In every wood, in every spring
There is a different green

from “I Sit Beside the Fire” by JRR Tolkien

I’m always reminded of the above whenever anybody irritates me by saying “If you’ve seen one you’ve seen them all,” but today I’m reminded of it for a different reason.

Charley mentioned to me a while back that some cultures don’t differentiate between green and yellow, instead calling them different shades of the same colour. I realised that we do it in English too. Most of the time the only people differentiating between mauve and puce — both weird purplish colours — are paint companies. (Did anybody else know that all sorts of colour names have specific numerical definitions, at least according to wikipedia? Puce is #CC8899.) This begs the question, how many colours are there?

The first obvious problem is that you have to define what a colour is. Ask a web designer and they’ll say about 16 million, while a kindergartener might name a dozen. Someone who thinks they’re very clever might say there’s only three primary colours. I can’t help but suspect that the three fundamental colours are biological. We have three types of cones that detect light in our eyes, but some animals have 4 or 5, effectively giving them 4 or 5 primary colours. Birds, for example, have a cone which can see ultraviolet light.

Further complicating things is that there’s no way to see what colours another person is seeing. While two people may say a ball is red, the mental image one person assigns to that particular combination of light that makes “red” might actually be “green” to the other person. Somewhere in our brains there’s a translation between input from our retinas and a mental image of a colour, and there’s no reason to think everybody has the same translation, even though the English word attached might be the same.

Now this point about colour being arbitrary is often used as an example to support some idea that reality is subjective — I think that was Charley’s original point in bringing this up. However, colour is special in that there is no second sense to confirm what we see. Two people see a ball, and since both can touch it and confirm it’s there, they know that they both see the same ball, but there’s no way to compare mental pictures.

The strangest artefact of this conversion of wavelengths or energies into a mental image is the twisting of a linear scale into a circular one. Why should the end of the spectrum wrap back onto the other end? Red goes to orange goes to yellow goes to green goes to blue goes to purple goes to red. This I can’t find a biological explanation for, but if anybody knows I’d like to hear.

Granted, the underlying physics of light is quantum so there is a specific number of energies of light that a person’s eye can see, but human perception muddies it all up. Trying to understand the resultant continuous perception in a discrete kind of way doesn’t seem informative to me, as convenient as it might be. The problem of discretizing continuous variables plagues psychology, philosophy, and all the social sciences. I think we’d get a lot more from these disciplines if we made a habit of conceptualizing them in continuous terms.

I spent some time looking at a few graduate programs today, and I’ve realised a few things.

I’ve really known this all along, but I’m definitely prefer being an annonymous student in the back of the class to the keener up front on a first name basis with the prof. Maybe just metaphorically. I still sit up front after all. The idea of defending a Ph.D thesis, for example, is a little daunting. But of course I know I certaintly won’t get myself anywhere if I don’t try.

Today I was concentrating on degrees which combine Philosophy and Physics. I don’t think the two are mutually exclusive by any means, but it’s very difficult to find universities that have programs that deal with the connection. They all tend to be largely Philosophy programs concentrating on Philosophy of Science, whereas I would like a program founded mostly in current physical theory with philosophical considerations.

Yes, I am a scientific elitist. And though the term has negative connotations, I really can’t shake myself away from it. Philosophy without being based in science is, I think, completely uninformative. Even worse, I found myself scoffing at every Department of Philosophy web site that mentioned “research”. There are no discoveries in Philosophy. Indeed it’s a common criticism to call string theory philosophical.

I guess the main thing holding me back right now is just that — this feeling that anything philosophical is inferior. A Ph.D in Physics holds a lot more weight with me than one in Philosophy. Not just because everybody tends to be impressed at the difficulty of the former, but I really feel that you can say more with science.

Nonetheless, just as Philosophy without physics is meaningless, in some sense so is physics without philosophy. Maybe that’s what I can write my thesis about. For now I just have to see how my philosophy minor goes, and try to decide what to do for grad school.

I think I’m finally starting to get to a point where I can make some references to things I believe in. I have lots of ideas about philosophy, science, ethics, and the univerise in general, but they’re all just a big mess in my head. I’m never able to argue anything coherently and I’ve always hated that.

Though there are things that they all say that I disagree with, I’m finally discovering that men like Bertrand Russell, David Bohm, and Alfred Korzybski had ideas that fit very well with what I think I probably believe.

One problem I’ve had quite a lot with how physics tends to work is that there’s far too much emphasis on the mathematics. It seems as though many people take it to be that the universe works the way it does because it is governed by math. It’s certainly an elegant idea, and I’m certaintly not going to deny that the universe behaves very much in accordance with mathematics, but I cringe at the idea that it is governed by it. Never does an electron solve for its equations of motion before deciding which way to move.

I think this is where Korzybski’s general semantics can really come into play. Mathematics could be considered a map of the universe, but of course is not the universe itself. Yet I’m not sure if I’m willing to commit entirely to this. Physics — mathematics — might be unique in being the only map that, once we had a unified theory, you could get all the information you needed about the universe is you just poke at it long enough.

I used to be able to identify at least 12 and possibly as many as 20 constellations in the sky. When people would ask me where something was or what a particular star was supposed to be a part of, they’d often get annoyed and say that the whole idea was a pretty big stretch.

Pretty much everybody can spot the big dipper, though not many say it really does look like a bear’s behind. Cassiopeia is even worse… since when does a ‘W’ look like a queen? Don’t even get me started on Triangulum.

A big part of the problem is light pollution. Even in small town New Brunswick I have a hard time seeing some of the less major constellations, and you pretty much have to drive clear into nowhere to see something like the Milky Way. Probably just as important, though, is a bit of imagination. Draco and Cygnus are easy. Orion maybe not so much.

What brought all this on? Well today, in a seemingly unrelated enterprise at work today, I was plotting my standard deviation to see if I had any hope of converging a few iterations down the line. Up pops the graph and I immediately saw something jump out at me. But then again, with a standard deviation like 140, I had been having a pretty long day. Anyway, mouse over to see what I saw.

I discovered while doing a little casual reading on fourier transforms (because who doesn’t love analyzing a good spectra on a Friday afternoon?) that I’m not an equations kind of guy. Oh don’t get me wrong, I’m more than happy to use equations and come up with equations to calculate things, but when reading through a mathetmatical textbook like this one I find myself just skipping over the equations to read the text.

Also, this guy needs to learn, that a sentence does not always need, three commas.

There are visual learners and auditory learners. I think there are equation learners and word learners. I’m a word learner. Maybe there’s a better term for it. I can look at an equation and see nothing at all, but then as soon as there’s a sentence attached to it, I’m good to go.

I did have a nice little epiphany somewhere in chapter 3 about how we’re actually using fourier transforms. The light comes in all at once and by performing the transform you can pick out what frequencies there are. Nice. It’s like playing a cord on the piano and being able to hear what individual notes make it up.

And did you know there’s a 300 level math course at McGill on colouring? I bet the first thing they do is provide a formulaic definition for “colouring” and take all the fun out of it.

Magnetic pole reversals have always been a bit enigmatic, and I’ve found they tend to pop up quite a bit when people need strange and poorly understood scientific phenomena in anything from great novels and bad movies to the slightly more bizarre. It’s strange that it’s much simpler than, say, quantum mechanics, but because everybody is so used to north and south being fixed directions and not so concerned with what’s going on in an atom, it tends to freak people out a bit more.

We know that the north and south poles flip directions every once in a while. Every few hundred thousand years, anyway. The slightly freaky part is that we’ve never known what the flipping is like (although people speak as if they’re a gradual process and possibly quite dangerous for inhabitants of the planet… *cough* dinosaurs *cough*) and they occur randomly. It happens to the sun every few years, but of course nobody lives on the sun to care. Basically it’s potentially a huge global catastrophe that could be thousands of years away, or it might have already started.

But now there’s some new research coming out saying that the reversals are not random after all. I was hoping the article would have predicted when the next reversal should be, but it seems like they haven’t been able to take it that far yet. Anyway, it might just make for a nice show in Tahiti, in which case we don’t really have to worry too much about it. As long as the nightingales don’t get confused.

The sightly disquieting thing about physical concepts that involve lots of factorials (i.e. statistical mechanics) is that it seems like the author of any given textbook is trying to be much more excited than is warranted.

“We denote the number of possible permutations by N! And we’ll define another quantity (U-m)! Wow! This is so much fun!”

Meanwhile Quantum Physics spends all its time trying to convince you that you have no common sense. Most people think that the whole uncertainty business doesn’t really affect us on a large scale, but I learned a while back that galaxies exist because of it. You don’t get much bigger than that! And all this business about particles popping into existence and annihilating with each other is what allows electrons to de-excite and emit photons. I.e., we’d all be blind without quantum uncertainty.

Meanwhile my prof in classical mechanics seems to habitually make up words whenever he feels like it. I mean seriously. Fiducial? Anzats!? And when going over some old solutions today, it seemed to strick me as slightly metaphysical, what with the journey to the Heaviside Layer. And by that I mean, using the Heaviside function. Whatever. It’s not like they’re two completely different concepts or anything.

I love it when you go into an exam fully expecting to fail, spend the first ten minutes staring at the exam paper thinking “I don’t even know what equation to start with”, and then getting an epiphany somewhere along the way so you can suddenly derive the answers to everything. Except the one about Gaussian statistics. I don’t really know what those are. Still though, I’m happy.

Statistical mechanics has a lot to do with random fluctuations and entropy. It’s made me realise just how much concepts of order and randomness don’t make complete intuitive sense to me.

Take, for instance, a string of a million “random” numbers. If the set is truly random, that is, each digit has a an equal chance of being any one of the numbers from 0 to 9, then each of those numbers will appear about an equal number of times — one hundred thousand times, in this case. They won’t all be exactly that, but you can go as far as to predict the average number that they’ll differ from that. A child wandering around a house at random should spend an equal ammount of time in each room. (As long as each room is the same size and maybe some other constraints, I suppose.)

Even stranger still, you can tell whether or not a human typed out those numbers or if they were truly randomly generated. A human typing merrily away will at some point think “gee, I haven’t hit 8 in a while”, and will then hit the number 8. But they’ll also think that too many 8’s in a row doesn’t look random enough. Yet, a real random set of numbers will have strings of repeated numbers. There’s a formula to predict how many strings of how many repeats there should be, though I forget what it is. I bet that in a million random numbers, you’ll have at least one part with ten 8’s in a row.

This is how you can tell if the night sky in television or movies is fake or not. If the stars are evenly distributed in the sky, you can bet somebody put those stars in manually. If there are clusters and blank spots, it’s more likely a real starscape or a picture generated by a computer. Or at least made by somebody who knows all this stuff already and wants to make a realistic starscape.

My point is that it doesn’t seem right for it to be possible to predict the properties of a random sequence of numbers. You might get a string of one million 8’s in a row, but the chances of that happening are 1 in ten to the millionth power. I guess that’s the rub. Yet I’m still troubled. How can something really be random if we know what to expect?

Herbert Callen, you crack me up.

Clearly he fails to take into account the deliciousness of potato skins, especially when coated in melty cheese and bacon bits.

Regardless, this is totally the kind of thing I could study at Oxford. Or at a university that might actually accept me. Whatever.

I think this one explains itself. I also tried to map out the magnetic field of my refrigerator, but it turned out to have lots of different domains of magnetisation, which changed by moving the fridge magnets around. Good times.

Geekmas Part IV would be the story about how I finally managed to make that little video, but let’s not get into that. It was one of those times where I had to download a dozen different programs which were all designed to do one thing but only one of them actually did it. Thanks, Sothink.

PS. I voted today :)