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Stuff, and lots of it...
2012
unknownj
Before I go to bed again (I have a midterm tomorrow, hence going to bed at about 11pm), just a few thoughts...

Tomorrow is my Stats & Probability midterm - I'll find out whether I really can do the course standing on my head without any help, or whether I in actual fact suck. Doesn't count towards my final grade, so that's okay.

What does count towards my final grade is my AI stuff - I've done 25% of my Logic course and 15% of my Java course. So 40% of a course, each of which are worth 10% of this year, which is worth 40% of the degree. So, 1.6% of my degree is done already. Doesn't seem like much, but trust me, when I was doing the work, it certainly did :o)

It's weird, when I listen to guitar, I can see the music. Or, rather, I can see the distance between the notes, sort of. It's not like frets or anything, it's not exactly a spacial distance. Not in one dimension, anyway. It's difficult to explain. But interestingly, it's linked to how I see numbers, so maybe I can now see why music and mathematics are related. Permit me to go off on a tangent....

When I was little, I (like most people I would guess) imagined numbers to sort of be a ladder, with rungs and stuff for each number. And it was an entirely visual process - you could see this ladder, but never draw it, because the perspective you viewed it from depended on the number you were looking at. If I look at the number 7, the ladder is at a different angle to if I'm looking at 8. So it can't be drawn, not in reality anyway.

So anyway, probably thanks to my grandfather, I lost the idea of integer mathematics very early on - perhaps too early on. It would certainly explain my inability to entirely get to grasp with programming that's based on integers. I don't necessarily believe in their significance. By the time I'd done a couple of years at primary school, my ladder was looking more like a stick with notches on it, and eventually it was just a smooth stick. The significance of which is that it allows for fractions, decimals, that sort of thing, and treats them like any other number.

And I believe that's a damned good approach - it was around that time that I suddenly found myself to be easily the best at maths in my school. Like I said - probably thanks to my grandfather, who taught me a lot of complicated things as a child simply because I was very willing to listen and learn when it came to maths. So here I am, with this stick, suspended in space as it were, on which the numbers are written. Fast-forward to GCSEs, and I start learning about complex numbers. 3 + 4i. That sort of thing. Everybody but me struggled with this concept, it seemed, and why? Because I already had the complex plane as a part of my perception of numbers. In fact, my perception of numbers allows for a second type of complex number to be added - rather than a complex plane, we have a bi-complex system. But I digress...

Anyway, yes, so I can see numbers, complex numbers are no harder than difficult fractions and decimals, which in turn are no harder than integers. Which is why I used to rule at math. Until Uni, of course, where it's all methods and procedures and the actual arithmetic is painfully sparse. My particular abilities are in the perception and handling of numbers and algebra (which works the same way, more or less), not in remembering probability distributions and methods for the solving of initial value problems on second order linear ordinary differential equations. You get my point...

Anyhow, the actual point here (if there still remains one), is that I'm starting to see music in a similar way. It's this pole hanging in space, and all the notes are on it. And you know the weird thing? Even though A# and Bb are apparently more or less the same note (although, despite them being played the same on both piano and guitar, you'll find me surprisingly reluctant to accept that fact), I see them differently. They're at the same place on my line, but they're viewed from different angles. And one point viewed two ways is never the same from both perspectives because its context changes based on its surroundings, which in turn change depending on the direction you approach it from. If you see what I mean.

So, in short, I see numbers as distances and points in space, and I'm starting to see musical notes that way, and contrary to what I've been taught to believe I'm seeing the same note two different ways just because it seems to work that way. Perhaps it's just the lunacy finally catching up with me.

Speaking of music and mathematics (the relevance of which will become apparent shortly), as I was, I have to give a presentation accompanied by an essay in February, for which I have to start preparing now. Here are the options I've narrowed it down to...
1. How to play simple games
In "I've got a picture", player 1 is dealt a card. He must then look at the card and bet 1 to 5 units on it being a picture. Player 2 either concedes the bet or doubles the stakes. Player 1 wins if it is a picture, otherwise player 2 wins. What strategies should the players play? This, and other simple games will be considered
I like the looks of this. It's all about mathematical psychology to a point, and I do like that. The point of the game is based on player 1 being forced to bluff if he doesn't have a picture, and thus having to either deter player 2, or minimize his losses. But player 2 knows about these tactics. And so it becomes, perhaps, seemingly random. It'd be nice to do that, it'd mean playing with lots of numbers and probability theory. All of which I'm quite good at. Or, there's...
2. Lose all your money
Gambling is widespread in our society, but most is almost entirely based upon chance with a poor percentage return, e.g. the lottery, scratch cards, fruit machines. This project looks at gambling from a mathematic viewpoint
Clearly this would be fun to do...
16b. Music and Mathematics
What indeed is the note A and what does it have to do with root 2?
Interesting, bringing maths to a subject I like. But it might make me see music more scientifically, which would suck - I like the artsy side to it more...
18. Plimpton 322
Plimpton 322 identifies a remarkable Babylonian clay tablet. Its purpose is unknown but its significance is undisputed....
It's a long description, so I'll summarise - it's pre-Pythagoras by a few hundred years, yet the tablet contains tabulated numbers linked to Pythagorean triples - integer solutions to A^2 + B^2 = C^2. Doing this presentation will involve learning the Babylonian number system, which sounds really interesting - it's thousansd of years old, so it'll differ quite a bit I fancy - it's always nice to broaden one's horizons with an alternative approach...
22. Noiseless Coding
A source issues a stream of data, for instance letters in our alphabet, and from experience you know the long-run frequencies of each letter. How can you represent the data-stream in some similar alphabet, for instance dots and dashes, as concisely as possible? Morse code represents "e" by o and "t" by -, but for "q" it uses - - o -, and the other rare letters also have codes of length 4. Morse died in 1872 but it is only recently that a theory has developed.
This is a subject I've randomly given thought to in general in my own time, so I've already had some experience of the topic. For starters, my symbolic alphabet represents groups of letters too - for instance, "th" is more frequent than "q" in language, so it seems only right that, probabilities permitting, it should have its own "letter" in the symbolic language. Of course, if "t" + "h" is shorter than the code for "th" it would not be used. Similarly, "qu" would have a length shorter than the combined length of "q" and "u", because it is more common than both the letters if taken to be independent. Anyway, yes, I have lots of ideas on that, see. Anyhow......

Most of what I want to do here is (obviously) based on probability - game playing, smart encoding, that sort of thing. Play to your strengths, and all that... Speaking of probability (wow, I'm pretty circular in this entry), it's only 5 hours before my midterm, which means I'd be getting up in 4 hours. And given that I've already slept tonight for a few hours (well, 11:30pm to about 2am, and also this afternoon between about 2:30pm and 5pm), I can probably just stay up from this point...

Speaking of my nap earlier - it scared me. Whenever I nap in the afternoons, I suffer a degree of amnesia on waking up, where I'm totally disoriented - I don't know how I got there, what time it is, what day it is, anything. Today when I woke up I was worried that I'd slept 24 hours straight through my midterm, just because I didn't know any better. I used to be okay with sleeping any time, but after the rigid schedules of America (where (with the exception of one day) I only slept at night) and working in the summer, I've gotten used to waking up in mornings, and when I don't, I have no idea what's going on, what day it is, what week it is, anything.... Oh well :o)

This entry is reaching the critical length at which sod's law and irony take over and crash my client out of spite, just because it'd annoy me the most at this point. So I think I'll just post this, and have done with it. Maybe go to the shop and get a snack, then perhaps walk down to the beach. It's a shame I'm not on the east coast, since then I could watch the sunrise over the water. Still, South works almost as well, so perhaps I'll do that...

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