Understanding History
The Principle of Simplicity
Two principles mentioned in these notes are old enough to have Latin formulations. One is associated with William of Occam (variously spelled). In one version, it runs thus:
Entia non sunt multiplicanda praeter necessitatem.
Or, "entities should not be multiplied beyond what is necessary." A historical explanation should not be more complicated than it needs to be, to cover the observed facts. It is the first of the Rules of Reasoning in Philosophy which begins the third section of Isaac Newton's Principia Mathematica. Newton's statement is:
Rule 1. We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances. To this purpose the philosophers say that Nature does nothing in vain, and more is in vain when less will serve; for Nature is pleased with simplicity, and affects not the pomp of superfluous causes.
The simpler theory is better that the more complicated theory. All this has its intuitive appeal. A difficulty arises when we try to be precise about what we mean by "more complicated," and thus what we mean by "simpler."
See AlsoThe Simplicity Principle and why six is the perfect number for better managementSimplicity in the Philosophy of ScienceWhat Are the Gestalt Principles?The Art of Maximizing Work Not DoneThe Copernican conception can be used as an example. Ptolemaic astronomy posited circular orbits for the planets, because the circle was considered the most perfect shape, and the universe was considered to be a perfect creation. Differences between these theoretical circular orbits and the observed motions of the planets led to the positing of epicycles, additional circular orbits superimposed on the basic one. One set of epicycles did not quite suffice to account for the actual motions, so other epicycles were added to the system. Eventually the agreement with observation was fairly good, though never perfect. Copernicus's contribution was to notice that the assumption of an elliptical orbit accounted at once for the actual observed motion. He was able to get rid of the epicycles. A single equation, not a nest of equations, governed planetary motion.
Someone might object: This violates the principle of simplicity, because the equation of a circle:
x² + y² = a²
is simpler than the equation of an ellipse:
x²/a² + y²/b² = 1
That judgement would be wrong. Simplicity is not to be judged by the elements of the system, but by the complexity of the system. An orbit plus modifications is more complicated than an orbit by itself. Since the (elliptical) orbit by itself will account for observations, the modifications of the (circular) orbit are unnecessary. They are excrescences. Occam's razor will accordingly shear them off.
Laplace's masterpiece Mécanique Céleste (1799-1825) applied Newtonian principles to all celestial motions. He made few and simple assumptions, among them that Newtonian gravity held throughout the system. Napoleon, to whom he presented an abridged account (Exposition du Système du Monde, 1796), famously remarked, "You have written this huge book on the system of the world without once mentioning the author of the universe." Laplace's equally famous reply took a certain amount of nerve:
See AlsoWhat are Rules of Simplicity?Sire, je n'avais pas besoin de cette hypothèse
The assumption of universal gravitation sufficed. He did not need the God hypothesis.
DangersOccam's razor is often wrongly applied. The key is the the phrase "praeter necessitatem" in the Latin formula. Not all complications are forbidden. On the contrary, complications necessary to cover the facts are not only allowed but required. However simple or even beautiful a theory may be, if it does not cover the facts, it is not viable. A complex theory may be a sign that the thing it is trying to explain is not yet deeply understood. But it may also be the correct explanation of a genuinely complex phenomenon.
To many, "simple" means nothing more than "familiar." A familiar theory is simple because it requires no mental effort. This is not the sort of simplicity envisioned by the principle. Historians should never make things simpler than they are, either for their own convenience or for that of their students. Those who are incapable of making a further effort of thought, those who cannot update their familiar notions, are disqualified from having opinions in the first place, let alone retailing those opinions to others.
The fallacy of a too simple theory was understood by the ancients.
You can't talk of ocean with a frog in a well: he is confined to his own space. You can't talk of ice with a summer insect: he is limited to his own season. You can't talk of the Way to a quiddling scholar: he is bound by his own knowledge. (Jwangdz 17:1a)
This is merely using a tube to peep at the sky, or an awl to probe the depth of the earth. Are they not too small for the purpose? (Jwangdz 17:4)
As for the dangers of not recognizing what work is being done by the seemingly unused parts of a theory (or a physical situation), we have this:
The earth is nothing if not wide and vast. The amount of it a man uses is no more than what he actually puts his foot on. But if you dug away the earth from around his foot, all the way down to the Yellow Springs, would the man still be able to use it? (Jwangdz 26:7)
First, one must be judicious in including enough data, and in choosing an analysis adequate to the range of the data. Next, one must be subtle in assessing the functions of the elements in the resulting explanation. Once one has met these basic requirements, useless elements may safely be eliminated by Occam's razor.
7 Nov 2000 / ContactThe Project / Exit to Outline Index Page
FAQs
What is the principle of simplicity explanation? ›
In psychology and cognitive science, the simplicity principle posits that the mind draws interpretations of the world—mental models or mental representations—that are as simple as possible, or, at least, that are biased toward simplicity.
What is the theory of simplicity? ›The basic concept of simplicity theory is unexpectedness, defined as the difference between expected complexity and observed complexity: This definition extends the notion of randomness deficiency.
What is an example of the principle of simplicity in perception? ›Simplicity
The law of simplicity indicates that our mind perceives everything in its simplest form. The image below, for example, when studied in depth is made up of individual components that have no meaning when viewed separately, yet our mind automatically perceives them in combination to spell out the word 'logo'.
The simplicity principle, traditionally referred to as Occam's razor, is the idea that simpler explanations of observations should be preferred to more complex ones.
What are the four laws of simplicity? ›1 REDUCE The simplest way to achieve simplicity is through thoughtful reduction. 2 ORGANIZE Organization makes a system of many appear fewer. 3 TIME Savings in time feel like simplicity. 4 LEARN Knowledge makes everything simpler.
What is the simplicity principle in human concept learning? ›The principle of simplicity, or parsimony—that one should choose the simplest hypothesis consistent with the data—is one of the most ubiquitous in all fields of inference, including philosophy (as Occam's razor); in machine learn- ing (under a variety of names, in- cluding the “minimum description length principle”); ...
What is the psychology behind simplicity? ›In Psychology, the simplicity principle posits that the mind draws interpretations of the world – mental models or mental representations that are as simple as possible or at least are biased towards simplicity.
What is the principle of simplicity in philosophy? ›It often goes by the name of “o*ckham's Razor.” The claim is that simplicity ought to be one of the key criteria for evaluating and choosing between rival theories, alongside criteria such as consistency with the data and coherence with accepted background theories.
What does simplicity teach us? ›Simplicity is staying in the present and not making things complicated. Simplicity is learning from the wisdom of native cultures. Simplicity is giving patience, friendship and encouragement. Simplicity is appreciating the small things in life.
What is an example of simplicity in real life? ›For example, when your space is neat and minimal, you no longer need to spend hours cleaning and tidying up. Of course, you still need to do these tasks, but they will take significantly less time. Creating a minimalist wardrobe is another way that simple living can give you more time and thus make your life easier.
Is simplicity a Gestalt law? ›
The law of Pragnanz—or principle of simplicity—is a fundamental Gestalt psychology law concerning how humans process visual information. It states that people usually perceive complex things as simplified forms to easily recognize and understand what they see.
What is the simplicity principle of perception? ›The simplicity principle states that the human visual system prefers the simplest interpretation. However, conventional coding models could not resolve the incompatibility between predictions from the global minimum principle and the local minimum principle.
What is the moral of simplicity? ›Simplicity avoids waste, teaches economy, avoids value clashes complicated by greed, fear, peer pressure, and a false sense of identity. From simplicity grows generosity and sharing. Simplicity is putting others first with kindness, openness, pure intentions - without expectations and conditions.
Why simplicity is powerful? ›While many changes work from the inside out, simplicity has a powerful way of working from the outside in. It provides the opportunity to remove the layers and connect with what is most important. Simplicity will make you more open-minded.
What is the best quote for simplicity? ›- "Complexity is impressive, but simplicity is genius." - ...
- "Simplicity is about subtracting the obvious and adding the meaningful." - ...
- "Life is really simple, but we insist on making it complicated." -
“Occam's razor, or the principle of parsimony, tells us that the simplest, most elegant explanation is usually the one closest to the truth.” What happens when four years of your lab's work, a beautiful hypothesis, and an explanation lauded by your scientific peers is “crushed by data”?
What is simplicity in explanation? ›That is, simpler explanations are believed to be more likely to be true in virtue of being simple. While choosing between competing explanations involves deciding which is most likely to be true, simpler explanations gain a probabilistic boost just for being simple.
What is Thoreau's idea of simplicity? ›Thoreau said: “If you can't do more with less, you should simplify.” He believed simplifying life involved reducing distractions to focus more on important things in life. A simple life requires personal reflection and awareness of all aspects of life to determine what is most important to you.