I have been asked to talk to you about creative thinking. While I am glad to do this, I feel some trepidation about discussing a non-technical subject, and I think I should tell you why.
It seems to me that engineering and science are sharply set apart from
all other fields of human activity. If I tell you that a certain theory
predicts the behavior of electrons or neutrons, or that a network designed
in such and such a way will have such and such properties, you can check
my statements by observing the particles or by testing the network. In contrast,
even a historian or a witness to an event can offer you only his documents
or his word to testify that what he recounts actually happened. You can't
check by making an experiment. When one deals, as I shall, with surmises
about partially-known experiences and events, you will be still farther
from being able to verify what I say. If I put forth an idea as being plausible,
you should be forewarned that people in other times and other places have
found witchcraft and astrology to be plausible, and a host of other things
which we regard as ridiculous. If I pose as an expert in creative thinking
or as an authority on creative thinking, I should at least warn you that
I have heard people whose individual actions and decisions I respect greatly
give forth generalizations and analyses for which I had much less respect.
Although I talk with some trepidation, I have no real pangs of conscience. I will be honest and thoughtful to the best of my ability, and I have warned you. Thus, despite my doubts, I shall thoroughly enjoy talking about creative thinking. People like to discuss ill-understood problems which seem more "human" and more "profound" than the technical details of engineering and science. I hope that some day someone will be able to talk about creative thinking in a sounder way than I am able to, but he will probably get less pleasure from his science than I shall from my fancy.
The other part of my trepidation has another cause. Suppose
that what I say is true and wise and constitutes good advice.
What is the use of saying it? Through a good while at the
Bell Laboratories I have seen certain people, figuratively,
of course, hitting themselves on the heads with hammers,
sawing off their noses, trying to walk through brick walls,
riding off rapidly in all directions at once, lying under the
flapdoodle trees waiting for the fruit to fall in their
mouths, and generally behaving in what seem to me
uninstructed if not irrational manners. Surely, someone must
have told them better. Sometimes I've tried to myself. Yet
year after year they pursue the same courses. What good does
it do to tell people non-technical things, anyway?. You may
be able to persuade a man to add 2 and 2 and get 4 rather
than 5, but can his conduct in more general matters be
influenced? I don't know, and if it can't, maybe that is a
good thing. In any event, I
don't intend to let this doubt as to the utility of what I say dull my pleasure in saying it.
With these warnings and explanations, I propose to tell you how I feel about creative thinking. Don't believe me if you don't want to. Don't expect to get much good out of what I say. I hope it gives you some pleasure.
I think the words of the subject deserve a little attention, although I don't intend to give them a precise meaning. I think of creative thinking as referring to the fact that something has been created through thought. In our case, it may be a physical theory; the understanding of a class of phenomena; it may be an invention; it may be a way of getting around a difficulty; it may be an overall or a detailed design for a communication system. What I want to do is to distinguish creative from original and especially from bizarre or novel. To me, creative thinking produces something substantial and reasonably permanent, something which may be understanding, art, or a piece of equipment.
Now, not all substantial accomplishments are the results of thinking. A dictator may have a whole class of people liquidated; an executive may order that no one with more than ten years' service shall achieve district status. The results produced in such cases can be substantial and reasonably permanent, but thinking is not necessarily involved.
In considering creative
I associate thinking with
that ordered progress which we see so clearly in engineering
and science and which we may find lacking in many other fields of human endeavor.
In navigation, the quadrant marks a clear advance over the astrolabe, and the sextent marks an even greater advance over the quadrant. A vacuum tube of today is just plain better than a vacuum tube of 1920, and the same thing is true of today's refrigerator. Today, through wave mechanics, we understand things about the motions of electrons and about the constitution of atoms which were completely hidden from us thirty years ago.
In engineering and science, progress is evident in a series of steps, each of which adds to what we already know or to what we already have done or can do. It is a great part of the satisfaction of one who works in these fields to contribute to this progress. It is of this progress, this adding to our technical capabilities and knowledge, that I associate the words creative thinking,
When I think back over fifteen years at the Bell Laboratories
and consider the examples of creative thinking which I have
seen, one thing which strikes me most forcibly is the variety
of people who have added to our technical capabilities and
knowledge, and the variety of ways in which they have done
this creative thinking. People are widely different and
sometimes exasperatingly different. Moreover, the difference
is not so much that some people can do one job and others
can't; it is that some people will do a job in one manner and
another. When we add the fact that there are many ways to achieve a particular piece of creative thinking to the fact that there are many sorts of creative thinking to be done, generalization becomes very difficult and it is perhaps best to turn to particular examples.
As one rather extreme case, I know a man at the Bell Laboratories who has a record of turning up one good thing after another. One can describe his field roughly by saying that he works on small component parts. He works in a diversely equipped laboratory and shop, with the aid of a technical assistant, and there he not only invents devices and processes, but he makes samples and even whole lots for other people to work with.
I find this man a very puzzling phenomenon. He works with devices and processes which to me seem bewilderingly complex. Of all the multitude of things which he might try, he has some way of hitting on the right things, time after time. He must have some guiding principle of creative thinking which helps him. I find this particularly striking because I have talked with him about his work repeatedly, and I have never got the slightest clue to his way of thinking.
I suppose that the uninitiated might say that anyone messing
around in a laboratory will come up with something new and
useful. Experience shows that this just isn't so. For
experimental work to be fruitful, there must be choice as to
what is tried and the results of experiments must be
It is clear that the man of whom I am speaking is doing creative thinking of a high order. The fact that I cannot fully understand the nature of his creative thinking shows a lack in me, not in him.
Does this man represent an important aspect of creative thinking? I know several men around the Bell Laboratories who are much like this. But even more important, I think that the thing on which the man I have described relies so strongly helps many of us in some lesser degree. I think I could even cite a homely example of this.
Once upon a time a man started to build an elaborate oscilloscope. When it was almost complete and was working in a halting fashion, he left the Bell Laboratories and went to work for Hughes, where he lived happily ever after. The oscilloscope was turned over to a T.A. for debugging. Instead of improving, the device suffered a series of relapses until it wouldn't function at all. At this point it was turned over to another T.A., who is now a T.S.A, by the way. The oscilloscope took a miraculous upturn and was working well in a week or so. In my estimation, this showed at least some creative thinking on the part of the TA.
We can describe the sort of thinking I have been discussing
by a name if we wish: intuition; skill; art. I am even
willing to speculate on its ingredients. Partly, I think it
grows through long familiarity. A boy who plays with erectors
and graduates through hot rods will acquire a feel
for things mechanical. He learns by some informal and partly unconscious process. For such learning, I think that both interest and long acquaintance are necessary. I believe that something else is necessary as well; innate ability.
This type of intuitive thinking is extremely valuable. How are we to get enough of it? I can't give any directions for teaching it or practicing it; I think that we can only recognize it where it occurs and value it highly. We must to some extent take it as it is. In the fairy story, the man killed the goose that laid the golden egg in a foolish investigation of the source. Intuitive thinkers must be treated tenderly if they are to continue to function. One might even extend the parallel, and invent a man who despised the goose because it couldn't tell how it made the golden egg. In this connection, I can only drag up two old saws; "gold is where you find it"; and, with some possible confusion of thought, "don't look a gift horse in the mouth."
Because I have praised and valued intuitive thinking, even in extreme forms, you may wonder whether I am advising you to practice it. The answer is, not unless you can. I do say, by no means despise it. A device can be good, an invention can be valuable even when its author cannot explain it to another's satisfaction, But for heaven's sake, don't try this approach unless you know by experience that you are good at it.
Let us turn to another sort of creative thinking. I know one
man who sits in an office and makes marks on pieces
of paper. He thinks about other people's experiments. He makes up mathematical theories which purport to tell, in terms of known physical laws, what ought to happen when experiments are performed. He analyzes experimental results and tries to find out what caused them. He can explain to any competent man in detail just what he has done and why he did it, although one may still wonder what inspired him to do it.
Is this man's thinking a mere gloss on someone else's work; is it only an explanation of what we already know? No, it is not. Sometimes this man finds that other's ideas about things are just wrong-headed and misleading. In such cases he clears up their confusion and reorients their thinking and their work. In other cases he foresees consequences which others have not thought of. When he formulates problems in mathematical form they become simpler and less puzzling, and he can foresee necessary consequences which would escape one who thought in looser terms. Such a man can make discoveries and inventions; these are not reserved for the intuitive experimenter.
Such theoretical workers provide the backbone, the skeletal structure of engineering and science, without which these fields would collapse into an amorphous mass of unrelated devices and facts. Without them we would not have that clear and steady progress in art and understanding which distinguishes engineering and science from other fields of human endeavor,
Do I advise all of you to become theorists? There is
something to be said for this in a small way at least, for we
know what the tools are. As opposed to an intuitive appreciation of things, physics and mathematics can be taught by fairly straightforward methods. But, this is not necessarily true of the ability to use them. I have known people with a good knowledge of physical laws, with an extensive knowledge of mathematics and with considerable skill in its manipulation who simply didn't know what to do with their knowledge. Such people either can't get started on a problem, or else they get hopelessly bogged down in details. Certainly, you shouldn't learn more mathematics and theory than you can digest, make your own, and use effectively.
I have described two extreme sorts of people whom I have met; very intuitive men who accomplish experimental results no one knows how, and theorists who proceed by consistent and well ordered reasoning. Of course, most of us have some of each of these qualities. I am thinking at the moment of two people who as nearly as I can see get their good ideas while carrying out experiments; they are prompted to creative thinking chiefly through the behavior of the apparatus they work with. Yet, each of these men is quite capable of expressing what he has done in clear-cut, even mathematical, terms. I think also of a mathematician who with his own hands builds machines and gadgets embodying his ideas.
I believe that this mixture of experimental insight and
theoretical understanding is perhaps the most successful
equipment for creative thinking. The
that, however complex the situation, nature always knows the right answer, by definition, of course. Anyone who works in a laboratory continually encounters unexpected phenomena, and some of these the creative thinker can recognize, foster and turn to use.
On the other hand, theoretical or analytical ability can in itself be both a guide to understanding new phenomena and a means for deducing something useful from something which might otherwise be merely new and puzzling.
What I have said so far has been about types of people and their methods of tackling problems. The problems themselves are worthy of consideration. Under what circumstances do people exercise their power of creative thought? How do new ideas and things arise? Here I would like to cite a particular, minor, personal example, and I will follow it with others.
Over ten years ago I was working on a type of tube using an
electron beam. No one had a method of design which took
space-charge into account and produced a gun of predictable
properties. I worried about the matter for some time and
finally I thought of a means of design. I spent quite a
while working this out theoretically and convincing myself
and others that it was sound. Then I wrote a paper describing
it and published it in the Journal of Applied Physics.
Certainly, something was created here, for I have found that
practically everyone who works with dense electron beams
makes use of my work.
In this case the thing which was created was really a published article which helped other people to design electron guns. The tube I was working on never came to anything. The bare idea of the gun wasn't the end product, for I later found that a friend of mine had speculated about the same idea, but he hadn't worked it out or written about it.
One moral I would like to draw from this illustration is that any challenging job can be a spur to creative thinking. I didn't set out to do something new or something clever; I was forced to think by being faced with a problem which I took seriously and wanted to solve.
Of course, to serve as a stimulus a job must be a real and an interesting challenge to the man who works on it. Some men seem to find no challenge in fields they haven't read about in the newspapers or heard commended in college. I think that this is unfortunate and worth thinking about.
Surprisingly interesting things can come out of jobs which
may seem very prosaic. Claude Shannon's application of
Boolean algebra to switching problems may seem to some more
interesting than the original problems. Shannon's work on
communication theory might provide another example. From what
I know, this was inspired by some discussions of novel ways
of modulation such as mixtures of amplitude and phase
modulation, and finally pulse-code modulation, Today,
communication theory is a broad field related to physics,
psychology and I don't know
what all. I myself have been led to far and interesting fields in connection with traveling-wave tubes, yet as far as I am concerned, as much as anything this arose through repeated insistence on the part of Ralph Bown that resonant circuits limit the bandwidth of vacuum tube amplifiers and that someone should do something about it.
I have said that work on a challenging job can inspire creative thinking, but you will note that an initial inspiration is not enough; one must do something about his insights and ideas in order to create anything. In the case of the new means for designing an electron gun, I at least worked out some of the ideas and published a paper, while a friend who had the same general ideas but less interest in the matter did nothing. Ideas which are not developed and carried to some conclusion become as if they never had been. The process of creative thinking can easily be interrupted before anything is really created, and in such cases whatever time and effort have been expended are totally lost.
Some simple, isolated ideas can be worked out and given physical form or published by one man in a short time. In other cases the process of creation is long and necessarily involves many people. I think particularly about some aspects of the L3 carrier development, and about the work that led to the 416A microwave triode.
An example drawn from the L3 development is the application of quality
control and statistical methods to every
vital component used in the system and to the system as a whole. For one thing, this meant that everyone working directly on the project had to keep continually in mind the meaning and details of this approach. For another thing, those who worked directly on the project had to cooperate closely with groups which produced components such as, for example, vacuum tubes. For the first time, specifications were put on all tube parameters affecting system performance, and for the first time tolerances were set on the basis of control limits of a process which was known to be in control.
I am in no position to go into further details here, but the point is that this seemingly simple idea of applying quality control in system design could be called into real existence only through persistent work over a period of years by a whole group of people.
Another example is provided by the development of the 416A
triode. The original and startling germ of a creative idea
was that after all these years a triode might still be the
best amplifier for microwaves, if only the spacing were close
enough and the grid fine enough. An auxiliary idea was that
close enough spacings could be attained and held by grinding
the cathode and a surrounding ceramic co-planar, and then
supporting the grid from the ceramic. These were, however,
mere germs of an idea. Something real and complete was
brought into existence only after years of concentrated
effort, including the inauguration of a program of cathode
studies which is still being pursued for other purposes.
My position so far has been that one needs some ability, intuitive or theoretical, and preferably both, for creative thinking. Frequently, one needs the inspiration of working hard on a job. One further needs the persistence to bring an idea into real being. There is, of course, more than this: one needs the right environment; the right job.
I believe that there are certain general specifications which an environment should meet to foster creative thinking. For one thing, a man should get credit, encouragement and reward if he does produce good, new things. He should feel that his supervisor is helping him and advertising his success, not competing with him or exploiting him. If the man is in a position to exploit his idea himself, he should be allowed to; if it must be turned over to someone else, the originator should get his fair share of credit. In any event, he should be encouraged to publish what he has done, for his own good and for the good of the Bell Laboratories.
For another thing, a man should not be plagued with any irrelevant matters
which he can be spared. It is hard enough for him to keep the technical
of a job in hand and to take care of his personal relations with other
technical men. To encounter red tape or inefficiency or inadequacy in
purchasing, in shops, in space allocations and changes, in personnel matters,
and, especially, in interdepartmental relations cannot help but have
What about actual physical working arrangements? Some of the best work of which I know has been done in gloomy, dirty, noisy and even crowded university laboratories. This of course shows a certain triumph of the intellectual or spiritual over the physical, and indeed I believe that the matters I have mentioned a little earlier are much more important than are physical surroundings.
It seems to me reasonable that one should have good physical surroundings if his employers can afford them. Some people may be sensitive to noise, and why should a laboratory or an office be noisy? Some people may be sensitive to heat, and air conditioning is nice if one can afford it. Personally, except for some cases in which certain standards are set by technical requirements of special jobs, I regard the nature of surroundings as something to be chosen more with regard to custom, decency, and respect for people as human beings, than with regard to their influence on quality or quantity of work. If I were to make a personal choice as to surroundings, I would like most of all authority to change and arrange them to suit convenience, without regard to general plans or rules. I think that this is something which can easily be overlooked by people who no longer do laboratory work.
These general matters of satisfactory supervision,
satisfactory facilities and, perhaps, suitable physical
surroundings, I believe to be very important. I think that
for most people the specific nature of the job they are asked
to do is of
less importance. A person with some intuitive grasp of engineering and an understanding of some basic physical laws and mathematics can tackle almost any engineering problem and do creative work, granted the right general atmosphere. There are, of course, exceptions. I believe that highly exceptional people who have to be carefully fitted to a particular field or job are in the minority. I have no trouble thinking of examples, however; people who succeeded after changing jobs where they had failed before, and people whom I cannot imagine doing anything very much different from what they are doing now.
For instance, an extremely intuitive person who thinks with his hands in a laboratory is not the man to do long-range systems planning. He belongs in a niche by himself, in research or advanced development. A man with a really profound knowledge of mathematics and broad interests shouldn't be tied down to a single long-range project, where he will soon have contributed everything his particular talents have to offer. And, a small minority of workers seem to be real self-starters, who break into intellectual combustion spontaneously without the spur of a job and think truly profound thoughts. In their exceptional case, a set task is bad, rather than good, and they should not be burdened with demands or instructions.
On the other hand, for each of such exceptional people I have
certainly seen at least one rather unsuccessful man who
didn't like and didn't work very hard at a job of which he
could have made something, but who longed for some other
work, and in
many cases for work which he could not do well. Occasionally such men do produce a stream of ideas outside of their field, but most often the ideas are not very good, because they don't strike at the heart of the problem, and the ideas are seldom worked out far enough to be anything but material for conversation.
Now I have talked about types of ability, about a job as an inspiration, about carrying ideas from a glimmering into real being, and about working conditions and jobs. You may believe that I have omitted the really vital point; granted some sort of ability, some sort of problem and reasonably satisfactory surroundings, how does one get the sort of idea that can really advance the art and put us on territory where we weren't before?
One source of ideas which no one should overlook is the ideas
of others. The world is full of half-born ideas; ideas that
came too soon; ideas that were not fully appreciated by the
men who had them; ideas that someone is trying to promote. I
have got some of my very best ideas from other people,
usually through personal contact or current publication.
There must be many ideas in the technical literature of past
years, but in my personal experience these have most often
been turned up by the patent department to show that I hadn't
invented something when I thought I had. As an example of an
idea which I got from another, I will cite the
traveling-wave tube. In this case, I saw in a device which
was on the point of being abandoned as a solution for one
problem potentialities which other people seem to have been
Sometimes, however, one can't find what he wants by shopping around. How, then, does one get an idea when he is forced to have it himself? And how does he bring it from a germ of an idea into true being?
Happily, there is much more agreement on this than one might imagine. One gets new ideas by inspiration or accident, and one tests, verifies and makes something of them by expert knowledge and hard work.
Let me tell the story of a couple of my ideas. I don't claim that they are very good ideas, but they are about as original as any I have ever had.
One evening W. B. Hebenstreit and I were working late at the Laboratories, on a book which, incidentally, never got written. We had been trying to deduce mathematically the effect on tube noise of the fact that an electron beam is made up of electrons with many velocities. Because many velocities were too much for our feeble mathematics, we considered a beam composed of electrons of two velocities only. We quickly deduced growing waves. The double-stream amplifier had been conceived. It came into being through further straightforward mathematical work and through experimental work by A. V. Hollenberg. Finally, alas, it was dropped because its alleged advantages came to appear illusory.
For a number of years I have been interested in communication
theory. Because of this interest, I have repeatedly
tried to concoct new and advantageous ways for encoding messages for transmission. Some two years ago I had been thinking a lot about systems with a random element, which have certain alleged general advantages. One day I was talking casually with Claude Shannon, and he described to me in a few words the system a worker outside of the Bell Laboratories had devised. I didn't pay much attention while he was talking, but something of what he had said stayed with me. Then, later in the day, I saw certain advantages of this new system. The next day I went to see Claude and told him that this was a fine idea. As I explained the advantages, he agreed, but he observed that the system I was describing wasn't the one he had told me about at all. I had invented a new system by listening carelessly and pursuing my own thoughts. Since then I have done a good deal of analytical work and further "inventing" in this connection and A.L.Hopper has made an experimental system. I still have hopes for this one.
While I had each of these ideas by accident, I had them only
because I had been thinking for a long time in the general
field and racking my brains for ways of doing things. Then,
suddenly, there was an idea. Sometimes the idea or the
glimmering of an idea comes in a less accidental manner,
suddenly on the street as one did to the mathematician Henri
Poincare, or at night in bed. But it doesn't come without
adequate preparation. And, without adequate skill and
considerable effort, nothing will come of the
idea; inspiration and accident form only the starting point
of creation, not its accomplishment.
It is because of belief in this sort of genesis of inspiration that I feel that interest in and hard work on a job are more important than just what job it is. If your job poses problems, if you take them seriously, if your boss inspires and encourages you, then, granted even reasonable ability, inspiration will come, and if you follow the inspiration up with sound analysis and work you will have created something.
Now I will admit that there is one catch to this. Sometimes people have good ideas, or the germs of good ideas, outside of the field of their immediate work, There are several things which one can do in such a case.
One course is to write the idea down in your notebook, perhaps to get it patented if you can, but to do nothing further. Some day, someone who really needs the idea in his work will have the idea independently and will really work it out. At this point you can flaunt your notebook and perhaps your patent in his face, his boss's face, your boss's face, and so on. Such behavior may give a lot of satisfaction to some people, but I don't see just what it accomplishes,
Another course is to seek out someone to whom you think the idea might be of use and to try to sell the idea to him, or rather, to give it to him. The important thing is to persuade him to take it. As a secondary consideration, you may write a memorandum, or a joint memorandum, or take out a patent if he insists.
Sometimes you can't sell an idea. If the idea still seems
good to you, it is appropriate to state it clearly and as
completely as you can in a memorandum and send it to all the people you think might make use of it. Or, you can go further and publish it.
Sometimes an idea will seem so good and attractive that you want to work on it yourself. If it's that good, your boss is likely to be impressed with it himself, and so will other people, and you will get a chance to work on it if you wish.
It seems to me that I have covered a lot of ground, and that I ought to give some sort of brief summary and drawing together of what I have said. I will make this very brief.
To me, creative thinking implies two things. First, something reasonably substantial and enduring must be created, whether this be embodied in a publication or a piece of apparatus. Second, something must be added to the body of engineering or science, something which can be clearly recognized as a step forward.
Creative thinking can proceed either from a logical approach to a problem, or through an intuitive grasp of it. In exceptional people the logical or the intuitive elements predominate very strongly. If you are one of these, you may succeed only in a rather special sort of job. With a moderate amount of both of these qualities you can do creative thinking in connection with almost any job, provided that you find the job challenging and that you aren't unduly distracted by non-technical or irrelevant matters,
Things which make a job challenging are good general working
conditions and a good boss who inspires you, and who sees
that you get recognition and rewards.
There is a large element of inspiration and accident in the genesis of creative ideas, but the inspiration doesn't come and the accidents don't happen to people unless they are prepared through hard work and hard thought.
Creative thinking doesn't end with the initial idea. Unless one checks and analyzes the idea and reduces it to an appropriate substantial form, which may be a publication or a physical device, nothing has been accomplished. Knowledge is what people know, not what they have surmised or forgotten. The ratio of inspiration and perspiration varies from creative idea to creative idea, but the perspiration is always there.
Finally, I might add that few satisfactions are so great for
the effort spent, or so enduring, as that of having taken a
real step ahead in engineering or science. In these pursuits
progress is real, and it is recognized and appreciated by all
the fraternity of workers. I believe that in no other field
of human endeavor can the average worker achieve as secure
and enduring a place through his creative accomplishments.
Next to good pay, this should be a considerable inspiration
and satisfaction to us.
This talk was discovered by my father, Herbert Anton Schneider,
in his papers. He was at Bell Laboratories, Murray Hill, NJ
when he heard it. He wrote '1952' on the top, so presumably
he obtained the text
January of that year.
He sent me a copy.
granted me permission
to put the talk on the web
with no restraints or copyright reservations.
The pages were scanned
by a Microtek ScanMaker 4
Power Macintosh 7600/120
with OmniPage Pro 8.0
and then edited into html.
To retain the flavor of the original text, which
was typewritten, I have kept
it broken by the original pagination.
I have made corrections indicated in the text.
There were a handful of other changes. To avoid disrupting the flow
but to keep a record
since this is a historical
document, I have put them into invisible HTML comments.
This document is at
I thank Denise Rubens for careful proofreading.
Thomas D. Schneider
permanent email: firstname.lastname@example.org (use only if first address fails)
This talk was discovered by my father, Herbert Anton Schneider, in his papers. He was at Bell Laboratories, Murray Hill, NJ when he heard it. He wrote '1952' on the top, so presumably he obtained the text January of that year. He sent me a copy.
John Pierce granted me permission (as html) to put the talk on the web with no restraints or copyright reservations.
The pages were scanned by a Microtek ScanMaker 4 on a Power Macintosh 7600/120 with OmniPage Pro 8.0 and then edited into html.
To retain the flavor of the original text, which was typewritten, I have kept it broken by the original pagination. I have made corrections indicated in the text. There were a handful of other changes. To avoid disrupting the flow but to keep a record since this is a historical document, I have put them into invisible HTML comments.
This document is at https://alum.mit.edu/www/toms/pierce/creative.thinking.html
I thank Denise Rubens for careful proofreading.
Thomas D. Schneider
origin: 1999 May 4
updated: 2005 April 2