Let us now look at the act of changing, which is called "process". A good deal of controversy has arisen over this in reading ancient texts, because "process" (kinesis) has been translated "movement," which is only one kind of process, though perhaps the most obvious. But Newton's First Law of Motion (that a moving body, left to itself, will continue moving at a constant speed in a straight line) seems to say that movement is not a change, but an act in equilibrium; and so the waters have been muddied when people look at Aristotle or St. Thomas in the light of Newton.
But first of all, both Aristotle and St. Thomas admitted the existence of acts that look like processes and are not, where no change is really going on. They called these "acts of a being in act," such as actually thinking of something you already know, like two and two are four. You actively possess that knowledge, and so you have not been become different by calling it up from within you. Hence, if it could be shown that movement (changing position) involved no real difference in the body, they would have no problem with saying that it wasn't a process. We will see, however, that "in the real world," as they say, movement is in fact a process. What Newton did was make an abstraction from real-world situations.
In any case, what they meant by kinesis (or "motus" for St. Thomas) was "the act of a being in potency insofar as it is in potency." That is, it is what an unstable body is doing to get itself out of instability. Obviously, any body which is maintaining its energy is not "in process," then.
It sounds as if their definition is reasonable, and so let us make a similar one of our own:
Process is the act by which an unstable body regains its equilibrium. Or, if you want to put it metaphysically, process is a change as a property of some body.
In other words, process is the act itself of changing. In the view advanced above, this would mean that the body in question is either gaining or losing energy; and the process is the act of acquiring or giving up energy.
It follows from this that process is always a "vector" activity, since it will necessarily have a direction (from instability to the purpose); and it also implies what Aristotle said, that process is an "incomplete" activity, since it is the act by which a body goes from a state of incompleteness to its equilibrium.
Let us put this into a formal conclusion::
Conclusion 9: All processes have a definite purpose, and processes are the only acts that have a purpose.
As Aristotle also said, even though process is not activity in the fullest sense, it is the most obvious case of "doing something," because the body in process is becoming different because of its process, while activity in equilibrium seems to be "doing nothing" because the body is just staying the same. It was Aristotle's genius to realize that a body that is staying the same is actively maintaining itself, and that this self-maintenance is the ontologically prior meaning to "activity," while the activity by which the body gets to equilibrium is a second-rate kind of activity in reality.
Since processes involve instability, then it is also obvious that we can say the following:
Conclusion 10: Purely spiritual beings do not undergo process.
There may be (and, as we will see, there are) processes in the spiritual dimensions of bodies that are organized with a basically spiritual act, provided that this spiritual act also has in one of its "reduplications" of itself a quantity. We know, for instance, that we acquire knowledge, and that our consciousness changes; but it does so because one of its "dimensions" is the nerve-energy in the brain, which undergoes changes. We will see more of this in the next Part. But if one is talking about a pure spirit, there is no sense in which it is unstable, and hence its activity is necessarily in equilibrium.
Process philosophers, of course, will have none of this, because for them "being" is "becoming"; and this, of course, is because they have missed the Aristotelian insight I spoke of just above, that process is not coextensive with "activity," and in fact, since it implies instability and self-contradiction, is an activity that does not make sense by itself, let alone being the activity that is supposedly the intelligibility of everything. But I don't think we have to belabor this.
Since process is the act of a body, it won't be surprising to find that it is itself a form of energy, with a quantity. But process, since it begins somewhere and ends somewhere, has actually two quantities, one dealing with the difference between the beginning and the end, and the other the quantity of the act of getting from one to the other. These two are actually independent of one another, and not reducible to each other. Let us define them:
The length of a process is the difference in energy level between the initial instability and the final equilibrium.
The velocity of the process is the quantity of the process as an act.
You can see that the two quantities are independent of each other if you consider going from Boston to New York at thirty miles an hour as opposed to sixty miles an hour or five hundred miles an hour. The length of the process is the same in each case (Boston to New York); but the velocity is very different.
The same is true of other processes than movement, like heating water. You can bring water from freezing to boiling at a rapid rate (velocity), or slowly; but the length of the process is the same. And, of course, you can heat water from zero to fifty degrees Celsius at the same rate as you heat it from zero to a hundred.
But how is the distance between Boston and New York a difference in energy levels? Because you are in different positions with respect to the gravitational fields of your surroundings. Perhaps with respect to the earth's center there is no change to speak of in energy-level; but there certainly is with respect to the pull of the Empire State Building. Obviously, in the case of travel on the earth's surface, the sensory notion of distance ("distance-as-it-appears") is more convenient to work with than energy-distance (which is the reality the former is based on); but in physics, the energy-distance is actually the more meaningful concept.
The reason for this is that in physics, the length of the process is the net result of the change, and differences internally that cancel each other out are ignored in the final analysis. Thus, in looking at going from Boston to New York in relation to the earth's gravitational field, the difference in elevation between the two cities is the length of the process; because every time you go down a hill, the work you did in going up is canceled by the work gravity is doing to your car in pulling it down; and so the net work is the actual length of the process. Similarly, if you heat some water and then let it cool and then heat it up and so on, the length of the process of heating is the difference between where it started and where it ended.
This does, however, indicate a different characteristic of a process that we should take into account:
The path of the process is the process considered as a number of smaller processes added together.
It is the confusion of the path of the process with either the length of the process or the process itself that has led to a number of conundrums in philosophy, notably Zeno's paradoxes.
For instance, Zeno allegedly proved that it is impossible to move across a room, because before you get there, you have to get half-way; and before you get half-way, you have to get half of that distance, and so on. Before you even take the first step, you have to move half of that distance, and before you move any finite distance at all, you have to have moved half of it; and so it is not possible to move at all.
The mathematical notion of the "limit" does not, in spite of the mathematicians, solve this problem. In the first place, they set it up another way: in order to get to the other side of the room, you have to go half-way first, and then half of the remaining distance, and then half of that, and so on; and there is always a finite distance between you and the other wall.
But then they say that this reduces to the series (1/2 + 1/4 + 1/8 + ... 1/2n ...), which sum becomes a fraction closer and closer to 1 the larger n becomes; and hence the "limit" of that series is 1. But the fact that 1 is the limit doesn't tell you that you'll ever get there; it just says that 1 (the other side of the room) is (a) the place you'll never get beyond, and (b) the place you can get as close to as you want, but never will reach(1).
In other words, the "limit" just defines where the other side of the room is; but it doesn't allow you to reach it--unless there is a "last" number.
What is the fallacy here? It is that of thinking of the process as actually made up of smaller processes added together; it is the confusion of the process with its path.
If you walk across the room, then at the beginning of the process, you set up an instability in yourself whose purpose is being at the other side of the room, not half-way. The process that then occurs is one act, not a series of them; it does not stop half-way and then resume (unless you set up a new instability in yourself by deciding to stop, of course). It is only by imagining this one process as if it were a series of processes each of which stopped half-way toward its goal that you get into a problem; but obviously, this is to falsify what the process is, because its goal is the end, not some intermediary point. That is, you pass through the half-way point, and are never at it, because you are still unstable there.
That is another of Zeno's paradoxes, by the way, because at any point, you are at rest, and he asserts that this is true of every point in the path, and so you are never moving. But you are never at any point in the path, since the point has no size, and so you have passed through it as soon as you "get there." The fallacy here is that of understanding the points of the path as if they were end-points, when the path-points as such are imaginary.
That is, a process, as one act, is no more a series of small processes than is your weight a series of one-pound weights added together, in such a way that for you to be your weight, you would have to be half of it and then half of the rest of it, and then half of that, and so on. No, your weight is your weight, and the fact that you can measure it as if it were a series of smaller weights added together does not make it a series of them. Or a sound of 80 decibels is not a sound of 40 decibels + a sound of 20 decibels + a sound of 10 decibels + a sound of 5 decibels, and so on. It is a sound that has a quantity; and the fact that we think of this quantity as a sum of units does not alter what the quantity is. In the same way, the act of walking across the room, or any process, is one act, and its length is one quantity, not a series of them, no matter how we might break it up in thought to measure it.
We get into trouble with processes rather than with the "static" acts in equilibrium like color, mass, temperature, and so on, because we think of processes as going "through time," while the others are all there "all at once," and so the former seem to be a heap of quantities and the latter don't. But this is looking at things backwards, actually, because as we will see shortly, time is derived from comparing processes, and is not something you measure processes "against."
But before we do this, we have to mention the other quantity of the process: its velocity. I say "velocity," not "speed," because "velocity" in physics is the vector concept, which includes direction, and speed is just the number that belongs on this velocity; and since process is always directed, velocity is the correct term to use.
The length of the process is a scalar quantity, because it is a simple difference in energy, and it doesn't really matter which is the beginning and which the end; the directedness of the velocity takes care of that. That is, if you heat water to fifty degrees hotter, the length of the process is the same as if you cool it to fifty degrees cooler; whether you are heating or cooling is taken care of by the act itself--the process--with its directedness.
The point that is really significant about the velocity of a process is that it can be directly measured, and doesn't have to be measured indirectly by looking at a clock. Since the process is an act, it can exert force on some measuring instrument to show how "strong" it is--which is, of course, its quantity as a process, or the speed of its velocity.
For instance, the speedometer of your car (which, you will note, measures speed, not velocity, since it doesn't care whether you are going forward or backing up) does not use a little clock; as the wheel turns faster and faster, some of its energy creates greater and greater force on the instrument, which makes the needle go higher; and the force (and hence the position of the needle) is proportional to the speed at which the wheel is turning and so the speed at which the car is moving. Hence, the speedometer is not really measuring "miles per hour" or "kilometers per hour"; it is really measuring something like "vels," which are then interpreted in terms of a ratio between the length of the process (miles) and something that is happening on a clock.Next
1. The notion that the distance from the other wall "approaches zero" and the leap to the "epsilon neighborhood" introduces a self-contradictory "fudge factor," implying that the number which is the limit (if it is believed to be reached) is "as close as you want" to the other side. But of course, if there is any finite distance between where you are and the other side, then there is still an infinite distance, in the sense that you still have an infinity of halves of the remaining distance to go. The mathematical solution to this is that the derivative (the limit) is in fact an exact amount, equal to the fraction 0/0, which is the only time in which division by zero is not a contradiction. The trouble is that, in itself, the inverse operation, 0 x n = n, where n is any number you want to name. What the calculus does is show that in certain cases there are processes that make the fraction constantly closer to 0/0, and give evidence of never going beyond this fraction; and so in these cases (the ones in which the calculus applies) the number has a definite quantity. For example, if you are traveling at a constant 30 miles per hour, then in ½ hour, you will have traveled 15 miles, in 1/4, 7.5 miles, and so on; so when the time reaches zero (at an instant), you are still "traveling through that point" at 30 mph.
What I am saying is that, though Leibniz's and Newton's notions of the derivative "worked," the theory "explaining" it is defective.