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<p>Which is why the exporters are celebrating. They’ve never fared better against Chinese manufacturing.</p>
<p>But relatively it’s “high” nonetheless (at least compared to India, China et al), or it was when the outsourcing craze began.</p>
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<p>Well said. Like others have mentioned, this isn’t a zero sum game. An Engineer could use the perspective a Liberal Arts Foundation provides and vice-versa</p>
<p>(Full Disclosure: I’m a High School Sophomore)</p>
<p>“But you need more importantly to understand how to see how calculus applies to the world and how it can model the world. Teachers are so frustrated trying to teach kids how to integrate and differentiate that they don’t have time to show kids how calculus can be applied to their daily life.”</p>
<p>Can you give an example of this in the daily life of a person who is not a scientist or engineer?</p>
<p>How does calculus apply to the real world & how does it model the world? Well, let’s see … the frustration I felt in my several college calc courses models the frustration I felt as the parent of toddlers … and the frustration I have experienced as a parent of teenagers. I would say that the very hard work I had to do to successfully navigate the world of calculus, which was totally “out there” to me, taught me how to navigate the world of parenthood (similarly out there). </p>
<p>Oh, you mean LITERALLY. My bad.</p>
<p>I can give a great example, although it will be (intentionally, on my part) a source of ambivalence:</p>
<p>The mortgage securitization phenomenon – which until approximately last month has been lowering the cost of home financing steadily for about a generation – had its genesis in people’s ability to use mathematical functions to predict reasonable ranges of prepayment and default characteristics for different types of mortgages and borrowers with different credit characteristics, and also to determine how much regional diversification was necessary to provide relatively homogenous characteristics among different portfolios. While you could do stuff like that without calculus on a rough basis, calculus permits a greater degree of precision and confidence, which probably lowered borrowing costs, regardless of credit level, by 50-100 basis points (that’s just a guess – I haven’t seen a real study).</p>
<p>(Of course, sometimes the algorithms turn out to be not so reliable. Not because the math is bad, but because of a kind of Heisenberg effect: when you make risky loans more affordable, the new risky loans may be even riskier than the old ones on which your model was based.)</p>
<p>I don’t use calculus in my daily life, and most people do not. However, I was pragmatic when it came to my kids’ college preparation choices in high school. My advice was- you may THINK you know what you want to do with your life, but that will probably change. Leave your options open by preparing yourself such that you can choose any major once you leave for college. That included the most rigorous classes (AP) in all fields. </p>
<p>Personally speaking, I did not have an adequate background in high school in math and science. I was a musician, took lots of humanities and stayed away from sciences (no physics, no upper level math, easiest chemistry, etc). Once in college, I could not have pursued engineering, math, science, or pre-med without serious remediation. It was as if doors were shut from the get-go. </p>
<p>My son has a friend right now whose dreams of going into health professions are going to be sidelined because of a science class. Does a physician use calculus? No. But she has to take a year of it to get into med school, as well as Chemistry, Physics, Orgo, Bio. I’ve never heard of someone being unable to get their med school requirements because they couldn’t pass english or humanities- it’s usually the sciences that do them in.</p>
<p>All I’m saying is that it’s wise for high school students to prepare themselves so that all options are available.</p>
<p>Re: Calculus…</p>
<p>Yeah, not everyone uses calculus. When I used to tutor, I had to constantly explain to my students why they would ever possibly need geometry. They insisted that nobody was ever going to hold them up at gunpoint and ask them to prove that two triangles were similar.</p>
<p>And yeah, I would say, that was probably true.</p>
<p>Still, once you’re proficient in geometry, there’s really no end to the sorts of things you see it actually applies to. It’s amazing. Divide a pizza into fifths. Figure out whether it’s shorter to go around the block or to cut across the field. Estimate whether you’re going to get rained on if you walk under that narrow awning and the wind is blowing towards the building. Make your kid’s Halloween costume.</p>
<p>Like geometry, calculus is a tool. I’d say that geometry is more along the lines of hammers. Everyone should have geometry in their toolbox, because it’s pretty useful. Calculus is more along the lines of a miter saw.</p>
<p>And so, you ask, what the heck are you going to use a miter saw for?</p>
<p>There are some of us, in our lives, who will never, ever need to use a miter saw. And that’s fine, and there’s nothing wrong with it. Miter saws (and calculus) are not crucial for functioning in this world. But for those of us who’ve used a miter saw, you just start seeing all these amazing applications for miter saws… I could make a set of shelves for the garage… I could make a drawer for the kitchen cupboard so that we could actually use all the storage space in there… I could find the area under that curve and figure out exactly when the bathtub will overflow if I leave the faucet on at a particular rate of flow…</p>
<p>So yeah, you don’t have to use calculus, and we’re not judging you for not using it. It’s just like our miter saw, or our Kitchenaid stand mixer, or any other multi-purpose gadget that, once discovered, we feel as though we could never live without. But just as it’s difficult for a handyman to explain his love for a miter saw, just as it’s difficult for a gourmet to convey their affinity for their Kitchenaid stand mixer, it’s tough for mathy-sciencey-engineery folks to explain why calculus makes them a little dewy-eyed.</p>
<p>Wow.</p>
<p>I don’t know what a miter saw is. That’s probably really embarassing. I know what a “saw” is; I have a couple. I could buy a great set of shelves for the garage at IKEA. I would probably hire someone to build drawers for the cabinet. My father-in-law was a physicist with a full workshop full of tools and a 40-year woodworking hobby, and his drawers were . . . not so hot.</p>
<p>Those practical-uses-of-geometry examples are great for third graders, but you hardly have to understand all the marvels of the Pythagorean theorem to understand that cutting across the diagonal is shorter than walking around the block.</p>
<p>And, as for calculus – are you suggesting that calculus is useful only if you lack common sense entirely? Why would you want to know exactly how long you could leave the water on before your tub overflowed? How would you get the precise formula for the curve of your tub, if you did want to know that? How would you know the rate of flow? (Wouldn’t it be faster to let it overflow once, watching the clock and the rate of flow, and then you would know the volume of water it held, which would give you the tools to calculate an answer arithmetically for any constant rate of flow?) </p>
<p>When I was taking calculus years ago, I remember being pleased to know I could calculate the volume of a donut. I also remember that thought was invariably followed by “Who the hell wants to calculate the volume of a donut?” and “Actually, I can only calculate the volume of an ideal donut.” Not such a thrill, actually.</p>
<p>aibarr, I must note that you gave a couple of good examples of when a person might find a use for a miter saw…but none for calculus.</p>
<p>Again, how about a real-life example?</p>
<p>Besides, I would argue that calculus is not a tool like a miter saw, but more like a backhoe. It’s most useful for big problems, requires a lot of training to use, and is generally operated by professionals.</p>
<p>The computers you are all using would not exist without calculus.</p>
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<p>I know I’m an engineer and that the way I look at things in the privacy of my own head may make liberal arts majors want to scream “NERD!” but when I would walk across campus I would often analyze the shortest distance between the library and the civil engineering building. They had diagonal walkways that cut straight through everything, but when there were hills, the walkways would follow the contour of the hill… made it a little more complicated than what a third-grader could do.</p>
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<p>This is kind of the difference between the engineering-trained mind and the non-engineering trained mind. The way I look at it is far nerdier. I could sit there and time how long it took for things to overflow in my garden tub in my apartment, or I could estimate the curve of the tub, estimate the flow of the faucet, and do a quick bit of calculus to figure out how long I can walk away for, at least, until the tub overflows. (YES, I <em>know</em> it’s insanely geeky, that’s why I don’t tell people that I’m doing it. Still, I can walk away from the tub for a good eight minutes while you’re checking back on your tub’s progress every couple of minutes.)</p>
<p>I also kick butt at those “guess how many M&Ms are in the curved glass jar” things. The only variable is knowing what the approximate density of loose-packed M&Ms is. (This is why I typically do these things in the privacy of my own head.)</p>
<p>I have a fun car. Quick, sporty. It’s fun to accelerate into curves, but I’ve had some speeding tickets, so I start off ~10mph slower and accelerate so that I hit the curves at a max of 5 mph above the speed limit. I don’t actually do calculus on this (because you shouldn’t do calculus when you’re driving) but since I have enough familiarity with how those curves look, I know I should hit 60 mph <em>here</em>, then 65 about <em>here</em>, and that should put me at 70 mph <em>here</em>, at the outer arc of the curve.</p>
<p>I have this really curved coffee cup provided by my company, and I’m kind of a snoot about my coffee, so I have a french press, and it measures things in milliliters. I’m mildly embarassed to admit that I approximated the curve of the coffee cup and integrated from the lower radius in centimeters to the upper radius in centimeters to figure out about how many milliliters of coffee I needed to make in order to not have my cup overflow when I poured the coffee into my cup from my french press. See?? Seeee why I didn’t give examples?? =P </p>
<p>It’s one of those things that can be used everywhere, but you don’t ever really want to say what you use them for, because it’s just ridiculously overkill… but it makes it just a little bit easier. Pour coffee like a pro? Maybe you’re awesome at coffee. Maybe you just do calculus in your head like the lame dweeb that you are.</p>
<p>It’s like this tool where once you’re adept at using it, you start seeing integrals and derivatives in everything, and you habitually bring out the shotgun.</p>
<p>Now, I do use this in my everyday life, as an engineer. I have to calculate the centroids of weird shapes pretty much all the time, to calculate the moments of inertia of various shapes to understand how they’ll behave when I make them out of steel and hang them on a building. So while you guys may think that it’s like using a shotgun to kill a fly, in my mind, I already know how to use the shotgun pretty well and I’m sure as heck going to nail the fly if I use it. Also, if I solve things using more than one method of calculation (I do a lot of these things using geometry <em>and</em> calculus) then I’ll end up with more confidence in my answer.</p>
<p>I just don’t tell anybody I’m doing it. If I use calculus to make my morning coffee, I know full well that it makes me a freak.</p>
<p>Still, all these mental jumping jacks are why I can look at a numerical situation and figure it out very quickly. That’s what engineering and thinking-in-calculus have trained my brain to be able to do, and it’s the very thing that my job requires. “If the computer has calculated this correctly, this should be at about <em>this</em> number… and it is; good… and this should be about <em>here</em>… Okay, excellent, this is correct.”</p>
<p>Now, I don’t make fun of <em>you</em> for <em>not</em> using calculus. Please don’t make fun of <em>me</em> for using calculus. It’s not like I’m getting out my slide rule when I do this stuff, it’s just that I’ve done it enough and I know what enough curves look like that I can approximate these things pretty quickly and with little effort… I just do it all the time, so it’s a useful solution for me. Don’t go out and learn calculus just for the mundane little details of your life, though, that’d be pretty unnecessary. You buy a miter saw if you’re going to install crown molding, you learn calculus if you’re going to be using it fairly often. Common sense and a little extra time can easily take the place of most of the things I use calculus for. Still… if you’ve got it at your disposal, it’s pretty handy.</p>
<p>aibarr, your posts are very eloquent; you make me wish I remembered more of my college calculus than I do!</p>
<p>I do what I can, owlice… Just glad that the first post after mine didn’t make fun of my weird calculus tendencies! ;)</p>
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<p>Doesn’t this sound like the “plastics” commercials? I still don’t really understand what plastics really <em>are</em>… =(</p>
<p>Aibarr, we all do stuff like that. Sometimes I read the fine print on forms!</p>
<p>Alibar, great post!
Sound like stuff that makes a great essay If you are a applying for college. 
FYI, My daughter just a made video to enter to Seventeen Magazine contest for scholarship, something about why teen should not get pregnant, and she made a film similar to your post. It was about why her friend who likes math is inspired to studying engineering. I think they are going to share the award if they win.</p>
<p>Maybe if someone at Hamilton Beach had used a little calculus, I wouldn’t have a coffee pot that leaves a messy puddle on the counter everytime I pour. You’d think figuring out how big/wide/long the spout needs to be would be trivial but apparently it’s not because this is the second coffee pot we’ve had this problem with.</p>
<p>I already participated on the why calculus thread as a pro-calculus person - though I think the argument that statistics is more useful has merit. I had to have calculus for architecture, but never actually used either in grad school or in my real life. (I do use trig occasionally.) Nevertheless I have no regrets learning calculus. I felt like it was one of those subjects that lets you appreciate the beauty of math the same way Shakespeare helps you appreciate the beauty of language. It’s not like you need Shakespeare in daily life, though it can be fun to recognize the famous quotes.</p>
<p>Why do you need to know calculus? I’ll ask you, why does my son, a future engineer, need to know what Bunburying is? Why should he have to write an essay about it? I’ve never seen anyone more confused in my life!</p>
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<p>For the same reason that if my former engineering boss had read “The Handmaid’s Tale,” he would have sensed trouble when I wrote “Nolite Te Bastardes Carborundorum” on a post-it note and stuck it on my file cabinet!! As it were, everyone was bowled over when I quit a month or so later and added myself in with the 40% attrition that that particular branch was afflicted with…!! ;)</p>
<p>Well you could also have just been less mysterious and put up a post it note that said, “don’t let the bastards grind you down”. LOL, sounds like you made an excellent (and popular) move.</p>
<p>Friend of mine, service academy graduate, had illegitimi non carborundum inscribed on his ring.</p>
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<p>[Illegitimi</a> non carborundum - Wikipedia, the free encyclopedia](<a href=“http://en.wikipedia.org/wiki/Illegitimi_non_carborundum]Illegitimi”>Illegitimi non carborundum - Wikipedia)</p>
<p>The somewhat dubious use of the phrase has been around for a while. What a great inscription for a class ring.</p>