January 16, 2013 @ 8:09 am · Filed by Mark Liberman under Linguistics in the comics
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Today's Frazz:
Update — the follow-up:
January 16, 2013 @ 8:09 am · Filed by Mark Liberman under Linguistics in the comics
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Khaled said,
January 16, 2013 @ 8:47 am
I've seen this before, in a Fox Trot: http://www.gocomics.com/foxtrot/2009/02/08/
Stan said,
January 16, 2013 @ 9:03 am
British crisp makers Golden Wonder ought to look into this.
Rod Johnson said,
January 16, 2013 @ 9:12 am
0.618 is roughly 2/3? I guess.
MattF said,
January 16, 2013 @ 10:25 am
Another Frazz:
http://www.gocomics.com/frazz/2012/02/25
Andrew said,
January 16, 2013 @ 11:30 am
It's a shame that a mathematically-related cartoon has that distressingly-common abuse of "such that".
Brett said,
January 16, 2013 @ 11:43 am
I think it's the "golden" part that makes this especially funny.
Ellen K. said,
January 16, 2013 @ 12:10 pm
Andrew,
How is that an abuse of "such that", why is it particularly distressing in a mathematically-related cartoon, and what wording do you suggest the cartoonish should have used?
Ellen K. said,
January 16, 2013 @ 12:13 pm
Cartoonist
Brett said,
January 16, 2013 @ 2:40 pm
@Ellen K.: Here's a description of the mathematical use of "such that": http://mathworld.wolfram.com/SuchThat.html —in short, the phrase is used to specify which elements of a set (or more general collection) are possible referents.
And here, mathematicians are chided for using "so that," when they mean "such that": http://www.jmilne.org/math/words.html . The problem in the comic is the opposite; it uses "such" where a mathematician would only accept "so."
Bob Moore said,
January 16, 2013 @ 3:21 pm
It should be "so that" rather than "such that". "Such that" introduces a noun-modifying clause, but there the modifying clause modifies the verb, or the whole sentence, depending on your analysis.
Tom Recht said,
January 16, 2013 @ 3:46 pm
I share Andrew's peeve against "such that" without a nominal antecedent (I would write "so that" in this context), but honestly, this battle is lost. The usage seems to be pretty recent, though; at least there are no clear examples in the OED. Presumably it originates as an extrapolation from cases like the following, especially the last:
1771 Encycl. Brit. II. 695/2 At the point..K, such that the points K, H, and B may be in the same right line, let there be fixed a fourth staff.
1840 D. Lardner Treat. Geom. 288 Let a distance CB be taken on the conjugate axis, such that the square of CB shall bear to the square of CA, the same ratio [etc.].
1876 G. O. Trevelyan Life & Lett. Macaulay II. ix. 137 Statesmen, who had assumed an attitude such that they could not..avoid being..insincere.
1895 S. P. Thompson & E. Thomas Electr. Tab. & Mem. 60 The number of them is chosen such that in a cross section of the field [etc.].
In that last example, "such that" may have been intended to depend on "number", but it's very easy to take it as modifying the VP, leading to uses like "they crumble such that".
David L said,
January 16, 2013 @ 5:07 pm
I don't think "so that" can be right. If he said "they crumble so that each layer down, the chips are roughly two-thirds of the size of the chips above them," the meaning (to me) would be that the chips are crumbling, therefore the specific size ratio develops. Which in my experience with chips is not the case.
What he means, presumably, is "they crumble in such a way that etc," i.e. it is a special kind of crumbling that is going on here. I like his version better as a somewhat abbreviated way of saying this.
Tom Recht said,
January 16, 2013 @ 5:55 pm
@David L, the point is exactly that the meaning "in such a way that" is expressed by "so that" in older English, and by "such that" in newer English. It's just that you stand on the opposite side of the Great So That/Such That Divide from Andrew, Bob Moore and me.
David L said,
January 16, 2013 @ 6:24 pm
@Tom: Fair enough. "So that" in the sense you mean sounds positively 19th century to me, though (and I am not a youngster…).
David Morris said,
January 16, 2013 @ 6:43 pm
The cartoonist seems not to know his Fibonacci from his Phideas.
Rohan F said,
January 16, 2013 @ 7:39 pm
David Morris: Fibonacci numbers and the golden ratio are intimately connected. For two Fibonacci numbers F(n) and F(n+1), F(n+1)/F(n) approaches the golden ratio as n becomes arbitrarily large. I was actually quite impressed that the cartoonist was clearly aware of the connection between the two.
Andy Averill said,
January 16, 2013 @ 9:44 pm
@Rod Johnson,
1/0 + 0/1 = 1/1
1/1 + 0/1 = 1/2
1/1 + 1/2 = 2/3
1/2 + 2/3 = 3/5
2/3 + 3/5 = 5/8
3/5 + 5/8 = 8/13
…
chris said,
January 17, 2013 @ 12:04 am
@Andy Averill: Fraction addition does not work that way. Also, 1/0 is undefined.
David Morris said,
January 17, 2013 @ 5:03 am
Rohan F: sure they're related, but if you had to choose *one* mathematical model to best and most easily explain a series of progressively smaller areas, it would be the golden ratio.
Rohan F said,
January 17, 2013 @ 8:02 am
David Morris: who said anyone had to choose *one*? The artist used both and, I thought, to good effect. You said the artist "seems not to know his Fibonacci from his Phideas" [sic]; my impression was quite the opposite: the use of both implies not only that Jef Mallett does know the difference, but that he's also aware that there is a relationship between the two, which implies an even deeper understanding of the maths than simply referring to Phidias would. Aside from which, I certainly wouldn't like to try and come up with a pun on the name of Phidias that's both as easily interpreted and as outright funny as "Fibonachos".
I notice that Frazz attempts to explain it in today's comic but is rudely interrupted, so I guess we'll never know for certain:
http://www.gocomics.com/frazz/2013/01/17
Ellen K. said,
January 17, 2013 @ 10:23 am
"So that" doesn't work there for me because it would imply that the chips have the mental capacity of wanting a certain outcome. Or at least that they are crumbling that way because someone (perhaps the chip designer) desires that outcome.
As written, the comic simply describes how they crumble without reference to why.
I've no idea how this relates to the mathematical usage. Not a mathematical term I learned, and I don't follow the information at Brett's link. (I'm not uneducated in math; I pass calculus, though that was many years ago now.) But even knowing it's a math term is enough to understand Andrew's objection.
I think "in such a way that" works as an alternative wording that avoids the math term and means the same thing in ordinary English.
Still curious what Andrew would suggest as an alternative, but I guess he hasn't been back.
Ellen K. said,
January 17, 2013 @ 10:46 am
Okay, now that I've read Brett's second link, I see it agrees with what I said about "so that". That usage doesn't fit any of it's "so that" examples.
And it seems to fit perfectly with the first, non mathematical, definition of "such that".
BobC said,
January 17, 2013 @ 1:56 pm
Maybe I'm overanalyzing this, but if the chips in each layer are 2/3 the size of the chips in the layer above, that yields the geometric sequence
1, 2/3, 4/9, 8/27, etc., where each number is 2/3 of the previous number. Each term in the Fibonacci sequence – 1, 1, 2, 3, 5, 8, 13, etc. is formed by adding the two previous terms. Not the same thing.
Ellen K. said,
January 17, 2013 @ 2:23 pm
@BobC
If you do the math, other than 1,1,2 (which would be the end of the sequence in the comic), they do each number is roughly (and the word roughly is important!) 2/3 of the one that follows. And starting with 8 and 3, more particularly, just a hair under .62 (which is smaller than 2/3, thus the "roughly"; in the realm of dividing foods in the part, that counts as roughly 2/3!).
Theophylact said,
January 17, 2013 @ 3:06 pm
Rohan F: Today's "Frazz" is in fact another mathematical joke.
Andy Averill said,
January 17, 2013 @ 6:40 pm
@chris, that's the fastest way to get to the golden mean using continued fractions. You add the two numerators and the two denominators together and get the next number in the sequence.
DEP said,
January 18, 2013 @ 2:17 pm
What does the "Blue Chip" refer to?
Brett said,
January 18, 2013 @ 5:42 pm
@DEP: My first thought was that he was contrasting blue corn chips with golden ones, although there might have been another joke their that I missed, since "blue chip" has other meanings.