Infinitely cool…
How to Count to Infinity (or “Yes, Virginia, some infinities are bigger than others…”)
Many more sixty-second epiphanies at MinutePhysics’ You Tube channel (or via New Scientist TV)
***
As we check in to Hilbert’s Hotel, we might spare a thought for Joesph Fourier; the French mathematician, physicist, Egyptologist and administrator who died on this date in 1830. Fourier introduced Jean-Francois Champollion to the Rosetta Stone, which Champollion subsequently decoded/translated. And after calculating that a body the size of earth, at earth’s distance form the sun, should be cooler than our world is, discovered what we now call “the greenhouse effect.” But Fourier is best remembered for his contributions to mathematical physics through his Théorie analytique de la chaleur (1822; The Analytical Theory of Heat), which introduced an infinite mathematical series to aid in solving conduction equations. (The technique allowed the function of any variable to be expanded into a series of sines of multiples of the variable– now known as “the fourier series.”)
True greatness is when your name is like ampere, watt, and fourier—when it’s spelled with a lower case letter.
- Richard Hamming (in a 1986 Bell Labs Colloquium)
The Widening Gyre…
click here, and again, for larger version at source
TURNING and turning in the widening gyre
The falcon cannot hear the falconer;
Things fall apart; the centre cannot hold;
Mere anarchy is loosed upon the world,
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned;
The best lack all conviction, while the worst
Are full of passionate intensity.Surely some revelation is at hand;
Surely the Second Coming is at hand.
The Second Coming! Hardly are those words out
When a vast image out of Spiritus Mundi
Troubles my sight: somewhere in sands of the desert
A shape with lion body and the head of a man,
A gaze blank and pitiless as the sun,
Is moving its slow thighs, while all about it
Reel shadows of the indignant desert birds.
The darkness drops again; but now I know
That twenty centuries of stony sleep
Were vexed to nightmare by a rocking cradle,
And what rough beast, its hour come round at last,
Slouches towards Bethlehem to be born?- “The Second Coming,” W.B. Yeats
***
As we remark that the spiral will continue we know not where, we might send eclectic birthday greetings to Persian polymath Omar Khayyam; the philosopher, mathematician, astronomer, epigrammatist, and poet was born on this date in 1048. While he’s probably best known to English-speakers as a poet, via Edward FitzGerald’s famous translation of the quatrains that comprise the Rubaiyat of Omar Khayyam, Omar was one of the major mathematicians and astronomers of the medieval period. He is the author of one of the most important treatises on algebra written before modern times, the Treatise on Demonstration of Problems of Algebra, which includes a geometric method for solving cubic equations by intersecting a hyperbola with a circle. His astronomical observations contributed to the reform of the Persian calendar. And he made important contributions to mechanics, geography, mineralogy, music, climatology and Islamic theology.
Objectiv(ist) advice…
Dear Ayn,
I’m dating a man who I think I love, but I’m afraid he’s having an affair. He comes home late, he acts suspiciously, and he even has red lipstick on his collar. Should I confront him or just hope for the best?
— County Affair
Dear County,
Red lipstick? Your husband is a communist. Divorce him and sell his clothes, children, and pens to make money to spend on cars, human slaves, and bigger pens. This will simultaneously stimulate the economy and punish the slaves for not having jobs. Slaves: what lazybones!
Hope this helps,
Ayn
More advice-for-the-sniveling at Megan Amran’s “Ann Randers” in McSweeney’s.
***
As we remind ourselves that the economic debacle of 9-15-08 was maybe not so surprising after, given Chairman Greenspan’s devotion to Ms. Rand, we might spare a thought for a strong woman of a very different sort; free-thinker Emma Goldman died on this date in 1940. A political activist, writer, and speaker, she founded Mother Earth magazine in 1906. She played a pivotal role in the development of anarchist political philosophy in North America and Europe in the first half of the twentieth century.
Anarchism, then, really stands for the liberation of the human mind from the dominion of religion; the liberation of the human body from the dominion of property; liberation from the shackles and restraint of government. Anarchism stands for a social order based on the free grouping of individuals for the purpose of producing real social wealth; an order that will guarantee to every human being free access to the earth and full enjoyment of the necessities of life, according to individual desires, tastes, and inclinations.
- from the title essay, Anarchism and Other Essays, 1910
Perhaps even more than constituted authority, it is social uniformity and sameness that harass the individual most. His very “uniqueness,” “separateness” and “differentiation” make him an alien, not only in his native place, but even in his own home.
Like this:
Grace period…
Archaeologist William Saturno of Boston University excavates the house in the ruins of the Maya city of Xultun.
It’s with mixed emotions that your correspondent notes the emergence of firm evidence that the painfully powerfully-prescient Mayans did not in fact believe that the world will end this year…
In a striking find, archaeologists in Guatemala report the discovery of a small building whose walls display not only a stunningly preserved mural of a brightly adorned Mayan king, but also calendars that destroy any notion that the Mayans predicted the end of the world in 2012.
These deep-time calendars can be used to count thousands of years into the past and future, countering pop-culture and New Age ideas that Mayan calendars ended on Dec. 21, 2012, (or Dec. 23, depending on who’s counting), thereby predicting the end of the world.
The newly found calendars, which track the motion of the moon, Venus and Mars, provide an unprecedented glimpse into how these storied sky-gazers — who dominated Central America for nearly 1,000 years — kept such accurate track of months, seasons and years.
“What they’re trying to do is understand the large cycles of cosmic time,” said William Saturno, the Boston University archaeologist who led the expedition. “This is the space they’re doing it in. It’s like looking into da Vinci’s workshop.”
Before the new find, the best-preserved Mayan calendars were inscribed in bark-paged books called codices, the most famous being the Dresden Codex. But those pages hail from several hundred years later than the newly found calendars…
After retracting the invitations and canceling the caterers– so much for what would have been, literally, the party to end all parties– readers will find the full story in the Washington Post.
***
As we reconcile ourselves to more of the same, we might recall that it was on this date in 1839 that a huge 33-year-old man named Thomas Rees, AKA Twm Carnabwth, led a group of men dressed in women’s clothing in an attack on the toll gate at Efailwen, in Wales. The group called itself Merched Beca (“the Daughters of Rebecca”), and went on for another four years to attack and destroy toll gates in Wales. The “Rebecca Riots,” as they became known,” were the reaction of local tenant farmers and farmer workers to the imposition of tolls on local roads (and other taxes and rent increases they perceived as unfair). In the end, some rent reductions were achieved, the toll rates were reduced (but not eliminated: destroyed toll-houses were rebuilt), and the protests prompted several other reforms (e.g., Turnpikes Act of 1844, which simplified rates and reduced the hated toll on lime movement by half). But surely most significantly, the riots inspired later Welsh protests.
Depiction of the Rebecca Riots, Illustrated London News 1843
To See What Condition My Condition Was In…
Could Quantum Mechanics be wrong?
The philosophical status of the wavefunction — the entity that determines the probability of different outcomes of measurements on quantum-mechanical particles — would seem to be an unlikely subject for emotional debate. Yet online discussion of a paper claiming to show mathematically that the wavefunction is real has ranged from ardently star-struck to downright vitriolic since the article was first released as a preprint in November 2011.
The paper, thought by some to be one of the most important in quantum foundations in decades, was finally published last week in Nature Physics (M. F. Pusey, J. Barrett & T. Rudolph Nature Phys. http://dx.doi.org/10.1038/nphys2309; 2012), enabling the authors, who had been concerned about violating the journal’s embargo, to speak about it publicly for the first time. They say that the mathematics leaves no doubt that the wavefunction is not just a statistical tool, but rather, a real, objective state of a quantum system…
The authors have some heavyweights in their corner: their view was once shared by Austrian physicist and quantum-mechanics pioneer Erwin Schrödinger, who proposed in his famous thought experiment that a quantum-mechanical cat could be dead and alive at the same time. But other physicists have favoured an opposing view, one held by Albert Einstein: that the wavefunction reflects the partial knowledge an experimenter has about a system. In this interpretation, the cat is either dead or alive, but the experimenter does not know which. This ‘epistemic’ interpretation, many physicists and philosophers argue, better explains the phenomenon of wavefunction collapse, in which a quantum state is fundamentally changed by measuring it…
Read the full story in Nature.
***
As we listen for the tell-tale purr, we might spare a thought for Gerbert d’Aurillac (who became Pope Sylvester II); he died on this date in 1003. Gerbert/Sylvester was never canonized; indeed, in his day, he dogged with rumors that he was a sorcerer in league with the devil… which appear to have been the work of reactionary forces resisting both Sylvester’s attempts to rid the Church of corruption (especially simony, the sale of sacraments and indulgences) and his attempts to popularize mathematics, astronomy and mechanics for lay audiences. Inspired by translations of Arabic texts, he built clocks, invented the hydraulic organ, crafted astronomical instruments, and renewed interest in the abacus for use in mathematical calculations (in the process of which, he seems to have introduced Arabic numerals [except zero]). It’s not a stretch to suggest that Gerbert/Sylvester began Europe’s long march out of the Dark Ages.
