Posts Tagged ‘Kepler’
“The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.”*…
As Tom Siegfried explains, the “music of the spheres” was born from the effort to use numbers to explain the universe…
If you’ve ever heard the phrase “the music of the spheres,” your first thought probably wasn’t about mathematics.
But in its historical origin, the music of the spheres actually was all about math. In fact, that phrase represents a watershed in the history of math’s relationship with science.
In its earliest forms, as practiced in ancient Egypt and Mesopotamia, math was mainly a practical tool for facilitating human interactions. Math was important for calculating the area of a farmer’s field, for keeping track of workers’ wages, for specifying the right amount of ingredients when making bread or beer. Nobody used math to investigate the nature of physical reality.
Not until ancient Greek philosophers began to seek scientific explanations for natural phenomena (without recourse to myths) did anybody bother to wonder how math would help. And the first of those Greeks to seriously put math to use for that purpose was the mysterious religious cult leader Pythagoras of Samos.
It was Pythagoras who turned math from a mere tool for practical purposes into the key to unlocking the mysteries of the universe. As the historian Geoffrey Lloyd noted, “The Pythagoreans were … the first theorists to have attempted deliberately to give the knowledge of nature a quantitative, mathematical foundation.”…
More at: “How Pythagoras turned math into a tool for understanding reality,” from @tom_siegfried in @ScienceNews.
Apposite: Walter Murch’s ideas on “planetary harmony” (and Lawrence Weschler’s book on him and them)
* Henri Poincare
###
As we seek beauty, we might recall that it was on this date in 1595 that Johann Kepler (and here) published Mysterium cosmographicum (Mystery of the Cosmos), in which he described an invisible underlying structure determining the six known planets in their orbits. Kepler thought as a mathematician, devising a structure based on only five convex regular solids; the path of each planet lay on a sphere separated from its neighbors by touching an inscribed polyhedron.
It was a beautiful, an elegant model– and one that fit the orbital data available at the time. It was of course, nonetheless, wrong.
“Werner Heisenberg once proclaimed that all the quandaries of quantum mechanics would shrivel up when 137 was finally explained”*…
One number to rule them all?
Does the Universe around us have a fundamental structure that can be glimpsed through special numbers?
The brilliant physicist Richard Feynman (1918-1988) famously thought so, saying there is a number that all theoretical physicists of worth should “worry about”. He called it “one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man.”
That magic number, called the fine structure constant, is a fundamental constant, with a value which nearly equals 1/137. Or 1/137.03599913, to be precise. It is denoted by the Greek letter alpha – α.
What’s special about alpha is that it’s regarded as the best example of a pure number, one that doesn’t need units. It actually combines three of nature’s fundamental constants – the speed of light, the electric charge carried by one electron, and the Planck’s constant, as explains physicist and astrobiologist Paul Davies to Cosmos magazine. Appearing at the intersection of such key areas of physics as relativity, electromagnetism and quantum mechanics is what gives 1/137 its allure…
The fine structure constant has mystified scientists since the 1800s– and might hold clues to the Grand Unified Theory: “Why the number 137 is one of the greatest mysteries in physics,” from Paul Ratner (@paulratnercodex) in @bigthink.
* Leon M. Lederman, The God Particle: If the Universe Is the Answer, What Is the Question?
###
As we ruminate on relationships, we might spare a thought for Georg von Peuerbach; he died on this date in 1461. A mathematician, astronomer, and instrument maker, he is probably best remembered for his streamlined presentation of Ptolemaic astronomy in the Theoricae Novae Planetarum (which was an important text for many later-influential astronomers including Nicolaus Copernicus and Johannes Kepler).
But perhaps as impactful was his promotion of the use of Arabic numerals (introduced 250 years earlier in place of Roman numerals), especially in a table of sines he calculated with unprecedented accuracy.
“Happy accidents are real gifts”*…
On the morning of July 25, 1610, Galileo pointed his telescope at Saturn and was surprised to find that it appeared to be flanked by two round blobs or bumps, one on either side. Unfortunately, Galileo’s telescope wasn’t quite advanced enough to pick out precisely what he had seen (his observations are now credited with being the earliest description of Saturn’s rings in astronomical history), but he nevertheless presumed that whatever he had seen was something special. And he wanted people to know about it.
Keen to announce his news and thereby secure credit for whatever it was he had discovered, Galileo sent letters to his friends and fellow astronomers. This being Galileo, the announcement was far from straightforward:
SMAISMRMILMEPOETALEUMIBUNENUGTTAUIRAS
Each message that Galileo sent out contained little more than that jumbled string of letters, which when rearranged correctly spelled out the Latin sentence, “altissimum planetam tergeminum observavi”—or “I have observed that the highest planet is threefold.”
As the outermost planet known to science at the time, Saturn was the “highest planet” in question. And unaware that he had discovered its rings, Galileo was merely suggesting to his contemporaries that he had found that the planet was somehow divided into three parts. Announcing such a discovery in the form of an anagram might have bought Galileo some time to continue his observations, however, but there was a problem: Anagrams can easily be misinterpreted.
One of those to whom Galileo sent a letter was the German scientist Johannes Kepler. A keen astronomer himself, Kepler had followed and supported Galileo’s work for several years, so when the coded letter arrived at his home in Prague he quickly set to work solving it. Unfortunately for him, he got it completely wrong.
Kepler rearranged Galileo’s word jumble as “salve, umbistineum geminatum Martia proles,” which he interpreted as “be greeted, double-knob, children of Mars.” His solution was far from perfect (umbistineum isn’t really a grammatical Latin word, for one thing), but Kepler was nevertheless convinced that, not only had he correctly solved the riddle, but Galileo’s apparent discovery proved a theory he had been contemplating for several months.
Earlier in 1610, Galileo had discovered the four so-called “Galilean moons” of Jupiter: Io, Europa, Ganymede and Callisto. Although we now know that Jupiter has several dozen moons of varying shapes, sizes, and orbits, at the time the announcement of just four natural satellites had led Kepler to presume that there must be a natural progression in the heavens: the Earth has one moon; Jupiter, two places further out from the Earth, has four; and sat between the two is Mars, which Kepler theorized must surely have two moons, to maintain the balanced celestial sequence 1, 2, 4 and so on (his only question was whether Saturn had six or eight).
Kepler got the anagram wrong, and the presumption that Jupiter only had four moons had been wrong. Yet as misguided as both these facts were, the assumption that Kepler made based on both of them—namely, that Mars had two moons—was entirely correct. Unfortunately for Kepler, his theory would not be proved until long after his death, as the two Martian moons Phobos and Deimos (named after Ares’s sons in Greek Mythology) were not discovered until 1877, by the American astronomer Asaph Hall.
Nevertheless, a misinterpretation of the anagram had accidentally predicted a major astronomical discovery of the 19th century, nearly 300 years before it occurred…
Serendipity in science: “How A Misinterpreted Anagram Predicted The Moons of Mars.”
(For an account of Isaac Newton’s use of anagrams in his scientific communications, see here.)
* David Lynch
###
As we code and decode, we might recall that it was on this date in 1781 that English astronomer William Herschel detected every schoolboy’s favorite planet, Uranus, in the night sky (though he initially thought it was a comet); it was the first planet to be classified as such with the aid of a telescope. In fact, Uranus had been detected much earlier– but mistaken for a star: the earliest likely observation was by Hipparchos, who (in 128 BC) seems to have recorded the planet as a star for his star catalogue, later incorporated into Ptolemy’s Almagest. The earliest definite sighting was in 1690 when John Flamsteed observed it at least six times, cataloguing it as the star 34 Tauri.
Herschel named the planet in honor of his King: Georgium Sidus (George’s Star), an unpopular choice, especially outside England; argument over alternatives ensued. Berlin astronomer Johann Elert Bode came up with the moniker “Uranus,” which was adopted throughout the world’s astronomical community by 1850.
“The truth is not always beautiful, nor beautiful words the truth.”*…
Does anyone who follows physics doubt it is in trouble? When I say physics, I don’t mean applied physics, material science or what Murray-Gell-Mann called “squalid-state physics.” I mean physics at its grandest, the effort to figure out reality. Where did the universe come from? What is it made of? What laws govern its behavior? And how probable is the universe? Are we here through sheer luck, or was our existence somehow inevitable?
In the 1980s Stephen Hawking and other big shots claimed that physics was on the verge of a “final theory,” or “theory of everything,” that could answer these big questions and solve the riddle of reality. I became a science writer in part because I believed their claims, but by the early 1990s I had become a skeptic. The leading contender for a theory of everything held that all of nature’s particles and forces, including gravity, stem from infinitesimal, stringy particles wriggling in nine or more dimensions.
The problem is that no conceivable experiment can detect the strings or extra dimensions…
John Horgan examines physicist Sabine Hossenfelder‘s claim that desire for beauty and other subjective biases have led physicists astray: “How Physics Lost Its Way.”
* Lao Tzu, Tao Te Ching
###
As we contemplate certainty, we might recall that it was on this date in 1595 that Johann Kepler (and here) published Mysterium cosmographicum (Mystery of the Cosmos), in which he described an invisible underlying structure determining the six known planets in their orbits. Kepler thought as a mathematician, devising a structure based on only five convex regular solids; the path of each planet lay on a sphere separated from its neighbors by touching an inscribed polyhedron.
It was a beautiful, an elegant model– and one that fit the orbital data available at the time. It was, nonetheless, wrong.
Detailed view of Kepler’s inner sphere
“The map is not the territory”*…
With the advent of GPS systems and cell-phone-based mapping guidance…
…many of us have stopped paying attention to the world around us because we are too intent on following directions. Some observers worry that this represents a new and dangerous shift in our style of navigation. Scientists since the 1940s have argued we normally possess an internal compass, “a map-like representation within the ‘black box’ of the nervous system,” as geographer Rob Kitchin puts it. It’s how we know where we are in our neighborhoods, our cities, the world.
Is it possible that today’s global positioning systems and smartphones are affecting our basic ability to navigate? Will technology alter forever how we get around?
Most certainly—because it already has. Three thousand years ago, our ancestors began a long experiment in figuring out how they fit into the world, by inventing a bold new tool: the map…
Get your bearings at: “From Ptolemy to GPS, the Brief History of Maps”
* Alfred Korzybski
###
As we follow the directions, we might recall that it was on this date in 1595 that Johann Kepler (and here) published Mysterium cosmographicum (Mystery of the Cosmos), in which he described an invisible underlying structure determining the six known planets in their orbits. Kepler thought as a mathematician, devising a structure based on only five convex regular solids; the path of each planet lay on a sphere separated from its neighbors by touching an inscribed polyhedron.
It was an elegant model– and one that fit the orbital data available at the time. It was, nonetheless, wrong.
Detailed view of Kepler’s inner sphere
You must be logged in to post a comment.