Wikipedia:Reference desk archive/Mathematics/2006 July 30

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[edit] Graphing

Is there anything available online (preferably free) into which I could type a formula, that would show me a multidimensional graph of it? Black Carrot 20:06, 30 July 2006 (UTC)

You do not state which operating system you use, but Gnuplot is free and works for Linux and Windows. It is available here [1]. Madmath789 20:17, 30 July 2006 (UTC)

See also NuCalc, available for free as "Graphing Calculator" on the Apple Macintosh. There is a non-free version for Windows. --Canley 07:14, 31 July 2006 (UTC)

What do you mean by "multidimensional" ? 2D graphing software is plentiful, 3D graphing software is available, too, but graphing 4th dimensional manifolds and higher could be a bit tricky (unless the 4th dimension is time, then a movie of a changing 3D graph should do the trick). StuRat 23:01, 31 July 2006 (UTC)

I tried downloading Gnuplot, but my computer got all whiny about having to download that much. I'll try again later. By multidimensional, I mean at least 3D. I'd like to see some things graphed that take more than one input. BTW, is there anything available that tries to show 4 or more spatial dimensions? Black Carrot 18:05, 1 August 2006 (UTC)

I suppose you could map the 4th spatial dimension to time and show it in the form of a movie, even if that dimension isn't really time. For 5 or more dimensions you'd be stuck with showing multiple movies. For example, lets say you wanted to show people's wealth as a function of age, education level, income, and gender. You could show wealth as the height (Z coord), with income as the X coord, education level as the Y coord, age as time during the movie, and male and female as two parallel movies. Gender is discrete, unlike the other dimensions, which are all continuous, so would be a natural choice for separation between movies. (If needed, you could always make a continuous category discrete by breaking, say age, into age groups, but this should be avoided, if possible.) These movies could be side by side or superimposed with two different semi-transparent colors representing male and female. To be stereotypical, we could use pink and blue. StuRat 04:26, 2 August 2006 (UTC)

Right, but when I said spatial, I actually meant spatial. Come on, it's not as though we're actually seeing a 3D graph in the first place, we can collapse dimensions together without losing information. So, is there anything, other than severe unfamiliarity, getting in the way of a multidimensional graphing system? And if so, and if the problem is with our minds being somehow unable to grasp it, then how do topologists imagine so many dimensions? Black Carrot 20:33, 2 August 2006 (UTC)

They can imagine them mathematically, but not visually. StuRat 06:37, 3 August 2006 (UTC)

This is a problem with practical interest, and no killer solution. Clifford Beshers and Steven Feiner have done some work on this as part of the AutoVisual project at Columbia University. Not surprisingly, there is commercial interest in data exploration, as exemplified by Tableau Software among others. Thomas Banchoff at Brown University has explored specifically 4D visualization for years; here are some other resources. --KSmrq^T 18:24, 4 August 2006 (UTC)