Posts Tagged ‘nuts’
“Your life has a limit, but knowledge has none”*…
Kurt Gödel’s Incompleteness Theorems put a cap on what we can “know” from within the logical and perceptual systems in which we live. While Gödel’s focus was trained on mathematics, his insight has seen much broader application (e.g., here).
Alexander V. Gheorghiu argues that it’s not so simple– and that what we claim as “true” is not a ceiling we are forever failing to reach but something that changes as we climb toward it…
On the evening of 8 September 1930, the German mathematician David Hilbert stepped up to a microphone in Königsberg and addressed his countrymen by radio. He was 68, recently retired, and at the height of his fame. The talk was a defense of pure reason, delivered in the city of Immanuel Kant, and it ended with two phrases that would later be carved on his tombstone: Wir müssen wissen. Wir werden wissen. We must know. We shall know.
Are certain questions closed to the human mind? Are there truths about the world that we can never know? Hilbert thought that, at least within mathematics, this could not be the case. For him, mathematics was a game played with symbols: one could fix the right axioms as rules of the game and every mathematical problem could be solved. He was wrong.
The day before his Königsberg address, at a small academic meeting in the same city, a 24-year-old Austrian named Kurt Gödel had quietly announced that no such system for arithmetic could exist. Whatever reasonable set of rules you fix, something true must lie beyond them and thus beyond our knowledge. We can’t know. We won’t know. Gödel’s results, known as the Incompleteness Theorems, are landmark achievements of 20th-century logic. Recent work in philosophy and mathematics has begun to illuminate the gap they opened, and with it something deeper about the foundations of knowledge itself. The story begins in the same city, but two centuries earlier…
[Gheorghiu unpacks the arguments of Kant, Hilbert, and Gödel, then traces the work done since. He concludes…]
… In 2005, Tor Sandqvist, a doctoral student at Uppsala University, submitted a thesis that took up [Michael Dummett‘s]’s challenge: to justify the ordinary practices of mathematicians without any appeal to truth. Where Dummett had given the conditions a solution must satisfy, Sandqvist gave a solution. He produced a precise mathematical justification of deduction as mathematicians actually use it, grounded entirely in practices of assertion. The boxer’s fists were untied.
It was rediscovered a decade later in the Department of Computer Science at University College London, where a group of logicians recognised what Sandqvist had actually built, and developed it into a full framework on a par with the orthodox truth-conditional view. The framework now stands equal to the truth-based account, analogous to the situation after Gödel’s PhD thesis. What about mathematics? The UCL team have recently shown that the Dummett-Sandqvist framework gives a way to understand what Gödel’s Incompleteness Theorems are about, and it is not the limits of knowledge.
If meaning comes from practices of assertion, then our concepts are settled only as far as our practices have settled them. A system of definitions is a kind of constitution that determines something. The US Constitution, for example, is meant to enshrine a form of democracy. But what a constitution defines answers to how it is amended.
Principia Mathematica is a constitution for arithmetic. To read it as a constitution is to assume it is consistent; otherwise, it would be nonsense. So, when we amend it by asserting that ‘Principia Mathematica is consistent,’ we are not changing the subject: the new axiom says aloud only what the practice already did. Gödel’s theorems apply afresh to the enlarged constitution: the amended system has its own unprovable truth, its own consistency it cannot certify. No amendment is the last; each faithful extension opens room for the next. To grasp a concept like arithmetic is not to survey a finished structure; it is to hold a principle for going on: a rule for laying the next stretch of line, not a map of where the line ends. Dummett called this openness indefinite extensibility.
Faithful is the word doing the work, because not every amendment is. Gödel claimed the US Constitution could deliver a dictatorship. That does not make dictatorship a form of democracy. Whatever loophole he had in mind, it would have contradicted the practices the Constitution already enshrined. An amendment can betray what a constitution defines. But it can also unfold it, drawing out what the founding commitments demanded all along. Only the second kind is what Dummett has in mind.
The constitution of our language is our current practice for public discourse. As it is extensible in this way, what we claim as ‘true’ is not a fixed structure with a ceiling we are forever failing to reach, but something that can change. Gödel’s verdict never applied to mathematics, but only to some edition of the constitution. Within the Sandqvist system, we can attend to the extension systematically. Hilbert’s words outlive his programme: Wir werden wissen. We shall know. Not because the answers are waiting at the end of a ladder, but because truth goes exactly as far as we have built the rungs…
Eminently worth reading in full: “The Ladder of Knowledge,” from @aeon.co.
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As we stand on the shoulders of giants, we might note that today is National Nut Day.
“Uniformity is not nature’s way; diversity is nature’s way”*…
The U.S. boasts an impressively vast array of agricultural and botanical species. In an attempt to document that fact, The United States Department of Agriculture collected over 7,500 botanical watercolour paintings of evolving fruit and nut varieties in its Pomological Watercolor Collection, assembled between 1886 and 1942…
Independent publishing house Atelier Éditions is now revisiting this documentation of American pomology with the release of its latest book: An Illustrated Catalog of American Fruits & Nuts. “I came across the collection a few years back while researching botanical artworks,” says Pascale Georgiev, editorial director of Atelier. “There was such potential for a book with this collection, and it fits with our way of building archival or collection-based volumes.” The book is a biophilic wonder, with beautiful images of fruits popping with gentle colours and careful watercolour work. Accompanying them are often texts by well-versed experts, giving a fascinating insight into the agriculture behind the produce.
“We only produce and consume a handful of varieties today, mainly hybrids that cater to our desire for a certain sweetness, juiciness, smoothness, even specific shapes and lack of seeds,” says Pascale on the importance of the book’s current publication. “In some respects, the collection is a time capsule, and a reminder about the importance of diversity and conservation,” she adds…
Joey Levenson in discussion with Pascal: “We talk to Atelier Éditions about its new Illustrated Catalog of American Fruits & Nuts,” in @itsnicethat. More at Atelier Éditions.
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As we fancy favorite fruits, we might carefully compose a birthday greeting to Pierre Athanase Larousse, the French grammarian and lexicographer, born in Toucy on this date in 1817. In 1856 Larousse and his partner Augustin Boyer published the New Dictionary of the French Language, the forerunner of the Petit Larousse. On December 27, 1863 the first volume of Larousse’s masterwork, the great encyclopedic dictionary, the Grand dictionnaire universel du XIXe siècle (Great Universal 19th-Century Dictionary), appeared.
Then, in 1938, the Larousse publishing house published an encyclopedia of gastronomy, Larousse Gastronomique edited by Prosper Montagne.
And Happy Mole Day (or to be more precise, October 23 at 6:02 pm, in honor of Avogadro’s number: 6.02 x 1023 items are in a mole — it’s the chemist’s version of a dozen)
“The keeping of bees is like the direction of sunbeams”*…
And moving those bees…
About 75% of crops and one-third of the global food supply rely on pollinators such as honeybees, according to Our World in Data. But farmers have to rely on commercially managed honeybees trucked in from other states to help pollinate certain crops, such as almonds, because there aren’t enough wild bees to do the job. And trucking bees hundreds or thousands of miles is not simple…
Honeybees are disappearing due to shrinking habitats and the growing use of pesticides. When there aren’t enough bees to pollinate fields of crops, companies pay beekeepers to transport their colonies of bees for pollination season.
“The great pollination migration” happens every year in February when the almonds bloom in California.
Pollinating the seemingly endless fields of almond trees in California requires 85% to 90% of all honeybees available to pollinate in the U.S… Bees are trucked into California from across the country…
Earl and Merle Warren are brothers, truck drivers and co-owners of Star’s Ferry Transport, based in Burley, Idaho. They started hauling bees for a local beekeeper in 1990 and moved about 50 loads of approximately 22 million bees each last year for companies such as Browning’s Honey Co.
“This is not like a load of steel or lumber. These are live creatures. This is those beekeepers’ livelihoods, so we do everything possible to keep them alive,” Earl Warren said.
Some beekeepers estimate that every time you move a truck of bees, up to 5% of the queens die… Minimizing stress for bees is critical, so beekeepers rely on experienced truck drivers to navigate difficult situations such as warm weather, few opportunities to stop during the day and inspections…
A fascinating link in the modern food chain: “A day in the life of a honeybee trucker,” from Alyssa Sporrer (@SporrerAlyssa).
* Henry David Thoreau
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As we ponder pollination, we might spare a thought for a scientist whose very field of study was (and is) made possible by bees, Anders (Andreas) Dahl; he died on this date in 1789. A botanist and student of Carl Linnaeus, he is the inspiration for, the namesake of, the dahlia flower.
“Give me juicy autumnal fruit, ripe and red from the orchard”*…
American fruit and nuts…
Pascale Georgiev, editorial director at Atelier Éditions, was researching botanical artwork a few years ago when she came across the US Department of Agriculture’s pomological watercolour collection, an archive of 7,500 watercolours of fruit and nuts grown in the US between 1886 and 1942, mostly created before photography was widespread. The discovery led to a new book, An Illustrated Catalog of American Fruits & Nuts (Atelier, £44), full of images that Georgiev describes as irresistible. “The belle angevine pear… makes my heart sing and I’m partial to a plum named tragedy.” She’s also proud that the book showcases women working in science: “Nine of this US department’s 21 artists were women. A rare thing at the time.” Most of all she’d like readers to think about biodiversity. “I hope they share my delight in discovering the history of the fruit we consume, alongside beautiful artworks.”
A glorious collection: “Get fruity: vintage botanical watercolors,” from @guardian.
* Walt Whitman
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As we ruminate on ripeness, we might recall that it was on this date in 1950 that the daily comic strip Peanuts premiered in eight newspapers: The Washington Post, The Chicago Tribune, The Minneapolis Tribune, The Allentown Call-Chronicle, The Bethlehem Globe-Times, The Denver Post, The Seattle Times, and The Boston Globe. Its creator, Charles Schulz had developed the concept as a strip (L’il Folks) in his hometown paper, The St. Paul Pioneer Press, from 1947 to 1950. At its peak, Peanuts ran in over 2,600 newspapers, with a readership of 355 million in 75 countries, and was translated into 21 languages.
“Being crazy isn’t enough”*…
There are only three foodstuffs in American English the names of which can also mean “crazy”; learn the (fascinating) story of each at “Why Are Bananas, Nuts, and Crackers the Only Foods That Say ‘Crazy’?”
* Dr. Seuss
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As we entitle insanity, we might spare a thought for the man who introduced “crazy” to literature, Miguel de Cervantes Saavedra; he died on this date in 1616 (though some scholars put it a day earlier)– the same day as Shakespeare died, and (most likely) Shakespeare’s birthday. As Somerset Maugham said,”casting my mind’s eye over the whole of fiction, the only absolutely original creation that I can think of is Don Quixote.”
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