Tuesday, June 4, 2013

The Razor is Probably Occam’s



Occam’s Razor is one of the most fundamental rules in science. According to Merriam-Webster, it is:

A scientific and philosophic rule that entities should not be multiplied unnecessarily which is interpreted as requiring that the simplest of competing theories be preferred to the more complex or that explanations of unknown phenomena be sought first in terms of known quantities

Here’s an example that should make this clearer:

Let’s say you just put a slice of pizza in the oven to reheat, but you didn’t place it on a cookie sheet to keep it from dripping. You then proceed to go to the living room to watch some television. All of the sudden, you smell smoke. Where is this smoke coming from? Here are 3 scenarios:

  1. Aliens have inserted a device into your brain which makes you perceive the smell of smoke in order to further their experiments, which will eventually lead to the subjugation of the human race.
  2. Someone in a nearby apartment has burned a bag of popcorn.
  3. The cheese from the pizza is dripping onto the oven coil, causing it to burn and thus produce smoke.

Scenario 1 is quite farfetched, since it tends to rest on a number of assumptions that are not only complicated, but which are not based on any legitimately documented phenomena. In other words, while there may be stories of alien probes and mind control devices, no one has actually been able to provide sufficient evidence that aliens have ever visited earth let alone that they have the technology to cause people to smell smoke. In addition, how could making someone smell smoke help aliens take over the world? It is simply not logical.

Scenario 2 is quite plausible. The chemical process involved in burning materials is well documented. You have also previously experienced the smell of your neighbor’s burnt popcorn. However, this scenario requires you to make assumptions (i.e. that your neighbor was making popcorn) which have not yet been verified.

Scenario 3 is the most plausible. Why? Because you already know that you put your pizza in the oven without anything to keep the cheese from melting onto the coils. Per the definition, “explanations of unknown phenomena [should] be sought first in terms of known quantities.” Since you know about the pizza, this explanation should be sought first.

Occam’s Razor can also be expressed mathematically. For example, let’s say there are a number of possible events which have their own probability of occurring, and:
  • The probability of Event 1 happening is 1/2.
  • The probability of Event 2 happening is 1/3.
  • The probability of Event 3 happening is 1/4.
  • The probability of Event 4 happening is 1/5.
(Remember that the probability of getting heads after a coin toss is 1/2 and the probability of rolling a one on a six sided die is 1/6)

To determine the probability of multiple events happening, you multiply the probabilities of each event together:
  • The probability of Events 1 and 2 happening is 1/6
  • The probability of Events 1, 2, and 3 happening is 1/25
  • The probability of Events 1, 2, 3, and 4 happening is 1/125
Thus, the fewer the events required to explain a phenomena, the higher the probability the events led to the phenomena. Now, consider the aspect of Occam’s Razor which states “explanations of unknown phenomena [should] be sought first in terms of known quantities.”  In probabilistic terms, explanations are more probable when they are based on established knowledge of the context of the phenomena. Thus, when you see a moving light in the sky at night, the probability of it being an airplane is greater than the probability of it being a flying saucer. In mathematical terms, you could say the probability of it being an airplane is 4/5, whereas the probability of it being a flying saucer might be more like 1/1,000 (to be generous).

Resources

Good video overview of Occam’s Razor

In depth Wikipedia article on Occam’s Razor

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