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 managementWhat are Rules of Simplicity?The Art of Maximizing Work Not DoneSimplicity in the Philosophy of ScienceThe 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 the Gestalt Principles?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.
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FAQs
What is meant by the principle of simplicity? ›
The principle of simplicity or parsimony—broadly, the idea that simpler explanations of observations should be preferred to more complex ones—is con- ventionally attributed to William of Occam, after whom it is traditionally referred to as Occam's razor.
What is the theory of simplicity? ›Simplicity Theory (ST) is a cognitive theory based on the following observation: human individuals are highly sensitive to any discrepancy in complexity. Their interest is aroused by any situation which appears "too simple" to them. This has consequences for the computation of. (narrative) Interest.
What is the principle of simplicity Russell? ›It is the "natural view" urged by "every principle of simplicity," that we are experiencing real, physical objects that exist outside ourselves and do not depend on our perception for their existence. Russell concludes his assertion of simplicity with a look at why the view seems natural in the first place.
What is the philosophy of simplicity? ›The philosophy of simplicity aims to break that cycle of habits by introducing easily manageable tactics in all areas of life. What is simplicity in life? From our regular day-to-day lives to complex business relationships, simplicity is a highly sought-after state of being.
What is an example of the principle of simplicity in perception? ›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'.
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.
Why simplicity is so powerful? ›Simplicity can benefit your overall mental health by providing more clarity in your mind, so you have less to worry about. Plus, lower anxiety can contribute to positive self-esteem and makes it easier to enjoy life and try new things. More Fulfillment.
What is the paradox of simplicity? ›The paradox of simplicity states that while simplicity supposedly enhances performance and helps people achieve their goals, they may not necessarily prefer or choose the simplest alternative.
What is an example of simplicity? ›- I think, in the end, it had to do with the simplicity and unexpectedness of their project. ...
- She's inspired by nature's simplicity and the healing power of love. ...
- Simplicity, though, doesn't translate into being less revealing. ...
- I really liked the density and the simplicity of it.
What is Rules of Simplicity? A set of criteria, in priority order, proposed by Kent Beck to judge whether some source code is “simple enough”: the code is verified by automated tests, and all such tests pass. the code contains no duplication. the code expresses separately each distinct idea or responsibility.
What is the doctrine of simplicity? ›
Divine simplicity is central to the classical Western concept of God. Simplicity denies any physical or metaphysical composition in the divine being. This means God is the divine nature itself and has no accidents (properties that are not necessary) accruing to his nature.
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 simplicity principle? ›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 is the Zen concept of simplicity? ›Exemplified by the concept of kanso, simplicity suggests that beauty and usefulness should not be expressed excessively; it is not necessary to gloat or to decorate exorbitantly. Thus a feeling of freshness, order and cleanliness is achieved.
What is simplicity according to the Bible? ›2 Corinthians 11:3
Simplicity means single, without ulterior motive, pure, sincere, and unambiguous. Vincent's Word Studies (vol. 3, p. 346), defines it as "single-hearted loyalty." It is the opposite of deceit, guile, error, and wandering.
Simplicity leads to clarity rather than confusion and decisions rather than hesitations. Keeping things organized and harmonious is the greatest benefit of simplicity. Simplicity is what brings harmony, tranquility, and peace within.