Colour by numbers

Mr Toastmaster, fellow toastmasters and guests. I saw a little man upon the stair A little man who wasn’t there He wasn’t there again today Gee, I wish he’d go away That little poem, which you may have heard before, is a good way of describing imaginary numbers. Does anybody know what imaginary numbers are. Well, they’re numbers that logically, don’t exist, and yet mathematically, must exist. For instance, 2 is the square root of 4, because if you multiply 2 by itself, you get 4. Similarly 3 is the square root of 9. Now, let me ask you : what is the square root of minus one ? Well, it has to exist because every number has a square root. It can’t be a negative number because two negatives multiplied give a positive answer. And it can’t be a positive number for the same reason. It has to be somewhere in between negative and positive that isn’t zero. Now that’s an imaginary number. Despite the fact that we can’t exactly define imaginary numbers we still use them. For example, Normal numbers can be written in a line like so : 1 2 3 4 5 Now, let’s take an imaginary number 2i. i the letter used to indicate imaginary numbers, unless of course you’re an electrical engineer, in which case it’s j. And add 3 to it so we get 3 + 2i. Well, we can’t say that 3+2i is somewhere along here between 3 and 4: 1 2 3 4 5 | x 1 2 3 4 5 Instead I have to use 3 dimensions and say that 3+2i lives up here above 3, in imaginary space. Not exactly easy, and it might strike you as a little daft. The more you get into complex numbers with imaginary numbers as part of them the more they seem like an occult symbolism or the mathematical equivalent of an abstract painting. But the amazing thing is they are used everywhere. Over the past 300 years scientists have found dozens and dozens of systems in the physical world that can only be described using imaginary numbers. For instance you can describe Direct Current circuits without them but you need them to describe Alternating Current circuits. You also need them in Relativity, quantum Mechanics, television and computer design, and in hundreds of other areas of our technology. It’s as if we can’t describe our world around us, the world of matter and energy, without including a factor that is so intangible, so inscrutable, that we may as well be talking about the sound of one hand clapping or the square root of a gooseberry bush. What is even more weird to me though, is the concept that we are living in a world without colour. Well, from where I’m standing I can see yellow walls, a green table, a brown piano, and of course, lots of people wearing a whole cacophony of colours. Well, according to physics, all of this is a hallucination. What is actually out there consists of clusters of colourless atoms and photons, and all the so called colours are my brain’s way of reacting to various wave-lengths of light carried by the photons bouncing off the atoms. If this is the case, why don’t we see the world like that. Bleached out, monochromatic, abstract, inhuman, emotionless. Even though we know the scientific, mathematical truth, why do our brains go on hallucinating a technicolour fantasy. Probably because it’s more fun. Now, as it turns out, temperature is even stranger than colour. It can be measured on instruments like the thermometer, and obviously we can feel fluctuations in temperature. But it only exists on certain levels. Specifically, it exists at the molecular level and above, because, what we call temperature is actually the rate of movement of molecules. Let’s say the podium here measures 10 degrees celcius. It makes no sense to say that the atoms in the podium are also 10 degrees celcius. Because of course atoms have no temperature, just as they have no colour. Only the clusters of atoms called molecules have temperature, and only in relation to their movements. The more you explore all these concepts the more you realise that what’s real is not what we see and what we see is definitely not real. What is real apparently, is colourless, temperatureless, abstract, and can only be expressed in terms of surrealist mathematics like the square root of minus one. So, in so called reality, I don’t know what I look like, I don’t know what I feel like, I may or may not be here talking to you, I may not even exist. But despite that, I intend to continue leading an enjoyable and colourful life.