The first thing to realize is what it means, in a language of tools, to ``understand'' something. The things that happen in nature exist, in some sense, ``outside'' us. We ``experience'' them when we are part of the interaction. Our thoughts, though, are not made of external events, but rather are constructs that mimic them in the mind. In other words, everything we remember, everything we can imagine, everything we can predict, everything we understand is one or another kind of ``model'' of external events that exists in the mind. The knowledge of physics is a collection of such mind-models. Its methods are various ways to use them.

We usually think of a ``technology'' as a set of prescriptions that enable us to do things, which we couldn't do without them. In just that sense, physics could be called an ``intellectual technology''. It is a set of models, and prescriptions for using them, that enable us to use the mind to correctly predict what will happen in the world around it.

The thing to recognize is that mind-models are much freer than the natural world they describe. If we consider any one thing that happens in nature, it necessarily always happens in just one way. However, we can choose to represent it with many different models, which may look nothing alike, depending on what we want to say about it. To cite a now-trusted example: we know that a roomfull of air is just a very large collection of very tiny molecules, constantly colliding with each other and with the walls. It is certainly correct to describe the air with a very (very very!) long list, telling what each molecule is doing at each moment. Presumably, somehow that list tells what the temperature of the air is, because we know the description in terms of atoms is, in a certain sense, complete. In this description, though, that information turns out to be very hard to recognize. The list itself is also very (very very!) hard to manipulate, because it is so large.

In this case, a completely different description is also possible. It is called a thermodynamic one, and it is one of the descriptions of ``collections of things'' that we referred to in the last section. The thermodynamic description omits the long list entirely, yet it brings properties of the air, like temperature or the speed of sound, to the front in the very first step. The air is the same, but the two mind models are completely different. They refer to completely different objects and emphasize completely different qualities of the air.

We will see this multiplicity of descriptions again and again as we explore the topics of modern physics. We might merely want to describe the motion of a falling rock. That problem was solved by Galilleo, with one of the simplest laws ever discovered. It turned out that Galilleo's law was not the final story about gravity, though, so the problem was solved again, with a slightly different law, by Newton. Again, though, depending on the circumstances, Newton's description may not suffice, and yet another description of gravity by Einstein will be needed to model the falling rock. This description is so radically different from Newton's that we will have to go back all the way to the level of language, and re-define our words, to even be able to state it. Then, perhaps if it is a very small rock, we will need to start over again in a completely different context, and redefine the language again, in order to use the Quantum Theory to describe what is falling.

The special thing about physics is what it means for these descriptions to be different, and how precisely it manages to incorporate many such different descriptions into a single framework. This brings us to the notion of abstraction, and what physics has taught us, philosophically, about the meaning of right and wrong.

First, it is clear that every mind-model must ignore something. The natural world, in all of its detail, is far bigger than any mind. If nothing else, it contains the mind as part of it, and the mind cannot ``contain itself''. Obviously, though, no real model ever comes close to encountering this barrier, and each one ignores almost every detail, keeping only a few. The reason physics didn't work for so long was that people had no good way to tell how important the details were that they ignored, or how to go back and incorporate them later if they became important. That was what Newton created.

Among other things, this inability to handle partial descriptions made it difficult or impossible to decide what was ``right'', or even whether any statement could be ``right''. Every statement ignored something. This is why, for instance, alchemy and astrology have flourished throughout most of man's history, while today they are minor, or even rare practices. People have recognized for thousands of years that many complex parts of nature influence each other. They just had no way to tell whether a prophecy was wrong because it omitted details, or was wrong ``in its essence''. It wasn't even obvious that there was such a distinction. If it seemed right sometimes, maybe it should be kept, but who could trust it?

The way we handle partial descriptions has always been referred to as abstraction. What physics taught us was a new way to think about this concept. When Mendeleev discovered that chemicals have something in common, he had a new way to refer to a whole collection of chemicals, not each one in itself, but together, denoting them by what they had in common. Giving this common essense a name, element, and referring to it as a thing in itself, is an example of the process of abstraction. It turned out that Mendeleev's ``elements'' really were objects unto themselves in nature, because each coresponds to a different kind of atom. That is an added benefit that nature often gives us when we abstract ``insightfully''. The process of abstraction, though, is something we can do with our mind models, independently of whether nature has corresponding ``objects'' or not. The concepts ``temperature'' and ``sound'' in thermodynamics are abstractions that do not refer to particular ``building block'' objects.

The lesson we have learned from physics is that when we make such an abstraction, we are referring to every one in a collection of special cases. We are simply giving attention to the things that all the cases have in common. Therefore, when we wonder if a statement about an abstraction is true, we must find out if it is true for every one of the special cases that the abstraction includes. In other words, the notions of right and wrong do not become more ``vague'' when we apply them to abstractions. They must simply fit more cases to be true. In return, though, if we can find true statements about abstractions, we can put aside the details of referring to each special case separately. This is often most useful when we have found that a particular abstraction is possible because it arises from one of nature's little hidden building blocks, like Mendeleev's atoms. Then, by discovering things about the building blocks, we can predict many things about every structure they combine to make.

Physical knowledge is organized by applying this notion of abstraction to the process of ``coming to understand things''. Consider:

Everything we eventually understand starts out as some pattern we recognize. We ask ``what was that pattern'' and try to put together words that isolate whatever is special about it. We may do this many times, with concern for more or even different details. When we find that we can recognize patterns in the behavior of nature, we make rules to predict them. The rules can either succeed or fail, but no rule ever even attempts to be infinitely detailed. Each predicts only certain features of what we can see, and succeeds or fails for those features. This is what people have always done.

The lesson of physics has been that it is not useful to think of any such rule as ``partially right'' or ``partially wrong'', with respect to the entirety of any natural phenomenon. Rather, we recognize that from the start, our ``pattern'' is an abstraction, a quality that many natural events share, but that does not completely specify any of them. Our goal, then, is to understand what class of occurences our abstraction can include, and to make statements that are absolutely right about the abstraction. We no longer look for ``partially right'' statements about ``exactly this part of nature''; rather, we ask for ``absolutely right'' statements about ``everything that looks like this''. The abstraction itself only refers to some qualities of each occurence, so it is only finitely detailed. That is why it makes sense to describe it with rules that are only finitely detailed. At the same time, finiteness of detail no longer compromises the basic notions of right and wrong.

It is hard to appreciate, at this early stage in the discussion, how valuable this interpretation has been. It will become clearer in chapter 3, when we discuss Dimensional Analysis, probably the most efficient single formalism for handling abstractions that there has ever been. It would be fair to say that the way Dimensional Analysis handles the abstraction of a dimension is a paradigm for the way all of physics handles the objects in its mind-models. Meanwhile, we can again look at how such a point of view is expressed, and what it buys.

Immediately, it gives us a concrete criterion for ``right'' and ``wrong'' that makes sense in the context of partial knowledge. There can be no more hiding ``partially right'' in the details. When we ``understand something'', we make a rule to describe the pattern, the abstraction that concerns us, and we tell what class of phenomena we intend it to describe. If the rule ever fails, for any member of the class, it is wrong, pure and simple. However, if it succeeds every time, it may be ``right'', even though there are other phenomena, outside the class, to which it does not apply.

An example would help about now: Galilleo's law for gravity, as we know in hindsight, can claim to describe every thing that falls near the surface of the earth. (``Near'' is itself a delicate term; we will come back to that in a moment. Also, the objects need to be compact enough that we can ignore the effects of air on them.) For all such objects, that law has always worked. It describes the abstraction of ``objects that fall in gravity near the earth''. In that context, it is as right as a law can be.

We also know, now, though, that the moon orbits the way it does because it, too, falls toward the earth. However, it is not ``near'' the earth, in the sense that Galilleo's law requires. Newton's law is somewhat more difficult to apply than Galilleo's, but it works for the moon, as well as for all the objects in Galilleo's domain. In fact, Newton's law works so well that only within the last century has anything been measured for which it fails. Therefore, for a long time, it was not known how big a class their abstraction should be taken to describe.

Today, we know from direct experiments, as well as from a large body of circumstantial evidence, that Newton's laws are also limited, and what those limits are. Their successor, Einstein's General Relativity, now includes Newton's predictions, as Newton's included those of Galilleo. Nowadays we wonder which things General Relativity will fail to describe. So far, none has been measured, but we have rough guesses about where the limits should lie.

(In these cases, the various descriptions fall naturally into a hierarchy, with each containing the other, and improving it either by providing more detail or successfully describing more cases. Another relation is also possible, whose example would be the thermodynamic description, and the very very very long list, for the roomfull of air. It turns out that sometimes, if the room is not all that big, and there are not too many molecules, there are some questions that are better answered with the list. Thus, one sometimes chooses one description over another, not because it is more accurate or more complete, but simply because it gets more directly the the desired point.)

The language of physics has become structured, so that it naturally talks about laws with this predisposition toward abstractions. The confidence of physics is possible because right and wrong are no longer grey or muddy concepts. The rules for testing physical predictions are simple and explicit. Any prediction that can successfully survivie them becomes a very good thing to trust. There is no way to make this point adequately by just saying it. We must leave it to hands-on experience, applying physics, to show how increadibly reliable, and powerful, physical law truly is.

One of the most modern ideas in physics, which we will discuss in the last chapter, is also one of the most striking examples of how deeply this veiw of abstraction should be taken. In the entire domains of Relativity and Quantum Mechanics, we will find that we must be careful of how we use words. We cannot assume that questions are even answerable until we have shown, experimentally what they mean. The ultimate case in point, though, will be a topic called renormalization. It is an aspect of Particle Physics which is a field at the nexus of both Relativitity and Quantum Mechanics. Like no other single affect we have seen in nature, it will teach us that even the words we use are very delicate abstractions. We cannot assume that the simplest words (like the words in the question ``where is the particle'') even refer to anything that actually exists, until we have told how we intend to measure it.

Renormalization will bring home a lesson in philosophy, which we have already seen at work. Not only in questions of detail, but at all, ``right'' and ``wrong'' are not notions that precede the asking of questions. Rather, they come into existence with the questions themselves, as criteria for the suitability of answers. How ``right'' a question can be is not even meaningful until the words in it have been well understood.

Finally, we can describe how an appreciation of abstraction has given physics an order. People have always made abstractions so that they do not have to keep track of too much detail (this could be seen as an internalized version of the library problem). Once we understand abstraction in the sense of physics, we see that it represents a trade-off between simplicity and precision. This trade-off is precise, though; we can keep track of exactly what has been sacrificed and what has been gained, because the categories are explicit.

An abstraction refers to many special cases. Therefore, by design it lacks criteria to single out any of them. In exchange, though, the abstraction itself may have very few features, and be describable with very simple laws. Sometimes we do not even care which of the objects we refer to. Maybe we want to throw something, and predict where it will land, but we don't care whether it is a rock or a baseball, as long as they both fly the same way. Other times, we will eventually care to be more specific, but first we want to understand the broad features of the answer. In either case, we choose simple abstractions first, that encompass wide classes of events. They obey simple rules, which are easy to remember and use, precisely because they have so few features that they cannot be very specific.

The special order in physics comes from the way it teaches us to use simple laws, even when we have more detailed laws available. We start with the widest class that tells us anything useful. In almost every problem in physics, the first thing we want to get is a sense of scale. In other words, roughly how big, how heavy, how many of something make up the final answer. The abstraction we use to refer to scale is the notion of dimensions, and the rules for handling them are collectively referred to as Dimensional Analysis. Almost always, we know more about a system than just its size, but we have to ask much more complicated questions to make use of that knowledge. Therefore, we start with dimensional analysis, and it tells us, independently of all the rest of the details, roughly how big an answer our question must have.

If we are only throwing rocks or baseballs, and we don't care which, maybe we stop there, because Dimensional Analysis has told us everything we want to know. If not, we look at the same problem again, and we choose a more detailed, more specific abstraction. The part of physics that handles this abstraction will probably give a more precise answer, but it will also probably be more difficult to use, and offer more opportunities to make mistakes. But this time, we go in knowing something about the answer. We know from Dimensional Analysis roughly how big it should be. Therefore, in searching for more detailed answers, we can guess ahead of time which avenues may be more useful to pursue, and check for mistakes as we go.

The process is repeated, until we have the answer we want or have arrived at something Physics cannot tell us. If the latter, perhaps we use our partial understanding to search for new rules that will take us where no-one has gone before.

In exactly this way, all of the knowledge of Physics is collected into a hierarchy, with simplicity at one end and precision at the other. If the ``knowledge'' could be seen, it should look something like a tree. It is not enough that there are few big branches at the simple end. The tree is useful because we know how to follow the coarse branches, through finer and finer levels of detail, and usually how to ``zero in'' on the description we want.

This order in physics is special, among all the things that people know. It is the one thing that makes it conceivable for physics to be, not only the broadest and most specialized field people know, but also the most directly suited for use as everyday knowledge. Like the physicist's confidence, it is a practical application of what we have learned, philosophically, about our ability of abstraction. Applying it to everything possible is the best solution yet to the various versions of the library problem. In creating a new source for confidence in ideas, it makes possible a new relation of ideas to authority, and offers a new paradigm for peoples' co-operation. Thus, this is a very important point.

Considerations like these are what make it difficult to give a satisfying, short answer to the question ``what is Physics'', until after one already knows. The things we have learned about the natural world have influenced how we speak, and even how we think about what we understand. It should not be surprising, then, if there are some ``frames of mind'' that physics particularly encourages, or in which it works particularly well. We have mentioned that physics is best learned with an active, participatory language of directions and tools. In the next chapter, because of issues related to the delicacy of abstraction, we will begin to see that more than ease of learning is at stake. The language has developed so far, because nature has require that, that many of the modern ideas in physics do not even have a meaning out of context of a language of tools.

Experience has also shown that the confidence of physics, ultimately based on individual experience with the natural world, is in many respects ``better'' than confidence based on authority. The extent to which physics has grown, while other aspects of human life have stayed so much the same, is a suggestion of this. Also, because nature does not change (the rules), the ``truth'' of physics is not capricious. It remains the same, for everyone who uses it, throughout time. This is why states and institutions have declared physical laws ``wrong'', but the physical laws, perhaps statements from only single men, have eventually prevailed. This source of confidence is responsible for the integrity of the laws, and it affects the integrity of our thought as we use them.

The general mental ``posture'' that incorporates these features could be called Intellectual Independence. It consists of taking an active relation to language, expecting things to be understandable, and attempting to work them out for onesself. We have tried to suggest the advantages offered by physics to such a frame of mind. For now, that will have to suffice. Hopefully, beginning (rapidly) with chapter 3, and continuing through the rest of the chapters, physics itself will convey the sense of power and freedom available to a person who can approach nature in this way. It is the freedom to understand what happens in the world around us, rapidly, confidently and ubiquitously.

One of the reasons physics should be a pillar of every person's common knowledge is that it is most powerful when practiced all the time. As we become practiced at using our experience to answer our own questions, we build on it, and can ask and answer more. With freedom to solve our own problems comes freedom to create. As understanding the events of nature becomes a habit, and an ongoing way of life, it sharpens our ability even to notice what happens. These are the ways that the tools we use in day to day life can shape who we grow to be. They are hard to explain in a few words, but when experienced, they are unmistakable and anything but small. The things they make us able to experience create not only power, but also richness in thinking and living.


Thu Aug 31 12:01:42 CDT 1995