We also must remember to do this. (A) Things that are equal to the same are equal to each other. The conjecture was introduced by Saul Rosenzweig in 1936, drawing on imagery from Lewis Carroll's novel Alice's Adventures in Wonderland, … Unlike in the classical, Aristotelian conception, modern mathematics relies ultimately on pure formalism in its use of logic. So I must ask you to grant ONE more Hypothetical.”, “Very good, I’m quite willing to grant it, as soon as you’ve written it down. Literally. The gardeners advise Alice to prostrate herself on th… Lewis Carroll, the writer of Alice’s Adventures in Wonderland, was also a mathematician. 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.”. The Red Queen's race is an incident that appears in Lewis Carroll 's Through the Looking-Glass and involves both the Red Queen, a representation of a Queen in chess, and Alice constantly running but remaining in the same spot. Note that “Alice in Wonderland” and “Through the Looking Glass and What Alice Found There,” are in the public domain. Appearing in Chapters Four and Five, the Caterpillar (also known as Russel) is a hookah-smoking insect who meets Alice after she has been shrunk to a tiny size. “We shall need them ALL!” (Achilles shuddered.) “And your present position is that you accept A and B, but you DON’T accept the Hypothetical—”, (C) If A and B are true, Z must be true.”. “You should call it D, not Z,” said Achilles. 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. When he did so, Achilles was still seated on the back of the much-enduring Tortoise, and was writing in his notebook, which appeared to be nearly full. Not the least of these is that, by reducing logic to uninterpreted symbols, all semantic content is removed from the conclusions of formal logic. Readers delight in the mysterious and mischievous characters, but cannot escape the feeling of profundity that pervades Carroll’s silly little tale. Alice in Wonderland was the title of a book by Lewis Carroll from Earth, as well as the general name by which the book and its sequel, Through the Looking-Glass, were collectively known. If A and B and C are true, Z MUST be true. Perfect for acing essays, tests, and quizzes, as well as for writing lesson plans. wholly … Here's a transformation to celebrate! How to restore meaning to systems of inference while still avoiding difficulties such as Carroll’s Paradox remains a thorny question for philosophers of mathematics. Achilles had overtaken the Tortoise, and had seated himself comfortably on its back. 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! So far, at least, as one CAN admire a treatise that won’t be published for some centuries to come!”. There, Parmenides, asserted in a poem that he had composed, that only the ‘Is’ is, whilst to speak of the ‘Is not’ is to take a ‘. 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. 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. We will call it. Alice's Adventures in Wonderland (1865) by Lewis Carroll is a most interesting tale. Specifically, he showed that merely having axioms—even the best and most perfect axioms—is not sufficient for determining truth in a system of … In … Early in Alice in Wonderland, she can’t get her physical size under control and she cries a river. “Even though it DOES consist of an infinite series of distances? The Birthday Paradox, although strange and counterintuitive to most people, can be proven using key mathematical concepts and probabilistic systems. The Tortoise was saying, “Have you got that last step written down? One example of this occurs in the “unbirthday” party scene. "Well, in our country," said Alice, still panting a little, "you'd generally get to somewhere else—if you run very fast … My world is divided into two halves. One example of this occurs in the “unbirthday” party scene. SHORTHAND isn’t invented yet!”, “That beautiful First Proposition by Euclid!” the Tortoise murmured dreamily. Lewis Carroll, the writer of Alice’s Adventures in Wonderland, was also a mathematician. Similarly, As Alice falls down the rabbit hole, so does the reader. At first glance it's childish nonsense (and this cannot be ignored), but the book is in fact a very deep and intellectual work. “And at last we’ve got to the end of this ideal race-course! 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. In other words, one’s assumptions must be explicitly augmented by the exact mechanisms by which one is to deduce consequences from those assumptions. The paradox is that this hypothesis, known as overdiagnosis, is biologically implausible and is not supported by any epidemiologic or clinical evidence. If you accept A and B and C, you MUST accept Z.”, “Because it follows LOGICALLY from them. And, of course, Dodgson (under the name Lewis Carroll) also wrote Alice in Wonderland, Alice Through the Looking Glass and many other books and poems. 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. Alice In Wonderland Life Unscripted!!! “Well, now, let’s take a little bit of the argument in that First Proposition—just TWO steps, and the conclusion drawn from them. ( Log Out /  I try to travel on the fine line between the two worlds of mine. Learn exactly what happened in this chapter, scene, or section of Alice’s Adventures in Wonderland and what it means. This page was created as a component of McGill University's Department of Integrated Studies in Education course EDEC 612. 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. mind blown. (D) If A and B and C are true, Z must be true. (B) The two sides of this Triangle are things that are equal to the same. 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. “You admire Euclid?”, “Passionately! For more information on the course, please click on the following link: Lewis Carroll, the writer of Alice’s Adventures in Wonderland, was also a mathematician. 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. Unless I've lost count, that makes a thousand and one. So it’s quite a NECESSARY step, you see?”. Let’s have Z first, and football afterwards!”, “I’m to force you to accept Z, am I?” Achilles said musingly. ), Josh Gordon (B.Eng. Now that you’ve accepted A and B and C and D, you MUST accept Z.’ So you’ve no choice, you see.”, “Whatever LOGIC is good enough to tell me is worth WRITING DOWN,” said the Tortoise. It has been suggested that that there are many references to mathematical concepts in his story. 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. share. The Dodo bird verdict is a controversial topic in psychotherapy, referring to the claim that all empirically validated psychotherapies, regardless of their specific components, produce equivalent outcomes. The Paradox: If that's right (or half right - there are other issues (see here)), then the dynamics of what happens to house prices will affect the CPI. And speak SLOWLY, please! This avoids the infinite regress in which the Tortoise traps Achilles. “Logic would tell you, ‘You can’t help yourself. Carroll’s humor in this piece disguises a point that is essential to understanding modern logic. (Z) The two sides of this Triangle are equal to each other. “Proceed! The titular character of the book was inspired by Alice Liddell, Lewis Carroll's neighbour in Oxford. Blog Archive 2007 (17) October (2) May (3) March (5) February (7) ... My world is a paradox too. For example, in The Annotated Alice Martin Gardener writes about the geometry forms encoded in the After falling down the rabbit hole, Alice enters the garden, where three playing card gardeners (2, 5, and 7 of Spades) are frantically painting white roses red. Here the narrator, having pressing business at the Bank, was obliged to leave the happy pair, and did not again pass the spot until some months afterwards. Change ), You are commenting using your Twitter account. . This concept in itself isn’t intuitive, and is arguably one of the main sources of confusion surrounding this paradox. 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. “Don’t wander from the point. “It comes NEXT to the other three. Change ). In this scene, many believe that Carroll might have been inspired the Birthday Paradox. When the traveling twin returns, he’s younger and older than his brother who stayed put. A Clue To The Eternal Paradox Is Revealed Posted on September 30, 2011 by Madame Paradox The time has come the walrus said to talk of my now-infamous Alice In Wonderland … This high number of pairs observed within a group of as little as 23 people is also highly counterintuitive to most. The formalist solution, while effective, has its own philosophical drawbacks. By contrast, in formal logic, rules of inference are reduced to rules of symbol manipulation. “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!”. It is named after the Dodo character in Alice in Wonderland. 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. Although filled with imagination, nonsense, and paradox, Lewis Carroll’s Alice in Wonderland rings with the theme of real choices. When Alice's neck grows, a pigeon interprets as a serpent. ( Log Out /  in Alice in Wonderland is centered around opposites, paradox, and mathematical symmetries. 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… Alice wouldn't have been there in the first place if not for the White Rabbit being late. Change ), You are commenting using your Google account. 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. In the case of the Birthday Paradox, we are essentially analyzing 253 different pairs of people and looking for a birthday match. ( Log Out /  “—an anomaly, of course,” the Tortoise hastily interrupted. “I see,” said Achilles; and there was a touch of sadness in his tone. 1 comment. The untouched illustration by John Tenniel is like a visual paradox, where the caterpillar’s face appears to be formed from the head and legs of a real caterpillar. The decor was definitely immersive and a treat to see. This quote sets the tone for the book, Alice's Adventures in Wonderland, as the story unravels one absurdity after another. “Let’s make that quite clear. 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. Compare with Zeno’s Paradox of the Tortoise and Achilles. The tale is filled with allusions to Dodgson's friends. 'Then,' said the cat, 'it doesn't matter.'" . Nobody goes to that restaurant, it’s too crowded. The cowering Angel and all of her minions are playing cards. ), Reyana Hadef (B.Sc. He carries a watch that is running backwards but when viewed Through the Looking Glass, it shows time correctly. The Paradox Escape Room for the Wonderland puzzle room was a really great interactive escape room with lots of puzzles to solve! Paradox for Kids I know that I know nothing.” Knowing “know nothing” is knowing something thus cannot be “know nothing”. 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. Change ), You are commenting using your Facebook account. Kenneth. 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. ), and Marco Zampino (B.Eng.). “A tortoise playing football would be—” Achilles was beginning. 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. 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. As crazy, psychedelic, surreal, fucked up and confusing as this film seems to be, it's a pretty simple one. Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. A sound understanding of the concept of permutations and combinations is required to be able to accept it. The Birthday Paradox – also known as the Birthday Problem – 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. 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. 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. Lewis Carroll (I’ll use Dodgson’s better-known pen name from now on) formulated his premises paradox in 1895. But in allowing herself to feel her emotions, Alice can then let them go, move on and make progress on her journey. In order to appreciate the solution to the Birthday Paradox, one must have, first and foremost, a solid understanding of the power of compound exponential growth. An imaginative, rather restless, young girl falls down a rabbit hole into a twisted, nonsensical world. In this scene, many believe that Carroll might have been inspired the Birthday Paradox. 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. save hide report. 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. Until I’ve granted THAT, of course I needn’t grant Z. Copyright © 1997-2021 Platonic Realms® Except where otherwise prohibited, material on this site may be printed for personal classroom use without permission by students and instructors for non-profit, educational purposes only. You see the distances were constantly DIMINISHING; and so—”, “But if they had been constantly INCREASING?” the Tortoise interrupted. What Achilles learns, to his lasting regret, is that modus ponens must be first granted as a rule of inference, for otherwise no conclusion can ever be reached. Alice tried to fancy to herself what such an extraordinary ways of living would be like, but it puzzled her too much, so she went on: `But why did they live at the bottom of a well?' There are several millions more to come. I thought some wiseacre or other had proved that the thing couldn’t be done?”, “It CAN be done,” said Achilles. 'I don't know,' Alice answered. All other reproduction in whole or in part, including electronic reproduction or redistribution, for any purpose, except by express written agreement is strictly prohibited. `Take some more tea,' the March Hare said to Alice, very earnestly. “How then?”, “Then I shouldn’t be here,” Achilles modestly replied; “and YOU would have got several times round the world, by this time!”, “You flatter me—FLATTEN, I mean,” said the Tortoise; “for you ARE a heavy weight, and NO mistake! We will call it. Even Alice herself has to battle with and overcome her emotions. (Z) The two sides of this Triangle are equal to each other. As depicted by John Tenniel in Chapter Two – The Garden of Live Flowers. Alice in Wonderland got its start as a simple story, told by a mathematics professor to a colleague's daughter. You can’t dispute THAT, I imagine?”, “If A and B and C are true, Z MUST be true,” the Tortoise thoughtfully repeated. Kindly enter them in your note-book. This thread is archived. In other words, what we would ordinarily consider meaning is lost. He carries a watch that is running backwards but when viewed Through the Looking Glass, it shows time correctly. Create a free website or blog at WordPress.com. One is black n white while the other half is bright and colorful. A summary of Part X (Section2) in Lewis Carroll's Alice’s Adventures in Wonderland. Now that you accept A and B and C and D, OF COURSE you accept Z.”, “Do I?” said the Tortoise innocently. The White Rabbit mistakes her for a sort of housekeeper by the name of Mary Ann. Wishing you a very merry un-birthday! Well now, would you like to hear of a race-course, that most people fancy they can get to the end of in two or three steps, while it REALLY consists of an infinite number of distances, each one longer than the previous one?”, “Very much indeed!” said the Grecian warrior, as he drew from his helmet (few Grecian warriors possessed POCKETS in those days) an enormous note-book and pencil. The. In Alice and Wonderland and Through the Looking Glass, characters frequently mistake Alice as something other than a little girl. “So enter it in your book, please. “I’ll do so,” said the Tortoise, “as soon as you’ve entered it in that notebook of yours. I accept A and B and C and D. Suppose I STILL refused to accept Z?“, “Then Logic would take you by the throat, and FORCE you to do it!” Achilles triumphantly replied. Of the many topics explored in the book, the reigning one is logic. She stumbles upon a table that displays a drink and some cake. “So you’ve got to the end of our race-course?” said the Tortoise. Please send comments, queries, and corrections using our contact page. “Now write as I dictate:—. “That is my present position,” said the Tortoise. New … Zeno’s Paradox of the Tortoise and Achilles. Many locks, keys, and puzzles are involved which were very well themed to Alice in Wonderland. It has been suggested that that there are many references to mathematical concepts in his story. One example of this occurs in the “unbirthday” party scene. Have you entered that in your note-book?”, “I HAVE!” Achilles joyfully exclaimed, as he ran the pencil into its sheath. 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. 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. 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”. “That’s ANOTHER Hypothetical, isn’t it? And then a rule telling you how to apply that rule, and so on. 90% Upvoted. Nov 18, 2018 - Explore Ace Jefferson's board "Paradox Me" on Pinterest. Alice in Wonderland paradox: The White Rabbit was late to Alice's court appearance. See more ideas about alice and wonderland quotes, wonderland quotes, paradox. It has been suggested that that there are many references to mathematical concepts in his story. At first, the reader is struck by the weird mention of a rabbit wearing a waistcoat. There are many instances where Carroll encoded these kind of clever math problems and concepts into his writing. This trap is impossible to avoid if logic is not formalized, because, as Douglas Hofstadter points out in Gödel, Escher, Bach (p. 170), in order to know how to use a rule (such as a rule of inference) you need a rule telling you how to apply the rule.