The Majestic Mangonel

So last night my wife discovers that on Tuesday my 6th grade daughter is to have created a catapult or trebuchet for science class, much to my surprise.

Although there weren't many parameters other than that it had to fire a golf ball into a newspaper wall and be about 2 feet tall, we Googled a little to see what we were up against. What we discovered was that there are a few sites that sell plans and a few others that show photos and so we worked from there. In the end we decided to base our catapult on a design called the Mangonel (from the Greek word "magganon" meaning an engine of war) which was descended from the Roman onager (Greek for "wild ass" nicknamed as such because it kicked like a mule when discharged).

In any case we spent about an hour last night planning and then three and half more this morning completing the project and thought we should provide some instructions for those like us who might need to do something similar in the future.

In order to provide the force the mangonel relies on torsion from a twisted cord in which the arm is inserted. We decided to use one of those black rubber straps used to fasten items to a car carrier. We replaced the metal hook with a small drill bit and threaded the bit through both ends of the strap creating a loop.

For the base we used some 3.5" by .5" boards and cut two of them 24" in length. We then drilled a 1 1/8" hole 10" from one end in both boards. After measuring the length of the strap when pulled taught we cut two more boards 16.25" in length. After screwing them all together we had our frame.

When the arm is released it's stopped by a pad and so we simply put one more board on top and fastened another 13" board in the center and used a rubber band to secure a bit of foam to the top.

Finally, we added two boards to the bottom so it would sit up a little along with cardboard wheels to give it that historical touch.

To load the catapult we ran the strap through one of the holes pulling it taught at the end with the drill bit. It took a little force but together we were able to pull the loop end through the other hole and slide a stick of sun block in it. Now the strap (or skein in the technical sense) is pretty tight. From there we slid the arm, which was a wood strip about 1.5" wide and cut to 18", into the middle of the strap at the center. By twisting the drill bit on one side and the stick of sun block on the other you can then create the tension in the strap. After about 8 turns we found the sun block would start turn back so we added a small piece of wood to the top that can be turned to stop it from twisting backwards. At this point the arm wants to swing forward and so we put two nails in the board on which the arm rests and a rubber band between them to hold it down and act as the trigger.

On the arm itself we created a small cardboard cup in which the golf ball rests and used duct tape to secure it.

All that's left is to load the golf ball and fire by releasing the rubber band and the arm swings up and releases the ball as it hits the padded board. It doesn't fire as hard as I had imagined and ends up propelling the ball about five feet on a line. Of course, the more you twist the strap the more force you get.

Einstein: His Life and Universe

"I think physicists are the Peter Pans of the human race. They never grow up and they keep their curiosity." - Nobel Prize winner Isidor Isaac Rabi

Throughout my entire elementary, middle school, high school and college educations I never had occasion to read a real biography of, write a paper on, or let alone actually study the technical work of Albert Einstein. Thinking about it now it sounds hard to believe but my only exposure to the famous equation E=mc² came from a book on science we had in our home (related to our antiquated encyclopedia set I think but can't recall anymore) that I picked up around the time I was twelve years old or so. I do recall thinking how simple and elegant that formulation is and, once I learned how fast the speed of light really was, trying to wrap my around the idea that such a small amount of matter could contain such a large amount of energy (a kilogram of mass if converted completely into energy would yield 25 billion kilowatt hours of electricity).


For Einstein the construction of the formula that equated mass and energy was merely a coda to his "miracle year" of 1905 which he published in a three-page paper in September titled "Does the Inertia of a Body Depend on it's Energy Content?" That was last of his papers from that year which also saw him devise the quantum theory of light, help prove the existence of atoms, explain Brownian motion, and of course produce the special theory of relativity in addition to what proved to be the most famous equation in science. As with much of Einstein's work, Walter Isaacson does a masterful job of taking the general reader through not only the chronology but the big ideas behind these discoveries and their historical context in his new biography Einstein: His Life and Universe. I had the pleasure of making Einstein and his world a more or less constant companion over the last two months and can say I thoroughly enjoyed the company.

The book is the first of what will likely be several new biographies of Einstein that draw on a set of letters newly published in 2006 by the Einstein Papers Project at Caltech. Most of these are personal letters and provide additional insight to Einstein's relationship with family and friends and Isaacson seems to quote from them liberally as he provides a straightforward chronology. That chronology is much more detailed from the time of his birth in 1879 through the completion of the general theory of relativity in 1915 and picks up speed considerably after that and especially from the time of his immigration to the United States in the early 1930s to where only scattered events from his final decade of life are mentioned.

But even if the book doesn't detail all the chronology, Isaacson does a wonderful job as he did with Benjamin Franklin: An American Life, in chronicling the key intellectual development, struggles, and triumphs of his subject. This is particularly evident in the chapters on the miracle year and the march leading up to the paper on general relativity. In the latter case what we learn in the book and what I found especially fascinating was that Einstein simultaneously pursued parallel physical and mathematical strategies in his quest to generalize relativity. The physical approach had to comport with Newton's laws and Einstein's own intuition about the physical world (on which he heavily relied in his earlier work) while the mathematical strategy was based on work previously done by Bernahrd Reimann among others. As the story is told in the book the mathematical approach, much to Einstein's surprise since his physical intuition served him so well in his earlier successes while he sometimes derided a reliance on pure mathematics, was the winner while the physical approach ultimately cost him several years as he attempted to refine what is known as his Entwurf theory (German for "outline"). This interesting detail has an appeal since it highlights the effectiveness of taking multiple approaches to solving a problem. The trick of course is in being able to work both sides simultaneously and this episode shows how even a genius had some difficulty in doing so.

As a side note to this narrative, Isaacson chronicles what turned out to be a race with mathematician David Hilbert in the fall of 1915 to publish the final equations after the two had corresponded earlier in the summer. In fact Hilbert published a version of the final equations on November 20 while Einstein didn't deliver the fourth in a series of lectures where he finalized his equations on November 25th. Although there has been some controversy over the priority of general relativity as a result, it was discovered about a decade ago that Hilbert changed his paper in December based on Einstein's version. In any case Hilbert always gave priority to Einstein.

In addition to the key episodes and papers, the book paints a portrait of Einstein's beliefs about the physical world and how those subtly changed over time. From his early career Einstein was heavily influenced by his reading of Ernst Mach who insisted that concepts only had meaning if one could create an operational definition of them and who derided Newton's views of "absolute space" and "absolute time" as a "monstrosity". This skepticism of received wisdom and adherence to what is observable helped Einstein break through the earlier framework when his contemporaries, who had all the same data, simply could not. But while Einstein would later abandon Mach after his general theory and instead rely more on his intuition about reality, Baruch Spinoza was also a huge influence and his belief in a deterministic universe would stay with Einstein until the end. When confronted with the implications of the revolution he started in quantum physics and its reliance on chance, Einstein famously couldn't believe that at the heart of all things determinism didn't rein despite the growing evidence that he was wrong. As a result he spent the remaining 30 years of his life in a quest to find a unified field theory that would marry electricity and magnetism with gravity and quantum mechanics that culminated with twelve pages of equations he scribbled in his last days in the hospital.

While Isaacson does a nice job of describing Einstein's sparring with the "young turks" of quantum physics including Niels Bohr and Werner Heisenberg, a second book titled Uncertainty: Einstein, Heisenberg, Bohr, and the Struggle for the Soul of Science by David Lindley documents that struggle in more detail. In particular Lindley includes in-depth portraits of Heisenberg, Bohr, and Erwin Schrodinger among others as well as the debates that raged in the famous Solvay conferences that occurred primarily between the first and second world wars.

As the years went on, of course, Einstein became known almost as much for his political views as for his scientific accomplishments which were increasingly seen as ancient history. His revulsion at the strict militaristic school he briefly attended as a youth instilled in him a deep disdain both for conformity and the military. It wasn't surprising that he embraced both socialism and pacifism through a refusal of individuals to bear arms, although the latter was markedly softened in the face of German militarism and anti-Semitism in the 1930s. Later he would advocate a world government with its own military which was enforced by his personal lack of nationalistic feeling. He never felt at home in the country of his birth, although he lived in Berlin for many years primarily because his second wife Elsa was from there, as he preferred first Switzerland and later America where he became a citizen in June of 1940. At the same time events in Europe increased his awareness of and solidarity with his Jewish heritage and throughout the book his support of and sometimes entanglement with the Zionist movement (including his dealings with Hebrew University and being offered the presidency of Israel much to David Ben-Gurion's displeasure) are discussed.

Isaacson also spends a good deal of the last few chapters in recounting Einstein's peripheral role in the development of the atomic bomb after having help draft the letter to President Roosevelt outlining the possibility. More entertainingly he describes the somewhat slapstick efforts by the FBI to obtain information and build a dossier on him while completely missing the one true Soviet spy he consorted with and whom he had an affair after the death of his second wife Elsa. Finally, he also talks a good bit about Einstein's firm resistance to McCarthyism. For Isaacson, Einstein valued political systems that cultivated personal freedom and especially freedom of thought. In America he saw as primary the first amendment and continued to speak out on a variety of issues despite the strictures that the Red Scare induced.

In the end Isaacson concludes that curiosity was the primary driver for Einstein. And when combined with his imagination and ability to visualize the physical reality behind his equations, it created a genius. Although I haven't commented much on the personal portrait the book paints, as with Franklin Isaacson seems to fairly show multiple sides of his personality. Both his warmth towards acquaintances and strangers as well as his self-induced emotional distance accompanying his often uncaring attitude towards his wives (Isaacson touches on but doesn't dwell on several of Einstein's mistresses through the years) and children, are on display. In that regard, which incidentally is a weakness of Doris Kearns Goodwin's Team of Rivals: The Political Genius of Abraham Lincoln, the book humanizes a figure that for me, as for many others I'm sure, had always been little more than the caricature of the absent-minded professor.

Rome

Here's an interesting little article on the HBO series titled "Rome". I was drawn to it since on my recent trip to Seattle I was able to catch a few episodes in the hotel and ironically was thinking pretty much the same thing as this author as I recalled my impressions of the excellent book on Cicero that I read awhile back. The shows were very well done with a little bit of soap opera thrown in and certainly well acted and seemed to take pains to try and be culturally accurrate.

Particularly, I found this passge to ring true to what I read previoulsy.

Finally, there is religion. Rome is saturated with it — there are prayers and oaths, offerings made to deities known and unknown, and religious processions and priestly orders. A pagan world, in other words, is not one in which we control the gods, as trendy leftists suppose, but in which we are ever at risk of offending some god for failure to make the right offering or sacrifice. Moreover, these gods rarely provide a guide to conduct or right behavior — they are inscrutable.