Years ago, after I gave a talk in Philadelphia, I came back troubled by something that happened there. I remember sitting in the airplane, trying to sort it out. I'd been talking about inventiveness. I'd told stories about creative people. I'd said that strange stories follow inventive people around because invention itself parts company with normality.

I'd told them how Einstein used the same soap for washing and shaving -- how he figured anything more would've complicated his life unbearably.

I'd told them about Norbert Wiener, the father of cybernetics -- how he came home from his office at MIT one evening. He got off the bus in his neighborhood. Wiener never had learned to drive a car. He wandered down his street in a brown study, thinking equations. Suddenly he stopped by a little girl playing marbles. He asked, "Little girl, could you tell me which is the Wieners' house?"

The little girl smiled and said, "Oh, Daddy, we live right across the street."

I'd told the group that invention is revolution. I'd said that, since invention is a trip into an uncharted land, it has to be eccentricity. It can be no other.

Afterward, during questions and answers, a bright young man asked, "Do you mean I can't be inventive and still live a normal life?" It was an ingenuous question, but I couldn't take it lightly. It was one of those questions that people ask when they aren't looking for information.

This fellow saw the issues with perfect clarity. I knew in my bones that he'd voiced the question because he hoped he could get a new answer. He was like the person who goes back again and again to the opera hoping that, just once, Don José will have the sense to walk away from Carmen.

His question was difficult and dangerous. He so clearly wanted to be let off the hook. He wanted the brass ring without having to reach out into space to get it. He didn't want to risk humiliation. He didn't want to step into the void.

I took a deep breath and answered. I said, "You cannot be inventive and live a normal life." Oh, I knew you could live a normal life, at least in the outward markers of normalcy. But at some point you have to go where others have not gone.

Perhaps the young man's question was best answered by the Romantic poet Coleridge. Coleridge ended his poem Kubla Kahn abruptly. He suddenly broke off and, in one last verse, he told his vision of the Creative Hero emerging out of his own tormented dreams. Coleridge wrote,

I would build a dome in air,
And all should cry, Beware! Beware!
His flashing eyes, his floating hair.
Weave a circle round him thrice,
And close your eyes with holy dread,
For he on honeydew hath fed,
And drunk the milk of paradise.

That man in the audience saw what other listeners hadn't understood. He knew why he should "close his eyes with holy dread" at the idea of drinking the creative milk of paradise. He knew what the inventive genie could do for him once it got out of the bottle. But he'd also caught a glimpse of the size and power of the beast.

He asked the question again on the way out of the building. He knew what was at stake. It bothered him. But, by then, it was I who was bothered. He reminded me that creativity is too large a thing to advocate lightly.

Without creativity we are nothing. But, when we step off onto those unexpected side roads that intersect the main arteries of our thinking, we are not welcome. Change is a threat to the world around us. Function creatively, and the world will certainly try to "weave a circle round [you] thrice." The creative daemon within us poses a threat that most people want to see sealed off.

The British once used a wonderful phrase to describe a creative person. They would talk aboutA Fine Madness. Well, I don't really know what sanity is or where it ends. But I do know that the abnormality that we call creativity does -- often enough -- reach outside the line of acceptability.

Let me tell you about Richard Dadd. Richard Dadd was mad, insane. That word is out of fashion these days, but Dadd was mad, even by today's forgiving standards.

Dadd was born in 1817. At the age of 26, already an established painter, he took a long trip through Europe and the Mid-East. He came back unbalanced. His family took him to a doctor who dealt in mental illness and its legal implications. Dadd, the doctor said, was dangerous and no longer responsible for his actions.

Just a few days later, as if on cue, Dadd murdered his father. He fled to Paris, and there he killed a perfect stranger. He was caught and shipped back to England. He spent the rest of his life in asylums. He finally died in one when he was 69.

Before the murder, Dadd had submitted two paintings in a competition for historical frescoes in the Houses of Parliament. They were hanging in Westminster Hall when he did the murder.

One survives. It's a dreamy Arabesque painting with camels and bearded Bedouins. The title isCaravan Halted by the Sea Shore. It anticipated the kind of Salon Art that would soon be so very popular in England and France.

Floods of visitors came to see his work after the murder. Journalists tried to diagnose his madness from the pictures. For the next 43 years Dadd painted and the arm-chair diagnoses continued. Of course some of his work did deal frankly with insanity. He made studies of madness. He called them, Sketches to Illustrate the Passions.

Nineteenth-century asylums were meant to keep patients out of the sight of proper Victorian sensibilities. But, one way or another, Dadd's paintings leaked out into exhibitions.

The Victorians were thrilled by what they saw. But then they also thrilled to the supposed madness of the Romantic poet and artist William Blake. One writer said of Dadd and Blake:

[They] may be classed together as examples of painters in whom a disordered brain rather aided than impeded the workings of a fertile and original fancy.

Well, Blake hadn't heard daemon voices commanding him to kill, as Dadd had. But his fertile mind, like Dadd's, had broken new ground. And the Victorians, creative as they were, certainly saw creativity as kin to insanity.

Dadd's most compelling work is a loving picture of Sir Alexander Morison, the doctor at Bethlem Hospital who nursed him back into painting after his rampage. Dadd shows an angular older man with a face that's gaunt, but open and compelling.

There's really no more madness in Dadd's art than there is in your creative work. In 1974, the Tate Gallery mounted an important exhibit of his art -- not because he was mad, but because the work was good. If Dadd was crazy in life that was one thing. But in art, his focus was clear, and his passions were set on the clean task of helping us see the world around us.

By the way, Dadd escaped the death sentence because England had just instituted an insanity defense shortly before he committed murder. He was also given liberty to paint because of recent English reforms in the care of the insane.

Either earlier or later in the 19th century, he would've fared much worse. But this was 1843, and the Romantic vision had, for a season, given madness a kind of sanctity.

Of course, you'll rightly tell me that Dadd's case was too extreme an example. Well, sure. But I'll tell you that the creative daemon is to be feared nonetheless. I really do warn you to view him with some measure of "Holy dread!"

Let me tell about another creative genius. This one never saw the inside of an asylum. But maybe he should've. He was John Fitch. Fitch was born in 1743 in Connecticut. That was 13 years before William Blake and, like Blake, I believe Fitch was a Romantic precursor.

Fitch's mother died when he was four -- his father was harsh and rigid. A sense of injustice and failure marked his life from the start. Pulled from school when he was eight and made to work on his hated family farm, he became, in his own words, "almost crazy after learning."

He finally fled the farm and took up silversmithing. He married in 1776 but soon left his nagging wife, who couldn't bear his manic-depressive extremes. For several years he explored the Ohio River basin. He spent time as a prisoner of the British and Indians.

He finally returned to Pennsylvania, afire with a new obsession. He wanted to make a steam-powered boat to navigate the Western rivers.

In 1785 and 86, Fitch and a competing builder named Rumsey looked for money to build steamboats. The methodical Rumsey gained the support of George Washington and the U.S. Government. But Fitch found private support. Then he rapidly reinvented a sort of Watt engine, moving from mistake to mistake until he produced America's first successful boat, well ahead of Rumsey.

It was a strange machine. Talk about a Romantic vision -- Fitch's boat was propelled by a row of Indian-canoe paddles. It really did sail out of the American wilderness and out of the Romantic inner recesses of Fitch's mind.

Yet, by the Summer of 1790, Fitch was using it in a successful passenger line between Philadelphia and Trenton. He logged some 3000 miles at 6 to 8 mph that summer. Still, in the end, it failed commercially.

People just didn't take Fitch's boat seriously. What they saw was a curiosity -- a stunt. And Fitch, probably because of his personality extremes, couldn't sustain his financial backing.

The failure broke Fitch. He retired to Bardstown, Kentucky, and struck a deal with the local innkeeper. For 150 acres of land, the man agreed to put him up and give him a pint of whiskey every day -- while he drank himself to death.

When that failed, Fitch put up another 150 acres to raise the dose to 2 pints a day. When that failed, Fitch finally gathered enough opium pills to do himself in.

They'd called him "Crazy Fitch" in life. Now they buried him under a footpath in the central square. In 1910, the DAR finally put a marker over the spot, identifying him as a veteran of the American Revolution. It says nothing about his steamboat.

And, I tell you, I am haunted by the picture of this six-foot-two figure in a beaver-skin hat and a black frock coat -- stumbling the streets of Bardstown -- the butt of children's jokes.

Fitch had been unable to see that his dream had not failed. History honors Fitch far better than he honored himself, for it was he who set the stage for Robert Fulton. Fitch made it clear that powered boats were feasible.

Fitch is, for me, a powerful -- and typical -- example of the person who functions creatively and who, necessarily, also functions at risk. Watt and Fulton took risks and won big -- but not before they too had suffered failure.

The trick, of course, is to risk big, lose one day, and come back to win the next. That's what happens when we take a healthy pleasure and confidence in our creative processes. But God help the creative person who has no tolerance for failure!

At any rate, stories like Fitch's really start accumulating in the mid-19th century. Next, I'd like to tell you about two European doctors who lived in the near wake of the Romantic movement.

The first was the German doctor, Robert Mayer: In 1840, when Mayer was 26, he shipped to the East Indies as the surgeon on a Dutch vessel.

Afterward, Mayer came back to Germany, married, and settled down as a town doctor. It might seem he was done with adventure. But something had touched Mayer in Java, and it changedhis life.

A powerful insight came on him while was letting blood from sick sailors. Nineteenth-century doctors did that by lancing a vein. Now you're all well aware that venous blood carries less oxygen than arterial blood -- that it runs darker. The first time Mayer opened a vein in Djarkata, blood ran far too red. He thought he'd hit an artery.

He soon learned that that was normal in the tropics. Then he realized: People burn less of the food they eat in a hot climate. They generate less heat. People knew that food fuels our power output. Now Mayer realized that it also fuels our heat supply. And we need a lot less heat in Djakarta than we do in Europe.

But this was 1840, and we didn't know that heat and work can be traded back and forth. We didn't yet have any first law of thermodynamics.

Mayer thought about that red blood on the long trip back. And he tumbled to the truth of energy conservation. He realized that work and heat were interchangeable.

Mayer had identified our most important physical law. But he didn't know classical physics. He didn't know formal math. He wrote a clumsy paper about the idea, and the editor ignored it.

So Mayer went back to study physics. He wrote a better paper in 1842, and it was published. But meanwhile, a young Englishman, James Joule, was measuring how many foot-pounds of work made a Btu. By 1847 Joule had honed his accuracy to 99 percent. And there the plot thickens.

Mayer had spun a correct theory for the number of foot-pounds per Btu. But no one would believe it until measurements were more complete. Physicists sorted through Mayer's theory and Joule's experiment. When they finally resolved the whole business, they overlooked Mayer. By 1850 Mayer was so angry and frustrated that he attempted suicide. For years after, he was in and out of asylums.

Finally, in 1863, the Englishman John Tyndall wrote an important text on Heat: A Mode of Motion. It began and ended with Mayer. Mayer was vindicated.

Twenty years before, insight had touched him in Java. His vision of bright blood and heat reallydid change history. But first, professional scientists -- people untouched by visions -- had to put that vision into familiar terms.

Mayer had undergone a blinding insight, a mental leap in the dark that took him all the way to the law of conservation of energy in a single step.

It was a leap that preceded method and logic. That in itself is insanity, isn't it? Of course, it almost drove Mayer mad. Mayer calls to my mind a couple of powerful lines by the poet Rilke:

... if you set this brain of mine on fire,
then on my blood I yet will carry you.

Now, you may say, what about that perfectly sane James Prescott Joule who really put the first law on solid footing soon after Mayer? Well, Joule was never institutionalized. But he had his own streak.

Joule married late in life, and he went off to honeymoon in the Swiss alps. He was met there by another upper-crust Englishman who spotted his new bride in a carriage beside the road.

Where was Joule? He was, as it turned out, skulking about the base of a waterfall below with a huge thermometer. He was trying to measure the rise in temperature of the water after it'd fallen several hundred feet and converted its potential energy into a fraction of a degree Fahrenheit.

Mad? No. But certainly eccentric.

I began today by quoting the Romantic poet Coleridge. That was no accident. Madness really did permeate the Romantic view of things. And as it did, the 19th century became an epic of truly unequaled creative output.

Intensity was sanctioned in a way we do not sanction intensity today. That kind of Romantic intensity is at the heart of the story of another highly creative 19th-century doctor -- a contemporary of Mayer's.

He was Ignaz Semmelweis. In 1847, Semmelweis's close friend Jakob Kolletschka cut his finger while he was doing an autopsy. Kolletschka soon died of symptoms like those of puerperal fever.

That got Semmelweis's attention. Puerperal fever was killing 13 percent of the women who gave birth in his hospital. The death rate was driving him nuts. He couldn't figure it out.

Something else also got his attention. A nearby obstetric hospital, run by midwives, was losing only two percent of its patients to fever.

No one had yet connected germs with disease. The first hint of that connection would come out of England six years later. Lister wouldn't show us how to kill germs for another 18 years.

Semmelweis was a Hungarian doctor teaching medicine in Vienna. He noticed that students moved between the dissection room and the delivery room without washing their hands. On a hunch, he set up a policy. He ordered doctors to wash their hands in a chlorine solution when they left the cadavers. When he did that, mortality from puerperal fever promptly dropped to two percent.

Now things grew strange. Instead of reporting his success at a meeting, Semmelweis said nothing. Finally a friend published two papers on the method. By now, Semmelweis had started washing medical instruments as well as hands.

As outside interest grew, we begin to understand Semmelweis's silence. The hospital director felt his leadership was being criticized. He was furious. He blocked Semmelweis's promotion. The situation got worse. Viennese doctors turned on this Hungarian immigrant.

Finally, he went back to Budapest. There he brought his methods to a far more primitive hospital. Yet he cut death by puerperal fever to less than one percent.

He did more. He systematically isolated causes of death. He autopsied victims. He set up control groups. He studied statistics.

Semmelweis wrote a book on his methods in 1861. The establishment gave it poor reviews. Semmelweis grew angry and polemical. He hurt his own cause with his rage and frustration.

In 1865 he suffered a mental breakdown. Friends committed him to a mental institution. There -- as though to close the circle on his brief 47-year life -- he cut his finger.

Within days, he died of the very infection that'd killed his friend Koletschka -- that'd started him on his campaign. He died from the same kind of infection from which he had saved thousands of mothers.

The same year Semmelweis died, Joseph Lister began spraying a carbolic acid solution during surgery to kill germs. In the end, it was Lister who gave our unhappy hero his due. Lister finally said, "Without Semmelweis, my achievements would be nothing."

One of my favorite case histories of creative madness comes from just a little latter in the 19th century. This time we meet the Russian mathematician Georg Cantor, born in 1845. That was just as Mayer and Semmelweis were hitting their stride.

Cantor catches my fancy because of something that touched me when I was in grade school.Time magazine ran an article calculated to snatch my imagination. Someone proposed a new number called the googol -- a one followed by a hundred zeros.

Later I learned that the googol wouldn't be much help in counting real objects, because we'd be hard pressed to find that many real objects in the whole universe -- even atoms. But still, what curious child hasn't wondered where counting ends and infinity begins.

And we have good reason for asking about infinity. Every engineering student knows that infinity isn't just the end of numbers. If we ask how real systems behave when velocities, or time, or force become infinite -- if we ask about the character of infinity -- we get some very unexpected, yet useful, answers to questions about real system behavior.

Georg Cantor also wondered about infinity. He was born in Russia and was taught by a father who wouldn't let him become a violinist and then didn't want him studying mathematics, either.

But when he was 17, his father died. Cantor went on to finish a doctorate in mathematics in Berlin, while he was still only 22.

His career wasn't long. He burned out before he was 40 and spent the rest of his life in and out of mental illness. But what he did do was spectacularly important, and it arose out of an innocent counting question. He began with an idea we find even in mother goose. Do you remember:

1-potato, 2-potato, 3-potato, 4
5-potato, 6-potato, 7-potato, more. ?

Counting is like matching one set of things with another -- in this case, numbers with potatoes. Cantor asked, "Is counting all the infinite number of points on a line like counting all the points in a surface?"

To answer the question, he had to invent something called transfinite numbers -- numbers that go beyond infinity. And to do that he had to invent set theory. And set theory has become a basic building block of modern mathematics.

Cantor fell into an Odyssey of the mind -- a journey through a strange land. He had to overcome the resistance of his father, of the great mathematicians of his day -- even of his own doubts. When he was 33, he wrote:

The essence of mathematics is freedom.

To do what he did, he had to value freedom very highly -- freedom coupled with iron-discipline -- freedom expressed through the driving curiosity of a bright child -- freedom to think thoughts that looked like madness to other people -- freedom to pursue innocent fascination until it finally touched the world we all live in.

But what a price Cantor paid for his freedom! He lived his troubled life until 1918. And, perhaps, this is a happier story than the others I've been telling you. For he lived long enough to finally see set theory accepted.

In the end, Cantor was vindicated for his soul-scarring voyage of the mind. But he still calls to mind that young man who came to me in Philadelphia. "Can I be creative and still live a normal life?" It's out of fashion to be driven as these people were. The question I mean to put to you today is, "Do we accomplish as much in 1996?"

No epoch in human history ever provided scientific advances like those in the Victorian era. Mid to late-19th-century physics was a remarkable edifice and -- I tell you -- it is littered with stories of the kind I've been telling today. I'll finish with just one more such story. This is the story of Ludwig Boltzmann.

On September 5th, 1906, the then 62-year-old physicist Ludwig Boltzmann slipped a noose around his neck and hanged himself. Boltzmann, more than anyone, had shown us how to predict the behavior of gases by describing moving molecules.

But he'd always lived at poor peace with himself, and now he despaired of being understood. He probably committed that irreversible act because scientists attacked his ideas about irreversibility.

I need to explain that: When molecules collide, they bounce off one another's force fields with no friction, no energy loss. If time ran backward, the collision would reverse itself perfectly. But that sets up an absurdity:

Suppose you open an air tank and air molecules begin rushing out. Then suppose the motion of each molecule could somehow be reversed. Wouldn't history itself run in reverse? Wouldn't the molecules rush back into the tank?

That's as silly as it is logical. Time looks directionless on the molecular level, where motion is perfectly reversible. But nothing is so perfect in our larger scale of sensory awareness. Here in the visible world the past cannot be undone. Time's arrow flies from past to future. Air never flows back into the tank.

Boltzmann turned superb mathematics on the question. He showed how rules of averaging won't let such a reversal occur. In any large collection of molecules, disorder continues increasing after you reverse the motions. The gas must keep flowing out.

The trouble is, his math didn't say why reversed molecular motions won't reverse history. Classical physicists, who hadn't bought his molecular mechanisms, attacked Boltzmann.

Soon after he died, quantum mechanics took shape, and Heisenberg's Uncertainty Principle said it isn't possible to specify reversed motions accurately. In a quantum universe, Boltzmann's math still makes perfect sense, and the idea that you can reverse time is nonsense.

Boltzmann was brilliant, but he had a history of depression and mental illness. Now he couldn't answer his critics, yet he knew he was right. Here's something he said, and -- I think -- something that offers a key to the kind of mad intensity that gave us so much good science a century ago.

[theory, said Boltzmann] fills my thought and action ... no sacrifice for it is too much for me ... [it is] the content of my whole life.

Boltzmann's theory became the hill he chose to die upon. He despaired and committed his terrible irreversible suicide just as Einstein and the new breed of physicists were taking him very seriously. Had he waited just a little longer, he would've seen his genius triumph.

His belief faltered. Yet he'd put irreversible change in motion. Time's arrow was in full flight. His ideas continued moving outward and, by now, they have touched the whole of 20th-century physics.

Despite all that, Boltzmann died, deranged by his own intensities. One more casualty of his own huge creativity. I'll stop here and simply leave you with the question I offered when we began -- the question that young man asked me. I leave you with the question: "Is it possible to be creative and lead a normal life?"

---

SOME SOURCES

MacGregor, J.M., The Discovery of the Art of the Insane, Princeton: Princeton University Press, 1989, Chapter Eight, "Victorian Bedlam: the Case of Richard Dadd."

Allderidge, P., The Late Richard Dadd, 1817-1886, London: Tate Gallery Publications, 1974.

Flexner, J.T., Steamboats Come True, Boston: Little Brown, and Company, 1978.

Lindsay, R.B., Julius Robert Mayer: Prophet of Energy, New York: Pergamon Press, 1973.

Turner, R.S., "Mayer, Julius Robert," Dictionary of Scientific Biography, Vol. ??, (C.C. Gilespie, ed.) Chas. Scribner's Sons, 1970-1980. pp. 235-240.

Deickmann, F., "Vor 150 Jahren: Robert Mayer und die Erhaltung der Energie," Lufthansa Bordbuch, March, 1991, pp. 52 and 54.

Rukeyser, M., Willard Gibbs, Garden City, NY: Doubleday, Doran, and Co., 1942. (Poet Muriel Rukeyser begins her biography of the thermodynamicist, J.W. Gibbs, with an account of Mayer's recognition of the conservation of energy in the year after Gibbs was born.)

The Correlation and Conservation of Forces: A Series of Expositions, (E.L. Youmans ed.) New York: D. Appleton and Co., 1865.

Tyndall, J., Heat Considered as a Mode of Motion, New York: D. Appleton and Co., 1863.

Today, Mayer is once again largely forgotten in textbooks. We give most of the credit to Joule. However, the building block of Mayer's theory was that the conversion factor, J ft-lb/Btu, (or dyne-cm/cal or N-m/J) could be obtained from,

J = R/(Cp - Cv)

R is the ideal gas constant expressed in work units. Cp and Cv are the specific heats at constant pressure and constant volume. They're expressed in heat units.

Our textbooks simply write, R = Cp - Cv, and we presume that students know how to convert heat and work units. One problem with Mayer's work was that he had an accurate value of R, but Cp and Cv data were flawed. Therefore his value of J was far less accurate than Joule's.

We call the law of conservation of energy, the First Law of Thermodynamics. It says energy is conserved over its many forms -- potential, kinetic, thermal, and so on. Energy can neither be created nor destroyed. In 1850 another German, Clausius, codified the law in the words, "Die energie der Welt ist Konstant," where we take the word Welt to mean universe, not world.

Today, of course, we amend the First Law to acknowledge that matter and energy are also interchangeable in nuclear reactions.

Risse, G.B., "Semmelweis, Ignaz Philipp," Dictionary of Scientific Biography, (C.C. Gilespie, ed.) Chas. Scribner's Sons, 1970-1980. (See also, the Encyclopaedia Britannica article on Semmelweis.)

Dauben, J.W., Georg Cantor: His Mathematics and Philosophy of the Infinite, Cambridge, MA: Harvard Univ. Press, 1979.

Tien, C.L., and Lienhard, J.L., Statistical Thermodynamics, (rev. printing) New York: Hemisphere Pub. Corp., 1971, 1979. See especially, Section 12.3 on the Boltzmann H-theorem.

Coveney, P., and Highfield, R., The Arrow of Time: A Voyage Through Science to Solve Times Greatest Mystery, New York: Fawcett Columbine, 1990.

The theoretical apparatus that Boltzmann put in place was truly immense. He took James Clerk Maxwell's ideas as a starting point and showed how to describe macroscopic behavior from the behavior of molecular movement. He built the bridges that connect the kinetic theory of gases to continuum thermodynamics.

He directed that his tombstone have carved upon it his equation relating entropy to molecular probability. That reflected justifiable pride in his most important theoretical result.

The demonstration that I refer to in the text is his so-called H-theorem. It proves that increasing entropy is inevitable in any spontaneous process in an ensemble of molecules. In other words, the second law of thermodynamics is derivable from molecular considerations, with minimal assumptions.