I still argue with the voice on my GSP. Don’t look at me that way: You do it, too! The voice has a British accent; we call her Petula. And I still argue when I want to stay on I-95 and she tries to send me onto US-1. But I do have a little more respect for her — or, at least, for the device — now that I’ve read Chad Orzel’s book “How to Teach Relativity to Your Dog.”

Orzel, a professor who also wrote “How to Teach Physics to your Dog,” explains in this more recent book that the technology of  global positioning systems relies on a principle of the theories of relativity first formulated by Albert Einstein. A principle of the special theory of relativity holds that a clock that is in motion will “tick” increasingly more slowly as the speed of its motion increases. The general theory of relativity, on the other hand, holds that a clock runs faster the higher it is — that is, the greater its altitude in the gravitational field.

The atomic clocks aboard the GPS satellites speed up because of their altitude and slow down because of the speed at which the satellites orbit the earth. At the altitude of those satellites, the clocks are quickened more than they are slowed, but they are still keeping time at a different rate than clocks on the surface of the earth. Each satellite emits a radio signal with the time on its atomic clock. The GPS unit picks up two or three of those signals, calculates the difference between the time on the satellite clock and the time on the surface of the earth, and uses that information to determine the distance to each satellite and, from that, the location of the unit on the ground.

Pretty cool, huh?

Still, I don’t read about physics because I’m interested in the practical applications so much as because I’m interested in the theories and principles. It can be mind-bending stuff, but if given enough concentration and persistence, it can lead to some moments of enlightenment about how the universe works. And studying the theories of relativity, in particular, can be an eye-opening series of reminders that things are not always what they appear to be.

Orzel’s technique in this book is to explore the special and general theories of relativity, and some other matters, as though he were discussing them with his real-life dog, Emmy. This is the writer’s way of making the material more accessible to people like me, but frankly, it gets tiresome. The dog’s constant references to Orzel as “Dude” and the overworked jokes about Emmy’s appetite, disdain for cats, and fixation with chasing rabbits, grow old pretty quickly. And the premise crumbles as the dog begins to talk about physics as if she were a graduate student at Princeton.

I think anyone who picked up this book thinking that the dialogue with the dog, and the use of dog-world examples, would make physics easier to understand would be disappointed. Orzel’s explanations are clear, but he could have been just as clear without the input from the dog. More important, with or without the dog, a reader won’t get much out of this book without focusing attention on it, frequently stopping to think hard about what Orzel has just written, frequently re-reading paragraphs or whole sections and consulting the glossary at the back of the book.

Both the special and general theories of relativity depend on the idea that the laws of physics work the same for observers who are in motion and observers who are stationary, even though an event — such as a person dropping a ball from above his head to the floor at his feet on a moving train — will appear differently to the person dropping the ball and a person observing the event while standing still on the station platform.

An interesting thing that comes up again and again in Orzel’s book is the fact that researchers are still discovering implications of these theories that Einstein expounded at the beginning of the 20th century. Already Einstein’s work has led to the understanding that the mass of an object is a measure of its energy and the two properties are connected by the constant e=mc²; that time and space are expressions of the same thing; that gravity bends light; that large objects bend space; that a moving object shrinks in length in the direction in which it is moving — the faster it moves, the more it shrinks.

Orzel’s also discusses black holes, those concentrations of mass so dense that even light can’t escape their gravity; the principles behind nuclear energy — both the relatively weak energy that holds atoms together and the enormous energy that can power cities or destroy them; the discovery that the universe is expanding at a constantly increasing rate; and the likelihood that this expanding universe began as a single point that exploded in what we know call the “big bang.”

The dog? I can take or or leave her. But reading this book — some of it two or three times — was worth the energy (which, by the way, equals mass times the speed of light squared)


Vincent Donofrio and Marisa Tomei in "Happy Accidents"

I’ve been reading some articles about time travel; it’s a good way to make your head spin without the aid of alcohol.

The subject came up because we watched “Happy Accidents,” with Marisa Tomei and Vincent Donofrio. In this film, released in 2000, Tomei plays Ruby Weaver, a woman chronically unlucky in her relationships with men. She thinks her luck has changed when she becomes involved with Sam Deed (Donofrio), until he tells her that he is a traveler from the future – specifically from the year 2470.


Sam claims that he saw Ruby’s picture when he was living in Dubuque, and that he traveled through time, to Brooklyn, in search of her – though he doesn’t say why. As any person would, Ruby initially thinks Sam is either joking or deranged, but Sam won’t budge off his story. Ruby is particularly disturbed by a notebook in which Sam has repeatedly sketched the face of a woman — he claims it’s Ruby’s face — and written the words Chrystie Delancey — he claims she’s his “contact,” another time traveler who was assigned to give him his orientation when he arrived in the past — that is, the present.

This tale grows quite intense; in fact, I was surprised to see it listed on IMDb as a comedy, because there’s nothing funny about it.  It keeps us guessing whether we’re watching a fantasy in which Sam is telling the truth, or a tragedy in which Sam is either playing mind games with Ruby or is insane.

Underlying the story itself is the paradox that the notion of time travel to the past always poses — the question of causality. Namely, if time travel to the past were possible, would the time travelers, either by their mere presence or by their overt actions, change the course of events, change the future.

Donofrio and Tomei

I don’t think this movie did very well at the box office, but it’s a worthwhile property. The story is compelling, Tomei and Donofrio are both magnetic, and there are strong supporting performances by Tovah Feldshuh as Ruby’s mother, Holland Taylor as Ruby’s therapist — a pivotal role, and Nadia Dajani as Ruby’s best friend.

Several years ago, I read a book entitled The Physics of the Impossible by theoretical physicist Michio Kaku. In that book, Kaku explored some ideas that have been presented over the years in science fiction literature, films, and TV shows, and organized them according to how plausible they were. As I recall, he concluded that under the known laws of physics, time travel into the past was impossible and time travel into the future was possible, but not likely to become reality for many many years. If you’d like to see a somewhat comprehensible explanation of Albert Einstein’s view of time travel, click HERE.


In a post last December, I mentioned in passing the widely held fiction that when Christopher Columbus set off on his first voyage, many if not most Europeans thought he would sail his ship off the edge of a flat earth and into oblivion. I was taught this in elementary school, and I have spoken to many people my age who remember being taught the same thing. More recently, I questioned my college students about this, and many of them said they had the same impression about Columbus.

The fact is that it was common knowledge among Columbus’ contemporaries in Europe that the world was round — a point that Nancy Marie Brown makes in her book, The Abacus and the Cross.

This book is not about Columbus; it’s about Gerbert of Aurillac, a French monk who lived in the 10th century. Gerbert had a thirst for knowledge and he became thoroughly schooled in the humanities and in the sciences.


His scholarship carried him to Spain, where he came in contact with a thriving Arab Muslim culture which had preserved enormous amounts of philosophical and scientific knowledge that had been lost to Europe. Gerbert seems to have had both the curiosity and the capacity of a Leonardo or Michelangelo, and he devoured as much learning as he could. He was engrossed in both mathematics and in music, for example, and in the relationship between the two disciplines. He scrutinized the properties of organ pipes, and he eventually designed a built a prototypical organ that was not driven by water — the common technique of his time — but by forced air.

He didn’t only strive to satisfy his own curiosity. He was an influential teacher whose students included royalty. In the process of carrying out this vocation he introduced Europe to the place system of arithmetic — vertical rows for the ones, tens, hundreds, and so forth — which was much more efficient than the clumsy Roman system and which the western world has been using ever since. In this connection, he also carried back from Spain numerals that had originated in India and that had been adapted by the Muslims — the forerunners of the so-called Arabic numbers we use today. As the title of the book suggests, he learned in Spain to use an abacus board to calculate, and he later designed his own versions and taught others how to use them.


Also among Gerbert’s interests was astronomy. He learned all about astrolabes, overlaid disks that were used to trace the positions of the sun and the moon and the stars and the planets — and tell time — and about celestial globes, which were three dimensional representations of the apparent paths of the heavenly bodies. He made his own models of these instruments, too, sometimes taking as much as a year to finish one.

As Brown points out, it is clear not only that Gerber, in the 10th century, knew that the world was round, but that Pythagoras determined that around 530 BC, and Erastosthenes figured out how to calculate the circumference of the globe by 240 BC. Some flat-earthers persisted, but by the time of Columbus the point was moot in western Europe. Columbus knew the world was round; his mistake was in underestimating the circumference.

Being a churchman in that era, and one who enjoyed consorting with powerful people, Gerbert inevitably got drawn into the constant political turmoil in Europe, and his fortunes rose and fell along with those of his patrons.

He almost ended on a high note when he was elected Pope Sylvester II in 999 AD.


Even that didn’t turn out so well, because he had to flee Rome for a while along with his patron of the moment, the Holy Roman Emperor Otto III. Sylvester died in 1003.

During his lifetime and for a long time after his death he was the subject of rumors that he consorted with the devil or engaged in sorcery. Ironically, this was because of his pursuit of knowledge in astronomy and mathematics, which in some ignorant minds were associated with the occult.


When it comes to killing each other, we humans owe ourselves credit for ingenuity. Long before the Christian era, we were designing elaborate and effective instruments of mayhem — although it turns out that the “flaming death ray” attributed to Archimedes wasn’t one of them. I learned about that this week in a story in the Christian Science Monitor. Although that story was about something that Archimedes did not accomplish, it still left me impressed yet again with the genius of people in what to us are ancient times.

Archimedes was born around 287 BC in Siracusa (Syracuse), Sicily, which was a Greek colony at the time. In terms of intellect, he was in the same category as Leonardo, Newton, and Einstein, and he did groundbreaking work in mathematics, astronomy, physics and engineering. Like many of the ancients, Archimedes is the subject of some stories that are either only partly true, possibly true but undocumented, or simply false.

Archimedes' "death ray" directed at a Roman ship

According to one tale, apparently first known in the Middle Ages, Archimedes designed a system in which mirrors were used to direct concentrated beams of sunlight at Roman ships, causing them to catch fire. This supposedly occurred during a siege of Siracusa that lasted from 214 to 212 BC, the Second Punic War. Archimedes was killed by a Roman soldier in 212 during that siege.

The Monitor story reports on new findings that debunk the “death ray” story but propose an alternate explanation that, to my mind, is no less impressive.


According to the CSM, studies done at the University of Naples have indicated that it is more likely that Archimedes used — are you ready for this? — steam cannons to fire at the Roman vessels:

“The steam cannons could have fired hollow balls made of clay and filled with something similar to an incendiary chemical mixture known as Greek fire in order to set Roman ships ablaze. A heated cannon barrel would have converted barely more than a tenth of a cup of water (30 grams) into enough steam to hurl the projectiles.”

The story cites some supporting authorities for this idea, including Leonardo Da Vinci, who spent a lot of his own time dreaming up horrible ways for people to kill each other in battle. (See my June 8 blog entry for more on Leonardo’s diabolical side.)

While I’m being a little flippant about this, I never tire of learning about the accomplishments of our forbears in the distant past. I was amused by the headline on the Monitor’s story, which said that Archimedes’ death rays were probably “just a cannon.” Just a cannon – two centuries before the birth of Jesus. Reading about people like Archimedes reminds me of the potential of the human mind — and of how much more I might accomplish with my own if I were to make the effort.

You can read the Monitor’s story by clicking HERE.

Portrait of Archimedes by Domenico Fetti (1620)