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Happy Tau Day

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Re: Happy Tau Day

#61

Post by jeffwass »

gravypod wrote: post #59
jeffwass wrote: post #41

Earlier quoted context omitted.

I honestly can't tell if you're being sarcastic or not.

I don't understand your comment. Have you watched the video linked within this post? This video is very good at pointing out many of the benefits of tao. [0] [0] - https://www.youtube.com/watch?v=H69YH5TnNX

You wrote "This is to uniform a hole slew of previously unrelated equations that can now be represented similarly."

You seem to be saying that introducing a new constant tau=2pi and redefining a slew of previously unrelated equations in terms of tau instead of pi is suddenly going to make them "uniformly represented".

I don't understand why they're not considered uniformly represented when defined just as consistently using pi?

Re: Happy Tau Day

#62

Post by sevenless »

contravariant wrote: post #16
nabla9 wrote: post #15

While choice between tau and pi is arbitrary from mathematical point, things like pedagogy, notational simplicity and aesthetics matter. The reason why I think π is probably better choice is because small multiples of constant are cognitively easier to process than fractions. 2π is easier to write and see as single object than τ/2. All we need to do is to make slight cognitive adjustment and think and teach 2π as a n…

Treating 2π as a single entity is probably the best option for now. Not sure if formulas like 1/2 (2π) r^2 will ever catch on, but in more complicated formulas it's probably better to not simplify things like (2π)^4 / 6 to 2^3 π^4 / 3.

The idea of 2π as symbolic entity in its own right, should be easier to accept than τ.

Introduce a single symbol that joins 2 and π, a bit like the Jupiter symbol (http://unicode-table.com/en/2643/), and pronounced 'two-pi'. Like τ it also starts with a T, for turn.

That would be totally backward compatible in reading, writing and speech.

Re: Happy Tau Day

#64

Post by Bromskloss »

skrebbel wrote: post #30

If mathematics has a bikeshed, this is it. I enjoy the ridiculousness of it all, but people who consider this anything other than a well-executed joke really should get a hold of themselves.

I find it worthwhile to think about questions like this, whose answers, on some level, do not matter, but, on another level, can be felt to be more or less in line with insights about the underlying structure.

Examples of other questions in the same category:

- Whether the natural numbers should be defined so as to include zero or not (and, relatedly, whether counting should start on zero or on one).

- How to structure a database or a piece of computer code (including the details of how to formulate individual lines of code).

Re: Happy Tau Day

#65

Post by gravypod »

jeffwass wrote: post #61
gravypod wrote: post #59

Earlier quoted context omitted.

I don't understand your comment. Have you watched the video linked within this post? This video is very good at pointing out many of the benefits of tao. [0] [0] - https://www.youtube.com/watch?v=H69YH5TnNX

You wrote "This is to uniform a hole slew of previously unrelated equations that can now be represented similarly." You seem to be saying that introducing a new constant tau=2pi and redefining a slew of previously unrelated equations in terms of tau instead of pi is suddenly going to make them "uniformly represented". I don't understand why they're not considered uniformly represented when defined just as consistentl…

Have you watched the linked video? If not I will not be able to explain what's going on as well as the presenter.

He is able to show that many common physical calculations for volume or area all relate to the same generic form.

He also is able to present many other cases where pie wins out. It is very much worth a watch.

Re: Happy Tau Day

#66

Post by jerf »

jeffwass wrote: post #32
jobigoud wrote: post #22

Earlier quoted context omitted.

> 2π is easier to write and see as single object than τ/2 The point is that you shouldn't have to write 2π in the first place. So notational simplicity would mandate the use of τ, not π. Noting that you will have to write τ/2 for a half turn is moot, in your case you'll also have to write π/2 for a quarter turn anyway.

It gets worse! When using solid angles over a sphere, you're still going to need to use 2Tau steradians to cover a sphere. This factor of 2 will continue to cause confusion for the Tau fans. Therefore we must also define a new constant Sigma = 4pi so we can cleanly and easily deal with steradians. Anybody up for writing the Sigma Manifesto?

Does it help the pedagogy and understanding? Does it help form equations that match the form of other equations in some mathematically-meaningful way?

Then, yes, I'd support it just fine. So the sarcasm fails.

One of the other things I don't see mentioned very often in this discussion is that mathematics evolves. We almost never get it right the first time. The original Maxwell's Equations were 20 equations, rather hairy ones at that, now expressed in 4 with superior notation. Derivative and integral notation did not spring fully-formed from Newton or Leibniz, it has evolved. Matrix notation evolved. Number notation has evolved.

The idea that pi itself may have to evolve because it wasn't quite right is perfectly natural and normal. What's bizarre is the idea that it must be held to be perfect, that criticism is all-but-morally wrong, and that anybody even talking about it is crazy.

I blame our terrible math system, for teaching people that math consists entirely of edicts handed down from, I presume, aliens, or possibly some form of diety, since apparently it can't be humans as we're not allowed to touch the Holy Notation. But that's not how it works in reality, and there's nothing bizarre about the idea that we might want to change pi; what's bizarre is the idea that such a thing is blasphemy.

Re: Happy Tau Day

#67

Post by Bromskloss »

libeclipse wrote: post #14

It's just the same useless argument every year. Just use what you want. I've been taught pi since secondary school. I understand it well and can use it effectively. Never have I sat there and thought, "if only there was a shortcut to multiplying this by 2". There's whole sites, videos and movements to get tau popular. I just personally don't understand the point.

I use 1.07 pi; it should be the same, as it is only a matter of convention.

Re: Happy Tau Day

#68

Post by jerf »

jonsen wrote: post #54
nenreme wrote: post #36

Earlier quoted context omitted.

But pi links to diameter, not radius.

A slice has two sides. 2*r = d.

That's wordplay, not mathematical content. You're actually taking students farther from understanding with that.

You really can't overestimate what can block up a student with this stuff.

Re: Happy Tau Day

#69

Post by lazyant »

I'd rather multiply by 2 75% of the time than divide by 2 25% of the time (just a wild-ass guess of how often one or the other appear in common equations)

Re: Happy Tau Day

#70

Post by sevenless »

jobigoud wrote: post #34
dri_ft wrote: post #21

Earlier quoted context omitted.

Often it is. It's a perfectly good answer to, for example, "why do we drive on the side of the road that we do?"

If the choice really is arbitrary then yes. If there was a compelling argument to driving one side or the other then it would cease to be a good answer IMHO. https://en.wikipedia.org/wiki/Dagen_H

Given that most people are right handed and right eye dominant it's surprising there isn't a widely accepted 'right answer' for the best side of the road to drive on.
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