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Posts Tagged ‘Einstein

Why did 5 eat 6?…

 

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).

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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.

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Written by LW

November 22, 2013 at 1:01 am

Let’s Go To The Numbers…

 

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.”

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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.

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Step Right Up!…

The rakishly-named Jen Wayne Gacy maintains what has to be one of the most unusual– and fascinating– Pinterest collections online.  Your correspondent’s personal favorite:  “Slideshow/Freakshow.”

Tour the netherworld at “Slideshow/Freakshow.”  (And learn the lingo here.)

[TotH to Richard Kadrey's Damn Tumbler]

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As we purchase our peek behind the curtain, we might note that it was on this date in 1923 that Albert Eistein demonstrated that time is relative:  he delivered his Nobel Prize lecture… two years late.

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Written by LW

July 11, 2013 at 1:01 am

Pieces of pi…

In 2010, Japanese engineer Shigeru Kondo set a record, calculating the value of pi to 5 trillion digits… then last October, he smashed his own mark, identifying the first 10 trillion decimal places.  (He used a home-made computer that ran so hot that the temperature in his apartment was over 100 degrees…)

The quest will no doubt continue– pi is an irrational number that exerts an irrational fascination.  Meantime, readers can take a peek at this work-perpetually-in-progress.  Web design firm firm Two-N has created this nifty visualization and search tool, allowing one to find any one of the first 4,000,000 digits of pi:

Bonus: “50 Interesting Facts About Pi

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As we ruminate on randomness, we might send carefully-calculated birthday greetings to Hermann Minkowski; he was born on this date in 1864.  Minkowski developed the geometry of numbers and used geometrical methods to solve difficult problems in number theory and mathematical physics; he is probaly best remembered for realizing that his former student Albert Einstein’s special theory of relativity (1905), presented algebraically by Einstein, could also be understood geometrically as a theory of four-dimensional space-time.  Einstein embraced the geometric approach in the development of his theory of general relativity– and the four-dimensional space (the three physical dimensions plus time) involved has since been known as “Minkowski spacetime.”

Minkowski’s best friend was “mathematical hotelier” David Hilbert.

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Written by LW

June 22, 2012 at 1:01 am

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.

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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.

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Who owns the fish?…

From the good folks at Coudal Partners, a puzzle purportedly created by Albert Einstein…

There are five houses in a row in different colors. In each house lives a person with a different nationality. The five owners drink a different drink, smoke a different brand of cigar and keep a different pet, one of which is a Walleye Pike.

The question is– who owns the fish?

Hints:
1. The Brit lives in the red house.
2. The Swede keeps dogs as pets.
3. The Dane drinks tea.
4. The green house is on the left of the white house.
5. The green house owner drinks coffee.
6. The person who smokes Pall Malls keeps birds.
7. The owner of the yellow house smokes Dunhills.
8. The man living in the house right in the center drinks milk.
9. The man who smokes Blends lives next to the one who keeps cats.
10. The Norwegian lives in the first house.
11. The man who keeps horses lives next to the one who smokes Dunhills.
12. The owner who smokes Bluemasters drinks beer.
13. The German smokes Princes.
14. The Norwegian lives next to the blue house.
15. The man who smokes Blends has a neighbor who drinks water.

There’s nothing up anyone’s sleeve (as though fish had sleeves…); and everything one needs to know is there.

Successful solutions can be confirmed here.  And readers can find a second fish puzzle here, and a little teaser called “Da Vinci’s Other Code” here.

As we scratch our heads, we might wish a Joyeux Anniversaire to silk weaver Joseph Marie Jacquard; he was born on this date in 1752.  Jacquard’s 1805 invention of the programmable power loom, controlled by a series of punched “instruction” cards and capable of weaving essentially any pattern, ignited a technological revolution in the textile industry… indeed, it set off a chain of revolutions: it inspired Charles Babbage in the design of his “Difference Engine” (the ur-computer), and later, Herman Hollerith, who used punched cards in the “tabulator” that he created for the 1890 Census… and in so doing, pioneered the use of those cards for computer input.

Joesph Marie Jacquard (source)

Adventures in Cosmology: Starting out Simply…

Why was entropy so low at the Big Bang? (source: Internet Encyclopedia of Philosophy)

Back in 2010, SUNY-Buffalo physics professor Dejan Stojkovic and colleagues made a simple– a radically simple– suggestion:  that the early universe — which exploded from a single point and was very, very small at first — was one-dimensional (like a straight line) before expanding to include two dimensions (like a plane) and then three (like the world in which we live today).

The core idea is that the dimensionality of space depends on the size of the space observed, with smaller spaces associated with fewer dimensions. That means that a fourth dimension will open up — if it hasn’t already — as the universe continues to expand.  (Interesting corollary: space has fewer dimensions at very high energies of the kind associated with the early, post-big bang universe.)

Stojkovic’s notion is challenging; but at the same time, it would help address a number of fundamental problems with the standard model of particle physics, from the incompatibility between quantum mechanics and general relativity to the mystery of the accelerating expansion of the universe.

But is it “true”?  There’s no way to know as yet.  But Stojkovic and his colleagues have devised a test using the Laser Interferometer Space Antenna (LISA), a planned international gravitational observatory, that could shed some definitive light on the question in just a few years.

Read the whole story in Science Daily, and read Stojkovic’s proposal for experimental proof in Physical Review Letters.

As we glance around for evidence of that fourth dimension, we might bid an indeterminate farewell to Ilya Prigogine, the Nobel Laureate whose work on dissipative structures, complex systems, and irreversibility led to the identification of self-organizing systems, and is seen by many as a bridge between the natural and social sciences.  He died at the Hospital Erasme in Brussels on this date in 2003.

Prigogine’s 1997 book, The End of Certainty, summarized his departure from the determinist thinking of Newton, Einstein, and Schrödinger in arguing for “the arrow of time”– and “complexity,” the ineluctable reality of irreversibility and instability.  “Unstable systems” like weather and biological life, he suggested, cannot be explained with standard deterministic models.  Rather, given their to sensitivity to initial conditions, unstable systems can only be explained statistically, probabilistically.

source: University of Texas

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