[Physics FAQ] - [Copyright]
Updated 1997 by Sugihara Hiroshi.
Original by Phil Gibbs, 1996.
Occam's (or Ockham's) razor is a principle attributed to the 14th century logician andFranciscan friar William of Ockham. Ockham was the village in the English county ofSurrey where he was born.
The principle states that "Entities should not be multipliedunnecessarily". Sometimes it is quoted in one of its original Latin forms togive it an air of authenticity:
"Pluralitas non est ponenda sine neccesitate"
"Frustra fit per plura quod potest fieri per pauciora"
"Entia non sunt multiplicanda praeter necessitatem"
In fact, only the first two of these forms appear in William's surviving works, and the thirdwas written by a later scholar. William used the principle to justify manyconclusions, including the statement that "God's existence cannot be deduced by reasonalone". That one didn't make him very popular with the Pope.
Many scientists have adopted or re-invented Occam's Razor, as in Leibniz's "identity ofobservables"; Isaac Newton stated the rule as: "We are to admit no more causes ofnatural things than such as are both true and sufficient to explain theirappearances".
The most useful statement of the principle for scientists is"When we have two competing theories that make exactly the same predictions, thesimpler one is the better".
In physics we use the razor to shave away metaphysical concepts. The canonicalexample is to compare Einstein's theory of special relativity with Lorentz's theory, which says that rulers contract and clocks slow down when in motion through the ether. Einstein'sequations for transforming spacetime are the same as Lorentz's equations for transformingrulers and clocks, but Einstein and Poincaré recognised that the ether could not bedetected according to the equations of Lorentz and Maxwell. By Occam's razor it hadto be eliminated.
The principle has also been used to justify uncertainty in quantum mechanics.Heisenberg deduced his uncertainty principle from the quantum nature of light and theeffect of measurement.
Stephen Hawking writes in A Brief History of Time:
"We could still imagine that there is a set of laws that determines events completelyfor some supernatural being, who could observe the present state of the universe withoutdisturbing it. However, such models of the universe are not of much interest to usmortals. It seems better to employ the principle known as Occam's razor and cut outall the features of the theory that cannot be observed".
But uncertainty and the non-existence of the ether cannot be deduced from Occam's Razoralone. It can separate two theories that make the same predictions, but it does notrule out other theories that might make a different prediction. Empirical evidenceis also required, and Occam himself argued for empiricism, not againstit.
Ernst Mach advocated a version of Occam's razor that he called the Principle ofEconomy, stating that "Scientists must use the simplest means of arriving at theirresults and exclude everything not perceived by the senses". Taken to itslogical conclusion, this philosophy becomes positivism; the belief that there isno difference between something that exists but is not observable and something thatdoesn't exist at all. Mach influenced Einstein when he argued that space and timeare not absolute, but he also applied positivism to molecules. Mach and his followersclaimed that molecules are metaphysical because they were too small to detectdirectly. This was despite the success the molecular theory had in explainingchemical reactions and thermodynamics. It is ironic that while applying theprinciple of economy to discard the concept of the ether and an absolute rest frame,Einstein published almost simultaneously a paper on brownian motion that confirmed thereality of molecules and thus dealt a blow to positivism. The moralof this story is that Occam's razor should not be wielded blindly. As Einstein putit in his Autobiographical notes:
"This is an interesting example of the fact that even scholars of audacious spirit andfine instinct can be obstructed in the interpretation of facts by philosophicalprejudices".
Occam's razor is often cited in stronger forms than Occam intended, as in thefollowing statements. . .
"If you have two theories that both explain the observed facts, then usethe simplest until more evidence comes along".
"The simplest explanation for some phenomenon is more likely to be accurate thanmore complicated explanations".
"If you have two equally likely solutions to a problem, choose the simplest".
"The explanation requiring the fewest assumptions is most likely to be correct".
...or in the only form that takes its own advice...: "Keep things simple!"
Notice how the principle has strengthened in these forms that should morecorrectly be called the law of parsimony, or the rule of simplicity.To begin with, we used Occam's razor to separate theories that would predict the sameresult for all experiments. Now we are trying to choose between theories that makedifferent predictions. This is not what Occam intended. Should we not testthose predictions instead? Obviously we should eventually, but suppose we are at anearly stage and are not yet ready to do the experiments. We are just looking forguidance in developing a theory.
This principle goes back at least as far as Aristotle, who wrote "Nature operates in the shortest way possible".Aristotle went too far in believing that experiment and observation were unnecessary. The principle of simplicity works as aheuristic rule of thumb, but some people quote it as if it were an axiom of physics, which it is not. It can work well inphilosophy or particle physics, but less often so in cosmology or psychology, where things usually turn out to be more complicatedthan expected. Perhaps a quote from Shakespeare is more appropriate than Occam's razor: "There are more things inHeaven and Earth, Horatio, than are dreamt of in your philosophy".
Simplicity is subjective and the universe does not always have the same ideas aboutsimplicity as we do. Successful theorists often speak of symmetry and beauty as wellas simplicity. In 1939, Paul Dirac wrote "The research worker, in his effort toexpress the fundamental laws of Nature in mathematical form, should strive mainly formathematical beauty. It often happens that the requirements of simplicity and beautyare the same, but where they clash the latter must take precedence".
The law of parsimony is no substitute for insight, logic, and the scientificmethod. It should never be relied on to make or defend a conclusion. Asarbiters of correctness, only logical consistency and empirical evidence areabsolute. Dirac was very successful with his method. He constructed therelativistic field equation for the electron and used it to predict the positron.But he was not suggesting that physics should be based on mathematical beauty alone.He fully appreciated the need for experimental verification.
The final word is of unknown origin, although (as with so many one-liners) it's often attributed to Einstein:
"Everything should be made as simple as possible, but no simpler".
The pithiness of this quote disguises the fact that no one knows whether Einsteinactually said it (this version comes from the Reader's Digest, 1977 [US: July, UK:October?]. It may well be a precis of the last few pages of his "The Meaning ofRelativity" (5th edition), in which he writes of his unified field theory: "In myopinion the theory here is the logically simplest relativistic field theory that is at allpossible. But this does not mean that Nature might not obey a more complextheory. More complex theories have frequently been proposed... In my view,such more complicated systems and their combinations should be considered only if thereexist physical-empirical reasons to do so".
References:
W. M. Thorburn, "Occam's razor", Mind, 24, pp. 287–288, 1915.
W. M. Thorburn, "The Myth of Occam's razor", Mind, 27, pp. 345–353, 1918.
Stephen Hawking, A Brief History of Time.
Albert Einstein, Autobiographical notes
Isaac Newton, Principia: The System of the World
