This is an edited version of the presentation made by Dr. R. V. Moody to the Visiting Committee to the Faculty of Sciences of University of Alberta, on February 17, 1995. This was a non-academic audience consisting of professionals and business people from the Edmonton area. This article, and others of a similar nature, can be found on CAMEL, the web server of the Canadian Mathematical Society. Click here to find these articles.

Robert V. Moody
Department of Mathemmatical Sciences, University of Alberta

``It is a profound and necessary truth that the deep things in science are not found because they are useful; they are found because it was possible to find them.'' -Robert Oppenheimer

Why curiosity driven research? Let me begin with a rather extended example. In 1980 Philips and SONY jointly set out to develop what has rapidly become a fantastic success story - the CD player. This was an example of targeted research pure and simple: research directed at a realizable goal that has a direct application to our economic and social well-being. The magnitude of the task is indicated by the fact that Philips wanted to control 50%of the record industry before they began this project. The technical problems, of course, were immense.

What is far less visible, but was absolutely crucial to the developers of the CD, was that before they began, the BASIC science was already in place. This is the perhaps the most important point that I would like to make today:

1. Basic research is the foundation of targeted research

We could imagine asking a group of engineers of 125 years ago to create this same device, which can reproduce music in high fidelity, the music stored in digital form on small disks that are robust and cheap to make, that are not affected by dust and small scratches, and that are never physically touched by the device that reads them. But this was completely beyond the science and technology of the times. In fact the CD player is an absolutely amazing testament to twentieth century science, bristling with lasers, microchip computers and utilizing error correcting codes, digital wave sampling, the physiology of the ear, the technology of plastics, semiconductors, and so on.

But the fact is that virtually none of these wonders of science was developed as a result of targeted research. A substantial amount of it came out of the universities.

Listen to the words of Hendrick Casimir. Casimir made his name in mathematical physics but when he wrote these he was the Director of Research of Philips.

`` I have often heard statements that the role of academic research in innovation is slight. It is about the most blatant piece of nonsense that it has been my fortune to stumble upon.''

The fundamental importance of curiosity based research is what the history of science teaches us over and over again, but it is hard sometimes to truly appreciate it. I want to illustrate the point by looking at two crucial pieces of science that make the CD player possible.

Here is photograph of the surface of a compact disc showing the pits and lands which are the digital information which a CD player reads. Some idea of the size here: the lands are around 1 micron (one millionth of a meter). For comparison a human hair is about 75 microns thick. In each second your CD player reads in about 4.3 million bits of information which occupy just over a meter of track on the disc.

A laser beam forms a spot that is focussed on the track. Laser light has two key features: it is of one wave length, or one colour, and the waves that make up the light are synchronized - what is called coherent light. Thsee two properties of laser light, which could not be produced before the laser, are utilized in some very clever ways in the CD. The pits are 1/4 of a wavelength deeper than the lands. The lightwaves reflected from the pits come back 1/2 a wavelength out of phase.This phase difference can be detected and this is in fact how the information is read.

The inventors of the CD knew that they could never hope to have some 10 billion of these lands and pits perfectly reproduced on each plastic disc and even if they did, the slightest spec of dust and each little scratch could wipe out thousands of digits of the disc. That is why there is a second important feature: error correcting coding. This is something wonderful about CD's. If you scratch a record you destroy information on your record forever. If you scratch a CD the chances are that you will never hear the difference.

The stories behind the development of these two key features, lasers and error correcting codes are fascinating in their own right, but more importantly for our purposes they also raise a number of points about curiosity research that illustrate how it works.

The actual physics behind the production of coherent waves was suggested by Einstein in 1917. But no one could think of a way to implement this into practice. It took 40 years before researchers at Columbia and Maryland Universities produced the first such device: the maser, but it emitted radio- waves, not light.

The inventor of the ruby laser was Theodore Maiman . He had a Ph.D. in Physics from Stanford and was at the Research Division of Hughes Aircraft in 1960. His starting point was the maser.

Maiman wanted a solid-state device that produced light. He decided to try and base his device on the crystal, ruby. Now the current of opinion was that the whole idea of the production of coherent light was impossible by the means Maiman had in mind, and his colleagues told him so. Obviously Maiman felt very weighed down by this: here are Maiman's own words:

``The pressures were intense. The people I worked with told me it would not work. I kept imagining the reactions that would occur if I went ahead and built the equipment and it failed. I could have done it in a month or two after my [first] experiments .... but I did not want to look foolish. I proceded with extreme caution.''

In fact he proceded with such caution that his equipment worked the very first time he turned it on!

Now there are several lessons here: not just the obvious one that our hero came through in spite of all!

2. Curiosity driven reasearch is directed research

Maiman was NOT doing what we commonly call ``targeted research''. Maiman knew that coherent light would be wonderful stuff to have from a scientific point of view, but he could hardly have imagined all its uses from attaching retinas, laser surgery, the assembly of cameras, determining vast distances accurately, CD players and CD Roms, and so on. Yet his research was not aimless. It was ``targeted'' but it was targeted towards a purely scientific aim: of producing light that was coherent in wavelength and phase.

Curiosity based research is just as oriented as any other kind of research.

3. Peer review and peer pressure

Although Maiman had to struggle alone he was not doing research in a vacuum. His colleagues knew what his research was about and gave their estimations of its chance of success. They were wrong, but nine times out of ten they would have been be right. This is an important aspect of research. Every researcher works in a world-wide community of co-workers whose collective wisdom serves as a guide to what is and what is not reasonable research. Proposals for research funding are reviewed by other experts in closely related areas. Their opinion carries great weight in deciding the feasability of the research. This always needs to be balanced with the possibility that conventional wisdom may be wrong, as it was in Maiman's case. We obviously need to have faith in people who have good credentials and good track records to leave them the freedom to explore their ideas. Every research director knows difficulties of balancing these two sides of scientific exploration.

Of course if we had known that lasers could be made and all their wonderful uses, all of us would have given Maiman carte blanche and all the time and funds he wanted.

Here is a question. How much would you think it would be worth investing to invent the laser if it did not yet exist but we knew it could be done and we knew all of its psssible uses? It is an interesting thought when you start to question the cost of curiostity research. The fact is that a single piece of curiosity driven research can translate into billions of dollars in the long run.

4. Curiosity driven research makes economic sense

Let's go on to error correction. Remember that we said this is a crucial feature of the CD technology. Even on a brand new disc a CD player is correcting on the order of 10 mistakes a second. Without error correction, CD's would sound at best like scratchy LP's.

The idea behind error correcting is simple. The basic units of information on a CD are arranged in 32 bit words. There are some 4 billion possible such words. But we select only a small number of these as LEGAL code words - about a quarter of a billion). This is like the English language where only a small fraction of possible words are legitimate parts of the language. Think of the legal code words as the ones in the CD dictionary. Unlike in English, which evolved through time in a haphazard way, the legal code words are carefully chosen to be as different as possible from one another. Say each one differs from each other in at least 5 binary bits. Now the music is encoded using only legal code words, so when a word is read off the disc it is suppposed to be a legal code word. As it is read off it is essentially looked up in the dictionary. If it does not match a legal code word then there is a mistake in it - for whatever reason it is corrupted, be it from dust scratches, improper printing on the disc, etc. The processor then looks for the closest matching legal code word and replaces it with this match. This is a bit like replacing the non-word unibersity with a legal close word like university.

This is all very straightforward. The catch is this. If a word is received, we have to locate the nearest match very very fast. Don't forget the data flow of 4 million bits a second. This is far too fast to be looking up words in the huge dictionary of legal code words and then trying fo find good matches for words that are corrupted.

In fact the error correcting codes used in the CD system are wonderful mathematical codes for which no dictionary is needed and incorrect words are corrected in a few simple calculations on the word itself!

The mathematics behind the design of error correcting codes involves an area of abstract algebra called finite field theory that was first discovered by Evaste Galois around 1830. Galois is a romantic figure because he died at the age of 20 in a politically motivated duel. You might expect to hear now that Galois was into secret codes or something like that, but in fact his discoveries on finite fields were made as a result of his thinking about something entirely different: some purely mathematical problems on the roots of polynomials. It doesn't matter what polynomials are for this talk though you may remember solving quadratic equations in high shcool. The main point is that some purely mathemaical questions led him to discover some totally new an unexpected finite algebraic systems. These systems have been extensively studied by mathematicians ever since and are a part of the undergraduate curriculum of every mathematics program. Their use in error correcting coding came only in the late 1950's. In 1960 Reed and Solomon wrote a purely mathematical paper: ``Polynomial codes over certain finite fields.''These Reed-Solomon codes are the ones used in a CD player. Would targeted research towards error correcting codes have produced these finite fields? Very unlikely. There are a number of good coding schemes known now, and every single one of them depends on hard mathematics that was invented for completely different reasons.

As a matter of interest, the error correcting on a CD player is so good that it can fully correct an error bursts of well over 1000 consecutive bits.

One of the lessons that we can draw from this and countless other examples in modern technology and science is

5. The unpredictability and unexpectedness of science

Einstein could hardly have known that his observation aobut how photons interact with electron shells of atoms would translate into the laser, nor could Galois have even remotely imagined a compact disc player. It is a source of enormous difficulty in science that we cannot predict what science is going to be the really important science for the future.

But let's get closer to home. What does a mathematician of today do? Some of you will have seen Dr. Swaters demonstration on the mathematics of ocean waves. Dr. Riemenschneider and his group work on wavelets, a new branch of mathematics that has its origins in Fourier analysis and has key applications in signal and image processing. As a pure research mathematician at the University of Alberta what do I do?

Here is a picture which illustrates the typical structure of a crystal. This conception of the crystal as a repetitive motif of atoms is really a product of this century and needed two basic scientific advances before it could be discovered. One was the atomic theory of matter and the second was the discovery of x-rays that allowed us to ``see'' things at the atomic scale. When a crystal is illuminated with x-rays and a photographic image is taken a beautiful regular pattern of bright dots emerges. In contrast, non-crystals produce formless fuzzy patches of light and dark. This picture of dots is not, as one might first suppose the atomic structure itself. Rather is it diffraction pattern, a picture of the the interference patterns caused by x-rays being scattered by the regular array of atoms. Each bright dot is formed by the additive effect of reflected x-rays from hundreds of atoms. The diffraction pattern is in fact an indication of the fantastic spacial order of the atoms. The mathematics of this was all worked out in the early part of the century and the basic equation crystal = diffraction pattern of bright spots became a basic understanding in science. But in fact it was wrong!

Here is another diffraction pattern taken in 1984 by Schectman and his colleagues of a metallic compound that they had made by incredibly rapid cooling. It looks just the same but it caused a minor sensation when it first appeared. You will notice that there are 10 dots in th first ring, and indeed the whole structure has 10-fold rotational symmetry. This seems nice, but no reason to make it to the New York Times! Well the reason it caused so much fuss is that 10-fold symmetry cannot possibly appear in crystals. This is a simple piece of mathematics that has been known for ages. You will never see a pentagonal floor tiling; triangular, square, hexagonal yes; pentagonal no. So Schechtman was not looking at a cyrstal. But then what was he looking at? Well, it is a new class of substances that are appropriately called quasicrystals or now aperiodic crystals.

The illustration shows a computer generated 2-dimensional toy quasicrystal which you will see has a strong resemblence to the Schectman image though there is much more of the pattern now showing. You can sense the underlying symmetry of this pattern, but believe it or not it really has no repetitive (crystal-like) symmetry at all. I use the word ``toy'' here because real quasicrystals are three dimensional and the symmetry that we are interested in is a three dimensional analogue of 5-fold symmetry called icosahedral symmetry. But the main point is the same. The big puzzle is this: if there is no repetition, how does nature build these things? How does nature know that an atom should go here but not there so that in the end the stucure is so perfect that the thousands of atoms affecting the x-ray scattering conspire to produce bright dots?

No one really knows, and it reinforces the fact that we probably do not how even ordinary regular cyrstals grow.

My research over the past 3 years has been directed to trying to create a mathematics that can adequately express these new sructures and provide clues for the mechanisms by which nature can actually create them.

Who knows, a hundred years from now we may be spraying cars with quasicrystal paints to keep off the rust! But for me this is a curiosity problem pure and simple. We have difficulty studying these structures because we don't have the right mathematical formalism. Wherever there is wonderful structure, there is wonderful mathematics. There are a lot of things to learn here.

And the marvellous thing about knowledge, especially mathematical knowledge, is that it is accumulative.

6. Knowledge and research is accumulative

Knowledge that is sound and correct has lasting value. The theory of optics, that has been developed without interruption from the time of Newton over 300 years ago, was an understood prerequisite for Maiman's work on lasers. He could not have looked for coherent light if there was no theory that led one to speculate tha coeherent light could exist. No theory of light, no lasers, It is as simple as that! Mathematics of 2500 years (plane and 3-dimensional geometry) was a prerequisite for the invention of calculus of 300 years ago, the calculus was a prerequisite for the work of mathematical theory of electro-magnetic and light waves first formulated by Maxwell in the 1860's. You begin to feel how scientific knowledge blends into a vast continuum.

Let me close with a different perspective on curiosity driven research.

Some 65 million years ago the Cretaceous era ended with what the latest theories indicate may well have been a catatrophic meeting of the Earth with an astroid. Whatever happened the dinosaurs were devestated and the great Age of Reptiles was over. The fact that I can even say this is a example of wonderful insights of curiosity based research but off hand I can think no economic use of this knowledge (Steven Spielberg excepted). But I think that almost everyone finds this kind of thing fascinating. It is a brilliant coalesence of a couple of hundred years of knowledge slowly and patiently acuumulated by geologists, paleontologists, biologists, astronomers, chemists, and physicists.

Well, the hard luck of one kind of life form means new possibilities for others. Among the amimals to cross the Cretaceous-Tertiary boundary were little rodent like mammals. If present mammals are anything to go by they were scurrying around poking their noses into every nook and cranny exploring their surroundings: Early Curiosity Reseach!. These were the ancestors of all mammals. These were OUR ancestors.

7. Curiosity is part of our nature

You probably heard of the amazing discoveries on Christmas day of last year of new caves in France containing hundreds of pictures drawn by men some 10,000 years ago. And all of us have gazed in wonder and admiration at photogrphs of the pictures in the famous Lascaux Caves, recognizing in our human ancestors that common need to express and understand the world around them. Would we not be poor indeed if we were to take no further interest in past civilizations, if Greek were to be forgotten by all the world, if the heroic efforts to crack the enigma of the heiroglyphics or the study the origins of man and indeed of the universe itself, were to be abandoned because no one cared any more about the ideas and customs of other times or because they don't make economic sense? This is self-evident.

The need to know and define ourselve is an unending one. The University of Alberta cannot of course, maintain programs or expertise in all these things, but the knowledge world is a global one and each university in its own way must carry its share.

We do curiosity based research because it is in our nature to be curious, because economically and socially it provides us with enormous benefits that far outweigh the costs of doing it, and because if we are to survive as creatures of this universe then we will need to have as deep an understanding as possible of the forces, living and otherwise, that shape it.
