THREE EXAMPLES

The first statement is Galilleo's observation that, whenever objects are compact enough and dense enough that the resistance of air on them is a negligibly small factor, they always fall ``in the same way'', independently of what they are made of, how large they are, how heavy, and to the extent that the effect of the air is indeed too small to be separately noticed, even how dense they are, which is the ratio of how heavy to how large. ``In the same way'' has a precise meaning of comparison, because we can take several things and drop them from the same place, and take sequences of pictures at pre-determined times after each release in the same way, in which case each object will appear in a given picture at just the same place as all of the other things appear in their respective pictures.

Hearing such a statement, we have no doubt that we understand it, because we can think of every aspect of the description as something that we could actually do, which leads automatically to a certain interpretation of the claim as something that we could both test and use. After all, the world is a complicated place, and if you want to either build machines or predict things that will happen, any simplification or reduction in the number of things you must account for is a great convenience. An example which we will see in future chapters is the case of the pendulum clock, in which, in an important way, the swinging of the pendulum that calibrates the motions of the clock is a special case of ``falling'', and it is a great convenience in designing such things to know that it does not matter how big the pendulum is, or what it is made of, to how the clock will run.

In contrast, suppose we hear from someone that a set of experiments, which eventually led people to the discoveries of relativity, showed that anytime light is received (seen), it is always found to be moving at a certain speed which is always the same, independently of where or how it was created, how it has traveled since then, and what the observer is doing at the moment he sees it. What tends to be missing here? The first problem usually is that, simply because light is a less familiar and less obviously ``handle-able'' substance than something that one drops, the immediate process of translating the statement from its words into an imagination of something that the listener could actually do is never taken. This is an important loss because in fact it results in effectively all loss of understanding of the statement, without ever making this apparent. This is the insidious part of the difference between understanding and not understanding; it is painless, because the words alone cannot encode a check that they have been understood. For instance, one might regard Galilleo's statement about falling objects as only of passing interest unless at the moment one happens to be building a clock or doing some other work that involves falling things, but the fact that the statement is useful is apparent, and having heard it one is able to keep it available as a possibly useful resource for the future. However, hearing the statement about another thing that doesn't change, in this case the speed of light, one might think that it is an interesting point to note, but not think it of much importance or particular use. Such a response, which is probably the most common one, would fail entirely to notice that there is a problem in all this, which in fact is so big that this one observation alone forced us to entirely relearn what we mean by time and distance, and forced us to rewrite every law about nature that we thought we knew, if it was to deal with something that might be expected to move at any significant fraction of the speed of light (and many other cases as well). The failure to notice all of this occurs with nothing like pain, because the statement itself seems quite innocuous, and less taxing than a question about how steeply a ladder can be leaned against a wall before the base slips.

If, on the other hand, one had expected to understand this new statement in the same way as one had understood Galileo's, and taken the time to translate it from its words into an imagination of how one might actually arrive at such a concusion or make use of such a result, then one would at least receive a warning that something was seriously amiss, and the most tenuous part of understanding would be saved. This could happen because one might think, even as an imagination, about standing by a highway and looking at the light from oncoming headlights. And one might suppose that, in one way or another, the driver of one of the cars had measured the speed of the light as it left the headlights, while the watcher by the side did the same thing when he saw it. Suddenly the statement seems puzzling. After all, if the same man in the car throws something out the window, even if he throws it straight ``sideways'', it represents a real hazard to the person standing by the side, because it is not just going ``sideways'' at all. It is flying down the road with some speed close to that of the car. So if even the first part of the statement were true, and the light had indeed left the car at its claimed special speed, how could it not be going any faster than that when the watcher by the road saw it, since the car was traveling toward him? Or if the watcher saw the light at its characteristic speed, as claimed, how could it not have left the car at some slower speed to account for this observation? There are more puzzles than these in unraveling the language of such statements, addressed in detail in the chapter on the kinematics of Special Relativity.

The point for now is that the first thing that a language cannot encode is a check for its own understanding. That can only come when the listener takes an active and matter-of-fact relation to what he hears, demanding that each of the parts of the statement be intelligible in terms of something that he could do, at least in principle. If this active relation is lost, it strips the listener of even a criterion by which to judge whether he has understood, and secondarily results in his losing another active relation to the things he hears, which is his ability to see how they might be important or useful.

Another point to note in passing, which will be of great importance later, is just how much is assumed in every description of listening that has been made here. We were fairly careful to describe in the details how one might take pictures of falling things at particular times to make clear checks of Galilleo's claim. We were less careful and omitted any details of how one might actually measure the speed of light, but again one might imagine that some similar process could be employed, by letting light shine on things as it passed and catching its reflections in carefully timed pictures. But we were entirely careless in an area that would seem ridiculous if it did not turn out to be the issue of paramount importance in the whole discussion. In talking about taking pictures at definite times, or assuming some such activity, we assumed that we knew what we were talking about when we used the word ``time'', or that some self-evident meaning was shared by the speaker and the listener. Few claims might seem more ridiculous than that an intelligent speaker can talk to an intelligent listener in the 20th century and not be permitted at least to assume that both of them understand what it meant by the word ``time''. Except that in this case it happens to be true. The reader is invited to think further about the case of the car driver and the person standing on the road measuring speeds for the light they make and see, and to try to find a correct resolution without addressing the issue of what is actually meant by ``time'' much more carefully. This exercise stalled the entire thinking human race for (two?) decades without success.

The point to notice is that language actually encodes only the barest skeleton of the meaning it is intended to convey. The rest is assumed to be brought to the exchange by the listener, in the form of knowing what the words mean. But that is in fact the most backward of expectations. After all, if one admits that words have been invented, one then must recognize that the inventors lived in earlier times than those who inherit their inventions, and learning goes forward in time, not backward. Therefore, the people who create words, often populations of them, slowly and haphazardly over long intervals, always have more limited knowledge than their successors. So the successors, inheriting the words and yet claiming to learn something new, should not expect that the words will have been defined to account well for some new thing that is being learned. Therefore it is not ridiculous at all, especially with regard to the oldest words that seemingly regard the most basic of notions but for precisely that reason have been around since the oldest times, to be very cautious about assuming that they have meanings, that the meanings are universal or that they are not explicitly misleading.

The tool that we used to gain our first check for understanding was the creation of an active relation to words, making always an attempt to translate them into imaginations of what one could actually do. This same tool will be our most important one in overcoming the problem of bad definitions. If there were not such a tool, the foregoing statements would lead to futility. After all, the only reason a language is useful is that, at some level its words do have meanings, and the ability to assume that they are understood makes it possible to combine them to represent ideas, plans, directions or whatever is needed. So to advise that one never assume the meaning of a word is actually known, without providing a substitute way to provide it with a meaning, would be to advise abandonment of the language, which guarantees that it will accomplish nothing at all. We will see later how this process of meaning-giving can be done, and furthermore done efficiently. For now it suffices to caution that remarkably little is contained in any statement of language itself, with the rest provided by the listener. In conventional discourse, most of this must be assumed, and the problems arrise when some of the assumptions are wrong.

So far we have mentioned the obvious fact that you can't act on something if you don't understand it, and that simply the constant testing of what you hear to see if it is something you can translate into actions can be a highly effective way to test for the understanding itself. But just the fact that someone doesn't act on what he hears doesn't necessarily mean that it was not understood, because there are other reasons than being confused not to act on what one hears. One of the best is that one does not believe it. Here we encounter another major requirement that we place on our language. It must not only be a source of information or explanation, it must provide a source of confidence. Yet like the information it seems to carry, the confidence bestowed by words can reside very little in the words themselves, and far more in what we bring to our relation to them. And like understanding, the confidence can be lost in the same ways and for the same reasons, if one loses the active participant's relation to the language.

We consider two more pairs of examples. We mentioned in the first chapter that one of the important things that have been created within the methods of physics is a particular meaning for the notions of right and wrong. These are useful for two reasons. An obvious one is that the ability to identify mistakes can save a lot of effort from being spent following notions that don't work. Another, though, that is very important and more subtle, is that an ability to make definitive statements either about what is right or what cannot be right enables one to get on to close issues and go on to deal with other problems, without having constantly to argue and re-argue the same points to decide where the concensus on them lies at the moment. A very particular version of this involves the ability to say that something is impossible. This has always been a popular thing to assert, but in physics, perhaps for the first time in human history, these kinds of statements can be made both usefully and permanently. As such it represents an extreme of a new kind of confidence that has never existed before, and which should not be confused with what preceded it, and it is important to understand where this kind of confidence can come from.

For instance: There was a time when it was asserted by the erudite that it was and would always be impossible to build a vehicle that would carry a man at speeds much in excess of the speed of a running horse. The claim was that such speed would be fatal to a person, for some set of reasons. (This claim will be made purely absurd, all the way down to the meanings of the words, when we have said a little more about relativity. Unfortunately, appreciation of the humor of that will have to wait a few chapters.) Similarly and a few decades later, it was asserted that it was impossible to build a heavier-than-air machine that would carry a person.

There does not seem to be a time in recorded history when some statements of this type were not parts of the established or respected intellectual consensus of the day. And traditionally, they have a way of being overcome by inventive people who don't believe them and of making their propounders look naive as well as wrong. In this context we consider two other ``It's impossible''-type statements.

One of the basic results to which Einstein was led from his new understanding of the structure of space and time was that it was impossible to make an object attain a speed that was faster than that of light. A different one, which in spite of his prior discoveries even Einstein found objectionable was a claim, originally by Heisenberg, that it was impossible to build any apparatus that would, in the same event measure both the position of some object and what could be called ``its state of motion'', referring to the way that one can imagine measuring both of them with as much precision as is desired. The question is, will future generations ever regard these two statements in the way we can regard the statements about human speed and heavier-than-air machines, while sitting in a jet airliner going over the ground at 600 miles per hour? If not, why not, and what could make these statements different.

This point needs to be addressed for the following reason. When one looks at the history of repeated human mistakes, one wonders if as a species we will ever learn any lesson. In every time there are some people siezed by this particularly strongly, who become skeptics in response to seeing common sense and basic caution violated so flagrantly so often. And one hopes that for our own safety and progress, simple limitations on human gullibility make some such skepticism a part of all of us. But skepticism carries its own limitations, because it is itself a sort of ``impossible'' premise, that ``it is impossible to have confidence in a claim that something is impossible''. But just as it is a waste to miss good ideas by ruling them out from the start, it is also a waste to throw away powerful and deep discoveries about nature because they happen to resemble something foolish from the past. Since skepticism is itself an attitude that suppresses action based on words, if it is to be useful instead of harmful, it must be augmented with a way to tell the difference between foolishness and those most important of all discoveries, the surprising ones that were not obvious all along.

This skepticism at this time finds some very clear expressions. The common perception of a ``theory'' is as something like a speculation, possibly correct but likely irrelevant to day-to-day life and certainly not something in which to place confidence as long as it goes by that name. Unfortunately that is not the way the same word is used when it refers to ``The Theory of Relativity'' or ``The Quantum Theory''. We will come to the physicist's use of the word shortly. The reason it is unfortunate is that lurking behind this one word are statements, claims, descriptions and instructions for how to do things, which have passed more stringent tests in precisely the real world, and deserve a higher level of confidence, than any other statements it has ever been possible for a human being to make. It starts to sound silly to constantly present these topics in superlatives, but the content is so close to a pure form, an absolute, and so much closer than anything before it has ever been, that for once these are literally the appropriate words. Explanation of the details to support this come in later chapters.

The important point to understand is that the simple kind of disbelief that precludes even giving a second thought to the warnings about faster-then-horse and heavier-than-air machines leads to a disastrous waste if it is used to dismiss the statements about faster-than-light and concurrent-measurement machines, if it is applied because the two statements have been taken in the same way. But nothing in the form of the words can protect us from such a confusion, because again it is not the language itself that is the source of confidence, but something we bring to our relation with it.

It is not necessary to say too much about how we can reliably see that the first statements are wrong, from our current technological vantage point. And in general, a statement that something is impossible, given no more support than these statements had at the times they were advanced, is probably appropriately accorded the same skepticism today. And these statements are also not special or unusual in that regard. What is needed is an explanation that the other ``impossible'' statements can be anything different, and of how they can be recognized. We mentioned previously in discussing the speed of light that, while we might think of ways to take pictures, we had assumed that the definition of terms like ``at a certain time'' would be self-evident and present no problems, along with the warning that that assumption turns out to be wrong. Herein lies the crux of the solution to the faster-than-light statement. In order to understand even the constancy of the speed of light, Einstein found that in fact he was not able to form a sensible understanding of time with any of the definitions that had been used before. He had to figure out how to define the word all over to make sense of the experiments. The exceeding greatness of Einstein comes from the fact that he was able to find such a definition at all, and with remarkably few clues. But the particular form of the definition he eventually found was tightly constrained even by the things that had been seen already, and after he presented his way of defining the words, and the predictions he made about space and time based on them, far more and stricter tests were made in experiment after experiment, to see if any of them contradicted what Einstein had predicted would happen in each instance. Because his definition did indeed work, no contradiction was found at the time, and none has ever been found since then.

In the process of doing experiments and trying various ways to give meaning to ``time'' in terms of ways of actually doing things, people came to develop a very good understanding of the relation of time to distance, and of how measurements of these quantities can depend on the state of motion of the one measuring. It was learned that time could only be thought of in very tightly constrained ways without predicting things that experiments could show happened differently. By this process of building and coming to understand the meanings of words, by fitting them to experiments in the only ways nature would allow, it was learned that that certain statements that involve the notion of time cannot be made in any way that makes sense of the definition of the word. The statement that something cannot be made to move faster than light is one such conclusion. It does not arise because Einstein could not imagine a way to make something move faster than light; rather, in the process of understanding what kind of speed the speed of light is, and how it relates to the structures of space and time, he was brought to the realization that the whole idea of ``an object'' only has meaning when describing something that also goes slower than light. That is why anything else is impossible.

Different in the details, but very similar in its logic, turns out to be Heisenberg's statement about measuring concurrently both where some object is, and also ``where it is going'' (though the latter words are a little bit loose, and will have to wait until we define the notion of momentum to be said properly). This famous statement is often horrendously misunderstood, not helped by its name ``Heisenberg's uncertainty principle'', which makes it sound like a statement about the limitations of Heisenberg's own confidence. Curiously, unlike the statement about the speed of light, though, this one is rarely found recast in a language that emphasizes the heart of the matter. Acceptable descriptions of why one cannot exceed the speed of light have been available since shortly after Einstein's discovery of the result. But one rarely hears it explained that the reason one cannot measure Heisenberg's two quantities concurrently is that once one has found how nature requires the terms ``position'' and (properly said) `momentum' to be defined one discovers that in the sense of precisely specified properties these two by their very essense are never both properties of any object at the same time. As will be presented more fully in the chapters on the Quantum Theory, there is an important sense in which, even to say that a thing has a definite momentum as a property is to say that that object has only a very indefinite notion of position as something that can describe it. It can't be measured because it is a sort of ``not-'', or exclusion, of the other thing which is being measured.

The details of both of these points will be addressed more fully in their appropriate chapters. What we draw from them here are examples of the way in which a very particular understanding of the meanings of words is required to tell the difference between highly reputed foolishness and statements that seem even more outlandish but turn out to be true, and furthermore that, properly understood, should be accorded the highest confidence possible. In each case, the kind of understanding of the words that was required even to give meaning to such statements, and that in the process afforded them their proper confidence, was only attainable by defining, checking and using all of the words very carefully as descriptions of what one actually does or sees in experiments. The active relation to language as translated into doing is again the point of paramount importance.

We have reached a point where we can give a name to the most important factor that distinguishes the difference between the way we generally relate to language and the very particular way that is pre-supposed to relate to the language of physics, that both is responsible for its usefulness and leads to the source of its confidence. We can characterize our relation to language most of the time as a relation of inheritence. It is very trusting, in the sense that we are willing to adopt and use words in approximate ways, taking on faith that, simply by virtue of the fact that they exist and preceded us, they must have a meaning. Therefore, while we may admit to a certain vagueness in any particular instance, there is a certain assumption carried implicit that a sensible meaning is available, if we put forth the effort to extract it. Such a relation to language is tantamout to an assumption described in the introduction, that whenever words are combined to sound like a question, there must be a corresponding ``right'' answer.

In contrast, the language of physics is a language of invention. It is a sort of pure form of the language of instructions, in which every word, every sentence is intended to describe either something you can do or something you can see or experience. When you learn that it is possible to do something new, you have no reason to assume that a word or thought exists to describe it, because if what you are doing is really new there is not only no reason, there should be no way for a language-maker of the past to have created words to describe it. By the same token, when you learn to see in more detail, and come to realize that there are distinctions that were not apparent before, as when, even after you talk about counting ticks on a clock (a good concrete language because it describes a real thing you can do), you cannot expect that different people will count the same number of ticks if they are relatively moving (Ch ?), you must realize that the notions we have inherited may not make sense. This is precisely the case for the familiar but vague notion we have for millenia called ``time''. We intended it to represent a property we can compare that is common to the ticking of clocks and the beating of hearts and the passage of days and of ageing. But we did not notice, until the problem with the speed of light forced it upon us, that those observations are not enough to specify the idea, and before now it has been incomplete. It may still be incomplete, but nothing we have seen yet shows how that might be so, because the current use of the notion correctly describes everything we have been able to measure so far.