March 27, 2007

A reflexive too far

Stewart Nicol wrote me yesterday to ask if I could decipher the italicized sentence below, from the Wikipedia entry on the sigmoid function:

A reason for its popularity in neural networks is because the sigmoid function satisfies this property:

d/dt sig(t) = sig(t) (1 - sig(t))

This simple polynomial relationship between the derivative and itself is computationally easy to perform.

Call this the "sigmoid sentence".  Its most problematic part is the reflexive pronoun, which I have bold-faced; I have a small (though growing) collection of notable reflexives, but this one goes beyond anything I've seen so far.

I'll start by interpreting the sigmoid sentence: as I said to Nicol, it looks like sig(t) was so firmly in the writer's mind as the discourse topic that the writer found no need to actually mention it in the sentence.  Putting it in gives:

This simple polynomial relationship between the derivative of sig(t) and sig(t) itself is computationally easy to perform.

Now it makes sense; it says that the derivative of sig(t) is a simple polynomial function of sig(t) -- it's sig(t) - sig(t)2, a quadratic function.

Three side comments.  First, there's a smaller problem with the sigmoid sentence, the odd word choice "perform".  Actually, "computationally easy to perform" strikes me as just an over-elaborate way of saying "easy to compute".  All in all, the sigmoid sentence is not a bright moment in technical writing.

[Addendum: Wikipedia moves fast.  Mark Mandel reports that, in response to my Language Log posting, the sentence has been improved to: "This simple polynomial relationship between the sigmoid function and its derivative gives a computationally easy way to obtain the latter from the former."]

Second side comment: from the history of the Wikipedia entry, it seems that the sigmoid sentence was added to the neural-nets section of the entry on 27 July 2005 by a very active Wikipedian who goes by the name HappyCamper, and has been carried along ever since.  I haven't been able to find out anything about the writer personally, though HappyCamper strikes me as a native speaker of English.  If the sentence had come from a non-native speaker (like Jorge Stolfi, the originator of the entry back in 2004, who's a native speaker of Brazilian Portuguese), the astonishing reflexive might have been attributable to reflexive use in the writer's native language; it's well known that reflexives in many other languages are less tightly constrained than in English.

Third side comment: the entry doesn't mention it, but the sigmoid function comes up in linguistics.  It's graphed by the S-shaped curve that tracks the spread of one variant as against a competitor (in some context) over time, from the innovation of the variant, through an essentially exponential spread when the variant catches on, and then to the completion of the change in the triumph of the innovation.  Not all changes run to completion, of course, but sigmoidal spread is the typical course of the ones that do.  See, for example, Tony Kroch's account of the rise and spread of do-support in English, in "Reflexes of grammar in patterns of language change", Language Variation and Change 1.199-244 (1989).  In addition, the sigmoid function is the inverse of the logit function, which plays a big role in quantitative sociolinguistics; it's the basis for the VARBRUL program for analyzing variation.

Back to the reflexive pronoun itself in the sigmoid sentence.  To start with, it has no antecedent in its clause.  English usually requires reflexives to have such antecedents; see my earlier posting on reflexives for a brief account of this condition.  But there are circumstances in which reflexives can occur without such antecedents; these "override reflexives" are nicely treated in the Cambridge Grammar of the English Language (section 3.1.4 of chapter 17, pp. 1494-6).

First, there are various circumstances in which first- and second-person reflexives can occur without antecedents in their clause, or even in their sentence, or even anywhere in the preceding discourse, as in CGEL's example [39iii]:

They had invited Tim as well as myself.

(CGEL notes that the use of such reflexives "has been the target of a good deal of prescriptive criticism" -- in fact, it's on list after list of "worst errors in English" -- but maintain that "there can be no doubt... that it is well established".  It's certainly easy to collect examples from careful writers and speakers.)

But the reflexive in the sigmoid sentence is third person, not first or second.

As I pointed out in my earlier posting, third-person override reflexives are acceptable (for some speakers) in "logophoric contexts", in complements of verbs of saying or thinking, where they refer to the person responsible for the words or thoughts.  CGEL's example [39ii] is of this sort:

Ann suggested that the reporter pay both the victim and herself for their time.

But the sigmoid sentence is not a report of speech or thought.

Paul Kay has suggested to me that some of the first- and second-person override reflexives could "be thought of as, in an extended sense, logophoric.  The idea would be that the speaker can always assume the position of being in his or her own thought world, or that of the interlocutor."  Kay notes that this account could apply to a sentence from George W. Bush that Geoff Pullum has deplored here on Language Log:

And so long as the war on terror goes on, and so long as there's a threat, we will inevitably need to hold people that would do ourselves harm.

As for third-person logophoric reflexives, Paul Postal has reported to me that even people who find them unacceptable will accept them if the reflexive is extracted.  He reports contrasts between the i example, which he finds absolutely unacceptable, and the two following, which he finds much better:

i. *Victor imagines that you will praise himself.

ii. Himself, Victor imagines that you will praise.

iii. Victor may imagine that you will praise, and he certainly imagines that you will not unduly criticize, HIMSELF.

CGEL provides an example, [48], of this sort, involving the cleft construction:

i. ?She had wanted him to marry herself.

ii.  It was herself she had wanted him to marry.

CGEL attributes the increase in acceptability to contrastiveness, which is also a factor in Postal's extraction examples. 

But all these examples have reflexives with human antecedents, while the antecedent of the reflexive in the sigmoid sentence is inanimate.  And the sigmoid sentence involves neither extraction nor, in my judgment, contrast.

Now I leave clearly logophoric examples behind.  In line with Kay's observation, "Overrides with 3rd person reflexives characteristically occur in contexts where the antecedent refers to the person whose perspective is being taken in the discourse" (CGEL, p. 1495) -- for example, in free indirect style ("which can be seen as an extension of the central 1st person case"), as in this example from my collection:

Mma Makutsi looked at her watch.  Mma Ramotswe and Mr Polopetsi were away on their trip to Mokolodi -- she had felt slightly irritated that Mma Ramotswe should have chosen him to accompany her rather than herself  (Alexander McCall Smith, Blue Shoes and Happiness, p. 128)

We can see this as a representation of Mma Makutsi's thought, "I'm irritated that she should have chosen him to accompany her rather than myself."

Once again, the sigmoid sentence is not a report, even an indirect report, of thought.

There are third-person perspectival examples that are not in free indirect style (or logophoric).  The writer or speaker simply assumes the viewpoint of someone mentioned in the preceding context who is highly topical at this point in the discourse.  This mention can be in the same sentence as the reflexive:

Yet on June 26th Warren Buffett pledged to donate the bulk of his estimated $44 billion fortune to the charitable foundation created by the only man richer than himself, Bill Gates.  ("The new powers in giving", The Economist 7/1/06, p. 63)

or it can be earlier in the discourse:

Informed of her meeting with the British diplomat, Stalin accused Akhmatova of receiving "foreign spies."  It was the height of the cold war -- a conflict which Akhmatova believed was brought about by her meeting with the Englishman [Isaiah Berlin] (she "saw herself and me as world-historical personages chosen by destiny to begin a cosmic conflict," Berlin wrote).  Feinstein dismisses her belief as "megalomania," but in some ways it was bound up with her poetic myth, her image of herself as part of history.

    Certainly, the meeting had dire consequences for herself.  In August 1946 Akhmatova was attacked in a decree by the Central Committee.  (Orlando Figes, review of Elaine Feinstein's Anna of All the Russians, New York Review of Books 6/22/06, p. 42)

Even itself can occur in perspectival examples, so long as the antecedent is understood metonymically as an entity capable of having a viewpoint:

Now, however, the Homeland Security Department has proposed regulations that would give itself the authority to pre-empt state and local laws.  ("Chemical Insecurity", New York Times editorial, 1/23/07, p. A18)

The reflexive in the sigmoid sentence has an antecedent in the preceding context ("the sigmoid function"), and the sigmoid function is certainly topical, but it is NOT an entity capable of having a viewpoint.

I conclude that HappyCamper has extended override reflexives to new territory, requiring only topicality to license them.  This is well outside my zone of tolerance, and clearly outside Stewart Nicol's, since he couldn't even figure out what the sigmoid sentence was supposed to convey (and appealed to me, as a reflexives guy, for help).  I wonder how many people have made this extension; the sigmoid sentence is the first example I've come across.

[Addendum: readers are now telling me that there are huge numbers of examples of "between X and itself".  Well, of course there are.  But in all of these, "itself" is understood as referring to the denotation of X.  This is not the case with the sigmoid sentence, where "itself" refers to something, associated in some way with X, that has been mentioned in the preceding context and is highly topical at this point in the discourse.  That's the surprise.]

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Posted by Arnold Zwicky at March 27, 2007 03:28 PM