Ockham’s Razor – The Elegance of Simplicity

Aug 28, 2012 by

William of Ockham (1285–1347/49) was a 14th century English philosopher. His philisophical propsitions forms the basis of how we approach, understand and try to describe the world, especially in the world of Science. He espoused the maxim “Pluralitas non est ponenda sine necessitate;” or “Plurality should not be posited without necessity.”

Ockham’s razor also spelled Occam’s razor, also called law of economy, or law of parsimony, is a principle that gives precedence to simplicity; of two competing theories, the simplest explanation of an entity is to be preferred. The principle is also expressed as “Entities are not to be multiplied beyond necessity.” The ‘razor’ comes from the idea of shaving off any unnecessary assumptions from a theory or to parr down competing theories. This principle may sound ‘obvious’ to us but … that’s the point, that’s how we’re already trained to think. How different would our world be if we didn’t take this approach. Below is a discussion of this seminal view.



The Idea in Practice
 
An issue…

Crop circles are geometrical patterns of flattened wheat, barley, rye, and so on. Such formations, often extensive and highly intricate in design, have been found throughout the world in ever-increasing numbers since the 1970s. Much reported in the media, there was at first feverish speculation over their origin.

Some explanations…
Among the favoured theories were that: -

  1. the circles marked the landing sites of alien spaceships or UFOs which had left the distinctive patterns on the ground
  2. the circles had heen created by human hoaxers, who had come at night, equipped with ropes and various other tools, to create the marks and so stoke up media attention and speculation


Horses not zebras

It is sometimes tempting for doctors, especially young doctors, to diagnose a rare and exotic condition where a commonplace and mundane explanation is much more likely. To counter this tendency, US medical students are sometimes warned: ‘when you hear hoofbeats, don’t expect to see a zebra’ – most of the time, the more obvious diagnosis will be the correct diagnosis.

Both explanations appear to fit the available evidencey, so how do we decide which of these or the other available theories we should believe? In the absence of any other information, can we make a rational choice of one theory over its rivals? According to Ockham’s razor, we can: where two or more hypotheses are offered to explain a given phenomenon, it is reasonable to accept the simplest one – the one that makes fewest unsupported assumptions. Theory 1 assumes that UFOs exist, an assumption for which there is no clear supporting evidence. Theory 2 makes no assumptions about paranormal activity; indeed it assumes only the kind of prankish human behaviour that has been common throughout history. So we are rationally justified – provisionally and always allowing that new evidence may become available – in believing that crop circles are the work of human hoaxers.

In fact, in this case Ockham’s razor is spot on. It is now known that theory 2 is correct, because the hoaxers concerned have admitted as much. Is the razor always as reliable as this?



Limitations

Sometimes known as the principle of parsimony1. excessive frugality; extreme economy or stinginess.

2. Adoption of the simplest assumption in the formulation of a theory or in the interpretation of data
, Ockham’s razor is in essence an injunction not to seek a more complicated explanation for something where a simpler one is available.

If several alternative explanations are on offer, you should (other things being equal) favour the simplest. Ockham’s razor does not claim that a simpler explanation is always correct, merely that it is more likely to be true and so should he preferred until there are grounds for adopting a more elaborate alternative. It is essentially a rule of thumb or methodological injunction, especially valuable (one would suppose) in directing one’s efforts in the early stages of an investigation.


The KISS principle

Ockham’s razor pops up in engineering and other technical fields as the ‘KISS principle’. In developing computer programs for instance, there’s often an irresistable attraction towards complexity and over-specification, which usually manifests itself in an array of ‘bells and whistles’ that are ingeniously bolted on and promptly ignored by 95% of end users. The oft quoted maxim in this case is : ‘Keep It Simple, Stupid’.

The Razor in Action

how do we tell which scenario is simpler ?

Although not explicitly credited, Ockham’s razor is frequently wielded in scientific and other rational debates. For example referring to the philosophical “Brain in a vat problem”, (see an earlier article here…) two rival scenarios are set up, both apparently compatible with the available evidence: we are real physical beings in a real world, or we are brains in vats. Is it rational to believe the former rather than the latter? Yes, according to Ockham’s razor, because the former is much simpler: a single real world, rather than the virtual world created by the vat, plus the vat apparatus, evil scientists and so on. But here, as often elsewhere, the problem is shifted, not solved: for how do we tell which scenario is simpler.’ You could, for instance, insist that the number of physical objects is what matters and therefore that a virtual world is simpler than a real one. The razor may be used to slice away one layer of complexity, but it doesn’t of course indicate which one to throw away.



What is simplicity ?

The idea of simplicity can be interpreted in different ways. Is the injunction against introducing unwarranted entities or unwarranted hypotheses? These are very different things; keeping the number and complexity of hypotheses to a minimum is sometimes referred to as ‘elegance'; minimizing the number and complexity of entities as ‘parsimony’. And they can run counter to each other: introducing an unknown entity, such as a planet or a subatomic particle might allow a great deal of ‘theoretical scaffolding’ to be dismantled. But if there is such a basic uncertainty about the meaning of the razor, is it reasonable to expect any firm guidance from it?


Buridan's Ass

Judicious use of Ockham’s razor is supposed to facilitate rational choice between rival theories. Buridan’s ass – supposedly due to William of Ockham’s pupil Jean Buridan – illustrates the danger of over-rationalizing choice. The ass in question, finding itself placed midway between two haystacks, can see no reason to favour one stack over the other and so does nothing and starves to death. The hapless beast’s mistake is to suppose that there being no reason to do one thing rather than another makes it irrational to choose and hence rational to do nothing. In fact, of course, it is rational to do something, even if that something cannot be determined by rational choice.

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