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Happy Tau Day
Forget about Pi Day, today we celebrate something twice as good: Tau Day. For far too long, Pi has been the bride and Tau has been the bridesmaid. As Michael Hartl points out in The Tau Manifesto, "Pi is a confusing and unnatural choice for the circle constant." He is giving a talk at the California Institute of Technology based on the Manifesto, with pie served at the end. "Twice as many as you might expect," he says.
ha ha. You're not a nerd. ha ha!
As Weebl and Bob might say...
ha ha. You're not a nerd. ha ha!
shut up Nelson
Karma: Excellent. 15 moderator points expire sometime.
I would expect 2 Pi.
It's 4*Pi, which makes it TWICE as kick-ass as Tau!
SJW: Someone who has run out of real oppression, and has to fake it.
oh god, this argument again...fuck my life.
I guess I will have to go down to Bakers Square and get 2 pies today.
Time to offend someone
For the greater good!
There was a Pi Day post, so you can be discriminatory and not have a Tau Day post.
I have never heard "Shut your Tau hole!",and yet I hear "Shut your PI hole!" almost every day.
No, I wouldn't call this news for nerds. Because it's not news. But I do think it's relevant to nerds, especially those that take interest math and music.
It's creative. It's mathematical. It's something that a non-nerd would struggle to appreciate. It's even under idle. So what's the problem?
Wasn't this posted last year?!? I mean come on editors!
Back in 7th grade the teacher wanted us to show our work. Most of the time I could figure out the stuff in my head, so I didn't want to do that. In order to freak out the teacher, I memorized the multiplication table of (single digit) * 3.14
After that I could write stuff like 67*pi = 188.40 + 21.98 = 210.38 (vertically)
The teacher never commented on showing my work after that...
All ideas^H^H^H^H^Hprocesses in this post are Patent Pending. (as well as the process of patenting all postings)
Angles: 2Pi in a full circle? Somehow it's more satisfying if the proportion of a circle were between 0 and 1: xTau. So half a circle would be (1/2)Tau, not the whole-looking 1Pi.
If you look at various "important" equations, you often end up seeing 2Pi in there. Gaussian, Riemann, Fourier. Another one: h/2Pi, h being Planck's constant. Why not make 2Pi the constant?
Even Pi*r^2 is more appropriate as (Tau/2)r^2, if you compare with (1/2)mv^2.
I have to admit I was not violently emotional when I read the argument though.
Yes. The idea of a mathematical notation that has been around for generations being replaced with something that makes more sense is something I would consider "News for nerds". While the idea has been spoken about before on slashdot and thus Tau it self is not news, Today being a day to promote it is news.
Teach both sides.
93rd rule of Slashdot: No matter how obvious my sarcasm is, my comment will be taken seriously by someone.
Tau is already super overloaded. In grad school, we always wrote "2pi" as k_k, that is, k with a subscript k (it doesn't look as weird in handwriting, because the subscript).
Of course, it's pronounced "cake".
http://www.youtube.com/watch?feature=player_embedded&v=jG7vhMMXagQ#at=290
I was thinking we already had a Tau Day article on Slashdot, but searched revealed that 3/14 was Pi day: http://science.slashdot.org/story/11/03/14/1329210/Happy-Pi-Day
Just because the U.S. is a republic does not mean it is not a democracy. Democracy/republic are not mutually exclusive.
We have working with half the radius of the circle or twice the circumference given its diameter. Radius makes little sense, and it's 1/2 diameter...
Support my political activism on Patreon.
In modern greek, the letter "" is pronounced "taf".
Wait, it's not the 62nd of August yet... ...you insensitive clod!
"... Yer a Tau!"
3.141592 vs 6.283184. And odd numbers are clearly superior to even numbers :).
Besides, Pi is now so deeply ingrained in my brain, I'm afraid there is no hope of updating my brain to the Tau version.
:)
I like the idea of tau, especially as a teaching tool. The intuition for dividing up a circle is much better. The arguments over superfluous 2's in numerators or denominators seems, frankly, stupid to me--there's some constant floating around, what it is isn't really crucial to understanding the idea. However, I think it's pretty pointless for me to bring up tau in a college lecture as students have already been indoctrinated to think in terms of pi. I'm not optimistic anything will ever change at the high school level, so it's all academic really (no pun intended).
Tau is already used to describe the relationship of speed to the apparent speed of the passage of time. Also, both Pi and "Tau" are irrational, and since Tau is 2pi, this seems like a huge fucking waste of nerd time.
I still cannot find the droids I am looking for...
I might agree that it makes sense to switch from pi to tau after I agree it makes sense to change from imperial measurement to the metric system.
Note that at this time I do not agree that it makes sense to switch to metric, so we may be in for a bit of a wait...
Aren't Space Marines, perhaps even the Imperial Guard the best war to deal with the Tau?
"...a civilian some of the time, a soldier part of the time and a patriot all of the time." -Brig. Gen. James Drain
Pi is wrong, cute video
http://www.youtube.com/watch?v=jG7vhMMXagQ
I know changing from Pi to Tau seems silly but it's not at all about radius vs diameter for calculating the circumference, It's about everything else that uses Pi. When equations that use Pi are compared to other similar equations that use other constants they are always off by a factor of 2 in some way. Tau fixes that in all cases I am aware of (If you know any it does not please post them). "The Tau Manifesto" link goes over this in detail. Tau is simply a more fundamental constant then PI.
Teach both sides.
The lack of a constant between Pi day and Tau day proves that constants did not evolve on their own. Unless you can find a constant between Pi and Tau in the Holy Book of Knuth, or in the text of the Apocrypha/Art of Electronics, I must conclude that an intelligent designer created both Pi day and Tau day instead of a mere theory of slashdot dupe article evolution. Unfortunately the intelligent designer was not intelligent enough to make either day interesting enough for me to care, so sorry.
"Science flies us to the moon. Religion flies us into buildings." - Victor Stenger
(Which apparently triggers the lameness filter...)
IN MEMORY OF BILLY MAYS! DON'T JUST CLEAN IT, SCREAM AT IT!
Why does the lameness filter think Billy Mays is lame?
Sent from my iPhone
tau is fucking retarded. That's the problem.
Yeah, there are a few weak arguments to be made why 2*pi is a better choice for a circle constant than pi. Fine, argue. It's stupid, but I won't call you out for it.
Oh, hey, let's use a greek letter that is already used in many situations where the circle constant is used and define it to be our circle constant to cause ambiguity and confusion. What the fuck, people?!
exp(2 pi i x) where x is some simple expression of time or distance occurs a *lot*. Years ago, I invented a symbol for exp(2pi*i): a one with a tilde superimposed in the middle. e^(2pi*i) does indeed compute to 1.0, but taken to some power x, of course we don't mean (1)^x but what exp(2 pi i x) normally means. A one with a tilde superimposed reminds us to do this. This notation makes many formulas involving Fourier transforms, waves, AC circuit analysis, and quantum mechanics nice and elegant, and 1 with the tilde is not a challenge for Latex or Lout.
For 2pi, I sometimes use a circle with a dot at the center. Tau is way too overloaded, as has been pointed out already.
Just seems natural. or something. zen maybe.
And if he didn't know that, then he should get back to the books and stop wasting time.
The Kruger Dunning explains most post on
Look at the taijitu, a common symbol of yin and yáng in Taoism. Yin occupies pi radians of the symbol, as does its opposite yáng. The whole symbol, all tau radians of it, represents a whole made up of a balance of parts that are opposite. You need all tau radians to represent the balance of nature maintained by the active force called the Tao.
Seriously? A few weak arguments? I see 2pi way, way more often than pi.
Le français vous intéresse?
area = pi*r^2 is nice and simple - pie are square
area = (tau*r^2)/4 just doesn't roll off the tongue - quarter tau are square
Why call it tau? Couldn't you call it, say, two-pi
The symbol for tau is a line over one vertical mark (/ I). The symbol for pi is a line over two vertical marks (/ II). You could consider this to represent a fraction bar with a Roman numeral in the denominator, and thus tau and pi represent different denominators: tau is the circle constant divided by 1, and pi is the circle constant divided by 2.
makes more sense, except when calculating area. or volume. should we have separate constants, that are integer-ratio-multiples-of-pi, for each of those?
for a circle:
circumference=2*pi*Radius=tau*radius
area=pi*radius^2=0.5*tau*radius^2
for a sphere:
surface area=4*pi*Radius^2=2*tau*radius^2
volume=(4/3)*pi*radius^3= fuck it, why are you messing with pi?
do these people not realize that pi has applications beyond what they remember from basic geometry?
Hair Pi vs Camel Tau... tough choice
Everybody knows that tau is actually a variable which depends on velocity of one observer relative to another. Poul Anderson even wrote a nice SciFi book called Tau Zero.
Those who can make you believe absurdities can make you commit atrocities. - Voltaire
The international standard on the planet where I live is ISO 8601, which calls today 2011-06-28.
There isn't but there should be. I'm writing the gamma manifesto where instead of e - the euler constant - we use gamma. For the obvious reasons, gamma=2e.
Tau for uber math nerds, physicists, EE geeks and anyone else who needs to calculate an arc tangent and Pi for everyone who just needs to figure out what diameter pipe they need to fix their sink?
Non impediti ratione cogitationus.
I know changing from Pi to Tau seems silly but it's not at all about radius vs diameter for calculating the circumference, It's about everything else that uses Pi. When equations that use Pi are compared to other similar equations that use other constants they are always off by a factor of 2 in some way. Tau fixes that in all cases I am aware of (If you know any it does not please post them). "The Tau Manifesto" link goes over this in detail. Tau is simply a more fundamental constant then PI.
Tau is retarded. There's no point to it. Having a trig function have a 2 or not doesn't make it more elegant. 2 Pi is a constant. Tau is a constant. They're identical.
The rallying cry of this stupid meta-nerd Tau bullshit is "Pi is wrong!". That's just complete horse shit.
The main argument is
In particular, since a circle is defined as the set of points a fixed distance—the radius—from a given point, a more natural definition for the circle constant uses r in place of D:
Who gives a shit? What about when you want to define the area (you know, "the set of points a fixed distance—the radius—from a given point")? Pi R^2 is more "elegant" than Tau/2 R^2. What about when you want to use trig functions? We should be using Pi/2 for those, not Pi, and not 2 Pi.
And why are we concerned with a circle anyway? We live in 3D space (at least, for now) and we should be dealing with 3D objects. What's the volume of a sphere? 4/3 Pi R^3? Fuck that! It should be Lambda R^3 so it's more elegant!! Pi is wrong! Lambda is 4/3 Pi!
The bottom line is that if you want to talk about "elegance", you should be defining your point collections as {L = , M = x}, where L is the locus defined in your native dimension, and M is the magnitude (end to end or center to end, I don't give a shit). 1D? Line segment. 2D? Circle. 3D? Sphere. 4D? Yo Momma.
Add a Phi if you want to define a circle in 3D space, or a line segment in 2D space. Add a Theta or some shit if you want line segments in 3D.
The entire argument for Tau is imbecilic. It reeks of "I got a problem wrong on a test because instead of actually understanding trig functions, I memorized them, and memorized them wrong." This is fucking "KB = 1000B" all over again - utter horseshit that morons will point to as an excuse when they fuck up. "See? I was right!" No bro, you were wrong. At least with this Tau horseshit we won't have marketing departments behind the push for detrimental ambiguity.
Use Tau all you fucking want. Just understand that no one else gives a shit, and no one will be teaching it in schools.
Tau is already used to describe the relationship of speed to the apparent speed of the passage of time.
And pi is already used to describe conjugate momentum, as Tau Manifesto explains. Wikipedia lists a whole bunch of other meanings of pi.
No, radius is the principal measurement of a circle, a sphere, a hypersphere, and so on. The diameter is the mathematically unnatural measurement. The diameter is used nowhere but in the relation of circumference to diameter. All other calculations use the radius, and factors of 2 pi.
Pi was chose as it was because it is more practical to physically measure the diameter than the radius. This does not make it a mathematically sound choice, however.
But the real lesson is showing the work so when it's not that easy you can get a correct answer.
So it has become a problem of input devices. I think divide by 4 on each side, but how do I write this down as quickly as I think it?
we speak of a "radius of curvature" when describing curves other than circles. "diameter" presupposes a circle.
if you want to define the position of a circle, the simplest way is to give the coordinates of the center - and the radius.
but I cannot respect any man in a vest.
I listened to the tau music, then went back to listen to the pi music, then listened to the tau music again.
It's odd, the tau music is clearly "better" in a musical kind of way, but it's the pi music which is rigidly stuck in my head.
For the area you're forgetting your calculus. Area calculations are basically summation equations and those always have a 0.5 in there. Table 3 of "The Tau Manifesto" shows several other such equations.This is a minor point that becomes a big deal. By lacking consistency across math what should be obvious and beautiful similarities become lost and hard to see.
Those other calculations are not any more difficult then they were before. Changing to Tau here is again a net benefit for mathematics.
Personally the argument for Tau has nothing to do with trig. Zero. Pi in Trig is harmless, it's once you start using Pi for everything else that it becomes ugly and clearly the wrong constant. Read "The Tau Manifesto", it goes over all the place that Pi is not as good as Tau.
That is quite possibly the most beautiful song I've ever heard.
"I'm just here to regulate funkiness."
Everyone chant...
Ohm
Ohm
Ohm
Resistance is futile.
Knowledge is how to play a game, intelligence is how to win, wisdom is knowing what game to play.
I am not forgetting my calculus. Teaching calculus payed for my liquor fund through college. I'm trying to avoid having to learn a second version.
Let's see. One side has pies, the other side has twice as many pies. Can you say "arms race"?
I can't decide whether this fight is going to be delicious or if it is going to turn every mathematics conference and June 28th/March 14th into a Cold-War-style pietastrophe.
I'm sorry but if switching to Tau requires you relearn calculus you have bigger problems then switching to Tau
Celebrate a day based on 2*pi? No thanks. However, I will celebrate 2.556*pi day. I will likely even have cake on that day. It's the day that I turn approximately 11.46*pi years old.
My sci-fi novel, Ghost Thief, is now available from Amazon.com.
Having a trig function have a 2 or not doesn't make it more elegant.
Ok, let's go with one of the simplest trig functions around, converting angles.
With radians expressed in fractions of pi, a full circle is 2*pi radians.
With radians expressed in fractions of tau, a full circle is tau radians.
So half a circle angle.. is 1/2 tau radians. A quarter is 1/4 tau radians.
An eighth of a circle 1/4 pi radians. A quarter is 1/2 pi radians.
I know which looks more elegant to me...
And if you didn't know that, then you should get back to the books and stop wasting time.
Seriously, know your stuff before you start blasting others for re-using symbols.
In fact, using this as an excuse is downright retarded at best.
You do not deserve the name geekoid. You ain't no geek to me. Hand that card and name in.
Also, that language you are using, you should stop using it, it is silly, it re-uses words to mean countless different things depending on the context.
Pfft. Forget Tau Day. Today's my birthday. =D
I already have Tau. It is spelled "2*pi"
I usually didn't call it "Tau," because that is often being used to represent other things. In mechanics, it often represents Torque. In electrical engineering, it is used for a time constant.
Is this the newest incarnation of the idiots who keep trying to redefine pi to make it easier to work with? They never did well with it in school, so now they want to do away with it, start their own club, and make everyone learn their way for a change?
Wouldn't "seeing 2Ï" be a subset of "seeing Ï?"
"I'm just here to regulate funkiness."
What about not using greek letters in math at all? If a programmer would try to pull off that kind of stuff he'd be fired.
It is the only way.
Twice as many what as you'd expect? Pies that are being served at the end? Don't make me read the article to understand the summary.
As an engineer I am aware of how over loaded Tau is at the moment. I agree that Tau is not the best choice here but that does not change that 2 Pi is not as elegant as using another symbol and is something we should consider replacing. Math would be clearer and simpler for future generations if Pi was replaced.
The only explicit multiplication operator is the dot (slightly higher than the decimal point), for division a slash can be used if there is no space for a normal horizontal line between divisor and divident.
Are those not used in elementary and middle school in the US?
It's Perfect Number day, as 6 and 28 are both perfect numbers.
Proper divisors of 6: 1, 2, 3
1+2+3 = 6
Proper divisors of 28: 1, 2, 4, 7, 14
1+2+4+7+14=28
The next perfect number is 496, so all of the perfect numbers that can be dates are 6 and 28.
...the future crusty old bastards are already drinking the Kool-Aid.
Yes, math works better with relation to radius than diameter, but for a human, walking up to an already-drawn circle, you can either a) measure the diameter (100% effective and accurate) or b) estimate where the center is and measure to it (and get a result that is only as good as your estimation--half as good, actually, since doubling the number would double the error.) Thus "diameter" took off as "the main way we humans measure circles." Yes, you can very easily half the diameter, but what's the point if you're going to multiply by a constant to find the circumference? If you want to find out how much rope you need to tie around a well, would you 1) measure the diameter, 2) divide that number by 2, and then 3) multiply by tau, or would you 1) measure the diameter and 2) multiply by pi?
Same thing with Imperial vs. Metric measurements: yes, Metric makes the math easier, and we do indeed have ten fingers, but if you have something you want to divide, it's a lot easier to cut it in half, and half again, and half again, and anyone can do so easily--even on irregularly-shaped things like "a pile of cooking flour"--as opposed to trying to cut something into ten equally-sized pieces.
I'm not saying any of the above are absolutely better or worse than the others, but humans have certain natural tendencies, and that's where this stuff comes from, and why it's hard to change.
Dear Slashdot: next time you want to mess with the site, add a rich-text editor for comments.
Thar's a tau-day post every day, n' tau-morrow thar'll be posts too!
"Pi is a confusing and unnatural choice for the circle constant."
Unless you're trying to pack amphorae into a cargo hold and calculate your profit on the voyage.
Seriously, there's not much more natural and distinctive than
Korg: "How big is a circle"?
Ugg: "You mean how big across or how big around?"
Korg: "OoooOOOoohhhh, look who's been going to college!"
There's no question that "The Tau Manifesto" makes valid points that tau makes more sense than pi in some settings.
Still, I'm a little astounded by all the people that treat this as some profound insight. "The Tau Manifesto" itself is written in a tongue-in-cheek way, and it fits: it's not meant to be taken too seriously. At least, I never thought it was. The examples are hand-picked to make tau look good, and even among them, some are not fully developed: if they were, the arguments would fall apart.
Take the example of the area of the circle. If you generalize for n dimensions, all the talk about comparing it to formulas in physics (uniform acceleration, potential energy, etc.) to justify the 1/2 factor (which would be an argument for using pi) disappears: the general formula doesn't favor either pi or tau, it has ugly constants with both of them (it could even be argued that it looks better with pi).
And what's the point of saying "Tau fixes that in all cases I am aware of (If you know any it does not please post them)"? Things like this might go well in discussions about religion, not math.
If future generations can't deal with multiplying a constant by 2, they probably shouldn't be doing math.
Rearranging the formula for area so that it is consistent with several formulae for energy (as shown in table 3) seems to be more compelling an argument to the author than I find it. The author seems to make use of several exclamation points and rhetorical questions, which also tends not to impress me . Math would be no clearer after such a change, and even trying to make it happen will probably just lead to more confusion.
Still, complex numbers arithmetics is inherently 2-dimensional.
And e^(value*tau) compared to e^(value*2pi) really helps once you include it in complicated expressions, where the "2" starts to crop up, getting squared, added, multiplied and so on.
45 5F E1 04 22 CA 29 C4 93 3F 95 05 2B 79 2A B2
The article was written like that for the authors own amusement. See the FAQ section
By that logic nothing should ever be simplified or improved because "If you can't do it the way I did it you should not be doing it!"
Eagle, in his book "The Elliptic Functions as they Should Be" has already introduced tau as one-half pi, saying it's natural to use a one-legged letter as half of a two-legged letter.
In effect, engineers and physicists eliminated the constant '2' a long time ago by adopting the symbol omega, which is equal to 2pi*f, not pi*f, for angular frequency. That leads to the definition of complex frequency, s, which is used in most applications of Laplace and Fourier transforms.
Mathematicians and teachers of trigonometry are more likely to cling to the symbol pi.
I don't enjoy how he identifies 9 notes for a scale (or identifies it as a rule.) 9 chords to identify the numbers and leaving 0 as a rest, it's an ok interpretation, but I hope there's something better out there. The whole thing sounds and looks like a "made on a Mac" hipster nonsense.
This does not account for the Gamma Function. Using tau would make solving integrals actually ugly.
Maybe it is smart for angles, but that is about it.
Euler's Identity assembles the five basic constants of math into a compact equation: e, pi, i, 1 and 0. No two or tau in there. This is sometimes called 'The most beautiful equation in mathematics'.
Yes, I never disagreed that sometimes it makes more sense to use tau. Still, I play a lot with complex arithmetic (by hand! [1]) when learning quantum computation. I've never had a single instance where absorbing the "2" into a constant (tau) would make things dramatically simpler.
The main point, though, is that people seem to make it a bigger deal about it than what it is. It's just a constant. Sometimes it makes more sense (in a "pure" sort of way) to use tau -- especially in really simple examples, it seems. Sometimes, it makes more sense to use pi. Most of the time, though, it doesn't really matter, since there are other constants involved either way. It seems that the benefits of using a single standard (pi is already established) seems to vastly outweigh the trouble of getting used to another constant.
[1] BTW, if anyone knows where I can find some easy-to-use free software that deals *symbolically* with complex matrices -- in particular, multiplying, inverting and calculating eigenvalues and eigenvectors, I'd LOVE hear about it. I mostly use Sage (it's what I ended up using after searching a bit a few years ago), but I end up doing a lot by hand because it seems to refuse to deal with complex numbers in any sensible way -- it doesn't like to keep constants like pi or sqrt(2), and replaces them with inexact floating point values. Mathematica seems to do the right thing -- is there some free software that does the same?
(e = 2.71828183) ...that would be: February 72...
Never mind.
A pox on web designers who feel that window.innerWidth == screen.availWidth
The general formula for a circle does not favor Pi or Tau but the general formula for finding an area for simple shapes does favor Tao. The formulas shown are compared not because they are all for the same area of study but because they are all derived the same way mathematically. In a very real sense, they are all the same formula just with different variables. Looked at this way the 1/2 belongs there, the math says so, it's Pi that messed it all up and got it canceled out. The area formula is a false positive in favor of Pi.
Personally I don't treat this as a profound insight because Pi felt wrong for a long time. It kept coming up as 2Pi in formulas and only very rarely did it stand on it's own. You can't show a person 2Pi a million times and expect them to still think that Pi with out the 2 is worth much. I can't speak for others but I'm guessing lots of other people felt the same and once they saw "The Tau Manifesto" they had that uneasy feeling finally justified. The math is much cleaner with Tau. That does not mean much if you want to just get work done but if you enjoy the beauty of math it's a big deal.
Actually that question does much better in talks of math. I am far more interested in being shown cases where I am clearly wrong by the numbers then cases where I am wrong because of some old book said so. I learn and improve by actively seeking out things I think are true that are actually wrong. So if you can give me a case where I am wrong in this I would be happy to see it.
We serve the Greater Good.
We already use Tau for both torque and for shear area. The nature of both types of calculations typically involves circles, and therefore, pi. Yeah, I'm nitpicking, but the last thing I need is for my simple calculations to have three different uses of the same damned Greek letter.
Everyone knows pi. It's too late, it's been the standard for generations. The same goes for the English language - it sucks, but even though it makes logical sense to change to something better, good luck trying to get everyone on board that train.
"No fair, you changed the outcome by measuring it!" - Professor Hubert J. Farnsworth
To honor tau we should update math.c with M_TAU referring to M_PI_2. BTW, what would occur more often, M_PI, or M_PI_2 in actual code? And how often do people use 2 * M_PI?
This is a very stupid idea for one important and untouched on (the site barely touches on it but does not address the problem) d (sin x)/dx=cos x only in radians, therefore using tau instead of pi would create troubles for the derivative and make it unnecessarily complicated.
But if we redefine radian, lim sin(x)/x = 2
No sig today.
The general formula for a circle does not favor Pi or Tau but the general formula for finding an area for simple shapes does favor Tao.
I disagree. I don't think it "favors" tau or pi, I think the choice is arbitrary. Before you start thinking I'm an idiot, or simply trying to be difficult just to maintain the status quo, please read my whole explanation.
The example of calculating the area of the circle in The Tau Manifesto does an integral with the radius going from 0 to r. When dealing with a circle, if you think in terms of the radius (as opposed to the diameter), tau is more natural: this is unsurprising, since The Tau Manifesto itself defines it as tau=C/r. Obviously, when dealing of a circle, you think about the diameter (and not the radius), then pi is more natural: pi=C/d.
When you compare the integral (using the radius) with the other simple integrals from physics, you may get a sense of discovering an underlying pattern (in Table 3 (page 16) everything has the exact same formula structure) and all of a sudden everything seems to fit in place. It begins to look like it's obvious that you should choose to work with the radius, and not the diameter. Most of the feeling that tau is "simply better" or "more natural" seems to come from this realization (and other similar ones in the other examples in the Manifesto).
I claim that this is misleading, and it simply isn't true that "the general formula for finding an area for simple shapes does favor Tao". It just happens that, coincidentally, there's a simple way to calculate the area of the circle that integrates over the radius. But if you wanted to calculate the area of a square, or of a triangle, or, even better, some arbitrary shape, the simplest thing to do would NOT be to pick a point inside the shape and integrate over some "rings" (or whatever shape) while moving away from this point to the edge of the shape. Moreover, it is a coincidence that this way to calculate the area of the circle (integrating using the radius, which favours tau) works as beautifully as it does -- it doesn't look as good in any larger dimension (volume, etc.).
But that's just one example. There are many others, usually just silly or misleading in some other way. As for the claim that everywhere you see pi in a formula it's always multiplied by 2, that's just silly.
Still, I already said I agree that tau is better in some places. For example, e^(i*tau) looks more natural than e^(2*i*pi), for the exact same reason that sin(x)=sin(x+2*pi): in the "natural" definition of the trigonometrical functions, 2*pi is "one full circle back to the same point". But that seems to be the only real argument. It's been obvious for a very long time and it doesn't seem reason enough to justify a massive change in the way we write these things. Gratuitous incompatibility is bad!
Pie are round. Cake are square. Anyone edjumicated in Texas knows that. Long live the Tau!
Having to work for a living is the root of all evil.
While I still disagree with you on the area of a circle you make a good point. I still feel that there is a fundamental rule that is clearly visible in that group of formulas I and the author have not put together a good representation of it. Since I am an engineer and not a mathematician I don't think I will be able to correctly represent it by continuing so I will not bother to go in to it further.
I honestly can not remember many places were Pi was on it's own. If you can please do mention them.
A major part of the point of what I guess you could call the 'Tau movement' is that it is not at all incompatible. That's why (and again the Tao manifesto covers this) they are suggesting using Tau and not changing the value of Pi. You would simply be introducing a new constant that everyone could recognize as 2 Pi. Books could also have the two different versions of the formulas on the same page of their text books and they should be able to function just fine.
To be honest I actually do have one problem with the idea, Tau is already heavily used in other areas (it looks to much like a T to be ignored), another less used Greek letter should be chosen instead.
Why would we redefine radians? The whole point of radians is to have the angle correspond to the arc length on a unit circle. This also allows us to avoid constants when differentiating/integrating sin or cos, in other words to have lim sin(a+x)/x = cos(a) when x->0 and lim cos(a+x)/x = -sin(a) when x->0.
when it pertains to food - i like two pies more than one...
for all other purposes i don't give a damn.
Hardware met Software on the road to Changtse. Software said: “You are Yin and I am Yang. If we travel together we will become famous and earn vast sums of money.” And so the set forth together, thinking to conquer the world.
Presently they met Firmware, who was dressed in tattered rags and hobbled along propped on a thorny stick. Firmware said to them: “The Tao lies beyond Yin and Yang. It is silent and still as a pool of water. It does not seek fame, therefore nobody knows its presence. It does not seek fortune, for it is complete within itself. It exists beyond space and time.”
Software and Hardware, ashamed, returned to their homes.
Section 8.4. The Tao of Programming.
I rarely respond to comments. Also, don't ask for clarifications: a brain and Google are faster, believe me!
You should try out Maxima. I think it may be one of the backends for Sage, but if you use it directly you can program the symbolic engine to simplify how ever you want.
Whoa, thank you very much! At first look, it seems be exactly what I need! Now it seems I'll have to get used to Maxima's way of doing things. :)
And indeed, Maxima is even included with Sage, although I don't know what exactly Sage uses it for...
Rant of the year. Chapeau monsieur!
And ended up with twice as much ?
Don't blame me, it's usually 2 in the morning when I post
Manly American Football is played on a 100 yard field. Sissy Canadian Football is played on a 100 meter field. I refuse to see our beloved sports (e.g. Baseball is defined in yards as well) redefined, therefor causing old records to be irrelevant.
More realistically, I have no idea why base 10 is a great idea. Imperial has binary units (volume/mass) and base twelve units (hello 1/3!). Either standard seems better than base 10.
It's a fair point, but the main issue to my mind is that they didn't pick a base and stick with it, rather the conversion factors are all over the map. Teaspoons-to-tablespoons is a factor of three, but up to cups, pints, quarts, and (US) gallons is a power of two. Inches to feet is factors of twos and three, feet to miles is factors of two, five, and eleven. And fractions of inches are powers of two, unless you're dealing with mils in which case it's powers of ten. And there's no straightforward conversion between the length and volume measures, or (as you get into physics calculations) the length, weight, and force. One cubic foot is 7.48051948 US gallons.
Had the system been planned better, I think the disparate conversion factors could be quite acceptable: 12 inches per foot is reasonable, potentially helpful in cases that involve division by a factor of three. Working with arc-degrees and the fractions thereof (arc-minutes, arc-seconds) is similarly reasonable. The bigger problem is that some of the conversion factors aren't even integers.
Speaking personally - I build models and deal with small measurements a lot. In that context I'd rather deal with powers of ten rather than powers of two. I can do fractional math, obviously, but it's still easier to work out the drill bit sizes between 3mm and 5mm than it is to work out the drill bit sizes between 1/8" and 13/64" - even if I change the denominator (i.e. 3.5mm has an extra digit, so I'm effectively working in ten-thousandths of a meter instead of thousandths) the change to the numerator is trivial. Power-of-two changes to the numerator are pretty easy but not as easy, simply because my numerical representation isn't powers-of-two.
There is a flip side to that scale modeling scenario, which is that kit scales are in many cases chosen specifically to suit the foot-to-inch conversion factor. For instance, a six-foot-tall man would be exactly one inch tall in 1/72, or three inches tall in 1/24. That is handy, but it becomes less helpful if the measurement you're converting isn't that fundamental measurement on which the scale was based. The scales have factors of three - if you're starting with feet, one of those gets eaten by the inch conversion... But if you're starting with a measurement in inches and going for a fractional measure of inches, the factors of three have to be used to divide the numerator... eleven inches scales down to (11/9)/8 in 1/72 scale, for instance. Converting that to the closest power-of-two fraction means finding the right denominator... (22/9)/16 or (44/9)/32 or (88/9)/64 - scaling up the numerator enough to find a good answer, and then scaling it back down to a satisfactory precision. (44/9 is slightly less than 45/9=5, so 5/32 would be a good approximation..)
Dealing with a problem like that in metric is actually easier IMO, even though the unit conversions don't eat any of the scaling factors. 28cm / 72 = 3.5cm / 9, very close to 3.9mm. (Well, the 28cm measurement comes from a conversion from the 11" measurement I used in the inches example, so it may be a bit too convenient as 28 already carries two factors of two... If it were a prime number, as in the previous example - say, 31cm/72 = 10.33cm/24 = 3.44cm/8 = 4.3mm) It's convenient to not have to change bases at any point during the calculation, even if that means some cases are less convenient.
Of course, with the right calculator you can handle all those
Bow-ties are cool.
And I thought this referred to something else... 2pi? Booooring.
Two pi, don't bother me.
Yes, tau is a bad choice, it means far too many things already. But I'm happy to celebrate the curve torsion day. And proper time day. And Tau Ceti day.
This doesn't redefine the radian. It simply changes the way you write it down.