Simplicity

Simplicity

“Simplicity is the ultimate sophistication” – Leonardo Da Vinci

Humans seem to be fascinated with simplicity. We widely believe that, even if sometimes we tend to complicate things, the most beautiful things and the most profound truths are simple.

It is an age-old archetype. The rebel son leaving the house of his parents, seeking his own way. He builds a house of cards, tries new, complicated ways of living his live and chasing his dreams, only that in the end, in old age, realizes that simplicity is the key. And if he is among the lucky and gifted ones, he distills his own life experience and knowledge into a pure nugget of wisdom.

Yes, Wisdom is always simple. Have you ever encountered a complicated wise man? One using very complicated reasoning and conceptual structures in order to express his own worldview? I didn’t. I don’t think you did, either. Almost by definition, being wise implies simplicity.

That’s why we love quotes, like the one I posted before. Quotes, are, in a way, the result of mental digestion. You take a gifted man (a writer, a scientist, a philosopher etc), you put in all his life long learning, his struggles and sacrifices and in the end, the results are these small, yet very powerful strings of symbols, that relay a simple but striking message.

The human mind desires simplicity. And since the reality of our individual minds is the sole reality we can know, we all value simplicity. Even in the tallest ivory towers, in the mental abodes of acclaimed geniuses, top scientists and mystics, simplicity (here called parsimony) is revered:

  • The Holy Graal in science is a Theory of Everything, that unifies and explains all the forces that rule over the physical universe. That is a quest for simplicity.
  • The mystics and people in the search of spiritual awakening seek a state of absolute simplicity, of Unity with the essence of reality and their definition of the divine.

So why do we treasure simplicity and how does this piece of information help us in our journey of discovering the nature of reality?

You might have noticed, Seeker, that our first steps were only preparatory. In mentally exploring what we know about the world, we must first be sure we have the proper mental instruments. Last week it was about our sources of knowledge and we concluded that empiricism is ultimately, the sole source of knowledge. This week I am going to talk about Occam’s Razor.

What is Occam’s razor?

Also known as the “law of parsimony”, Occam’s (or Ockham’s, after the English Franciscan friar scholastic philosopher and theologian who stated it, William of Ockham) razor is a philosophical principle which can be summed up as: “Among competing hypotheses, the one with the fewest assumptions should be selected”. Or, in other words: You should not make more assumptions that the minimum necessary to explain something. If you can explain a phenomenon with that bare minimum, it makes no sense to postulate additional assumptions. It is called “a razor”, because you “shave off” the unnecessary assumptions.

This can be further rephrased in a negative “corollary”: If you do not have explicit evidence to believe that something is true, then you should not. This rule should be taken with a gain of salt, as I will show in another post, regarding solipsism. But for now, it is a good rule to keep in mind. We started by dropping the basket of knowledge and we now methodically pick up the apples, one by one. We learned about the scope and the limits of science, about empiricism and rationalism and now sharpen our skepticism.

Keep your razor sharp, and your mind sharper!

How do we use it?

In science, Occam’s razor is just a tool among many. It helps scientists develop theoretical models that are then verified through empirical observations. The preference for simplicity (or mathematical beauty) is not, however, in any way, a replacement for the empirical falsifiability, no matter how some theoretical physicists are mesmerized by the beauty of their equations. But it does help a lot – since there can be a very large number of alternative explanation to a phenomenon, choosing the hypotheses with the least complexity helps with the testing itself.

But what about metaphysics?

We already know that science does not provide an answer to everything, nor could or should it. Because for those questions we have philosophy and metaphysics. And when we seek to understand the nature of Reality, we deal with ontology, a field of metaphysics that covers the study of existence, of reality as it is, not just as we know it, like epistemology does. Turns out, Occam’s Razor is very important for both branches of metaphysics, ever since its ancient beginning. For example, Aristotle writes in his Posterior Analytics:

We may assume the superiority ceteris paribus of the demonstration which derives from fewer postulates or hypotheses”.

In the Middle Ages, Aquinas wrote:

“If a thing can be done adequately by means of one, it is superfluous to do it by means of several; for we observe that nature does not employ two instruments where one suffices”.

Even in modern philosophy, Kant held Occam’s Razor in high esteem:

“rudiments or principles must not be unnecessarily multiplied”

Newton even postulated parsimony as a fundamental law of reasoning in philosophy:

“Rule I: We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.”

Einstein said:

“The grand aim of all science…is to cover the greatest possible number of empirical facts by logical deductions from the smallest possible number of hypotheses or axioms”.

Finally, the great philosopher of science, Bertrand Russell, concluded:

“Whenever possible, substitute constructions out of known entities for inferences to unknown entities.”

Looking at the entire history of humanity, one can even say that Occam’s Razor is a key principle upon which the foundation of philosophy and science rests.

But why is it so?

It is not just for the sake of aesthetics  and the ease of dealing with fewer elements. It runs much deeper into the way use observe and understand our reality.

First of all, it is useful to differentiate what exactly IS Occam’s Razor within metaphysics. Simplicity is valued as both elegance and parsimony. The first deals with the syntax of an enunciation. The latter with the number of hypotheses needed. While in science, elegance is more often exemplified and appreciated (like in the beauty of {\displaystyle E=mc^{2}}), in metaphysics what matters more is parsimony. Another difference between the use of Occam’s razor in science and philosophy is that in the former it is a methodological tool (guiding the adoption of the simpler hypothesis to be tested, because it is easier), while in the latter, is an epistemic principle: “if theory T is simpler than theory T*, then it is rational (other things being equal) to believe T rather than T*”

There is also a trade-off between parsimony and elegance – when you work with fewer hypotheses, the full explanation of a phenomenon may look more complicated (in other words, the syntax becomes complicated). When you work with more hypotheses, the syntax can simplify.

Here, dear Seeker, we must pause a bit and reflect. Do we seek to express the relations between things in the world in a simple way? Or do we wish to extract knowledge about the nature of the things, in their innermost nature? Because for the first case, we have science. For the second case, we have metaphysics. Science describes how the world acts and interacts. Metaphysics seeks to explain the fundamental nature of the things you see interacting.

So for the purpose of this chapter in our journey, we will focus on Occam’s razor as being the law of parsimony and a epistemic principle.

Focusing on that, a modern approach to Occam’s Razor is the following:

Other things being equal, if T1 is more ontologically parsimonious than T2 then it is rational to prefer T1 to T2.

So, for example, if T1 implies that only one type of entities and T2 requires two of them, and they both explain the same empirically observable phenomena, then there is absolutely no reason to consider that T2 is “true”, and you should place all your bets in the T1 basket.

And now that we clearly defined at which particular “razor” we look, lets go back to the question posed: Why is simplicity (parsimony) good?

There are two types of answers for that:

  1. Based on rationalism.
  2. Based on empiricism.

The school of rationalism talks about 4 main types of arguments for parsimony. If we discard the theological one as being given by the historic context, we have three more to look at (the metaphysical argument, the intrinsic value argument and the principle of rationality). For the sake of simplicity (hah, contextual joke), I can sum them up as being focused on simplicity being good in itself, being a prima facia virtue, or being good for our epistemological minimalism – the mind works better with fewer variables. But just as with rationalism itself, I find these lines of argumentation lacking. I don’s see the value in pure conceptualization. If a principle is not empirically grounded, better suited to express our knowledge about the reality we experience, then it has no practical value, or no value at all. So let’s look at the school of empiricism‘s arguments.

And for this, I will introduce today’s philosophical sidekick in our journey, Willard Van Orman Quine, one of the greatest (analytical) philosophers and logicians of the twentieth century, and largely regarded as the greatest American empiricist.

Yeah, this guy.

Quine argues that parsimony carries with it pragmatic advantages and that pragmatic considerations themselves provide rational grounds for discriminating between competing theories. In other words, simplicity is better because it helps us understand the world better, and that understanding is the sole purpose of why we use Occam’s razor in the first place – to make a better sense of the world.

Empiricists see Occam’s razor as being a tool to be used to “cut” the ontologically inflationary hypothesis/paradigm for the sake of the knowledge about the world that we will be able to understand better. And I fully agree with this perspective. Philosophy should be a mental tool for a better understanding of the world and ourselves, and nothing more.

For example, when the ontologically more parsimonious Special Relativity replaced the status-quo empirically adequate theory (the Lorentz-Poincaré theory), at first, it was just a rational choice to pick the simpler and more elegant theory (it eliminated the idea of a fixed reference frame in the vacuum, the “ether”). The few cases where SR predicted empirical results that the Lorentz-Poincaré theory was unable to explain came only after.

For empiricists, this is a success story for the use of Occam’s Razor and its merits. But there’s a lesson to it, that we must learn, for I will use it later in our journey.

Under LPT, not only we had more than just one ontological entities (in philosophy this is the umbrella word for fundamental realities), but that extra entity, in this case the ether, was undetectable.

So, the intermediate conclusion that you should keep in mind from now on is that whenever a metaphysical paradigm postulates the existence of an observable entity (aspect of reality), always try to find an alternative paradigm that has the same (or better) explanatory power, and pick that one.

Additional arguments?

People love the usage of proofs. And I can hardly condemn that. The skepticism is a healthy mental habit. So let’s look at a few types of arguments that show why Occam’s Razor is undeniably important, and why most of the times, the simplest explanation is the correct one:

Statistics

There is a meta-study on the predictive validity of Occam’s razor, that includes 25 published papers with comparisons between simple and complex forecasting methods. It turns out that the complex explanations increased the degree of errors in forecasts by 27%.

Logical considerations and pragmatism

From an empiricist point of view, knowledge is derived from nature, through induction, by observing the facts. Choosing the simplest explanation is a way of using among the models, and so it is said that Occam’s razor underlies induction. However, we need to be pragmatic about shaky grounds – philosopher Elliott Sober states that not even reason itself can be justified on any reasonable grounds, so we must pick some first principles of reasoning as being fundamental, otherwise we cannot build up our argumentation.

So, just like we accept inductive reasoning as being reasonable (even though, through induction, we do not have the certitude of truth, only the probability), we can also consider Occam’s Razor as being a reasonable tool in making sense of this world.

Mathematics

Probability theory states that all assumptions introduce (to various degrees) the possibility for error; as a result, if an assumption does not improve the accuracy of a theory, its only effect is to increase the probability that the overall theory is wrong. William H. Jefferys and James O. Berger state, “A hypothesis with fewer adjustable parameters will automatically have an enhanced posterior probability, due to the fact that the predictions it makes are sharp.”

Also, around 1960, Ray Solomonoff founded the theory of universal inductive inference, the theory of prediction based on observations; for example, predicting the next symbol based upon a given series of symbols. This theory is seen as a mathematical formalization of Occam’s razor and it laid ground for multiple applications in AI development. Ray Solomonoff thus built a mathematical proof that any sequence of observations is best predicted by Occam’s Razor in a computable environment.

True, that excludes cases where models are not computable, but since basically everything is computable in our observations of the world, we can safely say that using Occam’s razor on our observations of the world is a good way to reach for the truth.

Conclusion and sum-up

The world is simple; when you understand it.

When you hear hoof steps behind you in Europe, it is most likely a horse, not a zebra and least of all, an elephant. Always use your critical thinking and try to reduce the things your believe in (in other words, what you think is true, but without evidence). This lesson, seeker, is one of the most important ones when trying to understand the nature of Reality.

So far, we showed:

  1. How the only thing we truly know it is true is that we exist, because we are aware (Sentio, ergo sum);
  2. That science has it’s own limitations, in both scope and methods;
  3. That direct observation of the world is, ultimately, the sole carrier of knowledge;
  4. And today, we talked about simplicity in thinking and in making assumptions.
Please don’t ignore unwarranted assumptions.

And in the next chapters of our journey, I will show you exactly what we take for granted in the mainstream worldview.

Sometimes the most obvious elephants are right in front of us and we ignore them daily.

But don’t worry, I’ll point them out for you.

"There is no wealth like knowledge, and no poverty like ignorance." - Buddha

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