August 16, 2006


Good news! The white smoke has at last risen from the International Astronomical Union. We now know whether Pluto is, or is not, a planet:

...Pluto's right to be called a planet... will be resolved by extending the accolade to three more celestial bodies...

And a wise decision it is, too, for the IAU to show its appreciation in this way. A refusal to do so could lead only to the frustrated rage of the disposessed, with predictable consequences.

It is all very exciting. Yesterday we thought there were only nine planets, but now we have learned that there are twelve! This surprising new information will surely have a considerable impact on our understanding of the solar system.

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I never could understand why they needed both Pluto and Goofy.
Well, I suppose this reordering was inevitable after the discovery of Xena. After all, they had to make Xena a planet.

Though, by all rights, the Xena moniker should have been given to a double planet.
Dr. Haridon, how will this affect Uranus?
'Planet' comes from Ancient Greek planetes, 'a wanderer.' I've been a planet for more than a decade now. These days, I wander aimlessly across the Western hemisphere, undecided as to where to go next. However, I think I'm still revolving in the same direction around the Sun as the other fellas. Wouldn't want to upset Kant and Laplace.
On the other hand, it may all well be another unsubtle plot by the inclusive diversity freaks. It's not like we don't have any antecedents for that. Umberto Eco reminds us of the preposterous lengths to which they can go:

... la cosmologie féministe, qui remplace la métaphore machiste et éjaculatoire du Big Bang par la théorie duGentle Nurturing, selon laquelle la naissance de l'Univers a eu lieu à la suite d'une longue gestation.
"This surprising new information will surely have a considerable impact on our understanding of the solar system."

Heh. Just as exciting as the millennium arguments: 2000? or 2001? The experts weigh in! Nothing gets the juices going in academia -- still less in its retarded stepchild the internet -- more than an utterly pointless debate.
2001 damit! dont mes with me on taht one.

but anyhow i was wondarign if anybodddy saw weh're taht was goign. i nevar know if peopople think stufs to obivouoius to mentoin or if ive so agresively underplayyed wahtevar microscopiec slivar of a pumchline i startad withl that it just wen't by under the radar.
Are you seeing anyone for that double personality disorder, Mr Hynes?

And if the alleged punchline was the endline of the post, then I suggest you should try good old fashioned jokes. For it does make a difference in our understanding of the Frame of the World whether there's nine or twelve of the rotating fellers. Or fifty-three, for that matter.
There's exactly the damn same number of the same damn objects whether you call them "planets" or "kittycats" or "badminton rackets". Associating a different arbitrary sound with some of them will not change any frames of reference that science cares about.
What is arbitrary in all this is the linguistic label, Anon, but not the taxonomic box in which you stuff a thing. Usually, responsible scientists revise classifications based on causal-explanatory reasons rather than merely linguistic considerations. Expanding the range of Solar planets can make a difference in terms of the cosmogony of that system, for instance. The fact that the first eight planets have orbits lying almost in the same plane, and that they revolve in the same direction used to be substantial evidence in favor of the nebular hypothesis. Adding more distant planets to the crew might make other explanations less likely--such as the collision hypothesis, par example.

In general the difference between a reasoned classification and a merely arbitrary one is readily apparent. Born with a penchant for paradox, Borges thought they're all equally conventional. Quoth the Argentine, in The Analytical Language of John Wilkins:

"These ambiguities, redundancies and deficiencies remind us of those which doctor Franz Kuhn attributes to a certain Chinese encyclopaedia entitled 'Celestial Emporium of Benevolent Knowledge'. In its remote pages it is written that the animals are divided into: (a) belonging to the emperor, (b) embalmed, (c) tame, (d) sucking pigs, (e) sirens, (f) fabulous, (g) stray dogs, (h) included in the present classification, (i) frenzied, (j) innumerable, (k) drawn with a very fine camelhair brush, (l) et cetera, (m) having just broken the water pitcher, (n) that from a long way off look like flies."

So which taxonomy makes more sense to you--Borges's or Carl von Linné's?
Y'know, I think I remember some Frog "theorist" read that Borges gag, thought it was real, and proceeded to draw some heavy conclusions from it, with lots of comma-separated lists to clue you that he's deep, profound, incisive, clever, French.

As for Linnaeus, his taxonomy wasn't as flamboyantly ridiculous as that one, but it was still a crock. It's a big part of the problem that a lot of creationists have, with that "micro-evolution" nonsense: They almost make sense if you think species are discrete. That Platonic garbage is a natural way to think of things, for us, and a very useful model of reality if you happen to be living in Kenya 3,000,000 years ago. It's a blunt instrument, handy for snap decisions.

It's handy to have an intensional and less whimsically-defined term, but if anybody's modelling the solar system, he'd be an idiot if he decided to take Ceres into account only because the definition of "planet" was modified to include it. The physical properties of Ceres are the same either way, and those are what science is concerned with.
There are people--Alfred North Whitehead was one of them--who think that Western philosophy is largely a set of footnotes to the Platonic dialogues. But, of course, everyone's entitled to their opinion re: Socrates's brightest student. This is still a free country, Abu Gonzales's wishes notwithstanding.

That being said, I find it rather amusing to see Anon deny and affirm Platonism in one and the same breath, as it were. For, if you deny that the world is carved at the joints into "real" (Platonic, that is) natural kinds, it makes little sense to then maintain that science (or physicists, in particular) are after the physical properties of things. At the very least, entities could still be divided into real kinds, based on their different properties. Properties which many of us, Anon included, take to be "real" (in whatever sense, rather than merely conventional, such as 'belonging to the emperor' and 'being drawn with a very fine camelhair brush.'

Perhaps the good doctor Haridon could shed some light on this thorny issue?

Note, however, that if one rejects Platonism, one is left with nothing but variants of conventionalism regarding the foundation of all classifications. Then, Borges's insight does indeed become a deep realization, to the delight of many a French professor. A more sophisticated version of that idea was defended, for most of the last century, by W.V.O. Quine.

Lastly, Poltroon's worries seem to have been partially put to rest. There's no word on Goofy, though.
You are presuming that there must be a clear division between a good classification and a bad one, which presupposes your conclusion. In Ayer's immortal words, "Huh?!" In fact, few if any classifications are perfect, but some are more useful than others. The utility is going to depend on the use to which you plan to put the one you've got, which is what "utility" means.

Obviously there are useful classifications, but the vast majority are are convenient approximations that should never be taken too seriously, not properties of reality in the Platonic sense. And some of them can be seriously misleading, which is what happens when you take an animal designed to steal carrion from lions and put it in charge of QA at Lockheed.

As an academic, you are no doubt familiar with sororities: For any given arbitrary group of rich girls, exactly how much alcohol must they consume before they change state from an irritation into an annoyance? Any point you pick is going to be arbitrary: There is a point early in the evening when they are indisputably irritating, and a point later on when they're indisputably an annoyance, but there is no abrupt change of state at any point in between.

What's the difference between a violin that's in tune and one that isn't? That the one in tune has its A string at 440 Hz? In that case, it's unlikely that any violin ever has been in tune, but in reality a very close approximation is okay, and a lousy one is not, and there's a smooth continuum in between the two. There's no state change in the sense of a liquid changing to a gas, because neither state is actually different from the other in any fundamental way. You can follow a whale's ancestors all the way back to some flea-bitten monstrosity that lived on land, and at no point will you see an abrupt state change from "whale" to "not whale". You can draw the line any place you like, but nobody looking at the two critters on either side of it will be able to guess with any confidence which is which (barring, no doubt, occasional drastic mutations that happen to be successful, but in any given case there may not have been one). This is why Linnaeus is being jettisoned in favor of cladograms.

Reality is full of gradual transitions, whether Pat Robertson likes it or not.

You are also assuming that it can't be true that all classifications are reductive horsecrap, because... because it would be inconvenient, or annoying, or something. But your convenience is irrelevant. The question itself is nonsensical anyway, naturally.

Plato was simply clueless, that's all. Philosophy has at times been useful, but only momentarily, because as soon as we can say anything meaningful about something, it becomes science instead. There's a classification for ya! Philosophy is the study of that about which we can say nothing meaningful.

Anyway, I thought the point of the post was that it's funny how people are talking like we've learned something about Pluto here, when in fact it's merely that some people have agreed to associate a noise they make with their mouths with a slightly different arbitrary set of parameters.
There's not a whole hell of a lot of integers in nature, basically.
Oh. A pragmatic instrumentalist. Or maybe a metaphysical quietist. How very unique. And, in the wake of Pierre Duhem and the later Wittgenstein, most original, too.

Instrumentalism (sometimes cross-bred with its first cousin, hypothetico-deductivism) seems to be the weekend philosophy of some working scientists. So let me guess: a biologist in the employment of a biotech company?

At any rate, it's rather hard not to notice how the anti-philosophical positivist imperceptibly slides into all sorts of ontological dogmas: 'Reality is full of gradual transitions' (a metaphysical statement if I ever saw one); 'There's not a whole hell of a lot of integers in nature, basically.' I wonder what Wittgenstein would make of all this Sinnlosigkeit.

Erm, between dilettantes here: Wittgenstein's meaninglful/nonsensical distinction rests on a verificationist account of meaning. That sort of position has been rather discredited, of late. So maybe we should also revise what used to rest on it? Or perhaps we should wait for that triumphal age when science will wrest away from philosophy the meaning of meaning. I'm confident the Large Hadron Collider might offer robust evidence to settle these problems once and for all.
Pragmatic multi-instrumentalist, thankyouverymuch. I play bass, too.

Couldn't care less about the later Wittgenstein, though. I love the early stuff but he totally sold out after Tractatus Logico-Philosophicus.

And what's metaphysical, precisely, about observing and describing the physical properties of a violin? Have you tuned a stringed instrument lately? It's not an abstraction.

Is there some number n of grains of sand which is a pile, where n+1 qualifies as a heap, and the distinction is not ridiculous? No. I will say that dogmatically: No.

I'm talking about the limits of language: The problem isn't the sand. It's the words "heap" and "pile", which are damnably vague.

Now, if language were a perfect fit for what we use it to describe, it would be too cumbersome to use: It's not practical to have a distinct noun for every sized collection of sand from one grain up to, say, 1*10^100 or something. So we talk about heaps, piles, mounds, and handfuls, and it's good enough for day to day. You don't have to classify a large cat very precisely if your goal is not to be eaten. I know Bill Gates is a zillionaire, and that's good enough for your and my purposes, but I bet he wants a few more digits worth of precision from his bank. So do they: Imagine if his balance just read "zillionaire", and he withdrew $100,000, and it still read "zillionaire". That would be a losing proposition for the bank.

This classification we're looking at here, of heavenly bodies, is purely linguistic.
Yesterday we thought there were only nine planets, but now we have learned that there are twelve!

Now they've decided there are only eight.
I have some doubts as to whether the later Wittgenstein really sold out. At any rate, there are robust attempts to overcome his linguistic idealism -- bot early and late -- in the works of Wilfrid Sellars, Gareth Evans, and John McDowell. I tend to think those guys are right. Which entails, among other things, that some classifications are better than others not because they may be more pragmatically useful, rather because the world is that way. Yeah, I'm old-fashioned like that.

As to heaps and piles, they're nothing but dried, smoked fishes formerly used by English hunters to save a doomed fox--red herrings. Any language has fuzzy terms. That's no definitive objection against belief in natural kinds. If you want formal rigor, try fuzzy logic. If you're after the truth, here's something to ponder: 'justice' and 'friendship' are fuzzy notions; but no one in their right mind would say that they're irrelevant or arbitrary ideas. And, if we are to believe the lessons of Quine, equally fuzzy are 'duck' and 'bachelor.' They're open-ended towards the future -- fuzzy at the fringes, as it were.

As to your point about the unwielding perfect language for us mere mortals, it's an idea that's been examined before, and swiftly dismissed--not because it would be too cumbersome, but because it's not a language. A proper language includes essentially general concepts, that is, Platonic essences. Without them, there is no thought; that is the point of the Kant's transcendental deduction of the categories. But I'll let a talented Argentine do the talking for me:

"Instead of 7013, [Ireneo] would say, for instance, "Maximo Perez"; instead of 7014, "the railroad"; other numbers were "Luis Melian Lafinur," "Olimar," "sulfur," "clubs," "the whale," "gas," "a stewpot," "Napoleon," "Agustin de Vedia." Instead of 500, he said "nine." Every word had a particular figure attached to it, a sort of marker; the latter ones were extremely complicated... I tried to explainto Funes that his rhapsody of unconnected words was exactly the opposite of a number system. I told him that when one said "365" one said "three hundreds, six tens, and five ones," a breakdown impossible with the "numbers" the negro Timoteo or a ponchoful of meat. Funes either could not or would not understand me. [...] Funes, we must not forget, was virtually incapable of general, platonic ideas."

(J.L. Borges, Funes el Memorioso, trad. Andrew Hurley)
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Sorry I said that about pointless debates, guys.
That's OK, WNB. Now that I think of it, it was rather insignificant, anyway.
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Well, maybe so. But I love the Borges quotes, man. He was a genius.

Wanna burn some more bandwidth? I don't think JLB's narrator's comments about Funes' number system are quite accurate. (But his narrators are often at least as crazy as the other characters, so I'm not pretending to tell him anything here.)

Still, let's take your example totally literally. Let Funes(N) be Funes' word for the number N. It's still true, though maybe very laborious for Funes himself to check, that

Funes(365) = Funes(3)*Funes(100) + Funes(6)*Funes(10) + Funes(5).[1]

Still, I've read that some modern mathematicians believe Roman numerals held back the development of calculus -- which doesn't logically depend on what number system is used. I'm sure it could be rewritten using Roman numerals, but that would be a very mean thing to do to students.

[1] Assumptions
a. Funes(N) is defined uniquely for the required values of N. {Ok, say for every finite N.}
b. Funes could somehow add and multiply correctly. {That is, assume that Funes(N)*Funes(M) = Funes(N*M) and that Funes(N)+Funes(M)=Funes(N+M).}
BTW Funes' multiplication table would be very large, I think also inherently incomplete. Presumably he knew some largest number called Funes(N), and then he didn't know Funes(2N).
PW, that's an interesting suggestion. I'd have to think about it for a bit. Here's some prima facie worries:

[1] How do you define the basic arithmetic operations in Funes(N)? I mean, do you use recursion for, let's say, addition?

[2] If you don't want to use recursion, then you need an infinite set of axioms to define even elementary operations in this number system. That is, each and every addition in the system will be defined sui generis via an axiom, individually. That requires an infinite memory.

[3] If you don't want an infinite set of axioms, then Funes must show that he has a well-ordering on his system. We have a mechanical decision procedure for that, in the case of the natural numbers (there is one for the rationals, too; but not for the real numbers--you have to assume the Axiomof Choice for that to hold). But Funes doesn't have recourse to a reiterable decision procedure to discover whether, say, the "number" Luis Melian Lafinur comes before or after the "number" a ponchoful of meat. He'll have to remember the entire ordering of this peculiar number system of his -- either by a one-to-one correspondence to our system of natural numbers, or in some other way. Again, this requires an infinite memory, and a needless reduplication of our numbers.

[4] There's nothing wrong with the requirement of an infinite memory -- after all, he is El Memorioso -- but modern cosmology tells us that the world is finite in space and time (or spacetime, if you wish). That is, Funes won't have enough time to remember all the numbers in his system. By the time he gets to 10 to the 80th power or so, the world will have collapsed gravitationally into itself.

[5] Lastly, Funes could refuse to enter "Cantor's paradise" and only confine himself to finitistic math. But that would be both uninteresting and pointless. If he wants the big prize, let him tackle the infinite with his own powers. Heh.

Erm, sorry for all the italics.
Um, speaking of bandwidth: maybe we should ask Arlington's permission before we burn his. He's the one who pays for it, after all.
I have to think about that.

In my example I just assumed that Funes knows the results of conventional addition and multiplication of integers, expressed in his own system. If he can remember a countable amount of information, then what I called the tables (what you call the axioms) for addition and multiplication aren't a problem. But sure that set of information is infinitely large.

If he can count, and we limit the problem to finite numbers, then in practice he doesn't need a table. He might count out N beans into one bowl, then M beans into a second bowl, then throw them all into a third bowl and count the result. For multiplication, count out N beans per bowl into M bowls, then dump them all into a trash can and count.

It's slow, but it would work for small numbers. Of course the problem is that the mathematics is being done by the computer, not by the mathematician. I can already hear undergraduates bragging: "He told us integers are outdated -- nobody uses them anymore. We have computers for that." But before we throw the first stone, who hasn't blindly carried out long division with pencil and paper?
For real numbers, yeah, I guess it becomes impossible for Funes to figure out anything interesting at all.

He can't really calculate, he is limited to observations.

I think with the planets the situation is more ambiguous, because we really can't say much about them from first principles. From a practical point of view, most of what we can do is observe.

You're probably right about H3's bandwidth, I'll try to taper off here!
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