Posts Tagged ‘Mathematics’
Is logical thinking a way to discover or to debate? The answers from philosophy and mathematics define human knowledge..
The history of logic should be of interest to anyone with aspirations to thinking that is correct, or at least reasonable. This story illustrates different approaches to intellectual enquiry and human cognition more generally. Reflecting on the history of logic forces us to reflect on what it means to be a reasonable cognitive agent, to think properly. Is it to engage in discussions with others? Is it to think for ourselves? Is it to perform calculations?…
The rise and fall and rise of logic: “What is logic?“
* George Orwell, 1984
As we ruminate on reason, we might send enlightened birthday greetings to Benjamin Franklin; he was born on this date in 1706. One of the Founding Fathers of the United States, Franklin was a renowned polymath: a leading author, printer, political theorist, politician, freemason, postmaster, scientist, inventor, civic activist, statesman, and diplomat. As a scientist, he was a major figure in the American Enlightenment and the history of physics for his discoveries and theories regarding electricity. As an inventor, he is known for the lightning rod, bifocals, and the Franklin stove, among other innovations. And as a social entrepreneur (who grasped the fact that by united effort a community could have amenities which only the wealthy few can afford for themselves), he helped establish several institutions people now take for granted: a fire company (1736), a library (1731), an insurance company (1752), an academy (the University of Pennsylvania, 1751), a hospital (1751), and the U.S. Postal Service (starting as postmaster of the Colonies in 1753, then becoming U.S. Postmaster during the Revolution). In most cases these foundations were the first of their kind in North America.
In a Franklin could be merged the virtues of Puritanism without its defects, the illumination of the Enlightenment without its heat.
– Henry Steele Commager
It’s become cliché that unusually many prominent people died in 2016. Is this true?…
[Image above: source]
* François Rabelais
As we usher in the new, we might spare a thought for the first woman in the Western world considered to be a mathematician: Maria Gaetana Agnesi, she died this date in 1799. While she thought and wrote broadly about natural science and philosophy, she is best remembered for her work in differential calculus– perhaps most particularly for her work on the cubic curve now know as the “witch of Agnesi.”
Hoss Cartwright, a former editor of the International Journal of Agricultural Innovations and Research, had a good excuse for missing the 5th World Congress on Virology last year: He doesn’t exist…
As grant funding and career advancement depend ever more heavily on publishing metrics, scientists are inventing “co-authors” with prestigious-sounding affiliations to give their papers more credibility with the journals to which they submit: “Why fake data when you can fake a scientist?”
* Groucho Marx
As we prune the pretenders, we might spare a thought for Persian polymath Omar Khayyam; the mathematician, philosopher, astronomer, epigrammatist, and poet died on this date in 1131. While he’s probably best known to English-speakers as a poet, via Edward FitzGerald’s famous translation of the quatrains that comprise the Rubaiyat of Omar Khayyam, Omar was one of the major mathematicians and astronomers of the medieval period. He is the author of one of the most important works on algebra written before modern times, the Treatise on Demonstration of Problems of Algebra (which includes a geometric method for solving cubic equations by intersecting a hyperbola with a circle). His astronomical observations contributed to the reform of the Persian calendar. And he made important contributions to mechanics, geography, mineralogy, music, climatology, and Islamic theology.
“All opinions are not equal. Some are a very great deal more robust, sophisticated and well supported in logic and argument than others”*…
Now more than ever: Get a free logical fallacy poster.
* Douglas Adams, The Salmon of Doubt
As we dedicate ourselves to discipline, we might send carefully-calculated birthday greetings to John Wallis; he was born on this date in 1616. An English mathematician who served as chief cryptographer for Parliament and, later, the royal court, he helped develop infinitesimal calculus and is credited with introducing the symbol ∞ for infinity.
In Chichibu, Japan, two hours northwest of Tokyo, there’s an odd museum; perhaps the only one of its kind. It’s called the Chinsekikan (which means hall of curious rocks) and it houses over 1700 rocks that resemble human faces.
The museum houses all kinds of jinmenseki, or rock with a human face, including celebrity lookalikes like Elvis Presley [below]. And according to a 2013 post on Kotaku, there are also movie and video game character rocks like E.T., Donkey Kong and Nemo…
Learn the back story and take the tour at “The Japanese Museum of Rocks That Look Like Faces.”
* William Makepeace Thackeray
As we practice being stone-faced, we might spare a thought for Christian Goldbach; he died on this date in 1764. A mathematician, lawyer, and historian who studied infinite sums, the theory of curves and the theory of equations, he is best remembered for his correspondence with Leibniz, Euler, and Bernoulli, especially his 1742 letter to Euler containing what is now known as “Goldbach’s conjecture.”
In that letter he outlined his famous proposition:
Every even natural number greater than 2 is equal to the sum of two prime numbers.
It has been checked by computer for vast numbers– up to at least 4 x 1014– but remains unproved.
(Goldbach made another conjecture that every odd number is the sum of three primes; it has been checked by computer for vast numbers, but also remains unproved.)
Goldbach’s letter to Euler (source, and larger view)
More than 20 million people in the U.S. are afraid of flying. Sitting in a chair that’s floating in the air may be technologically stunning to some, but that floating-in-a-tin-can feeling puts some passengers on edge and sends their minds racing: Do the flight attendants look worried? What was that bump? And, oh man, what was that noise?!
But you don’t have to worry. You’re more likely to drown in your own bathtub than you are to perish in an out-of-control flight. In fact, the last time a U.S.-registered airliner had any fatalities was in 2009.
So unless the sound you hear is the flight attendants telling you to assume a bracing position—which really only means there’s the potential for a problem—everything’s most likely O.K. Still, the unknown can be scary…
A breakdown—by sound—of most things you’ll hear on a flight and what each of those noises means: “A Nervous Flyer’s Guide to Every Ding, Buzz and Whir You Hear on an Airplane.”
* Jane Austen,
As we assume the crash position, 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).
* Carl Friedrich Gauss
As we count ’em up, we might send starry birthday greeting to Erasmus Reinhold; he was born on this date in 1511. A mathematician and astronomer, Reinhold was considered to be the most influential astronomical pedagogue of his generation. Today, he is probably best known for his carefully calculated set of planetary tables– the first– applying Copernican theory, published in 1551.