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."
The 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:
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 basic idea behind simplicity? ›The principle of simplicity or parsimony—broadly, the idea that simpler explanations of observations should be preferred to more complex ones—is conventionally attributed to William of Occam, after whom it is traditionally referred to as Occam's razor.
What is an example of the principle of simplicity in psychology? ›The Principle of Simplicity
You likely see it as five overlapping circles because the whole shape is harder to understand and describe. Another example would be Slack's old logo. Rather than seeing a combination of different colored squares and semicircles, you likely see the whole image of a multi-colored hashtag.
The explanatory virtue of “simplicity” tells us that all other things being equal, the simplest explanation is the better explanation.
What is the principle of the simplest answer? ›Definition and explanation
Occam's razor (also known as the 'law of parsimony') is a philosophical tool for 'shaving off' unlikely explanations. Essentially, when faced with competing explanations for the same phenomenon, the simplest is likely the correct one.
Simplicity describes a lack of ornamentation, like a Christmas tree that is only decorated with white lights instead of being fancied up with lots of ornaments, tinsel and multi-colored bulbs. The noun simplicity also means "freedom from hardship or effort" like the simplicity of hanging out on your porch.
What is simplicity in your own words? ›Simplicity, is the quality of being easy to understand, easy to do, easy to make others understand and do, simple and uncomplicated.
What is simplicity in explanation? ›Simplicity is the state or quality of being simple. Something easy to understand or explain seems simple, in contrast to something complicated. Alternatively, as Herbert A. Simon suggests, something is simple or complex depending on the way we choose to describe it.
What does simplicity teach us? ›Simplicity is staying in the present and not making things complicated. Simplicity is enjoying a plain mind and intellect. Simplicity teaches us economy - how to use our resources wisely, keeping future generations in mind. Simplicity is giving patience, friendship, and encouragement.
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”); ...
Why simplicity is important in theory? ›
There are many ways in which simplicity might be regarded as a desirable feature of scientific theories. Simpler theories are frequently said to be more “beautiful” or more “elegant” than their rivals; they might also be easier to understand and to work with.
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 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.
What is the strongest virtue? ›What is the greatest virtue, according to Aristotle? He concludes that the best of all virtues (and therefore virtue most important for a happy human life) is the intellectual virtue of wisdom.
How would you apply the virtue of simplicity in your everyday life? ›- Truth is simple, lies and cover-ups are complex. ...
- Acceptance is simple (but not often easy), denial is complex. ...
- Think clearly, and then speak clearly. ...
- Making excuses is complex, doing what you say you will do is simple.
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.
What does the Gestalt principle of simplicity represent? ›The Gestalt principle of simplicity represents the tendency for individuals to arrange elements in a way that creates closure or completeness. A binocular depth cue is a cue that helps detect distance based on the use of either eye. One's motivation can lead people to interpret the same situation differently.