I recently finished reading A Budget of Paradoxes (1872) by Augustus de Morgan.

Now-a-days, we are most likely to encounter the word paradox as referring to apparent truth that seems to fly in the face of reason, but its original sense, not so radical, was of a tenet opposed to received opinion. De Morgan uses it more specifically for such tenets when they go beyond mere heterodoxy. Subscribers to paradox are those typically viewed as crackpot, though de Morgan occasionally takes pains to explain that, in some cases, the paradoxical pot is quite sound, and it is the orthodox pot that will not hold water. None-the-less, most of the paradoxers, as he calls them, proceed on an unsound basis (and he sometimes rhetorically loses sight of the exceptions).

A recurring topic in his book is attempt at quadrature of the circle. Most of us have heard of squaring the circle, though far fewer know to just what it refers.

I guess that most students are now taught to think about geometry in terms of Cartesian coördinates,[1] but there's an approach, called constructive, which concerns itself with what might be accomplished using nothing but a stylus, drawing surface, straight-edge, and compass. The equipment is assumed to be perfect: the stylus to have infinitesimal width; the surface to be perfectly planar, the straight-edge to be perfectly linear, and the pivot of the compass to stay exactly where placed. The user is assumed able to place the pivot of the compass exactly at any marked point and to open it to any other marked point; likewise, the user is assumed to be able to place the straight-edge exactly touching any one or two marked points. A marked point may be randomly placed, or constructed as the intersection of a line with a line, of an arc with an arc, or of an arc with a line. A line may be constructed by drawing along the straight-edge. An arc may be constructed by placing the compass on a marked point, opening it to touch another marked point, and then turning it. (Conceptually, these processes can be generalized into n dimensions.)

A classic problem of constructive geometry was to construct a square whose area was equal to that of a given circle. Now, if you think about it, you'll reälize that this problem is equivalent to arriving at the value of π; with a little more thought, you might see that to construct this square in a finite number of steps would be equivalent to finding a rational value for π. So, assuming that one is restricted to a finite number of steps, the problem is insoluable. It was shown to be so in the middle of the 18th Century, when it was demonstrated that π were irrational.

The demonstration not-with-standing, people continued to try to square the circle into de Morgan's day, and some of them fought in print with de Morgan. (One of them, a successful merchant, was able to self-publish repeatedly.) De Morgan tended to deal with them the way that I often deal with people who are not merely wrong but are arguing foolishly — he critiqued the argument as such, rather than attempting to walk them through a proper argument to some conclusion. I think that he did so for a number of reasons. First, bad argumentation is a deeper problem that mistaken conclusions, and de Morgan had greater concern to attack the former than the latter, in a manner that exhibited the defects to his readers. Second, some of these would-be squarers of the circle had been furnished with proper argumentation, but had just plowed-on, without attending to it. (Indeed, de Morgan notes that most paradoxers will not bother to familiarize themselves with the arguments for the systems that they seek to overthrow, let alone master those arguments.) Third, the standard proof that π is not rational is tedious to mount, and tedious to read.

But de Morgan, towards justifying attending as much as he does specifically to those who would square the circle, expresses a concern that they might gain a foothold within the social structure that allowed them to demand positions amongst the learnèd, and that they might thus undermine the advancement of useful knowledge.[2] And, with this concern in-mind, I wonder why I didn't, to my recollection, encounter de Morgan once mentioning that constructive quadrature of the circle would take an infinite number of operations; he certainly didn't emphasize this point. It seems to me that the vast majority of would-be squarers of the circle (and trisectors of the angle) simply don't see how many steps it would take; that their intuïtion fails them exactly there. And their intuïtion is an essential aspect of the problem; a large part of why the typical paradoxer will not expend the effort to learn the orthodox system is that he or she is convinced that his or her intuïtion has found a way around any need to do so. But sometimes a lynch-pin in the intuïtion may be pulled, causing the machine to be arrested, and the paradoxer to pause. Granted that this may not be as potentially edifying to the audience, but if one has real fear of the effects of paradoxers on scientific pursuit, then it is perhaps best to reduce their number by a low-cost conversion.

De Morgan's concern for the effect of these géomètres manqués might seem odd these days, though I presume that it was quite sincere. I've not even heard of an attempt in my life-time actually to square the circle[3] (though I'm sure that some could be found). I think that attempts have gone out of fashion for two reasons. First, a greater share of the population is exposed to the idea that π is irrational almost as soon as its very existence is reported to them. Second, technology, founded upon science, has got notably further along, and largely by using and thereby vindicating the mathematical notions that de Morgan was so concerned to protect because of their importance. To insist now that π is, say 3 1/8, as did some of the would-be circle-squarers of de Morgan's day, would be to insist that so much of what we do use is unusable.

---

[1] Cartesian coördinates are named for René Descartes (31 March 1596 – 11 February 1650) because they were invented by Nicole Oresme (c 1320 – 11 July 1382).

[2] Somewhat similarly, many people to-day are concerned that paradoxers not be allowed to influence palæobiology, climatology, or economics. But, whereäs de Morgan proposed to keep the foolish paradoxers of his day in-check by exhibiting the problems with their modes of reasoning, most of those concerned to protect to-day's orthodoxies in alleged science want to do so by methods of ostensibly wise censorship that in-practice excludes views for being unorthodox rather than for being genuinely unreasonable. When jurists and journalists propose to operationalize the definition of science with the formula that science is what scientists do — ie that science may be identified by the activity of those acknowledged by some social class to be scientists — actual science is being displaced by orthodoxy as such.

[3] Trisection of the angle is another matter. As a university undergraduate, I had a roommate who believed that one of his high-school classmates had worked-out how to do it.

On 24 December, the Stratfor computer site was learned to be hacked; e.mail, e.mail addresses, and credit-card information were stolen. Initially, Anonymous couldn't agree within itself whether its members were responsible, but the deniers fell silent.

The credit-card information was used to make charitable donations, which subsequently had to be returned (at a net loss) by the charities. Those whose e.mail addresses were stolen had them publicly dumped (and thus made available to spammers), and were subjected to hoax mailings by Anonymous.

And we were told that the e.mail itself would be released, so that the world could see that Stratfor were really a malevolent force, which revelation would ostensibly justify the hacking.

After seven weeks, the e.mail that was supposed to expose the wickedness of Stratfor has not been released. There's more than one possible explanation. Perhaps the responsible members of Anonymous have obscure but compelling reasons to release the information all-at-once, and to organize it before doing so. Perhaps these members have been found and whisked-off to secret internment camps, along with anyone who might have reported their disappearances. Or perhaps the e.mail would reveal no more than that Stratfor communicates off-the-record with sources, some of whom could (reasonably or otherwise) be regarded as villains, and perhaps other members of Anonymous noted that almost any reporting and news-analysis service does the same thing, so that Anonymous would appear to subvert freedom of the press.

(I kinda favor that third explanation. Like many members of the Occupation Movement — who also like to claim the prerogatives but duck the responsibilities of association, and to wear Guy Fawkes masks and fantasize about being Vs — many members of Anonymous seem inclined to try to silence those whose views they find greatly disagreeable, but only so long as these members aren't made to recognize that they're engaged in censorship. [Up-Date (2012:02/27): It has now been announced that the e.mail is being released in coöperation with WikiLeaks.])

But, whatever may be the reason, the e.mail has not been released, and that failure or delay is itself a news story — which story you've not read in the Times (of London, of New York, or of Los Angeles) nor heard from the major broadcasters. Possibly that's because they're such lack-wits that it hasn't occurred to any of them that there's a story here. I rather suspect, however, that it's because they're scared. A group such as Anonymous could take-down pretty much any of these news services just as they did Stratfor.

In the context of all the sabre-rattling going-on these days, a quotation is gaining some traction:

The world is not divided between East and West. You are American, I am Iranian, we don't know each other, but we talk and we understand each other perfectly. The difference between you and your government is much bigger than the difference between you and me. And the difference between me and my government is much bigger than the difference between me and you.

And our governments are very much the same.

I don't know what the original context of Ms Satrapi's remarks were, but now they are now being used as-if she were a proxy for the Iranian people and the listener for the American people. If either person is admitted to be exceptional in some relevant way, then there is no general lesson to be drawn! Ms Satrapi in fact lives in France, rather than in Iran; there wouldn't be much reason to fear her being bombed qua Iranian by Western military forces. So we're to take it that the typical American and the typical Iranian are so similar as to be able each perfectly to understand the other.

We're also told that our respective states are pretty much the same. With the previous claim about people, this would imply that very similar relationships obtain between the peoples and their respective states. But, more than this, we are further told that the differences between the peoples and their respective states is greater than the difference between the peoples.

Well, logical alarm bells go-off in my head. This set of claims of similarity is not consistent with direction of such remarks more to one people than to another. If the relationships are as claimed, then such remarks should and could be directed to both populations. But they're not, and for good reason.

The claims of similarity between peoples and of differences between peoples and states being greater than differences between peoples should at least be questioned, though they are not evidently false and might prove true.

My experience of non-Americans from almost anywhere is that they greatly over-estimate how well they understand Americans. However, though a claim of similarity of peoples being proved by mutual understanding is false, people can be quite similar each without understanding the other; perhaps indeed the differences between Americans and Iranians are not so great. I wouldn't simply reject the claim, but it would need some substantiation.

I'm not sure how to measure the difference between peoples and states relative to the difference between people and people, but let's accept the claim that that the former is greater than the latter.

The states are not very much the same. It would be hard to falsify a claim that the proportions or absolute numbers of knaves and of fools in each state are the same, but also hard to prove such a claim; in any case, the powers of the knaves and of the fools are not the same in one state as opposed to the other. While the United States indeed has got more repressive in some important respects, and unfortunately can be expected to continue to do so, it is simply not as repressive as is the Iranian state. For example, in America, one can still easily and openly criticize the state and social norms, and consume such attacks, without fear of being criminally charged. (I suspect that Ms Satrapi's claim that the states are very much the same results largely from a combination of nationalistic embarrassment and insufficiently critical consumption of French antipathy to America.)

(I note en passant that it would be a d_mn'd fine thing if the anti-war political left would remember the propensity to wickedness of the state when it starts to get excited by thoughts of expanding the state for the various purposes that the left favors. The anti-war political right and classical liberals don't lose sight of that propensity when talk shifts from war to other matters.)

The relationship between the Iranian people and the Iranian state is plainly quite different. The United States may have a very flawed democracy, even as democracies go, but neither major party in the United States is able to control elections to the extent that the Iranian regime has. (Elsewhere, Ms Satrapi has claimed that the ruling Iranian party actually received only 12% of the vote in the national elections of 2009.)

One makes the case for peace not to the Iranian people but to the people of the West because one can make the case to them, and because they can more readily insist upon peace to their respective states. I strongly suggest that, when the case is made, it be better made than by misrepresenting the relationship between state and state or between peoples and states. Proceeding with a reckless disregard for the truth persuades people that one is not to be trusted, and they may leap to the spurious conclusion that they should invest their trust in one's principal opponents.

Those who attempted to visit this 'blog yester-day met with this proclamation that it were suspended by its author in protest against SOPA and against PIPA. None-the-less, when the Woman of Interest asked me whether I thought that the black-out protests would be effective, my answer in the late morning was negative.

First, I was inclined in advance to believe that deciding positions had already been taken (albeït not announced) some days ago by a majority in Congress and by the President, and that final outcomes would not be actually swung by the sort of protest that could plausibly be expected.

Additionally, by late morning, I felt that a rather poor protest had been mounted. Wikipedia, most famous of the protestors, ostensibly blacked-out its pages, but had left them so that hitting Esc as they loaded caused the ordinary content to be delivered. Google merely changed its home-page graphic, partially (but, tellingly, not fully) covering-over their name with a cocked black rectangle; never mind that those who invoke searches with a browser text-field don't see that graphic anyway! Many sites did no more than change their color-schemes.

I think that least effective were those who expressed their ostensible support for the black-out by posting those expressions, through-out the day, on the WWWeb, while withdrawing nothing. Now, let me make it plain that I have no quarrel with those who simply didn't participate in the black-out, or those who shut-down only some of their sites; the former may be perfectly consistent, the latter perhaps efficient. But those who weren't blacked-out in the least and discoursed upon their support for the black-out on the WWWeb as that black-out were in-progress seem not to understand that they were providing content in attempted support of an effort to provide a sense of the loss of content that would follow upon the passage of something such as SOPA or as PIPA. And if the only content that one normally provide were tweets and such, then exactly that were what one needed to halt to actually support a black-out.

Those in that last group ought to understand that SOPA or PIPA wouldn't simply mean that the WWWeb no longer offered them so much information and passive amusement; such an act would limit their ability to express themselves as freely as they do now. Along with Google and YouTube and Tumblr would go Facebook and Twitter and Blogger and all the other centralized social-networking sites. (Which is not to say that more autonomous sites, such as mine, would be spared.) People who won't g_dd_mn'd shut-up would be quite hard hit — which might be an amusing thought, but freedom of expression is essential, and not to be reduced to quiet chatter-boxes and pontificators.

My participation in the protest, however, wasn't conditioned on a presupposition that it would sway the body politic. My actions were essentially symbolic, and it wasn't necessary for me to believe that I would sway anyone, though I would hope at least that there'd be one or two sympathetic readers.

And my negativity about the black-out doesn't mean that I expected or expect one of these bills to pass, nor for it to avoid a Presidential veto, nor for the Supreme Court to rule in its favor. I don't know about the first two. (The President will certainly require cover if he is not to veto a bill of this sort, but perhaps he will think that he can get that cover from a signing statement.) I would be unpleasantly surprised by the last; the Supreme Court seems more genuinely alert to concerns about freedom of expression in recent years.

Of course, I may be wrong about the effect of the black-out, however feeble it may look to me. Representatives and Senators have been spooked by scarecrows in the past. But, if the bills failed, that failure wouldn't itself demonstrate that the black-out had a deciding effect.

I would definitely caution at this point that what appears to be strategic retreat may be merely tactical. The interests behind these bills are not going to go away, and features of these bills may be withdrawn at one stage only to be reïntroduced at another (such as reconciliation).

---

The principal recommendation of many of those participating (however convincingly or pathetically) in the protest was that people should contact their Senators and Representatives. Well, the Senators from California are a knavish fool and a foolish knave, and the Representative for my district is at best a twit. I've tried moving those three in the past, and been met by silence or with inane boiler-plate. If they voted against these bills, it wouldn't be because of anything that I said to them. There's not even a sympathetic reader to be found amongst them. But I do know that other districts are not so grim.

There's a lot of talk these days about the political center, especially on the part of pundits who express concern about the lack of a centrist Presidential candidate amongst the Republicans. Rarely if ever does this talk explain what is meant by the references to the center, let alone why, really, one should want someone or something to be there.

In fact, people aren't talking about the same thing when they use this term.

For some people, the center means a center of mass of some sort. To the extent that one could average the political opinions of the voters or of the adult citizenry or perhaps of the adult population, the center would be this average. There's some real problems in locating this center. Some things resist averaging of any sort. And, because its determination has become significant in influencing opinion, people are all too quick to confuse the results of some collective decision-making process with a quantification of opinion; one sees this phenomenon in how election results are interpretted, and pollsters often design polls to advance the views that they want to promote.

For some people, the center is more tightly defined as a region in which the people whom they do not despise could reach agreement. It's still something of an averaging, but now the averaging excludes the opinions of the far left or of the far right or of both; and if these people acknowledge political opinions that are neither left-wing nor right-wing, the center will exclude those who are far out in any other direction. Of course, different people will regard different sets of opinions as far (which really means disagreeable to the persons in question); there is no common agreement amongst them as to where the center is located.

People such as I want to define the center in terms of the conceptual possibilities. For example, one might ask whether the state should redistribute wealth from rich to poor or from poor to rich. The center would seem to be to favor neither redistribution, either opposing both or being indifferent to either. Now, I say seem advisedly, because the mid-points are determined by the taxonomy. If the center is to be naturally defined, then, the taxonomy must be a natural taxonomy. And reasonable people might use different taxonomies. But what would surely make a taxonomy inappropriate would be for it to make it difficult or impossible to discuss something that otherwise could be discussed — for example, state redistribution from poor to rich (which is a very real phenomenon) or no state redistribution.

Not only do we see most people failing to be clear which of these notions of a center they are using; we see evident confusion — sometimes deliberate confusion — of their properties. The right- or left-wings of different jurisdictions will be implicitly defined based on local culture, but then lumped-together across jurisdictions as if ideologically equivalent. The center of mass for some culture (especially that of the writer) will be treated as if it is moderation. Whatever view the speaker favors is asserted to be the unbiased perspective and whatever policy the pontificator wants is called the balanced approach.

In most cases, whether some approach to policy falls in any one of these aforementioned centers is utterly irrelevant to whether it is a particularly good policy. The policies of the center of mass might be the best policies that one can get in the face of democracy or of a populace inclined to civil war, but they'll only be good on the assumption that there is a symmetry of insanities within the population. The policies of those whom one tolerates are only good on the assumption that one is genuinely wise in whom one excludes (which assumption begs the question). And there is no reason to see good policy in the conceptual center; nothing says that swallowing half as much arsenic as one might is better than swallowing none at all; all of the good policies with respect to some things are at or near extremes.

In eartly August, I wrote of how most of the political left had lost its sense of conviction in the decades following the '60s, of how their ability to believe had been restored by the 2008 Presidential campaign of Barack Hussein Obama, but of how that sense of belief was disintegrating in the face of the actual Presidency of Mr Obama. Well, a large share of the left has since found something new from which to draw Hope — the Occupation movement.

It's widely noted that the Occupation movement lacks a programme. They've made it plain that they think that there's a 1% who are the Enemy; but, aside from the intention to somehow beat wealth out of this group,[1] the movement as a whole is short on specifics. Individual members or groups within the Occupation movement may espouse something more precise, but other members deny any sort of responsibility for those proposals. There isn't even meta-agreement within the Occupation movement on a protocol for agreement.

In lieu of a programme, what the Occupation movement gives us is a sort of attitudinal posture. That ought to remind people of something. In particular, it ought to remind people of Barack Hussein Obama in 2008. Granted that, in his case, the ambiguïty was a deliberate choice, whereäs in the case of the Occupation movement it results from collective indecision. Still, once again, a large share of the political left has invested itself in a cypher.

---

[1] The urging of state action may not itself be immediately violent, but the whole point of using the state is to employ its capacity for violence, to threaten or worse.

I recently acquired a copy of this image as a page removed from an issue of Theater Magazine. I'm not sure that I would have got it had I known that it came thence; I'm not comfortable the practice of dismembering old books and magazines for their images, except in cases where there is truly negligible interest in the volume or issue in question being held together.

In any case, I think it a very nice picture.

Paul Krugman walks into a bar, and asks How much for a scotch, neat? The bartender looks at him, and thinks What could a Keynesian know about money? So he says One trillion dollars. Krugman gets on the phone, calls the Fed and the White House, and they send over $1 trillion. As Krugman is drinking, the bartender remarks You know, we don't get many Keynesians in here. Krugman replies Well, with these prices, it's no wonder!

[This post was delayed from yester-day, as my hosting service had a technical failure, and it took me rather a long time to persuade them of such.]

I read

This past week it was reported that the hacktivist collective known as Anonymous claimed credit for taking offline over 40 websites used for sharing pedophilia — and for exposing the names and identifying information of more than 1500 alleged pedophiles that had been using the sites.

But the actual list is of user aliases, not of personal names.

Not only are pædophiles not being exposed here, but non-pædophiles who've had the misfortune of pædophiles' using the same aliases (by chance or from malice) are going to come under suspicion by those who think that they recognize them on this list.

Further, if agents of law enforcement were themselves working to track-down the actual legal identities of the pædophiles, their investigation has now been severely compromised, possibly fatally so.

Once again, Anonymous has done less good than they have led the gullible to believe, and have caused more damage than they have acknowledged.

A recent comment by Zenicurean notes, implicitly, that economic pædagogy often uses a widget as a hypothetical economic good.

I most frequently use the veeblefetzer (borrowed from Harvey Kurtzman) when I want a good about which the audience will know little or nothing, and the hot dog when I want a good that will seem familiar.

I like the hot dog as an example in part because it has a long tradition in economic education while being fairly absurd as an artifact.

I also like it because it is easy to explain the idea of a shift in the demand curve using the hot dog. First, I present my students with a set of prices, polling them as to how many hot dogs they would buy at each of these prices; that gives us an initial demand curve. Then I discuss some of the things that are permitted to go into hot dogs, and we repeat the process for the prices. (So far, the demand curve has always shifted inwards.)

But the main reason that I like to use hypothetical hot dogs is because I think back to a question on the economics GRE when I took it.[1] In the set-up for the question, a family was working-out its annual budget, and decided that they would spend $800 per year on hot dogs, regardless of the price of hot dogs.[2]

The question was of what sort of demand elasticity were here displayed. Elasticity is a measure of sensitivity or responsiveness, with a general form of

or of (Whether there's a negative sign and whether an instantaneous form is used is based on what's convenient and practicable.) In the case of demand elasticity, the y is quantity demanded, and the x is unit price. One might think that demand responsiveness could be measured more simply by slope (Δy/Δx or dy/dx), but elasticity has a useful property. When elasticity is less than 1 in absolute value, responsiveness is sufficiently weak that expenditures (the product of quantity demanded and unit price) increase as price is increased; whereäs if elasticity is greater than 1, responsiveness is sufficiently strong that expenditures shrink as price is increased. The seller gets less revenue by increasing prices in the second case, where the curve is said to be elastic (sensitive); the seller gets more revenue by increasing prices in the first case, where the curve is said to be inelastic (insensitive).

If the elasticity is exactly 1 (in absolute value) then quantity demanded drops or rises to exactly off-set any price change; expenditures are constant as price changes. This is called unit elasticity. (BTW, a demand curve that is everywhere unit elastic will be a hyperbola.)

On the GRE, I was supposed to identify the demand curve of the family in the question as unit elastic, and so I did. But, because I'm not autistic, I was also greatly amused by this example. Imagine a family that is conscientious enough to budget, but they eat hot dogs. Imagine a family that budgets, but budgets such that if a hot dog costs $1600 then they will try to buy half a hot dog, and if a hot dog costs a penny then they will buy eighty thousand g_dd_mn'd hot dogs!

I laughed when I read this question. And, because I made multiple passes through the test, I glanced at that question repeatedly, laughing each time. I was the only person in room laughing. (The room had people taking different subject GREs, and I may have been the only one taking the economics test.)

When I use hot dogs as an example, it's mostly just in fond memory of that hypothetical family, crazy for hot dogs.

---

[1] This tale may seem somewhat familiar to those who read my now long-since-purged LJ.

[2] The amount may have been $600 per year, or perhaps $400 per year; it has been quite some time since I took that test, and I don't remember. But, mutatis mutandis, my remarks hold.