In defence of anecdotal evidence

Anecdotal evidence is worthless, right? It comes about through uncontrolled conditions, and the people reporting it may report selectively (whether or not they intend to be biased). Thanks in part to the works of writers such as Richard Dawkins, we have learnt to dismiss anecdotes and personal testimonials, bringing us closer towards a world governed by Reason and statistics. And we can consign anything supported merely by anecdotes to fire. Hurrah!

For many things in the natural world, it is relatively straightforward (if expensive) to isolate the thing to be tested, conduct experiments or controlled trials, and then quantify the effect of that thing, with well-defined error bars. There are well-established principles and procedures for designing clinical trials, which is why we can resolutely label things like homeopathy, claims about the MMR vaccine, and everything Deepak Chopra says as bullshit, even if there are occasional success stories.

But – and perhaps Dawkins and co. haven’t realised this yet – humans are complicated, and social phenomena, which involve multiple humans, are very complicated. It is impossible to control the environment in which they arise. Also, individual experiences are unique, and it is difficult to give meaningful definitions or boundaries (see also this post), and to ensure that everybody uses the same definition. Related to this, people do not always accurately report their experiences: something that is perceived to be ‘shameful’ will be underreported even if it is actually quite common.

For these reasons, many social phenomena have not been studied quantitatively. But

Absence of evidence is not evidence of absence.
 

If anything, it is evidence that you haven’t yet done a good enough job collecting evidence on the subject.

When nothing else is available, and when it is not possible to conduct a systematic, controlled and quantitative study, then anecdotal evidence is the best you can do, and it needs to be taken into account, provided it comes from a credible reporter, who has no vested interests. And you must hear that evidence, even if you do not give it much weight.

In more technical language, I am arguing that probabilities are subjective measures of a degree of belief, not objective, and that any evidence should update your posterior probability, even if not by very much.

What I’ve said so far has been relatively abstract, but a failure to understand this has truly harmful effects when we dismiss anecdotal evidence. When hundreds of people report that they have been victims of something, then we need to start taking their testimonials seriously.

The Everyday Sexism Project has collected reports from tens of thousands of women about the sexist abuses that they have suffered. These are idiosyncratic and can’t be categorised; they might have happened repeatedly over a long time, or be one-off events. These acts are often not visible: even the person doing or saying the sexist things might not realise that they are being hostile. An individual claim of sexism might be dismissed by suggesting a variety of mitigating circumstances, or even by assuming bad faith on the part of the reporter! But what is more likely: that misogyny exists in our society, or that thousands of women have conspired together to make up that myth? (You may find Occam’s razor useful.)

Everyday sexism is just one example of microaggression, which also happens in other contexts such as race and religion. Moreover the fear of being subject to a racist attack is just as relevant as the number of actual attacks. Fear has a chilling effect on society, and has a measurable effect on the economy, but by its very nature it is difficult to measure.

Other examples include people’s testimonials of an NHS (or other public service) that is unable to provide a good experience. When thousands of people across the country complain about this, then it is no longer an egotistic individual or a problematic local service; there is something nationwide happening.

In summary,


When thousands of anecdotes are given, then it is no longer "merely" anecdotal evidence.

As with the etymological fallacy, the failure to give anecdotal evidence the weight that it sometimes deserves is a dangerous fallacy, because it is easy to commit it, thinking that you are rational and your opponent is not. This arrogant attitude poisons a discussion.

A spectral solver for Schrödinger’s equation

Here is a MATLAB program for solving the 1D time-dependent Schrödinger equation:
http://jftsang.com/code/schrodinger_spectral.m

You can specify a potential function and an initial condition, and the solver calculates the wavefunction at future times. Hopefully this will be useful for getting some intuition as to how solutions to Schrödinger’s equation behave.

Details

The solver uses a spectral method which performs the time-integration exactly. Errors come from the spatial discretisation. The calculation is done in a periodic domain, so edge effects may affect your solution, especially in scattering problems.

Postprocessing

Fourier-transforming the solution in space tells you about the relative strengths of different wavenumber components of the solution, and therefore about the momentum distribution at each time.

Fourier-transforming in time tells you about the different frequency components in the solution, which you can use to identify energy eigenstates. Note that you might have to calculate the solution for a long time before you have enough periods for the Fourier transform to be precise enough.

Not-so-continuum mechanics: A talk for the LMS

I will be speaking at the London Mathematical Society’s Graduate Students’ Meeting tomorrow morning, on Not-so-continuum mechanics: Mathematical modelling of granular flows. It’s meant to be a gentle introduction to granular phenomena, and I will introduce a basic version of the μ(I) rheology, a fairly (but not universally!) successful description of granular flow. Here’s a practice version of the talk.

The talks are meant to be aimed at `a general mathematical audience’. My talk assumes no mathematical knowledge beyond A-level Mechanics. I’m having some trouble understanding some abstracts for the other talks, and I’m not sure if my talk is just better-aimed at a general audience, or if theirs are, and there are just huge gaps in my mathematical training (which there are: I’ve never done any algebra beyond basic group theory, or any number theory or combinatorics).

Genesis, academia version

In the beginning, God created the universe. On the first day, God said: ‘Let there be light.’ And there was light. And God saw the light, that it was good.

On the second day, God made the firmament to divide the waters which were under the firmament from the waters which were above the firmament.

On the third day, God created the dry land, and the trees, flowers and grass, and saw that it was good.

On the fourth day, God created the sun, the moon and the stars, and introduced the seasons.

Whilst doing so, the Head of Department (on whose right hand sits God) asked him to review a number of funding proposals, which meant he didn’t have time to make more stars to fill up the vast void of space.

On the fourth evening, God noticed a bug with the light code that meant that the speed of the light from distant stars depended on the season. So he stayed up late fixing that.

On the fifth day, God unexpectedly had to give a lecture because his colleague went to a conference without telling anybody.

On the sixth day, God was creating Man, and was trawling through pages and pages of Matlab documentation when a system administrator decided it was time for a server reboot. The code for telepathy has been lost.

On the seventh day, God finally had some time to catch up with a huge number of emails. Undergraduates will understand why human supplications seldom receive a response.

A frivolous observation on milk

When microwaving a mug of milk, it sometimes goes all over the microwave. (The same happens with canned soup.) I’ve noticed that this tends to happen more often with whole milk than with semi-skimmed milk. My hypothesis is that in whole milk, the higher fat content means that an elastic layer of fat builds up on the surface, which traps any vapour, preventing it from leaving and causing its pressure to increase until the layer bursts suddenly.