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Posts Tagged ‘Numbers

“When you have mastered numbers, you will in fact no longer be reading numbers, any more than you read words when reading books. You will be reading meanings.”*…

Errors of judgment about large numbers can have a big impact on the way you view policies and government decisions. The rationale goes like this: The National Science Foundation received $7.463 billion for fiscal year 2016 through the Consolidated Appropriations Act. The total United States budget outlay for 2016 was $3.54 trillion. If you’re someone who perceives the difference between a billion and a trillion as relatively small, you’d think the US is spending a lot of money on the National Science Foundation—in fact, depending on your politics, you might applaud the federal government’s investment or even think it wasteful. But, if you understand that a billion is a thousand times less than a trillion, you can calculate that the Foundation got a paltry 0.2 percent of the budget outlay last year. (It may be more straightforward to think of the budget as roughly one-half to one-third of reported costs for the proposed US-Mexico border wall, and let your values guide you from there.)…

On the significance of scale: “How to Understand Extreme Numbers.

[The image above is, of course, from the ever-wonderful xkcd.]

* W.E.B. Du Bois

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As we nudge ourselves toward numeracy, we might spare a thought for Sewall Wright; he died on this date in 1988.  A geneticist, he was known for his influential work on evolutionary theory and also for his work on path analysis. He was a founder (with Ronald Fisher and J.B.S. Haldane) of population genetics– a major step in the development of the modern evolutionary synthesis combining genetics with evolution.   He is perhaps best remembered for his concept of genetic drift (called the Sewall Wright effect): when small populations of a species are isolated, the few individuals who carry certain relatively rare genes may fail, out of pure chance, to transmit them. The genes may therefore disappear and their loss may lead to the emergence of new species– although natural selection has played no part in the process.

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Written by LW

March 3, 2017 at 1:01 am

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

 

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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

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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.)

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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

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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…

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Written by LW

February 16, 2015 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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Got your number…

Euler’s Number (e): 2.7182…

Euler’s number is also known as the exponential growth constant. It is the base for natural logarithms and is found in many areas of mathematics.

Application: In finance, Euler’s number is used to determine compound interest, which is extremely vital in understanding the time value of money — the backbone of finance.

Moreover, Euler’s number is crucial when describing any decaying relationship – think Carbon 14 dating.

… and then there are the other 9 “10 Most Important Numbers in the World.”

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As we activate the abaci, we might send carefully-calculated birthday wishes to Stephen Smale; the Wolf Prize-winning mathematician was born on this date in 1930.  Among many other accomplishments, Smale helped develop the logistic model for population growth– one of the foundational insights that allowed the development of chaos theory (and thus, enhanced our understanding of the way in which natural systems actually work)– one of the 17 Equations That Changed the World:

Written by LW

July 15, 2012 at 1:01 am

We’ve got your number…

From the Mathematical Association of America, NumberADay:  “Every working day, we post a number and offer a selection of that number’s properties.”

And so they do…

438 = 2 x 3 x 73.

438 is a Smith number because the sum of its digits is equal to the sum of the digits of its prime factors: 4 + 3 + 8 = 2 + 3 + 7 + 3 = 15.

438 is 110110110 in base 2 (binary) and 666 in base 8. It is 3223 in base 5 and 141 in base 19.

The term “438 match” or “438 game” has been used by cricket news media to describe the famous 2006 One Day International in which Australia scored a world record 434 in their innings, only to see South Africa respond in their innings with 438.

And more… which one can find– along with the dope on dozens and dozens of other digits– at NumberADay.

 

As we resolve to practice on our abaci, we might send elegantly-derived birthday greetings to mathematician Sofia Vasilyevna Kovalevskaya; she was born on this date in 1850.  The first major Russian female mathematician, she made important contributions to analysis, differential equations and mechanics, was one the first women to edit a scientific journal, and was the first woman appointed to a full professorship in Northern Europe (Stockholm University).  But while (after much lobbying by her admirers) she was granted a Chair in the Russian Academy of Sciences, she was never offered a professorship in Russia.

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Amaze your friends and colleagues!…

Need to hammer home an arithmetical point?  Dramatize a quantitative comparison?  NumberQuotes has the juice.  One simply types in the number–any number– to be analogized, hits “return”– and up pops a series of striking similes.  For example, if one needs to be clear just how over-the-top excessive $250,000 dollars is (in whatever context), one can choose among:

– $250,000 would buy a Caffe Latte Grande for everyone living in Richardson, Texas

– 250,000 Burger King Whoppers would weigh as much as 9.29 African male elephants

– 250,00 is the number of bus and truck mechanics and diesel engine specialists employed in the US

… and so many more options.  Compelling comparisons aren’t just for Ronald Reagan any longer– now anyone can pick a number, any number, and click here.

As we spice up our speech, we might recall that it was on this date in 1930 (the number of theatrical and performance make-up artists working in the U.S…), on the passing of Empress Zewditu, that Haile Selassie (nee, Tafari Makonnen) was proclaimed Emperor of Ethiopia.  While he was, by virtue of his office, the titular head of the Ethiopian Orthodox Church, Salasse is worshipped as God Incarnate by the Rastafarians (who named their faith by conflating “Ras”– “Head,” equivalent to “Duke”– and Salasse’s pre-Imperial first name, “Tafari”).

The Lion of God

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