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Happy Tau Day

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Re: Happy Tau Day

#91

Post by kej »

sevenless wrote: post #84
wtbob wrote: post #43

Earlier quoted context omitted.

> 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…

I hope you realized NASA using imperial caused the loss of a Mars rover.

Mixing units caused the loss. All-imperial would have worked just as well as all-metric.

Re: Happy Tau Day

#92

Post by hexane360 »

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…

But I think the standard unit system is one of many reasons engineers rely on formulas for 100% of their calculations. When you have that many conversion factors just to get between energy, force, distance, power, etc., you lose out on the universality of physics. At that point you find someone who has already done all the unit conversions and isolated it in a nice factor out front.

Also, IMO stuff in decimal is almost always easier to compare than fractional. When someone asks me for a size up from an 8mm wrench, I know to grab the 9mm. When someone asks me for a size up from 5/16", it'll take me a bit to get to 11/32".

Re: Happy Tau Day

#93

Post by kazinator »

dri_ft wrote: post #21
greydius wrote: post #8

Earlier quoted context omitted.

"Because that's the way we've always done is" is never a valid argument.

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?"

How is "because we've always done it that way" an answer to "why do we drive on the side of the road that we do?"

It's more or less just a re-statement of the question.

And it's wrong: we haven't always driven on that side of the road.

We don't always drive on that side now; it depends on where in the world we find ourselves.

Left versus right is symmetric: there is no inherent advantage. Both choices have exactly the same advantages and disadvantages, just with "left" and "right" swapped.

Whether or not to include a factor of two isn't symmetric in this way.

Re: Happy Tau Day

#94

Post by kazinator »

sevenless wrote: post #70
jobigoud wrote: post #34

Earlier quoted context omitted.

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.

Maybe it's because driving involves both eyes and both hands.

Re: Happy Tau Day

#95

Post by kazinator »

kej wrote: post #90
kqr wrote: post #79

Earlier quoted context omitted.

You be the judge of that. Compare e^(iπ) = -1 to e^(iτ) = 1. The whole business of re-writing the identity as e^(iπ) + 1 = 0 is nothing but a hack to get around the weirdness of π as a constant.

Writing it equal to 0 isn't a hack, it's a common method of understanding a function. You factor polynomials by setting them equal to 0, for example. In the case of Euler's identity, what we're really asking is "what values of x make e^(i x ) + 1 = 0 true?" and the answer is "every multiple of π". Using τ instead hides half of the answers.

You mean "every multiple of 2π". The value -1 only comes around once per revolution of the unit circle!

Re: Happy Tau Day

#96

Post by jeffwass »

ska wrote: post #73
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.

Mathematics has no shortage of bikesheds.

Let's assume the bikesheds are spherical, with radius r. They'll have surface area 4pi*r^2 and, oh never mind...

Re: Happy Tau Day

#97

Post by kazinator »

kej wrote: post #90
kqr wrote: post #79

Earlier quoted context omitted.

You be the judge of that. Compare e^(iπ) = -1 to e^(iτ) = 1. The whole business of re-writing the identity as e^(iπ) + 1 = 0 is nothing but a hack to get around the weirdness of π as a constant.

Writing it equal to 0 isn't a hack, it's a common method of understanding a function. You factor polynomials by setting them equal to 0, for example. In the case of Euler's identity, what we're really asking is "what values of x make e^(i x ) + 1 = 0 true?" and the answer is "every multiple of π". Using τ instead hides half of the answers.

You mean "every multiple of 2π, shifted by π". The value -1 only comes around once per revolution of the unit circle!

The solutions to

   e^(ix) + 1 = 0
are

  { π, 3π, 5π, ... }
Whereas the solutions to

  e^(ix) - 1 = 0
are:

  { 0, 2π, 4π, 3π, ... }
i.e.

  { 0, τ, 2τ, 3τ, ... }
Also, note that when we set a polynomial to zero, the roots appear subtracted on the opposite side from the independent variable:

  (x - r0)(x - r1)...(x - rn) = 0
In the Tau-oriented Euler formula written homogeneously, there is a vague analogy to this since we're similarly subtracting that 1:

  e^(ix) - 1 = 0

Re: Happy Tau Day

#98

Post by [deleted] »

kej wrote: post #91
sevenless wrote: post #84

Earlier quoted context omitted.

I hope you realized NASA using imperial caused the loss of a Mars rover.

Mixing units caused the loss. All-imperial would have worked just as well as all-metric.

[deleted]

Re: Happy Tau Day

#100

Post by [deleted] »

kazinator wrote: post #94
sevenless wrote: post #70

Earlier quoted context omitted.

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.

Maybe it's because driving involves both eyes and both hands.

[deleted]
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