5 ms·
"However, the exponential effects of aerodynamic drag" quadratic? otherwise we're in trouble
by leecarraher 10y ago
"However, the exponential effects of aerodynamic drag"
quadratic?
otherwise we're in trouble
- aetherson 10y agoPeople in informal language constantly use "exponential" to mean "more than linear." Which drives me completely insane, but I think it's time to just accept it.
- herge 10y agoWell, it's big-O of exponential!
- JoshTriplett 10y agoPeople often use big-O (asymptotically bounded above) when they really want big-Θ (theta, asymptotically bounded above and below). Strictly by the definition, for instance, binary search is O(e^x), as well as O(x^12), O(x), and O(lg x). However, binary search is Θ(lg x), and not Θ(any of those other functions).
- JadeNB 10y agoI think that your parent was making precisely that point as a joke.
- mjhoy 10y agoWith big theta you strictly have to talk about best and worst cases, because for e.g. insertion sort, what's true of worst case is not true of best case (and vice versa). For big-O, what's true of worst case is also true of best case, so talking about worst case suffices. Big-O is less precise and therefore more useful, because average case usually = worst case anyway.
- smallnamespace 10y agoWhy can't you use big theta to talk about average case?
- mjhoy 10y agoYou can, but strictly speaking you have to say, "big theta of the average case"!
- xutopia 10y agoMaybe you can explain it for the ignorant masses in terms we would understand? :D
- sanderjd 10y agoIt's the difference between x^2 (quadratic) and 2^x (exponential). Plug in some increasingly large values for x and you'll see how different they are.
- distortedsignal 10y agoLinear: n * x^1 Quadratic: n * x^2 Exponential: x^n In all cases, x is assumed to be a variable, and n should be assumed to be a constant > 1. If you pick the same value for n and put these functions into El goog, the answer should become fairly clear.
- Dylan16807 10y agoThat's not right at all. Exponential is constant^x. Also you can put "n *" in front of all of them if you want, but multiplying by a constant is usually omitted because it doesn't affect the shape of the graph.
- aetherson 10y agoThat's not correct, exponential should, in your example, be n^x, not x^n.
- sixbrx 10y agoHell I'd be happy if it were used to describe sequences with more than just two values. I hear it constantly used in comparisons of just two quantities where the intended meaning is just "a lot more".
- nickff 10y agoYes, this gets to me too. You can fit any sequence of n points with a curve described by a polynomial of n-1 degree. therefore, you need at least 4 points to know that the curve is not cubic, and an infinite number to know that it is exponential (though you can usually surmise as much sooner, because many natural phenomena are exponential or logarithmic).
- 83457 10y agoPeople in informal language constantly use "insane" to mean "frustrated."
- deleted 10y ago[deleted]
- yessql 10y agoWhat frustrates me is people saying "exponentially more" when comparing two things, like the Bolt has exponentially more range than the Leaf. I mean, you could fit an exponential curve to those data points, but also logarithmic, so why bother?
- alanh 10y agoYes, people who use “exponential” to describe the difference between two numbers are almost certainly illiterate in one way or another.
- ScottBurson 10y agoThere's no hope of curing this in the popular press, but I think technical people should still be careful with the term. I think it's great that someone's called it out on HN.
- hollerith 10y ago>I think it's time to just accept it Well, I'll continue to downvote comments here that do it. Mathematical concepts are an important part of our culture and of the public conversation.
- termain 10y agoIt's quadratic. Polynomial would also have been acceptable. But what they meant to say is "superlinear". Like aetherson, this drives me nuts.
- yardie 10y agoI'm guilty as well. Even though I know, mathematically, the difference colloquially it just roles off the tongue easier.
- ScottBurson 10y agoYes. To be precise, power, which is energy per unit time, is cubic in velocity: it takes 8 times as much power to go twice as fast (because of air resistance). But for a given distance, the energy required to traverse it is quadratic in velocity: it takes only 4 times as much energy to cover the distance at twice the speed, because it takes you half as long to get there. ETA: There are other sources of drag, of course -- tire drag, and mechanical friction in the drivetrain -- but AFAIK the power required to overcome those is linear in speed, and so the energy is constant for a given distance. Anyway, at highway speeds, air resistance dominates.