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The Pi Manifesto

thepimanifesto.com

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Re: The Pi Manifesto

#11

Post by scythe »

cpa wrote: post #10
scythe wrote: post #9

Earlier quoted context omitted.

At best, it's a cubic form, since the spring constant is also a variable. Similarly 1/2 a t^2 is a cubic form. pi r^2 however is a quadratic form.

Nope, check the introduction section of your wikipedia link. It's like saying that f(x) = ax is a function of two variables. Indeed it is, but it's commonly accepted in mathematics to use it as a function of one variable (x), with a parameter a.

Unless you take every spring in the Universe to have the same spring constant (nonsense), k must also be treated as a variable. The energy relation for an individual spring is a quadratic form, but the energy relation for all springs is either a cubic form or a set of quadratic forms (or a bijection from the real line to the set of unary quadratic forms, if you want to be really technical and boring).

f(x) = a * x is an example of a function of x which only becomes a function when a value is assigned to the variable 'a'. In other words, it is a type of function.

>Indeed it is, but it's commonly accepted in mathematics to use it as a function of one variable (x), with a parameter a.

In introductory calculus, sure; in those areas of mathematics where the term 'quadratic form' is actually used, things have to be defined more precisely.

Re: The Pi Manifesto

#12

Post by cpa »

scythe wrote: post #11
cpa wrote: post #10

Earlier quoted context omitted.

Nope, check the introduction section of your wikipedia link. It's like saying that f(x) = ax is a function of two variables. Indeed it is, but it's commonly accepted in mathematics to use it as a function of one variable (x), with a parameter a.

Unless you take every spring in the Universe to have the same spring constant (nonsense), k must also be treated as a variable. The energy relation for an individual spring is a quadratic form, but the energy relation for all springs is either a cubic form or a set of quadratic forms (or a bijection from the real line to the set of unary quadratic forms, if you want to be really technical and boring). f(x) = a * x is…

Ah, I think I see your point. You would be happier with E = 1/2k x^2 is a family of quadratic forms, indexed by the real number k, I guess. A bit nitpicky to me (as long as k != 0), but fair.

Re: The Pi Manifesto

#13

Post by pixcavator »

scythe wrote: post #11
cpa wrote: post #10

Earlier quoted context omitted.

Nope, check the introduction section of your wikipedia link. It's like saying that f(x) = ax is a function of two variables. Indeed it is, but it's commonly accepted in mathematics to use it as a function of one variable (x), with a parameter a.

Unless you take every spring in the Universe to have the same spring constant (nonsense), k must also be treated as a variable. The energy relation for an individual spring is a quadratic form, but the energy relation for all springs is either a cubic form or a set of quadratic forms (or a bijection from the real line to the set of unary quadratic forms, if you want to be really technical and boring). f(x) = a * x is…

Does this help: f_a (x) = a * x? Is this a function of x in your opinion?

Re: The Pi Manifesto

#14

Post by jannes »

TLDR:

- The area of a unit circle is Pi.

- The Tau Manifesto is full of selective bias. They pinpoint formulas that contain 2π while ignoring other formulas that do not.

Re: The Pi Manifesto

#16

Post by edw »

wccrawford wrote: post #2

I disagree with change for change's sake. This whole tau thing is born of some idealist that thinks things only make sense his/her own way. The only thing I didn't see in the article is that the symbol visually looks like a T, so when you see it in a formula, you have to really look at it to know what's going on.

I would add that this stupid tau thing speaks to the conspiratorialist instinct common to many HN readers. You see, the self-evident truth of tau's superiority has been masterfully obscured by powerful dark forces in an attempt to protect their crude economic self interest, and if you don't agree, you're obviously either part of the conspiracy or one of the sheeple that's been snowed by it.

Re: The Pi Manifesto

#17

Post by fexl »

yobbobandana wrote: post #8
fexl wrote: post #4

When you ask hard-core Tauists what the area of a unit circle is, do they actually answer "tau over two"? Or do they just say "pi"? By the way, this whole discussion reminds me of what W.V.O. Quine called "mathematosis".

personally, i'd answer "half tau". half tau r^2 is a fine equation for an area.

:) Still, two syllables instead of one.

I suppose if I found myself writing "2 * pi" or "4 * pi^2" a lot, I might throw in a dash of tau here and there for brevity. Otherwise it's all the same to me.

Re: The Pi Manifesto

#18

Post by natural219 »

I just want to ask all of the Pi/apathetic people-- how long did it take you to understand radians? For me, it was a week before I was comfortable naming any angle in radians in a reasonable amount of time (this is after a week of drilling).

This is just my point of view, but calculating radians was a significant roadblock into making quick trigonometric calculations. In fact, I'd have to say it was the biggest roadblock. This has nothing to do with how "clean" it looks or how I "feel" about how it's presented.

That said, I don't think it's worth it to make the switch because of all the hassle. I'm just curious about all of the hostility towards Tauists.

tldr; it has nothing to do with any mathematical formula looking "cleaner," but everything to do with teaching math effectively.

Re: The Pi Manifesto

#20

Post by fexl »

pixcavator wrote: post #13
scythe wrote: post #11

Earlier quoted context omitted.

Unless you take every spring in the Universe to have the same spring constant (nonsense), k must also be treated as a variable. The energy relation for an individual spring is a quadratic form, but the energy relation for all springs is either a cubic form or a set of quadratic forms (or a bijection from the real line to the set of unary quadratic forms, if you want to be really technical and boring). f(x) = a * x is…

Does this help: f_a (x) = a * x? Is this a function of x in your opinion?

There's my cue to drag in the lambda calculus:

  \g = (\a\x ...)
  \f = (g a)
Now f is is a function of x.
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