Tuesday, October 9, 2018

What, exactly, is the problem

I just read an article by Conrad Wolfram about math. The actual blog is here, and an interview about the article is here. Both are interesting and worth reading, but are not necessary before reading the rest of my blog.

No, I'm not going to make you do math. But allow me to begin at the beginning, as Asimov so famously said in his essays.

I hated arithmetic and math in school. There was an unpleasant incident with some adults shouting arithmetic at me, and wondering why I didn't get that 5+7=12. And another in grade 5 or so where the math teacher started with "Let x = blah" and proceeded with word problems like if Bill had some apples and Mary had twice as many, and the total was whatever, how many did Bill have. My response of "if Bill can count, ask him," did not go over well.

Once we got to geometry, that was more fun, mainly because I'd read about non-Euclidean geometry. My high school teachers hated marking my math because I mostly got the concept, but I was shite at doing the actual computations. At one point, briefly, I understood simple calculus and binary math. Business math (present value, annuities, and such) was fun, and one of the better classes I've ever taken. Statistical math (lies, damned lies, and statistics) was fun too.

Calculators became available while I was in grade school, and there was a huge debate if they should be allowed in schools. It was a short debate in our school. No. Such things were the work of the devil, and we had to learn our read'ng, rit'n, and 'rithmetic, the way it had always been done. One of my math classes had a giant slide rule mounted over the blackboard, and our class got taught how to use it, one of the last times that class was given. (A slide rule is, is, oh heck, ask Mrs Google yourself.)

That concept has gradually changed over the years, but not to hear some people talk about it. It's like they think any education beyond the most basic levels is bad. It was good enough for them and their parents, it should be good enough for our children.

Except, not. The world has changed. If the question is, how much seed to I have to buy to sow a crop on my land, the answer is not difficult to work out. Now the questions are, what are the drivers of climate change, which are the biggest, how will the changes affect our world, and what can we do about it. Not quite so simple.

Math isn't just a computational tool. It's a way of describing a problem in clear and unambiguous language, when asking Bill is not an option. Once done correctly we can (usually) program a computer to calculate the answer, though some things are unknowable (the last digit of pi), or will take longer than the life of the universe on our current computers (factoring huge numbers to see if they are prime). Sometimes just stating the problem clearly tells us we don't need to know the answer, because we don't have the problem right yet.

Getting back to our world, I want to see math taught better. Part of the reason idiots like Trump and Ford get elected, and why that loathsome reptile Kenney thinks he can get elected, is they play fast and loose with the facts. For example, politicians love to push the crime button. They make it sound like the (immigrant) barbarians are at the gate and we're all going to be killed in our beds unless we let them turn the full invasive surveillance powers of the state upon us.

Except it isn't true, as even a brief reading of the crime stats would show you. A bit of background in statistics would help people understand the difference between an anecdote (your neighbour being robbed because they left the garage door open) and data (there are x many robberies per year in Calgary where the thieves gained entry through an open door, and measured over decades the trend line is down.)

Math has a terrible rep. It's more than just manipulating numbers. It's more about manipulating concepts and bringing rigour to debate. It's easy for politicians to barf out word salad that makes no sense and serves only to incense their base. I think that's one of the reasons why populist politicians want to cut education and muzzle scientists; without facts and data being brought to the debate, it's easier for them to get the power and goodies they crave.

It's much harder for them to talk details using the numbers. For example. Politicians simultaneously say that immigrants are uneducated criminals and terrorists that are here to steal your job and do criminal terrorist stuff. They don't say it quite so bluntly, of course. It's buried in word salad and dog whistles to their target group.

Except there are more people killed by cows than terrorists. As an aside, these refugees are fleeing a situation that most of us in Canada cannot comprehend. They didn't create it, it was imposed on them, and leads them to make horrific choices like putting their child on a boat that might or might not make it to (relative) safety, while they have to stay behind. Should they escape such a situation, why ever would they want to destabilize their new home? Like any other parent, they want a safe place to raise their children.

And yes, many refugees are well educated, but find it difficult to gain the equivalent accreditation here. Thats why you see people that were engineers or doctors in their home country driving cabs here. (I could say much more on this topic, but that's a whole other blog.)

Another example: How much exactly is the differential between WTI crude, and the WCS price over time, and how does that affect the economics of building a pipeline? What exactly are the risks of a pipeline rupture given various assumptions about maintenance? How do we balance the economics of delivering oil to salt water for export, and the risk of a rupture,  to the impact of a rupture on the people that live nearby? How does all that compare to the economics of shipping oil by rail, or by ship?

If we're going to talk about the economics of oil (for good or bad) in a changing economy, that is all about the numbers and the assumptions made. They can be clearly stated; it just doesn't seem to be in anyone's interest to do so.

Damage to a pristine ecosystem and a way of life is nearly impossible to quantify, but we can account for that by emphasizing the consequence part of the risk equation. Plus we should put some skin in the game for the oil executives and regulators involved, on the scale of if there's a leak, you all go to jail till it's cleaned up.

Another local example. City council is discussing lowering the speed limit in residential neighbourhoods from 50 kph to 30 kph. The reduction in impact forces is clear and straightforward. However, as always, it's not so simple. Exactly how the person is struck would appear to have a dramatic effect on the outcome. Getting struck by some big-ass pickup would surely give a different impact that being struck by a Smart car. What else happens? Do they bounce off a curb, or strike a street sign? How old is the person and does that matter? Does it matter if they are running, walking, or riding a bicycle? How does being tall and skinny vs short and fat change things? Does the slower speed give the driver more time to swerve, and does the sideways component of the impact forces change the outcome? Lastly, and perhaps most importantly, how big a problem is it, in the sense of how many people are struck by cars in residential areas outside of existing school and playground zones? I say it's an interesting proposal, but there's a lot more data I want to see. (There is a lot of scholarly data here, if you're interested.)

They say it will add little time to car journeys. What is the actual aggregate increase in time? For me, each one way trip to get to the left turn at Safeway currently takes about 2 minutes, the lowered speed limit would increase that to about 3 minutes. See! The proponents say. One minute more against the life of a kid. Not so fast. Until we see the answer to the question above, we don't know how many kids. And that is a minute per one way trip, another for the return, times as many trips as you take in a period of time. Times as many people as take trips. Make some assumption that those minutes take up some amount of time that could be put to tasks that increase the GDP, thus lowering Canadian trade productivity. Is it worth it? Nobody knows. Rather than yell at one another, let's do the math and find out.

People talk about enforcement; what is the point of it when existing rules are not enforced? Note please, these are the people that bitch the loudest when they get a photo radar ticket. Let's assume for a moment that there is some level of speed enforcement done for school zones. How much would it cost to extend that to every residential area? What is the resulting ticket revenue? Is it cost effective?

I see people speed through construction zones, where the cost of a mistake is killing a construction worker, or writing off your car because you caught a tire on a sharp shoulder, leaving you to roll into a 3 foot deep hole where they're building a road bed. There are days I think the solution is to buy a lot of portable photo radar cameras, train a small army of people to operate them properly, give them some motor scooters to get around, and blanket the many (MANY!) construction zones, plus playground and school zones. Eventually the financial impact would set in, and people would modify their behaviours. I'd like to see that math on that too.

Lastly, if there is a problem, is the speed limit the best way to solve it? It assumes that all people are equally likely to collide with a pedestrian, and I'm not sure at all that's true. I see lots of traffic going by on our street, and the faster traffic is overwhelmingly by young drivers on the way to and returning from the little mall with a 7-11 and a liquor store. Three guesses which of those they are going into, and the first two don't count.

Instead of tinkering with the speed limit, what if we dramatically increase the consequences of a collision? What if striking a pedestrian was an automatic loss of your license for a year, and a fine of 10 percent of your gross income from all sources, plus paying all the pedestrian's medical related bills that are not covered by Alberta Health Care or their own medical benefits. Would that change your behaviour? Is there a way to model that to see what would happen?

Those sorts of things are why I want to see kids getting past the computational aspects of math. We have calculators and computers for that. I want to see them learn to ask the right questions, and learn to set it up so that they can be confident the answer applies to the question they asked.

As a reward for chewing through a wall of text, you get a pair of dahlias and a flower tower from Sept 24. This is after lots of cool rainy weather, so it's a little worse for wear, but still hanging in there.

1 comment:

  1. Always a pleasure. And so we come to one of my hobby horses. Let's teach the definition of risk. Risk = Impact (usually measured in $) x the probability of an event occurring expressed as events per unit of time. A better understanding of risk would help get rid of one shrill sound in the barrage of noise being foisted upon us. Cheers, Sean


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