Jun. 12th, 2007
(no subject)
Jun. 12th, 2007 09:47 pmI'm in desperate need of a mathematical physicist.
As implied in my earlier post, I'm reading Isaacson's biography of Einstein, and I have no problems so far understanding the concepts of Einstein's work. It's really a recap of stuff I studied in college, anyway. However, when it comes to the math, I'm sort of similar to early Einstein in that I never really put much emphasis in math in my academic career. In fact, in four quarters of High School calculus, followed by three semesters of college calculus, my grades were D-D-D-D D-D-C (why did I get a C in college-level Advanced Calculus after four quarters and two semesters of D's? Don't ask, I can only guess myself.)
Anyway, I get the concepts behind his theories. I can grasp space-time, relativity (special and general), E=mc2, energy, matter, quantum (pro-dice wielding deity, and con-), Plank's constant, covariance, accelerating elevators vs. gravitational fields, Newtonian swinging buckets of water, the oddities in Mercury's orbit, gravitational lensing, and even his tragic acceptance of a democratic socialist utopia. However, his his tensor equation involving the curvature of space-time:
Gμν = 8 π Tμν
Here's where my math fails me. I understand that the left side involves mass, and is the combination of a bunch of complex multi-dimensional calculus that I will never understand. I understand the right side is the curvature of space-time. I understand because of this the relationship of mass and curvature, how one influences the other and how this cascades into the dance of everything interacting with everything else. I even instinctively grasp how pi must relate to the curvature on the right-side as it's so involved in anything curved through even Euclidean geometry.
But why is that 8 there? We're talking about a 4-dimensional curvature. 8 is 23 which would imply (maybe) 3-dimensional space. I could understand if that constant were 81 or 16. Or even some irrational number like the constants of pi or e. Or something imaginary like i. Why 8 though? It's so even and round and rational and (to the computer engineer in me) completely ordinary. Why 8?
As implied in my earlier post, I'm reading Isaacson's biography of Einstein, and I have no problems so far understanding the concepts of Einstein's work. It's really a recap of stuff I studied in college, anyway. However, when it comes to the math, I'm sort of similar to early Einstein in that I never really put much emphasis in math in my academic career. In fact, in four quarters of High School calculus, followed by three semesters of college calculus, my grades were D-D-D-D D-D-C (why did I get a C in college-level Advanced Calculus after four quarters and two semesters of D's? Don't ask, I can only guess myself.)
Anyway, I get the concepts behind his theories. I can grasp space-time, relativity (special and general), E=mc2, energy, matter, quantum (pro-dice wielding deity, and con-), Plank's constant, covariance, accelerating elevators vs. gravitational fields, Newtonian swinging buckets of water, the oddities in Mercury's orbit, gravitational lensing, and even his tragic acceptance of a democratic socialist utopia. However, his his tensor equation involving the curvature of space-time:
Gμν = 8 π Tμν
Here's where my math fails me. I understand that the left side involves mass, and is the combination of a bunch of complex multi-dimensional calculus that I will never understand. I understand the right side is the curvature of space-time. I understand because of this the relationship of mass and curvature, how one influences the other and how this cascades into the dance of everything interacting with everything else. I even instinctively grasp how pi must relate to the curvature on the right-side as it's so involved in anything curved through even Euclidean geometry.
But why is that 8 there? We're talking about a 4-dimensional curvature. 8 is 23 which would imply (maybe) 3-dimensional space. I could understand if that constant were 81 or 16. Or even some irrational number like the constants of pi or e. Or something imaginary like i. Why 8 though? It's so even and round and rational and (to the computer engineer in me) completely ordinary. Why 8?