Variables in Math

I am in need of a math person to help me:


Is time classified as a variable? I'd think it should be, but you can't say something like "as the number of things on the desk increases, so does time". Okay, well, you could, but the things on the desk would be dependent on time as opposed to time being dependent on the number of things on the desk. Or it should seem, given that anything else would be difficult to comprehend. Or have I confused the definition of a variable?

I suppose, at bare bones, my question is whether I can correctly state this list:

-length
-width
-height
-time

I want to say "yes" because as the list gets longer, the number of dimensions increases. Does time count as a fourth dimension, or is it farther down on the list?

[this isn't too too relevent to my original question (or maybe it is) but is a dimension synnonymous with a variable? The way I've phrased my question above makes it seem like it would be, but I'm questioning my question now... hmm, after thinking about it some more, I wonder if a dimension is usually a variable, but a variable isn't necessarily a dimension... ]



...help?

Time is an independant variable. All things depend on time. As time increases, the population of a certain country either increases or decreases with it. A lot of statistics that are out now with population, global temperature, GNP, etc, are all of that dependant on time. So I would definitely say that time is a variable.

TIME is also an excellent news magazine.

As for demention = variable, someone else will have to answer that one.

Is time classified as a variable?

Yes! Usually represented by "t." And I think you can say, "As time increases, so does the number of things on the desk," basic equation! Something like x + ty, where x is the original amount of object on the desk, t is time, and y is the amount of new objects (or something like that) that appears per segment of time, whatever you alloted it to be.

Can you clarify what you mean by that list? I'm not entirely sure I understand what you're asking.

The list:

I mean that in the first dimension, things are measured one way, by length. Then in the second dimension, by length and width. And in the third dimension, by length, width, and height. Is the next step/item in the list to measure by length, width, height and time? or are there more measurements to go through between measuring by length/width/height and measuring by length/width/height/.../time? So can I say length is the first dimension, width the second, height the third, and time the fourth?

"As time increases, so does the number of things on the desk," basic equation!

What I was wondering though was whether you can state the inverse? Or does that break some rules of the universe? When I originally stated the question, I was wondering if it could be a variable in general, thinking [but not naming it] in terms of it only being a dependent variable as the only kind of true variable (since it's the thing that varies). Now I realize that I can say that it's a variable in general, but just as a tangent, can it be considered a dependent variable as well as an independent variable?

Thank you, Flemzo and Mesh, for your input. Any other opinions, anyone?

P.S. Flemzo, I do enjoy reading TIME every week, though I find the Economist more informative

I don't think time can be used as a dependent variable, since nothing can be done to change it. At least, not in most math word problems I've encountered.

Thanks Arieda.

Tangenting: why can't time be dependent on something? Just because "the rules" say so? Or am I making the three-year-old "but why to everything?" arguement? I dunno. Maybe I'm just talking myself in circles at this point?

Amelia---


Time can be a dependent variable. Consider, for example, the CSTR (Continuous Stir Tank Reactor) model: it is dependent not only on chemical concentration, rate of feed, temperature, and reaction rate, but also time. Many states of systems are described as "evolving" in time.

Strictly speaking, however, mathematics treats even time like any other variable--there's nothing unique or special about it. It does not define a dimension (this is a question of physics, actually--not mathematics!) so much as a state in which a system can be analyzed.

As another example, consider a predator-prey model that incorporates periodic harvesting from an elementary differential equations perspective:

x'=f(t,x)=ax(1-x)-h(1+sin(2*pi*t))

where a and h are positive parameters. Here, time certainly does play an important role in the solution of the equation, and indeed the prey-population is highly dependent on the interval of time selected.


Hope this helps,
Brad


PS: your tangent: in making time a dependent variable, a system depends on time (not the other way around). If you wanted to describe how time changes mathematically, there are plenty of examples in the areas of quantum field theory and superstring theory that gives rise to formal notations for such an endeavor.

Incandescence wrote:Amelia---


Time can be a dependent variable. Consider, for example, the CSTR (Continuous Stir Tank Reactor) model: it is dependent not only on chemical concentration, rate of feed, temperature, and reaction rate, but also time. Many states of systems are described as "evolving" in time.

Hang on, I'm confused.

How is time a dependent variable if the model relies on it?

Aren't dependent variables reliant on something else?

What's time relying on in this situation?

I can't think of how time would rely on anything other than a clock. Which is my lame attempt at humour.

Razor--


Calculus is a study of variations--that is to say, of rates of change. This puts time explicitly in the position of a depdent variable...


Best,
Brad

Thank you, Brad.

(this is a question of physics, actually--not mathematics!)

oops. There's not much separation in my head. Anywho.

so much as a state in which a system can be analyzed.

So if I wanted to graph the height a basketball is thrown in relation to the distance it's thrown all as a function of time [I think this is along the same lines as the differential equation example, but I know nothing about differential equations so it doesn't mean a whole lot to me, even if it's "elementary"], I could, but the idea of time doesn't go much further than this?

Just so I'm clear: there exists no dimension such as time, correct? Time is under a completely separate category?

If you wanted to describe how time changes mathematically, there are plenty of examples in the areas of quantum field theory and superstring theory that gives rise to formal notations for such an endeavor.

Sadly, sources rely on the reader having some knowledge of higher mathematics to understand, or so it seems to me. But that's neither here nor there.

making time a dependent variable, a system depends on time (not the other way around)

I know, but is there ever a time where it would be the other way around? Or is that completely impossible?

Amelia--


Mathematics does not discriminate with its dimensions. Dimensions are a problem of physicists/engineers.

But I think pretty easily we can imagine, from some quantum mechanics, that there could be a system which produces its own frame-of-reference and time-scale--here I have in mind certain atomic phenomena, though clearly one can argue Einstein's relativity produces the same phenomenology for galaxyies and solar systems as well.

The "time machine" is a classic example.


Take care,
Brad

A dependent variable is any variable that relies on another (read: independent) variable.

Having said that, you could turn an dependent variable into an independent variable, simply through rearranging the formula through algebra.

So what I'm saying is that time is a variable and depending on the formula it can be a dependent or independent variable. It isn't exclusively one or the other. We like it as an independent variable because we can measure time more easily.

Of course, there are instances during which you might need to know how much time it will take. That is when time will be dependent on other variables.

Thank you, Griff. And thank you again, Brad.


I suppose everything's more or less cleared up now (read: I'm out of questions for the moment).

Time isn't, in technicalities, a fourth dimension, but one could view it as a dimension. The fourth dimension extends the cube one more. 0-D: Dot. 1-D: Line. 2-D: Square. 3-D: Cube. 4-D: Hypercube. A hypercube is a cube extended another dimension, one which we cannot percieve. Doesn't seem much like time, does it?

No, variables aren't really dimensions, but people refer to time as "the fourth dimension". I believe this was popularized in H.G. Wells's "The Time Machine", where the main character described the fourth dimension as "time".

Ooooh. Totally off topic (well not quite) but anyone interested in the theory of time being a fourth dimension and creating the hypercube should watch the films cube and hypercube. Especially the second which is sometimes called 'Cube 2.' There's a third too but I haven't seen that yet.

info on cube - http://en.wikipedia.org/wiki/Cube_%28film%29

info on hypercube - http://en.wikipedia.org/wiki/Cube_2:_Hypercube

info on cube zero -
http://en.wikipedia.org/wiki/Cube_Zero