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Posts Tagged ‘Bernoulli

“Once is happenstance. Twice is coincidence. Three times, it’s enemy action.”*…

 

complexity

A couple of weeks ago, we considered the human urge to find significance, meaning in everyday occurrences: “All mystical experience is coincidence; and vice versa, of course.” Today, we consider the same phenomena from a more mathematical point-of-view…

Was it a chance encounter when you met that special someone or was there some deeper reason for it? What about that strange dream last night—was that just the random ramblings of the synapses of your brain or did it reveal something deep about your unconscious? Perhaps the dream was trying to tell you something about your future. Perhaps not. Did the fact that a close relative developed a virulent form of cancer have profound meaning or was it simply a consequence of a random mutation of his DNA?

We live our lives thinking about the patterns of events that happen around us. We ask ourselves whether they are simply random, or if there is some reason for them that is uniquely true and deep. As a mathematician, I often turn to numbers and theorems to gain insight into questions like these. As it happens, I learned something about the search for meaning among patterns in life from one of the deepest theorems in mathematical logic. That theorem, simply put, shows that there is no way to know, even in principle, if an explanation for a pattern is the deepest or most interesting explanation there is. Just as in life, the search for meaning in mathematics knows no bounds…

Noson Yanofsky on what math can teach us about finding order in our chaotic lives.

* Ian Fleming

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As we consider the odds, we might send carefully-calculated birthday greetings to Johann Bernoulli; he was born on this date in 1667.  A member of the mathematically-momentous Bernoulli family, Johann (also known as Jean or John) discovered the exponential calculus and (with Leibniz and Huygens) the equation of the catenary.  Still, he be best remembered as teacher and mentor of Leonhard Euler.

220px-Johann_Bernoulli2 source

 

Written by LW

August 6, 2018 at 1:01 am

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

 

This animation shows the movement of the north magnetic pole at 10-year intervals from 1970 to 2020. The red and blue lines indicate “declination,” the difference between magnetic north and true north depending on where one is standing; on the green line, a compass would point to true north. Visual by NOAA National Centers for Environmental Information

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

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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.”

Bernoulli and Newton

source

 

“What is the difference between a taxidermist and a tax collector? The taxidermist takes only your skin”*…

 

A Ferris wheel of chipmunks, formerly part of the Dead Pals of Sam Sanfillippo

 

Last October, Atlas Obscura co-presented a Rogue Taxidermy Fair with its fellow Brooklyn-based (and former Roughly Daily subject) Morbid Anatomy in celebration of a new book on “rogue taxidermy.”

The Crucified Sheep

 

Read more about– and see more of– the Fair at “The Crucified Sheep, Tattooed Frogs, and Crocheted Skeletons of a Rogue Taxidermy Fair in Brooklyn,” and revisit (R)Ds earlier look at rogue taxidermy here.

* Mark Twain

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As we strike a pose, we might recall that it was on this date in 1697 that Isaac Newton received and solved Jean Bernoulli’s brachistochrone problem.  The Swiss mathematician Bernoulli had challenged his colleagues to solve it within six months.  Newton not only solved the problem before going to bed that same night, but in doing so, invented a new branch of mathematics called the calculus of variations.  He had resolved the issue of specifying the curve connecting two points displayed from each other laterally, along which a body, acted upon only by gravity, would fall in the shortest time.  Newton, age 55, sent the solution to be published, at his request, anonymously.  But the brilliant originality of the work betrayed his identity, for when Bernoulli saw the solution he commented, “We recognize the lion by his claw.”

 source

 

Written by LW

January 26, 2015 at 1:01 am

“Nothing is more memorable than truth beautifully told”*…

 

If physicists and mathematicians can’t be rock stars, they can at least have rock star logos.  Dr. Prateek Lala, a physician and amateur calligrapher from Toronto has obliged with 50 nifty “scientific typographics” of important cosmologists and scientists through the ages.

 

Inspired by the “type biographies” of Indian graphic designer Kapil Bhagat, Lala designed his logos to make the lives and discoveries of various scientists more engaging and more immediately relatable to students.

Dr. Lala’s work was for a poster that was published in the latest issue of Inside The Perimeter, the official magazine of Canada’s Perimeter Institute for Theoretical Physics.  One can subscribe to the magazine by email for free here.

Meantime, one can read the backstory, and see many more of Dr. L’s lyrical logos at CoDesign.

* Rick Julian

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As we ponder personal branding, we might send dynamic birthday greetings to Daniel Bernoulli; he was born on this date in 1700.  One of the several prominent mathematicians and physicists in the Swiss Bernoulli family, Daniel is best remembered for or his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics.  His name is commemorated in the Bernoulli principle, a particular example of the conservation of energy, which describes the mathematics of the mechanism underlying the operation of two important technologies of the 20th century: the carburetor and the airplane wing.

A contemporary and close friend of Leonhard Euler (see above), Bernoulli was the son of Johann Bernoulli (one of the early developers of calculus), nephew of Jakob Bernoulli (who was the first to discover the theory of probability), and the brother of Johann II (an expert on magnetism and the propagation of light).  Daniel is said to have had a bad relationship with his father: when they tied for first place in a scientific contest at the University of Paris, Johann, unable to bear the “shame” of being compared as Daniel’s equal, banned Daniel from his house.  Johann Bernoulli then plagiarized some key ideas from Daniel’s book Hydrodynamica in his own book Hydraulica, which he backdated to before Hydrodynamica.  Despite Daniel’s attempts at reconciliation, his father carried the grudge until his death.

 source

 

 

Written by LW

February 8, 2014 at 1:01 am

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