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Happy Tau Day

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Re: Happy Tau Day

#41

Post by jeffwass »

gravypod wrote: post #38
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.

This isn't to save time multiplying by two. This is to uniform a hole slew of previously unrelated equations that can now be represented similarly.

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

Re: Happy Tau Day

#42

Post by MrManatee »

I have found the idea of tau useful even though I have never used it in writing.

One argument in favor of tau is that in many formulas pi often has the multiplier 2 in front of it. If these formulas are written in terms of tau, they may become slightly easier to memorize and manipulate. Perhaps so, but I don't really care about this. It’s not a big difference. Besides, there are also lots of formulas that are easier to memorize and manipulate using pi instead of tau. The probability density function of the standard Cauchy distribution f(x) = 1/pi * 1/(1 + x^2) is one example.

However, to get a deep understanding of mathematics, I want to understand the connections between different parts of mathematics. If I see a mathematical formula with the constant pi in it, I ask myself: "How is this connected to circles?" The idea of tau taught me that that 2pi is the natural state of affairs. If I see pi by itself, I need to ask myself: "How is this connected to half-circles? Or has the multiplier 2 been cancelled away?”

So, why does the pdf of the standard Cauchy distribution above contain pi instead of 2pi? What is the standard Cauchy distribution anyway? Take a gun that shoots particles in random directions, and place it one unit distance away from an infinitely long wall. Standard Cauchy distribution is where the particles will hit the wall. The particle will only hit the wall if it is shot in a direction towards it. This corresponds to 180 degrees - and there you have it: the connection to half-circles. Of course, you also have to work out the technical details. But on an intuitive level, when I see pi in the pdf of the standard Cauchy distribution I don’t think about how the missing multiplier makes it easier to remember a bunch of symbols; I think of particles hitting a wall.

Re: Happy Tau Day

#43

Post by wtbob »

devishard wrote: post #25

Okay, tau is a little better. Meanwhile, millions of lines of code are written in languages with no type system to speak of, millions of Americans use imperial measurements, billions worldwide speak languages that are inefficient and ambiguous, and many many people aren't even educated enough to know about pi or tau. We have much more damaging problems than multiplying by 2. Given the gigantic amount of effort it wou…

> millions of Americans use imperial measurements

There are two types of countries: those using 'metric' units, and those who have been to the Moon.

There's absolutely nothing fundamentally wrong with standard units (indeed, they are better for concrete manipulation). One can do science and engineering just as well with grains as with grams, with cups as with litres, with inches as with centimetres. They could do with a bit more regularisation (e.g. to make a fluid ounce a cube exactly 1, 1¼, sqrt(2) or 2 inches — each has advantages — and adjust the ounce accordingly), but they're each completely acceptable for their purpose.

The advantage of the standard units is that they are easy to physically convert: cutting a yard into feet or a foot into inches is each (⅓ in one case; ⅓, ½, ½ in the other); dividing a gallon into cups is easy (½ × 4); dividing a pound into ounces is easy (½ x 4).

The number of times a person converts between barleycorns and parsecs in a lifetime is approximately zero, while the number of times he takes one physical quantity of a unit and breaks it into smaller quantities is pretty common; optimising for the former is IMHO kinda foolish.

Re: Happy Tau Day

#44

Post by camiller »

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.

The only thing useful about it is you have an excuse to eat two pies....

Re: Happy Tau Day

#45

Post by devishard »

panglott wrote: post #40
devishard wrote: post #25

Okay, tau is a little better. Meanwhile, millions of lines of code are written in languages with no type system to speak of, millions of Americans use imperial measurements, billions worldwide speak languages that are inefficient and ambiguous, and many many people aren't even educated enough to know about pi or tau. We have much more damaging problems than multiplying by 2. Given the gigantic amount of effort it wou…

> billions worldwide speak languages that are inefficient and ambiguous All humans speak languages that are inefficient and ambiguous. Thank goodness!

No, not all humans speak. That's why I said what I said.

It's splitting hairs, of course. :)

Re: Happy Tau Day

#46

Post by adwf »

jeffwass wrote: post #27
adwf wrote: post #4

Earlier quoted context omitted.

To use your own argument, 2*pi is far, far more common to encounter in physics/maths ie. real world examples, therefore minimizing friction would be using Tau ;)

So to save confusion over a mere factor of two, you're proposing devoting an entire new Greek letter to just double a constant, and requiring students to understand pi anyway to make sense of hundreds of years of mathematical and scientific corpus? It's just like that xkcd comic about introducing a new standard and now having N+1 standards. Except in this case the new standard offers only a factor of two.

Relax, the whole thing is a joke, including my comment above.

Re: Happy Tau Day

#48

Post by jimktrains2 »

wtbob wrote: post #43
devishard wrote: post #25

Okay, tau is a little better. Meanwhile, millions of lines of code are written in languages with no type system to speak of, millions of Americans use imperial measurements, billions worldwide speak languages that are inefficient and ambiguous, and many many people aren't even educated enough to know about pi or tau. We have much more damaging problems than multiplying by 2. Given the gigantic amount of effort it wou…

> millions of Americans use imperial measurements There are two types of countries: those using 'metric' units, and those who have been to the Moon. There's absolutely nothing fundamentally wrong with standard units (indeed, they are better for concrete manipulation). One can do science and engineering just as well with grains as with grams, with cups as with litres, with inches as with centimetres. They could do wit…

> There are two types of countries: those using 'metric' units, and those who have been to the Moon.

What about Liberia and Myanmar?

Re: Happy Tau Day

#49

Post by ubertaco »

Angostura wrote: post #28

Pi is better because 'a slice of pie' links nicely to radius and makes it easy for kids to remember. QED.

Exactly. It's much a "stickier"/"easier" mnemonic to tell a(n English-speaking) grade-school student "the area of a circle is 'pi r squared'" and let them giggle at the incongruity of the fact that no, silly, pie is round!

It builds a connection to a thing they already know, and it's "silly"/"absurd" enough to be "sticky" in terms of memorization.

Re: Happy Tau Day

#50

Post by FeepingCreature »

jeffwass wrote: post #27
adwf wrote: post #4

Earlier quoted context omitted.

To use your own argument, 2*pi is far, far more common to encounter in physics/maths ie. real world examples, therefore minimizing friction would be using Tau ;)

So to save confusion over a mere factor of two, you're proposing devoting an entire new Greek letter to just double a constant, and requiring students to understand pi anyway to make sense of hundreds of years of mathematical and scientific corpus? It's just like that xkcd comic about introducing a new standard and now having N+1 standards. Except in this case the new standard offers only a factor of two.

It's not about the factor, it's about making the connection to the circle obvious.
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