Wednesday, 8 June 2016

Seven tools for thinking #5 Occam’s razor

All things being equal, the simplest solution is usually the best one.
William of Ockham

You’ve probably heard the old adage that if you hear hoof beats in the middle of the Wiltshire countryside you shouldn’t assume a herd of zebras is on its way. The simplest explanation for a phenomenon is the likeliest and in this case you’re probably safer to expect to see some horse. Of course, this isn’t always the case. If you’re on the African savannah then zebras are a more reasonable expectation. And sometimes the simplest explanation won’t turn out to be true, but it’s a sensible starting point for investigation.

This simple rule of thumb, has been widely attributed to the 14th-century English logician and philosopher, William of Ockham (or Occam), but actually it’s been around a lot longer than that. Aristotle first suggested the idea that perfection equals simplicity: “The more perfect a nature is, the fewer means it requires for its operation.” Its Latin name is lex parsimoniae, the law of parsimony, exemplified in the maxim, ‘It is pointless to do with more what is done with less’. This is pretty straightforward and tells us to avoid concocting fanciful theories if a simple one will suffice. Daniel Dennett gives this example:

If exposure to extremely cold air can account for all the symptoms of frostbite, don’t postulate unobserved “snow germs” or “Arctic microbes”. Kepler’s laws explain the orbits of the planets; we have no need to hypothesise pilots guiding the planets from control panels hidden under the surface.

So far so good. Occam’s razor is the principle on which the scientific method is built. For instance, the physicists Hendrik Lorentz and Albert Einstein both concluded independently that the closer we get to moving at the speed of light, the more we slow down. But while both arrived at the same results from their equations, Lorentz’s explanation relied on changes that take place in the ‘the ether’. Because Einstein made no reference to a non-existent , mystical substance, his explanation was accepted as the most likely.

Unfortunately though, simplicity is not always so simple. Dennett goes on to explain:

One of the least impressive attempts to apply Occam’s razor to a gnarly problem is the claim (and provoked counterclaims) that postulating a God as creator of the universe is simpler, more parsimonious, than the alternatives. How could postulating something supernatural and incomprehensible be parsimonious? It strikes me as the height of extravagance, but perhaps there are clever ways of rebutting that suggestion.

Just because an explanation springs easily to mind and does require much thinking about doesn’t mean it’s either simple or sensible. We run into this kind of intuitive thinking in education all the time. teachers are often guilty of assuming an intervention is effective because they see students getting on with stuff and apparently enjoying it. Does this mean their intervention will be effective in the long term? It’s easy to say yes of course it will, but how do we know? After all, students producing work and being engaged are poor proxies for learning.

Then there are times we look at improved results and claim they are caused by our intervention. We see causation where there is only correlation. Some narratives are persuasive and plausible; we want to believe them, but as research from Ofqual shows, results fluctuate naturally and it’s not unusual or unreasonable to expect results to go up or down by between 19-9% a year! Of course we want to take credit for successes and shift the blame for failures, but maybe none of it has anything to do with our efforts?

All of this is moot. We must always remember that Occam’s razor proves nothing. It serves instead as a heuristic device – a guide or a suggestion – that states that when given two explanations for the same thing, the simpler one is usually the correct one.

However, we should be wary of fooling ourselves into believing that simplest is always best. It isn’t, but it probably will be most of the time. Occam’s razor is useful, but it has its limits. It’s great for picking between competing explanations, but a bad way to try to disprove complex ideas – after all, new information might always come to light. Dennett agrees:

The prospect of turning it into a metaphysical principle or fundamental requirement of rationality that could bear the weight of proving or disproving the existence of God [or that improved exam results can be attributed to Year 11 intervention classes]  in one fell swoop is simply ludicrous. It would be like trying to disprove a theorem of quantum mechanics by showing that it contradicted the axiom “Don’t put all your eggs in one basket”.

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