2 ms·
Damnit, this is just as bad as the tau manifesto. The point is that it doesn't matter what the bloody constant is, we don't need any -more- goddamn manifestos.
by scythe 15y ago
Damnit, this is just as bad as the tau manifesto. The point is that it doesn't matter what the bloody constant is, we don't need any -more- goddamn manifestos. Call it an arc constant or an angle constant or whatever you want.
However, there is one massive abuse of terminology that is driving me insane, which is the use of the phrase "Quadratic forms". E = 1/2 k x^2 is not a quadratic form. A quadratic form is a homogeneous polynomial of degree two, and it's a topic discussed in number theory:
http://en.wikipedia.org/wiki/Quadratic_form http://en.wikipedia.org/wiki/Quadratic_form
The vast majority of people will never encounter a legitimate quadratic form. Call it a quadratic equation or whatever -- it's not a quadratic form. Both the tau manifesto and the pi manifesto got this bit manifestly wrong.
- cpa 15y agoI don't see why E = 1/2 k x^2 isn't a quadratic form. It's a quadratic form in a vector space of dimension 1 (here, the real numbers), which matrix is just (1/2 k). In fact here, we're dealing with a (degenerated) conic. What's your point? Should the author have written E(x) = ...? Besides, tau is pointless because a tau pie isn't nearly as fun as a pi pie.
- scythe 15y agoAt 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.
- cpa 15y agoNope, 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.
- scythe 15y agoUnless 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.
- cpa 15y agoAh, 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.
- pixcavator 15y agoDoes this help: f_a (x) = a * x? Is this a function of x in your opinion?
- fexl 15y agoThere's my cue to drag in the lambda calculus: \g = (\a\x ...) \f = (g a) Now f is is a function of x.