It's not logical at all to wage a war against "logic." ...But it kills time, so wutev

http://www.youtube.com/watch?v=BTxZXKsJdGU&feature=related

tl;dw:  Rape Clubs exist.  As in, people get together and plan out the rapes and it's an actual organization.

"You can't have your cake and eat it, too" does not refer to anything about selfishness or trying to have too much.

It has to do the physical impossibility of eating and having cake at the same time.  If you eat it, you don't have it anymore.  If you have it, you're not eating it.  It's not greed or anything--go drink some water.  Drink it all.  Do you still have water?  No, you don't.  You drank it, you idiot.  Spit it out.  Now you have it--but you're not drinking it, you just spat it out.  What's wrong with you?

Get this correct, please.

Sincerely,

I'm Better Than You

Einstein did other things besides quantum physics.

In fact, the mathematicians and scientists I most respect made very wonderful contributions in all fields of math and science, from quantum physics to thermodynamics to electrodynamics to calculus theory to number theory and blah blah blah.

And those are why I respect them.  The coincidence between all of my favorite mathematicians and scientists is that they all also made enormous contributions in hydrodynamics/hydrology/hydraulics, which deals with water, which I am quite interested in.  And I never really noticed this until a few months ago.

And, yeah, Einstein made many contributions to both hydrodynamics and, in particular, sediment transport (which I don't give a damn about, but it was what I studied at my co-op job).

In fact, if you look hard enough, most of the well-known scientists were mathematicians more than they were physical scientists.

It's just more proof that math > physics, and while mathematicians can do physics, physicists cannot necessarily do math.

Especially when physicists will say "1 divided by 0 is infinity."***  Apparently physicists, in studying our universe, have decided that this is some sort of truth.  If I were a fucking moron who failed very hard at life in general, I would say "wow, they can't even get that basic thing right, maybe I should question EVERYTHING ELSE they think!"  Fortunately, I'm more intelligent than that.


***Note:  the proper way of saying this is 1/n approaches infinity as n approaches 0.  It's approaching, not exact.  There is a difference, and in fact the greatest integer function, [[x]], is precisely why "approaching" can lead to very different results than "exact."  Find the limit of [[x]] as x approaches 1.  It doesn't exist (it approaches 0 on from the left and 1 from the right), but [[1]] = 1, so we're good.  This is actually the reverse situation of what I presented--here we couldn't approach, but we could BE, yet 1/n blah can approach but can NOT be.


Oh, you crazy physicists.  Fuck you, Chapters 31-43 or whatever that cover electric fields, electronics, and magnetic fields.  I hope one day we go Fahrenheit 451 on your ass.  Oh, and Great Gatsby and Billy Budd (GOOD LORD, IF NOTHING ELSE, THEN BILLY BUDD) can also burn.

Good Lord.

Forget the music elitists, politics elitists, Trek vs. Wars elitists, etc.

Math elitists will treat you like scum because of things you don't know that they do and thus you should, too.

That said, the people on LiveJournal and FreeInformationSociety (the very few who can do math on there) are quite helpful and nice.

Am I speaking from personal experience?  Yeah.  Someone posted a very erroneous topic about how there are different sizes of infinity using two circles with the same center but different sizes (concentric circles).

He said if you fill the small circle up with an infinite number of radii, then extend them to the larger circle, although the smaller circle was full, in the larger one, the radii all get "pushed" a little farther (draw two concentric circles.  Just draw a whole bunch of lines in the smaller circle and then when you're done extend them to the larger one.  You see they get farther apart, which they do), and thus you could fill in the larger circle with MORE radii.

Of course, that entire idea is flawed (infinity is pretty dense.  If you have an infinite number of radii, there is no space between lines at all and so even stretching them out to infinity, the lines never get farther apart).  ...Even if you don't like that parenthetical, try and "fill up" your large circle.  To bring those "filler" lines back to the center, you have to, guess what?  Pass through the smaller circle.

"But wait, the small circle was full."  Yes, it was, which is the problem.  He clearly didn't understand how lines or infinity work.

Responses by people mathematically knowledgeable?

"topic is stupid"
"Wrong wrong wrong wrong wrong."
"How about no?"
"This makes my eyes hurt."
"The people trying to explain infinity here clearly have no idea what they're talking about."

Nobody (but me) actually pointed out his flaw in reasoning.

But then, people who just run around saying those above things aren't really mathematicians and are just people who are good at math, so it's all good.

http://www.buffalonews.com/260/story/570428.html

But I am finally officially a math major.  THANK GOD.  I finally got all the paperwork in changing the major from Mechanical Engineering to Math just today (and I'm really fucking sick, too).  Aww, I <3 Dr. Miller and Dr. Neumann (Adv Cal and Senior Seminar profs, respectively).

Also, I gave a presentation on Taylor's theorem, one of the 3 most important results in calculus (the other two being Mean Value Theorem and L'Hopital's Rule).  I got a 42/50 for the presentation (which is an 84% B, which is good considering he said our first presentations would all suck and if we got a B we must have done something impressive--he's a hard man to impress--and one of the other projects made a C even though I thought they did pretty damn well), and I got all the review sheets (we all critique each other) back, and I see a particular pattern here.  The back of the class wasn't terribly happy and I got about a 5/8, but people who were near the front gave me a 7/8 (nobody ever gets an 8/8 for the overall presentation.  To do so is blasphemy to Dr. Neumann).

Turns out, Taylor's Theorem is REALLY FUCKING HARD TO EXPLAIN analytically (as opposed to what you'd learn in a sophomore calculus class), so we had this project and Dr. Neumann assigned it specifically that it was going to be a hard topic to deliver and he would wind up taking two days to teach it (of course, it was my fault for volunteering for the project).

Taylor polynomials say that you give me any function that is continuous (no breaks or holes in the graph, just a nice smooth line with curves if any) and differentiable (no sharp points on the graphs, nice CURVES), then I can take a very simple polynomial and approximate the function.

Taylor's Theorem says that the error term (take the difference between actual and approximation) goes to 0, which implies that Taylor polys converge to the actual function).

It's nothing too fantastic in a calculus book, but holy shit does this open up a whole new world of analysis.  Not only that, but its very existence DEPENDS on a whole shit ton of analysis (our entire Adv Cal book was building up to this, and it is building up to integration.  So, 5 chapters building up to Taylor's Theorem).

One application is a neat little thing anyone who's still reading might blink an eye at--

There is no such thing as a single continuous straight line.  Every line you see, every curve you see, is actually an approximation of infinitely many, infinitely small straight line segments.  Is there a proof of this?  Yes.  Do I know it?  Part of it.  The actual proof itself is awful brief, but explaining it is something I am not terribly adept at doing (I'd make an idiot of myself, even to people who didn't know it) and requires a hefty background in just what straight lines are.  It basically just comes down to an infinite series of line segments centered around some point.

What does THIS imply?  It's actually a REALLY GOOD THING that everything is nothing but infinitely many infinitely small line segments.

This means we can break shit up.  This gives mathematical validity to dual particles-and-waves theories.  If we jump the gun, it tells us, ultimately, that we can also map the human body as a function.  What does THIS imply?

See those sci-fi movies in the future where someone gets sick and has to lie down on an operating table or something, and people produce a graph of his body and shoot lasers into IT and it actually affects his real body?  Well, this possibility is very plausible since the human body can be mapped.  We merely lack the technology to do it right now, but math was always eons ahead of its time.

Person A generates a type of humor.  Person B generates the very same type of humor.  The problem?  Person B's humor flows against Person A's, quite possibly to show A doesn't really have a sense of humor and just expects people to all flow with A's.

A of course gets emotional and completely misses the entire thing B was doing.

What does all this mean?

Well, there are two kinds of people in this world:  those who can extrapolate information from incomplete data.

Math isn't really as concrete and universal as most of you think.

Go to Europe and ask them what csc(x) is.  More specifically, ask any current engineer or scientist about it.

They'll kinda blink eyes at you unless they work with Americans or Asians.

Most Europeans do not use cosecant or secant (in all honesty, they ARE unnecessary functions).

Not only that, but a lot of PHYSICAL things are governed, mathematically, via the exponential function e^x.  In truth, however, they are hyperbolic, such as sinh(x).  It is true that sinh(x) = (e^x - e^-x) / 2, but that is not an exponential function.  In fact, two distinct things are growth and decay (often referred to as EXPONENTIAL growth and decay, el oh el) and the economic principle of supply and demand.

In fact, almost all of thermodynamics is hyperbolic, but it "looks complicated" so we just write it off as exponential.

"But wait.  Merely writing things off as X instead of Y doesn't make math nonuniversal."

Yes it does in this manner:

If I throw a ball over some distance and let another ball drop straight down, the physical paths they take are VERY different (as are the equations dealing with them).  However, at some point in time, a certain amount of distance they travel relative to time (aka velocity) can be governed by precisely the same equations.

Precisely.  Not approximately.  Granted, this is probably a very small amount of time and a very small amount of distance, but pbbt.

And that's the thing.  Depending on on how you observe the physics, the math changes.  Go look up centrifugal force:  no such thing, but people use it anyway.  The physics doesn't exist (well, physics isn't really math), but the derivations to create this "centrifugal force" are quite real and quite powerful for not existing.

Analysis is the very key to this.  Real numbers are a subset of complex numbers, but sometimes a complex analysis tool cannot be used to understand real numbers (which is VERY ironic because complex analysis is usually 10000000000000x easier than real analysis), in spite of the "fact" that complex analysis can "most definitely" be used in real analysis.

Oh, math.  You're so mysterious.

First Tuesday/Thursday class I did not want to leave at all.

Senior Seminar in Math is just SO MUCH FUN OMG I'M LIKE A SCHOOLGIRL AT AN NSYNC CONCERT

There is one good reason you should never post pictures of yourself posing all sexy online.

Your children might find them in the future.