## Almost every 90 seconds

Max Heiman wrote to me with a nice point. I present it here as a guest post.

An ambiguity in a New York Times story caught my eye:

But in the wake of the financial crisis, attendance at the [Museum of American Finance] ― located at 48 Wall Street, near the epicenter of last year’s market collapse ― has risen to about 200 visitors a day, nearly double its tally last summer. (The Metropolitan Museum of Art averages that many visitors almost every 90 seconds.)

Quiz: does the Met average more or less than 200 visitors every 90 seconds?

If I were to read, "The winner ate 200 hot dogs in almost 90 seconds", my reaction would be, (1) "Gross!", and (2) "It took slightly longer than 90 seconds to eat all those hot dogs."

But in the museum example I interpreted the meaning (after a pause) in the opposite way, as 200 visitors arriving in slightly less than 90 seconds.

What struck me as interesting is that I realized that, during that pause, I was thinking about how the sentence wasn't written — specifically, in the unambiguous form "[the Met] averages almost that many visitors every 90 seconds" — and then deciding that the ambiguous version in front of me must mean the opposite.

I realize there are some problems with this analysis. For example, the author could have written "[the Met] averages more than that many visitors every 90 seconds" but this didn't occur to me as the 'unambiguous' counterpart to what I read.

My main point is that I noticed my mind trying to resolve ambiguity not by taking apart the sentence that was there, but by comparing it to the sentences that weren't.

— Max Heiman

1. ### JimG said,

August 24, 2009 @ 6:24 am

I think the sentence means that the museum almost reaches 200 visitors every 90 seconds. Occam's Razor might have us assume only that the journalist and editors weren't precise, and that the museum's average is 200 visitors in 91 seconds. IMO, it's more common to write this way about almost meeting a standard, and I think it's an overinterpretation to find that the sentence means the museum gets more than 200 visitors every minute and a half.

BTW, as of mid-2008, MOMA was asserted to have averaged 5.2 million visitors per year, open 55 hours a week plus 8 hours on holiday Mondays — Somebody else can choose a calendar and do the math.

[(myl) Leaving out the holiday Mondays, that tally works out to 90*5200000/(55*52*60*60) = 45.45 visitors per 90 seconds. Obviously, this is roughly a factor of four slower than the claimed rate of visitation.

The holiday Monday times will be added to the denominator of the expression, not the numerator, so the estimate of visitors per 90 seconds will go down, not up.

MOMA is not the Metropolitan Museum, however — but the MM's annual report for 20072008 cites "4.45 million visitors to the main building alone", and this page of worldwide museum attendance figures lists which the Metropolitan's figure as 4.82 million (and MOMA's as 2.8 million!), which suggests that the calculation will not be very different from the one given above.

Hypothesis: the correct average rate is about one visitor every two seconds; the writer remembered this as two visitors per second, and reckoned that 180 visitors every 90 seconds, on average, could be described as 200 visitors "almost every 90 seconds", since 180 is almost 200.]

2. ### Rubrick said,

August 24, 2009 @ 6:35 am

My interpretations of the original quote and the hot dog version were exactly the opposite of yours (and in keeping with JimG's analysis).

3. ### Chris H said,

August 24, 2009 @ 6:42 am

I also can't tell if the Met is supposed to is supposed to match the finance museum's new tally, or its tally last summer.

4. ### Ray Girvan said,

August 24, 2009 @ 6:43 am

To me, "200 hot dogs in almost 90 seconds" = (say) 200 hot dogs in 89.9 seconds. But to me it feels unidiomatic: I'd write it as "in just under 90 seconds".

5. ### Laura said,

August 24, 2009 @ 6:46 am

I also interpret it the way JimG does – though it did give me pause. The reason for this is that there is a contrast, and so the writer wants to show as big a difference as possible between the two mueums' visitor numbers. If it was more than 200 visitors every 90 seconds, they'd say so. Therefore, this can only mean that they get nearly 200 visitors every 90 seconds (or, if you like, 200 visitors is almost every 90-second period). But again, as Max points out, I am comparing it to what isn't there – a pragmatic analysis seems to be the only way out of this ambiguity. (Is that a defining feature of an ambiguity?)

I often notice similar constructions in relation to sales: "up to half price!" – is it more or less than half price? Some shops get round this with the clunky "Better than half price" offer, but don't seem to like "less than half price" so much – maybe the word 'less' is offputting to shoppers.

6. ### Faldone said,

August 24, 2009 @ 7:09 am

My first interpretation was the opposite of JimG's To get his meaning I would have written "almost 200 visitors every 90 seconds."

7. ### Terry Collmann said,

August 24, 2009 @ 7:50 am

I can't read the quote in any other way than meaning "200 visitors in less than 90 seconds".

8. ### MattF said,

August 24, 2009 @ 8:44 am

Had to think about it, but decided that the phrase in question means "averages up to that many visitors every 90 seconds." I.e., that "200 visitors every 90 seconds" is an upper bound on the average.

9. ### Ginger Yellow said,

August 24, 2009 @ 9:14 am

I'm with Rubrick (and hence JimG) on both quotes.

It seems there's a difference in how we (or I, at least) interpret "almost every 90 seconds" and "in almost 90 seconds"

10. ### ø said,

August 24, 2009 @ 9:38 am

200 visitors in almost 90 seconds would be unambiguous to me. (The average is a bit less than 90.)

200 visitors almost every 90 seconds probably means the same, but I'm just guessing.

The half-price comment reminds me that I enjoy fishing for ambiguity in expressions like "That figure is only approximate." (approximate = close, but "only approximate" probably means not very close)

11. ### Mr Punch said,

August 24, 2009 @ 9:39 am

I read the sentence as missing a couple of commas:

"The Metropolitan Museum of Art averages that many visitors, almost, every 90 seconds."

12. ### Dan Milton said,

August 24, 2009 @ 9:47 am

Aware as I am of Language Log's attitude that Vox Populi determines usage, I still can't refrain from ventilating one of my peeves.
From Wikipedia: "The epicenter or epicentre is the point on the Earth's surface that is directly above the hypocenter or focus, the point where an earthquake or underground explosion originates. The word derives from the Greek ἐπίκεντρον (epikentron), "occupying a cardinal point", from ἐπί (epi), "on, upon, at" + κέντρον (kentron), "centre"[1]."
Unless the market collapsed in a subbasement of 48 Wall St., "center" would have been quite sufficient.

13. ### Franz Bebop said,

August 24, 2009 @ 9:48 am

There's a similar ambiguity in this phrase:

I almost ran a 4-minute mile.

In both cases, the ambiguity is between "almost" referring to the entire fraction (200 visitors / 90 seconds, or 1 mile / 4 minutes) versus referring to just part of the fraction (90 seconds, or 4 minutes).

My main point is that I noticed my mind trying to resolve ambiguity not by taking apart the sentence that was there, but by comparing it to the sentences that weren't.

Is this a surprise? Does your mind need to "take apart" a sentence consciously in order to interpret it?

Hypothesis: on some level, the ambiguity of the phrase was crystal clear to your mind, and what you were evaluating was, which of these perfectly valid interpretations makes any real-world sense, under the circumstances? Producing alternate sentences seems like a good way to go about this. Hold each interpretation up to the light, so to speak, and see which one makes sense.

14. ### J. W. Brewer said,

August 24, 2009 @ 11:23 am

Dan M. Is your peevishness directed to the basic metaphor of a decline in market prices for securities as earthquake-like (perhaps because metaphors are inherently bad, because necessarily untrue in some peevishly literal sense?), or to the specific positioning of the metaphorical epicenter given that underlying metaphor? If the latter, what's your alternative nominee for the location of the metaphorical epicenter? (Note that it said "near" not "at" 48 Wall, which is about block and a half away from the New York Stock Exchange, although of course most of the other institutions collectively referred to as "Wall Street" are no longer literally physically headquartered on or even necessarily near Wall Street.)

15. ### Jonathan said,

August 24, 2009 @ 11:28 am

That's 64,000 visitors for an 8 hour day. How many days is the museum open? This sounds like more than 4 times more than the 5.2 million figure. I can't believe the MOMA sells more than two tickets ON AVERAGE for each second that it is open (allowing for slow times, and the fact that they won't be letting people in when the museum is about to close). Or does it mean that in any given 90-second period there are 200 people in the museum? Either way it seems an odd way of making the comparison.

16. ### mgh said,

August 24, 2009 @ 11:50 am

Franz Bebop, exactly.

Jonathan, according to the annual report (PDF, p. 6, "Visitorship") of the Met (not MoMA), fiscal year 2008 saw 4.45 million visitors at the main building (the Met also operates the Cloisters, which had an additional 216,000 visitors). They note some extremely high-attendance days of 30,000 visitors, far less than would be predicted from 200 (or 400) visitors in slightly more than (or less than) 90 seconds.

-Max

17. ### Richard Sabey said,

August 24, 2009 @ 11:51 am

I reach the same conclusion as JimG.

"Every" is between "almost" and "90 seconds", so the reader can't interpret "almost" as modifying "90 seconds". Rather, "almost" must modify the phrase "every 90 seconds". Thus, to me, "200 visitors almost every 90 seconds" unambiguously means a rate which is close to, and less than, a rate of 200 every 90 seconds.

18. ### Graham said,

August 24, 2009 @ 11:59 am

JimG/myl – Isn't MOMA the Museum of Modern Art, not the Metropolitan Museum of Art? Are they different museums? If so, maybe the journalist is not guilty of bad arithmetic (although a 2 minute google search indicates that the Metrpolitan Museum of Art also gets around 5 million visitors a year with presumably similar opening times…)

19. ### Keshav Srinivasan said,

August 24, 2009 @ 12:15 pm

The meaning seems, at least to me, to be completely clear. When it says that the Met averages 200 visitors almost every 90 seconds, my mind automatically interprets that as "It is almost true that the Met averages 200 visitors every 90 seconds." In other words, visitors come to the Met slightly less often than a rate of 200 visitors per 90 seconds.

This interpretation is consistent with how other similar phrases are interpreted. For instance, suppose someone says, "My gas mileage is so bad that I have to go to the gas station almost every two days." What this means seems clear: I have to go to the gas station slightly less often than a rate of one visit every two days.

August 24, 2009 @ 12:30 pm

I tend to agree with JimG, which is putting MaxH firmly in the minority. The latter's interpretation of his hot-dog example seems particularly bizarre to me.

21. ### Nathan Myers said,

August 24, 2009 @ 1:05 pm

When I read it I instantly pictured a histogram, with the day divided into 90-second intervals. The count in many of such intervals should exceed 200. However, the meaning of "averages" in this context is strange; maybe I'm supposed to scrape the extras from each bin and bulldoze them into the short ones. After the top has been leveled, most bins are supposed to reach 200.

Extra points for making me think statistically. Minus points for distracting me by an odd construction that means the same as a familiar one.

22. ### Andrew said,

August 24, 2009 @ 2:02 pm

My instinct was the same as Nathan Myers' – it means 'during almost every period of ninety seconds' – though it's true that 'averages' is odd in this context. The meaning would then be close to 'almost 200 visitors every ninety seconds', although the way it's constructed is different.

This means that one gets similar results by reading 'almost' with 'every' (which is what a strict compositional reading would suggest) and with '200 visitors' (which is probably what is intended). The opposite meaning is achieved only if you take it with 'ninety seconds', but that seems very unnatural.

23. ### Mark F. said,

August 24, 2009 @ 3:06 pm

I tend to think it's so ill-phrased that trying to assign one reading or the other to it is futile. This seems especially so now that we know it's off by a factor of four anyway.

The problem I see with the reading "almost every (presumably nonoverlapping) 90-second period had at least 200 visitors" is that it suggests that either the rate of visitation was very uniform, or the average number of visitors per 90-second period was a lot more than 200. If the average rate were close to 200, with a moderate amount of variation, then a lot of 90-second periods would have fewer.

24. ### Andrew said,

August 24, 2009 @ 3:23 pm

Mark F: Yes, it would have odd implications. On the other hand, 'almost 200 visitors every ninety seconds' could be taken to mean that every ninety-second period, without exception, had almost 200 visitors. I wonder if the odd phrasing was intended to stop this implication.

25. ### Garrett Wollman said,

August 24, 2009 @ 3:40 pm

Wasn't Doug Hofstadter writing about the cognitive framing of "near misses" like this about twenty-five years ago? I seem to remember reading something of the sort, but I can't remember what he said any more.

26. ### Coby Lubliner said,

August 24, 2009 @ 3:43 pm

I agree with JimG and Richard Sabey in that there is no ambiguity in the original statement, regardless of its correctness. I wonder if Max Heiman would have been confused had he come across "almost every day"; I somehow doubt it. Well, "every [period]" defines a frequency, and when modified by "almost" a slightly lower frequency, i.e. a slightly longer period.

27. ### Jerry Friedman said,

August 24, 2009 @ 6:06 pm

I'm in no doubt that the meaning was, "The rate is almost one every 90 seconds."

I wonder whether this example has more to do with syntax than semantics. It corroborates my only theory in linguistics, which is that lots of people are surprisingly immune to syntax. This theory is based on one fact: When I show my students Moses Hadas's famous line, "This book fills a much-needed gap," none of them get it immediately, and a lot of them don't get it even after some thought. Likewise if you search the Web for "much-needed gap", you'll find that a lot of people use the line as praise.

The same thing seems to be going on here. Where almost comes in the sentence doesn't matter; the author knows what he or she means, and so do the majority of readers, based on the kinds of meaning that almost is used for, not the syntax. But it confuses some readers, so it's bad writing.

(I show my students Hadas's line to emphasize the importance of reading math and physics problems carefully, since many of them start working with the numbers without noticing the syntactic relations that often indicate the conceptual relations. But maybe I should find an easier example.)

28. ### roscivs said,

August 24, 2009 @ 11:41 pm

Weird. I interpret "almost 90 seconds" in both cases to mean something like "89 seconds". So if you eat 200 hot dogs in almost 90 seconds, perhaps it took you 87 seconds instead. I agree that it doesn't seem very idiomatic, however.

29. ### Haamu said,

August 25, 2009 @ 1:00 am

This seems to be the linguistic equivalent of a Necker Cube. For me it resolved after a moment's thought to the opposite of what Max perceived.

90 seconds is a period or interval. 89 seconds is almost 90 seconds. 91 seconds is not: it is more.

Every 90 seconds, on the other hand, is a frequency, and since frequency is the reciprocal of period, it stands to reason that the opposite should be true: Every 91 seconds is almost every 90 seconds. Every 89 seconds is not: it is more.

So "[200] visitors almost every 90 seconds" is 200 every 91 or 92 or 93 seconds, not every 88 or 89 seconds.

30. ### Noetica said,

August 25, 2009 @ 4:25 am

Here's my favourite, in the same broad class of uncertainties:

Ever since long-life, non-incandescent light bulbs first appeared in Australia, they have been promoted with these two statements:

1. They give 5 times as much light as normal bulbs of the same wattage.
2. They last "up to 8 times as long as normal bulbs".

Now, the first claim is questionable, and perhaps a matter of definition. The spectral characteristics of the two types are different. Generally, I find that a 20-watt long-life was not as good as a 100-watt normal. Never mind.

But the second claim is almost meaningless. The devil is in the "up to". Consider this statement:

3. Normal bulbs last up to 8 times as long as normal bulbs.

An impressive claim, and probably true. I think I want some of those normal bulbs! There are a few outliers that last 8 times as long as the quickest to burn out. But wait: the claim is ridiculously modest. Some bulbs last only a second or so. Make that "up to 80,000 times as long".

We're obviously supposed to compare the life of the longest-lived bulbs with the average life, you object? Well, certain outliers last 8 times as long as the average. Statement 3 still holds.

So what are we to make of statement 2? If the average life of one sort is 8 times the average life of the other sort, fine. Say so! Some sort of weaker claim is being made: but no one explains what that might be, among the few coherent candidates. Not in the information the consumer sees, anyway.

31. ### Franz Bebop said,

August 25, 2009 @ 5:02 am

I think this thread has sufficiently (re-)established the motivation for employing mathematical notation rather than natural language.

32. ### mollymooly said,

August 25, 2009 @ 10:39 am

My two cents on this unintended poll: "almost" in sentences of the given type means "An impressive statistic is not true; but a slightly less impressive equivalent is indeed true". Adjust relevant number up or down accordingly.

80s joke:
"Ronald Reagan is still a virile man: Nancy tells me he makes love almost every night. Almost on Monday, almost on Tuesday, …"

33. ### Graeme said,

August 25, 2009 @ 7:18 pm

I confess I don't get this thread – except to say what precision merchants we are when it comes to anything numerical (yet praise the fluidity and ambiguity in language, especially evolving vocabulary).

No casual reader (and it is a newspaper reporting an analogy for colour) would read this any way but that 'almost' means 'not quite'.

'On average' ie over a representative period.
'Almost' ie not quite. Journo wanted to accentuate the relative numbers; would not have underestimated.
'90' seconds, chosen as the nearest round number. Journo could have recalculated to 'per minute', but then the number of patrons may have become a fraction and the link to the base figure of 200 would have evaporated.