Can you show me an example of how a 10 dimensional graph could be useful?

These two are the most talented practitioners of information presentation that I know about :
Edward Tufte
David McCandless.
I don’t think I’ve seen anything with 10 dimensions represented, but these two would be my guides if I needed to attempt it.

Ten different dimensions on one graph is usually too much. I think Tufte suggests that five or six are the maximum you can display without leading to complete confusion. You can play with width of line, color of line, line in space, multiple lines, annotation of lines, and lines or points or areas within a geographic space. There’s lots of other things to do, as well.

I agree that Tufte is one of the leading experts on presenting data. I have his books in my office and went to one of his presentations, years ago. But like @dabbler I don’t know about ten dimensions.

The best I can think of is to turn the ten dimensions into a formula, like a regression, and display that formula and measures of fit on a graph.

The first example I can think of is in stock trading. If you want to have 10 (give or take) factors (e.g. price of gold, movement of the s&p, interest rates, etc… or whatever else you want) and then display them on a graph. I don’t know how you’d do it to make it clear but that is at least an area where 10 (or more) factors are useful.