November 28, 2004

More Babylon, less Waste Land

Posted by Curt at 08:58 AM in Literature | permalink | 4 comments

This is a time for resuscitating some strange literary ghosts. Take this little paeon to e.e. cummings. Cummings doesn’t really hold any particular interest for me in his own right; his little word-games are amusing enough, maybe, but they give me about the same feeling as playing vintage original-Nintendo games. It’s barely entertainment, through a pretty heavily nostalgic filter. And yet the reviewer, maybe the author as well, I don’t know, seems to be trying to set him up as some kind of martyr for uncompromising, imperishable art. To me, the value of being uncompromising in art is not a lot higher than it is in, say, marriage. And in any case, cummings’ little doodles just don’t really even evoke the pathos even of the selfish isolated aesthetic mind like, say, the works of Ambrose Bierce. Whether comic or tragic, they were in any case written for the amusement and digestion of just a few, which these critics seem to consider all for the best, but, somewhat inconsistently, the fact that they have only been, throughout much of the last century, appreciated and admired by the select strikes them as profoundly unjust.

Where did the invocatory strain, and more importantly its appreciaton, go in poetry? The greatest period in English poetry, after the Elizabethan, is the early Romantic period. There’s nothing particularly impenetrable about most of Keats, or Shelley, or Wordsworth. There’s nothing like the ideal that Wallace Stevens expressed negatively in condemning Eliot’s poems because “they do not make the visible / a little hard to see” (if not Eliot then for God’s sake who—that’s practically the only thing with which he concerns himself). Let me put it another way—when scientists talk about the beauty of some law in physics, Newtonian gravitation, for example, or general relativity, are they praising Einstein’s ability to make the simple obscure? Of course not, quite the contrary, because while the phenomena and the concepts his work evokes are indeed confoundingly obscure, and respecting their complexity is a pre-condition for the veracity of the solution, his grand achievement, and the reason people find aesthetic as well as scientific value in it, is because it brings relative simplicity and clarity to a realm that would otherwise be a miasma. To be able to explain so much, so comprehensively, upon such a simple and solid foundation, that amazes humanity.

There seems something purer and more instinctive in that aesthetic response than in probably the majority of the poetry-reading community because scientists don’t belabor and over-refine their aesthetic criteria, in fact they probably weren’t even looking for beauty until it manifested itself. The connection is that, in its greatest periods, poetry had that effect as well. Great poetry, like all great art and again, like scientific theories, is as complex as it needs to be and no more so. The simplicity of those great poems by the Romantics is the source of their power, because rather than conducting us into an isolated hermetic realm like Eliot or cummings, they have a resonance throughout our existence. They speak one great message at many different levels, rather than many messages confusedly and contradictorily. To take another example: the cathedral of Chartres does not impress with the convoluted or complicated nature of its effect: it is rather the pure and deep simplicity of the work which is breath-taking, and even the complexity of the structure inspires admiration primarily for how it concentrates and elevates that one great goal. Among the great poets, the work is so deeply instinctual that it seems almost unconscious or auto-didactic, virtually spontaneous.

That strain didn’t last very long in English poetry. In America we had a prolongation of a similar level of enthusiasm and of high quality in Whitman, Hart Crane and maybe a few others (maybe even Stevens himself). But that vein, like its equivalent in Latin America, quickly got bogged down and tattered by politics. The only place in the West, I think, that preserved that spirit until at least quite recently is Russia. Russia’s literature for the past 200 years has been the greatest in the world, without even any close competitors. There are no doubt many reasons for that, not the most insignificant being that the great Russian Romantic, Pushkin, made a deeper impression than his counterparts in the West, and has indeed never been discarded or even forgotten or disregarded for a moment. He, and the great ones following him, from Lermontov to Blok to Arseny Tarkovsky, speak simply but never plainly, like prophets. Their invocations express more and demand more than anyone else’s. The same spirit is apparent even in prose: who else could have written at the beginning of a novella, like Tolstoy: “his life was most simple and most ordinary and therefore most terrible.” No writer anywhere in the world can match the integrity, apolitical and yet with profound political consequences, and the brilliance of Solzhenitsyn. Pasternak complained that all the Russian writers except Chekhov preached to their readers. But the issue is not whether there’s any value in Dostoyevsky’s mysticism or Tolstoy’s Christian pacifism, but rather that only they had such an exalted view of the depth of the issues and the task confronting the writer, and no one else ever had such an ability to carry it out.

I used to think I loved Russia because nowhere else did it seem like poetry and the intellect were so honored. But France, for example, is just as obsessed with literature, but with a profoundly different effect. There’s something more ordered, more self-satisfied and ultimately more limited about the spirit here. The great poet and musician Vladimir Vissotski complained that, as much as he admired France, he and his audience in France could never understand each other. For the French, a song is simply a song: after-dinner entertainment, or a poem, whereas he could never understand how it could only be that.

My point is not that we should all be less materialistic and focus on poetry more. That’s what American poets spend their careers doing as a self-justication, and you don’t have to even observe the current state of Russia to guess at the negative consequences of that. Rather, it seems to me that poetry can only really be important, and beautiful, when it’s a part of life, when it’s breathed and spoken, not when it becomes a matter of little word-puzzles for professors or an impenetrable edifice with which to chastise the unlettered masses and provide careers for innumerable academics in deciphering it and hunting down allusions and influences. Poetry seems to be one of the few genres that has escaped the politicization of literary criticism in America, but, since political interpretation seems to be the highest form of honor that American academia bestows, that doesn’t say much for the vitality of poetry there.

p.s. I’m inclined to be open to the view of hip-hop as a form of popular native poetry, but that raises far too many issues to be addressed at the moment. Suffice it to say that, whatever one’s view of its aesthetic value, I think in that realm most of the same patterns are evident as in literary poetry, which I have just delineated.

November 27, 2004

Not so much a howl as a low murmur

Posted by Curt at 06:46 AM in Ramblings | permalink | 1 comment

I’ve only met one real hippie in Paris. Some of the American students I know here would have been surprised by that upon first arriving here. One in particularly, a friend of one of my friends back at school, much attached to wearing plaid sport jackets with corduroys and basketball shoes, a champion of the harmonica as a respectable instrument and, of course, still trying to act as a latter-day John the Baptist for Bob Dylan, I think expected more. I imagine he thought that the absence of large numbers of fundamentalist Christians and Republicans, combined with the usual French attitude towards our most obvious sacred cows meant that France would be a paradise of free love, joint-smoking on the sidewalks and philosophy mixed with jam sessions: in other words, the American college experience without disapproval from the elders. Well, the girls are out of range, the philosophy comes rapidly but angrily and smoking a splif (no real joints here) in public will practically get you sent to the military brig. I’ve almost come to think that obsessive rule-abiding here is itself the source of the need for periodic revolutions. After all, if the government hadn’t still been persecuting Jews in 1904 in the name of the official Catholic religion, the public might not have instigated the massive public backlash which led to the establishment of official secularism. It may be that if one does not bend the rules constantly, they become brittle more often, and must be broken and re-formed. It’s a form of progress which is more official and less personal.

Anyway, naturally the only hippie I’ve met here was an American. I was at a party hosted by a number of Italian political science students in some back-alley in the 15th, one of those overlooked residential neighborhoods between les Invalides and the river.

A Spanish girl I was talking to said: “Oh, but there’s another American here!” I suppose expecting me to be thrilled, because, after all, Americans come to live in France to meet more Americans. But I had to admire the sheer anachronism before me. I thought I might be having an imagined memory of meeting my youngest uncle back in the ’60s, maybe shortly after he got married in a Hawaiian shirt in a Buddhist ceremony on some hill-top. He wasn’t in France legally, he said (I suppose he would have been ashamed if he was). I bit my lip as he related the wonders of self-discovery to be found in Hermann Hesse, and advised me to consult “the teachings of the Native Americans.” Only the North Americans, he helpfully qualified, since “the South American cultures were fucked-up” (I think Samuel Huntington, Pat Buchanan and maybe one or two others may possibly share this view). The Native American tribes, you see, had devised the perfect social system. No more risking the huge errors that can result from electing leaders by means of popularity contest, or the similarly low probability of decent leadership arising from the uninterrupted line of progeny in a hereditary lineage. No, the Native Americans simply adopted the most blatantly obvious means of securing good leadership by always selecting the wisest member of the tribe as chief. What simplicity! What genius! As for man’s individual search for meaning, he earnestly enjoined me to study Buddhism. The confusion of values and truth in our present age is illusory. Norhing can be more easily resolved: according to the Buddha, all truth is necessarily incomplete. It is only by taking one belief and its antithesis that we can perceive the truth (Hegelian dialectic sounds so much less romantic). The contradiction between our beliefs and the converse is a guarantor of the truth that lies within them! Now I would never dismiss the possibility of these ideas, but does it not at least seem likely that the chiefs of Native American tribes had a vested interest in propogating the belief that the leaders are always the wisest members of the tribe, and that taking contradiction as a principle of truth makes only the truth untrue?

November 24, 2004


Posted by shonk at 06:11 PM in Literature , Ramblings | permalink | 6 comments

As most of you have no doubt noticed, I tend to buy a lot of books. Aside from the fact that I’m something of a compulsive reader, I’m really enamored of the whole ritual of owning a book, from the initial purchase to the freedom to dog-ear and underline to the imposing solidity of a well-stocked bookcase.

That’s all completely irrelevant to my point, other than to establish that I buy a lot of books. And, increasingly, the books that I buy, especially books published in the last decade or so and aspiring to literary merit, are adopting a sort of rough matte finish as a necessary part of good cover design. Apparently there’s something about matte finish that graphic designers think screams this book has literary merit.

Now, admittedly, there’s something more compelling about the matte-finish-and-chiaroscuro-graphics school of cover design than the glossy-cover-and-embossed-letters school that reigned supreme in the ‘80’s and still dominates in the thriller/romance sector of the market. The understated look certainly suggests greater intellectual depth.

But I wonder if it’s necessary to make the matte so rough that it actually gives the book a distinctive, gritty texture. The other day I bought five books at the local Barnes & Noble, and four of the five had a distinctly gritty texture to them. As I held them in my hand and the covers lightly scraped against eachother, it almost felt as if sand had gotten lodged in between the books in the stack. Call me old-fashioned or obsessive-compulsive, but there’s something vaguely unsettling about that.

Personally, I blame book critics. You see, I have this fear that the graphic designers at all the big publishing houses have read too many reviews of over-pretentious pseudo-literature; you know, the sort of reviews that overuse terms like “metafiction” and “narrative” and always manage to call something or someone “dysfunctional”. Well, these graphic designers, as I envision them, notice that words like “gritty”, “textured” and “chiaroscuro” are overused in positive contexts in these sorts of reviews as well, and say to themselves: “Hell, we’ll give ‘em gritty, textured and chiaroscuro. Just use that rough matte and take some soft-focus pictures of something indistinguishable and we’ll be all set to go.” And sure enough, there you go, a book with a distinctively gritty texture with an indecipherable cover photo.

Of course, I’m probably overreacting. But then again, maybe not:

When you pick up the front page of any news publication, you are looking at someone’s attempt to win a design contest; everything that comprises that page—the words, the images, and even the white spaces between those words and images—are nothing more than props. In the eyes of the modern newspaper designer, all of those elements have equal value. This is not an exaggeration; stroll past any newspaper design desk and you will hear people talking about the “creative use of white space.” This means people are discussing ways to better utilize the parts of the paper that are blank (this includes the gaps between columns and the borders at the top and bottom of a page). Just think about that for a moment: People are literally discussing the creative significance of nothingness.
—Chuck Klosterman, Sex, Drugs, and Cocoa Puffs, pg. 216

(Speaking of books, this past summer I was bored one day and decided to compile a complete list of books I own. That list is now available for your perusal and is permanently linked from the Books sections. I’m willing to lend virtually any of the books on that list to people I trust will return them.)

November 22, 2004

Blame Physics!

Posted by shonk at 05:01 PM in Words of Wisdom | permalink | 1 comment

A t-shirt I just saw:

Guns don’t kill people
Physics kills people

Needless to say, worn by a physics grad student.

November 19, 2004

Old-world angst

Posted by Curt at 02:20 PM in Words of Wisdom | permalink | comment

In the end, however, Europeans have not sought to counter U.S. hegemony in the usual, power-oriented fashion, because they do not find U.S. hegemony threatening in the traditional power-oriented way. Not all global hegemons are equally frightening. U.S. power, as Europeans well know, does not imperil Europe 's security or even its autonomy. Europeans do not fear that the United States will seek to control them; they fear that they have lost control over the United States and, by extension, over the direction of world affairs.

If the United States is suffering a crisis of legitimacy, then, it is in large part because Europe wants to regain some measure of control over Washington 's behavior. The vast majority of Europeans objected to the U.S. invasion of Iraq not simply because they opposed the war. They objected also because U.S. willingness to go to war without the Security Council's approval -- that is, without Europe's approval -- challenged both Europe's world view and its ability to exercise even a modicum of influence in the new unipolar system.
--Robert Kagan, from The Crisis of Legitimacy: America and the World

Vivevo in una simulazione di attivitą. Un'attivitą noiosissima (I was living in a similation of activity. An extremely tedious activity).
--Italo Svevo, Zeno's Conscience (La conscienza di Zeno)

November 08, 2004

Election Redux

Posted by shonk at 12:41 AM in Politics | permalink | 8 comments

Realized I haven’t commented on the election since it happens. Basically, I have nothing to say about the whole thing. Primarily, I was rooting for an electoral tie, just because it would have been delightfully ludicrous. Barring that I was hoping for Kerry to win the electoral vote but lose the popular vote, because (a) it would have been wonderfully ironic and (b) because legislative gridlock is always desirable and there wasn’t a chance in hell the Democrats were going to control either house of Congress. Okay, neither of those things actually happened and, to be honest, it all played out pretty much how I expected. I mean, I hate to say “I told you so”, but, well, I told you so:

Bush is going to win this election. For better or for worse, his arguments are essentially positive: I will do X because I believe it is the right thing to do. Whether or not he believes his own arguments, and whether or not what he does exemplifies whatever beliefs he may actually have (and I’m skeptical that he has any), he’s arguing from an essentially stronger position than Kerry, all of whose arguments boil down to the following: I am not George W. Bush.


None of the above should be construed as an endorsement of Bush. Rather, it seems to me unlikely that someone running on an essentially negative platform, like Kerry, is going to defeat someone who at least pretends to be running on a positive platform.

As it stands, the only thing I wish I’d emphasized more strongly is the fact that Kerry supporters, by and large, tried to portray possible Bush voters as idiots, fools and evil psychopaths. Needless to say, not the best strategy for attracting those voters who might be sympathetic to Republican ideas on the war or anything else while also being sympathetic to the Democrats (who, so far as I can tell, didn’t take much of a stand on anything other than that they didn’t like Bush one damn bit). And it looks like at least one voter’s mind was swayed by exactly this fact (props to cosmicv for the link):

Your attitudes, language, and behavior toward people like me: reasonable, thinking Christians who are quite moderate politically and who are just as well-informed as you are (yes, I’ve read all the PNAC essays, too, and yes, they scare me, too) is reminiscent of nothing so much as an abusive ex-lover, a crazy and drunken stalker. “I’ll make you love me, or you’ll regret it, you worthless bitch! Come here and let me beat you over the head and tell you how stupid and worthless you are! Then you’ll see it my way!”

I’m not saying I agree with her stance on the war, Social Security or anything else, nor am I suggesting that domestic violence metaphors couldn’t be applied in the opposite direction with equal justification, but I suspect there are many, many others who felt and feel the same way. Something to think about.

(See also David Brooks’ column, especially the second-to-last paragraph)

November 07, 2004

A beginner's guide to producing new results in mathematics

Posted by shonk at 06:45 PM in Geek Talk | permalink | 1 comment
  • First, choose a problem that nobody’s ever solved before. Be careful, though: the most common beginner’s mistake is to choose a problem that’s much too difficult. Fermat’s Last Theorem was an old favorite, but since Andrew Wiles proved that a while back, the new favorites are the Riemann Hypothesis and the Poincaré Conjecture. Rather, as a beginner, you want to pick something that’s within your grasp. I suggest picking two random 200-digit numbers (no need to make them up on your own; get your computer to do that) and adding them together. With probability 1, nobody in the history of the world has ever added these two numbers together before.

  • Next, plug it into Mathematica or Maple. No red-blooded, God-fearing mathematician would ever dream of trying to solve a problem without plugging it into a computer and seeing what the answer is first. Sure, the numerical solution will probably be so vague as to be worthless, but this is how things are done.

  • Now it’s time to get down to business: write the problem up on the chalkboard in your office. Of course, you could just write it down on a sheet of paper, but there are several objections to that. First, paper is much too permanent; if you end up getting stuck and you’re working on a blackboard, you can always just claim the janitor erased your chalkboard at a crucial stage. Second, it’s extremely important to always have cryptic and incomprehensible scribbles filling your chalkboard to intimidate students and colleagues that might drop by. It’s even better if you have three or four calculations overlapping eachother on the board.

  • You’ve got the problem written down on your chalkboard, so now there’s nothing left to do but to solve the damn thing. Remember to take your time. Cross pieces out, even though you could just erase them. Once you’ve made some progress (and built up a goodly amount of chalk on your fingers), step back to ponder the next step. Rub your chin. Run your hands through your hair. Smooth down your shirtfront. Take a bathroom break. Do whatever it takes to transfer the chalk on your hands to various other parts of your anatomy and attire. Under no circumstances should you try to remove any of this chalk before going to teach your next class. Remember, having chalk smeared all over your face, hair, shirt and crotch is all part of the cachet.

  • At some point throughout the course of the above, we’ll assume you’ve actually solved the problem. Contemplate the beauty of your solution. Write it down on paper in an indecipherable hand. If you feel like it, consider typing it up, but be sure to include a few errors. This is necessary so as to confuse the readers of your solution and throw them off your track. Whenever there’s a difficult calculation, simply gloss over it and state the end result; odds are none of your readers will actually expend the effort to do the calculation themselves, so you’ve covered your ass in case you flipped a sign somewhere.

Congratulations! You’ve just proved a new result in mathematics. Of course, if you really just added two random gigantic numbers, the probability that anybody cares is 0. Better luck next time.

November 01, 2004

Don't Vote!

Posted by shonk at 09:13 PM in Politics | permalink | 24 comments

This summer, when I had more time on my hands than sense, I thought about making up some anti-campaign posters to put up around town. Needless to say, at this point I’m much too busy (and lazy) to actually follow through, but I still think it’s a good idea.

So what is an “anti-campaign poster”? Well, basically the idea would be to come up with something that would simultaneously ridicule the candidates and their militant supporters, the inane “get out the vote” campaigns, and the very process itself.

One of my favorite ideas was:

Which white, millionaire Yale alumnus and Skull & Bones member do you want deciding economic policy?

This point hasn’t, in my opinion, been emphasized enough. The feeling I get from most Kerry supporters I know is that they’re voting for Kerry, not because of who he is or what he stands for, but because he’s not Bush. Well, that’s all well and good, in theory at least, but how different are they, really? They both went to Yale, they’re both middle-aged, they’re both white, they’re both millionaires, they’re both members of the super-elite Skull & Bones, neither did much to actually earn his money, one went AWOL from the National Guard while the other organized protests with Hanoi Jane (Fonda) and they’re both all about increasing spending. Okay, admittedly, one looks like a chimp while the other looks like a horse, but that’s not really much to go on.

My other favorite idea was:

The only candidate to win a clear majority in this election will be ‘None of the Above’

Let’s not kid ourselves, nobody’s getting a “mandate” from the electorate, because the majority of the electorate either doesn’t care who wins or doesn’t like either one of the candidates (or thinks the entire process is morally bankrupt, but I’m guessing us radicals don’t comprise a significant percentage). And let’s be honest, there are good reasons for being part of that “silent majority”. For one thing, there’s Drew Carey’s take: “”Quit pretending that it matters, would you? Can you vote for all the nefarious cabals that really run the world? No. So fuck it.”

Also, as Steven Landsburg points out: “Even if you voted in the most hotly disputed state [Florida] in the mostly hotly disputed election [2000] in American history, your vote did not change the outcome.” The consensus seems to be that Bush won Florida by 530-odd votes; if any one person had acted differently, either by voting or not voting, Bush still would have won by 530-odd votes. Landsburg goes on to evaluate the likelihood that a single Florida voter could sway the election this time around:

If Kerry (or Bush) has just a slight edge, so that each of your fellow voters has a 51 percent likelihood of voting for him, then your chance of casting the tiebreaker is about one in 10 to the 1,046th power—approximately the same chance you have of winning the Powerball jackpot 128 times in a row.

Needless to say, as JTK has pointed out several times in the past (for example, commenting on Brian Doss’s post), you would do more to enhance your candidate’s chances of winning by buying a PowerBall ticket and mailing it to him than by voting for him. With that in mind, I rather like Virginia Warren’s idea regarding letting people pay for votes:

The benefits of a vote market would be quickly realized if the ban were lifted. For one thing, it would muzzle the tedious affirmations of mysticist, lever-wanking airheads who flounce about proclaiming “Every vote counts!” It wouldn’t take long for them to finally be shown the exact worth of an individual vote on the open market.

Given Landsburg’s numbers, let’s just say there aren’t currency denominations small enough to adequately express the market value of a single vote in a presidential election (and, needless to say, Michael Moore is overpaying).

Anyway, after tossing the numbers around, demonstrating that even if the preferences are split 50/50, your chance of casting the deciding vote is smaller than your chance of being murdered by your mother, Landsburg feels compelled to almost apologize for his advocacy of non-voting:

The traditional reply begins with the phrase “But if everyone thought like that … .” To which the correct rejoinder is: So what? Everyone doesn’t think like that. They continue to vote by the millions and tens of millions.

True enough, but I think Joe Sobran’s take is more compelling:

Nonvoters are often described as lazy, apathetic, lacking in civic spirit. Voting is touted among us as a moral imperative. If you don’t vote, we are told, you have no right to complain. Voting, in fact, is the way we are encouraged to complain!

It’s hard to know where to start refuting such imbecility. The act of making an X in a box, or its high-tech equivalent, is close to worthless as a means of either self-expression or imparting information. When masses of votes can be won by wearing silly hats and repeating silly slogans, it’s pretty hard to maintain the belief that election results reflect an aggregate wisdom in the electorate. I marvel that faith in democracy has survived the advent of C-SPAN.

Sobran goes on to give a moral argument for not voting, which I think is compelling but won’t reproduce here. Rather, I think Robert Anton Wilson’s response to the question “Who are you going to vote for?” does quite nicely:

I’m voting for myself because I don’t believe anybody else can represent me as well as I can represent myself.

Think about that for a second, and ponder just what casting a vote for someone else says about you.

With all that in mind, why do people still vote? Surely if there’s anything we learned from the 2000 election, it’s not that “every vote counts”. Rather (and either JTK stole this from me, or I stole it from him; I can’t remember which) the lesson we learned from 2000 was: if the election’s close enough so that every vote counts, the only votes that are going to matter are the 9 on the Supreme Court.

Okay, but that’s just illustrating the point, not answering the question. So why do people vote? The answer, I think, can be found buried within Hunter S. Thompson’s otherwise incoherent pastiche of his own writing from 3 decades ago:

The genetically vicious nature of presidential campaigns in America is too obvious to argue with, but some people call it fun, and I am one of them. Election Day — especially a presidential election — is always a wild and terrifying time for politics junkies, and I am one of those, too. We look forward to major election days like sex addicts look forward to orgies. We are slaves to it.

That’s right: people vote because it’s fun, because it’s a thrill, because they get a rush from forcing others to submit to the will of their chosen despot. What that says about human psychology is probably best not considered too deeply, but I figure it’s as good an answer as any.

Take that, logical positivists!

Posted by Curt at 11:38 AM in Geek Talk | permalink | 3 comments

A propos of my brother’s last post and the comments regading it, here’s another example of a flaw in the application of logical principles to reality. Context: in my philosophy of science class I’m reading “The Philosophy of Natural Science” by Carl Hempel. Hempel was a member of the Vienna Circle, much devoted to Carnap, etc. Today he is probably most famous for formulating the so-called “paradox of confirmation” for logical statements, which as I understand goes as follows (I’m using his example): given two logically equivalent statements, such as for example (1)”all crows are black” and (2)”all non-black objects are not crows,” any evidence p which supports one of the statements supports the other as well. Hence, for example the statement p “object x is not black and is not a crow” supports statement (1) as well as statement (2), therefore any non-black non-crow, a fish, a book, a blueberry pie, all provide evidence that crows are black. The obvious response is that this is ludicrous, since p has nothing to do with crows and is therefore irrelevant to the question of whether crows are all black. But let us re-imagine the question. While it may seem that taking non-black non-crows at randomn would provide no evidence regarding the color of crows, if all of the non-black objects in the world were gathered and recorded and none of them were crows, would one not have to concede that the complementary point, “all crows are black,” would have been proved? Or take another example: say we had a box with 10 objects in it, of which an uncertain number werere crows and 4 of the objects were black, and say one decided to test the two statements “all crows in the box are black” and “all non-black objects in the box are not crows.” If an object were pulled out of the box at randomn and proved to be not black and not a crow, then we would know that more than 15% of the non-black objects were not crows, which definitely provides indicative evidence for both of the statements. And by the time 5 non-black non-crows had been pulled out, we would be all but certain that all the crows in the box were black. Therefore, I think that the seeming paradox is simply an illusion of scale. Of course, on a practical level, the paradox holds true, at least in this case: the category of non-black non-crows is so huge that finding examples of them probably won’t provide much evidence of anything. Therefore, the principle of logical equivalences does virtually nothing to advance the investigation. And in fact, I think it is likely that the problem would exist not only in empirical investigations but also in the investigation of certain mathematical properties, for example. Something to keep in mind for those who are convinced of the infinite power of logic to solve both abstract and practical problems.