21. Mukasey's Paradox - Los Angeles Times Mar 4, 2008 The recent decisions of Atty. Gen. Michael B. Mukasey to block any prosecution of Bush administration officials for contempt and to block http://www.latimes.com/news/opinion/la-oe-turley4mar04,0,4839406.story

Hello Visitor Register Sign-In LAT Home My LATimes ... SEARCH You are here: LAT Home Opinion Opinion Sunday Opinion ... Write to Us Archive: Editorials Op-Ed Letters News ... E-Mail Newsletters RSS Feeds Help Contact Us L.A. Times Archives Reprint Requests ... Subscribe Mukasey's Paradox When you think about it, his manipulations are a beautiful, twisted thing. By Jonathan Turley March 4, 2008 The recent decisions of Atty. Gen. Michael B. Mukasey to block any prosecution of Bush administration officials for contempt and to block any criminal investigation of torture led to a chorus of criticism. Many view the decisions as raw examples of political manipulation of the legal process and overt cronyism. I must confess that I was one of those crying foul until I suddenly realized that there was something profound, even beautiful, in Mukasey's action. In his twisting of legal principles, the attorney general has succeeded in creating a perfect paradox. Under Mukasey's Paradox, lawyers cannot commit crimes when they act under the orders of a president and a president cannot commit a crime when he acts under advice of lawyers. Such a perfect paradox is no easy task. Most attempts fall apart because of some element of logical consistency. The closest example to Mukasey's Paradox is the Grandfather Paradox: If you go back in time and kill your grandfather before he meets your grandmother, you would not be conceived and therefore you could not go back to kill your grandfather. That one can play real tricks with your head.

22. Paradox Lost I’ve been waiting to do that comic since I first came up with paradox Lost. .. paradox Lost is protected by ninja hordes and lazer hippos. http://paradox-lost.com/

It's 4:15 AM and the tones are nearly done. I'll finish up the last panel later today. Now: sleep.. Way Too Far! Monday, March 31, 2008 Archived Strips 03/31/08 - Way Too Far! 03/24/08 - We Found Her! 03/17/08 - That Ship's Special 03/10/08 - Can We Keep It? 03/03/08 - Just a Tree... 02/25/08 - Hatch! 01/23/08 - Work To Do 12/12/07 - The Story So Far! (by Vaz) 12/05/07 - Captain 11/28/07 - Artweek: "The Literate Ninja" 11/21/07 - "The Monster of Mugwood" Page Five 11/14/07 - "The Monster of Mugwood" Page Four 11/07/07 - "The Monster of Mugwood" Page Three 10/31/07 - "The Monster of Mugwood" Page Two 10/24/07 - "The Monster of Mugwood" Page One 03/01/07 - System "AMI" Online 02/11/07 - Not Alone 08/27/06 - One of those Days 08/19/06 - Overload 08/12/06 - Fool of a Took! 08/01/06 - Anywhere is Better than Here! 07/21/06 - The Cargo 03/16/06 - Fire! 03/06/06 - Bring 'Er In, Mates! 11/29/05 - Weer'd Beard 11/23/05 - Yarr! 11/16/05 - Playing Rough 09/10/05 - Pirates! Oni P. Nami and Kogs! 08/16/05 - Fwazap! (Again) 08/08/05 - Resue Mission 07/26/05 - PLT: "Broke" 04/07/05 - Pillow People: "The Joys of Water" 03/20/05 - Fallen: Stage One Complete 03/09/05 - Contact: Tira Brielle 03/03/05 - Un-X-pected Results 02/03/05 - That Whole Destiny Thing 01/26/05 - Backup: Special Agent Ace Clef 01/15/05 - Wait, Again?

23. Pixel Paradox Screensavers And Pixel Paradox Games - Handcrafted Screensavers Fo Pixel paradox Screensavers and Pixel paradox Games Handcrafted Screensavers for Home and Office PCs Free Game Downloads. 3D, Las Vegas, Egypt, http://www.pixelparadox.com/

ixel P Windows Screensavers by Category SEARCH ... IPISD JUST RELEASED SCREENSAVERS A Day in Dubai Christmas Snowman 3D FREE GAME DOWNLOADS Hidden Expedition: Titanic Mystery Case Files: Ravenhearst Diner Dash 4 Dream Day Wedding ... and more! COMING SOON SCREENSAVERS Mayan Codex Buildings of Frank Lloyd Wright The Titanic in Color Extreme Insects Stained Glass ... and more! Welcome to Pixel Paradox home of handcrafted screensavers for your home and office and arcade games for your PC. Featured Pixel Paradox Games Mystery Case Files: Madame Fate Yahtzee Jojo's Fashion Show More Pixel Paradox Games - click here Featured Pixel Paradox Screensavers Sword of the Samurai Mucha Art Nouveau People of Tsarist Russia Egypt of David Roberts Deep Space Fantasy Battles of the Civil War Egypt Tomb Scenes Las Vegas Neon Nights More Baseball Legends Native Americans of the 1800s The Book of Kells Portraits of American Presidents Hypnotica 3D See More Screensavers - click here Click the screensaver image below.

24. Paradox Cafe paradox uses, when affordable and available, organic produce, organic grains flours, organic tofu and tempeh, free range eggs and hormone free meats. http://www.paradoxorganiccafe.com/

Welcome to the Philosophy Location PaRaDoX Favorites And Then ... Soups 3439 SE Belmont Portland, OR 97214 Hours* M - W 8 am - 9:00 pm Th - Sa 8 am - 9:30 pm Sunday 8 am - 3 pm *Summer hours may vary E-mail Paradox Staff Top of Page Whole Menu served all-day! PaRaDoX Favorites Add cheese, sour cream, salsa, guacamole or gravy for an additional charge Your choice of one egg or tofu served with your choice of potatoes or rice; finished off with either toast, a wheat biscuit or corn rice bread. Your choice of seasoned potatoes or brown rice topped with our seasonal vegetable blend and your choice of one egg, tofu or tempeh. Choose from vegan french toast or pancake or a NON vegan waffle; sausage or potatoes; one egg or tofu. Sub veggies for potatoes for an extra $ 1.50 Corn or wheat tortillas layered with our house chili and cheese topped with your choice of an egg or tofu, with rice, sour cream, and salsa. Your choice of two eggs or tofu, garden or chicken sausage with one wheat biscuit and almond gravy and seasoned potatoes. A blend of seasonal vegetables, your choice of egg or tofu, our house chili

25. Russell's Paradox [Internet Encyclopedia Of Philosophy] Examines selfreferential linguistics used to describe properties and sets. http://www.iep.utm.edu/p/par-russ.htm

Russell's Paradox Russell's paradox represents either of two interrelated logical antinomies. The most commonly discussed form is a contradiction arising in the logic of sets or classes. Some classes (or sets) seem to be members of themselves, while some do not. The class of all classes is itself a class, and so it seems to be in itself. The null or empty class, however, must not be a member of itself. However, suppose that we can form a class of all classes (or sets) that, like the null class, are not included in themselves. The paradox arises from asking the question of whether this class is in itself. It is if and only if it is not. The other form is a contradiction involving properties. Some properties seem to apply to themselves, while others do not. The property of being a property is itself a property, while the property of being a cat is not itself a cat. Consider the property that something has just in case it is a property (like that of being a cat ) that does not apply to itself. Does this property apply to itself? Once again, from either assumption, the opposite follows. The paradox was named after Bertrand Russell, who discovered it in 1901. Table of Contents (Clicking on the links below will take you to those parts of this article) 1. History

26. The Power Paradox This presents us with the paradox of power The skills most important to obtaining power and leading effectively are the very skills that deteriorate once http://greatergood.berkeley.edu/greatergood/current_issue/keltner.html

HOME CURRENT ISSUE ARCHIVE SUBSCRIBE ... LINKS Volume IV, Issue 3: Winter 2007-08 The Power Paradox True power requires modesty and empathy, not force and coercion, argues Dacher Keltner It is much safer to be feared than loved, writes Niccolò Machiavelli in The Prince, his classic 16th-century treatise advocating manipulation and occasional cruelty as the best means to power. Almost 500 years later, Robert Greene's national bestseller, The 48 Laws of Power, would have made Machiavelli's chest swell with pride. Greene's book, bedside reading of foreign policy analysts and hip-hop stars alike, is pure Machiavelli. Here are a few of his 48 laws: Law 3, Conceal Your Intentions. Law 6, Court Attention at All Costs. Law 12, Use Selective Honesty and Generosity to Disarm Your Victims. Law 15, Crush Your Enemy Totally. Law 18, Keep Others in Suspended Terror. You get the picture. As seductive as these notions are, they are dead wrong. Instead, a new science of power has revealed that power is wielded most effectively when it's used responsibly, by people who are attuned to and engaged with the needs and interests of others. Years of research suggests that empathy and social intelligence are vastly more important to acquiring and exercising power than are force, deception, or terror. This research debunks longstanding myths about what constitutes true power, how people obtain it, and how they should use it. But studies also show that once people assume positions of power, they're likely to act more selfishly, impulsively, and aggressively, and they have a harder time seeing the world from other people's points of view. This presents us with the paradox of power: The skills most important to obtaining power and leading effectively are the very skills that deteriorate once we have power.

27. Zeno's Paradox Of The Tortoise And Achilles (PRIME) Zeno s classic paradox, from the Platonic Realms Interactive Math Encyclopedia. http://www.mathacademy.com/pr/prime/articles/zeno_tort/

BROWSE ALPHABETICALLY LEVEL: Elementary Advanced Both INCLUDE TOPICS: Basic Math Algebra Analysis Biography Calculus Comp Sci Discrete Economics Foundations Geometry Graph Thry History Number Thry Physics Statistics Topology Trigonometry eno of Elea ( circa 450 b.c.) is credited with creating several famous paradoxes , but by far the best known is the paradox of the Tortoise and Achilles. (Achilles was the great Greek hero of Homer's The Illiad .) It has inspired many writers and thinkers through the ages, notably Lewis Carroll and Douglas Hofstadter, who also wrote dialogues involving the Tortoise and Achilles. The original goes something like this: The Tortoise challenged Achilles to a race, claiming that he would win as long as Achilles gave him a small head start. Achilles laughed at this, for of course he was a mighty warrior and swift of foot, whereas the Tortoise was heavy and slow. Achilles said nothing. Zeno's Paradox may be rephrased as follows. Suppose I wish to cross the room. First, of course, I must cover half the distance. Then, I must cover half the remaining distance. Then, I must cover half the remaining distance. Then I must cover half the remaining distance . . . and so on forever. The consequence is that I can never get to the other side of the room.

28. Shaded Paradox, The Severus Snape FL, V1 Shaded paradox is the fanlisting for Severus Snape from the Harry Potter series. http://legilimens.org/paradox/

Welcome to "Shaded Paradox" the Fanlisting for the darkly mysterious Severus Snape of the Harry Potter Series, approved by thefanlistings.org Statistics Script Used: Enthusiast Last Updated: 09th March 2008 Member Count: Pending Members: Newest Members: Michelle Aurora , Kitty, Jackie Stevens-Lock, Vapor, Cate , Jeca, Melissa D, LiaBlack , ChiisaiHana, Lucia Natasha , Crossikka, Lisanne, Carina, Emily, Nasty, BloodStained, Ice, Aloise, Angyal131, and Melissa Growth Rate: 2.8 members/day Major Updates Aug.06.07 # This fanlisting will be changing locations this weekend. This minimalist approach has served the FL well, but I've decided to expand this into more of a fansite and not just a fanlisting. Hopefully that'll help eliminate all the spam applications this FL gets. And info needs updating. Since we all "know" now, don't we. If you've read the last book that is. # I have decided that the Severus Snape FL needs the love of more than just one obsessed fan, so let me introduce Momoka , the new co-owner of this fanlisting! Yay. :) There shall be changes and revamps soon and hopefully with the combined effort of two Snape-lovers, there will be more frequent updates and more too keep the fans occupied. # Finally added the 2000 Members TFL Award to the " about " section. Woo!! Come on everyone, we can make it to 5000! Heh.

29. Paradoxes And Dilemmas An essay with links to related material on common paradoxes and dilemmas, particularly of the social type. Included are the Voting paradox, http://perspicuity.net/paradox/paradox.html

Paradoxes and Dilemmas By: Leon Felkins Written: 12/10/95, Latest Revision: 12/31/07 This section is still in work and will likely remain so! There is a place where Contrarieties are equally True... . - William Blake (1757-1827) - from "Milton" Book the Second, Plate 30 My Favorites A definition of paradox appropriate for this essay is that given by the Random House Unabridged Dictionary; 'any person, thing, or situation exhibiting an apparently contradictory nature'. A concept can appear to be a paradox due to our lack of understanding or the inadequacies of language. While such paradoxes may be resolved in time with better understanding, it is unlikely that the paradoxes mentioned here will be so easily resolved. The Voting Paradox I should make it clear that what I am referring to here is the apparent paradox for the individual voting in a general election. The term, "Voter's Paradox" as often used in the scholarly Social Choice publications refers to a situation in which the personal preference ordering of three or more alternatives can result in a group ordering that is not transitive. I will describe this paradox further below . But my subject here is the "insignificant vote" situation in general elections. This paradox is quite representative of the general problem of the Social Dilemmas which I discuss here and has to do with the fact that an individual's vote has no significant impact on the outcome of an election. The

30. Global Warming Paradox? - TierneyLab - Science - New York Times Blog The researchers offer several possible explanations for this apparent paradox. Paul Kellstedt, the lead author and a professor of political science at Texas http://tierneylab.blogs.nytimes.com/2008/02/29/global-warming-paradox/

var nyt_google_hints = "evolution;space;psychology;genetics;computer;math;brain;body;sex;food;health;religion;ethics;politics;risk;climate;energy;environment"; var nyt_google_ad_channel = "bl_science"; Home Page My Times Today's Paper Video ... Times Topics Science All NYT document.write(day + " " + month + " " + myweekday + ", " + year); Science World U.S. N.Y. / Region ... Autos February 29, 2008, 12:16 pm Global Warming Paradox? By John Tierney Tags: climate change global warming Risk Analysis Global warming is an extreme collective action dilemma, with the actions of one person having a negligible effect in the aggregate. Informed persons appear to realize this objective fact. Therefore, informed persons can be highly concerned and reasonably pessimistic about their ability to change climate outcomes. More broadly, and again quite speculatively, I think that Americans have a great deal of faith in technology and technological solutions to problems. We have seen science do things (like send people into outer space, and to miraculously save them, Apollo-13 style, when things go badly) unimaginable for 99.9% of human history. UPDATE: My colleague Andy Revkin has some thoughts at DotEarth on the difficulty of communicating the risks of global warming.

31. Paradox Poetry.com Welcome to paradox Poetry.com We invite you to take a look at Neopoet.com, a new poetry community from the same people that brought you paradox. http://www.paradoxpoetry.com/

Navigation Home Poetry Collection by Genre Submit Poem Check Submission Status ... Your Account Search Friends Submit Poetry on AnyLit.com Chat Poetry.org Recent Changes Unfortunately, the publication of new poetry on ParadoxPoetry.com is suspended. We invite you to take a look at Neopoet.com , a new poetry community from the same people that brought you Paradox.  Full of Myself ClintWilson writes: The ship was sunk; I was alone, Out on the open ocean. I hung on to a chunk of wood, Which made a bobbing motion. The wood became so waterlogged; I knew it soon would sink. I could not last much longer; I was going in the drink. Posted by Editor on Wednesday, April 05 @ 00:00:00 GMT  (2401 reads) Read Full Poem... 10 comments  Subterranean Secrets jeffreyWmosher writes: Indigo waters devour the takers and the makers There is no one who can undress the historical sites of the nights divide There is a rising of the level of the ocean tide Steal away the metamorphosis of fantasies obscured Wander in the ancient mine as the diamond shards carve the stale air inside Wander in and take the vibe Wander in and let your skin subside Posted by Editor on Saturday, December 31 @ 00:00:00 GMT

32. Math Forum: Zeno's Paradox The great Greek philosopher Zeno of Elea (born sometime between 495 and 480 B.C.) proposed four paradoxes in an effort to challenge the accepted notions of http://mathforum.org/isaac/problems/zeno1.html

Zeno's Paradox A Math Forum Project Table of Contents: Famous Problems Home The Bridges of Konigsberg The Value of Pi Prime Numbers ... Links The great Greek philosopher Zeno of Elea (born sometime between 495 and 480 B.C.) proposed four paradoxes in an effort to challenge the accepted notions of space and time that he encountered in various philosophical circles. His paradoxes confounded mathematicians for centuries, and it wasn't until Cantor's development (in the 1860's and 1870's) of the theory of infinite sets that the paradoxes could be fully resolved. Zeno's paradoxes focus on the relation of the discrete to the continuous, an issue that is at the very heart of mathematics. Here we will present the first of his famous four paradoxes. Zeno's first paradox attacks the notion held by many philosophers of his day that space was infinitely divisible, and that motion was therefore continuous. Paradox 1: The Motionless Runner A runner wants to run a certain distance - let us say 100 meters - in a finite time. But to reach the 100-meter mark, the runner must first reach the 50-meter mark, and to reach that, the runner must first run 25 meters. But to do that, he or she must first run 12.5 meters. Since space is infinitely divisible, we can repeat these 'requirements' forever. Thus the runner has to reach an infinite number of 'midpoints' in a finite time. This is impossible, so the runner can never reach his goal. In general, anyone who wants to move from one point to another must meet these requirements, and so motion is impossible, and what we perceive as motion is merely an illusion.

33. The Light Cone: Twin Paradox Applet The Light Cone Twin paradox Applet. This requires a JAVAenabled browser. In order to see the associated tutorial, you need a frames-capable browser. http://physics.syr.edu/courses/modules/LIGHTCONE/java/TwinParadox.html

The Light Cone: Twin Paradox Applet This requires a JAVA-enabled browser. In order to see the associated tutorial, you need a frames-capable browser. If you don't have one, you can access the applet itself: Twin Paradox Applet Last modified: Sun Apr 16 14:33:23 2000

34. Morphological Paradoxes A review of some of the key questions in modern morphology. http://www2.hawaii.edu/~bender/paradox.html

[back to list of essays] MORPHOLOGICAL PARADOXES Byron W. Bender University of Hawai`i n. A seemingly contradictory statement that may nonetheless be true: the paradox that standing is more tiring than walking. One exhibiting inexplicable or contradictory aspects : "You have the paradox of a Celt being the smooth Oxonian" (Anthony Burgess). An assertion that is essentially self-contradictory, though based on a valid deduction from acceptable premises. A statement contrary to received opinion. [ Latin paradoxum, from Greek paradoxon, from neuter sing. of paradoxos, conflicting with expectation : para-, beyond; see PARA-1 + doxa, opinion (from dokein, to think...).] American Heritage Dictionary. INTRODUCTION It is my intention in this brief paper to raise what I consider to be some of the key questions in morphology today. In so doing, I will be anything but neutral, and perhaps even provocative, in the way I state them. If that is how I am perceived, I will have succeeded in my purpose, which is to arouse curiosity and stir debate. On many of them we have been floundering all too long; the time has come to face them head-on. The answers are not easy, and will not be found in this paper. At most, I will suggest a few avenues to explore. [This is the written version of a talk on morphology given as a guest lecture in Ling 615

35. The Twin Paradox This contrasts sharply with the situation among mainstream physicists/hidebound reactionaries (take your choice), where the paradox has been no more than http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.htm

[Physics FAQ] [Top] [Intro] [Next] Original by Michael Weiss. The Twin Paradox This hardy perennial seems to generate endless running threads on the sci.physics.* hierarchy. This contrasts sharply with the situation among mainstream physicists/hidebound reactionaries (take your choice), where the "paradox" has been no more than an entertaining (and educational) exercise since it first saw the light of day. It's too much to hope that this FAQ entry will change any minds, except maybe an "undecided" or two. But perhaps it can reduce the traffic on this topic. Read the sections as whim and mouse-clicks take you, though you might want to read the Introduction first. Introduction Where we introduce our heroes, Earth-bound Terence and star-bound Stella, and settle on a few things, like terminology. Also, the "acceleration" explanation of the twin paradox. The Doppler Shift Explanation Suppose Stella and Terence each film the other's clock through a telescope throughout the trip; when does Stella see Terence's clock run fast? The Spacetime Diagram Explanation Where we take an Olympian view, and gaze with the Fates upon the world lines of Terence and Stella.

36. ConnectionStrings.com - How To Connect To Paradox All connection strings for paradox accessible at one location. Find your paradox connection string syntax and learn more accurate ways of connecting. http://www.connectionstrings.com/?carrier=paradox

37. "The Christian Paradox: How A Faithful Nation Gets Jesus Wrong" By Bill McKibben And therein is the paradox. America is simultaneously the most professedly Christian of the developed nations and the least Christian in its behavior. http://www.harpers.org/ExcerptTheChristianParadox.html

HOME SUBSCRIBE ARCHIVE SUBJECTS ... SKIP to main content USERNAME PASSWORD Subscriber? Lost password? Jan Feb ... NEXT TITLE The Christian paradox: How a faithful nation gets Jesus wrong TYPE Article BY Bill McKibben PUBLISHED August 2005 VIEW PAGES PDF RESPONSES OR CORRECTIONS October 2005, page 5 October 2005, page 5 What it means to be Christian in America. An excerpt from this report appeared in August 2005. The complete text appears below. Asking Christians what Christ taught isn't a trick. When we say we are a Christian nation—and, overwhelmingly, we do—it means something. People who go to church absorb lessons there and make real decisions based on those lessons; increasingly, these lessons inform their politics. (One poll found that 11 percent of U.S. churchgoers were urged by their clergy to vote in a particular way in the 2004 election, up from 6 percent in 2000.) When George Bush says that Jesus Christ is his favorite philosopher, he may or may not be sincere, but he is reflecting the sincere beliefs of the vast majority of Americans. And therein is the paradox. America is simultaneously the most professedly Christian of the developed nations and the least Christian in its behavior. That paradox—more important, perhaps, than the much touted ability of French women to stay thin on a diet of chocolate and cheese—illuminates the hollow at the core of our boastful, careening culture.

38. Home - Paradox Community Mambo the dynamic portal engine and content management system. http://www.thedbcommunity.com/

Downloads Search Links Support ... Home Home 31 March 2008 Main Menu Home Articles Community Classified ... Submissions Login Username Password Remember me Forgotten your password? No account yet? Create one Conditionally Colouring Records Written by Jan Stegehuis 05 September 2007 Preface I have included a fully functional demo (Paradox® 9), based on the technique described below. After downloading into the folder of your choice, make that folder :WORK :, run the form and follow the instructions. The form allows to select individual records and indicate those with a different colour. Last Updated ( 05 September 2007 ) Read more... Convertion of integer to roman numbers Contributed by Pierre Charbonneau P.Eng. 06 April 2007 In publication and display, we often want to put automatically the current year in roman numbers but how ? Last Updated ( 14 May 2007 ) Read more... Welcome Written by Larry DiGiovanni 17 February 2005 Welcome to the Paradox Community, the largest global meeting place for Paradox Resources.  You'll find everything here from support, jobs, and case studies related to Paradox. Browse articles , browse the classifieds , or join in the discussion Before registering as a new user , please check to see if you already have a profile Last Updated ( 19 September 2005 ) More...

39. Project Paradox - Blogs By Stephen Ward Stephen discusses gaming and web design, and shares entertainment reviews, cures for boredom, relationship advice, and personal rants. http://www.projectparadox.com/

Project Paradox Blogs by Stephen Ward About Project Paradox Blogroll Site Map ... Building a Better Website Expert advice on search engine optimization web development , and website promotion Web Development Article on... For those who don't know, in addition to writing for this blog, I also blog professionally elsewhere. One of my most recent articles on the 10 Most Marketable Web Development... Simple PHP Math Captcha I can't profess much expertise with cryptography, but I hate form spammers as much as the next guy. That's why I designed this simple math captcha in PHP. Just include the... Subscribe Cures for Boredom Online games humor , and other fun stuff to pass the time Funny Book Reviews Scott Adams, the author of the Dilbert comic strip, recently published a book named, "Stick to Drawing Comics, Monkey-Brain!" He didn't wait for some stuffy "professionals"... Mouse Avoider Flash Game Consider, for a moment, how much time you spend using a mouse every day of your life. With all that practice, you probably think you're pretty agile with that little... Subscribe RPG Savvy Resources for World of Warcraft tabletop RPGs , and console RPGs Revised Feral Druid Build Most of the time, I create build guides for my own edification; researching what others consider the best build really helps me optimize my own character. Not too long ago, I...

40. Bertrand's Paradox Thus the paradox merely indicates that probability distributions in two dimensions warrant a more careful consideration than the second solution suggested http://www.cut-the-knot.org/bertrand.shtml

var MyPageLoc = document.location; var MyPageTitle = document.title; G o o g ... e Web CTK Sites for teachers Sites for parents Awards Interactive Activities ... Sites for parents Bertrand's Paradox Theory of Probability (much as the rest of Mathematics) is actually a recent invention. And the development has not been smooth at all. The first attempts to formalize the calculus of probability were due to marquis de Laplace (1749-1827) who proposed to define the probability p(A) of an outcome A as the ratio of the number of events that result in the outcome A to the total number of possible events. This is of course only meaningful if the number of all possible events is finite and, in addition, all the events are equiprobable. The notion which Laplace has also defined. All elementary Probability courses depend on that definition. However note that the definition is, in a sense, circular - a notion of equi probable is defined prior to the introduction of probable. Thus, at the time, the field did not seem to have a sound foundation. Attempts to extend the definition to the case of infinite number of events led to even greater difficulties. The Bertrand's Paradox is one such discovery that made mathematicians wary of the whole notion of probability. Consider the following problem: Given a circle. Find the probability that a chord chosen at random be longer than the side of an inscribed equilateral triangle.

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