situations, and nanoNando's is yet to open in your area so good luck eating.
                What these seemingly immortal physicists seek to do is find out which of the many possible bones is in the region they are looking at by gathering the characteristics of the region in question i.e. the state it is in (its momentum, position or number of times broken by a swan (primarily arms)) into what's known as a wavefunction describing the bone-state. They can then apply an operator which measured bone type to that wavefunction. Operators carry out operations. If that is surprising then kindly leave, but don't forget to take a gift bag.
                The bone operator is a neat little machine they've made which can take an input of the information about the area of your body as a whole and spit out an answer of which kind of bone lives in that little fleshy house. So, you apply the operation (in this case a bonectomy) to yourself and out plops an answer which will be the sum of all the possible answers, weighted by how likely each one is. So, if you're looking squarely at the end of your legs, the answer will be mostly feet and some toe. If you look at your chest there will be a lot of rib, sternum and spine going on. Similarly, if you look at an atom, you can ask your operators "if I was an electron spinning upwards with this much momentum and THIS much angular momentum" here you would be throwing your arms wide to demonstrate not only how much angular momentum you have, but also how much you don't understand that angular momentum is not measured in units of distance "then where would I be? And how much energy would I have?" and get a meaningful answer out. Unless you did the maths wrong due to advanced cretin-hood.
                In the same way that you have a finite number of bones but don't know which one is which by looking, the quantum in quantum physics means that there is a discrete set of values the thing you're trying to describe can take, be it momentum or bone name (note that if your electron has bones then you should consider reviewing whether that's an electron or a particularly small haddock).
                The quantum mechanical operator exists as a mathematical manifestation of an observable quantity, something which we can determine and is a real characteristic of the system. By applying the operator to the equation describing the state of the system, it effectively simulates the act of measurement by spitting out the possible finite number of situations in which that state can exist given the conditions you spat into it. Spitting is especially important when it comes to operators. In itself that's only about as impressive as a man eating a kilo of chicken kievs without vomiting. However, by simply applying some operators and thinking about how reality dictates the maths must behave, a group of people managed to correctly write down some maths which described completely non-intuitive situations that they couldn't possibly imagine or understand, let alone measure or observe. Whilst that is simply the job for which the men who came up with the equations were paid, the point is that applied manipulation of operators and quantum mechanics allowed a man with a piece of paper to come to a conclusion that both required and caused the construction of the Large Hadron Collider in Geneva to prove him right or wrong. The maths is so accurate and has been thought about so much that just a few pages of it has led to a 27km ring of some of the most energetic particles in universe recreating the conditions of the big bang being constructed underground in central Europe. That's a multiple-tonne-consumption-of-chicken-kievs tier achievement at least.
                But what about your disembodied eyes and the mystique surrounding your skeleton? Well it appears that the only group of people around when you were mugged by what was apparently a cartoon super-villain not only had a century to kill and confused "immediate medical attention" with "extended period of high level theoretical physics", but they managed to spend that entire hundred years replying to the single utterance you made, namely  the question "which bone is this". Their answer was: "one of the possibilities". Another job well done!

Tuesday, 14 May 2013

Fishing for Trousers


Give a man a fish, possibly delicious and upon some kind of table, and he will eat for about 1 minute per unit fish volume, as the saying goes. Give a man half a fish and he will eat for a similar amount of time, including that spent pondering on what you've done with the other half of the whole sea bream for which he paid. If one continues this process then a point is reached at which the man cannot even tell he has any fish, because technically he doesn't - all he has is an atom which happened to be part of a molecule which happened to be part of a protein which happened to be present in the fish before it was diced so very thoroughly. There's also a fairly good chance he won't be leaving a generous tip.
Whilst it is likely that complaints over a lack of fish will be prevalent following this asymptotic meal, it is not so likely that the man, whose hunger is matched only by his anger, will marvel at what he was given - a brick.
The effects of hunger on object identification are well understood. In dire enough circumstances it has been noted that a great many people will mis-identify the clearly inedible kebab as an item of food. In this case, the apparent plate of nothing was in fact a brick. It's the kind of brick from which not only buildings, but the bricks, cement, builder, and most (if not all) Barry Manilow records are made.
Bricks, traditionally speaking, shouldn't be particularly mobile without significant assistance. It's how you can always infer that there was at least an arm of some sort masterminding the flight of that lump of baked clay which careened so carelessly through your patio doors. In addition to their predilection for being static, it's generally accepted that bricks are made of something, as opposed to nothing. A brick made of nothing is a gap, and gaps are what walls are there to prevent.
The problem is that in the realm of quantum physics, tradition is ignored like human rights in one of the friskier third world nations. And where do we find our plated up brick? Making itself at home on quantum physics' sofa with a copy of the radio times, spilling gravy on all of the soft furnishings.
As such, our atom breaks each of these rules for good brickitude with nary of a thought of how quickly it will forgo its next scout badge for construction.
It's not entirely fair, since atoms are made of two main parts whereas your common-or-garden house brick is considered as a single lump of happiness. And it's from here that the problems arise.
In the middle is the main bulk of our fish-meal. It's a pile of neutrons and protons chumming about together as a nucleus and acting like a group of students with no concept of personal space playing strong nuclear-force twister. The remainder of the atom is a number of electrons who whizz around the outside in various rigidly defined orbits without a care in the world. they whizz so much in fact, that rather than being a physical thing in space, it's sometimes more convenient to think of them as a probability distribution of negative charge spread around the entirety of the three-dimensional orbit. The candidacy of our atom for full brickhood is beginning to collapse, since motion at extreme speeds and uncertainty as to where the brick is at any given moment are generally a little taboo when it comes to satisfying building codes. Homeowners like to know that their bathroom door is going to remain in the doorway and not trundle off into the space behind the fridge.
The issue is then compounded by the consideration that the orbitals of these electrons form the boundary of the atom, loosely speaking. So, travelling from one end of the orbit to the other, the diameter of the atom is generally of the order of 0.1 nanometres, or one thousandth of a millionth of a metre. This kind of journey is unlikely to be expensive on the bus. The diameter of the nucleus is typically of the order of 1 femtometre, or a thousandth of a millionth of a millionth of a metre. This is also going to be an economical trip.
The ratio of the volume of the atom compared to that of the nucleus, ends up as approximately 1:10^15, i.e. 1 with 15 0s behind it. i.e. 1:1000000000000000.
The nucleus contains around 99.9% of the mass of the atom. (Oprah Winfrey contains around 99.9% of the mass of the occupants of her studio during recordings).
The upshot of these short holidays and huge (tiny) numbers is that the vast, staggering majority of the atom is not in fact made of something, so much as nothing at all. Everything around you is as close as makes no difference to being entirely gaps. Even if the man had received his whole fish, he would have had only 1 part in a thousand million million of a meal. No matter how many sea bream he orders, his plate will always be empty; just like his wallet if he keeps paying for restaurant meals before they are served.

Sunday, 17 February 2013

Complex Trousers


                The world is a complex place. A very complex place. In a vote to determine the most complex thing in our 4 dimensions, probably held by the editors of the Daily Telegraph, the world be would sure fire winner - even without canvassing or a campaign endorsed by a professional wrestler. You may very well be of the opinion that setting up your wireless router is fairly complex, but the world is at least 3 times as complicated as that. At least. (Upon the inclusion port blocking the iPlayer, this comparison is of course reversed.)
                What makes the world complicated is that there an awful lot of things in it, and all of them are vying to be continue being in it. Some of them even want to be able to have access to online tutorials on how to get salsa stains out of the curtains from anywhere in the house, which only makes things worse. As one of these things, we take our competition with the other things to extreme levels; we have long since won our war against the insidious Dodo and are well on our way to crushing the last dying breaths from the dangerous and vitriolic practice of being nice to one another for reasons other than personal gain. We raise our arms to the blackening sky with each victory, safe in the knowledge that simplification is under way, and no-one needs to be helped out by anybody else with anything, or heavens forbid smiled at by a stranger.
                As the dust settled on the last remaining Dodo skeleton (because the nice lady who volunteered to clean it was executed as a war criminal) an observation was made by a manipulative bastard, who was able to alert his networked acquaintances from the comfort of the space behind the boiler. The observation read thusly - the removal of some elements of a very complex system makes the other aspects of a very complex system behave differently, in a very complex way. After waving his networked device around a lot in order to find what paltry signal he had available, this particular bastard played no further part in proceedings. We shall assume he contracted typhoid.
                The problem with how certain people perceive this observation is the same problem that the same people have when trying to unwrap sweets with their mouth, namely that they have everything the wrong way around and paper tastes awful. They remove one element from the overall system and watch as the butterfly effect takes place, causing the extinction of a subspecies of bee, begetting a fall in the numbers of rare flora and a sharp increase in the number of people willing to sit in a coffee shop to exploit the free wi-fi and discuss the lack of bouquets available to bribe their partners into forgetting that they shot the dog last weekend. At this point they make a bold declaration, a challenge to fill the gauntlet before it is cast down . "It all relies on a few too many coincidences doesn't it? This can't all have happened by chance or mistake?". They are taking something from the end of the system and saying that they could never work out how it affects everything else, let alone build the entirety of the rest of the system from it, therefore it can't be done. They're not so much putting the cart before the horse as taking a newspaper which happened to fall into one of the boxes being transported, looking at the horse and claiming the situation could never have happened by chance because they don't know what a cart is. They are expecting to be able to take a shiny new wireless router and infer the existence of the dinosaurs which must have died to become the oil which is manufactured to produce the plastics moulded to form the casing of the router itself.
                The interwoven cycles and creatures are not cosmic coincidences, neither is the suitability of Earth for the life on it too convenient to have happened by chance. The wrapping paper is stuck between the teeth of ignorance, but it just so happens that there are toothpicks on the table. The life on the planet exists because it is one of the possibilities opened up by the presence and proportions of the chemicals on it and the conditions that they produce when coupled with the positioning and behaviour of the planet in the solar system. The various species are interwoven because they co-evolved that way and anything which didn't fit into the harmonious plan was incapable of continuing to exist because it didn't fit in, and nothing else wanted it to (see also: Jim Davidson).  The complex relationships we observe are the result of a set of billions of criteria and how they interact, what they allow and what they don't. You can look at a piece from a jigsaw but you can't infer the whole picture from that one piece. Tragically, and as with so many otherwise perfectly interesting subjects for an infographic passed around at the kind of dinner party you wish you were invited to so that you could detail why you don't want to attend, it just comes down to statistics and very, very, very big numbers. Like, 6 or something,  I don't even know.
                So yes, everything may seem like an incredibly unlikely series of coincidences at this stage, but only if you're looking at it cross eyed and through a mirror behind wrong-tinted glass.

Saturday, 1 December 2012

Lazy Trousers


                Humans are pretty lazy. Almost everything we do is motivated by making things easier for ourselves such that we have ample time to spend looking at our pre-made sliced bread and wishing that someone would cut the crusts of for us. This pastime has of course fallen out of fashion recently since crust free bread has now become available, at the cost of any self respect our society could possibly have had left.
                The oft' referenced industrial capacity of the ant world seems positively burgeoning with energy and enthusiasm by comparison; they use their bodies as building materials, work incessantly for the good of a single all powerful matriarch and never once stop to complain if their personal tastes force them to take ten seconds to cut off the edges of their sandwiches. They might even just eat around the crusts and leave them looking sad on the plate, they simply don't perceive it as too much of a trial. Yet the ants in their autocratic wonderland are, fundamentally, just as lazy as we are. The problem doesn't stem from a reliance on technological solutions or a society of entitled facilitation however. It doesn't even have its roots in some bunch of hippy insectoids claiming that life is too short to cut your own carrots into sticks, like some kind of chump. The real culprit is far more dedicated to the art of the sloth. You have to literally make the course of action you want it to take into the path that requires the least possible expenditure of energy. It's mother Hubbarding physics.
                It's reasonable to think that a set of rules which is terribly busy enforcing exactly what should happen in every situation at every time simultaneously would want to take the shortest possible path to its goal. No-one sees water flowing uphill or cake cooking itself by sucking heat out of the freezer because thermodynamically that requires one not only to remove their own crusts but possibly eat them afterwards anyway, like some kind of barbarian playing a sick mind game, and physics simply doesn't have time for that - much less any inclination to be so vulgar. Everything that has ever happened has been the result of that action being the path that thermodynamics  thinks is of the least resistance. It's the reason firewood will lay motionless at it burns to death rather than stop drop and roll. It would sooner be incinerated than move. All the while physics sits there in its entropic reclining chair of questionably initiated heat exchanges, flopping its arms over the edge to reach the remote as the last few scraps of cosmic background microwave ravioli slide off its distended belly and onto the carpet. There they shall remain.
                So if the laws that govern how our world revolves and our chins hang are based on the principle of laziness then why should we hold ourselves to a higher standard. It'd all be far too much effort. Especially when you consider that at some point in our past, way back when no-one had disposable plates and bread was scarcely pre-sliced let alone de-crusted, the path that caused the least resistance somewhere for even a minute amount of time was to create life. The origin of every species was the course of action which required the minimum possible effort to be made, the ground state of the system. I can't be sure of what else was going on at the time since I was otherwise engaged as a series of mineral deposits across the prehistoric globe, but if everything that lives around us is the result of the easiest path then the other unrealised options would certainly have made for a fine series of postcards.

Thursday, 8 November 2012

Trousers in the Bargain Bin


                He's not so much half-heard and half-seen as fully perceived and consciously dismissed, lacking in the ethical hurdles and staggered viewpoints associated with the beggar and altogether less of a political minefield than the outwardly and obviously disabled. He causes them to vicariously live a life of ridicule and misunderstanding for which they resent him, doubly when the resentment turns to guilt. Not enough to make them act upon it, never enough to prompt a display of sympathy or an offer of help but always too much to be forgiven completely. Guilt feeds back into exclusion and revulsion gives way to verbal assaults directing themselves at someone who is already, in essence, a series of red, white and blue concentric circles.
                Our parenthetical pariah patrols the perimeter of the place, praying for pleasant perceptions, pitying pathetic prejudices and passionately pleading, pre-emptively predicting the persecution people pour prosaically upon him. But it's not enough and it's far too much, his voice won't be heard if it hides forever under his breath but the words it says, alternately venomous, wise, understanding and naive are trying to force too many things into a box which just won't fit them and refuses to open its lid far enough to try.
                 Weary beyond words without altering the situation, the routine orbit continues unabated hour by day by week until he's a regular fixture like the filth in the streets and the vermin in the periphery. He's gone so far into his own head that he may very well be out of his mind. It stops seeing each person as a new opportunity for relief so much as yet another faucet of dismissal. They blur into one constant stream of loathing and ignorance and like a current shearing against a rock they gradually wear him down into a pebble underneath the surface, barely causing a blemish in their surface and certainly not doing anything to alter their path.        
                Until, at last, during the march for want of anywhere to remain, a pair of broken eyes meets a pair of shattered irises. An oppressed body approaches an avatar of suffering at the hands of those with the neglected power not to cause others to suffer. The journey ends. They see something in each other that no-one else sees in either of them.  A kinship neither one thought possible but both had clung to as the dearest dream and ambition they had left, ever since true acceptance was made an impossibility. The walls flex, the boundaries grind together and the gates bend until the two who were forced to the outside, staring inwards, become the sole inhabitants of their private paradise with the fetid world that they rejected breaking against their fortress in futility.
                But wouldn't it be a shame if they were paedophiles. 

Friday, 28 September 2012

Trouser Farming


                One of the more appealing sights to be seen in the universe would be a farm. Not just any old farm to be found in the outskirts of Northampton or Windsor but a really quite incredible farm to be found in the in-skirts Sol. With so many solar systems cluttering up the galaxy and so many galaxies cluttering up the universe it is difficult not to call anyone who thinks that Earth is the only life sustaining planet in all of existence a bit arrogant. They probably think everyone else is selfish for being ahead of them in the queue at the checkout or for wanting to sit down on the same crowded bus that they want to sit down on. When you get a get a reasonably priced bag of apples from the supermarket and one of them is rotten you must suspect the others to be suffering the same fate, and likewise with a discounted bag of planets like the Milky Way, you've got to be a bit worried that there may be something similar to our own carbon based monkey rot going on in some of them. Steps should likely then be taken to purge these samples from the bag and perhaps even encourage the storage of unaffected specimens in a refrigerator to preserve freshness. Thankfully empty space is pretty chilly, noticeably more so than a commercially available personal fridge, so one may be forgiven for thinking this advice can be disregarded by any exoplanet not currently invading the personal space of a star. However, it takes a packet of meat roughly a day to fully freeze in the freezer at minus 20 degrees Celsius or thereabouts whereas Earth has been a planet in a cold sink of about minus 270 degrees Celsius for about 4.5 billion years and most of it is still pretty cosy, as evidenced by the existence of humanity, the oceans and reasonably priced beach holidays in Majorca.
                In the face of this monumental sanitation crisis, we gather up the various residents (or plagues) from the affected planets and stick them in a farm within our own solar system because we're a) lazy, b) incapable of reliable space travel over large distances and c) probably the nicest hosts who would cater for various differing dietary requirements with a minimum of snide comments. We would be given a window into the nature of life if we could witness its other forms which have evolved under conditions entirely separate to and different from our own. Would they have overcome issues like situational awareness with absorption of electromagnetic emissions and reflections in the same narrow band and detection of longitudinal air vibrations with their ears in the same range as us or make the same unforgivable mistake of adopting pebble dashing as an appropriate method of decorating a homestead exterior? Would they have also suffered mass extinctions and resurgences of life like we did? Space dinosaurs are unquestionably an appealing prospect so I for one hope so. It would be best not to tell any survivors that I hoped for their mass extinction however, it's exactly that kind of thing that causes first impressions to go badly.
                Why a farm and not a zoo or a lab then? Well, when your daughter's dog catches a serious case of "got into the cupboard and subsequently full of bleach" you tell them that he's gone to live on a farm. It comes across like the disappearance of the dog (and stark reduction in the cleanliness of the toilet) is less traumatic because a farm is a wonderful place for the dog to be, with lots of space to run around in, lots of affection from the proprietors of said farm and so much food that trying to eat cleaning supplies is barely an afterthought. Nobody ever tells the little girl that the dog has gone to be gawped at in a zoo and they certainly don't elucidate the child to the lack of canine companionship by telling her it's gone to a lab to be experimented on, tortured a little bit and ultimately dissected by the kind of man who thinks sliding a scalpel through a puppy is an acceptable afternoon occupation. Likewise then if we were to tell the owners of the other worlds we're taking their wildlife (and possibly them too) to a farm just outside Mars then they'll take it far better. The gawping and dissection can happen in the barn -  anything goes when you're in a barn.