In reference to European knowledge of Japan (or lack thereof), Christopher Columbus didn’t have trouble getting support for his proposed voyage westward to the Orient because the idea itself was ridiculed, but because the experts regarded Columbus’s arguments as fatally flawed. In 1492, everyone knew the world was round, and the circumference had been calculated to be about 25,000 miles by the ancient Greeks. The geographers also knew it was about 11,000 miles overland across Eurasia from the Atlantic to the Pacific. Simple subtraction said that Columbus wanted to sail 14,000 miles. This could not be done with the ships of his day, which could not hold nearly enough food and water for a voyage of that length.
Columbus argued that the world was only 18,000 miles in circumference, that he could resupply at the Azores or Canaries, that he wasn’t going to sail at the equator where the trip was longest, and that Japan was 2,000 miles off the coast of China. Hence, his proposed voyage was only 4,000 miles instead, which was barely possible. This was complete nonsense, and if he hadn’t been lucky enough to hit the unknown continents in between, his ships would have been lost with all hands long before he got across the Pacific. Most of Magellan’s crew died crossing the Pacific a generation later, despite newer and larger ships and being able to re-supply in South America. As it is, Columbus just made it across the Atlantic, and of course to his dying day still insisted he’d found the East Indies, which is presumably why the continents are not known as North Columbia and South Columbia. Amerigo Vespucci’s name was associated with the first map that explicitly showed the newly-discovered land as a separate continent.
Cynics have said that Queen Isabella is famous for having paid no attention to her geography lessons as a child. In reality, historians think that Spain supported Columbus out of desperation. The country was very poor to start with, and had bankrupted itself in the centuries-long “Reconquista” war against the Moors in Andalusia. Spain finally won that war in early 1492 and promptly expelled the Jews and Muslims from the country in an early example of Ethnic Cleansing. They undoubtedly felt they were justified on religious grounds, but economically, it was a disaster. They not only lost their skilled artisan class, but they essentially cut themselves off from all Mediterranean trade, and their need of another revenue source made them take the long-shot gamble to fund Columbus’s ships. (His thank-you note to Isabella explicitly made the connection between the victory in Granada, the Jewish expulsion, and his voyage.)
Speaking of the overland distance across Eurasia, maps both in Columbus’s time and today tend to be oblong, with the east-west dimension greater than the north-south, and in fact longitude and latitude are straight Latin for “length” and “width”. Presumably the inhabitants of Italy, Egypt, California, and Chile didn’t get to vote.
In defense of Columbus, he probably was fudging his numbers to support what he knew in his seaman’s gut must be true, for several reasons. Among them were:
Incidentally, most people’s pronunciation of Newfoundland is incorrect. The residents of said island pronounce it “new-fin-LAND”, rhyming with “understand”. They do not approve of the mainlander “NEW-fin-lun” or “NEW-fund-lind”. This is important, because Newfoundlanders are proverbially touchy, as in the sour joke, “What’s black and blue and floats in the bay?” Answer: “A mainlander who tells Newfie jokes.”
If Columbus had run into a hurricane and been sunk, the New World would have been discovered by Cabot only five years later. If Cabot in turn had hit an iceberg, the Americas would have been discovered in only another three years. The Portuguese sailed to India by using the trade winds — zigging out into the Atlantic to avoid the bulge of Africa, and then zagging directly for the Cape of Good Hope. The second commercial voyage to India allegedly ran into a storm, and on Christmas Day, 1500, their fleet bumped into the coast of Brazil before it could get turned around. (A glance at a map will show how easily this accident could happen.) Anyway, that’s why their landing place was named Natal, and why they speak Portuguese in Brazil instead of Spanish.
That “allegedly” in the last paragraph is because some historians think that the Portuguese already knew about Brazil and that the 1500 expedition intended to land there all along. Cf. Cabot and the “discovery” of Newfoundland. (The fishermen of Saint-Malo, Brittany, insisted they had found both Newfoundland and Brazil before anyone else, and the records of Bristol indicate several voyages in the 1480’s trying to locate an “Island of Brazil” somewhere in the Atlantic.) After the Portuguese landing, there was considerable diplomatic wrangling over whether they were poaching on the Spanish claims much further north and west. The dispute was finally submitted to the Pope as arbitrator. He split the difference, drawing a line halfway between and assigning everything east to the Portuguese and everything west to the Spanish, who wound up getting by far the better of the deal in the long run. In the short run the Portuguese were quite happy, since they got the rights to India and the “Spice Islands” of Indonesia in addition to Brazil. After Magellan showed that the Spanish could get to the Far East “the back way”, another diplomatic wrangle ensued to extend the Pope’s line over the pole and down through the Eastern Hemisphere. This is how Spain could claim the Philippines. 23Aug11 The other major sea-faring nations of the 16th and 17th centuries, the Dutch and English, were both Protestant and therefore paid no attention to the Pope’s line, cheerfully colonizing and committing piracy wherever they felt like it.
That Greek measurement of the circumference of the Earth was quite ingenious, by the way. Around 300 bce, someone told Eratosthenes, the director of the Library of Alexandria, that at noon on a certain date the Sun was directly overhead, cast no shadows, and reflected off water at the bottom of wells at Aswan in southern Egypt. Eratosthenes immediately recognized that since the Sun was not directly overhead on that date in Alexandria, he could measure the size of the Earth by (a) measuring the angle of the Sun at Alexandria on that date, and (b) determining how far south it was to Aswan. He measured the angle himself using the shadow of a handy obelisk outside the Library, and then he hired two men to independently pace off the distance up the Nile. By averaging their results and consulting the library’s best maps, he decided that Aswan was 500 miles south of Alexandria. Since his angle measurement had shown that the Sun was “off” by 1/50 of a circle at Alexandria, the Earth must be 50 x 500 = 25,000 miles around. Q.E.D. This is in fact within 1% of the correct value, although modern geographers know that Eratosthenes was lucky, since neither of his measurements were accurate to that degree.
Other ancient geographers had estimated the curvature by observations of how quickly ships of known height and speed disappeared over the horizon, giving numbers in the same ballpark. (Not even the most uneducated persons who lived on a seacoast had ever thought the world was flat.) Astronomers and navigators measured the altitude of stars at different latitudes. In ancient times, Phoenician traders went far enough down the east coast of Africa to report that the North Star got lower and lower and finally disappeared below the horizon when they crossed the equator. Over a thousand years ago an Arab astronomer noted that the Large Magellanic Cloud was below the horizon in northern Arabia and Baghdad but was visible from southern Arabia. That distance was well-known, and the astronomer convinced the Caliph to do an accurate survey just in case, so this provided another good estimate of the circumference. The word antipodes (hypothetical persons on the opposite side of the Earth with their “feet against” ours) predates Columbus by a hundred years. Here’s a book illustration from a Geography text of about 1350. Note this shows recognition that people didn’t fall off the spherical Earth because it somehow attracted everything toward the center. Newton didn’t “invent” the force of gravity, he showed that it was universal and that it obeyed mathematical law.
The world’s spherical shape had been assumed ever since men noticed in ancient times that the Earth’s shadow during an eclipse of the Moon was always circular, no matter what the angle, and only a ball could do that. In fact, from simple geometry, the length of the month, and the fact that the center of the moon takes about three hours to cross the Earth’s shadow, Aristarchus, one of Eratosthanes’ colleagues at Alexandria, had already demonstrated that the distance to the Moon must be 30 times the diameter of the Earth. Since the 25,000-mile circumference, divided by pi, gives a 7,962-mile diameter, the Moon must be 238,860 miles away. (The current best measurement gives 238,900!) Allegedly, given those two numbers, Eratosthanes then used the geometry of an eclipse of the Sun to calculate the size of the Sun and the distance from the Sun to the Earth, producing numbers only 2% off the correct values.
The discoveries of the New World are a classic example of ideas being “in the air”. For example, the US patent office received two applications for a working telephone (from Bell and Grey) only a couple of hours apart, and it took years of litigation for Bell’s (possibly fraudulent) claim to prevail. Fifty years earlier, at least five ideas for an electrical telegraph sprouted almost simultaneously from Faraday’s work on electricity and magnetism. (Before that, a telegraph was a semaphore system using towers spaced in line of sight to each other. Both the French and English used telegraphs during the Napoleonic Wars. 22May11 The best-known was the 200-mile line connecting the Admiralty in London to the fleet bases in Plymouth and Portsmouth, in use until supplanted by a Morse-style electrical telegraph in the 1840’s. I suppose those line-of-sight hills have now sprouted microwave transmission towers.)
Separated by half the planet, Darwin and Wallace simultaneously published their works on evolution through survival of the fittest without detailed knowledge of the other’s work. 16Dec11 (The idea had been “in the air” for almost a hundred years before Darwin; he didn’t get credit for inventing it, but for proving it beyond reasonable doubt.)
As soon as the lightweight internal combustion engine was invented by Otto, automobiles and airplanes began breaking out all over, even if Daimler and the Wright Brothers tend to get the credit. Hertz showed that oscillating electric currents produced electromagnetic waves, and both Tesla and Marconi took that idea and ran with it to produce practical radios.
In 1823, János Bolyai in Hungary and Nikolai Ivanovich Lobachevsky in Russia simultaneously discovered non-Euclidean geometry. Well, the great Karl Gauss probably beat them to it, but they didn’t know it. Gauss had a distressing tendency, when somebody produced a revolutionary paper, to say, “Hmm…, that looks familiar. Oh yes, here it is in one of my notebooks from when I was a schoolchild. Never seemed worth publishing.” An eminent historian of Science said that if Gauss had published all his findings in a timely manner, he would have advanced Mathematics by fifty years. Gauss may have been the last true polymath — one who knows everything — in human history. He even wound up featured on the German 10DM banknote.
Sticking to mathematics, in 1846, Adams in England and Le Verrier in France almost simultaneously calculated the position of a planet which would explain discrepancies in the orbit of Uranus. Adams made his prediction slightly earlier, but he was ignored until Le Verrier’s publication, at which time both a British and a Prussian astronomer started looking. Unfortunately for the British, the Prussian, working with Le Verrier’s numbers, had access to a much better star chart of the region in question, so he could eliminate known objects much faster and duly identified Neptune first.
22May11 Still in the realm of math, Newton and Leibniz simultaneously invented the Calculus, leading to centuries of rancor between English and Continental mathematicians. Newton got the idea of the Calculus quite a few years before Leibniz, but never published until after the German’s book came out. (If it had been up to Newton, he probably never would have published anything. Even his masterpiece, the Principia, where he expounded the laws of motion and of gravity, required twenty years of his friends hounding him before he finally surrendered and wrote down all his ideas. His other major book, Optics, never was published in his lifetime; those friends more or less raided his desk and published it after his death. As I said elsewhere about Tesla, Newton may not have been a mad genius but he certainly teetered on the edge.)
22May11 Are you getting a theme here, that in the old days absent-minded professors might get screwed out of their ideas because, to them, the thrill of discovery far outweighed the pleasure of seeing one’s name in print? (C.f. Tom Lehrer’s song about Lobachevsky — "Plagiarize! Let no one else’s work evade your eyes! ... But please, alvays call it research!" Note that Lehrer was a Harvard mathematician.) Today this is not a problem, because of universitys’ “Publish or Perish” rules and the ability, in the USA at least, to patent everything from the alphabet on down. (In case you didn’t know it, most of your genes are patented.)
16Sep11 Two 19th-century breakthroughs about the nature of light — Maxwell’s equations of electromagnetic waves plus the Michelson-Morley experiment demonstrating that the speed of light was invariant no matter what the motion of the source — made the Special Theory of Relativity inevitable. (Einstein himself called it “Invariance Theory”.) Had he not died four years before Einstein’s 1905 paper, an Irish mathematical physicist named FitzGerald might have come up with Special Relativity first. Einstein relied heavily on FitzGerald’s work. If Einstein had decided to go on vacation in 1905, then it might have been Hendrik Lorentz instead — the heart of Relativity is still known as “Lorentz Symmetry”, which he identified in 1904, and the apparent distortion of space and time at speeds close to that of light is the “Lorentz-Fitzgerald Contraction”, a pre-relativity attempt to explain the Michelson-Morley results. Another candidate would have been Hermann Minkowski, Einstein’s teacher and “inventor” of the concept of unified space-time. If all of them had been struck by lightning outside a scientific symposium, any of half a dozen other physicists would have published the theory within a few years.
On the subject of scientific symposia, here is the most famous scientific group picture of all time, familiar to all Physics majors. Taken at the 1927 Solvay physics conference in Brussels, the 29 people in this photograph received nineteen Nobel Prizes (Mme Curie got two), and their children and spouses received at least four more. Given the solemnity of the photograph, I suppose the attendees weren’t using symposium in its literal sense — a drinking party (Greek sym-, with, and potos, drinker, as in potion). The modern meaning is from Plato’s dialog of that name, which indeed had a convivial party of philosophers as its setting. 23Apr11 “Vertical symposium” at one time was a euphemism (particularly in military-industrial circles) for an after-hours gathering at the local bar.
Special Relativity modified Newton’s Three Laws of Motion for velocities close to the speed of light. Einstein’s General Relativity — using geometry to explain gravity by treating time as a fourth dimension — was a much greater intellectual achievement than Special Relativity, because at the time there were no serious experimental or observational discrepancies which made Newton’s Law of Gravity inadequate. Einstein basically decided his explanation was more esthetically pleasing because it did not require Newton’s “force acting at a distance”, not to mention the fact that SR didn’t work right when there were any forces involved. (Newton hadn’t liked gravitation acting at a distance any better than Einstein, but couldn’t find a way to avoid it. 29Jul11 Faraday’s concept of fields and lines of force was another attempt to sidestep the problem.) Starting in about 1920, astronomers and physicists came up with experiments where Einstein’s and Newton’s gravitational equations would give different results, and Einstein’s “pretty” General Relativity was fully vindicated.
Unfortunately, the other towering scientific achievement of the 20th Century is Quantum Theory, and the two concepts flatly contradict each other. Scientists and engineers have been able to live with this for almost a century because General Relativity usually comes into play only at very, very large “astronomical” distances and sizes where gravity is all-important, whereas quantum effects are usually noticeable only at sub-atomic scales where gravity is negligible. So astronomers and cosmologists use Einstein, designers of transistors and lasers use Born, Heisenberg, and Schrödinger, everyone dealing with the “real world” (even NASA) uses Newton, and those trying to explain Black Holes, Dark Energy, and the Big Bang use Advil. Nobody has yet managed to formulate a “Theory of Everything” to reconcile the contradiction, and the toe remains the Holy Grail of theoretical physicists.
Einstein and others devised many fiendish tests to “prove” General Relativity was correct and Quantum Theory was wrong. In each experiment so far where QT and GR make different predictions, Einstein and his friends have lost, so it’s assumed that a toe will involve some sort of “quantum gravity” modifying GR, with a hypothetical “graviton” particle to carry the force just as the photon carries the electromagnetic force. Ironically, Einstein’s Nobel Prize was not given for Relativity, but for another 1905 paper which is one of the two foundations of Quantum Theory — he not only “invented” the photon, he called it an “energy quantum” and the name stuck. The other foundation is Planck’s Law of black-body radiation, published in 1901, for which he received a Nobel Prize, but Planck never accepted Quantum Theory either — the two men effectively spent the rest of their lives disclaiming the logical consequences of their own work. In another irony, the only quantum manifestation which is big enough to be visible to the naked eye is a collection of atoms called a Bose-Einstein Condensate. Satyendra Nath Bose did the math to join Planck and Einstein’s conjectures, and he did not get a Nobel Prize. As consolation, physicists classify photons, the elusive Higgs particle, and such as bosons, while the components of ordinary matter (electrons, protons, and neutrons) are called fermions, for Enrico Fermi.
Einstein and Planck were realists, of course. They grudgingly admitted that Quantum Theory worked, but they felt that there must be some underlying mechanism that was compatible with classical physics and General Relativity. “But…but…but…it can’t really work that way.” They made frequent reference to the theory of epicycles, which went back to the ancient Greeks and which predicted the motions of the planets with much better accuracy than that of Copernicus. (Epicycles would now be called a geometric attempt at a Fourier series, which can, with the right parameters, match anything.) It took a hundred years for Kepler and then Newton to come up with something better — or rather, simpler. Einstein and Planck felt that Quantum Theory must be another “wheels within wheels within wheels” kludge that would suddenly become blindingly simple when a better explanation came about. Unfortunately, it can be proven that no classical theory can explain reality, if by “classical theory” one means that (a) the laws of physics are consistent, (b) that a particle can’t be two places at once, (c) that the outcome of an experiment does not depend on when (or if) you look at it (the famous Schrödinger’s Cat paradox), and (d) that an action cannot instantaneously (rather than at the speed of light) affect the entire Universe.
General Relativity is a classical theory, meaning Einstein plays fair with space, time, and cause and effect. Quantum Theory doesn’t. Faster-than-light causation, which has been demonstrated in many laboratories by now, is identical to time running backwards, with the effect happening before the cause. Recently, it was suggested that the two theories could be reconciled if Lorentz Symmetry was discarded — essentially saying that the laws of physics are not the same in all directions — but that introduces a host of problems, too. (For one thing, Quantum Theory does require Special Relativity — an often-cited example is that QT cannot explain the yellow color of Gold or the liquidity of Mercury at room temperature without invoking SR in the behavior of their electrons. Therefore, breaking Lorentz Symmetry breaks SR and GR and QT, all three. This seems somewhat counter-productive to understanding The World As We Know It.)
One familiar gadget which does have to take General Relativity into account is the Global Positioning System. According to Einstein, time runs at different rates in higher or lower gravity, and GPS receivers are so precise they have to compensate for the fact that clocks in the transmitting satellites are further from the center of the Earth and thus in a lower gravity field. I recently read a newspaper account of an athletic physicist who back-packed an atomic clock to the top of Mt. Rainier and demonstrated that it ran slower than it did down in Seattle. I also read an account of an experiment showing this with one atom. The scientists basically split it in half via quantum trickery. The two “virtual atoms“ traveled the exact same distance and then were recombined into the original atom. If the two paths were side-by-side, this worked fine. On the other hand, if the apparatus was rotated so that one path was above the other, the recombination wasn’t quite perfect because time ran slower for the upper one and it arrived slightly late!
In Einstein’s four-dimensional universe, everything is always moving at c, the speed of light. That is, the sum of the velocities through all four dimensions — three of space and one of time — must be exactly equal to c. Therefore, Relativity says that a body at rest in space is moving at c through time, and any spatial motion must subtract off of that and thus slightly slow it through time. This motion-derived time reduction is quite easily measured. Physicists know, for example, that a certain particle always decays into something else in a millionth of a second. However, if it is spun up to 0.99 c in a particle accelerator, observations show it now lasts a thousandth of a second instead — time is flowing a thousand times slower for the fast-moving particle. If you ship a very accurate clock by commercial air liner from New York to California, it will be measurably slow upon arrival due to the speed of the plane. (This is a different effect than the gravity anomaly mentioned earlier.) Another example is the fact that cosmic rays can be detected on the ground. Primary cosmic ray particles actually “break up” high in the atmosphere, releasing a shower of short-lived particles that can be measured at ground level. However, these secondary particles wouldn’t make it all the way to the ground before themselves decaying except for the time dilation from traveling so close to the speed of light. Those primary cosmic ray particles (each a single atomic nucleus) are moving so close to the speed of light that they strike with the force of a baseball pitcher’s fastball. I find it mind-boggling that, in theory, someone in a space suit could be killed by being hit with one atom!
Einstein’s instinctive rejection of quantum physics and its adherents was almost certainly aesthetic again — Quantum Theory was and is profoundly ugly, and even many of its users don’t really want to believe the Universe actually works that way. Unfortunately, Physics doesn’t seem to be a democracy or beauty contest. The current candidates for a toe invoke ten or eleven spatial dimensions, most of which are curled up too small to see, so theoretical beauty is not on the current horizon. On the other hand, so far none of these so-called superstring theories meet the minimum standard for any scientific theory, namely the ability to make a prediction that can be verified by experiment or observation. The quantum “Standard Model” that explains everything but gravity, on the other hand, makes by far the most accurate predictions (to maybe fifteen decimal places) in all of science, but nobody knows WHY. (The current search for the Higgs Boson is because its detection would allow the Standard Model to predict the masses of all particles and therefore of the Universe as a whole. This obviously would be a significant step to unifying quantum theory and gravity.)
One major problem with theories of gravity is the difficulty of performing experiments. The force of gravity is 100,000,000,000,000,000,000,000,000,000,000,000 times weaker than the electro-magnetic force, meaning it’s that much harder to detect the alleged graviton and do “gravital” experiments compared to electrical stuff with photons and electrons. (The CCD detectors in cheap consumer digital cameras can detect and count individual photons — 1…2…3…. So can the human eye’s retina, but the brain filters out any signal less than about seven photons to avoid confusion.) Fortunately, electricity comes in positive and negative varieties, so the tremendously powerful electrical forces cancel out in ordinary matter. There is no “anti-gravity”, however, so gravity is purely additive and must dominate if the mass gets large enough. Note that it took the entire mass of the Earth (6,000,000,000,000,000,000,000 tons) to generate enough pull to overcome the electrical forces in the stem of Newton’s apple holding it to the tree, and a tiny refrigerator magnet can overcome the gravitational force of the Earth to levitate a paper clip. It takes the gravity of a mass the size of the Sun (i.e., a million times the mass of the Earth — add six more zeros to the above number) to overcome the electrical forces that repel atoms and crush a star into a white dwarf. Add yet one more zero to get enough gravitational pressure to collapse the atoms altogether and form a neutron star.
