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Posts Tagged ‘Omar Khayyam

“If and when all the laws governing physical phenomena are finally discovered, and all the empirical constants occurring in these laws are finally expressed through the four independent basic constants, we will be able to say that physical science has reached its end”*…

The fine-structure constant was introduced in 1916 to quantify the tiny gap between two lines in the spectrum of colors emitted by certain atoms. The closely spaced frequencies are seen here through a Fabry-Pérot interferometer.

As fundamental constants go, the speed of light, c, enjoys all the fame, yet c’s numerical value says nothing about nature; it differs depending on whether it’s measured in meters per second or miles per hour. The fine-structure constant, by contrast, has no dimensions or units. It’s a pure number that shapes the universe to an astonishing degree — “a magic number that comes to us with no understanding,” as Richard Feynman described it. Paul Dirac considered the origin of the number “the most fundamental unsolved problem of physics.”

Numerically, the fine-structure constant, denoted by the Greek letter α (alpha), comes very close to the ratio 1/137. It commonly appears in formulas governing light and matter. “It’s like in architecture, there’s the golden ratio,” said Eric Cornell, a Nobel Prize-winning physicist at the University of Colorado, Boulder and the National Institute of Standards and Technology. “In the physics of low-energy matter — atoms, molecules, chemistry, biology — there’s always a ratio” of bigger things to smaller things, he said. “Those ratios tend to be powers of the fine-structure constant.”

The constant is everywhere because it characterizes the strength of the electromagnetic force affecting charged particles such as electrons and protons. “In our everyday world, everything is either gravity or electromagnetism. And that’s why alpha is so important,” said Holger Müller, a physicist at the University of California, Berkeley. Because 1/137 is small, electromagnetism is weak; as a consequence, charged particles form airy atoms whose electrons orbit at a distance and easily hop away, enabling chemical bonds. On the other hand, the constant is also just big enough: Physicists have argued that if it were something like 1/138, stars would not be able to create carbon, and life as we know it wouldn’t exist.

Physicists have more or less given up on a century-old obsession over where alpha’s particular value comes from; they now acknowledge that the fundamental constants could be random, decided in cosmic dice rolls during the universe’s birth. But a new goal has taken over.

Physicists want to measure the fine-structure constant as precisely as possible. Because it’s so ubiquitous, measuring it precisely allows them to test their theory of the interrelationships between elementary particles — the majestic set of equations known as the Standard Model of particle physics. Any discrepancy between ultra-precise measurements of related quantities could point to novel particles or effects not accounted for by the standard equations. Cornell calls these kinds of precision measurements a third way of experimentally discovering the fundamental workings of the universe, along with particle colliders and telescopes…

In a new paper in the journal Nature, a team of four physicists led by Saïda Guellati-Khélifa at the Kastler Brossel Laboratory in Paris reported the most precise measurement yet of the fine-structure constant. The team measured the constant’s value to the 11th decimal place, reporting that α = 1/137.03599920611. (The last two digits are uncertain.)

With a margin of error of just 81 parts per trillion, the new measurement is nearly three times more precise than the previous best measurement in 2018 by Müller’s group at Berkeley, the main competition. (Guellati-Khélifa made the most precise measurement before Müller’s in 2011.) Müller said of his rival’s new measurement of alpha, “A factor of three is a big deal. Let’s not be shy about calling this a big accomplishment”… largely ruling out some proposals for new particles

A team in Paris has made the most precise measurement yet of the fine-structure constant, killing hopes for a new force of nature: “Physicists Nail Down the ‘Magic Number’ That Shapes the Universe.”

[TotH to MK]

* George Gamow

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As we ponder precision, we might spare a thought for Persian polymath Omar Khayyam; the mathematician, philosopher, astronomer, epigrammatist, and poet died on this date in 1131.  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 works 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.

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“If thou thou’st him some thrice, it will not be amiss”*…

 

You

 

‘You’ is the fourteenth most frequently used word in the English language, following closely behind its fellow pronouns ‘it’ at number eight and ‘I’ at number eleven:

The fact that you follows closely behind I in popularity is probably attributable to its being an eight-way word: both subject and object, both singular and plural, and both formal and familiar. The all-purpose second person is an unusual feature of English, as middle-schoolers realize when they start taking French, Spanish, or, especially German, which offers a choice of seven different singular versions of you. It’s relatively new in our language. In early modern English, beginning  in the late fifteenth century, thou, thee and thy were singular forms for the subjective, objective and possessive, and ye, you and your were plural. In the 1500s and 1600s, ye and then the thou/thee/thy forms, faded away, to be replaced by the all-purpose you. But approaches to this second person were interesting in this period of flux. David Crystal writes in The Cambridge Encyclopedia of English that by Shakespeare’s time, you “was used by people of lower rank or status to those above them (such as ordinary people to nobles, children to parents, servants to masters, nobles to the monarch), and was also the standard way for the upper classes to talk to each other. … By contrast, thou/thee were used by people of higher rank to those beneath them, and by the lower classes to each other; also in elevated poetic style, in addressing God, and in talking to witches, ghosts and other supernatural  beings.” The OED cites a 1675 quotation: “No Man will You God but will use the pronoun Thou to him.”

“Needless to say, this ambiguity and variability were gold in the hand of a writer like Shakespeare, and he played with it endlessly, sometimes having a character switch modes of address within a speech to indicate a change in attitude.” [see the title of this post, for example]…

More of this excerpt from Ben Yagoda’s When You Catch an Adjective, Kill It: The Parts of Speech, for Better and/or Worse  at “You.”

[Via the ever-illuminating Delanceyplace.com]

* Sir Toby Belch to Sir Andrew Aguecheek, in Shakespeare’s Twelfth Night

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As we muse on modes of address, we might send elegantly phrased and 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 (what he called) the Rubaiyat of Omar Khayyam, Fitzgerald’s attribution of the book’s poetry to Omar (as opposed to the aphorisms and other quotes in the volume) is now questionable to many scholars (who believe those verses to be by several different Persian authors).

In any case, Omar was unquestionably 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.

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Written by (Roughly) Daily

May 15, 2019 at 1:01 am

“The secret of life is honesty and fair dealing. If you can fake that, you’ve got it made”*…

 

Hoss Cartwright, a former editor of the International Journal of Agricultural Innovations and Research, had a good excuse for missing the 5th World Congress on Virology last year: He doesn’t exist…

As grant funding and career advancement depend ever more heavily on publishing metrics, scientists are inventing “co-authors” with prestigious-sounding affiliations to give their papers more credibility with the journals to which they submit:  “Why fake data when you can fake a scientist?

* Groucho Marx

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As we prune the pretenders, we might spare a thought for Persian polymath Omar Khayyam; the mathematician, philosopher, astronomer, epigrammatist, and poet died on this date in 1131.  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 works 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.

 source

Written by (Roughly) Daily

December 4, 2016 at 1:01 am

“In Japanese and Italian, the response to [‘How are you?’] is ‘I’m fine, and you?’ In German it’s answered with a sigh and a slight pause, followed by ‘Not so good’.”*…

 

If you own a smartphone and are trying to learn a language, you probably have Duolingo. At this very moment the app—which tries to turn language learning into a rewarding game—may be not-so-subtly suggesting that you are overdue for some Spanish vocabulary practice.

 How many other people are learning Spanish, and where do they live?

Duolingo recently answered such questions by running the numbers on their 120 million users, spanning every country on the planet. The company identified the most popular language for each country, among the 19 it offers…

More at “The languages the world is trying to learn, according to Duolingo.” [Note the absence of Mandarin, Japanese, Arabic and other Asian and Middle Eastern languages– surely a reflection, at least in large part, of the offers available on Duolingo, which teaches in more languages than it teaches…]

* David Sedaris, Let’s Explore Diabetes with Owls

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As we prepare to conjugate, we might send elegantly phrased and 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.

 source

Written by (Roughly) Daily

May 15, 2016 at 1:01 am

“I know numbers are beautiful. If they aren’t beautiful, nothing is”*…

 

Euler’s identity: Math geeks extol its beauty, even finding in it hints of a myste­rious connected­ness in the universe. It’s on tank tops and coffee mugs [and tattoos]. Aliens, apparently, carve it into crop circles (in 8-bit binary code). It’s appeared on The Simpsons. Twice.

What’s the deal with Euler’s identity? Basically, it’s an equation about numbers—specifically, those elusive constants π and e. Both are “transcendental” quanti­ties; in decimal form, their digits unspool into infinity. And both are ubiquitous in scientific laws. But they seem to come from different realms: π (3.14159 …) governs the perfect symmetry and closure of the circle; it’s in planetary orbits, the endless up and down of light waves. e (2.71828 …) is the foundation of exponential growth, that accelerating trajectory of escape inherent to compound interest, nuclear fission, Moore’s law. It’s used to model everything that grows…

Now, maybe you’ve never thought of math equations as “beautiful,” but look at that result: It combines the five most fundamental numbers in math—0, 1, e, i, and π—in a relation of irreducible simplicity. (Even more astonishing if you slog through the proof, which involves infinite sums, factorials, and fractions nested within fractions within fractions like matryoshka dolls.) And remember, e and π are infinitely long decimals with seemingly nothing in common; they’re the ultimate jigsaw puzzle pieces. Yet they fit together perfectly—not to a few places, or a hundred, or a million, but all the way to forever…

But the weirdest thing about Euler’s formula—given that it relies on imaginary numbers—is that it’s so immensely useful in the real world. By translating one type of motion into another, it lets engineers convert messy trig problems (you know, sines, secants, and so on) into more tractable algebra—like a wormhole between separate branches of math. It’s the secret sauce in Fourier transforms used to digi­tize music, and it tames all manner of wavy things in quantum mechanics, electron­ics, and signal processing; without it, computers might not exist…

More marvelous math at “The Baffling and Beautiful Wormhole Between Branches of Math.”

[TotH to @haarsager]

Paul Erdős

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As we wonder if Descartes wasn’t right when he wrote that “everything turns into mathematics,” we might spare a thought for Persian polymath Omar Khayyam; the mathematician, philosopher, astronomer, epigrammatist, and poet died on this date in 1131.  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 works 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.

 source

Written by (Roughly) Daily

December 4, 2014 at 1:01 am

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