Why Occam is Important
Monday, 31 December 2007
‘Everything should be made as simple as possible, but not simpler’.
This is often presented as “K.I.S.S. — or Keep It Simple, Stupid”. The idea of keeping things as simple as necessary is very often accredited to a Franciscan monk from back in the 1300s — a chap called William from the English town of Occam (or Ockham) in Surrey.
William of Occam did indeed come up with a law of succinctness (parsimony) — but is this lex parsimoniae the same thing as advocating simplicity? As far as I can ascertain, Occam said:
‘Entities should not be multiplied unnecessarily.’
I do not think this is the same meaning — or intention — as Einstein’s, but to assist you in making up your own mind, here’re the origins as I found them:
‘Pluralitas non est ponenda sine neccesitate’;
‘Entia non sunt multiplicanda praeter necessitatem’;
‘Frustra fit per plura quod potest fieri per pauciora’;
I personally think William was advocating that in creating, building, writing, drawing, (etc) that you should not ADD anything that is not required. Whereas Albert was coming from a different direction — reducing, removing, deducting, and making things simpler.
Nevertheless, it has been the Einsteinian approach that has, over the years, been manipulated into what-is-known-as “Occam’s Razor”.
William Ockham (c. 1285–1349) is remembered as an influential nominalist, but his popular fame as a great logician rests chiefly on the maxim attributed to him and known as Occam’s razor Entia non sunt multiplicanda praeter necessitatem or “Entities should not be multiplied unnecessarily.” The term razor refers to the act of shaving away unnecessary assumptions to get to the simplest explanation. No doubt this represents correctly the general tendency of his philosophy, but it has not so far been found in any of his writings. His nearest pronouncement seems to be Numquam ponenda est pluralitas sine necessitate, which occurs in his theological work on the Sentences of Peter Lombard (Quaestiones et decisiones in quattuor libros Sententiarum Petri Lombardi [ed. Lugd., 1495], i, dist. 27, qu. 2, K). In his Summa Totius Logicae, i. 12, Ockham cites the principle of economy, Frustra fit per plura quod potest fieri per pauciora.
— Thorburn, 1918, pp. 352-3; Kneale and Kneale, 1962, p. 243.
OK, perhaps it does not matter whether you start with something basic and add nothing superfluous or whether you start with something complex and shave it down to something simple — as long as you arrive at something that is as simple (or as complex) as it needs to be — no more and no less. If that were so, then I would be prepared to allow Einstein to equal Occam.
However, when I first read ‘Entities should not be multiplied unnecessarily,’ I immediately took it to mean that people should not have too many children (perhaps I saw the word, ‘multiply’ and thought of the command to ‘go forth and multiply’ in the Western Christian tradition). My next thought was that we should not have too many cars, clothes, homes, rooms, and so forth, and we should work, play, eat (etc) just enough (not too much and not too little). I was immediately reminded of the ‘Golden mean’, and of Daedalus warning his son Icarus to fly the middle course between the sea’s spray and the sun’s heat. So the whole idea of a “Razor”, “austerity” and “simplicity” surprised me.
Is it possible that just because William was a mendicant monk living the austere and simple life behind the monastery walls, people think his ideas must have something to do with a vow of poverty or living a very basic life by removing all extraneousness and ornamenture to arrive at a core? Hmm; I do seem to remember that he spoke out against the wealth of the papacy.
- What this idea means, and how it is used, is pretty significant because it appears to be a cornerstone for many arguments by many great thinkers through the years. Furious rows have been generated by the scientific community as well as by the religious and the philosophical.
For example, I know that a lot of mathematicians and physicists think that Occam’s principle is that if you have two equally likely solutions to a problem, you MUST pick the simplest. Now, while this may be stretching things a bit, as far as William of Occam is concerned, it is however true that Aristotle said nature operates in the shortest way possible, but I am not so sure. I’ll come back to this later.
Obvious & Easy
Some go further and believe that all processes ought to begin with the most obvious and easiest. This comes from phrases such as “Say what you see” (from TV’s “Catchphrase”) and “If you hear hoofbeats, think horses not zebras”. Unfortunately, this sort of thinking is easily exploited by the unscrupulous — from con men to setting people up or influencing a jury. The most simple, the easiest, the obvious is not always the truth.
Many scholars take Occam to mean that the explanation of any phenomenon should make as few assumptions as possible, eliminating those that make no difference in the observable predictions of the explanatory hypothesis or theory.
The thing is, ‘Occam’s Razor’ has been claimed by loads of people, from Isaac Newton to Leibniz’s ‘identity of observables’.
Presently I find that it is often taken to mean that nothing should be done until it has to be done (things are left to the very last minute) , or that things ought to be “dumbed down” (never use a ‘big’ word or a complicated idea) — that things would be aimed at the lowest common denominator, the simplest thinking of the population. I have even been led to believe that Occam is responsible for the media’s concentration on base instincts — sex and money, opulence and pleasure!
My my, how we can interpret, misinterpret and re-interpret; we have managed to take a sentence from the 14th century and make it have polar opposite meanings — on the one hand avarice and abundance, on the other hand, minimalism and simplicity!
Like myself, Galileo Galilei hated the misuse of Occam’s Razor — and wrote of it in his publication, ‘Dialogo sopra i due massimi sistemi del mondo‘, which compared the Copernican system with the traditional Ptolemaic system. Although this was back in 1632, poor old Occam is still being abused and misused to this very day!
This is patently a ridiculous situation, so let’s try to sort out the mess. The crux seems to be in the idea of simplicity (we touched on this before — it comes from Aristotle), so let’s attend to that first of all.
Simplicity is desirable?
If a patient, exhibiting many symptoms, presents himself to a physician — is the diagnosis that he has a single rare disease (the simplest solution) that fits the symptoms, or that he has a number of more commonplace diseases (the more complex solution)? It is statistically more likely that this patient has several common diseases, which is known in the medical profession as ‘Hickam’s dictum‘ (The principle usually and delightfully stated as: “Patients can have as many diseases as they damn well please”). This is one very important argument against simplicity.
Another counter-argument against simplicity I found in Neuro-Linguistic Programming, which holds as a basic principle that ‘multiple descriptions are better than one’ to communicate better. Simplicity in communication and interrelations is undesirable because people respond differently to verbal and body language depending on a bias to the senses (to be glib, some people know what you are saying, while others hear what you are saying, or see what you are saying).
Most biologists know that simplicity is not always the preferred route taken by nature, and they are pretty active in warning about the limitations of Occam’s razor.
- So simplicity is NOT always the best way, not always appropriate, not always natural, and not always desirable.
Having said that, simplicity is more often the best way (just not always).
I don’t think Occam wanted a Razor, I think he was taking about taking a middle route, the Golden Mean. I give William credit for not being wrong, for not backing simplicity. The Golden Mean allows Occam to be meaningful to those biologists and medical professionals who know the limitations of simplicity.
The Razor came later, and although called Occam’s Razor, I don’t see it as authentically Occam — but, hey, that doesn’t matter; as the NLP folk say, “The meaning of the communication is the response it produces, not the intended communication” — so Occam’s Razor is what everyone says it is. It therefore means a lot of different things, and I am happy enough with that.
For many years I have had dialogues and quarrels filled with arguments and counter-arguments regarding this, and what I always try to do is separate Occam’s principle (have just enough) from Occam’s Razor (simplification). I have to say that in this I am not often very successful; it is a subtle point to try to get across.
Both Occam’s Razor and Principle are relevant today. They are empowering and enlightening. If we take enough — if we do not overdo anything, if we get the balancing act just right, then we can avoid the fate of poor Icarus!
While I may have seemed somewhat anti-Razor, I actually like the myriad forms of it — and I would think it a good thing to seek simplicity in most things — as long as the simplicity is not detrimental.
For example, I would like less dumbing down in the media — a middle route is best (not too high brow and not too silly either), but I would like a simpler, more streamlined political system. I really do think politicians are not good for us. In general, I would like to have public services as simple as possible (but not too simple), but fewer very rich people and fewer very poor people (which simply means more people with enough). I would love simple traffic management systems such as advocated by Hans Mondermann (see How To Stop Traffic Jams & Save Lives and Why The Car Is Best), and a better sense of community with better connections between government and people, and between groups of people (see How To Manage Racism, Sectarianism and Sexism).
I do not mind games with complicated rules, books with complicated ideas, challenging educational subjects, puzzles and so forth (as long as they are no more complicated than they need to be). I like to think for myself — and to be free and able to research for myself (see How To Get To Heaven Part 1, part 2 and part 3). However, I resent complexity in red tape and paperwork as much as I resent dumbing down and simplistic religious concepts (see How It All Began).
I don’t think I am unique in these respects, so I would urge people to think Occam, and get to work with that Razor of his!