Ockham's Razor and the Principle of Simplicity
by David Rudd Cycleback












































































































































When a lunch guest at your home asks for directions to the bathroom, you likely give the shortest, simplest route ("Go straight down that hallway and it's the second door on the left. You can't miss it."). Unless you can't stand the person or are playing a kid's game you don't give an unnecessarily long, circuitous route ("Go outside, circle the house twice, come back in through the cellar window …").

When giving driving directions to someone new in town, it is usually best to give the shortest, easiest route to the destination. If you give a bumblebee route the visitor will spend unneeded travel time and is more likely to get lost. There will be occasions where a more roundabout route is desirable. Perhaps the shortest route goes through a bad neighborhood or the visitor asks for the scenic route or has to pick up groceries along the way. Without these extra requirements, however, you will give the simplest, shortest route to the destination.

In science, mathematics and many other academic areas, simplicity is similarly desired. It is a standard preference that a scientific theory or model be as simple as is possible without sacrificing accuracy or necessary meaning. Another way to put it is that it is considered undesirable for a theory to have unnecessary parts, difficultly or complexity. If something is tacked onto a model because it is needed to make the theory work or work better, that is fine. If something unneeded is tacked on, it should be removed. If two models are otherwise equivalent and produce the same results, it is considered best to pick the model that is the simplest.

In modern science and mathematics the common reasons for simplicity are similar to for when giving simple road and bathroom directions. A scientific model that is needlessly complicated is harder to read, understand and communicate. In the classroom and the laboratory, it may confuse students and the teacher alike. The simpler model is easier to test. It's easier to identify which parts work and which parts don't. With a plethora of needless parts, it's harder and sometimes impossible to know what's working and what isn't.

Even in our normal lives, we simplify things in a scientific way when trying to figure out a mystery. If you hear a strange nighttime noise outside, you turn off the television volume and have the people in the room with you stop talking. The inside noises can only serve to mask or muddle the auditory information you're trying to identify. You want to reduce the auditory information to one source: the noise outside. The reason you don't want the other auditory sources is the same reason a laboratory scientist doesn't want extra, useless parts on his test model.



Ockham's razor
This principle of simplicity in scientific models and theories is commonly called Ockham's razor, or Occham's razor. It is popularly attributed to 1400s English friar and philosopher William of Ockham, also known as William of Occham. The razor alludes to the shaving away of unneeded detail. A common paraphrase of Ockham's principle, originally written in Latin, is "All things being equal, the simplest solution tends to be the best one."



Misunderstanding and misuse of Ockham's razor

The famous simplicity principle has been deftly used by famous scientists from Albert Einstein to Max Plank. It has also been misapplied, misunderstood, misinterpreted and misused by the uninformed. The following looks at common misuses and misunderstandings of the principle.

One common error in applying Ockham's razor is to use it as the absolute arbiter of good and bad, right and wrong. Ockham wrote "All other things being equal, the simplest solution tends to be the best one." He didn't say "the simplest is always right" or "the more complicated automatically is wrong." His "tends to be" implies that sometimes the simplest isn't the best solution. Look at the below equations for an example where simpler is not better:

a) 1 + 1 = 5
b) 1 + 0 + 0 + 0 + 1 = 2 + 0

Equation a is simpler and wrong. Equation b is long winded but correct. The relative quality of the two equations isn't judged by simplicity alone. In math, simplicity may be desired, but accuracy trumps simplicity. Most mathematicians would say that ' 1 + 1 = 2' trumps both a and b, as it is both simple and correct. In other words, they'd take equation b and simplify it.

In the first paragraph's directions to the bathroom, the circuitous route wasn't directionally incorrect. They would have lead the visitor to the same destination as the short directions: the bathroom. The simpler directions, however, were deemed better in the situation, including the social aspect of treating a guest politely.

Another common misuse of Ockham's razor is to apply it to two disparate models. The principle is not for arbitrating apples versus oranges. Remember, the principle starts with, "All (other) things being equal …." If model d and e are otherwise the same, use the simpler one. If model d and e are different animals, Ockham doesn't apply.

As this all shows, Ockham's razor is a useful tool but not the sole tool in making and judging models and equations. A scientist who uses Ockham's razor in the making a nuclear physics model, will also test the model for accuracy. A simple model that gives bad results sends the scientist back to the drawing board.

It is important to realize that scientists deal in often complex, vast and obscure areas, where the answers are not known. It's not like equation a and b, where anyone with a third grade education can pick out and the correct equation in three seconds. The scientist makes rough models to test theories and study complex ideas. The razor is often used to make the testing easier and more reliable. The rule is a practical rule of thumb for making a good model, not an arbiter of truth and accuracy.

Ockham's razor as value and aesthetic judgment
Whether good or bad, right or wrong, humans tend to use simplicity as a tool to judge aesthetics, morals, truth, good and bad. People often say things like good is simple, messy is incorrect, simple truths, the beauty is in the simplicity, disordered mind. In some form and degree these sentiments show up in the application of Ockham's razor, often producing dubious results when the sentiments are used too seriously. For some, Ockham's guide is not only used to identify correctness or convenience, but sometimes aesthetics, beauty and morals. This happened centuries ago, when simplicity was considered tied to religion, nature and the supernatural.

Below are two interesting quotes from Aristotle. Notice how the philosopher equates simplicity with truth, nature and perfection.

Aristotle: "Nature operates in the shortest way possible."
This of course is untrue. Nature can be complicated. It's a moral or aesthetic judgment that is factually wrong.

Aristotle: "The more perfect nature is the fewer means it requires for its operation."
This is a statement of personal aesthetic beliefs, and I would say dubious. There is no proof that simpler is better or worse than complex, and in fact complexity is required for somethings to work. A car with one wheels falls over. Duplication of wheels is required.

If a scientist likes beauty and simplicity in his models for beauty's and simplicity's sake, that is reasonable personal taste so long as this principle doesn't override accuracy … By the same token a mathematician wanting his equations to have neat margins and handwriting is reasonable, but this neatness doesn't make the equation right or wrong. The neatness may be important for his students' and colleagues' easy reading. This is important, but, again, doesn't make the equation more or less right or wrong.


When judging someone else's model, first understand what is the model's purpose

A common error in judging models is not knowing what the model is trying to represent and/or do. If you don't know what the model is trying to do, how can you judge if it is a good or bad model? Some models are trying to represent the essential meaning of the universe, while others are merely trying to give directions to the nearest 7-11 on the back of a napkin. No doubt the napkin sketch is a terrible model of the universe, but you'd look like a fool pointing out this obvious fact to the barroom crowd. You might as well also point out to them that the sketch looks nothing like the Taj Mahal.

In short, much dubious criticism of models is caused by the criticizer not understand the purpose of the model. His criticism is a product of his dubious assumptions and ignorance.

Once you understand the purpose, you can criticize the purpose itself. "Sure, that'll get you to the 7-11, but my recommendation is you go the Piggly Wiggly instead. It's about the same distance and the price are cheaper."


The problem of defining what is simple

The problem in simplifying models and theories and equations, is that what is simple differs from person to simple. Simplicity is subjective. Same goes for aesthetics when aesthetics is used to make models.

The following is a brief look at simplicity

Same subject models can look different from scientist to scientist due to the scientists' personal views of simplicity, aesthetics and order. There are often different but equally legitimate ways to order information. Due to personal views, one scientist may group the information by colors, another by shape, another by size.

Organize the following into two groups of related objects

Scientists, and non-scientists, often find it convenient and practical to group information. I asked different people, including a university applied science professor, to group the above objects into two groups of like objects. One person grouped by color (black objects and white objects), another by size, another by letters (he saw the objects as E's and C's. Interesting, as I drew the Cs as moons!), another by direction left or right (problematic as one doesn't know if a moon is faced left or right). Their reasons for pairing were equally legitimate, but produced different pairings. This should show you how one scientist's model can look different than another's, not due to scientific theory or knowledge but different views of aesthetics, simplicity and association.

When making a simple cosmic model, the human must realize that humans' concept of simplicity may not match the cosmos' concept of simplicity. Any scientific model is a representation of the human's way of seeing.

Some philosophers and scientists have rebelled against Ockham's razor, in particular when simplicity is used to define nature. They said that if nature is complex, a simple model can't be a true representation of nature. This view has merit when the simple models are used to depict the truth of nature. However, as we've already seen, some Ockham models are practical devises for specific purposes. They aren't pretending to represents the whole of nature.



Positivism is a practical philosophy related to Ockham's razor that says "sense perceptions are the only admissible basis of human knowledge and precise thought." It dismisses the subjective and that which can't be empirically measured and tested. It has been applied in science, and is much a definition of the scientific method.

Positivist models will be derived from verifiable and experienced facts, which of course is a good thing. However, they will also be products of our limited senses, excluding real but immeasurable things. Artists and the religious often say science can't explain everything, which is true. glass

(c) david rudd cycleback, all rights reserved