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The Trickle-Down Theory of Engineering

Although engineers are among the most valuable members of society, they are seldom recognized by the public. When, eight years ago, we asked random members of the public to name a famous engineer, the only name most could come up with was Scotty, chief engineer of the Enterprise. Eight years later, some can also name Dilbert, but it is not clear that this is a change for the better.

The public does not have a very high opinion of engineers. For example, they are generally considered less intelligent than scientists. Would anyone hesitate if asked whether Scotty is smarter than Science Officer Spock?

One of the reasons for these perceptions is that the nature of engineering is widely misunderstood, even by engineers. For example, if you ask the person in the street what engineering is, you will most likely get some confused, inarticulate answer, such as

``It is the systematic application of scientific knowledge to the betterment of the human condition''

Things haven't always been this way. If you think back about 250 years, we find Dean Swift's Gulliver's travels; in his third journey, Gulliver travels to the flying island of Laputa, which is inhabited by scientists. And these scientists are figures of fun -- they are depicted as engaged in projects to extract sunlight from cucumbers, train spiders to spin cloth, and so on. In the next two centuries, the industrial revolution took place -- but its heroes were engineers, not scientists, and the names we remember from that period are the names of engineers -- Watt, Stevenson, Treviathan. Even if we look at the fiction of that age, its heroes are engineers. H.G. Wells's hero in `Food of the Gods' is an engineer, Jules Verne's Captain Nemo takes pride in pointing out that the Nautilus draws on no new science, only the engineering application of what is already known. Then, in 1945, the scientists did something that got everyone's attention.

In 1945 it became clear that science could do something really useful: it could win wars. From now on, any nation that neglects its scientists can expect defeat, sooner or later, at the hands of more scientific nations. Scientists therefore take on a radically new importance. Wehrner von Braun, brought over from Nazi Germany to begin the United States space program, advised his subordinates, ``Don't call yourselves engineers; say you're scientists and they'll give you anything you want."

Well, is this true? Are engineers condemned to stand around, helpless and idle, until scientists reveal the truth to them? Or is there a distinctive brand of engineering knowledge, separate and independent from scientific knowledge? Are there laws of engineering, over and beyond the laws of science?

To answer this, let's look at the structure of science. I suggest that the defining goal of science is to develop a protocol for obtaining agreement between different points of view. A naive view of the world tends to be self-centered. Communication between individuals is hampered because each sees the universe from a particular point of view, centered on that individual. A simple example has occurred several times in this lecture; if I face you and give instructions in terms of left and right, there's the risk I won't be understood, since these words are relative to our orientations, and thus mean different things to each of us. I could avoid this by giving directions in terms of `north' and `south', since this is a frame of reference that is the same for each of us.

So we make progress by adopting a terminology that is neutral with respect to the direction we're facing. At each step in this progress, we give up some of what's personal in our description; this can be an inconvenience -- I can identify my left hand immediately, but I have to think a minute to find my north hand -- but it increases the audience who can understand me. Two scientists who appear to hold different viewpoints can resolve their disagreement because science offers a common language in which the two views can be compared. This language may show that one of the two views can be transformed into the other, or it may suggest an experiment which will show one description is right and the other wrong. So the ultimate aim of science is to develop what philosopher Thomas Nagel called `the view from nowhere'; that is, a description of the universe from no particular point of view. Sigmund Freud observed that each great revolution in science has involved a blow to human vanity; the Copernican revolution was one such blow, when we discovered that the earth was not the centre of the universe. In return for this blow to our vanity we obtain a description that could be recognised by intelligent life from Sirius, as well as ourselves. The Darwininan theory of evolution was another, when we discovered that we were one species among several million. (Freud modestly included his own discovery of psychoanalysis as a third great revolution, but not everyone would agree with him.)

Thus, there should be only one set of ultimate scientific laws; if the project of science is well-founded, any intelligent observer anywhere in the universe will come to the same set of laws -- whether the observer lives on a planet of Sirius or in Surrey.

If science achieves this aim, the structure of scientific knowledge will look something like this: [Inverted-tree diagram, showing all knowledge as deducible from a small set of axioms]

At the highest level is the grand unified theory, from which everything else can be mathematically deduced. As we go down the tree, the conclusions we deduce become more and more specific, and apply to smaller and smaller regions. For example, at this level we deduce that quarks and leptons exist; one level lower down, we deduce the existence of the nucleons -- protons and neutrons, formed by the combination of quarks. Lower down still, we deduce that stars exist.

The tree is formed by deduction. We don't know whether anything more is required -- given the ultimate laws of physics, is this the only universe that is possible, or are there accidental, contingent facts that determine that we live in this universe, rather than a very different universe describable by the same laws? For example, the laws of physics appear to be symmetric with respect to matter and antimatter, yet the universe we observe seems to consist mostly of matter. Is this a necessary consequence of laws we don't yet know, or is it an accident of history, a random event which could have turned out either way?

If there are any random events, then some of the points at which the tree branches correspond to the different possible outcomes of these events. If there aren't, if the universe is totally determined by the fundamental laws, then all the branch points correspond to choosing particular locations in space and time. For example, this branching point might correspond to whether we choose to look at the universe in its first 100,000 years or in its more mature state. On the mature branch, and all points below it, atoms exist. On the younger branch, the universe is too hot for atoms to form, and only charged particles are present.

This tree of knowledge fills the universe; facts about the interior of neutron stars are here, facts about life in Surrey are here. So it would appear that there is simply no room for laws of engineering; if these laws are true, then they must already be included in the tree; if they're false, then they aren't laws at all.

But in fact, there are many true statements that are not included here. For example, everyone in this room is over a metre tall. This is not a necesary or a universal truth, but it is true, though it can't be deduced from the tree. It's a generalization, true over the population we're currently interested in. There could be other generalizations -- statements true here, here and here, say, but not elsewhere -- that are of interest to us because these locations correspond to the parts of the universe and the period in history that we live in. Here's an example of such a generalization: ``Big machines are more efficient than small machines". This is true for many cases, though there isn't a single physical principle it can be deduced from. Consider a blast furnace; if we increase the linear scale by 10 times, we increase the volume of steel that can be processed 1000 times, but we only increase the heat losses 100 times.

Consider a diesel engine -- leakage around the piston is a linear phenomenon, whereas the total force on the piston crown is a square phenomenon.

Consider a fusion reactor. Neutrons escape at the boundaries. If we scale up 10 times, we increase the power output 1000 times, but only increase the necessary amount of shielding 100 times.

So it happens that three different physical laws -- fluid flow, heat transfer and nuclear radiation -- all yield the same conclusion. But the conclusion can't be deduced from physics. Indeed, the very idea of efficiency has no place in physics. It makes no sense, for example, to ask ``What is the efficiency of the Sun?'' Considerations of efficiency only arise when we're exchanging one thing we value for another thing we value, and are concerned to get a good rate of exchange.

Note also that this law -- large machines are more efficient than small machines -- would be false at an earlier stage in history. A large flint axe is no more efficient than a small one. And in the future, too, this law may either be false or of no interest; a big computer is no more efficient than a small computer.

So engineering laws are local; they are useful in a particular society at a particular stage in history.

Let me give you another example of an engineering law, one that is used every day by the engineers who design for mass production. You have an invention that you want to manufacture. You go to a production engineer and ask what it will cost to make a hundred of them; the production engineer asks for detailed drawings and considers several different manufacturing methods; a week or two later you get an answer, correct to within 20%. Now you ask what it will cost to make a million of them. The production engineer takes your invention, weighs it, and immediately gives you an answer correct to within 5%. He's using a very powerful law: for a long production run, the cost of the research, development, design and the manufacturing equipment is insignificant compared with the cost of the materials that go into the product. A car engine, for example, costs a few hundred dollars to produce, chiefly representing the cost of the iron or aluminium it's made of. I once worked at General Motors, and needed to have a single engine built -- nothing fancy, just an iron engine of novel design. It cost a quarter of a million dollars.

This law, too, is tied to this period in history. It is becoming less useful at this moment: the rise of flexible manufacturing techniques is making it possible to produce short production runs of customized products almost as cheaply as long runs of a standard item.

One more law, which I call Gelbart's law, after Dan Gelbart of Creo: ``No measurement has more than six significant figures (and the sixth is very expensive.)" This is true for almost all physical quantities, except time. The value of the number in Gelbart's law changes from one period in history to another; last century it may have been five, and a century before that, four. We'll see what important consequences this law has when we come to discuss chaos in Lecture 14.

A fourth law: it's easier to do the same thing a thousand times than to do one thousand different things. This law comes up in many places. One of the first such places was the Venice Arsenal in the fourteenth century -- this is the first time we hear of standardised parts. The same idea comes up at the beginning of the nineteenth century in America, where Eli Whitney used the idea of interchangeable parts to simplify and accelerate the production of muskets for the US army. The same idea can be applied to the organization of human labour, as in Adam Smith's observation of a pin factory. We can see analogous ideas -- standardization of a small number of designs and repeated use of these designs -- in the containerisation of freight in the 1950's and 60's, the rise of franchise operations such as Macdonald's restaurants, and the re-useability of object-oriented computer codes of the Seventies and Eighties.

A fifth law is Moore's Law: the number of circuit elements that will fit into a given area doubles every two years. This has held true since the early sixties, and is expected to continue true for another ten or fifteen years. One of its corollaries is that the speed of the fastest circuits, in MIPS, can be calculated from the formula

MIPS = 2^{(YEAR - 1984)}

Moore's law is not eternal -- a hundred years ago it would not just have been false, but incomprehensible, and we expect it to break down within the next twenty years. Nevertheless, it's been true throughout the careers of most contemporary engineers, and it's had a greater effect on our society than, for example, the law of general relativity.

These laws are generalizations across leaf nodes, generalizations that happen to be true because those are the nodes we inhabit at this period in history. There are other laws, engineering laws, which arise because the tree is partially obscured by clouds, clouds of different types. [Illustration of hydraulic engineers working on a harbour model]. This is a large model of tidal flows in Chesapeake Bay. The engineers in this picture are designing it using a method that could have been used by Archimedes, two and a half millenia ago. Thousands of years of subsequent scientific progress hasn't touched them. And yet the relevant laws of physics are known. Here are the laws, the Navier-Stokes equations. The solution to these equations would describe exactly how the water flows. Unfortunately, they're too difficult to solve for most cases of interest. So the best route for an engineer is to forget they exist, and use engineering methods. Exactly what those methods are, I'll discuss in greater detail next time. This is one type of cloud that covers the tree, the clouds of incomputability.

A second kind of cloud. I'll refer to this briefly, since we'll be exploring it in greater detail later in the semester. This is the cloud of chaos. This arises when we have the equations; we can solve the equations; and yet the solution is completely useless to us. How can this happen? In the field of weather prediction, for example, we can solve the equations predicting how a weather system will develop. We start with the conditions describing today, and calculate forward to tomorrow. Now, if we change our description of today's conditions in the fifth decimal place, tomorrow changes from sun to a snowstorm. and yet, we can't measure today's conditions to better than the third decimal place, and will never be able to. Yet there seems to be an engineering of weather prediction

Let's look at another region of the tree, one of the triumphs of twentieth century science, the field of quantum physics. This field contains the laws that govern the bonding together of atoms to form solids, among other things. Let us suppose we are civil engineers, designing a steel bridge. Clearly, it would be useful to know the strength of steel. So we turn to the relevant area of quantum physics, Schrodinger's equation. This can be used to predict the strength of the bond between atoms. Unfortunately, it can only be solved exactly for one case, the hydrogen atom. So engineers relying on it would have a very restricted choice of materials. We can bypass that cloud of incomputability, though, and turn to chemistry for a measured value of the iron-iron bond. Chemistry provides this value. Using it, we calculate the strength of structural steel - and obtain a value about ten times higher than we would measure for any steel we can buy. The real strength of steel depends on details of its method of manufacture and machining -- contingent details, details that depend on the current technologies in use in Pittsburgh and Japan. This tree does not and cannot show those details, because they are details about ourselves -- and we said at the beginning that the picture of the universe science strives for is one from which all traces of ourselves have been eliminated. So this is a third kind of cloud covering the tree, the cloud of contingency.

Let's stay with the last point, the engineer's need for knowledge about ourselves. If we had to name the single most successful piece of engineering design in the past two decades, I think I would name the Mac `desktop' interface for personal computers. This provided Mac with a competitive advantage that lasted ten years; Windows 95 is now about where the Mac interface was in 1985. (Though ironically enough, the interface was first developed by Xerox, in their Palo Alto research centre; rather than marketing it, they kept it in their labs to demonstrate to visitors. One of those visitors happened to be Steve Jobs.) Designing the Mac interface had almost nothing to do with physics, or even computing science; it had a lot to do with understanding human beings and how they think and work.

To sum up: I hope I have shown that engineers need a large body of expertise, separate from and independent of the sciences. This knowledge is contingent, rather than necessary; it is located in a particular culture and a particular period in history; it is approximate rather than exact, useful rather than true. If this is so, why is the trickledown theory so widely believed? One reason is our educational system. Universities have a marked preference for formal knowledge. It's so much more convenient to set an assignment or exam that involves solving a set of equations to get a single unequivocal answer. And the requirement that academics publish regularly in scholarly journals encourages a physics-type career of deep, concentrated research on a single area.

But engineering education has two roots. One is the academic tradition, and it is within this tradition that we expect to find the sciences we need. The second root is the tradition of apprenticeship. Engineering consists of a web of skills. Our culture tempts us to arrange those in a hierarchy; formal intellectual skills at the top, mere ingenuity lower down, and physical dexterity lowest of all. There is a temptation for us to concentrate on the formal intellectual skills, and leave those lower down to chance, or to second-class institutions. But if we were to do this, we would indeed be giving you an impoverished education, foredooming you to end up on welfare or in graduate school. Rather, we should strive to create an environment which offers opportunities for each student to discover and pursue those aspects of engineering at which he or she will excel. There are many kinds of engineer, and I am not going to say that the inspired tinkerer ranks below the theoretician.

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