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Posts Tagged ‘Mathematics

“Use what language you will, you can never say anything but what you are”*…

Lars Yenken‘s “The Great Language Game” is an interactive game, being played worldwide, that challenges users to distinguish among (currently) 87 languages based on their sound alone.  As Lars explains,

There are perhaps six or seven thousand languages in the world. Even so-called hyperpolyglots, people who learn to speak six or more fluently, barely scratch the surface. You and I will never be able to communicate in all these languages without machine aids, but learning to identify what’s being spoken near us, that’s within our reach…

Besides, it’s fun!

[TotH to reddit]

* Ralph Waldo Emerson

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As we prick up our ears, we might send thoughtful birthday greetings to 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.”

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No reservation? No problem!…

 

Jeff Dekofsky explains Hilbert’s paradox of the Grand Hotel, a thought experiment proposed in the 1920s by German mathematician David Hilbert to illustrate some surprising properties of infinite sets, in this TED-Ed animated lecture

email readers click here for video

As a special bonus, another amusing video (via Kottke)– an explanation of why it is that the sum of all positive integers (1 + 2 + 3 + 4 + 5 + …) = -1/12…  Euler actually proved this result in 1735, but the result was only made rigorous later; and now physicists have been seeing this result actually show up in nature.  (Spoiler alert: the answer turns on what one means by “sum” mathematically…)

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As we pray for more fingers and toes, we might spare a thought for Harald August Bohr; he died on this date in 1951.  While materially less well-known than his brother Niels, Harald was a formidable mathematician (founder of the field of almost periodic functions), a gifted athlete (an accomplished footballer who won a silver medal at the 1908 Summer Olympics as a member of Denmark’s team), an inspirational teacher (the annual award for outstanding teaching at the University of Copenhagen is called “the Harald” in his honor), and an out-spoken critic of the anti-Semitic policies that took root in the German mathematical establishment in the 1930s.

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Time travel…

 

Chino Otsuka, 1980 and 2009, Nagayama, Japan

In the photo series “Imagine Finding Me,” photographer Chino Otsuka revisits her childhood by digitally inserting herself in old photos of her as a child. Otsuka likens her double self-portraits to a kind of time travel:

“The digital process becomes a tool, almost like a time machine, as I’m embarking on the journey to where I once belonged and at the same time becoming a tourist in my own history…”

Chino Otsuka, 1975 and 2005, Spain

See (and read) more at Laughing Squid and at AGO.

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As we revisit Memory Lane, we might spare a thought for Kurt Friedrich Gödel; he died on this date in 1978. Considered (with Aristotle and Frege) one of the most important logicians in history, Gödel published the work for which he is probably most widely remembered– his two incompleteness theorems– in 1931 when he was 25 years old, one year after finishing his doctorate at the University of Vienna.  He demonstrated that:

  1. If a system is consistent, it cannot be complete.
  2. The consistency of a systems axioms cannot be proven within the system.

Gödel’s theorems ended a half-century of attempts, beginning with the work of Frege and culminating in Russell and Whitehead’s Principia Mathematica and Hilbert’s formalism, to find a set of axioms sufficient for all mathematics.

As the Anschluss swept Austria, Gödel fled to the U.S., landing at Princeton, where he joined Albert Einstein at the Institute for Advanced Studies.  In 1951, as a 70th birthday present for Einstein, Gödel demonstrated the existence of paradoxical solutions to Einstein’s field equations in general relativity (they became known as the Gödel metric)– which allowed for “rotating universes” and time travel… and which caused Einstein to have doubts about his own theory.

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Written by LW

January 14, 2014 at 1:01 am

“Common sense is calculation applied to life…”*

 

Josh Orter writes…

I updated my iPhone to the latest iOS version last week. Doing so required that “I agree” to Terms and Conditions amounting to 6,114 words: more than 37% longer than The Constitution of the United States (4,447). Although hardcore legalese enthusiasts may curl up with this masterpiece before the fire, mug of hot cocoa in hand, it will be read by virtually no one else. I clicked immediately, blissfully ignorant of my acquiescence…

Or maybe not so blissful. I was, in fact, vaguely annoyed at having just blindly accepted what amounts to a 24-page term paper (12-pt Times Roman, double-spaced). What, then, would fully informed consent cost?

$482,894,368, as it turns out.

With various reputable sources suggesting an average reading speed of 300 words per minute, 6,114 words would suck up 20.38 minutes of life for each user. Multiply by the average American’s hourly earnings of $24.09/hour (.4015/minute) and it’s $8.18257 in labor per updater.

A recently released study estimated Apple’s share of the 145 million-unit American  smartphone market at 40.7%. 59 million iPhoners.

59,015,00 x $8.18257 = $482,894,368

Perhaps more unsettling than money is the cumulative man-hours this particular endeavor would consume: 20-million.

59,015,000 x users x 20.38 minutes per= 1,202,725,700 minutes= 20 million hours…

Find other arithmetic adventures at Josh’s wonderful Stupid Calculations (“Where practical facts get rendered into utterly meaningless ones”).

[TotH to the ever-illuminating Flowing Data]

* Henri Frédéric Amiel

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As we carry the 1, we might recall that it was on this date in 1807 that Joseph Fourier’s monograph On the Propagation of Heat in Solid Bodies, was read to the Paris Institute.  An important mathematical work containing what we now call Fourier series, it was reviewed by renowned respondents including Lagrange, Laplace, Monge, and Lacroix– who objected to his innovation (the expansion of functions as trigonometrical series: the Fourier series).  Indeed, his work wasn’t published (in a revised and somewhat expanded form, as The Analytic Theory of Heat) until 1822.  Fourier’s contributions were ultimately judged so important that, in addition to the series, Fourier’s Law and Fourier’s transform were named in his honor.  And indeed, Fourier’s work, having first helped scientists and engineers understand heat transfer and vibrations, went on to help Watson and Crick discover the structure of DNA and to provide the underpinnings for quantum physics, radio astronomy, MP3 and JPEG compression, X-ray crystallography, voice recognition, and PET or MRI scans.

(Fourier was something of a polymath:  just before developing his mathematical advances, he went with Napoleon Bonaparte on his Egyptian expedition in 1798, and was made governor of Lower Egypt and secretary of the Institut d’Égypte, where he was involved in the discovery and decoding of the Rosetta Stone. And after the publication of The Analytic Theory of Heat, he discovered the Greenhouse Effect.)

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)

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Written by LW

December 21, 2013 at 1:01 am

Ways of seeing…

 

Photographer Víctor Enrich‘s NHDK project involves digitally reconfiguring the same building in Munich in 88 different “poses”…

The Barcelona-based artist is known for his “reconstructive” interpretations of architecture around the world (c.f., e.g., his images of  Tel Aviv shot back in 2010).  See more of Enrich‘s NHDK project at Colossal.

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As we consider different perspectives, we might send terrifyingly (and at the same time, amusingly) insightful birthday greetings to Edwin Abbott Abbott; he was born on this date in 1838.  A schoolmaster and theologian, Abbott is best remembered as the author of the remarkable novella Flatland: A Romance of Many Dimensions (1884).  Writing pseudonymously as “A Square,” Abbott used the fictional two-dimensional world of Flatland to offer pointedly-satirical observations on the social hierarchy of Victorian culture. But the work has survived– and inspired legions of mathematicians and science fiction writers– by virtue of its fresh and accessible examination of dimensionality.  Indeed, Flatland was largely ignored on its original publication; but it was re-discovered after Einstein’s General Theory of Relativity– which posits a fourth dimension– was introduced; in a 1920 letter to Nature, Abbott is called a prophet for his intuition of the importance of time to explain certain phenomena.

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Written by LW

December 20, 2013 at 1:01 am

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