Posts Tagged ‘Einstein’
“in this case there were three determinate states the cat could be in: these being Alive, Dead, and Bloody Furious”*…
Of all the bizarre facets of quantum theory, few seem stranger than those captured by Erwin Schrödinger’s famous fable about the cat that is neither alive nor dead. It describes a cat locked inside a windowless box, along with some radioactive material. If the radioactive material happens to decay, then a device releases a hammer, which smashes a vial of poison, which kills the cat. If no radioactivity is detected, the cat lives. Schrödinger dreamt up this gruesome scenario to mock what he considered a ludicrous feature of quantum theory. According to proponents of the theory, before anyone opened the box to check on the cat, the cat was neither alive nor dead; it existed in a strange, quintessentially quantum state of alive-and-dead.
Today, in our LOLcats-saturated world, Schrödinger’s strange little tale is often played for laughs, with a tone more zany than somber. It has also become the standard bearer for a host of quandaries in philosophy and physics. In Schrödinger’s own time, Niels Bohr and Werner Heisenberg proclaimed that hybrid states like the one the cat was supposed to be in were a fundamental feature of nature. Others, like Einstein, insisted that nature must choose: alive or dead, but not both.
Although Schrödinger’s cat flourishes as a meme to this day, discussions tend to overlook one key dimension of the fable: the environment in which Schrödinger conceived it in the first place. It’s no coincidence that, in the face of a looming World War, genocide, and the dismantling of German intellectual life, Schrödinger’s thoughts turned to poison, death, and destruction. Schrödinger’s cat, then, should remind us of more than the beguiling strangeness of quantum mechanics. It also reminds us that scientists are, like the rest of us, humans who feel—and fear…
More of this sad story at “How Einstein and Schrödinger Conspired to Kill a Cat.”
* Terry Patchett
As we refrain from lifting the box’s lid, we might spare a thought for Charles Babbage; he died on this date in 1871. A mathematician, philosopher, inventor and mechanical engineer, Babbage is best remembered for originating the concept of a programmable computer. Anxious to eliminate inaccuracies in mathematical tables. By 1822, he built small calculating machine able to compute squares (1822). He then produced prototypes of portions of a larger Difference Engine. (Georg and Edvard Schuetz later constructed the first working devices to the same design which were successful in limited applications.) In 1833 he began his programmable Analytical Machine (AKA, the Analytical Engine), the forerunner of modern computers, with coding help from Ada Lovelace, who created an algorithm for the Analytical Machine to calculate a sequence of Bernoulli numbers— for which she is remembered as the first computer programmer.
Babbage’s other inventions include the cowcatcher, the dynamometer, the standard railroad gauge, uniform postal rates, occulting lights for lighthouses, Greenwich time signals, and the heliograph opthalmoscope. He was also passionate about cyphers and lock-picking.
“To me there is no past or future in art. If a work of art cannot live always in the present it must not be considered at all.”*…
… Evangelical Christians look to the book of Revelations for clues as to what’s to come next; the secular world looks to contemporary art, which seems to operate in a world that has calcified into a self-propagating MFA‑ocracy as orthodox as any extremist religion. But when did making art and foretelling the future become the same thing? What’s the rush? The rush is already coming at us quickly enough. The future of art has to be something that will give us bit of slow. And I hope that it happens quickly…
* Pablo Picasso
As we celebrate, on 3.14.16, both Pi Day and Einstein’s birthday, we might send ontological birthday greetings to Maurice Merleau-Ponty; he was born on this date in 1908. a phenomenological philosopher who was strongly influenced by Husserl and Heidegger, Merleau-Ponty wrote about perception, art, and politics in the service of understanding the constitution of human experience and meaning. He served on the editorial board of Sartre’s Les Temps modernes. His work has been widely influential, from Hubert Dreyfus’s use of Merleau-Ponty’s thought in the seminal What Computers Can’t Do, to the rise of French, then European feminism. At his death (in 1961) he was working towards an understanding of “Ecophenomenology,” suggesting in notes left behind the need for “a radically transformed understanding of ‘nature'”: “Do a psychoanalysis of Nature: it is the flesh, the mother… Nature as the other side of humanity (as flesh, nowise as ‘matter’).”
Last week, scientists at The Laser Interferometer Gravitational-Wave Observatory, or LIGO, announced that they had confirmed Einstein’s century-old theoretical prediction of “gravitational waves,” a feature of his theory of general relativity.
Our friends at PhD Comics explain why that matters:
* Terry Pratchett
As we go with the flow, we might send carefully-calculated birthday greetings to Einstein’s rough contemporary Alfred North Whitehead; he was born on this date in 1861. Whitehead began his career as a mathematician and logician, perhaps most famously co-authoring (with his former student, Bertrand Russell), the three-volume Principia Mathematica (1910–13), one of the twentieth century’s most important works in mathematical logic.
But in the late teens and early 20s, Whitehead shifted his focus to philosophy, the central result of which was a new field called process philosophy, which has found application in a wide variety of disciplines (e.g., ecology, theology, education, physics, biology, economics, and psychology).
“There is urgency in coming to see the world as a web of interrelated processes of which we are integral parts, so that all of our choices and actions have consequences for the world around us.”
“If it was so, it might be; and if it were so, it would be; but as it isn’t, it ain’t. That’s logic.”*…
Your correspondent is headed into the chilly wilds for the Thanksgiving holiday, so this will be the last post until after the passing of the tryptophan haze. By way of keeping readers amused in the meantime, the puzzle above…
Find a step-by-step guide to its answer at “How to Solve the Hardest Logic Puzzle Ever.”
* Tweedledee, in Lewis Caroll’s Through the Looking-Glass, and What Alice Found There
As we muddle in the excluded middle, we might recall that it was on this date in 1915 that Albert Einstein presented the Einstein Field Equations to the Prussian Academy of Sciences. Einstein developed what was elaborated into a set of 10 equations to account for gravitation in the curved spacetime described in his General Theory of Relativity; they are used to determine spacetime geometry.
(German mathematician David Hilbert reached the same conclusion, and actually published the equation before Einstein– though Hilbert, who was a correspondent of Einstein’s, never suggested that Einstein’s credit was inappropriate.)
“A child[’s]…first geometrical discoveries are topological…If you ask him to copy a square or a triangle, he draws a closed circle”*…
Topology is the Silly Putty of mathematics. Indeed, sometimes, topology is called “rubber-sheet geometry” because topologists study the properties of shapes that don’t change when an object is stretched or distorted. As Cliff Pickover explains, this leads to the creation of some pretty confounding shapes…
Mathematicians continue to invent strange objects to test their intuitions. Alexander’s horned sphere [above] is an example of a convoluted, intertwined surface for which it is difficult to define an inside and outside. Introduced by mathematician James Waddell Alexander (1888 – 1971), Alexander’s horned sphere is formed by successively growing pairs of horns that are almost interlocked and whose end points approach each other. The initial steps of the construction can be visualized with your fingers. Move the thumb and forefinger of each of your hands close to one another, then grow a smaller thumb and forefinger on each of these, and continue this budding without limit!
Although this may be hard to visualize, Alexander’s horned sphere is homeomorphic to a ball. In this case, this means that it can be stretched into a ball without puncturing or breaking it. Perhaps it is easier to visualize the reverse: stretching the ball into the horned sphere without ripping it. The boundary is, therefore, homeomorphic to a sphere…
Read more at “The Official Alexander Sphere Appreciation Page.”
* Jean Piaget
As we twist and turn, we might send artfully-folded birthday greetings to Sir Erik Christopher Zeeman; he was born on this date in 1925. While he is probably most-widely known as a popularizer of Catastrophe Theory, his primary contributions to math have been in topology, more particularly in geometric topology (e.g., in knot theory) and in dynamical systems. The Christopher Zeeman Medal for Communication of Mathematics of the London Mathematical Society and the Institute of Mathematics and its Applications is named in his honor.
We might also spare a thought for Satyendra Nath Bose; he died on his date in 1974. A physicist and mathematician, he collaborated with Albert Einstein to develop a theory of statistical quantum mechanics, now called Bose-Einstein statistics. Paul Dirac named the class of particles that obey Bose–Einstein statistics, bosons, after Bose.
For over two decades, The Simpsons has been one of the best written and most entertaining programs on television. Simon Singh believes that he’s discovered the series’ secret sauce: it’s written by math geeks who unreservedly lard the show with math gags…
The first proper episode of the series in 1989 contained numerous mathematical references (including a joke about calculus), while the infamous “Treehouse of Horror VI” episode presents the most intense five minutes of mathematics ever broadcast to a mass audience. Moreover, The Simpsons has even offered viewers an obscure joke about Fermat’s last theorem, the most notorious equation in the history of mathematics.
These examples are just the tip of the iceberg, because the show’s writing team includes several mathematical heavyweights. Al Jean, who worked on the first series and is now executive producer, went to Harvard University to study mathematics at the age of just 16. Others have similarly impressive degrees in maths, a few can even boast PhDs, and Jeff Westbrook resigned from a senior research post at Yale University to write scripts for Homer, Marge and the other residents of Springfield…
More on the numerical nuttiness here.
And readers can test themselves against The Simpsons writing room in this multiple choice test (wherein one will find, among other amusements, the answer to the riddle in the title above).
As we wonder how cartoon characters count with only four fingers, we might pause to remember Sir Arthur Stanley Eddington, OM, FRS; he died in this date in 1944. An astrophysicist, mathematician, and philosopher of science known for his work on the motion, distribution, evolution and structure of stars, Eddington is probably best remembered for his relationship to Einstein: he was, via a series of widely-published articles, the primary “explainer” of Einstein’s Theory of General Relativity to the English-speaking world; and he was, in 1919, the leader of the experimental team that used observations of a solar eclipse to confirm the theory.
Dictionary of Numbers is an award-winning Google Chrome extension that tries to make sense of numbers encountered on the web by providing descriptions of those numbers in human terms. Just as a dictionary describes words one doesn’t know in terms one does, so Dictionary of Numbers puts unfamiliar quantities in understandable, recognizable terms… “Because ‘8 million people’ means nothing, but ‘population of New York City’ means everything.”
As we graduate from our fingers and toes, we might spare a thought for Jules Henri Poincaré; he died on this date in 1912. A mathematician, theoretical physicist, engineer, and a philosopher of science, Poincaré is considered the “last Universalist” in math– the last mathematician to excel in all fields of the discipline as it existed during his lifetime.
Poincaré was a co-discoverer (with Einstein and Lorentz) of the special theory of relativity; he laid the foundations for the fields of topology and chaos theory; and he had a huge impact on cosmogony. His famous “Conjecture” held that if any loop in a given three-dimensional space can be shrunk to a point, the space is equivalent to a sphere; it remained unsolved until Grigori Perelman completed a proof in 2003.