Why hello there, ye anonymous reader of the Olde Ari Journale (sic). How goes it? Are you satisfied with your life? Why do you like to read about those of others? Are you experiencing transferrance? Whatever works for you, like the old doctor says!
My life’s going a-okay. I had to endure 0, 1, 3, and 5 periods today, making for 2 tests with 1 tomorrow (ouch on Spanish!). I’ll be really glad to get off to college. It’s looking like it’ll be Vanderbilt University in Nashville, Tennessee, right now. Full tuition scholarship + grants + NM scholarship = great deal, great school, great price. Ayup. And for those of you who face similar situations in the future between “dream schools” that you were accepted to but can’t attend due to financial reasons (too varied to list here…) and ones that you can actually afford that are just as good for you: Remember, you got admitted, you’re just as good as any student there (with better economic sense!), so don’t get down about it!
Math Concept of the Day
Nonstandard Analysis
For the math-disinclined: It basically redefines the set of real numbers to include infinitesimals (called the hyperreals), i.e. those numbers that are greater than 0, but less than 1/n for all n >0. It was originally developed as an intuitive way to understand calculus (back in the good ol’ days of Leibinitz and Newton) until their methods were replaced by the rigid formality of delta-epsilon proofs (for limits, derivatives, etc) that we’re all familiar with today. It enables mathematicians and students to have a more conceptual picture of what exactly’s going on when they manipulate those differentials, and it allows for development for its own sake in proving more complicated theorems than those that are practical to be proved (or even possible) using regular delta-epsilon analysis. Essentially, higher order analysis. I’m not quite sure why it’s not at least mentioned in any calculus textbook as of yet (the actual details require a graduate-level analysis class).
As soon as I start taking CompSci again, I’ll put some CompSci concepts up too :). Maybe I’ll even throw in some physics when I take some more advanced courses next year…I’m so looking forward to college! Goodbye Troy! From what I’ve heard, college isn’t nearly as bad as Troy…ANYWHERE. Yay! Tentative schedule (barring any problems with the registrar, with whom I’ve checked things over at most places):
*2 math classes (if I can do some independent study of the rest of linear algebra… (gogo MIT OCW) then it’ll be complex analysis and partial differential equations). With a year or maybe 3 semesters of 2 math classes a semester, I think I qualify for a minor :).
*1 physics (required, probably AP Physics C type stuff with more fields (ohohoh!) covered than just E&M and mechanics)
*1 comp sci (whatever I have to take after CS AB: hopefully something fun -and- theoretical (my dream class :D))
*1 elective (history? philosophy? I’d love to do something on causation, scientism, limits of consciousness, free will/determinism…but honestly I’ve got lots of reading to do to catch up in any of those fields)
Current Thinking, major-wise: BS CompSci, MS CompSci, BA Math (considering doing something in physics or philosophy).
Question to ponder: Why does the universe seem to obey a “well ordering princinple” (to abuse a term from mathematics without remorse) in regards to the laws of physics, a close relationship with derivations from abstract mathematics (calculus, diff eqs, linear algebra, non-Euclidean geometry, etc, etc, etc), logical consistency, etc, etc? The very idea of cause and effect, so essential to our understanding of the universe, doesn’t even seem to be a necessary proposition for existence, once considered in this light. Why are the physical constants (Rydberg, Planck’s constant, universal graviation, etc, etc) defined the way they are? Why is e^(i*pi)+1=0? I personally think it points towards some sort of organizing force that passes beyond the material, but of course, everyone is entitled to their opinion (even if I have to BURN THEM for it :)).