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[DStu]

Tau > Pi

should ... not.....   rant ... about .. tau ............. aahh
...
this tau-hype is the most ridiculous thing I ever heard .…... I mean "the concept of pi is wrong" ....arrrgghhh.
If you can't understand that universal constants sometimes arrive in slightly variated forms, and that we cannot define universal symbols for every 2c and c/2 every time that happens unless we want to have so many symbols that you don't even have to think about "beauty",  maybe you should not talk about "concepts" at all. I mean there is nothing wrong about tau, I could rant equally about this "pi-hype" if 3000 years ago people would have found it more important to find out the proportion of the circumference of the circle to its radius than to square the circle, but it is like it is.
You don't understand math because you don't have a universal symbol for 2Pi, of course, that makes perfect sense. Fine, define it yourself at the beginning of your whatever and everything is fine, but don't bother the rest of the world with it!  ...  If that's really the problem that most kids have with math, we wouldn't have a problem. Yeah, you can not add two rational numbers, because, hey, you have learned that 3 years ago, so it's natural that you already have forgotten it, but maybe if we would have defined Pi a little bit better that all would not matter? aahh.... If you don't understand how the 2Pi as circumference of the circle translates into the other formulas, you have understood NOTHING and it does not at all help you to understand math to just change the formulas in a way that you don't need to understand what is happening.

Ich habe fertig!

[theory]

Isn't there a similar problem in electrical engineering?  All the signs are backward, and people have learned to deal with it, but if we had a time-travel machine obviously everyone would prefer it to be the "right" way even though it doesn't matter so long as you're consistent. 

[DStu]

Isn't there a similar problem in electrical engineering?  All the signs are backward, and people have learned to deal with it, but if we had a time-travel machine obviously everyone would prefer it to be the "right" way even though it doesn't matter so long as you're consistent.

I'm not sure. The point is, that pi is a usefull constant. The area of the circle is 1pi r^2. Smallest eigenvalue of the (pretty fundamental) Dirichlet-Laplacian on the unit interval is pi^2, which leads 1pi entering many formulas for e.g. heat transportation (and many other diffusive processes). The Gaussian integral int exp(-x^2) = sqrt(1pi). Which on the other hand leads to a 1/sqrt(2pi sigma^2) as normalization constant of the Gaussian with variance sigma^2.  Pi is so fundamental it appears in different contextes, but sometimes multiplied with constants.
The Pi is not giving some false sense of the "reality". If you care more about the diameter of a circle (compared to it's radius) and derived from that the standard trigonometric functions, you would prefer 2Pi, if you care more about it compared to it diameter, or about the circle's area, or about the half-cycle (like somehow in the heat-equation), then you would prefer pi. So there is no right or wrong here I would say

The convention of the electric charge somehow would be nice, but even more helpfull would be a trip to Thompson, Ritchie and Kernighan

[def]

So, there are arguments for and against both variants. Does anyone really think a historical grown convention is changed this way?
Compare it to how people name numbers:

The English way is great:
123456:
1hundred23thousand4hundred56

The German way:
123456:
EinhundertDreiundZwanzigtausendVierhundertSechsundFünfzig.
Each digit (or Zwanzig (twenty) instead of Zwei (two), likewise Fünfzig/Fünf) starts with a capital letter, and the order in which they occur is
132465.
This change of order when pronouncing the number can be so confusing especially for kids or other people who just begin to learn the language, or the numbers and how to calculate them. There is no reason not to change that for the better, more natural way, but the fact everyone grew custom to it and that it would be a bit difficult to change things. And that's it, nothing is changed.

The French way:
98:
Quatre-vingt-dix-huit
4x20 18
No comment.

[O]

A decent amount of people from Canada-USA Mathcamp get addicted to dominion while there and are introduced to Isotropic. In my experience a lot of the math handles come from people who went there. (I happen to be one of these people..)

Also, it makes sense that strategy games such as dominion attract mathematically (ergo logically) inclined people.

[ycz6]

A decent amount of people from Canada-USA Mathcamp get addicted to dominion while there and are introduced to Isotropic.

*cough*

[chogg]

Isn't there a similar problem in electrical engineering?  All the signs are backward, and people have learned to deal with it, but if we had a time-travel machine obviously everyone would prefer it to be the "right" way even though it doesn't matter so long as you're consistent.

I often feel that way.  On the other hand, it can actually be useful to separate the concept of "electric current" from "flow of charge carriers", since the same electrical current can stem from physical carriers moving in either direction.

Electric current in metals comes from negatively charged electrons, so it flows oppositely to the charge carriers.  On the other hand, ionic solutions can carry current with positive ions just as easily as negative ones.  Even in solids, semiconductors which are p-doped (I believe) have their current carried by "holes", which flow in the same direction as the current.

Still... honestly, I guess I'd probably switch the convention if I could.

[Axxle]

should ... not.....   rant ... about .. tau ............. aahh
...
this tau-hype is the most ridiculous thing I ever heard .…... I mean "the concept of pi is wrong" ....arrrgghhh.
If you can't understand that universal constants sometimes arrive in slightly variated forms, and that we cannot define universal symbols for every 2c and c/2 every time that happens unless we want to have so many symbols that you don't even have to think about "beauty",  maybe you should not talk about "concepts" at all. I mean there is nothing wrong about tau, I could rant equally about this "pi-hype" if 3000 years ago people would have found it more important to find out the proportion of the circumference of the circle to its radius than to square the circle, but it is like it is.
You don't understand math because you don't have a universal symbol for 2Pi, of course, that makes perfect sense. Fine, define it yourself at the beginning of your whatever and everything is fine, but don't bother the rest of the world with it!  ...  If that's really the problem that most kids have with math, we wouldn't have a problem. Yeah, you can not add two rational numbers, because, hey, you have learned that 3 years ago, so it's natural that you already have forgotten it, but maybe if we would have defined Pi a little bit better that all would not matter? aahh.... If you don't understand how the 2Pi as circumference of the circle translates into the other formulas, you have understood NOTHING and it does not at all help you to understand math to just change the formulas in a way that you don't need to understand what is happening.

Ich habe fertig!

Yeah, sorry.  I was thinking in a high school math teacher mindset.  Tau is a lot easier for non math oriented people to intuitively understand than Pi.

[chogg]

Yeah, sorry.  I was thinking in a high school math teacher mindset.  Tau is a lot easier for non math oriented people to intuitively understand than Pi.

Really?

I mean, I'm math-oriented, so I can't tell.  But I'm surprised  either would be easier than the other.

[Kirian]

Yeah, sorry.  I was thinking in a high school math teacher mindset.  Tau is a lot easier for non math oriented people to intuitively understand than Pi.

Really?

I mean, I'm math-oriented, so I can't tell.  But I'm surprised  either would be easier than the other.

Simple.  Pi times X radians = X/2 times around a circle.  Tau times X radians = X times around the circle.  Or, put another way, to circumscribe a pie one must go through a length of... 2pi.  Because the trigonometric functions are intimately related to the circle, it's much more useful, in teaching terms, to teach that one-third of a circle is equivalent to one-third of the circle constant... rather than 2/3 of the circle constant.

The unmodified sine and cosine waves have period tau; a phase shift of tau is the same as the original, while a phase shift of pi is the negative of the original.

----

A few other notes, mainly directed at DStu:  appealing to the area formula of a circle is actually a terrible argument, as area ought to be the double integral of the circle constant with respect to radius.  Similar double integrals appear in multiple physics contexts; never is double the constant of interest used as the base.

Now, sure, trying to take the time machine back and change this isn't going to happen.  We may well be stuck with this, even if aliens will laugh at us because of it.  But we can argue from history that Euler ought to have used 6.28 instead of 3.14.  Euclid defined the circle based on radius rather than diameter.  One constructs a circle from the radius, not the diameter.  And Euler really, really should have realized that e^(i*[tau]) = 1 looks better than--and makes more sense than-- e^(i*pi) = -1.

[DStu]

Yeah, sorry.  I was thinking in a high school math teacher mindset.  Tau is a lot easier for non math oriented people to intuitively understand than Pi.

I think my point is that it maybe is easier to apply without understanding it, but it is not easier to understand.  And if you understood it it's equally easy

as area ought to be the double integral of the circle constant with respect to radius

Don't understand that. If you mean that

Code: [Select]

area(r) = \int_0^r\int_0^s tau ds dr = 1/2 tau r^2 = pi r^2,
than that happens to be right, but I don't see on an intuitive level why that should be like that, other than it would be nice. Because, if you extend this reasoning to higher dimensions, you would believe that for the 3-d ball you have

Code: [Select]

volume(r) = \int_0^r\int_0^s\int_0^u tau du ds dr = 1/6 tau r^3 = 1/3 pi r^3,
which is clearly off by a factor of 4.

And that's why maybe you need to understand what's happening and not complain that the constants are in a way that you can apply them in the basic examples without understanding.

[WanderingWinder]

Yeah, sorry.  I was thinking in a high school math teacher mindset.  Tau is a lot easier for non math oriented people to intuitively understand than Pi.

I think my point is that it maybe is easier to apply without understanding it, but it is not easier to understand.  And if you understood it it's equally easy

as area ought to be the double integral of the circle constant with respect to radius

Don't understand that. If you mean that

Code: [Select]

area(r) = \int_0^r\int_0^s tau ds dr = 1/2 tau r^2 = pi r^2,
than that happens to be right, but I don't see on an intuitive level why that should be like that, other than it would be nice. Because, if you extend this reasoning to higher dimensions, you would believe that for the 3-d ball you have

Code: [Select]

volume(r) = \int_0^r\int_0^s\int_0^u tau du ds dr = 1/6 tau r^3 = 1/3 pi r^3,
which is clearly off by a factor of 4.

And that's why maybe you need to understand what's happening and not complain that the constants are in a way that you can apply them in the basic examples without understanding.

Wait, you're saying you 'don't understand that' and then telling him that he needs to understand what's happening and not complain?
He also happens to be right...

[Davio]

So, there are arguments for and against both variants. Does anyone really think a historical grown convention is changed this way?
Compare it to how people name numbers:

The English way is great:
123456:
1hundred23thousand4hundred56

The German way:
123456:
EinhundertDreiundZwanzigtausendVierhundertSechsundFünfzig.
Each digit (or Zwanzig (twenty) instead of Zwei (two), likewise Fünfzig/Fünf) starts with a capital letter, and the order in which they occur is
132465.
This change of order when pronouncing the number can be so confusing especially for kids or other people who just begin to learn the language, or the numbers and how to calculate them. There is no reason not to change that for the better, more natural way, but the fact everyone grew custom to it and that it would be a bit difficult to change things. And that's it, nothing is changed.

The French way:
98:
Quatre-vingt-dix-huit
4x20 18
No comment.

The Dutch way is similar to the german:
HonderdDrieënTwintigduizendVierhonderdZesenVijftig (Caps are for clarity to show where the digits start).
Order of occurance is 132465

I don't like this swapping of the digits and it's incredibly annoying when you're being dictated a (mobile) phone number. The other would say "Two.." and you type in "2" in your phone, the other person continues "and Thirty" and you have to wipe and put 32 there instead.

When I dictate numbers I always just go from left to right grouping 'em by 2 or 3. So a fake number would be: "Five Five Five (pause) Three One Two (pause) Six Nine Eight (finished)". This would be 555-312-698.


I don't care much for Tau, it's just an unnecessary esthetic thing. Pi suffices.

[DStu]

Wait, you're saying you 'don't understand that' and then telling him that he needs to understand what's happening and not complain?

I mean I'm not sure what he meant, but every meaning I could give to it I don't really agree.

And I didn't mean that he needs to understand (also somehow I wrote it, or you can/must read it like that), but that you can't just teach your students: "Here, the area-formula with integrals for the circle is the same as for the square, just with a tau, because hey, math is beautifull", because that reasoning will break down if you go to d!=2.

He also happens to be right...

I still don't get what exactly is right...

[chogg]

Yeah, sorry.  I was thinking in a high school math teacher mindset.  Tau is a lot easier for non math oriented people to intuitively understand than Pi.

Really?

I mean, I'm math-oriented, so I can't tell.  But I'm surprised  either would be easier than the other.

Simple.  Pi times X radians = X/2 times around a circle.  Tau times X radians = X times around the circle.  Or, put another way, to circumscribe a pie one must go through a length of... 2pi.  Because the trigonometric functions are intimately related to the circle, it's much more useful, in teaching terms, to teach that one-third of a circle is equivalent to one-third of the circle constant... rather than 2/3 of the circle constant.

The unmodified sine and cosine waves have period tau; a phase shift of tau is the same as the original, while a phase shift of pi is the negative of the original.

Thanks for the explanation; it was very clear.  Too bad it's prohibitively hard to change well-established conventions.  Guess we're stuck with pi and QWERTY. 

[Davio]

Aaaargh, QWERTY, don't even get me started on that one. I hate not having learnt Dvorak when I first started using a computer. As a software developer, I type quite a lot and I'm sure Dvorak instead of Qwerty would lead to faster development time and less errors, but where do I find the time to switch over?

[Geronimoo]

Or Azerty.... prob even worse

[DStu]

Aaaargh, QWERTY, don't even get me started on that one. I hate not having learnt Dvorak when I first started using a computer. As a software developer, I type quite a lot and I'm sure Dvorak instead of Qwerty would lead to faster development time and less errors, but where do I find the time to switch over?

At least you don't find {[]}\ on AltGr+7890ß

(where ß is next to 0)

[chogg]

Aaaargh, QWERTY, don't even get me started on that one. I hate not having learnt Dvorak when I first started using a computer. As a software developer, I type quite a lot and I'm sure Dvorak instead of Qwerty would lead to faster development time and less errors, but where do I find the time to switch over?

I switched to Dvorak for a year or so when starting grad school.  It wasn't that hard, though the first 2 weeks or so were quite frustrating!  It was very comfortable, but what brought me back was the Vim text editor.  I used a hybrid layout for a while, but I just found it easier to cave and use Qwerty.

What I really wish is that Dvorak had taken over before Vim was invented.

[timchen]

Tau > Pi

should ... not.....   rant ... about .. tau ............. aahh
...
this tau-hype is the most ridiculous thing I ever heard .…... I mean "the concept of pi is wrong" ....arrrgghhh.
If you can't understand that universal constants sometimes arrive in slightly variated forms, and that we cannot define universal symbols for every 2c and c/2 every time that happens unless we want to have so many symbols that you don't even have to think about "beauty",  maybe you should not talk about "concepts" at all. I mean there is nothing wrong about tau, I could rant equally about this "pi-hype" if 3000 years ago people would have found it more important to find out the proportion of the circumference of the circle to its radius than to square the circle, but it is like it is.
You don't understand math because you don't have a universal symbol for 2Pi, of course, that makes perfect sense. Fine, define it yourself at the beginning of your whatever and everything is fine, but don't bother the rest of the world with it!  ...  If that's really the problem that most kids have with math, we wouldn't have a problem. Yeah, you can not add two rational numbers, because, hey, you have learned that 3 years ago, so it's natural that you already have forgotten it, but maybe if we would have defined Pi a little bit better that all would not matter? aahh.... If you don't understand how the 2Pi as circumference of the circle translates into the other formulas, you have understood NOTHING and it does not at all help you to understand math to just change the formulas in a way that you don't need to understand what is happening.

Ich habe fertig!

I've never heard about tau before. But now that I read about it, it certainly make a lot of sense. An enormous amount of sense.

Yes, indeed it is just a factor of 2 difference. But how to define a symbol is really something very important. To the extreme it can affect how capable people can think about things.

I would imagine in theoretical physics IF tau is the definition used, the productivity can increase by more than 1%, certainly measurable.

On the other hand, it certainly cannot be changed, as it would cause more confusion. We already don't have enough Greek letters. We also happen to spend a whole lot of time just trying to understand everyone else's notation... so this extra effort to track the extra factor of 2 is actually not that bad...

[Davio]

Time to start using Unicode in the SI system.

ڴ = 2 ݖ + ﮩ

(obviously you have to read right to left  )

[blueblimp]

Aaaargh, QWERTY, don't even get me started on that one. I hate not having learnt Dvorak when I first started using a computer. As a software developer, I type quite a lot and I'm sure Dvorak instead of Qwerty would lead to faster development time and less errors, but where do I find the time to switch over?

I experimented with Dvorak briefly, and decided not to pursue it. Here's why: Dvorak is optimized for typing English text. Yes it might be a little bit better than QWERTY for typing English. But code is not very much like English, so I don't think Dvorak offers much benefit there.

[Kirian]

Aaaargh, QWERTY, don't even get me started on that one. I hate not having learnt Dvorak when I first started using a computer. As a software developer, I type quite a lot and I'm sure Dvorak instead of Qwerty would lead to faster development time and less errors, but where do I find the time to switch over?

I experimented with Dvorak briefly, and decided not to pursue it. Here's why: Dvorak is optimized for typing English text. Yes it might be a little bit better than QWERTY for typing English. But code is not very much like English, so I don't think Dvorak offers much benefit there.

I also tried Dvorak briefly.  This was in the era before phone texting was common and when IM was very common--and I found that trying to learn Dvorak meant I couldn't keep up with three ICQ conversations at once.  I probably would have gone further if not for that.

That said, for coding:

http://en.wikipedia.org/wiki/Dvorak_Simplified_Keyboard#Programmer_Dvorak

Look, braces, brackets, and parens no longer need Shift!  How often do coders need numerals anyway?  Counters, array indices, for, and while?  Probably more in pure C for pointers.