Rhetorical curveball
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Here's the first sentence of William Safire's latest On Language column, "Bending the curve":
Taking on the issue of the cost of health care, a Washington Post editorialist intoned recently that “knowing more about which treatments are effective is essential” — knowing about when to use a plural verb is tough, too — “but, without a mechanism to put that knowledge into action, it won’t be enough to bend the cost curve.”
The phrase in boldface blue was too much for reader Anthony Ambrosini:
Am I missing something? Which with a plural verb just implies a plural response to the question, and I doubt he thinks that knowing should take a plural verb. What's he on about?
I'm just as puzzled as Anthony is. Safire's parenthetical remark is true, more or less, but the maxim of quantity dictates that it should have some minimal relevance to its context. And this would imply either that the quoted phrase (“knowing more about which treatments are effective is essential”) involves an error in verb agreement (surely false), or that the quoted phrase is a case where it's especially tricky to determine verb plurality (also apparently false, unless you're borderline aphasic).
So come on, LL readers, help us out. Is Safire starting to have problems with linguistic impulse control? Is he using the aleatoric compositional methods pioneered by John Cage and Price Stern Sloan? Or is there some simple exegesis that we're missing?
One thing about Safire's column remains consistent — the failure of his staffers to do the research that he pays them for (or his failure to pay attention to the research they do):
Why has curve-bending become such a popular sport? Because the language is in the grip of graphs. The graphic arts are on the march as “showing” tramples on “explaining,” and now we are afflicted with the symbols of symbols. As an old Chinese philosopher never said, “Words about graphs are worth a thousand pictures.”
The first straight-line challenge to the muscular line-benders I could find was in the 1960s, when the power curve was first explained to me by a pilot.
The OED has citations for power curve going back to 1908:
1908 Philos. Trans. (Royal Soc.) A. 207 441 When the pressure observations are plotted to a suitable scale they coincide with the integrated power curve. 1934 Times 27 May 8/7 This Riley engine in acceleration is rapid and clean, it never fusses or vibrates, and the power curve must be a good one, for the engine capacity, throughout its range.
And there are plenty of other cgraphical curve-collocations earlier than 1960, e.g.:
1886 K. PEARSON in I. Todhunter Hist. Theory Elasticity I. 503 There exist certain materials for which even in a state of ease the *stress-strain relation is not linear; that is to say the stress-strain curve..is not a straight line even for very small elastic strains.
Though in fairness, I don't think that stress-strain curve has ever had much of a second life as a metaphorical expression.
I imagined that bell curve was an old expression, but the OED's first citations are from 1970 and 1973:
1970 Balance Sheet Oct. 64/2 Research may be used to classify the effort into three basic methods:..(2) through use of the normal distribution hypothesis (*bell curve) [etc.]. 1973 T. PYNCHON Gravity's Rainbow I. 51 Exit doors painted beige, but with edges smudged browner in bell-curves of farewell by the generation of hands.
This strikes me as an opportunity for antedating, rather than a genuinely late coinage. And indeed, a few minutes of web search turns up Godfrey H. Thomson, "Interpretation of Threshold Measurements", Psychological Review, 1920, p. 304:
The way that the expression is used in that passage leaves the impression that it was already a commonplace expression in 1920.
The only example of bell curve in Literature Online is from Martin Espada's poem "Do Not Put Dead Monkeys in the Freezer", 1996:
15 I was a lab coat and rubber gloves
16 hulking between the cages.
17 I sprayed down the batter of monkeyshit
18 coating the bars, fed infant formula in a bottle
19 to creatures with real fingers,
20 tested digital thermometers greased
21 in their asses, and carried boxes of monkeys
22 to the next experiment.
23 We gathered the Fear Data, keeping score
24 as a mechanical head
25 with blinking red bulbs for eyes
26 and a siren for a voice
27 scared monkeys who spun in circles,
28 chattering instructions
29 from their bewildered brains.
30 I did not ask for explanations,
31 even when I saw the sign
32 taped to the refrigerator that read:
33 Do Not Put Dead Monkeys in the Freezer.
34 I imagined the doctor who ordered the sign,
35 the moment when the freezer door
36 swung open on that other face,
37 and his heart muscle chattered like a monkey.
38 So I understood
39 when a monkey leapt from the cage
40 and bit my thumb through the rubber glove,
41 leaving a dollop of blood that gleamed
42 like icing on a cookie.
43 And I understood when one day, the doctors gone,
44 a monkey outside the bell curve of the Fear Data
45 shrieked in revolt, charging
46 the red-eyed mechanical head
47 as all the lab coats cheered.
It surprised me to see no literary uses in the 1930s through 1970s of such a simple and evocative phrase for such a basic and important concept. But Herrnstein and Murray's 1994 book The Bell Curve guaranteed that this term would enter the linguistic mainstream, in a variety of more-or-less metaphorical interpretations.
Ryan Denzer-King said,
September 15, 2009 @ 10:25 pm
I vote Cage fan. Either that or perhaps someone should have him take the Turing test.
John S. Wilkins said,
September 15, 2009 @ 10:39 pm
Have you looked through the available literature of the Galton lab? Galton came up with the idea, and I am fairly sure that the term would be in use from around the 1890s. [Well, Galton didn't come up with the normal distribution – that was Quetelet in the 1840s, but I think he named the bell curve.]
Possibly a good source here is
Gigerenzer, Gerd. 1989. The Empire of chance: how probability changed science and everyday life, Ideas in context. Cambridge UK; New York: Cambridge University Press.
Skullturf Q. Beavispants said,
September 15, 2009 @ 10:42 pm
My hypothesis is that Safire was confused by the accidental physical proximity of the noun "treatments" and the phrase "is essential". Of course, the sentence immediately before the blue one doesn't say treatments are essential; it says knowledge of treatments is essential.
I don't have trouble believing that some people at some times have "corrected" things like "I think eating dogs is unusual" to "I think eating dogs are unusual" (where the intended meaning is to attribute the unusualness to the eating and not to the dogs). Again, it's the accidental fact that the plural noun "dogs" happens to be located near the verb.
Dan Lufkin said,
September 15, 2009 @ 10:43 pm
I suspect that Safire's column is sometimes ghost-written by Mark V. Shaney.
fev said,
September 15, 2009 @ 10:43 pm
Yeah. Cage fan. Maybe next week he'll play the one where he sits there and doesn't say anything?
D said,
September 15, 2009 @ 10:57 pm
"Well, Galton didn't come up with the normal distribution – that was Quetelet in the 1840s"
Not Gauss?
James said,
September 15, 2009 @ 11:04 pm
I think Safire is making some weird comparison that just didn't come across properly. He might be trying to say that choosing the right treatment is just as essential, and just as easy, as knowing when to use a plural verb. His use of the word "hard" is meant sarcastically. Maybe it would have been better if he had said:
"knowing about which treatments are effective is essential" – knowing how to tie your shoes is hard too
Or possibly he is saying that knowing about plural verbs is just as essential, but just as hard to figure out, as choosing the right treatment. Maybe he meant more like this:
"knowing which treatments are effective is essential" – knowing which life insurance plan to pick is hard too
Bruce Rusk said,
September 15, 2009 @ 11:12 pm
A quick scan of JSTOR suggests that early usage favored the expression "bell-shaped curve." The first usage is in Science, from 1906, and there are many more from soon afterward. Perhaps this was later, or at around the same time, contracted to "bell-curve."
Bruce Rusk said,
September 15, 2009 @ 11:17 pm
Also, while Google Books has its usual metadata messes, it has an example from the 1887 Works of John Ruskin, describing an architectural form and not the plot of a statistical distribution.
Mark P said,
September 15, 2009 @ 11:42 pm
A quick Google search finds references to mathematicians deMoivre and Laplace using the normal distribution in the 1700s, prior to Gauss.
John Cowan said,
September 16, 2009 @ 12:00 am
Well, I myself have a Mark V. Shaney number of two, or one if you count email, and I can rule that hypothesis right out.
Nathan Myers said,
September 16, 2009 @ 12:18 am
We can be (against my inclination) charitable toward Safire this once, and let him simply be calling attention to the pleasing juxtapostion "are effective is essential". The larger sentence, though, remains nonsense; he seems to be suggesting that identifying effective treatments is easy. Of course it is easy for him, because he doesn't have to actually do it.
Mark L: <hint>Knowing when to use the definite article in the first sentence of one's own posting isn't hard, but it's not the same as putting that knowledge into action.</hint>
Skullturf Q. Beavispants said,
September 16, 2009 @ 12:25 am
I'm suddenly inclined to agree with Nathan Myers. We can take Safire's blue aside (not "blue" like a blue movie!) as saying, in essence, "note the successful navigation here of the sometimes tricky matter of singular and plural verbs."
Mark said,
September 16, 2009 @ 1:30 am
Here is Galton using "the well-known bell-shaped curve" in 1876:
http://books.google.com/books?id=6n0AAAAAMAAJ&pg=PA11&dq=%22bell+shaped+curve%22&lr=&as_brr=4&ei=s3awSo24HqrakQS1_aX-Aw#v=onepage&q=%22bell%20shaped%20curve%22&f=false
D.O. said,
September 16, 2009 @ 1:31 am
Power curve has at least 2 scientific meanings 1) power law: y = x&alpha 2) dependence of the physical quantity power (like engine power) on some parameter plus there is undoubtly at least one "business" meaning, which I cannot quite get. Safire's
might (it seems to me) refer to both 1 and 2 because it is a "straight-line challenge to the … line-benders" (looks like meaning 1 though inverted) and "the power curve … explained … by a pilot" is probably of type 2. If my analysis is right, W. Safire is quite a thing.
In addition, OED's 1908 reference is to meaning 1 while 1934 reference is to meaning 2. And how stress-strain relation got into there is not clear. It is not a power curve in either sense 1 or 2, though if it is "not a straight line even for very small elastic strains" (which might be true only for certain materials) it is most probably a power curve in sense 1 (for low strains).
Sparky said,
September 16, 2009 @ 1:50 am
>> the aleatoric compositional methods pioneered by . . . Price Stern Sloan
Awesome!
P.S. By which I mean, I congratulate myself on my being cool enough (or just old enough?) to get it.
Blake Stacey said,
September 16, 2009 @ 1:50 am
Pynchon actually used "bell-shaped curve" in his short story "Under the Rose" (1961), as quoted here:
Peter Taylor said,
September 16, 2009 @ 3:39 am
The text in blue throws me for an additional loop: how can knowing something be tough? Learning something can be tough, and so can applying knowledge and remembering something you once knew, but actually knowing it?
He loses me completely with his "straight-line challenge to the muscular line-benders" too, for his example appears to be about a non-straight line and has no "line-benders" in sight, so far as I can tell: from the examples which actually talk about bending lines I infer that a "line-bender" is either someone who wants to change a trend or someone who talks about "bending the line" and means "changing the trend".
peter said,
September 16, 2009 @ 4:00 am
Sorry to play pedant, but Cage's compositional methods were not aleatoric, although that is the common belief. He normally used the I-Ching to design the placement of the parts and durations of his compositions, AS IF by chance. But this procedure was not a chance procedure. To anyone who believes in the I-Ching, as Cage did, it is a means of manifesting in the world we live the underlying, synchronistic forces and trends of the cosmos, and is entirely deterministic. It only looks like chance to someone who does not understand or does not believe what is happening. IME, this notion is usually quite hard for contemporary westerners to grasp, so anti-deterministic and so focused on only the observable (non-spiritual) realm is modern western culture.
[(myl) John Cage, in a letter:
I'm not sure what this means, but focus on the spiritual realm doesn't seem to be among the possibilities.]
Franz Bebop said,
September 16, 2009 @ 4:01 am
Which assertion about "curves" is being refuted? I don't actually understand what Safire meant:
The first straight-line challenge to the muscular line-benders I could find was in the 1960s, when the power curve was first explained to me by a pilot.
I don't even understand this sentence. This isn't a claim about the first use of the phrase "power curve," in fact it implicitly concedes that the phrase was already in use, since it was being explained, not coined, and Safire hints that the phrase was in use in WWI. Besides, it's not the phrase in question, the phrase in question is "bend the curve," not "power curve."
[(myl) Right. Most of the sentences in the column make no sense at all, if you try to interpret them as attempts to state coherent propositions, rather than as playful and quasi-random dancing around with allusions, puns, klang-associations and other linguistic embellishments. But to the extent that a theme emerges from all the noodling, it seems to be a riff about metaphors derived from presentation graphs, and especially those that include the word "curve".]
What does Safire actually assert? This explanation was the first "challenge" to "line-benders." What on earth does that even mean? "Bending the curve" and "bending the line" are two different phrases, as far as I am concerned (in spite of any objections from mathematicians that a line is just a special curve). Either way, what could it possibly mean to "challenge" this bending? The wordplay here completely obscures what Safire was trying to say. We can't refute this assertion because there is no meaning to refute. As someone once said: "It's not even wrong."
Citations for "bell curve" and "power curve" are not relevant, since the phrase in question is "bend the curve."
[(myl) I'm skeptical that the word "relevant" is relevant to this particular example of Mr. Safire's increasing difficulties with linguistic impulse control. But to the extent that he's trying to say something about the history of phrases in common use that derive from presentation graphics (that is, graph in the sense of "diagram used to communicate a function or relation" rather than in the sense of "set of nodes and set of edges connecting pairs of nodes"), then it's reasonable for him (and for us) to discuss other such phrases.]
Bruce Rusk said,
September 16, 2009 @ 7:32 am
peter,
Really? You do realize, I hope, the irony of making that claim that Westerners have trouble understanding pattern within the apparently random in the context of a discussion of the bell curve? Statistical understanding of stochastic processes is very different from Yijing divination, but they are both consistent with the idea of "underlying forces…of the cosmos" producing predictable patterns.
Mark P said,
September 16, 2009 @ 8:18 am
The "power curve" that was explained by a pilot almost certainly had to do with the horsepower vs rpm of a typical piston engine. Knowing the power curve (for us lowly automobile drivers) can allow sporty drivers to accelerate more quickly because they can make sure the gear they are in allows the engine to spin fast enough to produce more power than is required for a constant speed.
References to graphical displays of data are pretty common in everyday use, or at least in some everyday use. People often say that a particular piece of software has a steep learning curve. Even "over the hill" is suggestive of a graphical representation of the progression of vigor and capability.
Exactly what Safire has against graphical representations is not clear. Doesn't he have a plotting package? Excel maybe?
Grep Agni said,
September 16, 2009 @ 8:32 am
Doesn't he have a plotting package? Excel maybe?
With respect, Excel is not a plotting package. Such an assertion is an abomination unto Nuggin.
peter said,
September 16, 2009 @ 8:39 am
myl said: "John Cage, in a letter:
"There is no split between body & spirit. We are one in and out. "Earth has no escape from Heaven."
I'm not sure what this means, but focus on the spiritual realm doesn't seem to be among the possibilities.]
Thanks, Mark. Isn't human language wonderful! I read the meaning of this sentence of Cage's be to diametrically opposite your interpretation, and directly supportive of my argument that Cage believed that spiritual forces determined events in the material realm.
Troy S. said,
September 16, 2009 @ 8:43 am
Aleatoric composition. Hm. This is a new concept to me. I'll have to look into John Cage. But it sounds like it must be along the lines of the famous Post Modern Essay Generator. And could it possibly explain the equally infamous word salad that is timecube.com?
peter said,
September 16, 2009 @ 8:50 am
Bruce Rusk said (September 16, 2009 @ 7:32 am)
"IME, this notion is usually quite hard for contemporary westerners to grasp…"
Really? You do realize, I hope, the irony of making that claim that Westerners have trouble understanding pattern within the apparently random in the context of a discussion of the bell curve? Statistical understanding of stochastic processes is very different from Yijing divination, but they are both consistent with the idea of "underlying forces…of the cosmos" producing predictable patterns."
Bruce, thanks for examplifying my point here, about people not understanding these ideas! :-)
I did not claim that westerners have trouble understanding patterns within the apparently random. I said that (IME, anyway) contemporary westerners have trouble understanding the notion that all is predetermined or determined by non-material forces, the idea that there is no such thing as chance. We are not talking about patterns, and any phenomena is usually not predictable (at least us humans). Being predictable is (in this cosmology) somethng different from being pre-determined or determined. These notions are not all strange to some other contemporary cultures, and would not have beeen strange to most Christians in the early modern period.
J. W. Brewer said,
September 16, 2009 @ 8:59 am
Wikipedia gives two different meanings for "power curve": the airplane-specific one Safire was alluding to is the second, whereas the OED cites seem likely (might need more context for one of them to be certain) to be the first and thus don't necessarily show how old the second is. http://en.wikipedia.org/wiki/Power_curve. And of course there could have been a considerable gap between the use of "power curve" for its literal aerodynamic application and a metaphorical extension of "behind the [power] curve." Neither of the wikipedia senses of "power curve," by the way, seem to mean "a curve of the shape typically found in a graph illustrating a 'power law.'"
But separately from the same column, I wonder if Safire is having some Recency Illusion issues with the claim of a newly "hot' usage of "optics/optical" to mean appearances as distinguished from substance. I've heard that usage (in legal circles that probably have some overlap jargonwise with political/policy-wonk circles) for a decade or more.
J. W. Brewer said,
September 16, 2009 @ 9:15 am
And just to play it out, the point of the second usage of power curve is that, perhaps somewhat counterintuitively, when a plane is flying at a sufficiently slow speed it requires more rather than less power just to keep going at the same speed, so presumably if you metaphorically get "behind the curve" you need to exert more and more effort just to keep from falling further behind, and may get into a vicious circle where you eventually cannot muster the power needed to do so (at which point, in the aeronautical original, you would stall and plunge to the ground). Mark P. is assuming the application in the airplane context of the first wikipedia usage for power curve (which is equally applicable to internal combustion engines whether being used in prop planes, pickup trucks, or whatever), but I don't think that is either consistent with Safire's discussion or independently makes sense of the metaphor.
I agree with Mark P. that Safire's overall point is bogus, although of course given myl's repeatedly expressed view that journalistic attempts to paraphrase statistical data in words frequently fail spectacularly, perhaps metaphors based on what particular graphs of statistical data look like are also at substantial risk of incomprehension.
N said,
September 16, 2009 @ 9:28 am
I second the call to match his writings against a Turing Test*. He writes as if he can't process non-continuous agreement. In his quest to nitpick language he overstepped and pointed out his own error rather than that of his subject.
*This could actually be performed without much difficulty, but more programming knowledge than I have. SafireBot, after ChomskyBot.
Mark P said,
September 16, 2009 @ 9:31 am
Grep Agni, since I doubted that Safire would have a real plotting package, I thought surely he has MS Office. I prefer Igor, but plotting packages are very personal thing.
Benjamin Zimmer said,
September 16, 2009 @ 9:42 am
If anyone's interested in antedatings of "bending the curve" (the purported topic of the column), see my Aug. 21 Word Routes column on the Visual Thesaurus, "The Lexicon of the Health Care Debate." I cite an early use from 1915 (in which scientific progress is imagined to "bend the curve" of the frequency of wars) and note that "bending the (cost) curve" has been an idiom of the health care debate in Congress since at least 2003.
[And now see the full story here.]
legionseagle said,
September 16, 2009 @ 10:26 am
Could Safire have been attacked by a sub-editor? I'm envisaging that the sentence he quotes may have had an original (mistaken) plural verb which a sub-editor corrected without realising that doing so turned the parenthetical snark into a boojum.
Andy Hollandbeck said,
September 16, 2009 @ 10:33 am
I would certainly say that the Cage's 4'33" is aleatoric. It's also one of the very few works of art that isn't abstract.
Even if Cage's compositional style isn't governed by chance, the fact that a performance is unpredictable and unpredetermined still, in my opinion, lands it in the aleatoric category. But now I'm spinning off into a discussion about what aleatoric music is.
As for Safire, I blame Microsoft Word. I don't know how they're involved, but they're my usual scapegoat for things like this.
John Roth said,
September 16, 2009 @ 11:07 am
Legionseagle got to it first – I agree with his suspicion that the original had a number mismatch, and that someone fixed it without realizing that it made the point of the next part incorrect.
Mark Liberman said,
September 16, 2009 @ 11:42 am
@ legionseagle, John Roth:
Use the web, Luke. Searching on the Washington Post's web site turns up the original, "The health-care sacrifice", 7/26/2009:
The original was (or at least now is) exactly as Safire quotes it — no error in sight.
Sili said,
September 16, 2009 @ 12:36 pm
I'm sorry, but I Ching is aleatoric. Chance is chance is chance is chance.
More importantly, though, Mozart was a pioneer of aleatoric composition. I don't know the Köchel, but an implementation was played on Radio 3 a while back – that where I know it from. In Mozart's case it was a matter of the which section to play and in what order to play them. So the compostion may not have been strictly stochastic, but the perfomance at least had to be.
JimG said,
September 16, 2009 @ 2:11 pm
Much ado.
Safire wrote: … knowing … is essential. … Knowing … is tough, too.
The first referred to knowing more about which treatments are effective, the second referred to knowing about when to use a plural verb.
What's wrong with either sentence?
Personally, I was less comfortable with the assertive "too" implying that the two adjectives might be parallel (i.e., essential = tough). I've long had a suspicion that Safire finds essential understanding to be too difficult.
And just BTW, I would be happier with better descriptive precision re the concepts of aeronautical thrust/drag and airspeed/lift curves and a propulsion power curve.
JimG said,
September 16, 2009 @ 2:25 pm
My apology; I omitted a conclusion re various types of mathematic curves.
Most curves can't be bent, because they're the expression of some well-defined function. They may be displaced up, down, right,or left. The function may be changed to make a curve tighter or more open, and this is what is called bending.
Cost is usually a component of the supply or demand curves, defining one of the axes against which the curve is plotted. I was left wondering whether Safire might better have referred to a demand curve, a supply curve, some expression of consumer preference or something else.
J. W. Brewer said,
September 16, 2009 @ 3:05 pm
There are different sorts of curves one can find in graphs relevant to discussing health care costs. Figure 2 in the article linked below (an interesting perspective from a Nobel* Prize winner who mostly leaves the current policy implications as an exercise for the reader), compares how one such curve looks today with how it might look under three different future scenarios, although the verbs the author uses are intransitive "twist" and "shift" rather than transitive "bend," which *might* imply some skepticism that conscious human agency can determine which of the scenarios ends up coming to pass:
http://www.american.com/archive/2009/september/forecasting-the-cost-of-u-s-healthcare
*consider pedantic footnote about how the economics prize isn't a Nobel Prize strictly speaking to have been inserted here
peter said,
September 16, 2009 @ 4:07 pm
Andy Hollandbeck said (September 16, 2009 @ 10:33 am)
"I would certainly say that the Cage's 4′33″ is aleatoric"
This piece is divided into three sections of different durations, and each section has smaller, non-equal parts. Cage used so-called chance procedures to determine the duration of these smaller parts, with the section durations and the overall duration derived by addition. An earlier piece which Cage described in 1948, called "Silent Prayer", was 4.5 minutes in duration, but that duration had been decided without the use of such procedures.
The downtown composer and musicologist Kyle Gann has a book on 4'33" currently with the printers.
bianca steele said,
September 16, 2009 @ 4:21 pm
Would one run afoul of libel laws if one cast aspersions on Karl Pearson's writing style?
[(myl) As I understand American laws concerning defamation, you can't defame the dead. Or anyhow, they can't sue you for it.
I suspect that opinions about the style of published works of living authors are quite safe as well. But in any case, the Pearson passage has a certain rough poetry:
There exist certain materials
for which
even in a state of ease
the stress-strain relation is not linear;
that is to say
the stress-strain curve..
is not a straight line
even
for very
small
elastic
strains.
I feel that this bears comparison with
so much depends
upon
a red wheel
barrow
etc.
But I should add that the author may actually have been Isaac Todhunter, as the quote comes from p. 503 of this work:
]
bianca steele said,
September 16, 2009 @ 7:32 pm
My memory of Pearson's prose is that it's generally more like the Godfrey Thomson quote you included. I'd have to check though. It might be some other statistician rather than Pearson himself I'm trying to think of.
Kenny Easwaran said,
September 17, 2009 @ 7:59 am
I believe Cage is standardly used as an example of aleatoric music, though of course one's understanding of "aleatory" might change depending on one's views about whether the universe is deterministic, whether there are patterns in chance, whether there is such a thing as chance, or so on. I believe he sometimes said that he used chance processes (whether I Ching or otherwise) to compose his music because it made the music more objective, in just the way that integral serialists like Boulez and the late Messiaen were trying to do by making everything as non-random as possible. Cage was trying to distance himself from the decisions – whether that meant letting some spiritual force express itself through his music or just observing the interesting patterns that came out is a question in Cage-exegesis that I can't answer (and I'm sure also can't be answered just by referring to the traditions that he references – he may have misunderstood them just as much as his interpreters have).
I think the term "aleatory music" is also sometimes used for the technique that Witold Lutoslawski and others have used, where the notes to be played are decided upon by the composer in an ordinary way, but the timing and tempo are determined independently by individual instrumentalists, so that the overall result is different every time in a way that no individual plans.
Interestingly, Iannis Xenakis is associated with a notion of "stochastic music" that he contrasts with "aleatory music". His idea is that he had some specific textural pattern he wanted (say, a bunch of pizzicato notes from the strings, gradually increasing in density over time) but didn't have particular preferences about the individual pitches or placement, so he used some stochastic process with the appropriate distribution to assign the notes.
Aaron said,
September 17, 2009 @ 10:43 am
The phrase could have been re-written to seem less awkward. I might suggest, "It is essential to know more about which treatments are effective." Notice the verbs and meaning is the same, but the new proximity brings clarity.
Back to the Cage discussion, all music and art is aleatory to some extent – that extent is sometimes up to the creator and sometimes not. Cage choose to increase the aleatory elements partly as a way to reduce his ego in the work. Yes, like Boulez. Still, having performed 4'33", I can say he was still there.