The Three Wise Men

Two things I love to read about are math and history. Both subjects have intrigued me for as long as I can remember. Not only were those topics I was drawn to in school, taking extra classes in both that weren’t required for my degree, but I also searched the bookstores for good books on both areas of study. I was particularly keen on the combination of the two, the history of mathematics. Like regular history, the history of mathematics was a history of the men (and sometimes the women) who made the discoveries and how these ideas built on each other. Regular history is also about people and discoveries and great events and battles. History of math held all of that too, even the battles … on occasion.

I remember when I first found Bell’s “Men of Mathematics” in a college bookstore. I took it home and stayed up most of the night reading since I just couldn’t put it down. I’ve filled my bookshelves and bookcases with stories about mathematics and how it was developed and the personalities involved. It isn’t just math. Other technical topics are interwoven in the advancement as these great mathematicians were also great physicists and great astronomers and great engineers, but mostly great physicists.

Since counting is a natural part of mathematics, and putting things in order is the essence of much math, it is only fitting that I discuss the three greatest mathematicians of all time. This is a pretty settled list. There is no real controversy about which three are in the list I’m about to describe. Oh, some would disagree that an individual is the greatest mathematician because they consider him the greatest physicist. But that’s about the only disagreement.

Aristotle

We will start back in ancient Greece, the cradle of mathematics. Other ancient cultures developed advanced mathematics, at least to a degree, but it is the Greeks and their math that has had the greatest influence on modern mathematics and the development of that math through the twenty plus centuries following the ancients. This is largely due to the development of the axiomatic method by these historical thinkers. Names like Euclid and Pythagorus and many others are at the basic foundation of mathematics and, for over a thousand years, their writings were used as text books by “modern” students up until the sixteen or seventeen hundreds. In fact, you will find Euclid’s Elements still being used at the turn of the twentieth century.

But the first wise man that I will describe in this trio of greatness is Archimedes. He lived in the late part of the Greek empire, around the time that the Romans were conquering. In fact, he was killed by a Roman soldier. If you look him up you will find out that he is listed as a mathematician, physicist, engineer, inventor, and astronomer as he made significant discoveries in all of these fields. Among his advances in physics are the foundations of hydrostatics, statics [mechanics], and an explanation of the principle of the lever. He is credited with designing innovative machines, including siege engines and the screw pump that bears his name. Modern experiments have tested claims that Archimedes designed machines capable of lifting attacking ships out of the water and setting ships on fire using an array of mirrors.

Archimedes is generally considered to be the greatest mathematician of antiquity and one of the greatest of all time. He used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of pi. In so doing, he came within a hairs breadth of inventing The Calculus. He also developed a form of numeric expression that we now know of as “scientific notation.” That is where you give a set of numbers and a power of ten to show the overall magnitude. This method was used by Aristotle to estimate the number of grains of sand on a beach. This was a tremendous advancement since simple number notation of that time was very clumsy and held back advanced numeric thinking. He also defined the spiral bearing his name, formulae for the volumes of solids of revolution, as well as his ingenious system for expressing very large numbers.

Archimedes died during the Siege of Syracuse when he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting the tomb of Archimedes, which was surmounted by a sphere inscribed within a cylinder. Archimedes had proven that the sphere has two thirds of the volume and surface area of the cylinder (including the bases of the latter), and regarded this as the greatest of his mathematical achievements.

Some of his writings have survived to this day, but his fame was also spoken of in other ancient documents and we have a pretty good picture of his work even though he lived a couple hundred years before Christ. In The Sand Reckoner, Archimedes counts the number of grains of sand that will fit inside the universe. This book mentions the heliocentric theory of the solar system proposed by Aristarchus of Samos, as well as contemporary ideas about the size of the Earth and the distance between various celestial bodies. By using a system of numbers based on powers of the myriad, Archimedes concludes that the number of grains of sand required to fill the universe is 8×10⁶³ in modern notation.

In his Methods of Mechanical Theorems, Archimedes uses infinitesimals, and shows how breaking up a figure into an infinite number of infinitely small parts can be used to determine its area or volume. Archimedes may have considered this method lacking in formal rigor, so he also used the method of exhaustion to derive the results. As with The Cattle Problem, another short work by Archimedes, The Method of Mechanical Theorems was written as a letter to Eratosthenes in Alexandria.

There are many reasons that Archimedes is held as the greatest of all of the ancient Greek mathematicians and natural philosophers. His work covered many different areas of study and he came so close to inventing calculus, which is what our next great mathematician is remembered for. He came at the end of a long line of great Greek thinkers and one wonders if the Romans, great engineers but not good scientists, had not concurred Greece, what more inventions would these natural thinkers have discovered. Would there come a Greek even greater than Archimedes?

We can’t change history, so we’ll never know the answer to that question. Instead, following the rule of the Romans, the western world fell into a period of darkness in which little scientific progress was made. For over fifteen hundred years Archimedes was a shining star of invention. Then, in the sixteen hundreds, new lights began to appear. On Christmas day, 1642, this gift to the world of mathematics (and physics and astronomy and …) was born.

Isaac Newton

In June 1661, Newton was admitted to Trinity College, Cambridge as a “sizar” — a sort of work-study role. At that time, the college's teachings were based on those of Aristotle, whom Newton supplemented with modern philosophers, such as Descartes, and astronomers such as Copernicus, Galileo, and Kepler. In 1665, he discovered the generalized binomial theorem and began to develop a mathematical theory that later became infinitesimal calculus. Soon after Newton had obtained his degree in August 1665, the university temporarily closed as a precaution against the Great Plague.

Although he had been undistinguished as a Cambridge student, Newton's private studies at his home in Woolsthorpe over the subsequent two years saw the development of his theories on calculus, optics, and the law of gravitation. In 1667, he returned to Cambridge as a fellow of Trinity.

It was during these few months at home that Newton had his eureka when, as the tale goes, he saw an apple fall to the ground and realized that the moon was constantly falling around the earth, which led to his development of the theory of gravity and his three rules for motion. He perfected his mathematical method we now call calculus in order to solve the equations that he created.

When Newton published his ideas about light and color in Opticks, Robert Hooke, head of the British Royal Society, criticized some of his conclusions. Newton was so offended that he withdrew from public debate. The ensuing controversy turned the shy Newton off to the process of publication. His conclusions about light were eventually shown to be true, as Newton knew they were since he had proven it with mathematics and experiment, but the experience led him to keep the results of his work on gravity and calculus secret for nearly twenty years. At issue was whether light was a particle or a wave. Oddly, both men were right as it was later shown at the advent of quantum physics that light displays both qualities depending on the experiment. However, most of the controversy back in the 1600's had more to do with the poor quality of prisms and optics available to perform experiments, which made it difficult for others to reproduce the results that Newton reported.

Later, Newton’s interest in astronomical matters received stimulus by the appearance of a comet in the winter of 1680–1681, on which he corresponded with John Flamsteed and Edmund Halley, both Royal Astronomers. After the exchanges with Flamsteed and Halley, Newton wrote out a proof that the elliptical form of planetary orbits would result from a centripetal force inversely proportional to the square of the radius vector.

As the story goes, Halley inquired of Newton about a particular mathematical relationship that would result in the elliptical orbits described by Kepler, and Newton instantly responded. When asked how he knew, he said he had worked it out years before. Halley then encouraged his publication of these ideas and even financed the publishing.

Newton communicated his results to Robert Hooke and the Royal Society in De motu corporum in gyrum, a tract written on about 9 sheets which was copied into the Royal Society's Register Book in December 1684. This tract contained the nucleus that Newton developed and expanded to form the Principia, one of the most influential scientific texts ever written. The Principia was published in July 1687 with encouragement and financial help from Edmond Halley. In this work, Newton stated the three universal laws of motion that enabled many of the advances of the Industrial Revolution which soon followed and were not to be improved upon for more than two hundred years, and are still the underpinnings of the non-relativistic technologies of the modern world. He used the Latin word gravitas [weight] for the effect that would become known as gravity, and defined the law of universal gravitation.

In the same work, Newton presented a calculus-like method of geometrical analysis by “first and last ratios,” gave the first analytical determination of the speed of sound in air, inferred the oblateness of the spheroidal figure of the Earth, accounted for the precession of the equinoxes as a result of the Moon's gravitational attraction on the Earth's oblateness, initiated the gravitational study of the irregularities in the motion of the moon, provided a theory for the determination of the orbits of comets, and much more.

Newton made clear his heliocentric view of the solar system — developed in a somewhat modern way, because already, in the mid-1680s, he recognized the "deviation of the Sun" from the center of gravity of the solar system. For Newton, it was not precisely the center of the Sun or any other body that could be considered at rest, but rather "the common centre of gravity of the Earth, the Sun and all the Planets is to be esteem'd the Centre of the World", and this center of gravity "either is at rest or moves uniformly forward in a right [or straight] line."

Certainly his work in physics would classify him as the one of the greatest of that branch of science, but pure mathematicians memorialize him for this invention of calculus, although his delay in publication allowed another contemporary, Gottfried Wilhelm von Leibniz, to independently discover the important mathematical method. This led to a long fight over priority which actually set British mathematics back since Newton’s notation was not as clear as the notation invented by Leibniz, and the British used Newton’s notation as an act of support.

Even the history of something as dry as mathematics has its controversy and national pride and prejudice.

Perhaps more important than all his fabulous discoveries was his impact as a sort of mentor to the enlightenment. It was Newton's conception of the Universe based upon Natural and rationally understandable laws that became one of the seeds for Enlightenment ideology. He received fortune and acclaim and even a civil service job and a knighting in response to his great work.

In his own words, he said, “I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.”

Carl Freidrich Gauss

Gauss, often called the “Prince of Mathematics” was also busy in other disciplines including physics and astronomy. Born at the time of the American Revolution, Gauss anchored the first half of the Nineteenth Century, a century that formed the foundation for all the wonderful discoveries to come in the Twentieth. He contributed significantly to many fields, including number theory, algebra, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics. He is honored in physics by a naming a unit of magnetism, the “gauss,” after him.

Although the mathematics discovered by the other two great mathematicians may be familiar to most high school graduates, even if they never took a course in calculus, Gauss’ work is more advanced and so average students not involved in advanced math may not have be experienced with the areas that he advanced.

Sadly one of Gauss’ principles was “few but ripe.” Therefore he only published ideas that he had fully developed leaving us to wonder at further ground breaking and original ideas he hinted at in letters, but never published. Mathematics would have gained greatly from even the random thoughts of this mathematical prince. He was so significant in the work that he did publish, one can only ponder what other gems of mathematics were not yet ripe in his genius, so he withheld any hint of his insights.

For the benefit of the non mathematical reader, I won’t go into the details of his discoveries except to note the number of modern day prizes, buildings, and astronomical and geological objects that carry his name and reputation. For the mathematical reader, there is no mystery why this modern mathematician is listed with the other two greats.

He supposedly once espoused a belief in the necessity of immediately understanding Euler's identity as a benchmark pursuant to becoming a first-class mathematician. I’ve written about that identity which I call the "most beautiful equation in the world," a view often expressed by other mathematicians. It is most interesting that Gauss thought of that equation as a touchstone for measuring math prowess.

The Most Beautiful Formula in all of Mathematical Thought

I have to admit that I had to study the identity, and I’m still amazed how it shows that an exponential with an imaginary number is somehow equivalent to rotation or how transcendental and irrational numbers can combine with imaginary numbers to produce the most basic integer. I now understand how, but — believe me — it wasn’t, nor is it now, intuitive. I still struggle to understand that damn and wonderful equation, and I run through the transformation in my head from exponential to trigonometric identities anytime I consider it. It is always something I have to go through step by step, rather than leap to the conclusion.

I think Gauss was correct. I will never, ever, ever be a world-class mathematician. All I ever will be is someone scratching the surface of the concepts invented and conquered by these three wise men and all the other wise men and women of science that have come before or since. In all reality, I don’t think I’ll ever get my Ph.D., nor would I have gotten it when in my twenties. I just don’t think I’m good enough. That realization is not going to stop me. I’ll give it my best, using every trick of learning and understanding that I’ve got stuffed up my sleeve. I’ll give it the “old college try.”

These guys are my heroes and my mentors. I will try … try my best … but I don’t guarantee the results. After all, as these three men demonstrate, my sights are set very high. I may miss the target all-together. Yet, I too, feel like a small boy, a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me. I may not comprehend that great ocean, but I see it out there … and it excites me to just look out at it. I don’t have what these great, or most great, scientists have, but I do match them in desire. I get it! … I may not understand it, … but I get it!!

Space the Final Frontier

There were so many unknowns and technical problems that had to be solved in the early days of space flight. One thing that no one really knew about was the effects of weightlessness. We’ve all seen the old black and white movies from the fifties … the sci-fi and the thrillers that showed astronauts and pilots spinning around in a centrifuge. That was a way to simulate the acceleration of rockets and jet planes and the extra pressure of acceleration acting as pseudo-gravity, which was measured in “g’s.” Special suits were developed to keep pilots from blacking out as the extreme maneuvers of high performance aircraft would drain the blood out of the brain leading to blackouts and crashes.

But it was much harder to produce weightlessness here on the earth. Scientists and engineers did devise a system of a large plane flying a hyperbolic loop across the sky that could produce weightlessness for about half a minute. The effect was very similar to what a person feels for about half a second on the top of the arc when swinging on a playground swing. This allowed some experimentation and training of personnel, but duplicating the hours and days of weightlessness that would occur in space was not possible without actually entering orbit.

Even the fact that spacecraft would experience weightlessness in an orbit around the earth was poorly understood by the general public. I’ve read several old science fiction novels that didn’t understand the basic physics of weightlessness and assumed the gravity of the earth or the moon or mars would affect the astronauts. So why are people and things weightless when in orbit around the earth? Obviously they are not beyond the reach of the earth’s gravity. After all, that force holds the moon in orbit around our globe.

It is not about being out of the reach of the force of gravity, but rather being in “free fall.” Free fall means falling without a force acting upon your body. If you sky dive from an airplane, you are falling, but the force of the air against the body slows you down and you feel that “acceleration” as weight. If you were falling in open space, with no air to slow you down, then you would not feel gravity. That is what an object in orbit does. It is falling around the earth and there is nothing to give weight.

Reentry into the atmosphere, however, does cause weight because the friction of the air is slowing down the space craft and that is what the centrifuge training was for … that and the launch when gravity is magnified by acceleration instead of canceled out by freely falling. So that is why voyagers in space have no weight except when undergoing changes in velocity, called acceleration, as rocket motors or air friction apply forces to the spacecraft and the occupants.

Since most of a space mission and even a voyage to the moon are done with the engines off and just floating, weightlessness is the normal condition of most of space flight. Not only did weightlessness have an effect on the people, their physiology and movement, but it affected the equipment taken into space too. Besides the often portrayed floating of things in the space craft or the need for squeeze bottles to drink liquids, the lack of gravity had a profound effect on the design of some equipment, and the physics of operation. Weightlessness didn’t have an effect on the flow of electrical currents and electronic circuit components such as transistors or switches, but it had a profound effect on the certain devices.

For example, engineers know that the standard meltable-link fuse is a simple, passive, reliable, and very effective way to protect against damage due to short circuits and overloads; it's normal and wise practice to use these on power and signal lines. Their operating principle is simple: when excess current flows through the fuse, the link heats and melts, and then the molten blob falls away, breaking the circuit and current path.

Whoops … the word "falls" is the key to why a fuse won’t work in the weightless world: there is no force (such as gravity) to cause the blob to go anywhere. It will melt and then stay in place, making and breaking the circuit intermittently. To operate reliably, “spring loaded” fuses were required. That way, when the link melted, the spring would pull the connection apart stopping the current flow.

Another counterintuitive situation has to do with cooling, an omnipresent concern for electronic and other systems. In the vacuum of space, of course, there is no option of conduction or convection cooling; only radiation cooling is possible. This complicates the design of satellites and must be carefully factored into the thermal planning and system design.

But what about the Space Shuttle, Skylab, or the International Space Station, all of which have a "normal" air atmosphere? That should allow convection cooling of the electronics as heating air rises, you might assume.

Whoops, wrong again … another mistaken assumption: the word "rises" has no meaning in this weightless environment. What happens is that the heated air just stays where it is, accumulating around the heat source and acting as a warm — and therefore destructive — blanket. So forced-air or active fluid-based cooling is needed, since passive convection-only cooling does not happen.

Let me explain these last paragraphs and the physics of heat transfer for you non engineers. There are three ways that heat moves from one point to another. The first is “radiation.” That’s how heat gets to us from the sun. The energy that we describe as heat moves across free space via photons. In other words, the heat is in the light (or more accurately, the radiation) from the sun. That’s why shade feels so good on a hot and sunny summer day.

Heat also moves by “conduction.” That’s why a metal handle on a pot on the stove gets hot. Heat is actually the vibrational movement of molecules. The fast moving (or “hot”) molecules bang into nearby molecules making them “hot” too. Metals are very good at conducting heat, while other materials resist this motion more. That’s why some pot handles are made of plastic or wood which doesn’t conduct heat as well. A hot pad is also a poor conductor of heat as is styrofoam. Now you can understand everything form home insulation to coffee cup design is premised on this physical phenomenon called conduction.

The third method of heat transfer is “convection.” It is based on the fact that “hot air rises.” You know … what makes a hot air balloon lift off. The reason is that hot air (or any hot fluid from air to water to oil to …) is less dense than the material when cool. If it is less dense, then gravity forces the more dense fluid “down,” thereby forcing the hot fluid “up.” That’s what is working in your old fashioned steam or hot water radiators. That’s also why it is hotter on the second floor of a two story house and quite cool in the basement. (Convection plus the insulation effects of the ground and solar radiation … it is a combination of physics.)

Convection is what makes the wind blow and thunderstorms and tornadoes and hurricanes and most of the weather effects. Convection is also how a “heat sink” works. Heat sinks are large metal devices that conduct the heat away from the transistor or I.C. or other electronic device. But then the metal fins common on a heat sink heat up the nearby air which floats away by convection, thereby cooling the device. So heat sinks don’t work in weightless air, since the heat is not carried away.

The lack of convection in a weightless condition had some advantages. The lunar spacecraft was a rather cold environment with the hundreds of degrees below zero space just outside the metal walls, the interior was a bit chilly. Yet the astronauts slept very comfortably because a thin layer of warm air from the heat of their body would wrap around a sleeping astronaut like a transparent sleeping bag and keep them warm all night. Normally, convection would disperse this heated air, but in the still air of the weightless spacecraft, the layer clung to the body keeping the sleepers quite comfortable.

Almost every small action, perspective, and operating mode we know on Earth has the presence of gravity effects as an unspoken, "given" assumption — and how its absence in space make these standard operating concepts almost meaningless. It's tough on equipment, and even worse on humans, with bizarre micro- and macro-consequences due to the absence of gravity impact as a pervasive force.

Another example was the simple “fuel gauge” designs on the lunar lander. Just like an automobile gas tank design, the “gas gauge” works with a float in the tank and gravity to force the liquid fuel to settle in the bottom of the tank. As the lunar lander approached the moon’s surface, only when the engines were firing did the fuel gauge work. This led to very stressful moments as the first lunar lander approached the moon’s surface and nearly exhausted the fuel in last minute maneuvering to avoid large boulders. NASA was counting down the fuel supply based on telemetry from the space craft, but they weren’t sure of the amount remaining. They were down to 15 seconds of fuel left when the “Eagle Landed.” At least that’s what their instruments showed, but they were very worried the readouts weren’t accurate due to problems making these devices work in space and during a weightless free fall toward the moon.

To the early NASA scientists and engineers, they had the responsibility to design reliable space craft that would sail into unknown waters. Truly dragons were there. Through a process of “baby steps,” and incremental advances, the staff and crew learned how to build craft and train astronauts that could operate in space. (Even though, as the picture above shows, space is not good for hair styles.) Now we have the perspective of not only the flights to the moon, but the months and years of survival in orbit in the International Space Station. Now we know from experience how to build devices to work in the weightlessness of space. At first we had to figure it out in our heads before our actual experience. The reason that all early astronauts were “test pilots” is that was exactly the job they were taking on.

Ballroom Dancing

When I first moved to Denver, I was working for Channel 9 on Bannock Street. I was hired since I had a First Class Commercial FCC license, but I was really just the station's gopher. “Hey Mickey, why don’t you go-fer coffee.” “Go-fer some RG-8 cable.” “Go-fer some hamburgers.” That’s proof I wasn’t performing a technical job. Only one in three requests was for anything to do with the broadcast industry.

Still, it was a good job and one thing I got to do a lot was “go-fer” the airport and pick up some celebrity or celebrity “wanta-be.” The station had a black Lincoln Town Car … not a stretch limo … but a limo in any case. I would go pick up people that were in town for the morning show or an afternoon interview show or whatever. If it was a large party, I drove a small bus, but mostly I was tooling around town in the black Town Car and they even let me take it home since I only had a motorcycle back then.

One time I picked up sixteen beauty queen finalist or semi-finalist or quarter finalist or whatever. They were on a tour across country traveling to Los Angeles for the pageant's final event and doing interview shows on local TV to increase the contest’s ad revenues. I was in the business. I understood the process. There was one who really caught my eye: her smile. her eyes. her hair; she was a beautiful blond … hello … it’s a beauty contest! Now at that point in my life there was only three things I was truly interested in: girls, girls, and … of course … GIRLS. So I planned my smoothest move on her.

You see, when I was a young lad, my mom used to send me to dance lessons. (How embarrassing.) She was a very classy lady and insisted that I learn BALLROOM DANCING. But now, what had once been a fate worse than death for a young boy only interested in baseball and fishing, I now used to my personal, girl catching, advantage. I had a white tuxedo, all custom fit to my six foot-two, 150 pound frame. (Yeah, I was a lot thinner back then … and a lot taller.)

I had found the greatest ball room dancing ballroom in all of Denver, the Ritz-Carolton. Whether is was the Big Fish Combo or Joey Thomas Big Band, I could knock them dead with my smooth moves. So I asked the young lady if she would like a pleasant night out on the town. She agreed and I told her to wear her grandest gown. (I knew they had these fancy dresses since it was part of the pageant.) I picked her up at eight in the black Town Car and me in my white Tuxedo.

I could tell right away she was impressed by my unique style and attitude and soon we were on the dance floor knocking them dead. She was really a good dancer too, although it seemed all natural to me since I’d be surprised if there was any other soul in the whole United States in the Sixties that had studied the esoteric footwork my mom had forced down my throat.

Now you young bucks out there familiar with the more common method of wooing a lady and those who quote poetry such as “Candy is dandy, but liquor is quicker,” you really don’t get it. Ballroom dancing, fancy clothes, and … champagne. Now that’s a drink straight from France, the loving capital of the world. It tastes like soda pop, but — believe me — it’s got its kick. And the ladies are so unsuspecting. Of course, yours truly imbibed freely too. After all, it was a party.

As we skipped the light fandango and whirled round and round on the floor I soon started to feel the bubbly as my head began to float, the room seemed to fly apart, and I felt decidedly nauseous. I had just got out of the service and my chosen branch was the Navy, so seasickness was something I was very familiar with. She, however, didn’t seem to be affected at all. We were such a striking couple that most the other dancers had stopped dancing and stood in a circle watching us twirling about the floor. They were all clapping and shouting encouragement. The whole room was throbbing, or maybe it was just the drink. No one wanted us to quit, but I had to go sit down.

I took her back to our table and called out for more champagne, and the waiter brought a tray of those classic stemmed glasses. Things were going exactly to plan when an old buddy of mine showed up. His name was Steve Miller and he had also just separated from the military, but he had been a Marine and served in Vietnam, very tough duty. I was quite confident and asked him to join us even though I realized he would be a rival in this carefully planned seduction, but I thought my plan was flawless and working so well I decided to spice up the evening with his presence.

Right away he started talking about his war experiences as I downed another glass. My date seemed enthralled. She had her elbows on the table and her chin in her hands and was staring at Steve intently as he told his stories. It was a gruesome description of death and dying and I could tell she was affected as the blood drained from her face leaving her pale as a ghost. What I didn’t realize was that the stories were connecting with her as the war hero wrought his tale.

I had planned so carefully and it seemed that everything was going so well. Tomorrow the sixteen contestants would leave for L.A. and, if I played my cards right, she would be mine for the night.

She said something about the truth being plain to see. I thought my eyes were wide open, but they might as well have been closed. You can guess the ending. She left that night with the Miller and I wandered home, slightly buzzed, and without a companion. As I sat at my kitchen table drinking coffee to recover my senses, I thought about the evening and penned a short poem, and then laid down on the couch and drifted off to sleep.

Shakespeare said, “If music be the food of love,” I thought, “then laughter is it’s queen.” I rose early the next morning and drove down to the station. Immediately I was sent with the van out to the airport to pick up a British band called the “Paramounts.” They were in town hawking an unsuccessful album. They’d had a small hit with their cover of “Poison Ivy,” and were in town seeking both fans and inspiration.

I had one of those throbbing heads that is the downside of the French grape and suggested we stop at a local watering hole for a Bloody Mary. They’d been on the plane all night and were most willing to join me for a drink or three. The bar was deserted at ten o’clock in the morning and there was a band set up on stage. Soon the rockers were up there playing and singing. I joined them and fired up the Hammond Organ and then thought about the lyrics I had written the night before. As the band took a break to replenish their drinks, I started playing little arpeggios on the organ and singing the lyrics I had written the night before. I started with a simple C - F - G, the simplest progression ever in the easiest key there is on a keyboard. Then I added some related minors, but still stuck with only the white keys. Soon the drummer joined me, but the rest just listened to the cool lyrics and the simple organ sounds.

When I had finished the musical composition before their very eyes and ears, they all laughed, applauded, finished the drinks, and headed for the studio. I had other duties that day and didn’t see them before they left.

Imagine my surprise when, on the radio a few months later, I heard … not only my words and melody, but even the simple organ centric production. It became a big hit for them, although they had changed their name to something they got from a cat. Most people misspell their name to this day and they went on to great success playing with large orchestras. Who knew that their start was a young man in a tux trying to woo a gal with ballroom dance. The truth is strange to see.

Does it Matter?

I saw a joke the other day: “Never believe atoms. They make up everything.” A fun play on words and basic science. But, is that true? Do atoms make up everything?

The answer is not well understood, but, according to modern science, it is a resounding NO. Since the 90’s we’ve realized that the normal matter made up of atoms in configurations classified as elements do not make up everything. In fact, they only make up about 4% of what we now know as the composition of the universe.

I’ll bet you find that statement a bit unbelievable. After all, the only things we know of here on this earth, or, as far as that goes, in our solar system and even our galaxy, are made up of various combinations of the little more than one hundred known elements and those atoms are all made up of protons, neutrons, and electrons.

Sure, we know about other atomic and sub-atomic particles. We know that protons and neutrons are made up of finer particles called quarks and we know there are other particles that exist such as mesons and neutrinos and a whole zoo of high energy particles. But there is something else out there, at least according to the latest measurements and theories, and we don’t know what this other stuff is.

Matter is a poorly-defined term in science. The term has often been used in reference to a substance or a particle that has rest mass. The rest mass, also called invariant mass, intrinsic mass, proper mass, or simply mass, is a characteristic of the total energy and momentum of an object that is the same in all frames of reference.

Matter is used loosely as a general term for the substance that makes up all observable physical objects. The idea that matter was built of discrete building blocks, the so-called particulate theory of matter, was first put forward by the Greek philosophers Leucippus (~490 BC) and Democritus (~470–380 BC). Democritus actually coined the term “atom.” He named the atom after the Greek word “atomos,” which means that which can't be split. The cool part is that he was right, well 90% right.

A few thousand years later, Albert Einstein showed that ultimately all matter is capable of being converted to energy (known as mass-energy equivalence) by the famous formula E = mc², where E is the energy of a piece of matter of mass m, times c², the speed of light squared. As the speed of light is 186,282 miles per second or, in metric terms, 299,792,458 meters per second, c² is a very large number and, therefore, a relatively small amount of matter may be converted to a very large amount of energy. Einstein’s theory was proven by the explosive power of the atom bomb.

Matter should not be confused with mass, as the two are not quite the same in modern physics. For example, mass is a conserved quantity, which means that its value is unchanging through time, within closed systems. However, matter is not conserved in such systems, although this is not obvious in ordinary conditions on Earth, where matter is approximately conserved. Still, special relativity shows that matter may disappear by conversion into energy, even inside closed systems, and it can also be created from energy, within such systems.

Scientifically, the term "mass" is well-defined, but "matter" is not. Sometimes in the field of physics "matter" is simply equated with particles that exhibit rest mass (that is, cannot travel at the speed of light), such as quarks and leptons. However, in both physics and chemistry, matter exhibits both wave-like and particle-like properties, the so-called wave–particle duality. It is difficult to understand the tiny world of atoms and particles, and it doesn't behave quite like things we experience in our life such as tables, chairs, and a glass of water. Our understanding of the makeup of the known matter is limited and mostly consists of sets of equations. But we do know about the matter around us, the kinds of atoms, and how the basic laws affect these objects.

We know a lot about the various elements and have organized them in the Periodic Table that is familiar to all students of chemistry and physics. We've worked out rules for the behavior of matter and energy and can explain common experiences such as why it rains or why the moon doesn't crash into the earth or how to build radios and atomic power plants to provide electricity to light up our lives. We are surrounded by gadgets that demonstrate our ability to manipulate and make matter work for us on an everyday scale in our homes, our highways, and our space ships. But now we think there is something else … out there! Something that doesn't fit the Periodic Table. Something that doesn't obey some of the laws we thought were universal.

Look up at the night sky. Our universe may contain 100 billion galaxies, each with billions of stars, great clouds of gas and dust, and, as recently discovered, there are planets and moons and other little bits of cosmic flotsam revolving around those stars. The stars produce an abundance of energy, from light to radio waves to X-rays, which streak across the universe at the speed of light.

Yet everything that we can see is like the tip of the cosmic iceberg — it accounts for only about four percent of the total mass and energy in the universe. Astronomers have discovered something new that they call "dark matter" while studying the outer regions of our galaxy, the Milky Way.

The Milky Way is shaped like a disk that is about 100,000 light-years across. That is, it would take light 100,000 years to travel across it. The stars in this disk all orbit the center of the galaxy. The laws of gravity say that the stars that are closest to the center of the galaxy — which is also its center of mass — should move faster than those out on the galaxy’s edge. This is based on Newton’s basic laws of motion. Just as a spinning ice skater will spin faster if she pulls in her arms, the inner planets of the solar system orbit the sun faster than the outer planets. The same response to gravity in the solar system should be seen in the revolving Milky Way galaxy.

Yet when astronomers measured stars all across the galaxy, they found that they all orbit the center of the galaxy at about the same speed. This suggests that something outside the galaxy’s disk is tugging at the stars. Since the source of this tugging force or gravity does not show up on our instruments, we call it “dark matter.’

Now large clouds of dust or other particles that do not emit any energy or light might be invisible to our telescopes and other instruments, but radiation and light from other galaxies shines through this dark matter and does not cause it to emit any energy that we can record. The clouds of gas and other particles that we know exist in space would not act this way, so this appears to be a new type of matter exerting a gravitational pull, yet not emitting any radiation or interacting with the radiation that passes through it … “dark matter.”

We know of particles, such as the neutrino, that are not effected by other particles or radiation. But neutrinos have no mass, so they won’t create any gravity. We don’t know of any particles with mass that are not affected or excited by energy passing by them. This dark matter does not behave like anything we know of now.

Calculations show that a vast "halo" of dark matter surrounds the Milky Way. The halo may be 10 times as massive as the bright disk, so it exerts a strong gravitational pull. We can’t “see” it, but we can definitely observe the effect of this dark matter.

The same effect is seen in many other galaxies. And clusters of galaxies show exactly the same thing — their gravity is far stronger than the combined pull of all their visible stars and gas clouds.

Further studies in the last twenty years have found another odd thing in our universe. We know the galaxies in our universe are flying apart. The big bang theory explains this expansion of the universe as the result of the initial velocity from this explosion that literally created our universe. However, the effect of gravity, especially when the dark matter gravity is added in to the calculation, should be slowing down this expansion.

However, it does not appear to be slowing down, but rather increasing in velocity. To explain this phenomenon, scientists have theorized the existence of some unknown repelling force that they have named “dark energy.”

Now don’t get hung up on the name. It does not mean that this stuff, whatever it is, is “dark” or “energy.” It is just a name in contrast to the “dark matter” term. You see, gravity is always attractive. There is no anti-gravity. Dark matter acts like ordinary matter and attracts things. This “dark energy” is just the opposite, it repels matter.

Further, by observing the motions and rotations of the galaxies and bodies in our universe, it is estimated that universe is made up of 4% normal matter, the stuff we experience every day in the laboratory, and 21% dark matter and a whopping 74% dark energy.

All of this is based on very recent discoveries and scientists are scrambling to produce theories to explain this and experiments to verify the theories. There is very little evidence of the existence of both dark matter and dark energy, but there is definitely something going on that doesn’t fit our current understanding.

So the use of the term “dark” for these two unknown substances is quite appropriate. It may be that our theory of gravity needs a major overhaul and that some new theory would explain all this behavior without postulating the existence of these unknown, “dark” substances. We only assume these things exist because the behavior we observe with our telescopes and instruments does not fit our current understanding. It is possible it is just our current understanding that is in error.

We also know that space itself — areas where nothing exists — are actually boiling and teaming regions of the creation and destruction of particles. Our quantum theories include the idea that there is an underlying background energy that exists in space throughout the entire Universe called “vacuum energy.” One contribution to the vacuum energy may be from virtual particles which are thought to be particle pairs that blink into existence and then annihilate in a timespan too short to observe.

They are expected to do this everywhere, throughout the Universe. Their behavior is codified in Heisenberg's energy–time uncertainty principle. Still, the exact effect of such fleeting bits of energy is difficult to quantify. So this is another possible explanation for the observed behavior.

It may be that another “Einstein” is working in some menial job like a patent clerk at this very moment, and he (or she) is about to publish a paper that will bring light to this darkness and revolutionize our understanding exactly like that brilliant young man with the crazy hair did about one hundred years ago.

Now do you understand why I love this physics stuff? The wonder; the excitement; the exploration; the discoveries; it’s out there for us to find and understand. The wonders of creation are so far beyond the understanding of man. That is our great challenge. To try to solve the mysteries of the universe. Don’t worry, there’s plenty more mystery to solve. The universe seems to have an unlimited amount of mystery for us to discover.

Montana Story

I was born in Montana. As a very young child my grandmother told me of the local Indian legend. It is a tale told to her by her parents on their ranch up near the Big Snowy Mountains in the Judith Basin of Central Montana. There was this beautiful and pristine lake high in the mountains that our family would often visit to enjoy the scenery, picnic, and possibly do a little boating or water skiing.

It was a small lake in a most picturesque location at the foot of heavily wooded mountains that came right down to the shore on two sides. There was a small flat valley area on either end of the lake and a gravel road led to one side where there was a small campground and picnic area.

She told me that hundreds of years before the white man came, Indian tribes would camp at the lakeside. There was game in the mountains and fish in the lake and plenty of firewood for the campfires.

There were two tribes that set up camp at opposite ends of the lake. They were at war with each other, but agreed to a peaceful coexistence amongst the pines at the water’s edge. But no one from one camp could go near the other for fear for their very lives. And that was how it stood year after year. People in one camp could look across the lake at the other side and see the campfires of their sworn enemies, but there was no contact.

Then, one spring, a young brave from one of the camps was staring across the lake and saw a young Indian maiden in the other camp. He was immediately taken by her great beauty and he soon realized that she was looking back at him since she too was struck with that phenomenon they often call “love at first sight.”

And so the summer passed. Each day the two lovers, and they were lovers although they had never touched hands nor spoken, would stare longingly across the waters at the other one and their eyes were filled with love and joy at seeing their beloved standing there.

But they could never meet for, like Romeo and Juliet, their warring families would never allow them to be together, much less embrace and marry. Toward Fall the pull of desire became so strong and it completely overwhelmed the Indian brave. So the young man jumped into the water and began to swim across the cold lake. His beloved saw him dive into the lake and begin swimming, and she, too, immediately leaped into the cold waters and started to swim out to meet him.

This attracted the attention of all the Indians in both camps and they ran to the shore of the lake to watch the two lovers swimming toward each other. Finally they met, exhausted, at the middle of the lake. They wrapped their arms around each other in a long awaited embrace. But the swim had been long and tiring and the cold water had sapped their strength, so they slowly sank below the waves in each other’s arms and drowned.

This scene, witnessed by both families, drove them to declare peace between the tribes and they even named the lake in the honor of the two lovers who gave their lives for that one embrace: Lake Stupid.

Route 66

History doesn’t have to be hundreds of years old to be “history.” In school you learn about battles and kings and nations and wars. But history can also be fifty years ago, during the life time of those still here to tell of it.

You don’t always learn history out of books or in school. There is history that those around you can describe. Experiences and lives that were lived before the advent of smartphones and iPods and Interstate highways. History that is decidedly American and a history that is the basis and foundation for what we are today as a nation.

The story of roads is as ancient as men and women who wanted to move from one place to another. Roads evolved out of paths and routes that carried early commerce and travel and armies. In the United States the rough paths that headed west became improved roads for horse and wagon.

Then, in the last one hundred years, the automobile took over the job of transporting goods and people and roads became even more important to our way of life. In 1908, Henry Ford introduced his low-priced, highly efficient Model T. Its widespread popularity created pressure for the federal government to become more directly involved in road development.

With rural interests adding to the battle cry of "Get the farmers out of the mud!" Congress passed the Road Act of 1916. It created the Federal-Aid Highway Program under which funds were made available on a continuous basis to state highway agencies to assist in road improvements. But before the program could get off the ground, the United States entered World War I.

Things took off again in the Roaring 20s when the Bureau of Public Roads (BPR) was authorized by the Federal Highway Act of 1921 to provide funding to help state highway agencies construct a paved system of two-lane interstate highways and the "US" highway was born. During the 1930s, BPR helped state and local governments create Depression-era road projects that would employ as many workers as possible.

When America entered World War II in 1941, the focus turned toward providing roads that the military needed. After the war, the nation's roads were in disrepair, and congestion had become a problem in major cities.

In 1944, President Franklin D. Roosevelt had signed legislation authorizing a network of rural and urban express highways called the "National System of Interstate Highways." Unfortunately, the legislation lacked funding. It was only after President Dwight D. Eisenhower signed the Federal-Aid Highway Act of 1956 that the Interstate program got under way.

These Interstate highways now criss-cross our land and wrap around our cities. They are a boon to cross country travelers as well as city commuters. As engineering and road design improved, these massive public building projects have become more sophisticated and safer as they carry happy vacationers and tired commuters on their way across the nation.

However, before the Interstate system was built, there were already great highways that connected states. Especially in the sparsely populated west, these roads became legendary as they carried vacationers to far off destinations as well as newly weds to new homes. Goods and services flowed along these early arterials and establishments sprung up on the side of these roads to provide food and lodging.

This was the start of the conversion from “hotel” to “motel” and from “restaurant” to “drive in.” The most famous of these early by-ways was Route 66. This U.S. highway stretched from Chicago down and across the southwest clear to Los Angeles, a distance of nearly twenty-five hundred miles.

U.S. Route 66 (US 66 or Route 66), also known as the Will Rogers Highway and colloquially known as the Main Street of America or the Mother Road, was one of the original highways within the U.S. Highway System. Route 66 was established on November 11, 1926 — with road signs erected the following year. The highway, which became one of the most famous roads in America, originally ran from Chicago, Illinois, through Missouri, Kansas, Oklahoma, Texas, New Mexico, and Arizona before ending at Santa Monica, California.

Route 66 served as a major path for those who migrated west, especially during the Dust Bowl of the 1930s, and it supported the economies of the communities through which the road passed. People doing business along the route became prosperous due to the growing popularity of the highway. It is along the shoulders of this road and many others like it that modern Americana was born. This was the womb for the “motor-hotel” and the casual diners and “drive in” eateries.

Soon it was immortalized in song and verse. “Get your kicks on route 66.” It became a popular song and rhythm and blues standard, composed in 1946 by songwriter Bobby Troup. It was first recorded in the same year by Nat King Cole, and was subsequently covered by many artists including Chuck Berry in 1961, The Rolling Stones in 1964, Depeche Mode in 1987, Pappo's Blues in 1995, John Mayer in 2006, and Glenn Frey in 2012. The song's lyrics follow the path of the highway.

The highway later spawned another hit song by Nelson Riddle, the instrumental theme song to a new television show named after the highway. Route 66 was a TV series in which two young men traveled across America in a Corvette. The show ran weekly from 1960 to 1964.

In an updated replay of On the Road, a novel, not a song, by Jack Kerouac, the two young protagonists traveled across America working odd jobs and experiencing life in the the early 60’s. Although the series title named the famous road, and was shot on location in many towns and cities across America, yet only three of the over 100 episodes actually occur on the namesake highway.

The show was a hybrid between episodic television drama, which has continuing characters and situations, and the anthology format, in which each week's show has a completely different cast and story. The two stars often played supporting roles to the differing main characters each week. (In fact, there were three stars. One of the original actors became ill and was replaced by a new character in the final seasons.)

This semi-anthology concept, where the drama is often centered on the guest stars rather than the regular cast, was carried over from series creator Stirling Silliphant's previous drama Naked City (1958–1963). Both shows were recognized for their literate scripts and rich characterizations. The open-ended format, featuring two roaming observers/facilitators, gave Silliphant and the other writers an almost unlimited landscape for presenting a wide variety of dramatic (or comedic) story lines. Virtually any tale could be adapted to the series. The two regulars merely had to be worked in and the setting tailored to fit the location.

It was in the earlier Naked City, well known for its location shooting on the actual streets of New York, that led to the idea of a location series shot all over the United States, and even some locations in Canada. Route 66 is one of few series in the history of TV to be filmed entirely on the road.

What may not be apparent to young people today is just how diverse the various areas of our country were even as late as the 1960’s. This show was filmed at a time when the United States was much less homogeneous than it is now. People, their accents, livelihoods, ethnic backgrounds, and attitudes varied widely from one location to the next.

The scripted characters reflected a far less mobile, provincial society, in which people were more apt to spend their entire lives in one part of the country. Similarly, the places themselves were very different from one another visually, environmentally, architecturally, in goods and services available, etc. Stars Martin Milner and George Maharis mentioned this in 1980s interviews. "Now you can go wherever you want," Maharis added by way of contrast, "and it's a Denny's."

The show would often showcase local attractions, hotels, restaurants, clubs, parks. This was an early glimpse of a nation moving to wheels of just what sights awaited them around the next curve in the road. It is a lost time, a glimpse still provided by reruns of this drama on the nostalgia TV stations. Appropriately shot in black and white, the series still stirs feelings in this old character. I see the cars and the buildings and the signs I grew up with.

Now, as I cruise the highways and by-ways of this great land, I see the same signs and hear the same accents. Only the mountains and rivers seem to change. The rest of America has been transformed into one, homogenous, and colorful commercial world. It doesn’t matter if you’re in Tulsa or Toledo, Billings or Boston, Los Angeles or Louisiana, Miami or Montana. It all looks the same. It all sounds the same. It all tastes the same.

One of the legacies of the Route 66 show left behind is a dramatic and photographic portrait of early 1960s America as a less crowded and less complicated era — if not a less violent one — in which altruism and optimism still had a place. That place was filled by two young men who seemed to represent the best in us, the willingness to stand up for the weak, old-fashioned values like honesty, and the physical courage necessary to fight in their own and others' defense. In their role of wanderers, they appeared to be peaceful rebels who rejected, at least for a time, material possessions and the American dream of owning a home.

Only those that remember history can see it as it was: before the Interstate highway, before the cell phone, before the flat screen color TV, before computers and social networks. Before Motel Six and Super 8 or McDonald's and Red Lobster, before Lowe's and Home Depot and Walgreen's and Walmart. Before all the cars looked alike and all the buildings looked alike and all the people dressed alike. That was my childhood. Although I saw most of it through a TV screen rather than a car window, I, too, was “On the Road.”