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How to Run, Manage, Govern a Human Society:
A Primer in Social Physics
How can I or anyone else claim that there is a set of principles, so embracing, that it can apply to all systems, simple and complex, living and nonliving, small and large? That arises because there is one science that is first among all the others. That science is physics, the laws of motion, or movement, and change in all systems. So said the philosopher-scientist, Aristotle, 2300 years ago. We physicists believe that the reality of that promise, made two millenia ago, has been amply realized by the further contributions to that science made by Newton 300 years ago, Maxwell more than 100 years ago, and Einstein somewhat more than 50 years ago. Let these comments not frighten you away. My problem is to expose those principles of physics, here to be applied as a social physics, in such simple terms that its applicability and rightness will become adequately apparent.
The idea of physics itself is very simple. It states that forces, agents of change --this notion is to be found in Aristotle and was made real and quantitative by Newton -- cause change in movement. That idea is not difficult. But now we have to apply it.
So we have a bunch of things -- atoms, particles of dust, ping-pong balls, living cells, people, even stars -- engaged in motion. When they move freely, we can imagine that there are no forces acting on them. (Aha, wise guys among you will ask what about the gravitational force and perhaps even electrical forces; how can you talk about particles moving freely. I'm going to say to you, be quiet; just imagine first that those forces were not acting; we can add them in later. I want to get across the idea of the effect of the very local bang-bang forces of collision). But when these things interact by colliding, there is a mutual mechanical force of collision. They have banged into one another, and such a force causes a change in motion. They each redirect their movement and continue again until they collide once more in new pairs.
That very simple description already contains a significant fraction of all of the principles of physics. But it is not enough to provide the foundation by which we can continue to describe the group motion, which is our intent. The question we have to examine is what happens during the time of collision. The answer to that question provides another significant chunk of physical theory.
At this point most readers will begin to shake and quake. Here, they think, is where physics becomes complicated and leaves the reader. Not at all. If we take the Aristotelian-Newtonian concept of force as agent of change in motion, we can see three equivalent views of such an effector of change.
In the most direct view, the action of a force is to change the motion, that is to make the thing, particle or what have you, accelerate (You push on a thing; it jerks forward by a change in motion).
In the second view, the effect of a force acting for a time (multiplying the amount of that force, how much the force measures, by the measure of the time it acts is known as the impulse) is to change the motion more directly. The impulse changes the momentum of the thing, how fast the thing is moving, not the acceleration, which is how fast the velocity changes. Momentum is the velocity of movement multiplied by the mass of the thing, how much matter it contains. Humans engage in this process all the time. If you take a bat, or a mallet, or a golf club, or bang into a chair, or flick an object on your table, the impulse, namely the collisional force multiplied by the time that force acted, changes the momentum of that object which is struck. If the object is massive, a big chair or ball rather than a little chair or ball, the change in velocity is of lesser magnitude for the same impulse. Slap a ball against a wall; see how the impulse of your slap starts the ball moving; see then how the impulse from the wall changes the momentum of the ball as it bounces back from the wall.
In a third view, the effect of a force acting through a distance, such as a push or pull on a box or on any other thing on the ground, for some distance, is to change the energy of motion of the thing on which the force acted. Multiplying the measure of the force and the distance through which the force acted is known as the work done on the thing. The energy of motion is measured by the product of half the mass of the thing multiplied by the velocity repeated twice.
Now these three paragraphs have created some cause for alarm, but like medicine, swallow it and it will quickly go down. What was said is that physics is and has to be concerned with forces acting in space and time on masses of matter. That is from where the changes in motion arise. So now that we have been introduced to the kinds of changes that result from forces and the forces of collisions, we can return to where we were.
When two bodies collide, we can describe their subsequent motion as follows: Because their forces of collision come in pairs (one hits the other and the other hits the one), the forces are equal and opposite - this being a third of Newton's laws of motion and change - their effect on the pair of colliding particles is nil, nothing, zero. Therefore paired aspects of their motion have not changed. Since each of the force collisions that occured involved a distance of collision (the work done by the collision) and a time of collision (the impulse of the collision), we can see that the pair of particles did not accelerate; the momentum of the pair of particles did not change; and the energy of the pair of particles did not change. Also, we can see that there was no reason for the mass of the pair of particles to change. Thus, even though the independent motions of each of the particles in the pair did change, the composite measures of the pair did not.
From this analysis, we infer that there were three fundamental properties of the pair that did not change. Those properties are known as the fundamental conservations of the motion of collision. The three measures that were conserved were the measures of their matter (before, during, and after the collision), the measures of their momentum, and the measures of their energy of motion.
Is this a big deal? Yes. As a result of the fact that three such conservations have to exist - no more, no less - we can determine the motion of the colliding pair of particles due to collisions pair by pair. Do you think this is a fabulous computation? Well yes and no. Watch any ball player, yourself or perhaps - if you have such - your much more skilled children, or any golfer, or any pool player. These performers make such calculations each time they exert a colliding force on some object. Thus the intuitive characteristics of such collisions are almost obvious. Perhaps their mathematical expression is more frightening, but it doesn't take mathematics for the three year old to begin to demonstrate objective skills of performance in accordance with these principles of conservations of motion (If the youngster can't do it at age three, he or she will do it at age four). But beyond that fact that even children can do it intuitively, you have to understand that physics is the only science that can make real and accurate predictions on the basis of such simple principles, principles that you can see even other nonhuman animals applying (a bat echo-locating, a hawk swooping on its prey, a monkey jumping from tree to tree).
Suppose now that you are willing to concede that it is possible to figure out what the result of any pair by pair collision is, what does that get you?
Let me point out where you are. In a gas, you have just described one collision between two atoms or molecules among a number of such particles that number in the billions of billions of billions. Numbers like that make even the American debt expressed in pennies look like a very very small pile of peanuts. Or, in a galaxy, you may be concerned with billions of billions of stars interacting. Or, in a living organism, you may be concerned with billions of cells interacting. In any of those cases, one would wonder how far along you are in describing the motion if all you could do is describe the effect of one pair of colliding particles. But here again the principles of physics come to the rescue and tell you how to describe the more total game of all the pairs of interaction.
In the most general sense, that physical game is known as the connection between the micro and the macro, the little and the big, the local and more global. For the micro game, we refer to the play as the resulting kinetic or dynamic interaction among atomisms. Atomisms are the generalized description of atomic-like or atomistic "things", the things that banged into each other in interaction without necessarily getting destroyed.
The atomic doctrine was first developed by the classical Greeks who sought out the primitive particles or material substances that might arise with indefinite division of material objects. They could not fully decide whether there were no such, a few such, or many such particles, nor what those particles were. Now we know that such atomistic particles come in nested levels, making up a complex hierarchy of such units. For example, we have a cosmos - one thing - which comprises perhaps one or more universes (for example, each its own black hole); within any such universe, there are galaxies; these galaxies - each again one thing - comprise large collections of interacting stars and cold matter; in and among that matter, there are a variety of other intragalactic matter systems - planets, planetismals, clouds, chemical systems, such as geochemical and biochemical systems; then atoms, ions, molecules; and finally leptons and quarks all in a so-called vacuum. According to our current demonstrations and understanding (the physicist's show-and-tell), the result of interactions among leptons and quarks is to produce the same or other leptons and quarks from the vacuum. At present, we can't find anything or things below them. That latter level of things is nearly as far as physics can go into nesting now. At the level most interesting for us in this book, we wish to concentrate on the biochemical systems which include us and our societies.
Note that the macro-micro game going on among the atomisms and their organized field of play is much more extensive than any simple game that people play. Consider a game of baseball. We may consider one interaction to be a batter up and facing an opposing team of 9 players. In 9 inning turns, three players from each of the two sides up at bat in turn have to be put out, starting from play initiated by a pitcher who is manipulating the throw of a ball by the laws of physics. Thus a game, minimally, involves 54 playing interactions, in which every such playing batter is put out in turn. But that is not the total play. Since the batters may score base hits rather than being put out, many more than 54 turns at bat are taken. It is more like 100-200 turns at bat that are taken. One hundred years have not exhausted the amount of differing drama of play to boys and girls that occurs in this game almost any night of the year, spring and summer. Yet that game is extraordinarily simpler than any natural atomistic system of field play. Nevertheless, physics can collapse the play of one of these mammoth field games to a relatively small measure.
In the simplest of atomistic games which lead to field phenomena (field phenomena - the organized play of a large ensemble of players interacting throught an extended space-time field of motional action among them), the result of the pair by pair motional interactions is to create a flow field. You can see such a flow field as it is produced by a fan, a hair dryer, a propeller or turbine driven aircraft, ship, or reaction spacecraft, a rotationally driven galaxy, a nuclear reaction-driven star, a water pump in one's basement, flow in a river, or the tides in the atmosphere or ocean. The amount of natural or Man-made phenomena that fall in this physical class of systems is phenomenal, enormous. It likely is the most common of all physical field phenomena. Thus the problem is of great generality. So how does one describe its general phenomena of motion?
We get to the more general motion of the entire field of players by introducing an intermediate description of the local ensemble. We imagine a local space-time box. in which a considerable number of interacting plays are taking place. Look at it as a small local ball field or region in the street where a ball game is going on. (We city kids were accustomed to such play in the streets). Namely, there are a considerable number of players in the spatial box, which nevertheless only occupies a small amount of space, and we observe the motion going on in that fixed box over a considerable length of time. However, we only examine the motion at certain intervals of time (as if, for example, we were only watching innings or just games).
What we get out of those discrete, intermittent observations are local averages, the statistics that every one who lives in that neighborhood knows. For example, every time we blink - making one of our intermittent observations - we can count how many particles are in the box. Or, as an equivalent measure, we can can count how much matter (mass) these particles have contributed to the content of the box. Those counts gives us one local measure, the local density. That is, you can have either the number density, or the mass density. Suppose you imagined the box to be one cubic inch in volume (say 1 inch by 1 inch by 1 inch), and you counted 10 particles in the box, or 10 grams in the box (an easy way to think of grams of mass is to think of a U.S. nickel. It has a mass of about 5 grams). Then we could say that the number density is 10 particles per cubic inch; or the matter density is 10 grams per cubic inch. Or, if we kept counting the contents of the box at different observation times, each time finding a different number - say 10, 13, 11, 15, 13, 11, 13, 10 - we could count up the total, 96, divide by the number of observations, 8, and get an average, 12, a statistic. We would say that the average density (number or mass) is 12 per cubic inch.
In the same way, we could get the average for the amount of momentum that is to be found in this local box. We get that average by adding up how much momentum each particle carries when we look at it. Then, similarly, we could find the average energy of motion in the box.
Remember that these three number measures represent the averages being carried, conserved, during all the much faster pair by pair collisions. So you may realize that this local intermediate level of measures that we have so established represents the local group conservations that are being carried on in the field. So it might seem that we haven't made much additional progress, except to have substituted one set of cumbersome computations of the pair by pair interactions for an even more cumbersome set of computations for a local group or globally for all groups of such computations. But, no, we have gotten a lot more.
Before we go on with the game, it is useful if we give those intermediate local measures names.
The first one we have already named. Corresponding to the conservation of number of particles or mass of particles we have the local measure of density. Corresponding to the conservation of momentum, we have the pressure. Pressure represents how much momentum per unit wall surface per unit of time that the particles in any extended region or box will deliver through any imagined wall space or by bouncing against any such imagined wall space; that is, we imagine the atomistic "balls" to be engaged in a handball game against any imagined wall. Cap off the flow through a hose or through a hole in a pressurized container or balloon, and you can feel or measure the pressure. It is the force per unit area of the hole that you had to exert to barely seal the hole off.
Corresponding to the conservation of motional energy of a pair of particles, we have the motional energy of the local group. Since it measures the energy associated with the specific volume, it is called the specific energy.
How can a person see that local energy? Well again there is an easy physical way. Put your finger into that field of atomisms, and feel its temperature with your finger (Watch out, don't burn yourself!). That is a measure of the energy that the atomistic things carry. Of course, if we want the true measure of the specific energy, then the temperature is not enough. The specific energy is contained in the measure of the motional energy every which way that the atomistic thing can move. The temperature is the common equal measure of that motional energy in any one way of moving, what we call one degree of easy freedom to move. We need to know how many degrees of easy freedom there are to move.
There are always at least three ways for a free body to move - forward-back, side-side, up-down. Any particle, however tiny if free, can move that way. But a fair sized ball can also spin three ways, which can add three more ways to move, and then there are ways of shaking or vibrating or rotating or associating internal parts.
The upshot of studying all those ways to move is to find that the specific energy can range from 3 to 12 times the measure of energy of motion that the temperature by itself might permit (if there were only one degree of motional freedom). If you really wanted to know how to get that measure, the idea is to see how fast a thermometer - which is a substitute for your finger, and also a known system whose degrees of motional freedom can be taken as a reference - moves toward the last few degrees of a final temperature. The measure you are trying to get is the so-called heat capacity; how much energy you have to put into a bunch of players to raise their temperature, say, 1° C. That measure tells you how many degrees of freedom that the energy could take, from 3 to 12. In any case, from such kind of detailed study, we find out and now know that our atomistic conservations, for a given ensemble of atomisms, can be represented by three local measures, density, pressure, and temperature.
These three local group averages for the three micro conservations are related in an invariant way. That relation is known as the equation of state of the group or ensemble. Come back to the little box or boxes in which we made the observations to determine the local averages. In every one of those freely connected and equally accessible boxes, the same equation of state exists. It no longer relates to only one box, but to all such boxes. There are many ball games going on throughout the whole field region. However the individual group measures may vary from place and time to place and time. More of that later when we have developed enough of a picture of what is going on.
First, why are these local conservation measures connected by an equation of state? Because, each time a new particle enters a box, it carries its number (or mass) count, its momentum count, and its energy count into the box. As long as these are the only conservational measures, then these three new fluctuations are connected just in the same way as the ones in the box already.
At this point, if you think very hard, you may begin to catch on to the game I am playing and either ask for your money back for this book, or tell me to hurry the story along. I can't afford to do either; the former for my sake, the latter for your sake. So bear with me. How are you going to really learn how to run a society successfully? Say that the game going on was not managing an ensemble of colliding atomisms, but running a team of competent baseball players. I think that you should begin to catch on that I'm not teaching you how to win the next ball game, but how to manage such a team or teams that you can stay in the competition.
So let me explain why that is a different ball game that I am playing. In what I am trying to teach you there are a lot of ball games going on. Each one is going on in its box, whatever is the name of the local team you identify with - the Yankees in Yankee Stadium, the Red Sox in Fenway Park, you name it. But you have to remember that all these ball games, ball teams, players, rules, managers are connected together in a league game, and that all the elements of play are loosely speaking comparably competent to continue the play. So the game I am trying to teach you is not how to win a next ball game but to manage with enough competence to stay in the play. The tricky and specific details you will learn soon enough, or you better soon learn by your own practice, or you won't remain in the league. There is no manager who can win all the time. The play of the game quickly transfers knowledge and players and managers all around. You don't win them all, or get a hit every time at bat, or put out a batter at every turn. There are statistics. Many young people, particularly boys and their older counterparts, from perhaps 8 years of age on up, can recite all the statistics. They know how many hits a player can average, how many games a pitcher can pitch and win, what the best play is in any situation. They are always second guessing the manager. But I am trying to teach you the foundation by which you can manage to stay in the game yourself and manage it. That, these outside observers do not know.
The "things" you are managing are known as "ball players". They are not just any old human thing. They are drawn from a special pool of people which you have to learn to recognize, acquire, and deal with, perhaps even train a little. They engage in a statistical mechanics-thermodynamics game, just as do the molecules in a gas or liquid, with the same physics specialized for each of their games. The application of the laws of physics, as performed by the players in each case, has to produce different statistical relations. For example, with ball players you need to select them and use them so that they average nearly one hit per five times at bat with perhaps one third of them capable of producing a hit per three times at bat. You have to have a pool of pitchers who can pitch enough strikeouts and not give up too many hits with their appropriate statistics, and you have to have fielders who do not make playing errors with more than a certain frequency of play. At this point I am leaving out the fiscal and monetary constraints under which you have to operate, but they are there. All the factors I have named are mechanical tasks performable in rather narrow limits only by certain kinds of people. One of the saddest tasks that I had to perform as a father was to inform my Number III daughter, when she was about 14 years old, the all-around playing pride of her team in a pony tail league, that her future in organized professional baseball play was dim and slim. "Try a personal sport, like golf or tennis", I said. (Parenthetically, she next elected shot-putting, later on juggling, only now tennis). And - oh, yes - the tasks that all these players perform are not only mechanical tasks like pitching and catching and hitting and fielding, but also thermodynamic field tasks or processes. That means that the players are converting mechanical energy of motion from one level of atomisms to another, for example for ball players to transform Wheaties to base hits and put outs, and to transform that ball play to the play of earned money, then from ball play on to a variety of internal emotions, such as elation, satisfaction, and anxiety. All these processes are involved in managing a ball team.
Well, I hope that this pep talk restored or revived your faith and eagerness to undertake such managerial study. If it didn't perhaps such study is not for you. So now back to lessons - Fur Elise before the Moonlight Sonata before the Emperor Concerto.
By the way, before we turn to the simplest Für Elise pieces in fluid mechanics-thermodynamics, let me at least indicate the kind of management problems you could have to face in such simple field phenomena as I've described so far, so that you will once again be able to grasp what you might be training for.
So now you see local connected averages in a simple flow field - of density, of pressure, of temperature or specific energy. In the latter case, if we have already selected a molecular player, say water molecules rather than oxygen, or hydrogen (or even just plain gin) molecules, we can deal with temperature. If we are going to mix up the molecular players, then we have to take into account their specific molecular properties, their specific heat, as well. That is a problem you always have to face if you are managing mixed players - say baseball players, golf players, and tennis players. Their actions are worth differently, work differently, and so forth. At this time we need to think simply so we will only think in terms of temperature.
Connected local averages means that if you elect two, the third is prescribed. What does that mean?
Take a closed empty rigid container. It has some particular volume (say 1 gallon, or 1 liter). Put a little amount of water in that container.
(This is not as easy as it sounds. The easiest way that it can be done without laboratory equipment is to take a bottle, which will have air in it, put water in the bottle and begin to heat the bottle until the water boils out, for example, using a double boiler. If you put a flap on top of the bottle, perhaps hinging a cork as a cover, the water will boil out as steam with no air returning. When you have boiled all the water out until only steam remains or whatever amount of water you want to leave in the bottle, then you can seal it with a cork or stopper. Now let the water cool off, and you have succeeded in the proposed task. Other ways might require a very good vacuum pump, a completely collapsible balloon later jammed into a box, a carefully constructed piston and cylinder, or heat and a system of valves).
The amount of water (as liquid water or steam) that you put into or left in the container determines the density of water in that container. Namely, if you divide the measure of the mass of water in the container by the volume of the container, that measure gives you the average density of water in the container. That is how you managed to fix the density.
Now you can manage to fix the temperature. How? You put the closed off container in an oven or a refrigerator, which is adjusted to the temperature that you want the water to have. That fixes the temperature.
Lo and behold, what you cannot manage to fix is the pressure in the container. That becomes fixed by the fact (a) that you filled it with a specific number or mass of water molecules, the "things" you chose to manage, and (b) that you fixed the temperature. That fixes the pressure. Choice of water, density (mass or number per volume), temperature (motional energy measure, in this case for water) fixed pressure. That is the meaning of the equation of state for water. Change the molecules and you would have another equation of state for those other molecules (The change in the equation of state would depend on properties of the molecule). By the way, I'll remind you again, you can determine the pressure in the container by measuring how much force is required to hold the lid sealed.
Let's manage the contents of that bottle a little. For example, suppose we first made certain that the walls of the container were all held at the same temperature. How? By putting the container in a totally temperature regulated bath, a refrigerator or oven, a surround of gas or liquid (or even sand). After a certain amount of time, the internal temperature in the water will all be the same as the wall temperature.
But now we find a surprise. At high temperature, we find that all the water is evaporated and the contents are only steam vapor. Also we find that as the temperature is raised further, the pressure is raised.
At sufficiently lowered temperature, we find a value at which steam starts to condense to droplets of water. The lower the temperature, the larger the pool of liquids droplets we find. Then - another surprise - we reach a temperature at which the droplets or pools of water freeze into a solid, water ice. There still is a "steam" vapor, but its vapor pressure has been diminishing all the way with temperature (How do I know? Put in a surface much colder that the container temperature, and you will see that "steam" or vapor condensing. You see such a process almost every morning as the dew on the ground or grass, which evaporates as soon as the surface warms up).
Thus we should appreciate that the equation of state for water or any other pure atomic or molecular substance can be rather complicated. Not only does the state of pressure, temperature, and density change, but also the phase of matter - gas, liquid, solid or combinations of these phases - can change with the state measures. We can manage to make pressure, temperature, and density do a considerable versatile variety of things. (As a very simple example: we used to put a piece of ice in a box, and even though the ice melted, it would keep the inside of the box cool, for example, near 32 ° F. For those who have forgotten, that was known as an ice box. Or you can put on a wet shirt on a hot day. As the water evaporates, it will cool you off. If you don't want to wet your whole body, just wet and shake your finger).
To exemplify a little more versatility than we have so far shown for the equation of state, let us suppose that we raised the temperature of the water vapor to extremely high values. We would find that we could reach temperatures that would destroy the molecules. The high motional energy of the molecules banging into each other at high temperature would crack them apart, achieving a chemical reaction. The water molecules would change their chemical state and separate into oxygen and hydrogen (Or you can burn the eggs you are frying). Or, we could add other ingredients to the water and cause it also to enter into other chemical reactions. So we see another aspect of an equation of state, the possibility for many chemical changes in state (chemistry, I will repeat many times after this, is the making, breaking and exchanging of bonds between atomistic components; this will remain true even when we deal with societies).
But let us now get to a more dynamic game, one worthy of calling fluid dynamics (hydrodynamics, using the Greek stem for watery or fluid matter). What we want to do is to take the changeable equation of state, changeable from time and place to time and place, and manage it to do things in time and place. Let us first do the simplest thing. In the surface of a closed rigid container, prick a small hole. The rest of the container wall maintains its temperature and pressure. The pressure falls over the hole. What happens? There is a flow of momentum out of the hole. In time the content of the container loses its contained momentum; that is, its pressure falls. Its temperature doesn't have to fall. We could continue to keep the walls warm.
In any case, what this simple example demonstrates is that by changing the equation of state measures between different regions of a matter field, it is possible to create flow fields, for example, flows of momentum, flows of energy, flows of density.
The description of these flows are represented by equations of change. There are as many equations of change as there are conservations. So in a simple flow field, we see three local conservations, three equations of change, one globally (throughout the field) for each local pair by pair conservation. Namely, there is a flow of mass or number, a flow of momentum, and a flow of energy. The description of these processes is very complex, and I will not try to develop the line of thought very much, just enough to give you a sense of how the keyboard squeaks. It has to have the competence to deal with all the problems I named before, but I won't touch them. Suffice it to say that depending on the atomistic material and its temperature or pressure range, there are measures, transport measures, that tell one something about the rules of flow. For example there is a measure for how fast one kind of atomism may move among other kinds. That is known as the mass species diffusivity (each type or species of atomism can have a different measure). There is a measure for how fast momentum will flow. That is known as the momentum diffusivity. The more common name is the viscosity of the fluid substance. (Water, because of its great fluidity, low viscosity, relaxes quickly, diffuses its momentum slowly; tar, because of its small fluidity, great viscosity, relaxes slowly, diffuses its momentum quickly). There is a measure for how fast energy will flow. That is known as the energy diffusivity. Its common name is the thermal conductivity. That tells you something about how fast you will say ouch when you touch a hot surface. Note that all these transport measures are known as diffusivities. A diffusion is the process of spreading out or scattering.
Let us now illustrate how to manage these processes independently. I think that by now you have the idea that management is a process that you do outside of the atomisms. So first let us manage a flow itself, which as you know already is a flow or diffusion of momentum.
Take a large container and pump it up with pressure. You understand that program now. Suppose, first, that you keep the temperature of the container constant, or nearly so. How? Leave it stand in the outside environment (or change that environment if you want to. Put the container in a refrigerator or oven). Push a little amount of material into the container. For example, you can blow small amounts of air in, breath by breath. Or you can push small amount of water in. How? Use a pump or pour it in by using the gravitational force.
As you push material in, gas or liquid, you finally begin to see the pressure rising. But I want you to think of a very large container. So it takes a long time to get the container or reservoir filled and the pressure up high. But finally it's there.
Now someplace in the reservoir, say near its bottom, make a hole, perhaps plug in a pipe, add a valve, so that you have a hole that you can open and close. Here, then, you will see how the pressure in the reservoir creates a flow or diffusion of momentum from the hole, pipe, or valve. You can manage it now.
Is this real and practical? Of course. It is the way your city, or your house, or your farm supplies water to every valve or faucet connected to its large reservoir. You don't win or lose the game (of managing such a flow supply), you just succeed in doing it.
Let's manage the flow another way, through temperature. This time fill up the reservoir, but don't pump its pressure up high. For example, with liquid water in the container, put the hole on top. Now heat the container so as to raise its wall temperature. Recall that with temperature rising in the equation of state, the pressure rises. After a while the water is converted to steam and its pressure then creates a flow of momentum. That is, through manipulating the energy (via temperature), we used the equation of state to transform that measure into pressure and then the pressure into a flow or diffusion of momentum.
Is this practical? Of course, it's the basis for the steam engine, also called the external combustion engine, because the driving heat came from outside and was applied to the container walls. Such a container is known as a "boiler". You likely have one in your house. It may be used in a combined fashion, partly used as a reservoir of pressure and partly as a reservoir for heat energy, to give you hot water or steam flow.
This suggests a third way to create a flow or diffusion of momentum. This is by a process of chemical conversion.
This time insert a mix of two substances, say liquid gasoline and air, or a fuel gas and air. With a starting or igniting hot spot (high temperature) produced somewhere in the mix, these two different sorts of molecules may undergo a chemical process. Chemistry is the making, breaking, or exchanging and joining of bonds among atoms and molecules of all sorts. In the case of a simple fuel and oxygen, the chemical process is one of breaking and exchanging fractions of each type of molecule. But that process gives off heat energy, and that heats up the old and new molecules. Then, as before, that raises the temperature of the materials. That raised temperature raises the pressure, because the density was fixed, and that creates a flow.
Is this practical? Yes, it is what happens in each cylinder of an automobile engine many times per second. A small amount of fuel and air is injected, pumped, into the cylinder. It is sparked electrically to start a combusion. The fuel and air "explode", producing high temperature and pressure. That pushes the little cylinder container into a larger volume configuration via a piston-like motion. That spins the crankshaft and wheels around. After each such explosion, the flow products are exhausted (you can see it go out the tail pipe). Why? Because you're not interested in this case in the flow, only getting rid of the flow after it has done what you wanted it to do, which was to turn the wheels. That management is known as an internal rather than an external combustion engine, because the management took place among the players. (By the way, if you have a car with a Diesel engine, then it doesn't use a heating spark to ignite the fuel. It just compresses the mixture enough which then explodes chemically).
We will add two more ways to make a flow of momentum. In one, we have a series of blades mounted on a shaft, at an angle to the shaft. Now, if you turn the shaft (a mechanical motion), those blades will "grab" the air and force it into motion. Why? Because that is known as a flow boundary condition. If I move a sheet of atoms or molecules past other sheets, because of some dynamic transport property of matter, in this case the momentum diffusivity or viscosity, the one sheet will drag the other sheet. Note, to make this work fairly well, the sheet of molecules I used for the drive was the surface of a solid, so that they remained united and stuck together. The molecules of the fluid that I dragged the solid sheet past could not oppose that motion too strenuously, so they had to move. That created a flow or diffusion of momentum also.
Is that practical? Of course, those blades may be a propeller or turbine in an airplane or a ship and they create the flow stream that makes those craft move. Here the momentum transfer was rather direct. When an entire ensemble of players are forced into motion directly, shepherded, that is known as convection rather than diffusion.
For a final example, I will use one that appears to be made more indirect. It's a little more subtle.
I take two containers. I join them on a common smooth face, say by butting them together. I fill each container with a different molecular substance, say one oxygen, the other nitrogen, one water and the other oil, or any pairing you wish to choose. I arrange to have the same pressure in both containers, as weak or strong as you want. (How? I might open holes in both containers, suspend a weighted and tapered piston in each hole, and keep filling both containers till the same weight in each piston "floats". You see this example in a pressure cooker. The weight of the float, for a given area of vent hole, determines the "pressure" of which the float rises and vents material). I also arrange the same temperature bath on both sides.
Now make and open a hole or a pipe between the two containers. You have the same pressure and temperature on both sides, so you might think nothing will change. But it will. Substance 1 will diffuse into substance 2, and vice versa. Because of the difference of materials, there will be a matter or mass diffusion, which thus creates a momentum diffusion of each substance separately.
Is this real? Certainly. Everytime you put milk or cream, or sugar, in your coffee, you see the process taking place without stirring. How do you think the water that rained on earth got back into the atmosphere? Largely by that evaporative, diffusion, process.
So now you see, there is an equation of state involving the relation among atomistic conservations. There are equations of change which you can manipulate from "outside" (at the walls) or "inside" (as a player) to manage and influence the play in space or time throughout the field. You can transform any one of the conservations, stationary (static) or changing (dynamic), into any of the other conservations, in a different static or dynamic form. Wow! That's the game of flow or field physics.
Now I could proceed to teach you that game in all of its mystifying and elegant details, but that is not what I contracted to do. So I am cutting the physics of simple flow fields short. You did not get to play the game very much.
I will give you a metaphor. My four daughters took music lessons at the Cleveland Institute of Music, three on the piano. The musical director of the piano department was Arthur Loesser, Frank Loesser's brother; and the Cleveland Institute and a competing sister school, the Music Settlement took turns with whose violin department heads were the concert master of the Cleveland Orchestra, or which of its other teachers played what instruments in that marvellous orchestra. (The heads of the Cleveland Institute, as I remember them, were Ernest Bloch, Beryl Rubinstein, Ciompi, and Victor Babin). Of course I am name dropping. But I don't have to tell you with what level of pride and desire for achievement and agony parents and children felt with such association and opportunity to have one's house filled with music and practice drawn from these associations. I would love to get you to feel about science with the same enthusiasm.
So my piano-playing daughters progressed through a standard repertory of play. You started with Diller-Quayle, Book 1, with one of the first pieces a simple duet form of the Valse Nobles (et Sentimentale) of Brahm's, with papa or momma playing the duet form with one finger as a practice substitute for the teacher at lesson time. Dum di dum dum, dum di dum dum, dum di dum dum, di-di-dah; dum di dum dum, dum di dum dum, dum di dum dum, et cetera (You can scan it in three-quarters time).
Now after proceeding through a standard repertoire, one ultimately might settle on playing two handed music, or choose ultimately four hand music. You can understand the latter choice better, when I tell you that the head of the Institute and of the piano department later became the couple, Vronsky and Babin. And if you chose, ultimately, to learn four handed piano from them, why then likely you might again return to those same Valse Nobles that you started from, but in concert form.
I am not going to teach you four handed piano playing. Whatever I have given you has to be enough, or you can pursue lessons elsewhere. Now, regardless of what exercises we introduced so far, we now have to turn to orchestral piano music! We go on to a different instrumental application of physics, physics for complex systems, which we will pass through like a blitz, so that we can get to the physics for complex living social human systems. So do not tell anyone that you studied much four handed piano playing (even though you had one lesson).
Review. What was presented so far was easy to read, easy to review. To help bind it in your mind, we will give it to you once again, more formal, more didactic, also more compact yet precise.