Gradient vector flow snakes!

In addition to this short film clip illustrating a “flow snake,” you can read more about this beautiful mathematical/fractal pattern in this formal paper by Alejandro Cartas-Ayala.

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Taxonomy of colors

Blue

Via kottke, we discovered this Color Thesaurus created by designer and author Ingrid Sundberg. Ms Sundberg’s original and beautiful “color thesaurus” provides a taxonomy or breakdown of all the shades of color within each major primary color group, including white, yellow, orange, red, purple, blue (pictured above), green, brown, and black, among others.

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How many squares (of all sizes) are on a chess board?

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Espresso art

Artist credit: Giulia Bernardelli

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Should Marco Rubio or Ted Cruz drop out? (Republican Primary Prisoner’s Dilemma)

Our friend and colleague Steve Landsburg makes the following two observations on his blog: (i) “for either Ted Cruz or Marco Rubio to become the Republican nominee, he must first consolidate the anti-Trump vote, which is to say that either can succeed only if the other drops out,” and (ii) “Cruz and Rubio have approximately equal chances of driving each other out” between now and the last primary. Given these premises, Professor Landsburg then proposes that Cruz and Rubio toss a fair coin to determine which man should drop out of the race. According to Landsburg (emphasis in original): “This [a coin toss] gives each of them only a 50% chance of survival. But if they’ve already each got only a 50% chance of survival, that’s no loss. And it substantially increases the value of survival, because it gets things over with now instead of a month from now.”

For our part, we like Landsburg’s proposal, but here is why we think neither Cruz nor Rubio will ever agree to let a coin decide their political fates. In brief, they are locked in a political version of the famous prisoner’s dilemma: both would be better off cooperating (i.e. agreeing to the coin toss), but the logic of defection (i.e. “I stay in; the other guy drops out”) results in mutual defection (both stay in and both lose).

Update (3/2): Ken B writes that our prisoner’s dilemma analogy does not apply here because Senators Cruz and Rubio “are not in a one time game [;] they have careers and future elections.” Ken B makes a good point. In our democracy, elections are really more like an iterated or repeat game since there are presidential elections every four years. But we think Ken B is wrong in this particular case because of the inherent uncertainty in future election cycles. Furthermore, unlike Kasich and Carson, both Cruz and Rubio are serious contenders, and both want to win their party’s nomination in this election cycle. As a result, this year’s election is for all practical purposes a one time game. Lastly, we would add that the payoff for mutual defection will occur very soon (i.e. both Cruz and Rubio will lose to Trump), as it now appears that Trump will wrap up the nomination in a matter of weeks unless either Cruz or Rubio drops out.

TCMR

Which one should drop out?

 

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Game theory: the way forward? (part 3 of 3)

In our previous two posts, we identified a blind spot in the work of John Rawls and Bob Nozick: the problem of betrayal–what game theorists call “defection.” In brief, Rawls’s original agreement might embody timeless principles of justice, and Nozick’s private protection groups might be the first step towards his political utopia, but in both cases, there is nothing stopping people from repudiating their mutual promises or double-crossing each other. What is the way forward, then?

Game theory offers some possible solutions to this trust dilemma. Even in the case of the deservedly famous Prisoner’s Dilemma, where fear of the dreaded “Sucker’s Payoff” leads the prisoners to betray each other (see below), Robert Axelrod and the late Bill Hamilton identified the conditions in which cooperation might yet still be possible: iteration (i.e. playing the game more than once) and uncertainty as to when the last round of the game will occur. But there is also a major blind spot with Axelrod and Hamilton’s work and with game theory generally. In addition to our two prisoners, game theorists silently assume a third player: a judge or strongman who is able to distribute the payoffs of the prisoner’s game and enforce its rules. But who is this secret third actor or deus ex machina? Where does he come from? Why should the prisoners pay him any heed?

In short, overcoming the problem of betrayal/defection–getting cooperation off the ground–appears to be a truly intractable problem, and yet we still see many examples of cooperation and mutual trust around us. Is there a better way of explaining the puzzle of cooperation? Is there a new way forward, one that does not rely on unenforceable original agreements (Rawls), or on ahistorical mutual protection agreements (Nozick), or on secret third-party payoff enforcers (Axelrod & Hamilton and all game theorists generally?) We are certainly open to suggestions …

Where is Player C, i.e. who distributes these payoffs and enforces the rules?

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Rawls vs. Nozick (part 2 of 3)

In our previous post, we identified a weakness in Rawls’s theory of justice: the possibility of betrayal once the veil of ignorance is lifted. Now, let’s turn to Robert Nozick’s classic tome Anarchy, State, and Utopia (1974), a book Nozick wrote in response to Rawls’s work. In Chapter 1 of Anarchy, State, and Utopia, Nozick postulates the emergence of voluntary private protection agencies in an ahistorical state of nature. In other words, instead of a hypothetical original agreement à la Rawls, Nozick imagines mafia-like protection rackets filling the legal and political void (p. 12): “Groups of individuals may form mutual-protection associations: all will answer the call of any member for defense or for the enforcement of his rights.” (As an aside, Nozick even retrodicts (p. 13) that “some entrepreneurs will go into the business of selling protective services.”) But there is a blind spot in Nozick’s theory of the pre-political state, the same blind spot that Rawls overlooks in his work: the possibility of betrayal.

In summary, since the private protection services and protection agencies in Nozick’s state of nature are the result of voluntary agreements, who enforces them? After all, Nozick’s imaginary protection agencies are operating in a lawless world, so these private protection agreements are not legally or morally binding in any meaningful sense. And without any external or credible enforcement mechanisms in a pre-political or stateless world, why should we assume that people in Nozick’s state of nature won’t betray each other when it suits them. That is, since Nozick’s private protection agencies are operating in a lawless and stateless world, what is stopping any member of any given private protection agency from repudiating his membership or from betraying a fellow member or from joining another rival protective association?

In a word: nothing.

At one point, Nozick briefly contemplates the possibility of a “breakup” (p. 13) of a private protective association due to internal discord or dissension, but he does not consider the systematic possibility of betrayal or breach among the members of his protection agencies. Nor does he explain why such private agencies would be immune to the problem of betrayal. Yet, we would expect betrayal to occur frequently in a state of nature. To sum up, then, Nozick–like Rawls–ignores the possibility of betrayal. Specifically, just as Rawls assumes that the hypothetical parties to his hypothetical “original agreement” won’t betray each other once the veil is lifted, Nozick too assumes that the private members of his private protection agencies won’t betray each other as well. But in a world where there is no penalty for breach–whether it be Rawls’s hypothetical post-original position or Nozick’s ahistorical state of nature–, these are false and fool-hardy assumptions. The original agreement or agreements for private protection are not self-enforcing.

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A critique of Rawls and Nozick and a new way forward (part 1 of 3)

For the next three posts, we are going to offer a critique of John Rawls’ theory of justice (part 1), followed by a critique of Robert Nozick’s theory of the pre-political state (part 2), and then offer our own alternative to their influential theories. Let’s start with Rawls, shall we? In his book A Theory of Justice (1971), Rawls presents an ingenious thought experiment consisting of a hypothetical or make-believe world in which hypothetical rational actors negotiate a hypothetical original agreement. In this make-believe world, people negotiate an “original agreement” from a hypothetical starting point, i.e. from the original position, an initial position of perfect equality. In addition, these negotiations occur from behind a veil of ignorance in which “… no one knows his place in society, his class position or social status, nor does anyone know his fortune in the distribution of natural assets and abilities, his intelligence, strength, and the like” (1971, p. 208). Now, here’s the payoff: according to Rawls, the outcome of these hypothetical negotiations will be consistent with the principles of justice.

There is a fundamental flaw, however, in Rawls’s elegant thought experiment. Simply put, what happens when we lift the veil? What’s stopping any of the parties to the original agreement from betraying the other parties to the contract or from repudiating any promises made in the original position?

For his part, Rawls states (ibid., p. 208) that the principles of justice agreed to in the original position “are the result of a fair agreement or bargain.” But with all due respect, so what? After all, there are no penalties for failure to abide by the original agreement once the veil of ignorance is lifted. Rawls’s response to this objection is to emphasize (p. 209) that “the obligations they recognize [in the original agreement] [are] self-imposed,” but Rawls is utterly unpersuasive on this point. After all, what difference does it make that the obligations agreed to in the original agreement are self-imposed if there is no penalty for breach? Once the veil is lifted, there is nothing stopping the parties to the original agreement from going back on their word. Worse yet, instead of providing penalties for breach or a credible external enforcement mechanism, Rawls simply assumes (p. 208) that “… having chosen a conception of justice [in the original position], we can suppose that they are to choose a constitution and a legislature to enact laws, and so on, all in accordance with the principles of justice initially agreed upon.” But Rawls is wrong. In a world where the possibility of betrayal is lurking in the background–our world–, we cannot assume this at all.

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Metallica v. Napster (Lesson 10)

Napster was the ultimate geek banner, a battle that had been fought by hackers on the biggest stage of all. Ultimately, the hackers had lost, but … it was still the biggest hack in history.”

–Ben Mezrich, Accidental Billionaires (Ch. 18)

We are going to focus on Napster in our next class (2/29), and we are going to re-enact a preliminary injunction hearing in the case of Metallica v. Napster. In that case, the rock band Metallica sued Napster for copyright infringement, in essence, accusing Napster of allowing its users to steal Metallica’s music. Accordingly, we are going to need two volunteers for this activity:

(1) One student will represent the rock band Metallica: you will argue why Napster’s file-sharing system is illegal and why your client is entitled to an injunction.

(2) The other student will represent Napster: you will argue why Napster’s file-sharing system constitutes “fair use” under federal copyright law.

Here is some background: Before Sean Parker discovered Facebook, he co-founded in June 1999 a company called Napster, a peer-to-peer file-sharing website that allowed users to share MP3 music files with each other (see image below, courtesy of the website “How Stuff Works”). At the time, Napster was huge. According to Wikipedia, for example, “verified Napster use peaked with 26.4 million users worldwide in February 2001.” By the way, Metallica wasn’t the only plaintiff who sued Napster. The powerful Recording Industry Association of America (RIAA) also brought a federal copyright infringement lawsuit against Napster in December 1999, and the RIAA eventually persuaded a court to issue a court order shutting down the website … But did the court make the correct decision? After all, how is a popular website like YouTube any different than the old Napster?

Critical thinking question: In your opinion, is file-sharing copyrighted materials unethical?

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Open borders

Via Valerio Vincenzo, check out these amazing and beautiful pictures of open borders in the Schengen area, a geographical zone consisting of a total of 26 European countries that have abolished their passport and border controls at their common borders. (Hat tip: kottke.)

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