(Roughly) Daily

Posts Tagged ‘Mathematics

“I’m gonna put a curse on you and all your kids will be born completely naked”*…


More at “Rejected Titles for Kids Say the Darnedest Things.” (Younger readers click here for explanatory background.)

* Jimi Hendrix


As we remark that an acorn never falls far from the tree, we might spare a thought for Christian Goldbach; he died on this date in 1764.  A mathematician, lawyer, and historian who studied infinite sums, the theory of curves and the theory of equations, he is best remembered for his correspondence with Leibniz, Euler, and Bernoulli, especially his 1742 letter to Euler containing what is now known as “Goldbach’s conjecture.”

In that letter he outlined his famous proposition:

Every even natural number greater than 2 is equal to the sum of two prime numbers.

It has been checked by computer for vast numbers– up to at least 4 x 1014– but remains unproved.

(Goldbach made another conjecture that every odd number is the sum of three primes; it has been checked by computer for vast numbers, but remains unproved.)

Goldbach’s letter to Euler (source, and larger view)

Written by LW

November 20, 2015 at 1:01 am

“Men of broader intellect know that there is no sharp distinction betwixt the real and the unreal”*…


During the period we now call the fin-de-siècle, worlds collided. Ideas were being killed off as much as being born. And in a sort of Hegelian logic of thesis/antithesis/synthesis, the most interesting ones arose as the offspring of wildly different parents. In particular, the last gasp of Victorian spirituality infused cutting-edge science with a certain sense of old-school mysticism. Theosophy was all the rage; Huysmans dragged Satan into modern Paris; and eccentric poets and scholars met in the British Museum Reading Room under the aegis of the Golden Dawn for a cup of tea and a spot of demonology. As a result of all this, certain commonly-accepted scientific terms we use today came out of quite weird and wonderful ideas being developed at the turn of the century. Such is the case with space, which fascinated mathematicians, philosophers, and artists with its unfathomable possibilities…

Further to yesterday’s nod to topography, and on the occasion of Halloween: hyperspace, ghosts, and colorful cubes – the work of Charles Howard Hinton and the cultural history of higher dimensions– “Notes on the Fourth Dimension.”

* H. P. Lovecraft, The Tomb


As we get down with the dead, we might recall that it was on this date in 1756 that Giacomo Casanova, who had been incarcerated in Venice as a blasphemer, cabalist, seducer, and ruffian, escaped from prison.  He made his way to Paris where, as “Jacques Casanova, the Chevalier de Seingalt,” he wrote his autobiography, launched the lottery, and made a killing.

Illustration in Casanova’s Histoire de ma fuite des prisons de la République de Venise qu’on appelle Les Plombs (Story of my Flight), 1787. From the German edition, 1788.


Casanova circa 1750-1755 (just before the escape)



Written by LW

October 31, 2015 at 1:01 am

“Life is like topography”*…


email readers click here for video

What if you could see Earth’s 5-billion year journey not just in a book or on screen, but on the planet’s very topography? That’s the idea behind the audio-visual performance Revolution of Topography, Cappadocia: Epic History of Humanity, which features 3D animations projection mapped onto the rocky surface of the Cappadocia Zelve Valley.

Produced by FikirbazZenger and directed by Ferdi Alıcı, Revolution of Topography has been billed as the world’s “largest mountain surface mapping”; and, with a 10-year screening time, will run for longer than any other projection mapping installation in history. The a/v installation, located at Cappadocia Zelve Valley Open Air Museum, will run through all phases of Cappadocia’s history, from geographical formation and topographical transformations to the emergence of civilization and religion…

More at “Mapping a Valley with Earth’s 5-Billion Year Journey.”

* “Life is like topography, Hobbes. There are summits of happiness and success, flat stretches of boring routine and valleys of frustration and failure.”

– “Calvin,” Bill Watterson


As we take the long view, we might send spatially-sophisticated birthday greetings to William Paul Thurston; he was born on this date in 1946.  A pioneer in the field of low-dimensional topology, he was awarded the 1982 Fields Medal for his contributions to the study of 3-manifolds.  In later years, while his research continued, Thurston took on the challenge of  mathematical popularization and education. He served as mathematics editor for Quantum Magazine, a youth science magazine, and was one of the founders of The Geometry Center.  As director of Mathematical Sciences Research Institute from 1992 to 1997, he started a number of programs designed to increase awareness of mathematics among the public.



Written by LW

October 30, 2015 at 1:01 am

“I may be going nowhere, but what a ride”*…


Nine salvaged bikes were reassembled into a carousel formation. The bike is modular and can be dismantled, transported and reassembled. It is normally left in public places where it can attract a variety of riders and spectators.

From artist Robert Wechsler, the Circular Bike.

* Shaun Hick


As we return to where we started, we might send carefully-calculated birthday greetings to Stephen Smale; he was born on this date in 1930.  A winner of both the Fields Medal and the Wolf Prize, the highest honors in mathematics, he first gained recognition with a proof of the Poincaré conjecture for all dimensions greater than or equal to 5, published in 1961.  He then moved to dynamic systems, developing an understanding of strange attractors which lead to chaos, and contributing to mathematical economics.  His most recent work is in theoretical computer science.

In 1998, in the spirit of Hilbert’s famous list of problems produced in 1900, he created a list of 18 unanswered challenges– known as Smale’s problems– to be solved in the 21st century.  (In fact, Smale’s list contains some of the original Hilbert problems, including the Riemann hypothesis and the second half of Hilbert’s sixteenth problem, both of which are still unsolved.)



Written by LW

July 15, 2015 at 1:01 am

“The camera is an instrument of detection. We photograph not only what we know, but also what we don’t know”*…


When top chemists and engineers at Harvard and MIT are preparing to reveal new research in the world’s premier journals, they call Felice Frankel.  For over two decades, Frankel has had a front-row seat at some of the biggest discoveries emerging from both ends of Cambridge, photographing experiments within the labs that created them.

Read her extraordinary story in “Photographer has front-row seat for big scientific discoveries“; and check out her work– from daisy-colored yeast colonies through rainbow-colored quantum dots to soft. flexible electronics that can be tattooed onto the skin– on her site.

* Lisette Model


As we find focus, we might remark that today is the birthday of not one but two extraordinary mathematicians:  Gottfried Wilhelm Leibniz (1646; variants on his date of birth are due to calendar changes), the German  philosopher, scientist, mathematician, diplomat, librarian, lawyer, co-inventor, with Newton, of The Calculus, and “hero” (well, one hero) of Neal Stephenson’s Baroque Trilogy…  and  Alan Turing (1912), British mathematician, computer science pioneer (inventor of the Turing Machine, creator of “the Turing Test” and inspiration for “The Turing Prize”), and cryptographer (leading member of the team that cracked the Enigma code during WWII).

Go figure…

Liebnitz (source: UNC)

Turing (source: Univ. of Birmingham)

Written by LW

June 23, 2015 at 1:01 am

“God made the integers; all the rest is the work of Man”*…



From Alex Bellos: the results of his global online poll to find the world’s favorite number…

The winner?  Seven—  and it wasn’t even close…

Leopold Kronecker


As we settle for anything but snake eyes, we might send symbolic birthday greetings to John Pell; he was born on this date in 1611.  An English mathematician of accomplishment, he is perhaps best remembered for having introduced the “division sign”– the “obelus”: a short line with dots above and below– into use in English.  It was first used in German by Johann Rahn in 1659 in Teutsche Algebra; Pell’s translation brought the symbol to English-speaking mathematicians.  But Pell was an important influence on Rahn, and edited his book– so may well have been, many scholars believe, the originator of the symbol for this use.  (In any case the symbol wasn’t new to them:  the obelus [derived from the word for “roasting spit” in Greek] had already been used to mark passages in writings that were considered dubious, corrupt or spurious…. a use that surely seems only too appropriate to legions of second and third grade math students.)


Written by LW

March 1, 2015 at 1:01 am

“Prime numbers are what is left when you have taken all the patterns away”*…


Der Hl. Augustinus und der Teufel


1, followed by 13 zeros, then 666, and then another 13 zeros, and a final 1:  a palindromic prime number named for Belphegor (or Beelphegor), one of the seven princes of Hell.  Reputed to help people make discoveries, Belphegor is the demon of inventiveness.  He figures in Milton’s Paradise Lost as the namesake of one of the “Principalities of the Prime”… So it is only fitting that these devilish digits bear his name.

The symbol of Belphegor’s Prime resembles Pi, only upside down. It is derived from a bird glyph first seen embedded in the Voynich Manuscript.


More prime provocation at Cliff Pickover‘s “Belphegor’s Prime: 1000000000000066600000000000001.”

* Mark Haddon, The Curious Incident of the Dog in the Night-Time


As we try to divine divisors, we might recall that it was on this date in 1968 that the first-ever 9-1-1 call was placed by Alabama Speaker of the House Rankin Fite, from Haleyville City Hall, to U.S. Rep. Tom Bevill, at the city’s police station.

Emergency numbers date back to 1937, when the British began to use 999.  But experience showed that three repeated digits led to many mistaken/false alarms.  The Southern California Telephone Co. experimented in 1946 in Los Angeles with 116 for emergencies.

But 911– using just the first and last digits available– yielded the best results, and went into widespread use in the 1980s when 911 was adopted as the standard emergency number across most of the country under the North American Numbering Plan.

And yes, “911” is a prime…


Written by LW

February 16, 2015 at 1:01 am


Get every new post delivered to your Inbox.

Join 1,158 other followers

%d bloggers like this: