Probability

      While coming home recently I was thinking about quantum physics (as usual. I'm on par with The Fonz in terms of coolness. Who's got two thumbs and an interest in particle physics? This guy. People who aren't aware of Happy Days are confused right now. Which makes up a large section of my reader base I believe.) when a thought occurred: today something less likely than a tree just disappearing happened. In fact, billions of events that are several orders of magnitude less likely to happen than a tree disappearing must have happened.
      Let's take a step back and look at the nature of probability. Say I roll a fair six sided die ten times, what is the probability I get ten sixes? The answer is one over six to the power of ten, which is about 0.000000016538171687920. I totally just did that in my head. Suffice to say, it's unlikely to happen. This is also the probability that any given combination (in a given order) will happen. One over it will give the number of possibilities, which is 604664176. So every combination of numbers is very, very unlikely, but obviously one is bound to occur. So we end up with a very unlikely, but also probably a dull, combination of rolls. The lottery is another good example of this. If I were to buy a ticket with the numbers 1, 2, 3, 4, 5 and 6 many people would say it's incredibly unlikely that I'd win. And they would, of course, be right. Because all the numbers are incredibly unlikely to be drawn, but that doesn't stop people from buying tickets. The fact is my ticket would be just as likely to win as any other, although it might have more of a split pot as I imagine a lot of statisticians would have bought the same ticket to make a point.
      So back to the tree. Quantum physics is a probabilistic set of rules, as opposed to the deterministic rules we automatically assume the universe abides by. I can't go into how or why that makes sense, partly because I don't have much time, but mostly because it quite simply doesn't make sense by conventional thought, it just is. So an electron can randomly go in any direction, even if it's part of a solid, it's just not very likely. The chances of it happening that all the components of an entire tree randomly stop being connected are incredibly small. Mind bogglingly small. But it's possible. And there are many things like it happening all the time, just not in an interesting way. It's exactly the same as with the die from earlier. Incredibly unlikely, yet uninteresting events happen when an event is bound to have a single outcome from a large set of possibilities. There's a bit more to this that I was going to get into, particularly about the law of very large numbers, but I think that can wait for another time. So I will leave you with this thought provoking question: If our universe is infinite, our lives short and time precious, why in the hell would someone end up on my blog after searching autism orgasm?

The Logic of Philosophy

      I'm posting today instead of Sunday because I'm going on holiday tomorrow. I'm posting at one in the morning because I'm not to good at the doing things. I'm really very tired and after I finish this post I'm going to pack. Like I said, not great at the doing things. I do know what I want to say in this post, but I might just fall asleep on the keys and post a thousand g's instead. Which, to be fair, would be better than most of my posts.
      Anyway, I recently got into an argument about what is more important, maths or philosophy (I say argument, it was more me making a snarky comment during someone else's conversation). I came down in favour of maths, but a few years ago I had the same conversation (though that time it was actually more of an argument) and defended philosophy. I'm a bit of a view-point slut. But the reason I changed my mind was not really because a change in how I prioritised the fields, but more how I categorised them. For me maths has little to do with numbers really, that's numeracy. The way maths is taught is like teaching A-level English students how to spell as the core of the subject: it's useful, but it's not really the core of the subject. No, the core of maths is really logic, things which can be shown to be true and the implications that those things have on other things.
      When I get a new formula or function I like to generalise by following through the procedures involved without using numbers. I feel this gives me a better understanding of what is actually happening to those numbers and why. So what does this have to do with philosophy? Well, ethics can really be seen as a series of formulas which balance different variables and give an answer of right or wrong. They are very generalised formulas in many respects, but even more so they are undefined in many ways. The greatest flaw of ethics is the inability to agree on what those variables should be. Should happiness be the ultimate goal, or a lack of suffering? Is self actualisation important or not? Should happiness be measured per individual or as society at large? These are all variables in the word formulas that make up ethics. If it were possible to completely define and quantify what is important it would likely be a simple task for a computer to tell you if an action is moral or not. Currently it is only possible to build on any chosen set of values and building from there. In this respect a lot of ethics is no better than theology. That's not to say the steps in these ways of thinking are illogical, for example utilitarianism is a good example of a whole system of thinking that has developed given a certain set of rules in a perfectly logical manner (it is similar to economic theory in this, and other respects), but rather that the systems developed are rather useless in the real world as without a consensus on the most fundamental aspects these systems of thought develop in different directions entirely, in a similar way to religious denominations, until the point that the systems of thought become so different they become completely incompatible with one another and then you're essentially left with a group of warring sects all fighting for their own point of view.
      Of course ethics is only one branch of philosophy, but I feel that the development of schools of thought that I've described here should be transferable in principle with most other branches.
      What I'm saying is that philosophy will forever be an incomplete attempt to use logic to build systems of thought with imaginary foundations. That's not to say it's not worthwhile, I believe philosophy is a very important field, just that it is nothing without logic. And logic must coexist with maths. In short philosophy is the study of reason, whereas maths is simply reason. So that is why I feel maths will forever be more the more important of the two.

      That went a bit deeper than I anticipated and lacked my normal level of humour. Though where I wrote "warring sects" I struggled not to put a "warring sex" joke in. Wow, I really need to pack.

Imperfect beauty

      When I did that post on maths and beauty I forgot to put a chunk of the point I was making into it. However, as long as I don't mention it I think I can get away with it.
      Anyway, as you'll remember from my previous post, beauty is directly connected to mathematics. However, human brains are not completely logical, not in anyway perfect at pattern recognition. There are too many other things that taint are perception. So the question is, can we ever truly experience perfect beauty? If it was purely based on mathematics then there should be a perfect formula that creates truly perfect music and art, akin to Plato's idea of forms. If this were the case there would be a finite amount of beauty an object could have and it could arguably be measurable how beautiful something is. But that's not the case, because we are not pure mathematical beings. The more important question perhaps is whether a truly logical being could experience beauty, because if not then it would be simply impossible for anything to experience perfect beauty.

Maths

      I might be a little distracted while writing this, I'm also watching Return of the Jedi. I'm writing a blog on maths while watching Star Wars; aren't I just the pinnacle of cool? Also I rewrote that sentence just so I could include a semi-colon. On the subject of my coolness many people think I'm uncool because of my love of maths. This is not true, I'm actually uncool because of my personality. But that's not the point, my point is most people enjoy maths, even if they can't stand numeracy.

      You may have heard that music is connected to maths, but you might not understand exactly how. The tuning used today in the West is known as equal temperament (as opposed to the outdated Pythagorean tuning, which is also interesting but a bit off topic) has a ratio between each note of 1:, which means if you do it 12 times (the number of notes in a Western octave) you get the 12th  root of 2 to the power of 12, which equals 2. So in a twelve note scale with ratio 1: the 12th note is twice the first note. There are also a bunch of other ratios involved in music. The point is that, unless you are actually tone deaf (which is rare), you can easily distinguish music that follows these ratios and music that does not which is how you know if something is in tune. What's more, you know these scales so well that you anticipate patterns and by either matching those patterns or deviating from them a musician can manipulate you to feel anything from the whole spectrum of human emotions. So really when you feel music you are just responding to a mathematical sequence.

      There are many other examples of the extraordinary everyday uses of maths, such as the complex trigonometry used to catch a ball, but my point is that just because you might not enjoy numeracy does not mean you do not enjoy maths, it might just mean you enjoy it in a different way.

Why we learn

      I often have conversations with people where I get told my facts are useless and that no one would ever need to know them. People always ask when they will ever use what they learn at school. This bugs me. You see, there are two types of people (actually there are 6,903,900,000 types of people right now, but let's not be pedantic): the applied and the pure. Someone who is more interested in the applied side of information thinks "How can I use what I learn in my day to day life?" Someone with a pure take on the world, which is what I tend to be, thinks "What can I learn from my day to day life?" This difference in objectives is most prominent in subjects such as maths. Trying to convince an applied scientist that it is important to solve Fermat's Last Theorem or Goldbach's Conjecture is typically an exercise in futility as they try and work out why we would ever need them.
      I'm not entirely sure where I'm going with this to be honest, it's just been on my mind for a while as I've been trying to work out how to use the second derivative of a cubic function to find the roots. Which is the kind of thing applied scientists tend to not get, as it is somewhat pointless. Especially as I could just find out by googling it. That is, if it's possible. Otherwise I'm going to be wasting quite a bit of time on nothing for the next couple of weeks.
      Anyway, hopefully next weeks post will be better, bye.

If civilisation was a person

Today I'm going to give you an insight into what I do with my time. Here is what I decided to do with several hours of my life, before deciding I might as well post it as a blog. Basically I scaled the life of civilisation, starting with the control of fire, to the length of the average life of someone in the UK. I did it in notepad, so there are quite a few spelling and formatting mistakes.

If civilisation was a person:

Born in 500,000BC with the control of fire and shelter

At 15 creates spears and pigments

Wastes most of the middle of life doing not much, then at 57 creates bone tools.

With 70th birthday approaching starts making up for lost time, inventing the bow, flute and boat, as well as mining and cloth, all before their 75th birthday. Also gets first pet when they domesticate the dog.

At 77 starts farming and making alcohol as well as more complex buildings. Develops metalworking, lead, dentistry and maps. Domesticates sheep, goats, cattle, chicken and the cat.

After their 78th birthday, and start of the last whole year they'll live, starts working hard. Creates irrigation, milking, beer, plough, ice skates, paved streets, carts, learns to write for the first time, creates drainage, comb, cement, soap, the button, the bathroom and toilet, chariot, oven, shipyard and dock, ruler, currency, dice, candles, ink.

Near their 79th and final birthday they create the umbrella, glass, perfume, the spoked wheel, rubber, the fork, central heating and the lens.

They now have about 174 days left alive. In the first 60 days the Latin alphabet is created, as is the anchor, plastic surgery, the catapult, the wheelbarrow, the compass, the suspension bridge, the horseshoe, clockwork, the toothbrush and the encyclopedia. During this time Jesus is born and dies the next day.

In the next 30 days steam power is invented, as is paper and the combination lock.

In the next 20 days toilet paper is finally invented and to write on it they create the quill pen. They even create the psychiatric hospital for people writing on their toilet paper. More importantly, alcohol is distilled for the first time. Under-arm deodorant, the gas mask, the mechanical musical instument, the first programmable machine, the metronome, artifical weather simulation, erectile dysfunction treatment, university, chemotherapy and kerosene are invented. Then they go and ruin it all by inventing something stupid like a gun.

In the following 20 days the double piston flamethrower is made, as well as many less destructive things such as sherbert, street lamps, libraries, the novel, magnifying glasses, fireworks, sunglasses, glass mirrors, condoms and the buttonhole. I'm not sure what they were using buttons for before they had holes for them.

For the start of the next 20 days virtually everything is guns with the matchlock, bombard, multistage rocket, naval mine, round shot, shell and wheellock all being invented by the same couple of Chinese guys, as well as the katana and musket by some other people. But it wasn't all bad, as soon after this vodka is created, causing world peace to spread through the lands, at least until the morning after when all the leaders got up grouchier than ever and started some more wars. The steam turbine and pencil are invented.

So they're left with 24 days, less than a month to live. They're about to enter the begining of the modern era. With less than a month to go, they haven't even invented half the things in modern use. In the next week the telescope, barometer, vacuum pump, pressure cooker, steam engine powered water pump, piano, decimal currency, tuning fork, steam piston engine and mercury thermometer are all invented. During this time tea and coffee becomes popular in Europe, Fermat's Last Theorem is formulated (which will be solved about 20 days later) and calculus is developed by both Leibnitz and Newton, at the same time.

During the next week stuff really starts heating up. The cast iron dome, marine chronometer, ice palace, lightning rod, electrometer, model helicopter, spinning jenny, two-cylinder engine, carbonated water, steam road vehicle, steamboat, watt steam engine, circular saw, iron cased rocket, hot air balloon, bifocals, power loom, automatic flour mill, threshing machine, artificial teeth, vaccination, gas stove, morphine, steam locomotive, bandsaw, sailor cap, electric mine, stethoscope, kaleidoscope, bicycle, monorail, electric motor, photography, electromagnet, lighter, internal combustion engine, friction match, fountain-pen, thermostat, multiple coil magnet, electrical generator, hansom cab, braille, refrigerator, combine harvester, revolver, incadesescent light bulb, sewing machine, electric printing press, stell plow, camera zoom lens, electric boat and the vulcanization of rubber are all invented or developed. The century on which Wikipedia has a subsection of 'Important people' entitled 'Pirates' ends, followed by the start of the industrial revolution.

In the next 2 days everything really starts happening. The artificial fertilizer, saxophone, steam hammer, anaesthesia, typewriter, fax machine, ice cream maker, safety match, rubber band, pneumatic trye, sewing machine, modern oil well, safety pin, airship, elevator, Bunsen burner, celluloid, condensed milk, heating radiator, undersea telegraph cable, oul drill, lead acid battery, repeating rifle, self-propelled torpedo, vacuum cleaner, revolving machine gun, mechanical submarine, pasteurization, player piano, underground railway, barbed wire, dynamite, paper clip, rail air brake, periodic table, chewing gum, stock ticker, jeans, modern direct current electric motor, heroin and the electic street car are all invented in these 2 days. That's just 2 days. During this time lots of other stuff happened, including the publishing of The Communist Manifesto, the Great exhibition in London, The origin of Species published and the American Civil War happens.

The next day, showing no tiredness, the rate of inventions further increases. The dynamo, electrix rail, carpet sweeper, loudspeaker, telephone, stapler, induction motor, phonograph, microphone, cash register, electric tram, photophone, roll film, safety razor, seismograph, metal detector, electric fan, blowtorch, alternating current induction motor, linotype machine,electric trolley car, roller coaster, automobile, motorcycle, dishwasher, gasoline engine, amphetamine, contact lens, gramophone record, ceiling fan, Kodak hand camera, ballpoint pen, photoelectric cell, wind energy, zipper, escalator, adjustable spanner and the Tesla coil are all invented in this day. The first power plant and grid are made, the Eiffel tower is erected and basketball is invented. This brings us to one week ago.

Now they are really getting into the modern era. In the next day colour photography, automatic telephone exchange, carburetor, radio, milking machine, x-ray, diesel engine, polar icebreaker, remote control, ignition coil, magnetic tape recorder, gas turbine, self heating can, disposable razor blade, air conditioner, fire fighting foam, neon lamp, the airplane, tractor, blood pressure monitor, sonar, helicopter, electric washing machine and the Haber process are all invented or developed.

They're slowing getting closer to the modern time and the inventions are really starting to show that. In the next day, Bakelite, classical conditioning, dental braces, gyrocompass, hydroplane, parachute, aerobatics, airliner, assault rifle, bra (people could fly before they invented the bra), crossword, stainless steel, liquid fuel rocket, strategic bomber, tank, pyrex, sonar echolocation, cruise missile, air ionizer, polygraph, radar, television, wind tunnel, autogyro and automatic power loom are all invented. During this day the first world war started and finished.

With just a few days left before dieing the rate of invention doesn't stop. In the next day the aerosol spray, LED, mecanical cotton picker, sliced bread (since which apparently nothing has been quite as good), antibiotics, 3D television (apparently they had that back then), EEG, CRT, military robot, insulin, paratrooper, pressure suit, radio telescope, underwater welding, microwave radar, nylon, jet engine, the first electronic digital computer, polyphonic synthesizer, fiber glass, LSD (it's surprising they bothered to continue after that), velcro, bazooka and nuclear reactor are all invented. The great depression happens and world war 2 starts.

They've got 4 days to go and they're going to keep going, aparently without bothering to write out a will. In the next day Slinky is finally invented, as are some less important things such as the microwave oven, nuclear weapon, mobile phone, bikini, AK-47, pocket calculator, transistor, polaroid, LP record, holography, atomic clocks, credit card, contraceptive pill, nuclear power reactor, carbon nanotubes, optical fiber, fusion bomb, hovercraft, nuclear power plant, radar gun, hard drive, digital clock, videotape recorder, jet boat, satellite, spaceport, space capsule, neutron bomb, pacemaker, instant noodles and perhaps even more destructive than nuclear weapons, spandex, are all invented.

The next day sees rock n' roll all the way to disco. The laser , digital photography, optical disc, cochlear implant, space flight, computer mouse, hypertext, quartz wristwatch, FM sythesis, space toilet, video game console, supersonic transport, video cassetter, cup noodles, space station, E-mail, karaoke, LCD, microprocessor, MRI, ethernet, GM organisms, personal computer, Rubik's cube, DNA sequencing and underwater assault rifle (real useful) are all invented. This takes you through the Beatles up to the begining of synthpop, so it's got that going for it.

The next day was yesterday. Yesterday the personal stereo, credit card sized calculator, solar powered calculator, spreadsheet, walkman, CD, flash memory, handheld electronic camera, CD player (I'm not sure what CD's were being used for before this), artifical heart, camcorder, D-pad, pocket television, PDA, internet, colour LCD, portable CD player, graphic calculator, DNA fingerprinting, blue laser, World Wide Wide, memory card, webcam and plasma colour display were all invented.

Now, it's today. And today we have invented GPS, the smart phone, blue LED, USB, auto-tune, mp3 player, plasma TV, Tivo, human genome sequence, flashdrive and synthetic life.

More importantly, I was born today. And with my 17th birthday coming up I will have lived nearly one day of civilisation's life. All of this of course assumes that civilisation now dies, which would probably put a bit of a downer on my birthday.

Anyway, I hope you've enjoyed this somewhat pointless blog, and keep in mind that civilisation, all of this, happened just so you can sit there, reading this blog. Not that you're insignificant or anything.