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Posts Tagged ‘paradox

“The distinction between past, present and future is only a stubbornly persistent illusion”*…

A dog dressed as Marty McFly from Back to the Future attends the 25th Annual Tompkins Square Halloween Dog Parade in New York October 24, 2015.

“The past is obdurate,” Stephen King wrote in his book about a man who goes back in time to prevent the Kennedy assassination. “It doesn’t want to be changed.”

Turns out, King might have been onto something.

Countless science fiction tales have explored the paradox of what would happen if you do something in the past that endangers the future. Perhaps one of the most famous pop culture examples is Back to the Future, when Marty McFly went back in time and accidentally stopped his parents from meeting, putting his own existence in jeopardy.

But maybe McFly wasn’t in much danger after all. According a new paper from researchers at the University of Queensland, even if time travel were possible, the paradox couldn’t actually exist…

Find out why: “Paradox-Free Time Travel Is Theoretically Possible, Researchers Say.

* Albert Einstein


As we ponder predestination, we might send cosmological birthday greetings to Enrico Fermi; he was born on this date in 1901.  A physicist who is best remembered for (literally) presiding over the birth of the Atomic Age, he was also remarkable as the last “double-threat” in his field:  a genius at creating both important theories and elegant experiments.  As recently observed, the division of labor between theorists and experimentalists has since been pretty complete.

The novelist and historian of science C. P. Snow wrote that “if Fermi had been born a few years earlier, one could well imagine him discovering Rutherford’s atomic nucleus, and then developing Bohr’s theory of the hydrogen atom. If this sounds like hyperbole, anything about Fermi is likely to sound like hyperbole.”


Written by LW

September 29, 2020 at 1:01 am

“To paraphrase Oedipus, Hamlet, Lear, and all those guys, “I wish I had known this some time ago”*…




“Irony” is a term that everyone uses and seems to understand. It is also a concept that is notoriously difficult to define. Much like Winona Ryder’s character in the 1994 rom-com “Reality Bites,” whose inability to describe irony costs her a job interview, we know it when we see it, but nonetheless have trouble articulating it. Even worse, it seems as if the same term is used to describe very different things. And following your mother’s advice — to look it up in the dictionary — is liable to leave you even more confused than before.

Uncertainty about irony can be found almost everywhere. An American president posts a tweet containing the phrase “Isn’t it ironic?” and is derided for misusing the term. A North Korean dictator bans sarcasm directed at him and his regime because he fears that people are only agreeing with him ironically. A song about irony is mocked because its lyrics contain non-ironic examples. The term has been applied to a number of different phenomena over time, and as a label, it has been stretched to accommodate a number of new senses. But exactly how does irony differ from related concepts like coincidence, paradox, satire, and parody?…

A handy guide to distinguishing the notoriously slippery concept of irony from its distant cousins coincidence, satire, parody, and paradox: “What Irony is Not,” excerpted from Irony and Sarcasm, by Roger Kreuz.

* Roger Zelazny, Sign of the Unicorn


As we choose our words, we might recall that it was on this date in 1483 that Pope Sixtus IV consecrated the Sistine Chapel (which takes its name from his) in the Apostolic Palace, the official residence of the Pope in Vatican City.  Originally known as the Cappella Magna (Great Chapel), Sixtus had renovated it, enlisting a team of Renaissance painters that included Sandro Botticelli, Pietro Perugino, Pinturicchio, Domenico Ghirlandaio and Cosimo Rosselli to create a series of frescos depicting the Life of Moses and the Life of Christ, offset by papal portraits above and trompe-l’œil drapery below.  Michelangelo’s famous ceiling was painted from 1508 to 1512; and his equally-remarkable altarpiece, The Last Judgement, from 1536 to 1541.

220px-Sistina-interno source


“One must not think slightingly of the paradoxical”*…



The Building of the Argo, by Antoon Derkinderen, c. 1901. Rijksmuseum.


The thought problem known as the ship of Theseus first appears in Plutarch’s Lives, a series of biographies written in the first century. In one vignette, Theseus, founder-hero of Athens, returns victorious from Crete on a ship that the Athenians went on to preserve.

They took away the old planks as they decayed, putting in new and stronger timber in their place, insomuch that this ship became a standing example among the philosophers for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same…

Of course, the conundrum of how things change and stay the same has been with us a lot longer than Plutarch. Plato, and even pre-Socratics like Heraclitus, dealt in similar questions. “You can’t step in the same river twice,” a sentiment found on inspirational Instagram accounts, is often attributed to Heraclitus. His actual words—“Upon those who step into the same rivers, different and again different waters flow”—might not be the best Instagram fodder but, figuratively at least, provided the waters that the ship of Theseus later sailed.

Two thousand years later the ship is still bobbing along, though some of its parts have been replaced. Now known colloquially as Theseus’ paradox, in the U.S. the idea sometimes appears as “Washington’s ax.” While not as ancient as the six-thousand-year-old stone ax discovered last year at George Washington’s estate, the age-old question remains: If Washington’s ax were to have its handle and blade replaced, would it still be the same ax? The same has been asked of a motley assortment of items around the world. In Hungary, for example, there is a similar fable involving the statesman Kossuth Lajos’ knife, while in France it’s called Jeannot’s knife.

This knife, that knife, Washington’s ax—there’s even a “Lincoln’s ax.” We don’t know where these stories originated. They likely arose spontaneously and had nothing to do with the ancient Greeks and their philosophical conundrums. The only thing uniting these bits of folklore is that the same question was asked: Does a thing remain the same after all its parts are replaced? In the millennia since the ship of Theseus set sail, some notions that bear its name have less in common with the original than do the fables of random axes and knives, while other frames for this same question threaten to replace the original entirely.

One such version of this idea is attributed to Enlightenment philosopher John Locke, proffering his sock as an example. An exhibit called Locke’s Socks at Pace University’s now-defunct Museum of Philosophy serves to demonstrate. On one wall, six socks were hung: the first a cotton sports sock, the last made only of patches. A museum guide, according to a New York Times write-up, asked a room full of schoolchildren, “Assume the six socks represent a person’s sock over time. Can we say that a sock which is finally all patches, with none of the original material, is the same sock?”

The question could be asked of Theseus’ paradox itself. Can it be said that a paradox about a ship remains the same if the ship is replaced with a knife or a sock? Have we lost anything from Theseus’ paradox if instead we start calling it “the Locke’s Sock paradox”?…

Is a paradox still the same after its parts have been replaced?  A consideration: “Restoring the Ship of Theseus.”

* Soren Kierkegaard


As we contemplate change, we might spare a reasoned thought for the Enlightenment giant (and sock darner) John Locke; the physician and philosopher died on this date in 1704.  An intellectual descendant of Francis Bacon, Locke was among the first empiricists. He spent over 20 years developing the ideas he published in his most significant work, Essay Concerning Human Understanding (1690), an analysis of the nature of human reason which promoted experimentation as the basis of knowledge.  Locke established “primary qualities” (e.g., solidity, extension, number) as distinct from “secondary qualities” (sensuous attributes like color or sound). He recognized that science is made possible when the primary qualities, as apprehended, create ideas that faithfully represent reality.

Locke is, of course, also well-remembered as a key developer (with Hobbes, and later Rousseau) of the concept of the Social Contract.  Locke’s theory of “natural rights” influenced Voltaire and Rosseau– and formed the intellectual basis of the U.S. Declaration of Independence.

220px-John_Locke source



Written by LW

October 28, 2019 at 1:01 am

“How wonderful that we have met with a paradox. Now we have some hope of making progress”*…


Consider the simple function Y=1/X:

Take one half and rotate it around X.

It creates the shape you see at the top of this post, known as “Torricelli’s Trumpet” for its discoverer, the 17th century mathematician Evangelista Torricelli.  It’s noteworthy for its peculiar topographical qualities:  while both the volume and the surface area can be calculated, and the volume is a finite number, the surface area is Infinite.  That’s to say that, while one can fill that three dimensional shape with a calculable quantity of paint, one cannot coat the exterior surface, as it would require an infinite amount of paint…  (Supporting math, here.)

(The figure is also known as “Gabriel’s Horn,” a reference to the Archangel Gabriel, who blows his horn to announce Judgment Day– an association of the divine, or infinite, with the finite.)

This contribution (from Pablo Ramos) is just one of the fascinating answers to the question of Quora: “What are the weirdest science paradoxes that are mathematically true but counter-intuitive?

* Niels Bohr


As we rotate our minds around x, we might send post-industrial birthday greetings to Daniel Bell; he was born on this date in 1919.  Bell spent the first twenty years of his adult life as a journalist, exploring sociological issues; in 1960, on the strength of a book he’d written– The End of Ideology: On the Exhaustion of Political Ideas in the Fifties— he was awarded a PhD by Columbia University, where he taught briefly before moving for the rest of his career to Harvard.  One of the leading intellectuals of the Post-War era, Bell is best known for his contributions to the study of “post-industrialism,” and for his acute unpacking of the interactions among science, technology and politics.




Suppose there is a town with just one male barber; and that every man in the town keeps himself clean-shaven: some by shaving themselves, some by attending the barber. It seems reasonable to imagine that the barber obeys the following rule: He shaves all and only those men in town who do not shave themselves. Under this scenario, we can ask the following question: Does the barber shave himself?

From Epimenides’ Paradox to the Omnipotence Paradox, more fun-with-logic at “Brain Twisting Paradoxes.”

As we return to first principles, we might wish a carefully-reasoned Joyeux Anniversaire to Félix-Édouard-Justin-Émile Borel, a mathematician and pioneer of measure theory and its application to probability theory; he was born in Saint-Affrique on this date in 1871.  Borel is perhaps best remembered by (if not for) his thought experiment demonstrating that a monkey hitting keys at random on a typewriter keyboard will– with absolute certainty– eventually type every book in the Bibliothèque Nationale (or, as oft repeated, every play in the works of Shakespeare, or…)– that is, the infinite monkey theorem.

Borel (image source)


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