Paul Penfield, Jr., God, the Scientist, God and Computers Lecture Series, MIT Artificial Intelligence Laboratory and Boston Theological Institute; Cambridge, MA; October 1, 1997.

God, the Scientist

Paul Penfield, Jr.


The concept of God is often invoked to explain phenomena. If the phenomenon is one that has a scientific explanation, then it is possible to compare the scientific merits of the two explanations, one based on science and the other or God or, more generally, on faith.

The nature of what constitutes a good scientific theory is not universally understood. As a result, sometimes reasoning based on faith is seriously promoted as scientific. Scientists tend to judge scientific theories on their accuracy, simplicity, and suggestiveness. Any faith-based theory that is represented as scientific should be subjected to those three criteria. We will illustrate this point with some very simple, perhaps trivial, examples.

Not all phenomena can be successfully explained by science. In some cases a scientific explanation is possible but not yet available. In others, such explanations will never exist. In still others, people will have different opinions as to whether and when such explanations will be developed.

In cases where science does not (yet) have a needed answer, what are we to do? We scientists use scientific theories as long as they seem to do the job. In the same spirit, we can use arguments based on faith so long as they seem to work, and as long as we keep in mind the assumptions made.

Without this kind of approach we would be severely limited in what we could do. Much of the work of many professions, including engineering, deals with human nature, for which we have no scientific theories. In addition, science itself rests on assumptions about nature and the rational thought process that are not, in the final analysis, provable. Finally, we scientists are ourselves humans, and so our activities "off the job" require dealing with matters for which no scientific theory will work.

God, the Scientist

Paul Penfield, Jr.


I am honored to be invited to give the first lecture in this series on God and Computers, being held in conjunction with the MIT EECS course of the same name taught this Fall by Anne Foerst. I will try to say a few things about the effectiveness with which God is invoked as a way of explaining things.

First, a disclaimer. I am not educated in philosophy or religion, I really know nothing about God, and have no particular religious training. I regard myself more as a scientist than a devout person, although I am active in a mainline Protestant Christian church in the town where I live, and I come from a family in which my grandfather and uncle were both Presbyterian ministers, and one of my cousins is a UCC minister. Their love of God and things religious never did rub off on me as much as it did on others in my family.

One thing that did rub off on me, however, was my family's love of good times and of singing. Picture me, if you can, at the age of ten with my family sitting around a camp fire after dinner. Someone breaks out a guitar and we all sing along, the songs we love. One old favorite that was sure to be sung, often with much amateur harmonizing, is called "Tell Me Why,"

 Tell me why the stars do shine,
 Tell me why the ivy twines,
 Tell me why the sky's so blue,
 And I will tell you, just why I love you.
    audio (39 seconds; 859K)

Good questions. Why do the stars shine? Why is the sky blue? One answer is contained in the second verse of the song,

 Because God made the stars to shine,
 Because God made the ivy twine,
 Because God made the sky so blue,
 Because God made you, that's why I love you.
    audio (46 seconds; 1020K)

This is what might be considered the romantic answer. It appealed to my teenaged sisters at that time, and perhaps it still does to their grandchildren. However, the small boys in the family sometimes came back with an alternate verse which might be considered the smart-aleck answer to these same questions,

 Nuclear fusion makes stars to shine,
 Adhesive tendrils make ivy twine,
 Rayleigh diffraction makes skies so blue,
 Chemical hormones, that's why I love you.
    audio (40 seconds; 878K)

Whatever you may think of the way this verse destroys the peaceful camp-fire mood, at least it does offer answers to these questions, based on science rather than on God. Why do stars shine? Is it because of nuclear fusion, as astrophysicists and smart-aleck little boys would tell you, or is it because God made them to shine? Or might both explanations be valid, and perhaps useful in different circumstances?

This is a small example, perhaps a trivial one, of our tendency to invoke God to explain what we humans may not understand. We are appealing to God, the Scientist.

Scientific Theories

So is God a good scientist? How would the answer "because God made the ivy twine" rate as a scientific explanation?

In science, explanations are provided by theories. I will have to say a few things about how scientists go about distinguishing good theories from bad, because many nonscientists may not appreciate what a scientific theory really is. For example, they might ask, "do you believe Einstein's theory of relativity," or "are Newton's Laws true?" To a scientist, these questions are not really appropriate. Let me explain.

To a scientist, a theory is really nothing more than a working hypothesis, one that is consistent with available evidence. A scientist may use a theory and compare its predictions with observations, but the concept of believing a theory, the way a religious person may believe in God, is not necessary. A scientist or engineer might have an opinion about how useful or how accurate a theory is, but a theory, after all, is just a tool. If it works, fine; if not, find a better tool. A hammer is a tool. You don't believe in a hammer, you use it when you think it will do the job.

Another common misconception is that a scientific theory is either true or false, and that a single experiment can invalidate a theory. However, a scientist would only say whether a theory is accurate enough; it is not a matter of it being right or wrong. For example, Newton's laws of motion, as usually formulated, fail for motion at very high speed because of effects of special relativity. This does not mean Newton's laws are wrong, it merely means they are only approximate, and have a limited domain over which they should be used. All theories and laws in science are approximate; the important question to a scientist is whether the approximation is good enough for the purpose at hand.

Now don't get me wrong. I am not saying that all scientific theories are equally good. Some are good, but some are bad. Scientists and engineers do judge theories, and the scientific community will reject bad ones by simply not using them.

There is another point. Nonscientists may not appreciate that there can be more than one theory for a scientist or engineer to choose from. There is sort of a free-enterprise competition among theories, and those that are used are those deemed most useful. For example, in mechanics, a scientist would have at least three different theories for calculating the motion of a particle under the influence of a force:

Newton's Second Law
Einstein's Theory of
Special Relativity
Einstein's Theory of
General Relativity

Now think for a moment about the camp-fire song. There seem to be two proposed theories about why the sky is blue. This is not unlike the case of mechanics. A scientist faced with the need to explain the color of the sky would be able to choose from two theories, just as another scientist calculating the motion of a particle might choose from among three theories of mechanics.

So how does a scientist tell a good theory from a bad one? I assert that a good theory is one that is:

  1. Accurate
  2. Simple
  3. Suggestive

Accurate. A good theory should allow any scientist to predict the results of experiments not yet performed, or observations not yet made, with a reasonable degree of accuracy, over a reasonable range of conditions. The larger its range of validity, and the more accurate the predictions, the better. For example, since Einstein's general relativity can describe systems undergoing acceleration, it has a wider range of validity than special relativity.

One aspect of accuracy is the ability of a good theory to work from first principles, without the need for ad hoc assumptions, or the need to estimate missing parameters. This feature of completeness, while desirable, is not at all common; many scientific theories involve parameters, such as the gravitational constant, which have to be found from experiments.

Simple. A good theory should be based on simpler concepts. It should be easy to use, easy to teach, and easy to explain to others. It should not require extensive computation. By this measure the theory of general relativity gets a low score because it uses complicated curvilinear coordinates, so it would often not be the theory of choice.

Suggestive. A good theory should lead a perceptive scientist to think of interesting new experiments, extensions to the theory, connections to other theories, or explanations of other phenomena. For example, the theory of general relativity suggested the existence of gravity waves, and the theory of special relativity suggested the equivalence of mass and energy.

Are Theories Based on God Good Science?

In this context, let's go back to the camp-fire song as ask how God the Scientist is doing. The theory "because God made the sky so blue" gets low marks on accuracy. Some skies are blue but others are not -- this theory does not account for clouds, or for observations made in outer space. On the other hand Rayleigh diffraction, which is the tendency of blue light to bend more than red light as sunlight passes through the atmosphere, provides a more accurate explanation. It does not, for example, make the mistake of predicting that the sky is blue at night.

In terms of simplicity, God the Scientist does not do too well either. It is true that the statement "God made the sky so blue" is very simple. However, this theory is not based on simple concepts. It seems that God made certain choices. For example, why didn't God make the sky to be green? Either the color of the sky is an arbitrary choice made by God, or it is related to some property of God, or it is an unpredicted parameter of the theory. Any way, God the Scientist is in trouble. If God has some property that sets the sky color, it must be one of thousands of such properties. Any model of God with so many ad hoc properties must be extremely complex. Alternatively, if the sky color is an unpredicted parameter, the theory fails to explain anything.

As for suggestiveness, Rayleigh diffraction is a good explanation. It not only explains why the sky is blue, it also explains why a sunset is red. On the other hand, invoking God in this context is not really explaining anything at all; it is just a way of closing off discussion, or of saying the explanation is so arcane that it is not worthwhile. This is the opposite of opening up interesting new questions.

It seems that God, the Scientist, did not fare too well in explaining why the sky is blue. Of course, in God's defense, it must be said that the camp-fire song really has nothing to do with science, and the romantic mood is in fact enhanced well by using God to avoid the scientific explanations. And besides, aren't we really stretching a point too far? Surely nobody would ever seriously try to use God to explain why the stars do shine.

Or would they?

Examples of Deeper Questions

The camp-fire song asks relatively simple, perhaps trivial, questions. But there are other, deeper questions, that science has not yet solved, and God is often called upon to explain. Let me mention three of these.

  1. How was the world (or, thinking more globally, the universe) created?
  2. What is life?
  3. What is cognition?

Creation. Although physicists have some pretty good theories about the big bang, there is still only speculation about what was there before. There are many religious myths about the creation. In my own Judeo-Christian tradition, we learn in Genesis that God created the world in six days. Christian fundamentalists accept literally, as a matter of faith, this biblical explanation; many of them will even tell you when it happened -- within the past 10,000 years. They might also quote Genesis 1:16,

And God made two great lights; the greater light to rule the day, and the lesser light to rule the night; he made the stars also.

(By the way, what were we just saying about nobody ever seriously using God to explain why the stars do shine?)

Life. Biologists are now beginning to understand the physical and chemical processes that go on in biological systems. Gradually the theory of evolution is being fleshed out with more details, and experimental evidence is accumulating. For example, recently there was a report [1] of very rapid adaptation of a species of lizard on Caribbean islands. It seems that within fifteen years after introduction to islands that had smaller branches for these lizards to perch on, they were found to have slightly shorter legs. This effect had been predicted before the experiment. It is not yet clear whether the adaptation was genetic.

Fundamentalists scoff at evolution, saying that it is "only a theory." Of course it is. Most scientists would agree, but then they would point out that it is a better theory than creationism, when judged by its accuracy, simplicity, and suggestiveness.

Cognition. This question seems to be very difficult for science. The object is to either imitate nature by building a machine that seems human, or to understand how and why the mind differs from the brain. So far the best efforts of biologists, neurophysiologists, computer scientists, philosophers, and others have not led to any real success. Sure, computers have been able to beat humans at some games, such as tic-tac-toe and even chess, but to my knowledge the Turing test has never been met. (The Turing test, for those who do not know, is a test of machine intelligence, defined by the late Alan Turing, a legendary pioneer in computer science. In this test a person asks questions and tries to tell whether the answers that come back are from another person or from a computer. A computer that is good enough to trick people into thinking it is human passes the test. So far none has.)

It is interesting to speculate about whether science will ever understand cognition, and more generally what are some limits to science.

Inherent Limits to Science

Among those questions for which the tools of science are not appropriate, I think it is useful to identify three categories:

  1. Later: the science is not here yet but will be eventually.
  2. Never: the science will never be here, for demonstrable reasons.
  3. Debatable: reasonable people differ on whether science will ever work.

There are lots of examples in the first category. The other two categories are more interesting.

An Example in which Science Will Never Work

Let me suggest a scientific theory that will never work (the second category). Consider a gas such as air. There is already a good theory about the behavior of such gasses at the scale of a few millimeters up, the so-called macroscopic scale. Concepts such as pressure, velocity, temperature, density, and so on are used. We know how to design airplane wings and we can predict with good accuracy how gasses flow around various obstacles.

There is also a microscopic picture, in which gas molecules are treated like little particles bouncing around, hitting each other. A theory which would be useful, and which will never happen, is to predict, through simulation of the microscopic molecules, the macroscopic motion and thereby to deduce properties of gasses. After all, there are a finite number of molecules; if we knew each molecule's position and velocity, why couldn't we calculate the configuration at any time in the future? Simulation is a very effective scientific and engineering tool, and it would be extremely useful if it would work in this case.

Unfortunately, it doesn't work and it never will, for many reasons. To understand one of them, just think of the number of molecules in question. This number is approximately what is known as Avogadro's number, which is the number of molecules in a mole of any chemical substance. It is really pretty big -- about 6 times 10 raised to the 23rd power. This is an enormous number, much larger than any number encountered in everyday life. To imagine how large it is, consider the best laser printer you can buy for your personal computer. This can print at a resolution of 600 tiny, barely visible, dots per inch. On just one sheet of paper, there can be 30 million separate dots of this size. That's a lot, but it is far less than Avogadro's number. Now think of the entire earth's surface, including all the land and all the oceans, covered with dots of this size. How many such dots would there be? The answer is pretty close to Avogadro's number.

Now consider the practical problem of calculating with this many particles. If each air molecule is characterized by its position, velocity, orientation, and angular velocity, then a computer process that simply looks at the data for each molecule, without even doing any calculations, would take a long time. In fact, if done on a very fast modern computer at the rate of fifty million per second, it would take about 5 billion years, which is the estimated age of the earth.

The conclusion from all this is that detailed microscopic simulation is impractical, simply because of the large number of molecules. Remember the criterion that a good scientific theory be simple and easy to apply? This approach fails, big time! The most that can be done is to predict the general nature of a few macroscopic variables, such as pressure. We cannot predict any detailed motion, or the values of any important parameters.

It is interesting to note that there are other reasons why this approach will never work. One of them is the huge size of the computer memory needed to store the data. Another is the extreme sensitivity of the calculations to very small changes in the assumed initial velocities and positions.

What does this example imply about science? It says that different areas of science may be separated by a gap that cannot be breached even using the fastest computers imaginable. Different approaches, different variables, different styles, and different theories are needed. Yes, fluid dynamics is really different from any molecular theory. In a similar but less extreme way, chemistry is different from physics, even though chemical systems surely obey all the basic laws of physics. And biology is different from chemistry. And, we are about to argue, the mind is different from the brain.

Cognition -- an Open Question

Now consider the question of cognition, which I believe is in the third category, that different people differ about whether it will ever be solved. One way of understanding the thinking process might be to perform microscopic simulation, based on a model of the brain. We know that the brain has a trillion neurons, each of them connected to a thousand others. Simulation using a neural model will not work, because of the large number of neurons, the complexity of the models for each neuron, the number of connections among neurons, the sensitivity of calculated results to the details of the initial conditions, and the speed of even the fastest computers that are likely to be available during the coming decades. The most we can hope for from neural simulation is the identification of a very few averages. This is similar to the case of air molecules, where all we can do is to predict the general nature of a few macroscopic variables. But to explain cognition it will be necessary to deal with many more cognitive quantities -- it will be necessary to predict at least as many results as a typical person has thoughts or feelings.

So neural simulation will not work. What about other approaches? For example, observe that the mission of computer science, when all is said and done, is to manage complexity. If cognition is so complex, perhaps the tools of computer science can help. I may be wrong, but I tend to be pessimistic about this approach. So far there is precious little evidence that the architecture of a brain is similar in any deep way to the architecture of a computer. Without some degree of fundamental similarity, there is no reason to suppose that the underlying concepts would be the same and that the tools of computer science would work. In my opinion, a more likely outcome, and a very useful one, would be to create a new computer whose architecture mimics the brain.

There is a field that has received a lot of attention recently, that goes under the name "neural networks." The structure of such systems is motivated by the structure of the brain, with its interconnected neurons. There is still no general understanding of such systems from a theoretical point of view, but they have been made to do useful engineering tasks. As far as I know, there have not been any helpful insights from such activities that have been applied back to help formulate a theory of cognition.

We have seen some approaches which don't seem to offer much promise. Are there other approaches that will work? There is no clear evidence one way or another, except that a lot of people have put a lot of effort toward finding them, without success. In my opinion, which may not be agreed by everyone, there will never be a good scientific theory that explains cognition -- a theory that, like other good scientific theories, is accurate, simple, and suggestive. I am not saying that research in this field is useless -- on the contrary, some progress will undoubtedly be made, and there will be lots of results obtained along the way which may be very useful, for example in guiding the design of man-made systems such as robots. But the lofty goal of explaining cognition scientifically will not, in my judgment, be achieved.

What to Do without Science

If we accept my assertion that cognition will not be understood by science, some things are thereby excluded from the realm of science -- those things that are naturally related to self-awareness, things that are felt internally, personally. Often lumped together under the name "human nature," these include thoughts, aesthetics, desires, feelings, emotions such as love, grief, jealousy, or hatred, and intellectual capabilities like instinct, judgement, intuition, and intelligence. These will not be adequately explained by any scientific theory.

What alternative do we have? If we need to reason about one of those topics, or for that matter about any of a number of other topics that are not now explained by science, it will have to be done by nonscientific methods. One such approach is to make assumptions that are not justified by science, and then proceed. These assumptions are sometimes called "leaps of faith." Science tries to avoid such assumptions, whereas religion and some other human activities seem to require them. Faith, of course, is an intensely personal matter; what one person assumes will generally differ from what another assumes. And science, by its very nature, produces results that can be reproducible by others.

I will call this approach "faith-based reasoning," whether or not God or religious concepts are involved. Faith-based reasoning inevitably lacks the scientific criteria of accuracy, simplicity, and suggestiveness. It is tempting to say that it is therefore bad science. Well, maybe it is, but maybe it is the best we have, and maybe if we keep in mind the underlying assumptions, we can have some reasonably useful theories. Lots of people we admire, such as artists, architects, doctors, managers, musicians, social scientists, and engineers, rely in part on science and in part on understanding of human nature and social systems. If human nature cannot be understood by science, and if we get too smug about discounting anything nonscientific, we may be left with no tools at all to work with.

Also, we scientists and engineers should not forget that science, as an endeavor, is itself based on a set of assumptions. We use mathematics, logic, deductive reasoning, and other tools that, in the final analysis, are not themselves provable by rational means. We all assume that the behavior of nature is not changing with time. How can we be sure? When you really get down to it, we use these assumptions underlying science for a very simple, pragmatic reason -- they work. We should be prepared to be equally pragmatic in considering whether to use faith-based reasoning. The important question is, "does it work?"

There is another reason we should not look down upon nonscientific reasoning too much. Science is itself a human activity, and we scientists are ourselves humans. We all have our own personal thoughts, hopes, dreams, feelings, and emotions that, I assert, cannot be explained by science. From time to time we all pursue activities that are not based on rational thought. I am sure everyone here spends time "off the job" doing such things as enjoying fine music or beautiful art even though there is no scientific explanation of aesthetics. Even on the job, science deals with artifacts and theories that scientists consider things of beauty.

As another example, consider the emotion of grief. Many of us in this room know what it is to experience grief resulting from the death of a close friend or relative. This emotion is very real. Some day science may have something to say about the neural patterns associated with grief, and perhaps even develop a specific mood-changing drug that inhibits these patterns. However, grief also has a deeper, emotional side. If you need to cope with this aspect of grief, you might find helpful support in societal mechanisms, including religious ones. Many people find that a faith based on a belief in God is effective in providing solace and comfort. Not many people would receive much consolation from knowing that their grief is somehow related to chemical imbalances, or patterns of firing of neurons. In other words, science doesn't help, but a belief in God does. Let's be pragmatic.

As for another emotion, love, I sincerely hope that all in this room have or will experience the joy that accompanies total, unconstrained love for another human being. It is a wonderful thing. It may be true that sex, the physical side of love, is somehow explained by chemical hormones, as the smart-aleck verse of the camp-fire song says ("Chemical hormones, that's why I love you"). But it is surely true that the deeper emotional and spiritual aspects, that ultimately are more satisfying and pleasurable, are better described by the romantic answer ("Because God made you, that's why I love you"). I wish for all of you the chance to say to your loved one, not "Chemical hormones, that's why I love you," but rather something less scientific like "Because God made you, that's why I love you."

Thank you for your attention.

I wish to acknowledge with thanks discussions with Charlotte Gosselink, Judy Hoehler, David Kerns, Sherra Kerns, Barbara Penfield, and Tom Wintle, and musical assistance from nine members of The Spectrum Singers.

[1] J. B. Losos, K. I. Warheit, and T. W. Schoener, "Adaptive Differentiation Following Experimental Island Colonization in Anolis Lizards," Nature, vol. 387, pp. 70-73; May 1, 1997.

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