Blacks are much more likely to be arrested on drug-related charges than whites, despite roughly equal levels of drug usage

The good news, if there were any to be gleaned from the data, is that the ratio is at least trending in the right direction, even if it’s still grossly disproportionate and completely out of whack with what it should be if blacks and whites were treated equally, in which case, going by the usage percentages, the ratio of black to white drug arrests should be 1.15, not 3.39.

Could it be that our drug policy would see less support if, instead of raids in the projects, police started busting down doors in predominantly white suburbs?

Insurance premium growth far outpaces inflation

In constant 2000 dollars, the average insurance rate for a single individual has grown by 58%.

It’ll be interesting to add 2010 to that chart, but we can still learn something from it even before that data point is in.  This law did not magically appear out of nowhere in March 2010.  Quite the contrary, it was a major point in the 2008 election and work on HCR began in earnest in 2009.  Yet, if you look at the graph, it doesn’t seem like anything in particular was happening in the 2007-2009 time frame.  Are we to believe the insurance companies were unaware of HCR and had absolutely no reaction to it until it became law, at which time they suddenly started gouging customers?

Let’s say we have some function f(x) and we want to “mix” it with some other function g(x). There are variety of ways we could do this, but one is the convolution,

We are, of course, free to Fourier transform this to get a somewhat nicer result.

Of course, if we want to apply this to images, we need a discrete expression, which of course we get by changing the integral to a sum.

In practice, we’re probably not going to work with line images, so this needs to be expanded at least to 2D and perhaps even 3D.

Probably the simplest (and one of the most useful) application of this is as a way to approximate derivatives, which I will post about next time, along with some python code to show how this actually gets implemented and how we deal with nasty things like the fact that images do not have infinite extent.

I took a look at the county by county results and compared that with the expected impact on the voters of each county.

There is a very weak, basically insignificant correlation between the percentage of each county that voted for 66 and the percentage that will see a tax cut.  Not much to see here.

Looking at voting results versus the percent of each county’s population that is seeing their taxes go up was more interesting.

Here, the correlation is much stronger, but not in the direction the “No on 66” crowd would have you believe.

It could be that the poorer people in wealthier counties simply voted overwhelmingly to gouge their neighbors, which is certainly possible, in which case the “no on 66” crowd would have a point.  We won’t know for sure unless some detailed polling is done.

I see the results of this “education” in my classes.  For example, there are many engineering majors who don’t know how to resolve vector components.  If we get lucky, at some point they saw an example that involved trig functions, so they just randomly guess until they arrive at the right answer.  Does x = r cosθ? r sinθ? r tanθ?  What is θ anyway?  That’s the good scenario.  The all-to-common reaction is a blank stare; the students simply have no idea where to even begin.  They know conceptually that vectors can be resolved into components, but haven’t the foggiest notion of how to go about doing it.

A similar disaster is unfolding in physics education.  Translating problems from words on a page to mathematical formulas that can be manipulated to get useful results has been de-emphasized and replaced with conceptual ideas and misguided notion of self-discovery.  While those conceptual ideas are important, that’s only one part of the whole story.  I have students who, despite having spent months in calculus-based physics, have no idea how to solve a basic kinematics problem.  Conservation of energy is a neat idea, but they can’t use it to solve problems.  Conservation of momentum is a powerful technique, but it requires being able to calculate momentum, which they can’t do.  Of course, this assumes the students even know what these things are, and there’s a good chance that they don’t, since using physics terminology is apparently too difficult and we should instead assume the students are limited to a third-grade vocabulary.

Students make it all the way to the end of the intro sequence without even knowing how to add vectors.  They get through the sequence by relying on drawing diagrams and writing about what things they might take into consideration when solving problems in the event that they actually knew any physics.  You may not be able to use conservation of energy, but if you can draw a bar graph that looks halfway reasonable and write down some assumptions, you can still scrape together enough points to pass.

Those who teach this curriculum have some diagnostic test results that they can point to and argue that their methods are better.  Having given these tests, it’s no surprise that classes which teach touchy-feely concepts over mathematically rigorous problem-solving score better.  The questions require little in the way of problem-solving skills or mathematical ability.  The tests measure conceptual understanding, which those who promote the approach then pass off as evidence that their students learn more.  Such a conclusion is clearly preposterous.

Having graded students work and worked with them on problems, it is obvious that they have not developed problem-solving skills and mathematical ability to any reasonable level.  What they demonstrate seems more appropriate for junior high than college.

In time, this approach will be shown for the disaster it is, much like “reform math.”  Unfortunately, it’s already too late for many people who haven’t learned what they should and don’t have the skills they need.

Perhaps this is an indication that I should get to work on the ODE solver portion of the C# code I’ve been (not) working on.

		public static double trace(double[,] matrix)
		{
			int n = Convert.ToInt32(Math.Sqrt(matrix.Length));
			double trace = 0;
			for(int i = 0; i< n; i++)
				trace += matrix[i,i];
			return trace;
		}

You may be wondering about the square root part. C#’s Length function returns the total number of elements in a matrix.  Since we’re passing in a square matrix, taking the square root gives the number of rows/columns.  At some point I should add code to check that the matrix is indeed square and error out gracefully if it isn’t.

I’ve also upgraded the site to WordPress 2.7 and changed the theme to something nice and simple.  The 2.7 migration shouldn’t result in any appearance or functionality changes, but the admin section is much nicer now.

I think the next thing I’m going to work on is finding the matrix inverses (probably via the Faddeev-Leverrier method) so I can find eigenvalues and eigenvectors.

There are, of course, countless libraries and software packages that could do these types of calculations me, and in practice I would in all likelihood use them.  Nonetheless, I think it’s useful to understand how those libraries work and thus, perhaps, when it is appropriate to use them as opposed to writing my own specialized code.  And of course, doing this is just plain fun.

• Physical constants
• Function approximation
• Derivatives
• Integrals
• ODEs
• PDEs
• Matrices (eigenvalue problems)
• Spectral analysis (fast fourier transforms, etc)

So far, I’ve mostly completed the physical constants bit, since that’s trivial and requires no real effort, and have started working on the approximation code, which is necessary to properly handle some of the latter things (e.g. determining slope at boundaries).

The basic idea is to make something that would cut down on the time required to write quick and dirty simulations.  It’s not intended to be the fastest or most elegant code, but simply something that works and gives correct answers.