Circular definitions are a tautology, trivially right. For example, "a circle is a circle". Or, they can involve more complex patterns, where the repetition is disguised in multiple cycles, hard to see, with components that are defined by components. But, such definitions carry no information, in Shannon terms. They are useless.
Considering the subject of Physics, which is basic to all science, hence it is a general context, a specific number of definitions seem circular. For example, the classic second law of Newton, with F= ma, is it a definition of force, or mass, or something else? Or, travelling wave, is it "a wave pattern that is seen travelling through a medium", as often stated, circularly, or something different?
This question goes beyond the mere definition question, of looking for a useful term or phrase, instead seeking to find a new way to define basic quantities in Physics, including "travelling wave" and F=ma, as examples.
Isn't the the basis of the identification of an physical object its position in space and time, or its approximation along a space-time continuum? Occupation of a point along that continuum is a non-circular way of identifying that physical object. You may not know what it is, but you know where it is as a first point of identification.
Dennis
Dennis Mazur
I see your point. Complicated things are defined through other things which could be even more complicated, then the second-order definition is needed, and so on. Its a really a vicious circle. Science breaks it by introducing axioms, and a "true" science has an axiomatic structure, just because of the reasons that you have pointed. For example classical mechanics is based on 3 axioms, which are the 3 Newton's laws. As a result, the entire classical mechanics is a set of logical consequences of these axioms. In other words, any result in classical mechanics is a structure like "if...then". If three Newton's laws hold, then this and that are true. And seems this works so far, look how astronomers predict the trajectories or other events.
Is this an answer to your question?
Dear Ed Gerck, I think that you meant Newton's Second Law and not the Third Law. The Third Law is a consistency condition on the First and the Second Laws.
Hello Ramzi,
Thanks for the autocomplete correction. By the way, the third law is also incorrect, as well as the first (which was actually published by Galileo, before Newton). In spite of his great genius and enduring work, we don't use the three Newton's laws anymore in Physics; in the past 150 years, a new framework has emerged, based on the more fundamental conservation laws, valid anywhere we know, including atoms to black holes.
Cheers, Ed Gerck
The answer, as noted above, is to go to a more primitive notion, differently defined. In physics one can go to topology, setting the stage to physics. So, a travelling wave is a translation in time, a notion independent of physics, in topology, and already known to students, since high-school.
This notion can give new ideas, such that sine and cosine are the same function, just translated. This simplifies a lot of formulas, and concepts, providing for a unification on a common basis. A repeating wave can be seen, thus, as a translation in space, a new idea.
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