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.]
zwicky at-sign csli period stanford period edu
Posted by Arnold Zwicky at March 27, 2007 03:28 PM