The Corona Virus Pandemic of 2019/2020

We are living through a life-changing experience. The ultimate outcome of the current Corona Virus pandemic can hardly be imagined at this time.

 To draw upon an aviation metaphor, this experience feels akin to piloting a small, vulnerable airplane while entering a thick and very extensive bank of high clouds and ground-hugging fog – visibility zero. Flying into such a complete white-out, one becomes dis-oriented at the controls. Familiar landmarks on the ground are no longer visible, and the proximity of threatening mountain peaks in the region becomes a frightening conjecture.

Climbing for altitude to 10,000 feet would provide margin against the higher mountains in the area, but our little craft and its human pilot are not engineered to operate efficiently at that altitude, so we drone-on into the vast unseen before us. We hope and we wonder how long it will take to emerge from this cloud into the light of day. Will we find ourselves flying comfortably toward a bright horizon, or will events portend something more calamitous for us and our little craft before we emerge back into visual flight rules and safely land?

A virus pandemic with fatal overtones such as Covid-19 constitutes a perfect storm capable of threatening our way of life not only in these United States, but simultaneously around the entire planet. What with the threat of climate-warming looming close behind, this planet’s human species seems to be arriving at a critical juncture along its time-line on this earth. What does the future hold?

We are, of course, still largely at the mercy of nature and whatever god operates behind the scene. This is true despite the enormous scientific and technical progress made over the last century or two, progress which has enabled a marvelous degree of understanding and a significant semblance of control over nature and our near-term fate.

Nature does have her “bag of tricks” which seems diabolically designed to regulate this planet, its animal life, and its human inhabitants using a number of “checks and balances.”

One aspect of the Covid-19 virus that is especially apparent is its disastrous effect on densely populated areas such as New York City. My wife and I will often mutter to ourselves when stuck in our own, local California traffic jams: “Too many people here, now.” The population density in Northern California is nothing like that in New York, Los Angeles, and other great metropolitan areas of the country, however. Could it be that mother nature is trying to tell us something by turning loose this highly contagious virus and zeroing-in on densely populated regions? Perhaps there is a lesson to be learned.

Trader Joe’s with “senior line” (including my wife) forming at 7:45 am!

It is instructive to consider the responses of countries around the globe to this virus and its pandemic. Germany and South Korea are two regions which seem to have been well-prepared to harness a well-disciplined approach to managing the threat. Others like Italy and Spain have suffered disastrous casualties because they were not as prepared and disciplined in the beginning. It seems clear that the smaller, well-contained societies would predictably have an advantage over larger, more diverse populations. It also seems excruciatingly and embarrassing clear that the United States of America was not well prepared for what it now faces, nor is the country uniformly heeding the advice of our finest scientific minds.

The world populations are, all of us, living through history-in-the-making. When the story is finally written, this pandemic will occupy a prominent place in the overall history of this planet and its inhabitants. Clearly, we had better embrace scientific fact and research more closely than ever before in the biological fields of virology, epidemiology and immunology. On the heels of polio, AIDS, E-Bola, and H1N1, we now face the most challenging virus of them all, and who knows at this moment what the outcome will be?

Already, many heroes have surfaced in response to the threat. The first-responders and the medical staffs who are working to the limits of human endurance with personal risk and a spirit of sacrifice are heroes already…and will continue to be. Most state governors and their staffs are grappling tirelessly while carrying immense burdens of responsibility on their backs. By and large, we ordinary citizens understand the game plan and have sacrificed much while using the only tool we have at our immediate disposal with which to fight this virus: social isolation. It seems to clear to me that staying the course of social distancing and implementing mass testing/contact tracing are the requisite answers to stave-off disaster in the short term. But eradication of this threat will require something else: tools from our medical researchers which will rid us of the virus.

The names of the inevitable heroes of this ongoing saga will soon be entering the history books. These will be the lead-players within small teams of scientists and researchers who, daily, are burning the midnight oil in medical laboratories around the world in the race to stop Covid-19. Like Pasteur, Darwin, Mendel, Salk, Watson and Crick – like all those who poked and prodded nature to understand her secrets and thus harness medicine in order to ward-off nature’s challenges, a tiny group of current researchers will soon write their names large in history’s log.

I say it will be soon, because it can be soon and it must be soon. At stake for those who succeed in thwarting this ugly virus are scientific immortality as well as large financial and professional rewards. Satisfaction in knowing of their service to humanity will closely contend for top honor. Never has there been such a golden ring waiting to be plucked by riders on the medical carousel, and never has there been such pressure. Who will they be? The prize is huge, not to mention the importance to humanity of a vaccine or effective therapeutic. Never has there been a world-wide audience so tuned-in to events as is the case right now, because we are all at risk. Our very way of life is threatened, right now. Unlike certain influential people in this country, I believe wholeheartedly in the sciences which attempt to understand and explain the physical universe in which we live, and that gives reassurance at this uncertain time.

As a student of science and science history, I am very familiar with the exploits of legendary monster-minds who have miraculously shaped man’s understanding of his world – names like Galileo, Newton, Darwin, and Einstein. I am extremely confident that today’s researchers and scientists will – and very soon – announce some exciting and welcome news to the world community. We will then exit this enveloping cloud of despair and fly straight toward a bright horizon and a safe landing. We are all waiting, hoping, and we are ready.

One last observation:  Here is a commodity which has been elevated to “rare and collectible” status by the folly of our natures. While not quite in the same category (yet) as gold and diamonds, one must smile at the fact that demand has soared and availability has plunged from day one of this crisis. But this is really not so surprising because shit does happen, and this is our front line of defense. Be well!

Apollo 11: One Giant Leap for Mankind!

Fifty Years ago, yesterday, a Saturn 5 rocket lifted off its launch pad at Cape Kennedy, Florida, on one of the most audacious adventures in the history of mankind. On board were three “spacemen” adventurers who carried the hopes and aspirations of people the world over on their shoulders.

The goal: to land a man on the moon’s surface and bring him safely back to mother earth. The odds of success? In 1961, when President Kennedy pronounced his determination for the nation to accomplish this before the end of the decade, many of the engineers with experience on the program which had not yet even sent Mercury astronaut John Glenn into local earth orbit thought Kennedy’s goal… “nuts.”

By the sheer force of national will fueled by an open checkbook for NASA from Washington, Kennedy’s daring commitment was realized. With over five months to spare before the decade’s end, astronauts Neal Armstrong and Edwin “Buzz” Aldrin landed on the lunar surface on July 20, 1969. The confirmation came as Armstrong beamed back to earth, the message, “…the Eagle has landed.”

July 16, 1969 dawned bright and mostly clear over the Florida Cape. On that momentous day, the mighty Saturn 5 rocket with its crew of Armstrong, Aldrin, and Michael Collins, ponderously lifted from earth on a thundering plume of fire and smoke. The spectacle and the sound of it mesmerized the thousands who came to watch the launch for themselves. Even at the more distant viewing points from the launch pad, the rolling, rumbling thunder emanating from the engines of the Saturn 5 was sufficient to rattle windows and elicit speculations regarding the power and fury of whatever powers might ultimately bring about the end of the earth, itself.

Speaking less from a poetic standpoint and strictly from that of the rocket engineers who designed her, the mighty Saturn 5 at lift-off was developing 7.5 million pounds of upward thrust by expelling 15 tons per second of combustion materials from its five engine nozzles! These are incredible numbers.















     Wernher Von Braun and the business end of the Saturn 5 rocket

This was Isaac Newton’s third law of motion on full and mighty display:
    For every action, there results an equal and opposite reaction.

In full accordance with Newton’s third law, the forces within the combustion chambers, required to violently expel fifteen tons per second of combustion products from the rocket’s nozzles in a downward direction gave rise to equal and opposite reaction forces on the upper, closed walls of the combustion chambers. It is this reaction force which provides the requisite upward thrust to the Saturn 5. One can appreciate the rolling, earth-shaking thunder which was experienced far and wide during a Saturn 5 launch when the violence taking place within its combustion chambers is fully appreciated.

It is poetic justice that the fundamental principle behind rocket propulsion should stem from the fertile mind of Isaac Newton as first revealed in his Principia of 1687, the greatest scientific book ever published!

We celebrate, today, not only the complete success of Apollo 11 as a mission, but the spirit and can-do attitudes of NASA, President Kennedy, Congress, and the American people who were all-in with their support and enthusiasm for the Apollo 11 program. Those several days when space was truly opened for exploration will stand in the record of this nation as among the best of times for America, notwithstanding the array of “other” concerns which faced us then.

The cold war with the Soviets was one of those concerns, and anyone who has paid attention to America’s many triumphs in space will appreciate that a major impetus for Kennedy to issue his man-on-the-moon challenge in 1961 was the realization that space exploration meant rocket technology and rocket technology was key to our nuclear missile defenses and our national security. Despite the need for such gnawing pragmatism in the space program, the altruistic legacy of man’s exploration of outer space remains first and foremost in the consciousness of the American people.

Like Pearl Harbor, VE-day in World War II, President Kennedy’s assassination in 1963, and 9/11 in 2001, Apollo 11 was one of those generational events which remain a life-long memory for those who lived through them. I remember clearly where I was and what I was doing fifty years ago. Linda and I were living in Santa Barbara, California, and I was half-way through my Masters Degree in electrical engineering at the University of California, Santa Barbara. We were renting half of a wonderful hillside duplex which overlooked that beautiful city with a line of sight toward the city harbor and west to the Pacific Ocean. As we intently watched all aspects of the Apollo launch on our little 19-inch black-and-white television during those several days, I recall countless time-outs to our front terrace-porch with coffee cup in-hand where I could enjoy the city view spread out below me while reflectively musing about the wonder of all that was happening on man’s remarkable journey to the moon and back. The few years we lived there encompassed some of the happiest times and circumstances of our young married lives; the triumphal success of Apollo 11 in July of 1969 played no small part in those special times for us and continues to provide joy in recollecting.

I have just finished watching the newly released DVD movie, Apollo 11, with my two young grandsons. The movie rates five-stars plus and does full justice to the drama and excitement of the event. As the movie ended, I counseled Matthew, my older grandson, that the times, the attitudes, and the circumstances which combined to make made Apollo 11 possible will represent a marker in humanity’s timeline, a marker which will always be remembered as “One giant leap for mankind.”

As a retired electrical engineer, I take time to reflect upon the countless scientific and technical people who made the moon landing possible:

-The physicists like Galileo, Newton, and Einstein who first unmasked the nature of gravity and the laws of motion.
-The electrical engineers/physicists who tamed electricity: men like Michael Faraday and James Clerk Maxwell.
-The metallurgists who, over many decades, came to understand the nature and strength of materials – titanium, for example, found in the rocket nozzles of Saturn.
-The “ordinary” electrical and mechanical engineers and computer programmers who designed the immense support platform of equipment needed to support a mission like Apollo 11.
-The countless, faceless, folks who are so large in number, but nevertheless provided critical skills and support in management and mission control.
-The technician who was called upon when a leaky valve on the rocket halted the countdown before launch. With, virtually, the eyes of the world upon him, he entered the rocket assembly some two-hundred feet above the pad to tighten some bolts in order to mitigate the situation. I can only imagine the pressures on this fellow who remains faceless and nameless. He has lived with quite a memory of that time and his role in it, I am certain.

And, finally, there were the dreamers, the ancient astronomers (natural philosophers) who looked to the heavens in wonderment centuries ago and asked, “How and why is this?”



The Collings Foundation’s 2019 “Wings of Freedom Tour”

In a few weeks, the familiar and unmistakable drone of World War II heavy bombers will be heard once again in the skies over-head. I am already getting excited! It is time for the annual reappearance of the Wings of Freedom Tour at nearby Moffett Field. Moffett will be one of many stops across America for the tour and its priceless collection of beautifully restored, vintage aircraft.

The stated mission of this annual tour is two-fold: first, to restore and preserve vintage aircraft in flying condition; second, to pay tribute to those who flew in the war while insuring that future generations will be reminded of those veteran’s experiences and sacrifices. The war years of 1941-1945 were, on balance, undoubtedly the worst of times; yet in many smaller ways, they were also the best of times for this country. The book, The Greatest Generation, by Tom Brokaw reflects the uniqueness of the times and the generation who lived them.

While I have no personal affiliation with the Collings Foundation, whatsoever, I wholeheartedly support their mission to insure that the contrasts and the color of those times are never lost to future generations. I write this endorsement of their tour strictly as an act of appreciation and thanks.

I especially look forward to re-visiting the Wings tour this year because I had the great, good fortune last Memorial Day to fly the Foundation’s most iconic warbird, the P-51D Mustang. For one glorious half-hour, I had the ability to take the rear seat controls of that beautiful bird under the watchful eye of pilot Nick, seated up-front. I posted, here, on that experience last year: it and other related posts can be located by entering “Mustang” in the search box on the top right of my home page.

My flight in Toulouse Nuts was the thrill of a lifetime for someone like me interested in aviation – especially the warbirds from World War II. The Collings tour offers anyone the chance to go up in one of several iconic airplanes that played a pivotal role in the war. A half-hour ride in the P-51D will cost you $2400, but a half-hour adventure aboard the B-17 Flying Fortress or the B-24 Liberator bomber runs $450. A nominal fee of $15 for adults and $5 for children, enables you to crawl at your leisure through the bombers mentioned for an up-close-and-personal ground adventure!

If you have not visited the Collings Wings of Freedom Tour, Google it on the internet to see if it will be coming your way this summer. Take your children and treat them to an eye-opening reality-experience that will make a lasting impression. The following photo says it all for me:

A veteran who flew on B-24’s provides a living link to hundreds of kids who are learning that a knowledge of history has far more to offer them than spending still more social media time on the internet. If you visit the tour this year, chances are that you will still encounter a veteran volunteer docent who was there decades ago and can relate, first-hand, what it was like to fly these great warbirds which won the war for freedom. Sadly, as each year passes, fewer of these folks are still with us who can pass on their memories and their realities to the next generation.

The B-24 Liberator, Witchcraft – the last one flying

The airplane in the background of the above picture is the very last of its kind still flying: The storied B-24, Witchcraft. The B-24 Liberator had the highest production run of any airplane in history – approximately 18,500 were built! Such a large number supports two facts: first, the importance of this, our largest, long-range bomber; second, the huge losses suffered during countless bombing runs over Germany. Given these facts, I deeply appreciate that the Collings Foundation does what it does to “keep ‘em flying,” as they say, while preserving this precious heritage for future generations to experience.

Go hear for yourself the sound of the B-24’s four piston engines coughing, smoking, and belching to life during engine startup. See for yourself that big bird lift off the runway, straining for altitude. Go crawl through the belly of the beast and see what its crews faced at thirty-thousand feet with freezing cold during six-hour missions into Germany and back (if lady-luck was with them that day)!

While you are at it, check out the signature, raspy/throaty roar of the twelve-cylinder, 1600+ horsepower Rolls-Royce Merlin engine as it catapults the P-51D Toulouse Nuts into the air on take-off. The P-51D was the greatest fighter of the war, bar-none! Its introduction to service as a long-range bomber escort in late 1943 saved countless bomber crews who would otherwise have gone down at the hands of German pilots. Aside from its unmatched ability to escort the bombers deep into Germany and back again, the P-51 proved superior to any fighter/interceptor in the German arsenal. Many nine and ten-man bomber crews developed a great fondness and admiration for their P-51 escorts – their “little friends,” as they called them.

Go catch the tour and see for yourself: you won’t be sorry that you did!

Hermann Minkowski, Albert Einstein and Four-dimensional Space-time

Is the concept of free-will valid as it relates to humans? A mathematics lecture presented in September of 1908 in Cologne, Germany by Hermann Minkowski not only paved the way for the successful formulation of Albert Einstein’s general theory of relativity in 1916, it also forced us to completely revamp our intuitions regarding the notion of time and space while calling into question the concept of human free-will! Some brief and simplified background is in order.

Prior to Minkowski’s famous lecture concerning Raum Und Zeit (Space and Time), the fabric of our universe was characterized by three-dimensional space accompanied by the inexorable forward flow of time. The concept of time has long been a stubbornly elusive notion, both in philosophy and in physics. From the mid-nineteenth century onward, there had increasingly been problems with our conception of “time.” The difficulties surfaced with the work of James Clerk Maxwell and his mathematical characterization of electromagnetic waves (which include radio waves and even light) and their propagation through space. Maxwell revealed his milestone “Maxwell’s equations” to the world in 1865. His equations have stood the test of time and remain the technical basis for today’s vast communication networks. But there was a significant problem stemming from Maxwell’s work, and that was his prediction that the speed of light propagation (and that of all electromagnetic waves) is constant for all observers in the universe. Logically, that prediction appeared to be implausible when carefully examined. In fact, notice of that implausibility stirred a major crisis in physics during the final decades of the nineteenth century. Einstein, Poincare, Lorentz and many other eminent physicists and mathematicians devoted much of their time and attention to the seeming impasse during those years.

Enter Einstein’s special theory of relativity in 1906

In order to resolve the dilemma posed by Maxwell’s assertion of a constant propagation speed for light and all related electromagnetic phenomena, Albert Einstein formulated his special theory of relativity which he published in 1906. Special relativity resolved the impasse created by Maxwell by introducing one of the great upheavals in the history of science. Einstein posited three key stipulations for the new physics:

A new law of physics: The speed of light is constant as determined by all “observers” in the universe, no matter what their relative motion may be with respect to a light source. This, in concert with the theoretically-based dictate from Maxwell that the speed of light is constant for all observers. Einstein decreed this as a new fundamental law of physics. In order for this new law to reign supreme in physics, two radical concessions regarding space and time proved necessary.
Concession #1: There exists no absolute measure of position and distance in the universe. Stated another way, there exists no reference point in space and no absolute framework for determining distance coordinates. One result of this: consider two observers, each with his own yardstick, whose platforms (habitats, or “frames of reference,” as it were) are moving relatively to one another. At rest with respect to one another, each observer sees the other’s yardstick as identical in length to their own. As the relative velocity (speed) between the two observers and their platforms increases and approaches the constant speed of light (roughly 186,000 miles per second), the other observer’s “yardstick” will increasingly appear shorter to each observer, even though, when at relative rest, the two yardsticks appear identical in length.
Concession #2: There is no absolute time-keeper in the universe. The passage of time depends on one observer’s velocity with respect to another observer. One result of this: consider our same two observers, each with their own identical clocks. At rest with respect to one another, each observer sees the other’s clock as keeping perfect time with their own. As the relative velocity (speed) between the two observers and their platforms increases and approaches the constant speed of light, the other observer’s clock appears increasingly to slow down relative to their own clock which ticks merrily along at its constant rate.

Needless to say, the appearance in 1906 of Einstein’s paper on special relativity overturned many long-held assumptions regarding time and space. Einstein dissolved Isaac Newton’s assumptions of absolute space and absolute time.The new relativity physics of Einstein introduced a universe of shrinking yardsticks and slowing clocks. It took several years for Einstein’s new theory to gain acceptance. Even with all these upheavals, the resulting relativistic physics maintained the notion of (newly-relative) spatial frames defined by traditional coordinates in three mutually perpendicular directions: forward/backward, left/right, and up/down.

Also still remaining was the notion of time as a (newly-relative) measure which still flows inexorably forward in a continuous manner. As a result of the special theory, relativistic “correction factors” were required for space and time for observers and their frames of reference experiencing significant relative, velocities.

This framework of mathematical physics worked splendidly for platforms or “frames of reference” (and their resident observers) experiencing uniform relative motion (constant velocity) with respect to each other.

The added complications to the picture which result from including accelerated relative motions (the effect of gravity included) complicated Einstein’s task enormously and set the great man on the quest for a general theory of relativity which could also accommodate accelerated motion and gravity.

Einstein labored mightily on this new quest for almost ten years. By 1913, he had approached the central ideas necessary for general relativity, but the difficulties inherent in elegantly completing the task were seriously beginning to affect his health. In fact, the exertion nearly killed Einstein. The mathematics necessary for success was staggering, involving a complex “tensor calculus” which Einstein was insufficiently prepared to deal with. In desperation, he called his old friend from university days, Marcel Grossman, for help. Grossman was a mathematics major at the Zurich Polytechnic, and it was his set of class notes that saved the day for young Einstein on the frequent occasions when Einstein forsook mathematics lectures in favor of physics discussions at the local coffee houses. Grossman’s later assistance with the requisite mathematics provided a key turning point for Einstein’s general theory of relativity.

Enter Hermann Minkowski with Raum Und Zeit

The initial 1909 publication of Raum Und Zeit

On September 8, 1908 in Cologne, Germany, the rising mathematics star, Hermann Minkowski, gave a symposium lecture which provided the elusive concepts and mathematics needed by Einstein to elegantly complete his general theory of relativity. Similar to Einstein’s 1906 special theory of relativity, the essence of Minkowski’s contribution involved yet another radical proposal regarding space and time. Minkowski took the notion of continuously flowing time and melded it together with the three-dimensional coordinates defining space to create a new continuum: four-dimensional space-time which relegated the time parameter to a fourth coordinate point in his newly proposed four-dimensional space-time.

Now, just as three coordinate points in space specify precisely one’s physical location, the four-dimensional space-time continuum is an infinite collection of all combinations of place and time expressed in four coordinates. Every personal memory we have of a specific place and time – each event-instant in our lives – is defined by a “point” in four-dimensional space-time. We can say we were present, in times past, at a particular event-instant because we “traversed-through” or “experienced” a specific four-dimensional coordinate point in space-time which characterizes that particular event-instant. That is very different from saying we were positioned in a specific three-dimensional location at a specific instant of time which flows irresistibly only forward.

What do Minkowski’s mathematics imply about human free-will?

By implication, the continuum of four-dimensional space-time includes not only sets of four coordinate points representing specific events in our past (place and “time”), the continuum must include points specifying the place and “time” for all future events. This subtly suggests a pre-determined universe, where places and “times” are already on record for each of us, and this implies the absence of free-will, the ability to make conscious decisions such as where we will be and when in the future. This is a very controversial aspect of Minkowki’s four-dimensional space-time with distinctly philosophical arguments.

For certain, however, is the great success Minkowski’s mathematics of space-time has enjoyed as a basis for Einstein’s general theory of relativity. Most, if not all, aspects of Einstein’s special and general theories of relativity have been subjected to extensive experimental verification over many decades. There is no instance of any validly conducted experiment ever registering disagreement with Einstein’s special or general theories. That is good news for Hermann Minkowski, as well.

Minkowski’s new reality takes us beyond the two-dimensional world of a flat piece of paper, through the recent universe of three-dimensional space plus time, and into the brave new world of not only four-dimensional space-time, but curved four-dimensional space-time. The nature of curved space-time serves to replace the Newtonian notion of a gravitational force of attraction which enables the celestial ballet of the heavens. For instance, the orbit of earth around the sun is now regarded as the “natural path” of the earth through the curvature of four-dimensional space-time and not due to any force of attraction the sun exerts on the earth. According to the general theory of relativity, the mass of the sun imposes a curvature on the four-dimensional space-time around it, and it is that curvature which determines the natural path of the earth around the sun. Minkowski and his mathematics provided the final, crucial insight Einstein needed to not only radically redefine the nature of gravity, but to also successfully complete his general theory of relativity in 1916. Einstein’s theory and its revelations are generally regarded as the most significant and sublime product ever to emanate from the human intellect. Take a bow, Albert and Hermann.

My eulogy to Hermann Minkowski

Albert Einstein is assuredly the most recognized individual in human history – both the name and the image, and that is very understandable and appropriate. Very few in the public realm not involved with mathematics and physics have ever even heard the name, “Hermann Minkowski,” and that is a shame, for he was a full participant in Einstein’s milestone achievement, general relativity. Minkowski’s initial 1907 work on Raum Und Zeit came to Einstein’s attention early-on, but its mathematics were well beyond Einstein’s comprehension in that earlier time frame. It was not until several years later, that Einstein and Marcel Grossman began to recognize Minkowski’s gift to general relativity in the form of his mathematics of four-dimensional curved space-time.

Hermann Minkowski delivered his by-then polished lecture on space-time at Cologne, Germany, in September, 1908. Tragically, he died suddenly in January, 1909, at the young age of forty-four – from a ruptured appendix. His latest findings as presented in the Cologne lecture were published in January, 1909, days after his death, sadly.

The “lazy dog” has the last bark

Albert Einstein and Hermann Minkowski first crossed paths during Einstein’s student days at the Zurich Polytechnic, where Minkowski was teaching mathematics to young Einstein. Noting Einstein’s afore-mentioned irregular attendance at lectures in mathematics, the professor reportedly labeled the student Einstein as, “a lazy dog.” Rarely in the annals of human history has such an unpromising prospect turned out so well! I noted with great interest while researching this post that Einstein long regarded mathematics as merely a necessary tool for the advancement of physics, whereas Minkowski and other fine mathematicians of the past tended to consider mathematics as a prime mover in the acquisition and advancement of knowledge, both theoretical and practical; they viewed physics as the fortunate beneficiary of insights that mathematics revealed.

In the late years, Einstein came to appreciate the supremely important role that mathematics plays in the general advancement of science. As proof, I will only add that the great physicist realized his dependence on the mathematicians Grossman and Minkowski in the nick of time to prevent his theory of general relativity from going off the rails, ending on the scrap heap, and leaving Albert Einstein a completely spent physicist.

Note: For a detailed tour and layperson’s explanation of Einstein’s relativity theories, click on the image of my book: The Elusive Notion of Motion – The Genius of Kepler, Galileo, Newton, and Einstein – available on Amazon