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Next: Units and Dimensions


In Art and Science we pondered the distinction between intuitive knowledge of the particular and analytical knowledge of the abstract. The former governs intimate personal experience - about which, however, nothing further can be said without the latter, since all communication relies upon abstract symbolism of one form or another. We can feel without symbols, but we can't talk.

Moreover, before two people can communicate they must reach a consensus about the symbolic representation of reality they will employ in their conversation. This is so obvious that we usually take it for granted, but few experiences are so unsettling as to meet someone whose personal symbolic representation differs drastically from consensual reality.

How was this consensus reached? How arbitrary are symbolic conventions? Do they continue to evolve? They never represent quite the same things for different people; how do we know if there is a reality "out there" to be represented? These are questions that have perplexed philosophers for thousands of years; we are not going to find final answers to them here. But within the oversimplified context of Physics (the social enterprise, the human consensus of paradigmatic conventions, as opposed to physics, the actual workings of the universe) we may find some instructive lessons in the interactions between tradition, convention, consensus and analytical logic. This is the focus of the present Chapter.

Each word in a dictionary plays the same role in writing or speech (or in "verbal" thought itself) as the hieroglyphic-looking symbols play in algebraic equations describing the latest ideas in Physics. The big difference is . . . well, in truth there isn't really a big difference. The small differences are in compactness and in the degree to which ambiguity depends upon context. Obviously an algebraic symbol like t is rather compact relative to a word composed of several letters, like time. This allows storage of more information in less space, which is practical but not always pleasing.

As for ambiguity in context, words are designed to have a great deal of ambiguity until they are placed in sentences, where the context partially dictates which meaning is intended. But never entirely. Part of the magic of poetry is its ambiguity; a good poet is offended by the question, "What exactly did you mean by that?" because all the possible meanings are intended. Great poetry does not highlight one meaning above all, but rather manipulates the interactions between the several possible interpretations so that each enriches the others and all unite to form a whole greater than the sum of its parts. As a result, no one ever knows for certain what another person is talking about; we merely learn to make good guesses.3.1

In Mathematics, some claim, every symbol must be defined exhaustively and explicitly prior to its use. I will not comment on this claim, but I will pounce on anyone who tries to extend it to Physics. A meticulous physicist will try to provide an unambiguous definition of every unusual symbol introduced, but there are many symbols that are used so often in Physics to mean a certain thing that they have a well-known "default" meaning as long as they are used in a familiar context.

For instance, if F(t) is written on a blackboard in a Physics classroom, it is a good bet that F stands for some force, t almost certainly represents time, especially when appearing in this form, and the parentheses () always denote that F (whatever that is) is a function of t (whatever it may be). This will be discussed further below and in later Chapters. The point is, algebraic notation follows a set of conventions, just like the grammar and syntax of verbal language, that defines the context in which each symbol is to be interpreted and thus provides a large fraction of the meaning of a given expression.

It is tempting to try to distinguish the dictionary from the Physics text by pointing out that every word in the former is defined in terms of the other words, so that the dictionary (plus the grammar of its language) form a perfectly closed, self-reference universe; while all the symbols of Physics refer to entities in the real world of physics. However, any such distinction is purely æsthetic and has no rigourous basis. Ordinary words are also meant to refer to things (i.e. personal experiences of reality) or at least to abstract classes of particular experiences. If there is a noteworthy difference, it consists of the potency of the æsthetic commitment to the notion of an external reality. "Natural" language can be applied as effectively in the service of solipsism as materialism, but Physics was designed exclusively to describe a reality independent of human perception, "out there" and immutable, that admits of analytical dissection and conforms to its own hidden laws with absolute consistency. The physicist's task is to discover those laws by ingenuity and patience, and to find ways of expressing them so that other humans can understand them as well.

This may be a big mistake, of course. There may not be any external reality; physics may be just the consensual symbolic representation of Physics and physicists; or there may not be any physicists other than myself, nor students in my class nor readers of this text, other than in my vivid imagination. But who cares? Solipsism cannot be proven wrong, but it can be proven boring. And since Physics lies at the opposite end of the æsthetic spectrum, no wonder it is so exciting!

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Jess H. Brewer - Last modified: Sat Oct 24 19:10:34 PDT 2015