mathematics

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Humanities Scholars Baffled By Math

Via the Wall Street Journal:

In the latest study, Kimmo Eriksson, a mathematician and researcher of social psychology at Sweden’s Mälardalen University, chose two abstracts from papers published in research journals, one in evolutionary anthropology and one in sociology. He gave them to 200 people to rate for quality—with one twist. At random, one of the two abstracts received an additional sentence, the one above with the math equation, which he pulled from an unrelated paper in psychology. The study’s 200 participants all had master’s or doctoral degrees. Those with degrees in math, science or technology rated the abstract with the tacked-on sentence as slightly lower-quality than the other. But participants with degrees in humanities, social science or other fields preferred the one with the bogus math, with some rating it much more highly on a scale of 0 to 100.

Specifically, 62% of humanities and social science scholars preferred the paper with the irrelevant equation, compared with 46% from a background of mathematics, science and technology.

This is a significant result, and I hope the experiment is repeated and replicated. It is all well and good for humanities and social science scholars to mostly eschew the use of mathematics in their work. But if humanities scholars begin to take work more seriously simply for the inclusion of (faux-) mathematics without themselves understanding the mathematics, then maybe it’s time for humanities and social science scholars to increase their mathematical and statistical literacy so as not to be so easily tricked by faux-mathematical rigour.

And this isn’t just a case of not understanding the equation — it seems like a nontrivial chunk of humanities and social science scholars have quite an inferiority complex. That should be a great embarrassment; there is nothing inherently inferior about the study of the human condition, or its (mostly non-mathematical) tools.

Last year, I wrote:

Well-written work — whether in plain language or mathematics — requires comprehensible explanations and definitions, so that a non-specialist with a moderate interest in the subject can quickly and easily grasp the gist of the concepts, the theory, the reasoning, and the predictions. Researchers can use as complex methods as they like — but if they cannot explain them clearly in plain language then there is a transparency problem. Without transparency, academia — whether cultural studies, or mathematics, or economics — has sometimes produced self-serving ambiguous sludge. Bad models and theories produce bad predictions that can inform bad policy and bad investment decisions.  It is so crucial that ideas are expressed in a comprehensible way, and that theories and the thought-process behind them are not hidden behind opaque or poorly-defined words or mathematics.

But in this case, I think the only real solution is mathematical and scientific literacy.

On the other hand, prestigious mathematics journals have also recently been conned into publishing papers of (literally) incomprehensible gibberish, so it is not like only humanities and social science scholars have the capacity to be baffled by bullshit.

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The Mathematicization of Economics

If one thing has changed in the last one hundred years in economics it has been the huge outgrowth in the usage of mathematics:

This is largely a bad development, for a number of reasons.

First of all layers of mathematics acts as a barrier to public understanding. While mathematics is a useful language for communicating complex ideas, those without training in mathematics will struggle to grasp what an author is trying to communicate if a paper consists mostly of equations untranslated into English. This is bad practice; it is easier to baffle with bullshit in an unfamiliar language than it is in plain English.

Second, mathematical models are always simplifications. Human action and economic behaviour is complex and unpredictable. While mathematical models can sometimes approximate a pattern quite well and so have some limited uses as toys, the complexity of human behaviour means that there are always unmodelled variables that can throw off a model’s output. Over-reliance upon or excessive faith in mathematical models can lead to bad forecasting and bad policy decisions. The grand theoretical-mathematical approach to economics is fundamentally flawed.

Third, attempting to smudge the human reality of economics into cold mathematical shackles is degenerative. Economics is a human subject. Human behaviour is not mechanical, it is not mechanistic. Physicists can very accurately model the trajectories of rocks in space. But economists cannot accurately model the trajectories of prices, employment and interest rates down on the rocky ground.

Economics would benefit from self-restraint in regard to the usage of mathematics. Alfred Marshall made some useful suggestions:

  1.  Use mathematics as shorthand language, rather than as an engine of inquiry.
  2.  Keep to them till you have done.
  3. Translate into English.
  4. Then illustrate by examples that are important in real life
  5. Burn the mathematics.
  6. If you can’t succeed in 4, burn 3. This I do often.

I hope the blowout growth in mathematics in economics is a bubble that soon bursts.

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How to Predict the Future

I’ve spent most of today reading.

The modern world appears divided into two camps (no — not those who believe the world can be divided into two camps, and those who don’t): those who believe that man has mastered nature, and those who know better.

The first camp share two chief delusions:

  1. That human beings — through the use of simulations, models, mathematics and other predictive techniques — can routinely make accurate predictions about the future.
  2. That these predictions should be deployed — usually via the power of government — to advance society.

The first supposition has been shown to be largely wrong, both empirically (predictions from models and simulations routinely miss — sometimes by wild margins, as they did during the 2008 meltdown) and rationally (economies are nonlinear systems where the output is not proportional to the input, and therefore chaos will always skew predictions). The second supposition is problematic, because it is dependent upon the first one being true.

The problem is that human beings want to predict the future — and accurately. Businesses want to be able to know what products will be selling in six months, six years or sixty years, so they can make money from it. Children want to know what field to study at college, so that they can get a paying job. Governments want to know what interest rates will be in three months, six months or 10 years, so they can decide how much to borrow. Scientists want to know what amounts of greenhouse gases will be emitted over the next half century, so they can attempt to model climate change.

And most significantly, those in power want the (often-undeserved) authority granted by a “window on the future “.

The best way to come-to-terms with this problem is to treat it as an advantage and not as a disadvantage. It is inevitable that there will be some forms of mathematical, statistical and predictive modelling, just as it is inevitable that philosophers and historians will write predictive literary works. Some will be wrong, and some will be right. The key is that it must be safe to be wrong. Societies, communities, individuals and organisations should plan for the future based not on the idea that the future is predictable, but based around the fact that the future is uncertain, and fundamentally difficult to predict. This means that everything needs leeway to break.

Some crucial examples:

  1. An international financial system which is torn down via a default-cascade through default of one bank or one nation is not robust to bad predictions.
  2. A banking system which is torn down through debt-deflation during a credit contraction is not robust to bad predictions.
  3. A lifestyle in which one bad prediction leads to serious illness or injury is not robust to bad predictions.
  4. An organisation  or family whose wealth (or health) can be destroyed by uncontrollable externalities is not robust to bad predictions.
  5. A nation dependent on the import of credit, resource and goods from hostile nations is not robust to bad predictions.
This just means that economists, writers, historians, bureaucrats and just about anyone who claims that they need to predict the future (that’s all of us, occasionally) needs to frequently and honestly ask themselves the question: what happens if I am wrong?