Occam's Razor

Written: 2003-10-09
Note: at the risk of condescension, I must point out that this article is much easier to understand if you have a basic grasp of high school-level mathematics.

The Concept

If you see enough debates (on any subject, whether trivial or grand), you will eventually see something called "Occam's Razor". Now, the first thing you need to know about Occam's Razor (also known as "the logical principle of parsimony") is that it's a bit like righteousness: everybody claims it's on his side.

"But what is it", you ask? Occam's Razor is a philosophical principle which is also part of the scientific method. The original principle comes from a theologian named William of Ockham, who lived nearly a thousand years ago and devised it as a proof that the existence of God is not logical. That may seem contradictory for a theologian, but he was trying to show that you need pure faith to believe in God, and that logic will not help you. The principle he used was the concept of logical parsimony, which says that we should not multiply entities unnecessarily. This somewhat cryptic principle makes more sense when you think of it in terms of equations. For example, take the following curve:

Let's say four different people propose four different equations to model this curve:

[Eq 1]		Y = -3X²
[Eq 2]		Y = 1 + X - 3X²
[Eq 3]		Y = G		where G is unknown
[Eq 4]		Y = 4X² + 20

So which one's the best? Well, this is a hard question to answer without some numbers on that curve plot, but we can narrow it down a little bit. Let's continue:

Some people express Occam's Razor as "the simplest theory wins". If we accept that, then Equation #3 is clearly the winner. One small problem: equation #3 is impossible to evaluate! How do you calculate "Y = G" when you don't know what G is? How do you even know if there is a formula for G at all, or whether there is any such thing as G? I think we can agree that equation #3 is out. An equation which gives no results is useless. You see, "the simplest theory wins" is (ironically enough) an oversimplification of the principle of parsimony, so if we were to rephrase the aforementioned version properly, we would say that "the simplest workable, accurate theory wins" (a couple of extra words can make a big difference).

Therefore, Occam's Razor slices equation #3 away. It's simple, but it can't be evaluated so it's not workable. Now we're down to equations #1, #2, and #4. But if we look at the shape of the graph, we can see that equation #4 is obviously no good even without bothering to check numbers, because you can simply look at the shape of the curve and see that it can't possibly be a positive parabola.

Therefore, Occam's Razor slices equation #4 away. It bears no resemblance whatsoever to the curve, so it's not accurate. So that leaves Equation #1 and #2. Both of them could potentially produce that curve, but without hard numbers, we can't be sure. Obviously, if the numbers for the plot match one equation or the other, then it wins. But what if we test the curve in many places, and we find that it's closer to equation #1 about half the time, and closer to equation #2 about half the time? Well, that's where the number of terms becomes important. Since equation #2 adds an extra term which does not really seem to improve the situation, it's basically useless, so we should go with equation #1.

Of course, you might object that this is far too simplistic and abstract to apply to a real-life situation, so why don't we try a few applications? After all, it's trickier to apply Occam's Razor than to describe it. Remember that your objective is not to propose a theory, defend a theory, or attack a theory. Your objective is to compare theories. Keep your eye on the ball, and don't be led into the trap of either defending a theory against people out to prove it isn't perfect or attacking a theory on the basis that it isn't perfect. Life isn't perfect, and perfect knowledge is an unattainable ideal. Just remember that you're out to see which theory is better, and you'll be on the right track. With that in mind, let's move to our first example.

Example #1: UFO visitations

We all know the drill. The UFO argument sounds like this:

"UFOs are obviously real. Why, I myself once saw [lights in the sky moving around, hovering, funny noises, mangled cattle, etc]. Can you explain that?"

Mind you, UFO "phenomena" generally can be explained. Searchlights hitting cloud cover can create lights flitting around in the sky in ways which would be physically impossible for an aircraft. Cosmic rays can create strange-looking streaks of light on film footage taken in space. Many experimental US Air Force aircraft have been mistaken for alien spacecraft in the past (particularly the stealth fighter). Perfectly round crop circles can be made with a piece of rope and a wooden board (and snowshoes if you want to avoid leaving footprints), as demonstrated here. Personal tales of abduction can be easily explained as the simple tall tales of people with otherwise uninteresting lives. One famous UFO videotape was taken by a man who just "happened" to be a Hollywood special-effects artist. The similarity of worldwide stories is easily explained by the Internet and the mass-media, which have worked to propagate the same UFO stories over all of the world.

But after a while, so-called "UFOlogists" perversely begin to use these very explanations as disproof of themselves. "How many times must you hear people try to explain away UFO phenomena? Example after example after example after example; how many does it take before you realize that someone's trying to cover something up?" they ask.

So how does Occam's Razor apply to this? Well, it's obvious how it applies when you remember to express the competing explanations in the form of theories:

Theory #1: "aliens did it."

Theory #2: "it can be explained as events which can be physically rationalized, exaggerated recollections of said events, or hoaxes."

At first glance, theory #1 actually seems simpler and more straightforward. But appearances can be deceiving, so let's try expressing the two theories in equation form. If P = so-called "UFO phenomena", then:

[Eq 1]		P = A		where A is unknown
[Eq 2]		P = R + E + H		where R = events which can be rationalized, E = exaggerated recollections of same, and H = hoaxes

Hmmmm, equation #1 does look simpler, but A is unknown, therefore it is impossible to evaluate, and if you recall, an equation which you cannot evaluate is useless. "Ah, but this is different. This is not a mathematical equation; it's real life!" you might object. Well, that's where you'd be forgetting that science is actually the exercise of modelling real-life as equations. We don't need to know everything about these aliens to use them in a useful theory, but we need to know something, and we know nothing. Nothing at all. We know nothing about their technologies, capabilities, limitations (or for that matter, even their very existence), so they are a complete unknown. If they are a complete unknown, then the "alien explanation" actually doesn't explain a damned thing, does it? Therefore, while the first theory seems simpler on the surface, Occam's Razor actually slices it away because it's useless. Or, to put it another way, "alien spacecraft" does not explain hovering lights in the sky any better than "magic fairies".

The second theory, on the other hand, uses only terms which are known to exist, and which can therefore be evaluated. We know that many events can be rationalized. We know that human memory is highly unreliable. And we know that people can and do create elabourate hoaxes for many personal reasons. We can also test these terms to see if they measure up, ie- we can look at the known capabilities of human technology and the limitations of physics to see if these events can be rationalized.

"Ah, but what if there's something which can't be explained?" the UFOlogist will inevitably retort. Well, first and foremost, UFOlogists are experts in "unintentionally" underestimating how much we can actually explain (it helps that most of them lack scientific and technological knowledge). Many of them lie outright. But more importantly, you must recognize that if they give this retort, they obviously ignored the part about how terms which are impossible to evaluate do not "explain" anything, so you'll have to repeat it a few times (you might also have to show them the dictionary definition of the word "explain").

If an alien spaceship landed on the front lawn of the White House, and we could collect plenty of clear, reliable video and physical evidence (not to mention the radar tracking of its ascent and descent), we would then know much more about its capabilities and we would be able to use that knowledge to see if their known capabilities actually fit the anomalies being sold to us as "evidence".

Example #2: Religion

Sorry, but at the risk of offending some, I have to point out that religion is an excellent case study for Occam's Razor. In fact, not to belabour the point, but I must repeat myself in saying that Occam himself was a theologian, and used Occam's Razor as one of his spiritual arguments. Think of our entire worldview as a huge theory which exists in order to explain the universe. This gives you two competing theories:

1. The universe exists. It has natural laws that govern the behaviour of the world.

2. God exists, and created the universe, which has natural laws that govern the behaviour of the world. God is inscrutable.

Note the commonalities: in both theories, we have the universe and its natural laws. The second theory merely adds the "God" term, which cannot be evaluated because he's inscrutable. So the question becomes: how does the second theory outperform the first one? Once again, let us model this as a pair of competing theories which are expressed in equation form:

[Eq 1]		P = N		where P is phenomena and N is Nature
[Eq 2]		P = N + G		where G (God) is a mysterious unknown

In this case, the problem is rather obvious: the religious explanation merely adds a mystery term which cannot be evaluated in any way. This is the inherent problem with using an inscrutable God to explain mysteries: you cannot explain anything with an inscrutable answer, any more than you can solve a mathematical equation by simply saying "unknown". And this, said William of Ockham, is why believers must rely on faith.

Example #3: Conspiracy Theories

It is difficult to cover such a broad subject as conspiracy theories in one stroke. Indeed, conspiracies are indeed possible, and it would be irresponsible to suggest that all conspiracy theories must be wrong. However, there is a general trend among most conspiracy theories which violates the principle of logical parsimony. In essence, the general method of the conspiracy theorist is as follows:

1. Take some major event (popular targets include the September 11, 2001 terrorist attacks on America, JFK's assassination, the moon-landing, and Pearl Harbour) in which something bad happened and human negligence or incompetence was a factor.

2. Dismiss the accepted explanation (indeed, conspiracy theorists and pop culture icons such as "The X-Files" have successfully cast the very term "official explanation" itself in a negative light) by denying that such incompetence could exist unless it was deliberate (see Pearl Harbour), or by misrepresenting the details of the events in order to make the accepted explanation appear to be impossible (see the JFK assassination).

3. Try to determine "who stood to gain" from each event.

4. Look for (or fabricate) evidence that these parties were in fact responsible.

5. If step #4 fails, conclude that the lack of reliable evidence is evidence itself ... for a cover-up.

6. Use the existence of classified military documents as "proof" that this cover-up reaches up into the government (by presuming that they must contain what you're looking for, as if there is no other conceivable reason to classify military information).

A few problems leap immediately to mind with this process. First and foremost, it is obviously designed in such a manner that it is impossible to disprove, and an absence of evidence perversely becomes yet more evidence. But more importantly, it seeks to replace an explanation which relies upon individual incompetence with an explanation which requires a new entity: an organized conspiracy whose very existence has not even been verified. In essence, it discards a workable explanation which uses only terms already known to exist (human incompetence is hardly conjecture) in favour of an explanation which unnecessarily invents a new term.

A conspiracy theory would be reasonable if you could show actual hard evidence that the organization itself does exist and was involved, because in that case (to use the mathematical analogy) the equation simply does not fit the theory any other way. However, simply showing that certain people "stood to gain" from something does not prove that their conspiracy existed or that it caused the event in question. And as more than one person has said, never attribute to conspiracies that which can be explained by human stupidity.

Example #4: Matrix Philosophy

Perhaps the most annoying side-effect of the popularity of "The Matrix" (the Keanu Reeves movie which proved that even the most outrageously nonsensical story can still be a smash hit if it's stylish enough) was the sudden appearance of teenaged pop culture-spawned pseudo-philosophers across the country, many of whom seem to believe that this film actually makes us ask serious philosophical questions. Some would even argue that it has thrown our conception of knowledge and reality itself into serious doubt.

"Are we in a Matrix-style simulation? How can you know?" asks the newly minted pseudo-philosopher.

Leaving aside the obvious "get a life" jabs and the falsehood of the film's originality (VR, or virtual-reality worlds have been a staple of sci-fi and philosophy 101 for decades), the major problem with this idea is its sheer irrationality. It draws upon certain aspects of solipsism (an extreme form of skepticism, bordering on philosophical über-egotism, in which you do not acknowledge the existence of objects outside your own thoughts because their existence can't be absolutely proven; click here for an online article about solipsism) in order to argue that we might be living in a giant virtual-reality simulation.

The people who promote this point-of-view point triumphantly to the fact that it cannot be absolutely, irrefutably disproven. However, this argument hinges upon the assumption that if something cannot be absolutely, irrefutably disproven, then it is actually a reasonable theory. It is an understatement to say that this is false, because nothing can be absolutely, irrefutably disproven. One might as well ask if we actually a bunch of talking fleas living in Santa Claus' pants and deluding ourselves into thinking we're human.

OK, so how does Occam's Razor relate to this? If I may skip the little equation table to cut to the quick, it's yet another example of a term which cannot be evaluated. What side-effects would this simulation have? We don't know. What characteristics could we test for? We don't know. What we do know is that this giant VR simulation is a term which is not only undefined and therefore incapable of explaining anything, but is also completely unnecessary in order to explain anything, so the theory is irrational. This is the purest essence of the logical principle of parsimony, or Occam's Razor: to show what's wrong with a theory that technically cannot be disproven.

Conclusion

If you still don't entirely understand the logical principle of parsimony, try looking it up elsewhere. I am not exaggerating when I say that you really need to understand this concept before embarking on a debate of this or any other subject, because a lot of people like to mention it, and an even larger number of people like to violate it.