First off, let me point out that my prediction of an earthquake of magnitude 5 or greater every day in June somewhere on earth is doing just fine.
There were six on June 1, including one of magnitude 6.4 off the coast of Chile… three on June 2… four on June 3… and there has already been one today. As I said, this is not very useful prediction. The point is, it’s very easy to make useless predictions about earthquakes.
As far as I can tell, the USGS won’t let me build a map showing just the quakes so far this month – but I should be able to do it easily in Mathematica. Just not this morning.
Second, Roger Federer is in the final of the French Open… so I expect to be watching that tomorrow morning, instead of doing mathematics.
Third, I have understood the Buckingham Pi theorem in dimensional analysis (finding dimensionless numbers like the Reynolds number)… it is apparently nothing more than the rank–nullity theorem in linear algebra, that the rank of a matrix plus the dimension of its nullspace is equal to the number of columns.
I have, of course, a book full of marvelous examples to work out. The challenge is not in finding a basis for the nullspace (the Singular Value Decomposition will do that)… the challenge is not even in finding a basis with integer components (row reducing the augmented transpose will do that)… the challenge is selecting from among the huge number of basis vectors with integer components. Well, maybe I’ll find a way to do that, too, while I play with examples.
Then there’s color.
It was Fairchild’s “Color Appearance Models” that got me started on color theory again. Let me say, however, that my basic fascination with color – despite all of the mathematics I’ve done – is an interest in color harmony, the choosing of colors for graphic arts.
On the one hand – for the mathematics – I have made it through Fairchild this week; on the other hand — for the art — I have found several more Internet resources for color harmony.
It appears to interpolate the numerical specifications… I doubt that I would always wants to blend colors that way… but this is a fine start from which to consider alternatives.
And it might be useful for getting dark neutrals.
Artists suggest that instead of mixing red, for example, with black, you can get a more interesting dark neutral color by mixing red with green. Let’s see.
(I’ll get around to checking out that result, and comparing it with “mixing with black”, later.)
You might also consider moving up that URL to learn more about the author and his interests.
Here, for another, is a little program that will give you the colors for what I would call a geometric scheme such as “split complementary” – which he calls “triad” and I would not. I wish it had a few more possibilities, so I’ll probably end up writing something myself… but this is a good start.
You might note that it used the artists’ color wheel, with green opposite red, rather than the “other” or CMY color wheel, with cyan opposite red. I talked about these two here.
One of the other things I need to program is something that will map a given color (say HSB) onto the artists’ color wheel.
Need some ideas? Here’s a generator of random colors.
Someone on the Apple ColorSync Users list pointed out this interesting PDF about color wheels.
There is a thorough and fascinating site devoted to color. Actually, of course, there are many… but I only encountered this one recently. I probably found it here but here is the site home page itself, as you would expect.
There is an interesting take on the artists’ color wheel versus other color wheels. By asserting that only one was “right”, he got a lot of responses – mostly in the form, “you’ve obviously never mixed two paints in order to produce a third color”. As I said before, I disagree with him; I believe that the different color wheels admirably serve different purposes. Nevertheless, his post is worth reading, because he knows the relevant facts. He just assumed there was only one valid purpose for a color wheel.
There is a rather beautiful site about color theory – so he’s good in practice as well as in theory. As usual, my link points to a specific page, rather than to home. And I ended up buying books by Itten and Albers, based on his recommendations.
… I daresay that today I’ve made up for a few recent very short diary posts.
Finally, I suspect that I will be doing reaction rates (chemical engineering) and dimensional analysis (finding dimensionless numbers) later today. And I hope I get to play with color this evening.
And yet, I did this post before turning my alter ego the kid loose this morning, so it’s time to find out what he wants to play with in mathematics.