Given that for a phenomenon, explanations of arbitrary complexity can be made, which view of the world should we choose?

OCCAM’S RAZOR PRINCIPLE ·  According to the Occam’s Razor principle, among competing hypotheses, the one with the fewest assumptions should be selected. It is attributed to the English Franciscan friar, scholastic philosopher, and theologian William of Ockham (1287 – 1347).

Unlike in pure logic or mathematics, theories in natural sciences are much more difficult to test. You have to find specific experiments which have no or just a few unknown (or uncontrolled) variables in order for them to be repeated. For example, this is a difficult topic for any study involving people because you cannot simply create a “clone” of someone and repeat an experiment. Instead, you need to track gender, lifestyle, age, income, genetics, etc. to at least find some correlation and eliminate unwanted influences. And sometimes experiments are outright impossible because of principle (we will see this later in chapter 3.4 with Heisenberg’s Uncertainty principle), technological, or monetary limits; think for example about weather or climate scientists who cannot run their experiments on a “second Earth” but have to rely on models.

COMPLEX ARGUMENT FALLACY ·  It is a Complex Argument Fallacy if you use a more complex argument (that leads to the same conclusions as the more simple one) to argue against an existing argument. The new argument requires more assumptions to be true. An extension of this argument is to simply declare a problem or situation as “complex” while dismissing simpler solutions. For example, a child could declare that her situation is “complex,” complaining she is running out of pocket money, while the reasons are very clear (her expenses). This way, the chance to even discuss a subject is negated instead of addressing actual issues. This fallacy is also often used in connection with an argument from authority, implying that only “experts” are allowed to have an opinion on the subject. Of course, sometimes, there are no simple solutions and a problem is complex, requiring experts to discuss. That is why the complex argument fallacy is a reminder to reflect before either calling a situation too complex, or trying to apply basic solutions that are too simple.

This difficulty of following the scientific method automatically leads to different theories for phenomena. This is unlike what we see in mathematics, or chemistry: there are not many alternative interpretations of mathematics or chemistry, but there are many competing interpretations of psychology, philosophy, biology, and physics (in terms of interpretation of quantum mechanics).

Thus, if you are faced with different explanations for the same phenomena, you should decide in favor of the one that adds the smallest number of hypotheses (assumptions about how the world is) or variables. The point is that for any phenomena and theory, you can always find a more complex theory that explains the phenomena but adds additional, very possibly superfluous or simply incorrect elements. Without some kind of guide or limit, you will never make progress. In addition, any explanations that cannot be falsified—we remember Carl Sagan’s invisible, weightless dragon from the first book (“Now, what’s the difference between an invisible, incorporeal, floating dragon who spits heatless fire and no dragon at all?” [Sagan, 1997, p. 170–88])—should be discarded right away: someone can always try to evade rational inquiry in the form of falsifiable experiments by coming up with more and more fantastic stories or complex statements.

The question is which view of the world we should choose. The “should” implies that this is ultimately a question of ethics. Obviously, if we evaluated theories independent of their complexity, our mind would be powerless as we would have to look at every possible theory and could not simply stop because its explanations are too convoluted or even infinite.

Occam’s Razor is not a property of nature that somehow prefers simple solutions over complex ones. Occam’s Razor does not even require that nature needs to be understandable. It is more a rule of thumb that, so far, has served us well in science and protected us from complex theories in instances when nature was, in actuality, much simpler. It expresses more the idea that when we look at nature, we first assume that its phenomena are complex, when in reality, the complexity simply stems from a lot of intertwined processes. Or to look at it from the other side: extraordinary statements require extraordinary evidence. And last but not least, simpler theories are simply easier to test and falsify if necessary.

Example

In the Middle Ages, people began to question the strange path of planets on the night sky. Mars is in “retrograde” every two years, following a strange circle (from the viewpoint of an observer on Earth, see Figure 3.1). While the explanation that Earth is simply the center of the universe (geocentrism) sounded like the most obvious idea at the time—from our perspective, the Earth does not move, but everything else does—the resulting diagram was anything but simple. It seems random. Drawing all the planets with the Earth at the center results in this flower-like diagram (Figure 3.2).

Figure 3.1:An illustration of the seemingly irregular path of Mars on the night sky from the point of view of Earth (image source: Brian Brondel, 2007).

Figure 3.2:An illustration of the paths of the planets of the solar system with a geocentric world view (Encyclopaedia Britannica, 1st Edition, 1771).

This overly complex view of the solar system persisted until the Middle Ages. It was not an issue of technology; in Ptolemy’s notes of the year 140 you can find thousands of star and planetary data and geometric ideas. The problem was more about the ability to read, the mathematical knowledge to read the notes, and ultimately the lack of availability of the notes.

Surprisingly, what ultimately led to a greater understanding of the universe were not telescopes, but the printing press. Only with the publication of Ptolemy’s notes, in Almagest, the data found their way into the hands of people like Nicolaus Copernicus. Nearly 1,500 years after the data were first collected, Copernicus solved the problem of the complexity of the planetary orbits with heliocentrism—the idea that the Sun, not the Earth, is the center of the solar system.

 Figure 3.3: An illustration of the heliocentric world view, with the sun, not Earth, being the center of the solar system.

While both views of the world, geocentrism and heliocentrism, are mathematically correct because they accurately predict the orbits of the planets, the system of Copernicus was much easier to handle. It added a layer of abstraction by looking at all the planets as separate entities instead of seeing the universe as an inexplicable series of snapshots, with the only task of science being to describe and to catalog instead of to understand.

Biography —Nicolaus Copernicus

Nicolaus Copernicus (1473 – 1543) was a Polish astronomer and polymath. The idea of heliocentrism—the Sun at the center of the solar system as opposed to the Earth being at the center of the universe—reached a wider audience with Copernicus’ publication of De revolutionibus orbium coelestium in 1543. It triggered the Copernican Revolution which was a significant factor in the launch of a new age: the Scientific Revolution.

 Figure 3.4: An illustration of the concave Hollow Earth hypothesis with the space being compressed in a way that the whole universe is in an infinitely small point in the center (image inspired by Joshua Cesa, 2010).

To get a better feeling for creating a hypothesis, let us look at the so-called “Hollow Earth hypothesis.” This is a pseudo-scientific theory that we are actually living inside the Earth and not outside, with a “miniature sun” and a “star sphere” at its “center,” and with a staunched space-time structure so that the distances to the sun and the stars are equal to our observed distances (see Figure 3.4). If we moved toward the center, we would become apparently “smaller” and “slower.” But just as Copernicus asked how the geocentric model would look if you changed the point of reference from Earth to the sun, you could wonder how the model of the “Hollow Earth” hypothesis would look if you turned the space-time structure inside out, moving from “skycentric” back to a geocentric or heliocentric view of the universe.

Interestingly, you would end up with the heliocentric model! So, at its core, the Hollow Earth hypothesis is a “correct” model of the world, the physical laws would work in the same way, but the staunching of the space-time structure would complicate and obfuscate everything. And this is the moment for Occam’s Razor, simply pointing out that including this staunching does not add anything and needs to be discarded.

When applying Occam’s Razor, you have to keep in mind, though, that you first have to be aware of the complexity of the system in question and also to place it in some sort of context. It is not enough to know the (apparently) simpler solution, you have to know the whole context in order to decide what “simpler” in terms of Occam’s Razor actually means.

Example

Imagine a time traveler from the year 1000 who has the chance to visit our world today. He will believe that something like the mobile phone is the product of a singular genius rather than an array of corporations around the world, exchanging goods and services required for the phone based on free, mutual trade. From his limited view, international cooperation of millions of people is less believable than magic.

For any given data, there can always be different models. Occam’s Razor is useful when deciding which of the models is preferable by ranking them by their complexity.