Serious introductions to physics, modern or otherwise, where by ``serious'' is meant the kind of introductions that are intended to leave the reader with the ability to actually answer questions and solve problems, usually begin as their first step with an introduction to Newton's laws, the notion of force, and the celebrated equation F = ma. Yet we have taken a long time to get this far, because while historically Newton's work may have been the first recognized major intellectual coup of physics, logically it lies many steps advanced from the beginning of any true introduction. A mind with only experiences from the natural world, but little familiarity with man's way of organizing and reckoning them, is not led invariably and immediately to think about nature in the way Newton taught us, and when Newton's laws are presented as a first step, not only is it likely that by their newness they will seem unnecessarily strange and confusing, but if they are presented as a starting point, there is a danger of misrepresenting the reasoning process of physics as one whose starting points are to be accepted for reasons of tradition and history.
Newton himself inherited a large intellectual resource, not only of data, as from the studies of planetary motions so carefully performed by Keplar, but of method and attitude, most notably from his close predacessor and partial contemporary Galilleo, as well as a large body of well-developed mathematics and logic, which had attained sophisticated forms already in the work of Euclid, much of which is still used unchanged today. Newton's acknowledgement of this groundwork is most often related in his statement ``If I have seen further than others, it is because I have stood on the shoulders of Giants'. Much more will be said shortly about what exactly Newton built on the shoulders of those giants. For now we note that, while what has been presented in the preceding chapters, on language and the processes of dimensional analysis, and especially about the discovery of the fundamental constants, is historically largely out of order with Newton's seminal work, it is in an important sense logically more basic and precedent to what will be discussed in this chapter.
In spite of this post-historical logical order, it is important to note that Newton did not have a formal process of dimensional analysis to employ in estimating answers to questions, because he was in large part responsible for demonstrating even that questions about the physical world were answerable, and for providing a framework within which such answers could be generated. It was only after some accumulated experience with Newton's work, as employed by many people, that it became apparent that there was an undercurrent of consistency in the answers that was simpler than, and independent of, many of the details of the questions asked, and the recognition of this more basic level of order was eventually worked into a formal understanding of the relations that have since come to be known as dimensional analysis. Yet, once these relations were understood, it became apparent that they also did not rely on any of the particular methods of calculation created by Newton, and in fact represented a more basic, and correspondingly less detailed, independent description of the patterns of nature, of which Newton's laws and methods were logically a refinement.
It is not uncommon that the processes of discovery and invention take these tortuous and not-well-ordered paths. In the intellectual climate that preceded Newton's work, dimensional analysis could likely not have been invented, because, as wild and foreign as this sounds in context of the present culture (or more accurately, what the present culture could be; unfortunately, it sounds more foreign than it actually is), the essential view of nature was of something capricious, which could be recognized, but not concretely or reliably anticipated, and something which it certainly was not man's place to try to control. The methods of dimensional analysis, while rock-solid in their predictive consistency, give only classes of answers, like scaling relations for which they cannot provide the precise constants of proportionality, or approximate answers, like the relative strength of the dependence of some motion on various properties of an object, so that the relative ``importance'' of different properties in producing the observed pattern can be estimated and compared. (This point is developed through examples in previous chapter's homework.) With our hindsight that very definite predictions can be made in answer to a great variety of questions about the natural world, we have come to value approximation, because we now understand in many cases how to refine approximations to ever more precise answers, and even in those cases for which the refinement is not known, we have become so confident of the predictability of nature that we view the approximate answers as the first steps toward understanding new problems, to be used as touchstones while looking for further steps. In the ultimate attitudes that have been born of modern quantum field theory (discussed in the final chapters of this book), we have even come to view approximate answers as the only kinds possible, because approximate questions are the only ones that can be asked in a definite way. (This is the attitude which motivates the sense of ``right'' and ``wrong'' regarding the answers to questions, mentioned in the introduction and in the chapter on language)
All of this inheritence of intellectual orientation is the result of the successes of physics that began with Newton's work, and did not exist as part of the culture that preceded it. The the importance of approximation would not be expected to be appreciated, when it had not yet been demonstrated that questions even could be answered definitely, and thus that the approximate answers were first steps toward better and more definite ones. (Without a quantitative understanding of the nature and importance of approximation, there is nothing obvious that distinguishes it from complete error of principal.) It was in this climate, where it was assumed that most questions about the future behavior of nature could not even be approached by man, and yet paradoxically where it was also taken as implicit in much of the philosophical prejudice, that it was in the nature of questions to be definite even to the point of having a priori meanings (as religious ones were and still are generally interpreted), that Newton had to search for order from experience, and if he found it, to present it so that it could be recognized. In this sense it appears natural that before the work of Newton, even the great progress in mathematics and logic that had existed for centuries, and amazingly even the great discovery of the first part of the law of Gravitation by Galilleo, did not create a revolution that made physics a prime mover of people's minds.
What Newton provided that overcame this circumstance, which therefore gave physics for the first time the power to change the world, was a set of detailed rules for predicting the motions of objects, so precise that they could be shown to agree with experience to the precision of the measurements then possible, in a wide range of circumstances. The absolute and uncompromised success of these predictive rules gave the first concrete demonstration that the motions of the natural universe, from the planets to small objects on earth, could be both predicted and related to each other in a single framework that made them readily understandable and manipulable by a human mind. And because they were capable of great precision, providing not only all of the constants of proportionality, but also great detail, even in the context of the epistomology of the day, they counted as irresistable evidence that the human mind could indeed encode and predict the behavior of nature. It is on the base of this proof-by-demonstration that all of our modern predispositions about nature and man's understanding of it have been built.
Thus while Newton inherited a great body of knowledge and even of attitude, it is important to understand how much less he had even than a coherent prescription for dimensional analysis from which to begin. Because of the way we have chosen to present this material, making use of so many of the logically more basic steps that have nonetheless come to be understood only after, and because of Newton's work, there is a danger that the simple and elegant form of Newton's laws could appear as a natural and almost mundane refinement of what has been described already of language and dimensional analysis. To take Newton's laws as no more than this would be an unfortunate and serious misunderstanding of both their historical importance and of the great genius that was for the first time capable of creating them, only after which so much else has been possible.
Despite the relevance of this perspective, though, after Newton, dimensional analysis has come to be understood as the independent and logically simpler tool for orientation that it is, and even later than that, the important structures and assumptions that set apart the language of physics are becoming clearer. Not to make use of them would be to waste a valuable resource. Thus it will be appropriate if, with the hindsight of modern culture shaped by physics, and the technology of dimensional analysis in place, the technical aspect of Newton's work seems the natural progression from what we have already discussed. Yet it is also appropriate at some moments to forget the luxury that such logical precedent now allows us, and to view Newton's laws primitively, as they are often presented, not to be led into an impression that the important origin of physics lies in tradition, but to be reminded of the stature of mind that was responsible for seeing to such great depths, and to formulate them clearly in spite of the fact that they are so far advanced beyond the first step in the introduction that the culture of the time provided for their creator.
While we will not make any techinical use of this historical note, it is appropriate to remain aware of its contextual importance, because above and incorporating all of his technical achievements, Newton more than any other man in recorded history was responsible for creating the fundamental disposition that the world is a knowable place, and for providing the means to make that premise irrefutable. That is presumably also why, after at least 6000 years in which much of the pattern of human life progressed with comparatively little change, in the last 300 it has been altered, literally and in attitude, so extensively as to be in some respects beyond recognition from what it was before.
Having mentioned very briefly the cultural and philosophical impact that places Newton's work in perspective, we turn to the concrete technical aspects of what he created and how it forms the next step in our understanding of natural processes.