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Posts Tagged ‘paradox

“The opposite of a correct statement is a false statement. But the opposite of a profound truth may well be another profound truth.”*…

Zeno shows the Doors to Truth and Falsity (Veritas et Falsitas). Fresco in the Library of El Escorial, Madrid (source)

As Joel David Hamkins explains, an ancient puzzle leads ultimately to a remarkable observation on the malleable nature of infinite sums…

The Greek philosopher Zeno of Elea (c. 490–430 BC) argued in antiquity that all motion is impossible. It is simply impossible to walk through town or even across the room, to go from here to there. What? We know, of course, that this is possible—we walk from here to there every day. And yet, Zeno offers us his proof that this is an illusion—we simply cannot do it.

Zeno argued like this. Suppose it were possible for you to move from some point A to another distinct point B.

Before you complete the move from A to B , however, you must of course have gotten half way there.

But before you get to this half-way point, of course, you must get half way to the half-way point! And before you get to that place, you must get half way there.

And so on, ad infinitum.

Thus, to move from A to B , or indeed anywhere at all, one must have completed an infinite number of tasks—a supertask. It follows, according to Zeno, that you can never start moving—you cannot move any amount at all, since before doing that you must already have moved half as much. And so, contrary to appearances, you are frozen motionless, unable to begin. All motion is impossible.

Is the argument convincing? On what grounds would you object to it? Do you think, contrary to Zeno, that we can actually complete infinitely many tasks? How would that be possible?

It will be no good, of course, to criticize Zeno’s argument on the grounds that we know that motion is possible, for we move from one point to another every day. That is, to argue merely that the conclusion is false does not actually tell you what is wrong with the argument—it does not identify any particular flaw in Zeno’s reasoning. After all, if it were in fact an illusion that we experience motion, then your objection would be groundless…

Learning from an enigma– plus “the most contested equation in middle school” and more: “Zeno’s paradox,” from @JDHamkins.

* Niels Bohr


As we interrogate infinity, we might send-well-groomed birthday greetings to Frank Joseph Zamboni, Jr.; he was born on this date in 1901.  An engineer and inventor, he is best known for the modern ice resurfacer, seen at work at hockey games and figure skating competitions (completing its rounds, Zeno notwithstanding); indeed, his surname is the registered trademark for these devices.



Written by (Roughly) Daily

January 16, 2023 at 1:00 am

“The way of paradoxes is the way of truth”*

Circular references…

Cyclic TV Reference Paradoxes occur when a chain of fictional TV show references form a cycle. Each show’s reality depends on another being fictional, so a cycle of these dependencies is a paradox [like the one above].

Using subtitles, a large dataset of TV references were generated. This tool displays this dataset in a graph where the nodes are TV shows, and the edges are references. References can be viewed by clicking on individual nodes in this graph. Cycles can be selected to inspect a specific instance of this paradox.

Prepare for your head to spin, then head over to Cyclic TV Reference Paradox Finder. Creator Jamie Pinheiro (@jamiepinheiro) unpacks the backstory and explains his technique here.

* Oscar Wilde


As we get meta, we might recall that it was on this date in 1994 that people all around the U.S. (and some parts of the world) watched police in a low-speed chase of a not-so-mysterious white Ford Bronco.

Just five days earlier, it was discovered that O.J. Simpson’s ex-wife and her friend Ron Goldman were brutally murdered outside of her home. Simpson became a chief suspect and had agreed to turn himself in but apparently decided to take a u-turn. Traveling with a friend, A.C. Cowlings, Simpson was carrying his passport, a disguise and $8,750 in cash. Instead of surrendering to police, Simpson took them on a low-speed chase on the L.A. freeways all the way back to his home in Brentwood [where he was arrested].



Written by (Roughly) Daily

June 17, 2022 at 1:00 am

“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 (Roughly) Daily

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 (Roughly) Daily

October 28, 2019 at 1:01 am

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