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No, really, pi is wrong: The Tau Manifesto (Tau Day, 2010)

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Re: No, really, pi is wrong: The Tau Manifesto (Tau Day, 2010)

#111

Post by VMG »

steveklabnik wrote: post #51
tc wrote: post #2

Perfect; to my lisp startup file was just added: (defconstant tau #.(* 2 pi)) Regarding adoption, I think it's worth pointing out that these sorts of conventions can and do shift within a generation. I recall quite clearly while growing up the convention for indicating years = the year one [1] was B.C. and A.D. It seems like over the past few years we've definitively decided on B.C.E. and C.E. instead [2]. All it rea…

Ugh, I know this is slightly offtopic, but there's nothing more I dislike than B.C.E and C.E. I can understand not trying to promote a Christian-centric worldview, but by only changing the labels, they accomplish nothing. Now, the birth of Christ sets a 'common era,' which arguable makes it _more_ 'offensive' than just acknowledging what happened on that particular day.

I don't know what you folks are on about. My ddate clearly tells me

Today is Prickle-Prickle, the 33rd day of Confusion in the YOLD 3176

Re: No, really, pi is wrong: The Tau Manifesto (Tau Day, 2010)

#112

Post by andrew1 »

I don't remember noticing during my (mostly pure) maths degree that most of the time I was using pi that I was actually using 2 * pi. So there must have been a lot of problems where I would have been writing tau/2 using the proposed system, which I find less nice than simply writing pi. If it's a choice between splitting my writing between [pi and 2 * pi] and [tau and tau/2] I'd prefer the former, multiplication is nicer to look at than division (in my opinion).

Re: No, really, pi is wrong: The Tau Manifesto (Tau Day, 2010)

#113

Post by joe_the_user »

timwiseman wrote: post #106
joe_the_user wrote: post #62

What I would like to see is an informational analysis where you take something like a thousand common equations and look at how they would be expressed with pi versus with tau. If you can show they would take significantly fewer bits of information using tau, then tau would be objectively superior.

I repectfully think you may be overlooking two things: 1. While storing fewer bits may be objectively superior in one sense, it is overlooking the far more significant question of which helps a human understand and work with the equestions. Math is encoded into the universe, but our expressions of it exist for our own understanding. 2. We get a lot of choice in how we encode information, and that choice can change th…

I'm sure this would overlook many things. It would just supply one objective measure, not the only thing to consider.

Also, while there are indeed an infinity of representations of a given expression, there are a finite number of minimal representations, which can be found by exhaustive search if not some cleverer algorithm.

Re: No, really, pi is wrong: The Tau Manifesto (Tau Day, 2010)

#114

Post by blahedo »

aspiringsensei wrote: post #65
JeanPierre wrote: post #29

Part of me is saying yes, part of me is saying no. Let me elaborate: It makes all sense that tau should be the number used INSTEAD of pi: It simplifies things even more. (I hope I'm not the only one tired of writing 2*pi in papers.) But that doesn't make pi WRONG: It's defined by C/D, and the formulas make perfectly sense, even though you have to multiply by 2. Besides, it would mean a total rewrite of a lot of paper…

> total rewrite of a lot of papers, including a lot of mathematical books. Somebody at the textbook publishers is smacking their lips at the prospect of selling an entirely new edition with an incredibly minor change.

"Incredibly minor": not even close. This is the very worst sort of change to have to make, because you can't do it automatically, and doing it manually is fraught with opportunities for bugs.

Not to mention that the natural pedagogical order will change in several cases that a simple "translation" wouldn't reflect. A lot of CS2 books in Java---especially two or three years ago---spent a lot of time and trouble showing how to build a generic linked list using Object, casts and all, and then as a little addendum, introduced "generics" that let you use a specific type. By translating the book from old Java to Java 1.5 without rewriting it, they were losing pedagogical opportunities and introducing confusion. Or the CS2 book in Java that used .clone() all over the place: wtf, until you realise that it's been translated from an equivalent C++ book that used copy constructors a lot. Laaaaame.

So yeah, the publisher that treats this as an "incredibly minor change" is one whose books you should avoid.

Re: No, really, pi is wrong: The Tau Manifesto (Tau Day, 2010)

#115

Post by nvoorhies »

sroerick wrote: post #84
steveklabnik wrote: post #51

Earlier quoted context omitted.

Ugh, I know this is slightly offtopic, but there's nothing more I dislike than B.C.E and C.E. I can understand not trying to promote a Christian-centric worldview, but by only changing the labels, they accomplish nothing. Now, the birth of Christ sets a 'common era,' which arguable makes it _more_ 'offensive' than just acknowledging what happened on that particular day.

Don't forget, though, AD stands for Anno Domini, which means "in the year of our Lord." Which is a little more than just acknowledgement.

The "our" translation is just convention, not actually there in the latin.

Re: No, really, pi is wrong: The Tau Manifesto (Tau Day, 2010)

#116

Post by amalcon »

krschultz wrote: post #93
amalcon wrote: post #81

Earlier quoted context omitted.

The thing is, torque is a particularly bad thing to conflict with. While you're not using torque every time you work with pi, you usually end up using pi every time you work with torque. edit: It's much like using i for both sqrt(-1) and for current. Electrical engineers need to use both of these all the time, so they often use j for sqrt(-1) instead.

Or you could use M for moment and stop using tau for torque. Most mechanical engineers talk about moments with M instead of tau.

The electrical engineering thing demonstrates that you're unlikely to get a particular discipline to change its own notation. It would have made much more sense in retrospect to change current to something other than i, but that's not what happened.

Re: No, really, pi is wrong: The Tau Manifesto (Tau Day, 2010)

#117

Post by zbanks »

As eloquent as this manifesto is, it fails to actually address some of the arguments against tau.

In 2.1, it points out that d/dx sin(x) = cos(x) only holds if x is in radians.

This is key

Once you switch to expressing x in diameterians or tau-radians (or whatever you'll call them), this identity falls apart:

d/dx sin(x) = cos(x) / 2

d^2/dx^2 sin(x) = -sin(x) / 4

...

And so on. The trig functions lose their cyclical nature.

(More explanation on wiki: http://en.wikipedia.org/wiki/Trigonometric_functions#The_sig... )

I hate to be a Debbie Downer, but you can't ignore these things.

Re: No, really, pi is wrong: The Tau Manifesto (Tau Day, 2010)

#118

Post by jacobolus »

jb55 wrote: post #102
amalcon wrote: post #38

Earlier quoted context omitted.

I have no problem with people trying to do this in principle. I really don't care enough, but other people can. The symbol "tau", however, is an especially poor choice for a trigonometric symbol, because it's also used for torque. You won't get many physics teachers to change over if every time you try to calculate a torque from a force and radius, you run into a symbol conflict.

These arguments are assuming that tau would be a total replacement for pi in all situations. Why not just keep using pi in situations where you are doing calculations with torque?

The point of tau (or pi) is to do calculations with angles. One of the main uses of angles in physics is calculations having to do with torque. Basically, using pi for calculations that might involve torque is giving away one of the situations where tau would be most useful.

Re: No, really, pi is wrong: The Tau Manifesto (Tau Day, 2010)

#119

Post by vorg »

amalcon wrote: post #79
Groxx wrote: post #58

Earlier quoted context omitted.

How many symbols aren't in use, though? If you've got a notably better one, the "manifesto" may consider changing, but they seem (to me) to have pretty good reasons for choosing tau.

I'd ideally prefer to pick one that isn't used in angular things. Because non-English, non-Greek glyphs are somewhat underused for this sort of thing, and because of visual similarity to pi, I'd suggest the hebrew Het or Russian л. However, I really have no problem with continuing to use the multi-glyph symbol 2pi.

Why a multi-glyph symbol 2π when a single-glyph symbol 2π would be better. By creating a new symbol by joining the bottom-right of the 2 to the topleft of the π, we can make a new one-glyph symbol, perhaps put it next to € in Unicode.

And instead of saying two words "Two Pi", we could say it as one word "Twopi", with stress on the first syllable, much like the word "teenager" used to be spoken and written as two words a century ago.

Re: No, really, pi is wrong: The Tau Manifesto (Tau Day, 2010)

#120

Post by jacobolus »

zbanks wrote: post #117

As eloquent as this manifesto is, it fails to actually address some of the arguments against tau. In 2.1, it points out that d/dx sin(x) = cos(x) only holds if x is in radians. This is key Once you switch to expressing x in diameterians or tau-radians (or whatever you'll call them), this identity falls apart: d/dx sin(x) = cos(x) / 2 d^2/dx^2 sin(x) = -sin(x) / 4 ... And so on. The trig functions lose their cyclical…

We went over this a few days ago (also it’s described in the article, in case you missed it). You are mistaken.

sin(pi) = sin(3.14...) = sin(tau/2)

cos(tau) = cos(6.28...) = cos(2 pi)

etc.

The sin and cos functions are functions of radians, and the arclength of a radian does not change when you start expressing a circle as 1 tau instead of 2 pi.

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