### Arg

no maple makes miike a dull boy

that is all

Musings of a Math Nerd

- geometry (7)
- numerical (6)
- programming (6)
- crazy (3)
- calculus (2)
- maple (2)
- summary (2)
- vector (2)
- conference (1)
- nserc (1)
- openoffice (1)
- relativity (1)
- set theory (1)

So no updates for a couple days, but haven't been doing a whole lot of anything new until today.

Today I started rewriting my programs... again. Except this time, they're being implemented to work in four-dimensional space. How cool is that? It's not actually as simple as it sounds, though. Namely because, whereas in three dimensions every surface has only one straight line that is perpendicular to it (called the normal vector), in four dimensions those same surfaces have two lines that are perpendicular. Crazy, huh?

All I've been doing for the past two days is continue reading this general relativity book.

Except for yesterday afternoon, when I had this meeting with some other NSERC students, one from here, three from Dalhousie in Halifax, and four students University of New Brunswick. But here's the kicker: no-one left their respective schools. The meeting was only to introduce ourselves and to see the system. At our school we had two massive LCD displays side-by-side, with top-quality webcams above, a speaker system below, and microphones scattered about the room. The two screens are hooked up to a computer which runs the software. On the screen we see about a dozen video feeds across the three schools (which all have similar setups, though Dalhousie's was more advanced with five touch-sensitive screens since they developed the system) and we could all talk and interact in real-time. It was very cool. Throughout the summer we're going to be pushing the system to its limits, improving ease-of-use, as well as developing interaction techniques that will be used to eventually teach entire courses over this system. Very high tech, very cool.

Posted by Miike at 4:23 PM 0 replies Labels: conference, nserc

Today I started reading about this titular subject, and with a massive scientific irony, is possibly one of the easiest concepts to understand in physics, modern or classical. Ever wonder why the Earth pulls us down? Newton says because two masses attract each other... but why? I mean, we know why two magnets attract each other: they're constantly sending photons back and forth "telling" the other to move closer (or further apart). But there is no such chatter in Newtonian gravity. So how do we know which way is down?

Well many people know about "great circles". If you're looking at a map, the path of the plane traveling in a straight line appears an arc of a circle. That's because even though the plane is traveling in a straight line in three dimensions, the projection of the path of the plane into two dimensions is curved. The idea behind general relativity is that objects are always traveling in a straight line in four dimensions (the "spacetime continuum"), but when you project that line into three dimensions (aka, the universe that we observe) you get a curve!

Now you're probably wondering how mass is involved. Well, recall what I've been doing for the past couple weeks: calculating curvature. A straight line has no curvature. A slow tilt has small curvature. A sharp turn has high curvature. Well, with gravity and general relativity, mass is the curvature. In free space, nothing around you, you go in a straight line. Near a planet, you curve into it. Near a black hole, you curve into it faster.

Posted by Miike at 4:20 PM 0 replies Labels: crazy, geometry, relativity

Okay, so I've missed a few days. Here's what went down. I started calculating the other kind of curvature, which is basically multiplying the same two values that were previously added to find the first kind. And I had to do that in two ways. The first way was proving to be horribly inaccurate (machine error popping up), but the second way (which calculates dead-on) is only valid for 3 dimensions. Once we go to four when only the first way will work. Quite the dilemma.

Today I rewrote my programs entirely from scratch... again. Except this time there was a useful point. Consider the shapes I was working with. A sphere, torus, parabloid... those are all round, aren't they? You can spin them all you want around the z-axis and it won't change how they look. Any surface like this is called rotationally symmetric and mathematically that means its curvature is dependent on only one variable instead of two.

So now my algorithms calculate the exact same stuff they did before, except they do it in a tiny fraction of the time it used to take, and the error shrinks much faster as well. So woot!

Posted by Miike at 4:19 PM 0 replies Labels: geometry, numerical, programming

So originally, the programs I wrote hated me, but now they've come to love me.

Then Maple started hating me, but it adapted and now we get along semi-fine.

So now OpenOffice Calc @#$%!-ing despises me, crashing, calculating things wrong, just in general pissing me off. And all I need to do is verify my programs are creating the right answers...

Posted by Miike at 4:11 PM 0 replies Labels: maple, openoffice, programming

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