16 ms·
Pi is Wrong
- Benjo 16y agoThe pdf claims that for simplicity sake, the constant pi should have been a factor of two larger. Reminds me of electrical engineering "mistakes" such as the convention establishing electrons as negatively charged; or the ohm being very small/amp being very large compared to everyday usage.
- amalcon 16y agoI was about to write something very similar. There have always been a small number of people who claim that electromagnetic charges should be reversed: that is, that the positively charged particle should logically be what "moves" in the circuit. Most people just look at it, shrug, decide it doesn't really matter, and get back to doing it the way they've always done.
- teilo 16y agoThe small minority of people may have a point, but it's the wrong point, since the real problem with the notation of electric charge has nothing to do with the formulas which are used, but with the connotation that people give them of somehow representing a surplus or deficit of electrons, neither of which is true. The only real relationship between the charges is that they are opposite. The terms positive and negative have no other meaning. As for the formulas, either way will work just fine, as long as everyone is consistent. Pick something and stick with it.
- Benjo 16y agoAre you saying people confuse charged ions with flowing current in a circuit? My view of the problem is that it's hard to grasp what current actually is. The water in a pipe analogy works, but it's confusing because the electrons flow in the opposite direction of the hcurrent, making the "water" positively charged electron holes.
- sid0 16y ago> Are you saying people confuse charged ions with flowing current in a circuit? Charged ions moving in an electrolytic cell is charge flowing in a circuit. Electrons are not the only way to have a current.
- teilo 16y agoThat's the thing. When we are talking about current, we are not talking about how many electrons are moving, but about the transfer of energy from one place to another. The water analogy just doesn't work, because while the current itself flows at nearly the speed of light, the electrons themselves move very slowly. In an AC current, the electrons don't flow at all. They vibrate. And in a liquid, the energy transfer can just as well be by means of anion flowing backwards, as cations flowing forward. Yet we think of the current as only flowing in one direction. You see the problem? Trying to think of electrical energy as a "flow of electrons" OR a "flow of protons" completely skews one's understanding of what is taking place.
- sesqu 16y agosomehow representing a surplus or deficit of electrons, neither of which is true. If an electric charge of -4e doesn't represent a surplus of 4 electrons, what does it represent? Surely not a deficit of 4 protons, since they are much harder to move around? Perhaps you feel it represents a transient property of matter that just so happens to be closely related to, but not defined by, the movement of elementary particles? That's a reasonable position to take, if you don't have to effect a charge.
- Tiomaidh 16y agoAnd that electrical engineers tell you that current goes from + to -, while physicists say it goes from - to +. And the north magnetic pole is at the geographic south / vice versa. And horsepower != 1000 Watts. And Farads are bigger than I'd like them to be.
- anigbrowl 16y agoHe has a point. I've always found the diameter:circumference ratio so much more natural for thinking about geometry that when I used to program regularly I had a macro called 'tupi' which would expand to (2 * pi) at compile time. Whatever mental blind spot I have about it was causing me to introduce a bug about a quarter of the time I needed to reference pi, probably because some part of my brain was continually asking what point there was to a constant that needed doubling in order to be useful.
- jerf 16y agoI just starting futzing around with a project using OpenGL and literally just last night wrote myself up a pi2 constant after the third time I found myself writing 2*pi. And three's the charm for refactoring.
- ez77 16y agoBut diameter:circumference :: 1:pi, not 1:2pi. Do you mean radius:circumference?
- anigbrowl 16y agoQuite - making this sort of mistake repetitively was why I made a substitute. It's like a word I mispronounce every. damn. time. :-)
- tbrownaw 16y agoWhole amps and handfuls of ohms aren't that rare, they actually match pretty well to what comes out of the wall socket. And that 1.8v or 0.85v or whatever it is these days space heater that runs your computer takes really quite a lot of amps.
- ori_b 16y agoOn the other hand, Farads or Teslas...
- amalcon 16y agoCoulombs are my favorite, because it's the fundamental amount of "something" (as opposed to "something per time") that most of these can be traced back to: Ampere = Coulomb/second Farad = Coulomb/volt
- Benjo 16y agoYes, but >=kiloamps and <=milliohms are that rare, which makes it seem like the whole scale is off by a factor of 1000 or so.
- sliverstorm 16y agoFrankly, I have always appreciated that Ohms are almost never partial. milliohms are a rare occurrence, and I just think that's great and works out well, IMHO. Amps being too large is unfortunate, but it's not a big deal.
- benbeltran 16y agoWell, next monday we can celebrate 6/28 as 2pi day or proper pi day... Just in time article.
- pbhjpbhj 16y agoSo you're going to celebrate refactoring a mathematical constant to give a neater presentation on a day chosen based an apparently illogical ordering scheme for dates. That has to class as irony. Out of curiosity: Does anyone here genuinely believe that Pi should be the circumference÷radius and hold that dates should be written Month/Day/Year ? I've heard one reasonable defence of American date ordering based on actual priority of information (roughly: "you want the month first to broadly narrow down the locus but the year will be assumed"). But I still go with English or just [truncated] ISO dates.
- elbrodeur 16y agoI use UNIX time. So there.
- pbhjpbhj 16y agoI suggest you wait until Wed 8 Feb 2169 01:15:07 GMT+0000 (BST) to celebrate
- Tiomaidh 16y agoI see where you M/D/Y people are coming from, but can you at least agree that "June 28, 2010" -> "[Month 6] 28, 2010" -> "6/28/2010" is at least founded in some kind of logic?
- mhartl 16y agoWouldn't it be awesome if somebody already had this planned, complete with a domain name, a compelling candidate for the new constant, and even a whole freaking manifesto written just to promulgate proper pi? I for one wouldn't want to miss out on that, so if I were you I'd hint hint be watching Hacker News quite closely on June 28. ;-)
- btilly 16y agoOld news. This ranks up there with the fact that it was a bad idea to use base 10 instead of base 12. Absolutely and utterly true, but completely not worth the switching costs.
- jessriedel 16y agoIt's still important for everyone doing math to know that the convention is bad, though, even if it's not worth switching. Then it becomes clear in several instances that slight blemishes in the beauty of equations are of human origin. It also help you think of 2pi as an object.
- BahUnfair 16y agoTeaching this in the classroom could engage a lot of students that might otherwise be bored sh*tless of the regular curriculum. For those that do pay attention it could open their minds to a new way of looking at maths as a human tool rather than some universal law. It's a shame its taken me till freshman year and reading this article to make the connection that a 6th of a radian is a third of one quadrant. I can't imagine how much simpler this would have been to learn if it was 2pi.
- cwp 16y agoCan you provide a reference for this? I'd like to know the reasoning.
- kinghajj 16y agoThe Wikipedia article on duodecimal should give enough reasoning.
- btilly 16y agoThe reasoning is that when we divide something evenly, we usually want to divide it into a small number of parts. 12 divides evenly into small parts better than 10 does, and so more often provides a convenient division. For instance if we assume that half the time we need to divide into halves, 1/4 of the time into thirds, 1/8 into quarters and so on, then over 90% of the time you wish to split something into 1/2, 1/3, 1/4, 1/6 or 1/12. All of which are trivial in a duodecimal system. By contrast only 56% of the time do you wish to split into the similarly easy 1/2, 1/5 or 1/10 in decimal. Even if we say that 1/4 and 1/8 are OK in decimal, we still wind up with inconvenient repeating fractions over 3 times as often as duodecimals do.
- jessriedel 16y agoSame thing happened with the gamma function. MathOverflow: http://mathoverflow.net/questions/20960/why-is-the-gamma-function-shifted-from-the-factorial-by-1 http://mathoverflow.net/questions/20960/why-is-the-gamma-fun...
- JacobAldridge 16y agoWhen I saw the host and title I was concerned it may have been a rehashing of this urban legend - http://www.snopes.com/religion/pi.asp http://www.snopes.com/religion/pi.asp Relieved to see it was actually this article, which I've actually referenced a number of times in discussions with engineers to make myself sound like I know more than I actually do!
- Daniel_Newby 16y agoEven worse, in physics h-bar = h / (2 * pi).
- Dilpil 16y agoWhat about the fact that sin and cosine have such elegant Taylor series expansions if you use radians? In radians, sin = x - x^3/3! + x^5/5! - x^7/7!... In 'Double radians', we have a 2^n factor in front of each term.
- SamReidHughes 16y agoNo they wouldn't. This article is not talking about redefining what 1 radian means.
- carterschonwald 16y agothe idea may seem trite, but the pedagogical motivation for making certain symmetries more apparent in mathematics is sound. on an unrelated note, when will the scribd links switch to html5?
- ascuttlefish 16y agoI think any pdf link says scribd, even if it's not. Not sure why.
- bobmoretti 16y agoThe [scribd] in the title is actually a link to the same pdf, but on scribd.
- ascuttlefish 16y agoThanks! I was not aware of that.
- jmillikin 16y agoThe [scribd] isn't a comment, it's a separate link -- you can click on it to view a broken version of the original document. carterschonwald is commenting that the Scribd link uses Flash, rather than the recently released HTML5 Scribd implementation.
- carterschonwald 16y agoprecisely :)
- ascuttlefish 16y agoJebus, I never noticed that. Thanks!
- Qz 16y agoAs long as the html5 has buggy dancing scrollbars of doom on firefox, I will be grateful for flash scribd links. Everyone can hate on flash all they want, but the flash version in this link was a big relief compared to the html5 version.
- deleted 16y ago[deleted]
- codeflo 16y agoUnfortunately the article is down at the moment, but there's a beautiful identity that suggests that maybe pi/4 is a constant of nature, not pi: pi/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 ... That's arguing from pure mathematics. Judging from the comments, I think the article argues (from kind of an engineering point of view) that 2pi would be more convenient.
- evanmoran 16y agoWhen I read this article a while back the part that impressed me was how in intuitive radians become: 2/3 * NewPi = (2/3's around the circle in radians). It is a much more intuitive way to think about angles. Ask a third grader, how much cherry pie is missing. "About a two-thirds" they will say. They don't mention PI, and right now no one does. This is the way people think about angles naturally. NewPi makes this more intuitive by allowing you describe angle as a number between 0 and 1 (which is usually the way to go, see splines, animation, etc). 0.25NewPi just makes sense. It is a fourth of a circle, and this way of thinking would help kids understand radians instantly. Probably the only drawback is when doing wicked tricks on a snowboarding game such as SSX. Doing a 1080 just sounds cooler then a 3, but which is more intuitive?=)
- amalcon 16y agoYou can do this with regular pi; you only need to use diameter-ans instead of radians. You can do it without a pi at all; there's an actual (used) unit called the "cycle". 1 Hertz is defined as 1 cycle/second. The only problem with these units is that, like with degrees, d/dx sin(x) != cos(x). It messes with calculus.
- jasonkeene 16y agoHah exactly my thoughts!
- aston 16y agoNot true. Calculus would be the same (a radian is a radian). sin(pi + x) != cos(x) in the new system, though.
- zbanks 16y agoChain rule: Let x be angle in radians, y be angle in diameter-ians (2pi) x = 2y d/dx sin(x) = cos(x) d/dy sin(y) = d/dx sin(2x) d/dx (2x) = 2 cos(2x) = 2 cos(y) It's the same reason why you use radians for angles in calculus: degrees mess it up. http://en.wikipedia.org/wiki/Trigonometric_functions#The_significance_of_radians http://en.wikipedia.org/wiki/Trigonometric_functions#The_sig...
- detcader 16y agoI seriously have always suspected this. If you're going to use a value to represent the perfection of a circle, why not take the derivatives of its properties (area, then perimeter, and once more) until you get a constant? 2pi is that constant.
- deleted 16y ago[deleted]
- cgs1019 16y agoOne of my math professors pointed out that to be consistent, "π, φ, χ, ψ, ξ, and ι" should actually be pronounced "pee, fee, khee, psee, ksee and ee-ota," which I found kind of funny and fascinating. Of course, common convention beats out pedantic propriety and rightly so, I think. This sort of thought-provocation is quite valuable nonetheless, if for no other reason than to keep us aware of that about which we do not readily think.
- JBiserkov 16y agoThat's exactly how we pronounce them in Bulgaria (neighbor of Greece).
- edanm 16y agoVery interesting article. On a related not, check out the book "Negative Math": http://www.amazon.com/Negative-Math-Mathematical-Rules-Positively/dp/0691123098/ref=sr_1_1?ie=UTF8&s=books&qid=1277192051&sr=8-1 http://www.amazon.com/Negative-Math-Mathematical-Rules-Posit... This book builds up a mathematics in which multiplying two negative numbers gives you a negative, not a positive. The results are very interesting, particularly this: There are no complex numbers. The root of -1 is -1. This is another example of something you never think to question, you always assume is "just the natural way", but which was a somewhat arbitrary choice and can be changed.
- crazyjimbo 16y agoIt's also inconsistent if you assume that multiplication is distributive over addition: (-1 + 1) * -1 = -1 * -1 + 1 * -1 = -1 + -1 = -2 or (-1 + 1) * -1 = 0 * -1 = 0.
- deleted 16y ago[deleted]
- crististm 16y agosince when -1 * -1 is -1???
- edanm 16y agoPlease read my reply: I linked to a book which builds a Math where -1*-1=-1.
- crististm 16y agoI remember you can define algebras however you like with arbitrary commutativity and associativity rules but in this case you should also apply them and not assume they work in a certain way. If -1 * -1 = -1, this algebra disallows distributivity rule and the calculation only proves that.
- edanm 16y ago
- joeycfan 16y agoI pronounced the new Pi as 'tipy' which is ironic, since it has three legs and is therefore NOT tippy....
- ptarjan 16y agoPosted to mathoverflow: http://mathoverflow.net/questions/29070/is-defining-a-constant-2pi-more-elegant http://mathoverflow.net/questions/29070/is-defining-a-consta...
- jonsen 16y agoI find your downvotes and the rejective spirit over there puzzling. (Perhaps it's just to overflow ;)