On Occam’s Razor

Occam’s Razor is a principle that we use to bolster certain hypotheses in many areas of modern life, including science, religion, and historical analysis. Also known as the principle of parsimony, it suggests that we should prefer simpler explanations to more complex ones when the competing hypotheses have comparable explanatory power. As stated by Ptolemy, “We consider it a good principle to explain the phenomena by the simplest hypotheses possible.”

There are a number of reasons used to justify this principle. An aesthetic argument is certainly reasonable and worthwhile. Simpler models also have better predictive potential. They are more likely to be able to explain phenomena not considered in the original formulation of the hypothesis. Complex models are also vulnerable to over-fitting and post-hoc formulations, making them less falsifiable.

But this very practical principle has a blind-spot. It does not appreciate the significance of the potential for deception in the phenomena we are studying. Any agent that is going out of their way to deceive us will be complicating the situation. And any explanation for the phenomenon that takes this deception into account will necessarily be more complicated.

A Mystery Novel Trope

To illustrate my point, let’s look at a story that will sound familiar to anyone who enjoys mystery novels or movies. A man decides he wants to murder his wife to get her out of the way. He does not want to be punished for the crime of murder, so he decides to frame somebody else - say his brother - for the murder. He plants a variety of evidence to point to his brother being the killer, including prints on the murder weapon. The husband arranges for himself to have an alibi, and for the brother to have no alibi. He contrives for the wife and brother to get into a fight in a public setting leading up to the murder, so that there would be motive. He even stages a scenario where he is seen to rescue his wife from danger, putting himself in harm’s way, to make it less believable that it was actually him that committed the crime.

Now, a disinterested detective looking for a simple solution might easily be led to believe the the brother is the killer, and pursue that case. A more observant - and less naive - detective may point out the possibility of the husband being the killer. The disinterested detective dismisses the possibility. “It’s an open and shut case. All the evidence points to the brother, and you would have to believe that the husband spent months working out a clever plan to murder his wife and get away with it.”

I’m not a student of mystery fiction, or even much of a fan, but this seems to me to be a common trope of the genre. In this case, the disinterested detective comes to the wrong conclusion by preferring the simpler explanation, as Occam’s Razor suggests. It is an error to apply Occam’s Razor in this case, due to the intentional deception deployed by the husband.

Confidence Games

Confidence games - particularly long cons - also often take advantage of the principle of parsimony in cheating their mark. The long con can take place over the course of many weeks, and involve dozens of people in on the cheat. If at any point, the mark gets suspicious that they are being cheated, they might console themselves that it is safe, because so many people would have to be involved for it to be a cheat. Other techniques bolster this tendency, such as confidence itself, where the person or people pulling off the con take steps to build trust, and gain the mark’s confidence. As with the mystery trope, the mark would benefit from being overly paranoid in this situation, and not dismiss potential explanations because they are too involved or overly complicated.

A Cautionary Principle

We might want to come up with a cautionary principle here that would guard us against naively applying Occam’s Razor in the presence of agents of deceit. Occam’s Razor is commonly applied in areas such as science, religion, and historical analysis. In the case of science, we would want to be on the lookout for subjects of scientific study that are trying to deceive, such as galaxies, cells, and sub-atomic particles. While this may seem far-fetched, we should keep in mind that our understanding of galaxies, cells, and sub-atomic particles is quite limited. There’s a lot more that we don’t know about these things, than what we know. In other branches of science that are easier for humans to explore, such as zoology, numerous examples of deceptive practices can be found, from simple camouflage techniques to complex mimicry.

Given that nearly every scientific study relies on prior scientific results, we would also want to watch for deceptive behavior from the scientists themselves. Regarding religion, agents such as gods, angels, and devils might all be engaging in deceptive behavior. We should also be cautious of the authors of religious texts, as well as religious leaders, especially at formative moments in the religion. As for historical analysis, historical players such as government agents and corporations may be trying to deceive us. So might the journalists and historians that report on and interpret historical and current events.

The ideas of deception playing a role in science, and in religion, are very intriguing, and worth looking into. Both topics deserve careful and thorough treatment, so I will save these ideas for later. Here, I will present a single, simple example from history, and see where it leads us.

The example I am choosing is the OKC bombing. It makes for a good example because it is a recent enough and significant enough event to maintain our interest. On the other hand, because it is far enough in the past, and not on the scale of massive catastrophes such as 9/11, we are less likely to have knee-jerk emotional reactions when we are trying to analyse things rationally.

Two Accounts of the OKC Bombing

The official account of the OKC bombing, in brief, goes like this. On April 19th, 1995, Timothy McVeigh parked a Ford F700 truck in front of the Alfred P. Murrah Federal Building in Oklahoma City. Inside the truck was a 7000 pound bomb built from fertilizer, nitromethane, and diesel fuel. McVeigh had already lit the fuse when he parked the truck, and made his way to his getaway vehicle. The bomb exploded, killing 168 people, and destroying one third of the nine-story building.

Many conspiracy theories revolve around this terrorist incident. One such alternative account submits that the truck bomb would not have been strong enough to bring down the multiple steel-reinforced concrete pillars that collapsed during the attack. While the bomb was very powerful, the fact that there was several feet of open air between the truck and the building would have limited the effects of the blast. Proponents of this theory claim that there were further explosives placed inside the building. These were located in the basement, and directly attached to the pillars that collapsed. They were detonated by remote control nearly simultaneously with the explosion of the truck bomb.

The most common variation of this conspiracy theory alleges that the bombs inside the building were placed there by members the FBI. This adds multiple complicating factors to the explanation. Here, members of the FBI must have had foreknowledge of McVeigh’s plan to bomb the building, and must have had a certain level of familiarity with his plans. The most likely explanation would be that one of his conspirators was an undercover FBI agent, or an informant. The FBI must have had access to the basement, possibly with the complicity of some of the building’s security staff. And they must have been able to keep their involvement a secret. A number of people - perhaps mostly FBI agents - would have to have been involved, and kept quiet. Perhaps there was also some complicity with the news media to not give a platform to anyone breaking the silence, or to not report on any other evidence that would support the hypothesis of bombs inside the building.

OKC Bombing and Occam’s Razor

Let’s suppose we have taken an interest in the OKC bombing, and we are trying to determine for ourselves what actually happened. When comparing the two accounts described here, we need to balance the improbability of the truck bomb doing that level of damage from a distance, to the improbability of the FBI playing a clandestine role in making the terrorist attack worse than it would otherwise have been. Estimating probabilities like these depends on many factors, such as our knowledge of explosives. If this knowledge is limited, then we might rely on expert testimony. In this case our estimates would involve the trustworthiness and reliability of the experts at hand. Similarly, we would have to estimate how likely it is that members of the FBI would actually be motivated to behave this way. This estimate will depend heavily on our beliefs about what kind of organization the FBI is, and what it’s agents are really like. This will be heavily influenced by our knowledge of how the FBI has behaved in other circumstances.

Of course, proponents of both hypotheses present other evidence to bolster their own hypothesis, and discredit the other side. Let’s say we take all this evidence into account, and we are still not sure about what really happened. Let’s say that in our mind, the balance of evidence between the two possibilities is quite even. Do we then apply Occam’s Razor, and choose the official explanation for being simpler, and having less moving parts?

Applying Occam’s Razor here would be a mistake. We have presumably already taken into account the complexity of the second hypothesis when we estimated the likelihood of the alleged FBI involvement. The fact that the alternative account has a more complicated explanation is simply a reflection of the fact that the account itself is more complicated. If someone had constructed an argument with a hundred moving pieces, then Occam’s Razor might apply. But roughly speaking, this argument only posits two extra parts: that members of the FBI had the means, and the motive, to make the OKC bombing more horrific than it would otherwise have been.

I don’t think Occam’s Razor would typically be applied in this manner to this scenario. Instead, the person applying Occam’s Razor is not actually interested in understanding what really happened. They are not actually doing an investigation into the alternative hypothesis. Instead, they are using it as an excuse to dismiss this alternative account without investigation. Of course, nobody is obligated to “get to the bottom of” every historical event, and investigate every hypothesis proposed. But when we don’t do this, the only honest position to take is “I don’t know.”