@Flaw They're teaching fourier analysis in an introductory calculus class!?

@Mechanicalsnail hmm? Basic series always show up in early calc class. (mostly to break up the monotony of the massive lists of derivatives)

There's something on meta about improving questions per day

I told myself I should ask one qeustion here per day...I kept stopping myself from asking questions because I didn't know how silly they were that I just wasn't getting something

but I have to keep telling myself

if it confuses me, it probably confuses someone else out there too

I've also been very lax with studying lately (shame on me) and I blame pandas and pokemon

@jkerian That's Taylor series?

Fourier series tend to require lots of messy algebra.

The thing is, I feel like I'm not really learning anything.

The finished product is "useful" because it solves problems and we can do test questions with them. But I don't know how the tools work.

@Flaw You mean differentiation?

Try studying some real analysis.

Taylor series approximates a function at whatever point you set it. But why does a series of derivatives at "a" do that approximation?

It's interesting and studying from a different "angle" it can help build your intuition for calculus.

It took me a long while before I understood fully why the derivative of x^2 is 2x. And that's after manually figuring it out. Apparently teachers don't bother to teach why.

@Flaw See commons.wikimedia.org/wiki/File:Sintay.svg

en.wikipedia.org/wiki/List_of_real_analysis_topics

It would be more fun if they tried going from the perspective of how the first person discovered it

@Flaw Newton vs. Leibniz fight!

It's not really knowing if you define the things by what you already know, and try to teach "established" information.

It makes more sense (at least to me) to start from nothing, and slowly lead up to the idea

f(x) = exp(-x^-2)

@Flaw Isn't that how they usually teach calculus?

So far, not really.

Start with slopes between discrete $x$s, and then take the limit.

@Flaw You mean they're taking a purely algebraic approach?

Like "define D(x^a) := a * x^(a-1)" etc.?

well that was what happened

I managed to work out for some simple cases. But for trigonometric(and other) functions, I can't find out exactly how d/dx(sinx) > cosx

I have to have faith that a similar reasoning of D(x^a) := a * x^(a-1) applied when limits were taken

@Flaw Look at the graphs!

@Dave Hesei 24 being used in a use-by date of a souvenir.

I'm going to ask a (possibly dumb) question.

Do computers understand operations? Or are they simply programmed to give an output for a given input?

Does a computer understand what happens with 1+1? It will surely give me 2. But does it give me 2 because it understands what 1+1 is, or because it is programmed to return 2?

The CPU has an ALU (arithmetic logic unit) which pumps out output given input thanks to some clever hardware design.

The CPU says "add these numbers" and the ALU flips some switches to let the bits flow through it resulting in the addition of said numbers..

I'm sure jkerian can go into more detail if you're interested. :P But that's the high level gist of it.

I'm about to wander dangerously close to asking if a computer is sentient. Since "understanding" something is rather vague.

Well I guess the question I should be asking myself is if there is any observable/testable difference between being able to return 2 every time 1+1 is asked, and actually understanding it.

Yeah it doesn't "understand" anything.. Just processing a long list of operations, jumping back and forth in the list and possibly one day running out.

Because I found myself in a situation where I managed to answer some math question about taylor series, simply because I executed the correct steps required to get there based on some given formula. Without actually understanding anything in between.

I'd say humans are perfectly capable of "understanding" simple arithmetic with small numbers such as 1+1, but that whole "what is intelligence" bit is always fuzzy and people never settle on an answer on it so why bother.

Well yes of course you just need to trust the underlying theory at some point and say "this works because of that".. Trace that all the way back to 1+1 and you'll go nuts.

Is it possible to (artificially) construct the word equivalent to mamihlapinatapai (a look shared by two people, each wishing that the other will offer something that they both desire but are unwilling to suggest or offer themselves)(Guinness Book of World Records as the "most succinct word") in Japanese?

I quote wikipedia "The word consists of the reflexive/passive prefix ma- (mam- before a vowel), the root ihlapi (pronounced [iɬapi]), which means to be at a loss as what to do next, the stative suffix -n, an achievement suffix -ata, and the dual suffix -apai, which in composition with the reflexive mam- has a reciprocal sense."

reflexive - 自分; passive - られる; root (be at a loss) - 迷う; stative - ている, achievement suffix - ていた(?); dual/reciprocal sense - 相互

I present to you (a very likely ungrammatical) 自分相互迷われていた目付き

I'm pretty sure mashing all the components together is the wrong thing to do. But I need a break from doing my maths.

So you mash words

Mashing words is a lot more fun than getting stuck doing maths.

Take 2: [物言わず]腹ふくるるにらめっこ

@ento I like Take 1

@sawa regarding your comment in stackoverflow.com/questions/12650164/… . 1) That souvenir was indeed from Kyoto. You can see my itinerary at gist.github.com/3154209 2) Dave was apparently claiming that a Japanese calendar year being used for an expiration date couldn't happen. I was providing him with a counterexample.

Japanese people are more likely to understand オージービーフ than オージー, according to terabonne's comment at lang-8.com/424295/journals/1669920