Why are we not keeping up?

There’s a fascinating line in the opening pages of Here’s Looking at Euclid:

By age 16, school kids have learned almost no math beyond what was already known in the mid-seventeenth century, and likewise by the time they are 18 they have not gone beyond the mid-eighteenth century.

If the point of schooling is to teach the current best understanding of the world, we appear to be failing.

Granted, maths is unlike science in that the old ways are built upon rather than overturned. We still learn Pythagoras theorem but not geocentrism.

This necessitates teaching newer mathematical discoveries in addition to what came before it. But is there really no recent mathematical discovery that would be useful to learn in school? Or at least help us shape more rounded adults, equipped for the modern world? Boolean algebra mayhaps?

I was thinking about this as I came across the following passage in The Lady Tasting Tea:

As measurements became more and more precise, more and more error cropped up. The clockwork universe lay in shambles. Attempts to discover the laws of biology and sociology had failed. In the older sciences like physics and chemistry, the laws that Newton and Laplace had used were proving to be only rough approximations. Gradually, science began to work with a new paradigm, the statistical model of reality. By the end of the twentieth century, almost all of science had shifted to using statistical models… Popular culture has failed to keep up with this scientific revolution. Some vague ideas and expressions (like “correlation,” “odds,” and “risk”) have drifted into the popular vocabulary, and most people are aware of the uncertainties associated with some areas of science like medicine and economics, but few nonscientists have any understanding of the profound shift in philosophical view that has occurred

It’s definitely my experience that people are more comfortable with a deterministic model of the universe than a probabilistic one. But why are so many of us stuck in old paradigms even as our world has become immensely sophisticated and complicated?

If nothing else, a more widespread probabilistic model would lead to more nuanced discussions around new research and challenges like climate change. A more modern understanding of mathematics would help us all get the most of technological advances.

Many of the books I’ve read criticising modern education see it as a relic of the industrial revolution and empire, geared towards producing identical widgets to keep things running smoothly. Can’t help thinking that’s right. And we haven’t changed it much.

As always my emphasis.

It’s about who you know and trust

There is a pervasive idea in Western culture that humans are essentially rational, deftly sorting fact from fiction, and, ultimately, arriving at timeless truths about the world. This line of thinking holds that humans follow the rules of logic, calculate probabilities accurately, and make decisions about the world that are perfectly informed by all available information. Conversely, failures to make effective and well-informed decisions are often chalked up to failures of human reasoning—resulting, say, from psychological tics or cognitive biases… Models of social learning help us see that this picture of human learning and rationality is dangerously distorted. What we see in these models is that even perfectly rational—albeit simple—agents who learn from others in their social network can fail to form true beliefs about the world, even when more than adequate evidence is available. In other words, individually rational agents can form groups that are not rational at all.

This is from The Misinformation Age by Cailin O’Connor and James Owen Weatherall, which I first referenced a couple of days ago.

At first glance that your beliefs are a product of the people you surround yourself with is quite banal. Of course most us haven’t personally verified even a fraction of our “knowledge” – from the mathematical heuristics we learn in school to the actual size of Greenland.

In fact the ability to share information – both bad and good – is a major factor in our success as a species.

But unpack this a little more – as the authors of this book do masterfully – and it starts to dawn how devastating poor information hygiene really is. Your personal store of knowledge or model of the world isn’t so much the product of your own “filter”, but the filter of those around you. And around them. And around them….

And, as the models that O’Connor and Weatherall construct show, it isn’t just deliberate misinformation that can affect those in a social network. In fact, misinformation is only one way companies etc. can  subtly put their finger on the scale.

Rather, both deliberate and unconscious misunderstanding of uncertainty and randomness can filter through to the unwitting, not least by curtailing the possible or sending us down wrong tracks. And this is before adding the complexities of conformity bias, clustering and selection, distrust etc.

So, what to do? I don’t know. But consider this:

…we need to understand the social character of belief—and recognize that widespread falsehood is a necessary, but harmful, corollary to our most powerful tools for learning truths… When we open channels for social communication, we immediately face a trade-off. If we want to have as many true beliefs as possible, we should trust everything we hear. This way, every true belief passing through our social network also becomes part of our belief system. And if we want to minimize the number of false beliefs we have, we should not believe anything.

As always, my emphasis.

What are school tests trying to measure?

I’ve just started reading The Lady Tasting Tea, the story of statistics in/and modern science. But one of the early examples has gotten me thinking – how would a scientist go about testing the general intelligence/retained knowledge of a group of students?


Whatever we measure is really part of a random scatter, whose probabilities are described by a mathematical function, the distribution function.

It seems unlikely a contemporary scientist dropped onto planet B would propose the kind of one-and-done tests that students generally encounter at the end of subjects, semesters, years and school itself.

From the book:

Consider a simple example from the experience of a teacher with a particular student. The teacher is interested in finding some measure of how much the child has learned. To this end, the teacher “experiments” by giving the child a group of tests. Each test is marked on a scale from 0 to 100. Any one test provides a poor estimate of how much the child knows. It may be that the child did not study the few things that were on that test but knows a great deal about things that were not on the test. The child may have had a headache the day she took a particular test. The child may have had an argument with parents the morning of a particular test. For many reasons, one test does not provide a good estimate of knowledge. So, the teacher gives a set of tests. The average score from all those tests is taken as a better estimate of how much the child knows. How much the child knows is the outcome. The scores on individual tests are the data.

I’m quite biased here as I’m absolutely horrid at standardised testing – for a variety of reasons including medical. But it does seem to be yet another aspect of schooling that should be updated given our increasingly sophisticated understanding of the world. Randomness is not to be messed with.

(As usual my emphasis)

More proof Trump isn’t interested in learning anything

I’m not quite sure what to make of The Fifth Risk by Michael Lewis, and, to be honest, I’m not sure that he does either.

It’s the story of the Trump transition. Or, rather, the lack of one. The book isn’t particularly long. More like a Vanity Fair column that got out of hand. Some of the vignettes of public service meander, too many are hagiographic, and there are more than necessary.

Lewis also explicitly repeats themes – that most of the problems with government are practical rather than political, for example.

But Fifth Risk is a brilliant portrait of what happens when the people in charge are thoroughly unconcerned with learning anything new. Either because they think they know better, tribalism stops them recognising anyone else’s competence, or they just don’t want to know.

…A month after the election, Pyle arrived for a meeting with Energy Secretary Ernest Moniz, Deputy Secretary Sherwood-Randall, and Knobloch…“He did not seem motivated to spend a lot of time understanding the place,” says Sherwood-Randall. “He didn’t bring a pencil or a piece of paper. He didn’t ask questions. He spent an hour. That was it. He never asked to meet with us again.”

…Pyle eventually sent over a list of seventy-four questions he wanted answers to. His list addressed some of the subjects covered in the briefing materials, but also a few not: Can you provide a list of all Department of Energy employees or contractors who have attended any Interagency Working Group on the Social Cost of Carbon meetings? Can you provide a list of Department employees or contractors who attended any of the Conference of the Parties (under the United Nations Framework Convention on Climate Change) in the last five years? That, in a nutshell, was the spirit of the Trump enterprise. “It reminded me of McCarthyism,” says Sherwood-Randall.

…Pyle vanished from the scene. According to a former Obama official, he was replaced by a handful of young ideologues who called themselves “the Beachhead Team.” “They mainly ran around the building insulting people,” says a former Obama official. “There was a mentality that everything that government does is stupid and bad and the people in it are stupid and bad,” says another.

Then again, I’m not sure we didn’t already know this about the Trump organisation. So far I’ve read every book Lewis has written, and I will probably buy the next as well. But this one may be safe to miss.

The writing is pretty good though.