New York City Schools get graded

Today the New York City School systems are getting done to them what all our schools been doing to students - ranking them and assigning grades -- and they don't like it one bit.

I've posted before on how some things, like the "magic dice", have no "best" and cannot be put into some kind of rank-order.

The New York Times today has an article "Schools brace to be graded" that runs into this problem head-on and is producing a great deal of social conflict.

The point is an important one and I want to mention it again. I keep on seeing cases where people, absolutely sure that there must be some way to do this, valiantly try new and more complicated ways to "get it right" and rank something.

It is a dangerous concept and we need to grow up and get over it. It is a damaging concept. The whole idea is one of the pillars of intense competition between people, cultures, and nations and one of the ultimate causes of outright warfare - to be "best", to be "number one" - our people are killing themselves or going into deep depression over a quest that can never possibly be achieved because the idea is meaningless.

First they try one measure, which everyone knows is incomplete. Then they try a variety of different measures, which are also incomplete. Then, that's complex and confusing to have some high and some low scores, and they know nothing about "unity in diversity", so they try everything they can to "combine" all that information into a uniform single number or letter.

So, first they'll compute an average, then maybe a "weighted average", then something like the square root of the sum of the squares, then even more complex calculations that raise up so much dust that no one can figure out what they did, like the New York Schools, probably trying to be more "accurate" or possibly hoping that no one can challenge what they can't understand or explain.

But I challenge it, on fundamental grounds, that have nothing to do with how it was "computed" at all. It doesn't matter how it was computed - something as multidimensional and complex as a person or a school cannot be meaningfully reduced to a single number, period. The whole concept is flawed.

There is a direct analog in physics, which we can be confident is simpler than society and life as a whole. Scientists have a concept called "rank", but it is the nature of the beast that some set of measurements can be reduced to, and that is as far as you can reduce it.

So, yes, a few things can be reduced to "scalars", which are single numbers, like "temperature", that don't depend on context or what the observer is doing at the time.

Most physical things, however are more complex than that. The next more complex thing than a scalar is a "vector", which you may vaguely recall from school - a directed arrow kind of thingie, like "velocity". Velocity is different from speed, in that speed can be reduced to a number, like 85 miles per hour, but velocity includes a direction as well, such as "85 miles per hour heading due North." And, of course, physical things have those pesky "units" or "dimensions" that are somehow attached, so that talking about a number without units doesn't get the answer right.

So, most easy classical mechanics requires these "vectors" to write down the equations at all and solve them. You really can't even begin to solve the problems using just scalars, period.

That, however, is just the beginning of complexity. Scalars are the first of a long series of types of things called "tensors", and an be described with a single number. Vectors are the the next one up, described with "arrows", and cannot be reduced to single numbers, period.

Another example would be the torque you want to apply to something. You can't say you want a torque of "2", and skip the direction part. Clockwise or counter-clockwise? It matters a lot!!

The complex part cannot be left off just to make your math "simpler" or because you never felt like doing the work required to learn how to do the math correctly. It will not "come to you" -- you have to go to it.

Then there are things physicists deal with daily that cannot be reduced to vectors, even. An example is the "electromagnetic field". This field requires the next higher level tensor,. a second-dimensional one, to capture it correctly, which needs a matrix of numbers and rules for how it changes depending on where you stand and how you're looking at it.

If you use that math, it is actually relatively "easy" to describe in equations, and you get the "Maxwell equations", and can correctly figure out what's going on. If you don't use that math, you can't get answers that match reality and should stop trying.

Things get more complex than that fairly quickly. To describe gravity requires a mix of tensors up to a 4-dimensional thingie called the Riemann space-time curvature tensor.

Once you stop kicking and screaming in protest and accept that you have to use complex tensors, not scalars, and figure out how to do that, the equations suddenly get much easier, actually. It's like why scientists use metric not feet and pounds -- not because it's more sophisticated, but because it's easier.

Alfred Einstein stated that "All physical equations are tensor equations." That's it. You can't get away from this, if you believe Einstein.

And, the equation for space-time, in that formalism works out to this:

R= zero

Cool. Once you start putting mass and planets in there, it gets messy fast, but in a way you can manage with just careful bookkeeping. If you use tensors, you can write simple equations, and solve the problems. If you don't use tensors, and try to use scalars, forget it.

So, that's our social dilemma here. The description of people, schools, sports-teams, presidential candidates, etc. all require a level of math that we wish wasn't true, so we just go on pretending that we can say something meaningful without going to all that effort.

And, we end up assigning "grades" to students, then trying to aggregate different "grades" into single overall "grades" (grade point averages), and then trying to make meaningful decisions based on those single composite numbers, like rank students or schools -- and discover that we get absurd results.

Then, we punish those with "low scores" and apply pressure for them to "shape up" or "teach to the test", and have a mess on our hands.

The core problem here is that the physical objects we are trying to study - school systems -- are not intrinsic "scalars" but are probably at least level 3 or higher "tensors".

Actually physicists and mathematicians squabble over exactly what kind of complexity is required and whether it should be "tensors" or something else -- but they all would agree instantly that you can't reduce the world to a set of equations using just "scalars", like grades.

The first question we should have asked is "What is the smallest rank tensor we can use to meaningfully capture the complexity of this thingie?" and it would immediately be clear that scalar numbers ("grades") are too simplistic.

We don't like that answer, so we just go on doing the wrong thing, then we wonder why we have so much conflict, and why some well-loved schools end up getting low grades. Then we set social policy, public policy, and feedback based on those "grades".

Evaluate, yes. Try to reduce to single scores using the axe of some magical computation? NO!
New York City Schools