You can’t dispute THAT, I imagine?”, “If A and B and C are true, Z MUST be true,” the Tortoise thoughtfully repeated. Click on the image above to play the video clip! The gardeners advise Alice to prostrate herself on th… As crazy, psychedelic, surreal, fucked up and confusing as this film seems to be, it's a pretty simple one. Specifically, he showed that merely having axioms—even the best and most perfect axioms—is not sufficient for determining truth in a system of logic, for one also must be very careful about one’s choice of rules of inference. Alice in Wonderland paradox: The White Rabbit was late to Alice's court appearance. Blog Archive 2007 (17) October (2) May (3) March (5) February (7) ... My world is a paradox too. ), and Marco Zampino (B.Eng.). One example of this occurs in the “unbirthday” party scene. ( Log Out / It is exactly three inches tall which, according to him, \"is a very good height indeed\" (though Alice believes it to be a wretched height).Alice does not like the Caterpillar when they first meet, because he does not immediately talk to her and when he does, it is usually in short sent… Note that “Alice in Wonderland” and “Through the Looking Glass and What Alice Found There,” are in the public domain. When Alice's neck grows, a pigeon interprets as a serpent. It has been suggested that that there are many references to mathematical concepts in his story. And in order to refer to them conveniently, let’s call them A, B, and Z: (A) Things that are equal to the same are equal to each other. Kindly enter them in your note-book. Literally. 1 comment. Carroll’s humor in this piece disguises a point that is essential to understanding modern logic. Readers of Euclid will grant, I suppose, that Z follows logically from A and B, so that any one who accepts A and B as true, MUST accept Z as true?”, “Undoubtedly! (B) The two sides of this Triangle are things that are equal to the same. It is named after the Dodo character in Alice in Wonderland. Solvitur ambulando. . We will call it. And then a rule telling you how to apply that rule, and so on. It has been suggested that that there are many references to mathematical concepts in his story. HE, also, had better take to football.”, “And NEITHER of these readers,” the Tortoise continued, “is AS YET under any logical necessity to accept Z as true?”, “Well, now, I want you to consider ME as a reader of the SECOND kind, and to force me, logically, to accept Z as true.”. My world is divided into two halves. Readers may wish to note that Carroll is drawing on what has become a tradition, starting with Zeno of Elea and continuing with the modern author Douglas Hofstadter, of using a dialogue between the Homeric hero Achilles and the comical figure of the Tortoise to make an important philosophical point. Zeno’s Paradox of the Tortoise and Achilles. If you accept A and B and C, you MUST accept Z.”, “Because it follows LOGICALLY from them. Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. “That is my present position,” said the Tortoise. A summary of Part X (Section2) in Lewis Carroll's Alice’s Adventures in Wonderland. The tale is filled with allusions to Dodgson's friends. “Provided that YOU, for YOUR part, will adopt a pun the Mock-Turtle never made, and allow yourself to be re-named A KILL-EASE!”. Alice wouldn't have been there in the first place if not for the White Rabbit being late. I thought some wiseacre or other had proved that the thing couldn’t be done?”, “It CAN be done,” said Achilles. ( Log Out / Although it is highly unlikely that any individual pair of people will share the same birthday, the likeliness of at least one match can become significant when taking into account higher number of “tries”. Kenneth. In this scene, many believe that Carroll might have been inspired the Birthday Paradox. In order to receive the key to get through the doors, she has to drink the bottle that makes her grow and eat the cake that makes her shrink which is an example of the next departure phase belly of the whale. In his dialogue, which is fully reproduced below, Carroll tackles the single most important rule of first-order logic, modus ponens, which says that if a statement P is assumed, and if the conditional statement “P implies Q” is also assumed (or previously proved), then the statement Q itself is a logical consequence and may therefore be considered proved. (Z) The two sides of this Triangle are equal to each other. Unlike in the classical, Aristotelian conception, modern mathematics relies ultimately on pure formalism in its use of logic. He might say, ‘I accept as true the Hypothetical Proposition that, if A and B be true, Z must be true; but I DON’T accept A and B as true.’ Such a reader would do wisely in abandoning Euclid, and taking to football.”, “And might there not ALSO be some reader who would say ‘I accept A and B as true, but I DON’T accept the Hypothetical’?”, “Certainly there might. This thread is archived. The Tortoise was saying, “Have you got that last step written down? “That’s ANOTHER Hypothetical, isn’t it? This weblog has been created by four Masters students at McGill University, each studying to become teachers of high school mathematics: Daniel Gernazian (B.A., B.Mus., M.Mus., M.TM. Have you entered that in your note-book?”, “I HAVE!” Achilles joyfully exclaimed, as he ran the pencil into its sheath. Now that you accept A and B and C and D, OF COURSE you accept Z.”, “Do I?” said the Tortoise innocently. Change ), You are commenting using your Google account. Nobody goes to that restaurant, it’s too crowded. 'I don't know,' Alice answered. Although the original illustrations are black-and-white, in Alice’s Adventures Under ground and in The Nursery Alice, the Caterpillar is described as being blue. Alice In Wonderland: Extended Analysis Of Tough Alice. Alice's Adventures in Wonderland (1865) is a novel that tells the story of a girl named Alice who falls down a rabbit hole into a fantasy world populated by peculiar and anthropomorphic creatures. Alice In Wonderland - The Wonderland Paradox. For example, in The Annotated Alice Martin Gardener writes about the geometry forms encoded in the In this scene, many believe that Carroll might have been inspired the, states that in a random group of just 23 people, there is approximately a 50% probability that there will be at least a pair of people sharing the same birthday. “I see,” said Achilles; and there was a touch of sadness in his tone. Alice In Wonderland Life Unscripted!!! Since the symbols themselves are uninterpreted (which is what we really mean by “formal”), we have a system as austere and elegant as chess, where it is understood that the game arises from—and entirely consists in—the rules for moving the pieces on the board. 'Then,' said the cat, 'it doesn't matter.'" Compare with Zeno’s Paradox of the Tortoise and Achilles. We will call it. All other reproduction in whole or in part, including electronic reproduction or redistribution, for any purpose, except by express written agreement is strictly prohibited. ( Log Out / In Alice and Wonderland and Through the Looking Glass, characters frequently mistake Alice as something other than a little girl. “Well, now, let’s take a little bit of the argument in that First Proposition—just TWO steps, and the conclusion drawn from them. the reader to believe one more impossible thing—Alice's sister redreams the Wonderland adventure exactly as Alice had dreamed it—a supreme paradox which characterizes the con stant occlusion of boundaries between the two worlds. In … Wonderland is a place where conventional… The paradox is that this hypothesis, known as overdiagnosis, is biologically implausible and is not supported by any epidemiologic or clinical evidence. “It comes NEXT to the other three. When Alice questions this activity, they explain that they have planted the wrong color of rosebush, and must paint the white roses to hide their mistake from the Queen. And, if I failed to see its truth, I might accept A and B and C, and STILL not accept Z, mightn’t I?”, “You might,” the candid hero admitted; “though such obtuseness would certainly be phenomenal. https://betterexplained.com/articles/understanding-the-birthday-paradox/, http://mathforum.org/dr.math/faq/faq.birthdayprob.html, https://betterexplained.com/examples/birthday/birthday.html, https://www.khanacademy.org/math/precalculus/prob-comb/prob-combinatorics-precalc/v/birthday-probability-problem, https://betterexplained.com/articles/easy-permutations-and-combinations/, http://www.mathsisfun.com/combinatorics/combinations-permutations.html, http://www.mathsisfun.com/combinatorics/combinations-permutations-calculator.html, http://www.onlinemathlearning.com/complementary-events.html, http://www.math.uvic.ca/faculty/gmacgill/guide/pigeonhole.pdf, http://www.jamestanton.com/wp-content/uploads/2013/01/Microsoft-Word-UNIT-20_Pigeonhole-Principle.pdf. And WOULD you mind, as a personal favour, considering what a lot of instruction this colloquy of ours will provide for the Logicians of the Nineteenth Century—WOULD you mind adopting a pun that my cousin the Mock-Turtle will then make, and allowing yourself to be renamed TAUGHT-US?”, “As you please,” replied the weary warrior, in the hollow tones of despair, as he buried his face in his hands. Readers delight in the mysterious and mischievous characters, but cannot escape the feeling of profundity that pervades Carroll’s silly little tale. Early in Alice in Wonderland, she can’t get her physical size under control and she cries a river. Lewis Carroll, the writer of Alice’s Adventures in Wonderland, was also a mathematician. Achilles had overtaken the Tortoise, and had seated himself comfortably on its back. (B) The two sides of this Triangle are things that are equal to the same. Aside from exponential growth, another element of confusion lies in the fact that many people fail to consider that a comparison is made between every possible pair of people in the room, rather than fixing one individual and comparing them to the rest of the guests. Lewis Carroll (I’ll use Dodgson’s better-known pen name from now on) formulated his premises paradox in 1895. This concept in itself isn’t intuitive, and is arguably one of the main sources of confusion surrounding this paradox. Please send comments, queries, and corrections using our contact page. In the journal Mind in 1895 the Oxford logician and author of Alice in Wonderland Lewis Carroll published a playful dialogue between Achilles and the Tortoise that brought to light a central problem in logic as it was understood at the time. Porn parodies of children's stories including Snow White, Cinderella, Alice in Wonderland, Little Red Riding Hood, Pinocchio, Beauty and the Beast, Sleeping Beauty, Peter Pan and The Wizard of Oz. He carries a watch that is running backwards but when viewed Through the Looking Glass, it shows time correctly. Change ). One example of this occurs in the “unbirthday” party scene. The youngest child in a High School—as soon as High Schools are invented, which will not be till some two thousand years later—will grant THAT.”, “And if some reader had NOT yet accepted A and B as true, he might still accept the SEQUENCE as a VALID one, I suppose?”, “No doubt such a reader might exist. The works were published before January 1, 1923, and are in the public domain worldwide because Carroll died in 1898, ... such as the Barbershop Paradox. What else have you got in it?”, “Only a few memoranda,” said Achilles, nervously fluttering the leaves: “a few memoranda of—of the battles in which I have distinguished myself!”, “Plenty of blank leaves, I see!” the Tortoise cheerily remarked. Alice's Adventures in Wonderland (1865) by Lewis Carroll is a most interesting tale. But before we follow Alice into Wonderland, we should recall the roots of the controversy, in Elea in Lower Italy, in the early 5th Century BC. “Now write as I dictate:—. We also must remember to do this. An imaginative, rather restless, young girl falls down a rabbit hole into a twisted, nonsensical world.