james_davis_nicoll | I don't want to sound like a bigot

o_O;

How does forgetting calculus transform you into a bigot?

It doesn't. I said I didn't want to sound like a bigot so I did not then follow that up with something apparently designed with the specific intention of making it look like I dance around in white sheets. It's not rocket science.

"I don't want to set myself on fire" should be followed by something that doesn't involve setting myself on fire.

I don't want to sound like a bigot, but white people just can't do calculus.

I was interpreting it as "I don't want to set myself on fire, here's what I need to know to keep from setting myself on fire".

Plenty of bigots can do calculus, especially in the engineering community...are you sure you're not just bigoted against bigots? :)

Bruce

This right here would cause me to start reading your LJ, if I weren't already doing so.

*nod*

That makes way, way more sense than most things that follow "I don't want to sound like a bigot."

It's sort of like, "Maybe it's not my place to say this . . . um, so I'll shut up now, sorry."

Speaking as a high school math teacher in training, it bothers me that calculus is held up as the pinnacle of math. You probably forgot it because it isn't relevant in your day-to-day life the way algebra and geometry and logic are.

Also speaking as a high school math teacher in training, is there something in particular that you'd like to be reminded of?

It's the pinnacle of high school math, for many people, and the point where they finally crap out. That's just because of the vagaries of curriculum design.

The ones who go on are often undone by multivariable calculus in college (and they usually have no idea what one does with this stuff unless they're studying physics).

I've forgotten most of the esoteric techniques for doing integrals, and I don't care (that is what symbolic math software is for). The exception is integration by parts, because I had it drilled into my head in N dimensions doing quantum field theory.

unless they're studying physics

In high school, we invariably learned things in calculus that would have been extremely useful to know the previous week in physics....

Been there! Done that!

I have unhappily forgotten all my differential and integral calculus and what little I ever grasped of multivariate stuff. I'm stuck with vestiges of symbolic logic and predicate calculus, but that's so utterly different that we really ought to have a different name for it.

"Calculus" just means "a bunch of rules for calculating"; that the unqualified word came to mean "differential and integral calculus" is, I think, another accident of educational curricula.

Also, "stones within the body," as in A comparative view of the phlogistic and antiphlogistic theories: With inductions. To which is annexed, an analysis of the human calculus, with observations on its origin, &c. by William Higgins, Pembroke College, Oxford.

And the stuff that accumulates on your teeth, as galbinus_caeli said. I assume the root comes from a word for rocks, such as one might use as counters.

Been there done that TOO. It frightens me to know that I passed a *UNIVERSITY LEVEL* calculus course, SOmehow I knew enough about this stuff to pass a high-level exam in it. Twenty-odd (sometimes VERY odd) years ago. Bring me face to face with an integral today and I'll likely cry.

Amusingly, for me, I actually had a crash course in calculus early on during my physics class (due to extremely nerdy reasons I won't go into). It did in fact help.

Until my physics teacher said, "I don't care what you're learning for elided, you have to show your work the old fashioned way!"

At least he let me use a slide rule.

In university, we learned our entire first semester of calculus in the first two weeks of physics, because we needed it to do the physics.

But we practiced it more in calculus.

In my senior year in high school, my science class was nothing but prep for the AP Physics 2 C exam, and on the first day we learned everything we'd need to know about differential calculus (limit definition, deriving the basic rules, and this video).

Then later in math class (AP Calculus AB because a scheduling conflict prevented me from taking the BC class) the instructor began by saying "I don't care what some of you just learned in physics, you're going to spend the next 2 weeks doing delta-epsilon proofs with the rest of us."

You were lucky. By the time I got there the curriculum had shifted so that all the high school Physics had been reduced so it didn't require any Calculus (and only one quick mention of the connection between the two was made).

But more than that, Trigonometry had just been moved up to grade 12 Math, which was the same level as the first Physics course... and the school had missed this fact and scheduled Physics in the first semester and Math in the second (we had also just switched to semesters, so that probably contributed as well). The end result was that there were only three of us in the class that had it, and the rest did everything via "scaled diagrams". Tests were hilarious, as the three of us would be easily done in 15 minutes (and allowed to go to the cafeteria) while the rest of the class repeatedly failed to complete the entire test in 76. Which meant the three of us repeatedly got more than 100% on the tests, because the denominator would be dropped to the level most of the other students got to.

You use it to derive the area of a circle! Or the volume of a sphere!

I had spent a decent portion of high school and junior high wondering where the fuck those two formulas had come from, and was beside myself with joy when I finally got to multivariate calculus and thus had the tools to derive the formulas for myself. :-D

I was extremely gleeful to go from first principles to the eqn we used to calculate the duration of orbits using the POWER OF MATH and also a pencil.

It's even the stopping point for college students if they aren't majoring in science or engineering. And for most of them, while there is more breadth once you break through those three semesters of intro calculus, wind up at a deeper formulation of calculus like multivariate calculus or real analysis or differential geometry or algebraic topology or however else you'd care to phrase it.

The lion's share of the students who are specifically steered into the discrete side of mathematics afterwards instead of analysis are mathematicians and computer scientists. They're getting the combinatorics and the graph theory and the solid formulation of propositional and first-order logics that have (I think) far more practical application in the real world. Even on the analysis side, I think it's a crying shame that we ask humanities students to study calculus instead of linear algebra.

(As a smug graduate with a prestigious degree in science, I cannot lower myself to directly suggest that a deeper appreciation of statistics would also be useful. But please do seek out that recommendation from someone who isn't too proud to mention it.)

Combinatorics and statistics are key. I'm fond of calculus because I studied stuff that uses it, but, yeah, these discrete topics are more important for things like bullshit detection.

I wish bullshit detection was a course in itself.

Critical Thinking comes close with some instructors.

I've never seen that offered as a subject here in Australia, but I wish it was - where's that taught?

UW (James' alma mater) has it on offer. Here, have a look at the syllabus.

Ooh! I just wish that sort of thing was presented as a core high school subject.

There was actually a mini-course in critical thinking in my fifth- or sixth-grade class, I forget which (I spent two years with the same teacher and essentially the same classmates). It was the late seventies. There was a textbook and everything. They talked about reasoning from prejudice, emotionally loaded statements, various logical fallacies.

My understanding is that whenever people try this in primary or secondary education, it's politically unpopular because it's considered a stalking horse for liberal secularism.

Gotta hate that left-leaning bias of facts...

Again, in the close but not quite category -- my friend was part of the IB (International Baccalaureate) program, which offered epistemology courses.

Required you to take those, actually.

Speaking as one with both a liberal arts degree and an applied science degree, I think I can safely say that the discrete math (particularly combinatorics and probability) and the statistics were easily the most useful math classes I have taken in the 20-year period between the start of my HS calculus class and the conclusion of my statistics class.

The most useful things I ever learned in math were how to dissect a real-world problem and turn it into equations, how to make rough estimates, and how to restate my problem with my calculated answer to see if it makes sense.

As all the kids are saying these days, "This."

The most useful things I learned in math *ever* are basic trigonometry, geometry, and fractions (costuming and cooking). But I learned those before the beginning of my calculus class. ;-)

I'm not sure why a humanities student would benefit more from linear algebra than calculus. My own "you could actually use this, Citizen" reccomendations are probability, understanding of descriptive stats, and the use of arithmetic, algebra, and approximations for back of the envelope modeling.

I feel that calculus, being about instantaneous rates of change and areas of figures bounded by arbitrary curves instead of straight lines, is all but completely useless, outside of science and engineering and specific humanities fields such as economics or political science. So by my reckoning, linear algebra wouldn't have to clear much of a hurdle to be a measurable improvement. I think it reaches that level; thinking about performing a series of closely related calculations in parallel and considering the entities involved as unified multidimensional objects instead of lists of raw data has significant merit. Also, linear algebra is an important tool in many forms of modeling that would be a valuable part of someone's toolbox if it were there.

This is not to detract from my admiration of your list of valuable mathematical skills.

(deleted comment)

Jackson drilled in the techniques for solving differential equations with families of special functions. But I didn't retain them for very long.

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Also, the expansion of the div, grad and curl operators in spherical and cylindrical coordinates.

I had a horrible moment my senior year in college. I was taking a numeric analysis course, required for my computer science degree, and the closed-book takehome required us to do an integral. I came up to the teacher and said "I'm not going to look at *your* textbook, but can I please look at my freshman textbook to remind me how to do an integral?" He was bemused that anybody could forget calculus but gave permission.

Analysis of algorithms, however, I continued to understand well after I left college; nowadays I can still look at something blatant and say "Who, that increases geometrically, that ain't good", although I certainly couldn't take an arbitrary piece of code and determine what the constant was.

No, it's just that every once in a while I come across a problem that would be most easily solved with calculus and I can remember doing something similar in the past but not how I did it.

Bigot! Bigot!

I bailed out after the third semester of college-level math, matrix transformations and other such esoterica required for EE. Only thing I can remember out of all that is what an integral sign looks like.

(In my bigot's defense, I will say that my courses were further in the past than yours.)

He used to hang out with Tintin, didn't he?

Edited 2010-10-22 16:51 (UTC)

Hi fellow bigot!

Actually, it's been over 30 years since I studied any form of calculus. And within the last couple of weeks I've seen that I need to remember a whole lot of it in the next two years (network performance issues, FWIW). Wheee!!!!

Today's xkcd reminded me of the bigotry of trig. Trigotry, if you will!

Chief Sohcahtoa weeps a single tear.

:: Chief Sohcahtoa weeps a single tear. ::

Ouch. I think I just threw my brain out. I'm blaming you.

Oddly enough, I've never used that mnemonic[1] precisely because I'm just as likely to come up with the wrong syllables like in the strip[2]... so I got used to deriving it with the basic triangles and the curves whenever I forgot it.

[1] Actually, I forgot it even existed. It took me a while to figure out what the joke was.

[2] I'm the type of person that when I was told that "you can tell which hand is your left because when you hold it up it makes an L", I instinctively hold up both hands in the way that makes both have an L... because that's what I'm looking for.

Usually, when I can't remember which hand is right and which is left (which is most of the time), I can't really remember which way an "L" is supposed to go, either.

So I just imagine that the direction I'm facing is the front of the boat, and then remember that "port" and "left" both have four letters, and then I know that the side which would be port is left, and the side which would be starboard is right. Easy!

(Note: I learned to sail in small craft on the Charles River. Messing up "port" and "starboard" usually meant swimming in water which, at the time, wasn't really something you wanted to swim in. It's much better now, but "port" and "starboard" were really, really drilled into me.)

I don't know how widely this applies, but within the SCA groups I've played with, steering directions are almost always given as "Sword side" and "shield side"

Since xkcd does not have dates in its archive, for the benefit of future historians of James Nicoll I provide a link to said xkcd: Los Alamos.

In truth, I periodically go back and revisit my various math textbooks, whenever it annoys me that I've forgotten how to do most of what's in them. I never seem to make it as far as Diff Eq, though.

Differential equations was the moment when I realized that I couldn't just look at the equations and see the obvious connections anymore. I would have to do the homework not just to get the practice in, but to actually understand what was going on. It was my Humbling Moment.

My most recent humbling moment was when I realized I had forgotten the chain rule. Yeah, I hadn't done any calculus for quite a few years at that point.

Speaking of integration by parts, that reminds me of the afternoon that I taught my roommate calculus.

He was a brilliant CS major being put through college by his employer, in his last semester, who needed one final math credit to graduate and was in serious danger of flunking calculus. I knew the guy was way too smart and too quantitatively adept to be flunking calculus, so I figured I'd use the same technique I'd used when I picked up some extra bucks tutoring flailing math students in high school, and just have him do some homework problems while I watched over his shoulder.

What often happens with struggling math students is that they'll have crises of confidence, where (perhaps because they made trivial mistakes in the past) they just freeze up when they're on what is essentially the right path, and they can do much better with some encouragement. Miraculous-seeming results can be achieved.

In his case, one thing that was giving him a lot of trouble was integration by parts. And it turned out his problem was that he was trying to do almost all of it in his head. Every so often, he'd start to write down some intermediate steps in his work, and he'd apologize. I told him, look, I can't ever do these integration-by-parts problems myself without writing down what I think is u and dv, and then writing down the consequent v and du, and then plugging them all into the formula on paper. If I can't do it, someone who is having trouble with the homework assignments probably shouldn't be doing it. And by drilling him over and over to write down all the steps in his work, I got him through that, and through all the other stuff too, and he easily passed the course.

So he taught me to ski.

Yep. No matter how hard the TAs tried, I could only get so far into Diff.Eq and partials until their voices went into "Charlie Brown's Teacher" mode. Maybe it was that concussion I had as a kid, or maybe I was born without the partial differentials region in my brain... but that was the point at which math (and my budding science/engineering career) stopped for me.

-- Steve's calculus has completely rusted solid now... can't even do simple derivatives anymore. *sigh*

The worst thing Condorcet ever did was to invent the curly ∂ symbol for a partial derivative. We could probably have gotten by with just regular ds there, and it confuses math students everywhere by making them think there's something special about partial derivatives that they're missing. It's like the emperor's new clothes.

It does look smart when you draw a slash through it Feynman style.

I have a friend who has been known to take higher-level math classes for fun.

Calculus? Isn't that the stuff the dentist scrapes off your teeth twice a year?

Yeah, me too. (Math major in college, computer geek before and ever since. And I left college 33 years ago.)

"I don't want to sound like a bigot" gets me 2980 hits on Google. Yours is at the top. It is one of the rare examples that is not followed (immediately or not) by the word "but."

We should make a habit of emphasizing how much we don't want to sound like bigots. "I don't want to sound like a bigot, but do you know how late the library is open tonight?" "I don't want to sound like a bigot, but Jefferson City is the capital of Missouri."

Capitalist!

Ah yes. "I'm not a racist, but this ice cream is delicious!"

Um, yeah. I took the prizes in both Grade 13 and first-year university calculus and I still would need a serious refresher to brush it up, to say nothing of the more serious analysis courses I took later (except for simple formulas like differentiating / integrating a polynomial expression).

It's sad, at one time I used to be able to do the full integration by parts for proving that a solid surfaced Dyson Sphere simply could not work. The whole 'no gravity outward to remain upon the inner surface and consequently fall into the center sun' thing. (it was a classical charged body proof taught to us in our EE course)

These days, I'm lucky to remember SOH-CAH-TOA without saying it out-loud.

Doing it coordinate by coordinate is the hard way anyway; the easy proof is to use Gauss's Theorem plus spherical symmetry. (But Gauss's Theorem is really just a very generalized statement about integration by parts.)

plus spherical symmetry

But doesn't that lead to spherical cows getting strewn across the landscape? And they're useless as livestock due to the complexity involved with figuring out how to optimally stack them in the cow barn (plus it's impossible to milk their perfectly smooth udders).

This is why there are oompa loompas.

+1 chocolate point

I think it's safe to assume that a Dyson sphere is a sphere without worrying about it being a slippery slope to spherical cows.

On the other hand, I now have the reverse image of a giant cow showing up on galaxy's doorstep, and after it's brought in it starts firing off Nicoll-Dyson laser blasts while a quintillion Trojans pour out and proceed to ransack the galaxy.

Heh. I can't diagram sentences. Haven't had to do that for going on half a century.

It was only seven years ago that I revisited math, made it through two calculus courses, elementary statistics, and some discrete math, and it's all gone. I believe, as someone upthread said, that the statistics and combinatorics would be the most useful, if I still remembered anything of them.

And I never got to the point where Euler's Identity was just OBVIOUS, which was my goal.

If you want that, you should go down the Pure Math route to Complex Analysis, which is Euler's Identity's natural home.

It's not obvious, nor should it be. My notes on that day were "-1 doesn't have a square root or a natural logarithm, and the ratio of those two non-existent quantities is the same as the ratio between the circumference and diameter of a circle." Buh?

I dropped out of HS math before even taking calculus. I was failing badly (had been diagnosed as learning disabled in math years earlier, for whatever that's worth), and none of the teachers were willing to help me. Thanks, education system!

I don't want to sound like a bigot

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thank you, yes.

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