## Posts Tagged ‘**Mathematics**’

## “All numbers are by their nature correct. Well, except for Pi, of course. I can’t be doing with Pi. Gives me a headache just thinking about it, going on and on and on and on and on…”*…

It’s Pi Day!

In celebration, a few amusing– and illuminating– links:

10 stunning images show the beauty hidden in pi

How to Memorize Pi if You’re a Word Person (from whence, the image above)

* Neil Gaiman, *Anansi Boys*

###

**As we enumerate endlessly,** we might pause for a piece of pi(e)…

… in celebration of Albert Einstein’s birthday; he was born on this date in 1879.

“Everything should be made as simple as possible, but not simpler.”

## “A metaphor is like a simile”*…

“Fiction is like a spider’s web, attached ever so lightly perhaps, but still attached to life at all four corners.”

-Virginia Woolf

Just one of the “exhibits” in “an ongoing collection of the world’s most likable literary device”: The Simile Museum.

[source of the image above]

* Steven Wright

###

**As we remember that “liking” has a very long history,** we might spare a thought for Thomas Carlyle; he died on this date in 1881. A Victorian polymath, he was an accomplished philosopher, satirical writer, essayist, translator, historian, mathematician, and teacher. While he was an enormously popular lecturer in his time, and his contributions to mathematics earned him eponymous fame (the Carlyle circle), he may be best remembered as a historian (and champion of the “Great Man” theory of history)… and as the coiner of phrases like “the dismal science” (to describe economics)

“A well-written Life is almost as rare as a well-spent one.” – Thomas Carlyle

## “We never cease to stand like curious children before the great mystery into which we were born”*…

In scenario planning, one tries to identify the “driving forces”– the social, political, ecological, technical, and economic dynamics afoot– in the environment that are both likely to impact our future materially and outside our control; one then to knits the possible outcomes of those forces into alternative futures, plausible sketches of the opportunities and challenges that one might face.

There is a special class of driving force, what scenario planners call a wild card: a possibility that has relative low probability in the (usually 10 year) time horizon, but that, should it occur, would have massive consequence. Wild cards are often things like major earthquakes or geo-political conflicts… or environmental catastrophes. While one plans *for* the implications of the scenarios and their defining driving forces, one plans *against* wild cards; one creates action plans for the scenarios, contingency plans for the wild cards.

As climate change is slowly but surely converting yesterday’s wildcards (sustained droughts, regular, catastrophic wildfires and storms, etc.) into “regular” driving forces, it is perhaps prudent to look at some of the wildest cards that remain…

One day in 1905, the French geophysicist Bernard Brunhes brought back to his lab some rocks he’d unearthed from a freshly cut road near the village of Pont Farin. When he analyzed their magnetic properties, he was astonished at what they showed: Millions of years ago, the Earth’s magnetic poles had been on the opposite sides of the planet. North was south and south was north. The discovery spoke of planetary anarchy. Scientists had no way to explain it.

Today, we know that the poles have changed places hundreds of times, most recently 780,000 years ago. (Sometimes, the poles try to reverse positions but then snap back into place, in what is called an excursion. The last time was about 40,000 years ago.) We also know that when they flip next time, the consequences for the electrical and electronic infrastructure that runs modern civilization will be dire. The question is when that will happen…

The shield that protects the Earth from solar radiation is under attack from within. We can’t prevent it, but we ought to prepare. Learn more at “The Magnetic Field Is Shifting. The Poles May Flip. This Could Get Bad.”

* Albert Einstein

###

**As we ponder powerlessness,** we might recall that it was on this date in 1697 that Isaac Newton received a copy of Johann Bernoulli’s long-standing mathematical challenge, the brachistochrone problem: “To determine the curved line joining two given points, situated at different distances from the horizontal and not in the same vertical line, along which the mobile body, running down by its own weight and starting to move from the upper point, will descend most quickly to the lower point.” (Bernoulli coined the name from Gr. *brachistos*, shortest; and *chronos*, time.)

Newton solved it the same day, and forwarded his solution to the Royal Society—anonymously. When Bernoulli read the solution, he shrewdly guessed it was Newton’s work. By legend, he said, “I recognize the lion by his paw.”

## “Woe, destruction, ruin, and decay; the worst is death and death will have his day”*…

Not long ago an old matchbook laying on photographer Pablo Iglesias Maurer‘s desk caught his eye. Or rather, it was the postcard-like picture on it, of a resort complex built in the 1960s. It got Pablo wondering how the place looked now, and the answer has led him to make an amazing photo series called

Abandoned States.The picture came with the title

How to Run A Successful Golf Course, but when Maurer got to the place, it was clear the owner of Penn Hills Resort didn’t follow that advice. He pointed the camera at the decaying building at roughly the same spot and did a ‘5-decades-after’ shot of the place.Ever since then, Pablo was hooked. He ordered more 60s postcards from eBay and started going around the country capturing these once beautiful buildings that now stand abandoned only as faint memories of what once was…

See more of his results at “Photographer Finds Locations Of 1960s Postcards To See How They Look Today, And The Difference Is Unbelievable” and here.

* Shakespeare, *Richard II*

###

**As we contemplate continuity,** we might send never-ending birthday greetings to August Ferdinand Möbius; he was born on this date in 1790. A German mathematician and theoretical astronomer, he is best remembered as a topologist, more specifically for his discovery of the Möbius strip (a two-dimensional surface with only one side… or more precisely, a non-orientable two-dimensional surface with only one side when embedded in three-dimensional Euclidean space).

## “Exploring pi is like exploring the universe”*…

Pi is an infinite string of seemingly random numbers, but if you break down the first 1000 digits of Pi according to how many times each number from 0 to 9 appears, they’re all just about equal — with 1 being the outlier at 12% (although we wonder if they’d all average to ~10% given enough digits of Pi)…

More at “Visualizing The Breakdown Of The Numbers In The First 1000 Digits Of Pi Is Fascinating.”

###

**As we watch it even out in the end,** we might spare a thought for Hannah Wilkinson Slater; she died on this date in 1812. The daughter and the wife of mill owners, Ms. Slater was the first woman to be issued a patent in the United States (1793)– for a process using spinning wheels to twist fine Surinam cotton yarn, that created a No. 20 two-ply thread that was an improvement on the linen thread previously in use for sewing cloth.

## “Mystery has its own mysteries”*…

Finally, an answer to a question that puzzled Cantor and Hilbert (proprietor of The Infinite Hotel) and challenged Cohen and Gödel…

In a breakthrough that disproves decades of conventional wisdom [and confounds common sense], two mathematicians have shown that two different variants of infinity are actually the same size. The advance touches on one of the most famous and intractable problems in mathematics: whether there exist infinities between the infinite size of the natural numbers and the larger infinite size of the real numbers…

Connecting the sizes of infinities and the complexity of mathematical theories: “Mathematicians Measure Infinities and Find They’re Equal.”

* “Mystery has its own mysteries, and there are gods above gods. We have ours, they have theirs. That is what’s known as infinity.” – Jean Cocteau

###

**As we go big,** we might spare a thought for Paul Erdős; he died on this date in 1996. One of the most prolific mathematicians of the 20th century (he published around 1,500 mathematical papers during his lifetime, a figure that remains unsurpassed), he is remembered both for his “social practice” of mathematics (he engaged more than 500 collaborators) and for his eccentric lifestyle (he spent his waking hours virtually entirely on math; he would typically show up at a colleague’s doorstep and announce “my brain is open”, staying long enough to collaborate on a few papers before moving on a few days later).

Erdős’s prolific output with co-authors prompted the creation of the Erdős number, the number of steps in the shortest path between a mathematician and Erdős in terms of co-authorships. Low numbers are a badge of pride– and a usual marker of accomplishment: As of 2016, all Fields Medalists have a finite Erdős number, with values that range between 2 and 6, and a median of 3. Physics Nobelists Einstein and Sheldon Glashow have an Erdős number of 2. Baseball Hall of Famer Hank Aaron can be considered to have an Erdős number of 1 because they both autographed the same baseball (for number theorist Carl Pomerance). Natalie Portman’s undergraduate collaboration with a Harvard professor earned her an Erdős number of 5; Danica McKellar(“Winnie Cooper” in *The Wonder Years*) has an Erdős number of 4, for a mathematics paper coauthored while an undergraduate at UCLA.