The new math

SeaRaven · **Posted:** Sat Nov 08, 2003 9:17 pm

The Washington Post
JERUSALEM - Israeli soldiers shot and killed as many as four Palestinians in the West Bank and Gaza Strip on Saturday, an Israeli military spokesman and Palestinian security officials said, bringing to at least nine the number of Palestinians killed by Israeli security forces in the last two days.

SeaRaven · **Posted:** Mon Nov 10, 2003 1:20 am

FYI: The problem with that lede is that it presents a mathematical inequality that is either fallacious or altogether meaningless.

wordygurdy · **Posted:** Mon Nov 10, 2003 2:20 pm

SeaRaven,At the risk of sounding ignorant, I have to admit that I don't see the problem with that lede, especially if the next graf or the graf after that goes on to explain that five Palestinians had been shot and killed by Israeli security forces the day before. Five plus four equals nine, right?I'm not arguing with the premise that copy editors should root out and eliminate false mathematical equations. I'm just saying in this case I don't see the problem.How would you have changed the lede?

SeaRaven · **Posted:** Mon Nov 10, 2003 5:56 pm

The sentence suggests that it is giving us all of the information we need to add todayâ€™s number of fatalities with yesterdayâ€™s to reach a two-day sum of â€œat least nineâ€: X+Y>=ZX is given as â€œas many as four,â€ which could be 4, 3, 2, 1 or even 0, because the sentence leaves open the possibility that no one was killed today. Z is given as a range of whole numbers from 9 to infinity (theoretically). The temptation is to assume that â€œat least nineâ€ is obtained by adding X=4 to Y for a sum of Z=9, which would make Y=5. But that doesnâ€™t make sense, because 4 is a maximum and 9 is a minimum. We canâ€™t determine the minimum value of Z without knowing the minimum value of X. Since it might be true that X=0, it could be true that Y=9. It turns out that there were three known new fatalities, and a fourth was in dispute. (And six Palestinians had been killed the previous day, not five.) Therefore, it would have made more sense to use X>=3 in the lede and delay mention the possible fourth: JERUSALEM - Israeli soldiers shot and killed at least three Palestinians in the West Bank and Gaza Strip on Saturday, an Israeli military spokesman and Palestinian security officials said, bringing to at least nine the number of Palestinians killed by Israeli security forces in the last two days.OR:JERUSALEM - Israeli soldiers shot and killed as many as four Palestinians in the West Bank and Gaza Strip on Saturday, an Israeli military spokesman and Palestinian security officials said, bringing the number of Palestinians killed by Israeli security forces in the last two days to as many as 10.Either of those approaches is more logical than the original, but I would prefer to avoid the putting the running death toll in the lede and just report the â€œnewsâ€ there. That way there would be room to give proper attention to the disputed fourth death. The Post was trying to jam too many numerical concepts into the lede, and it just didnâ€™t add up.See what I mean?

wordygurdy · **Posted:** Mon Nov 10, 2003 6:25 pm

Yes, thanks, I see now. Having the information on the actual number of deaths makes the difference.

Dyslexic · **Posted:** Tue Nov 11, 2003 2:12 am

I've given this some thought and keep coming to the conclusion that it makes sense mathematically. Whether or not it makes sense semantically is another issue.Given:
x = Number of Palestinians killed on Saturday = {0..4},
The total number of Palestinians killed = {9..infinity},We have:
Palestinians killed on Saturday + Palestinians killed on Friday = Total number of Palestinians killed
(By logical inference)Which is equivalent to:
x + {9-x..infinity} = {9..infinity}Which is equivalent to:
Total number of Palestinians killed = x + {9-x..infinity}.
(By definition of {9..infinity})If someone can find a value for x that does not agree with lede, let me know.[ November 11, 2003: Message edited by: Dyslexic ]

SeaRaven · **Posted:** Tue Nov 11, 2003 9:05 am

<blockquote>quote:<hr>Originally posted by Dyslexic:
If someone can find a value for x that does not agree with lede, let me know.
<hr></blockquote>Right. That is precisely the problem: It's clearly true algebraically, but it doesn't answer any questions. There are too many possible solutions for it to have meaning in the context of this news story.As I said, the lede is either fallacious or meaningless, and you've outlined the meaningless interpretation.The fallacious interpretation is to assume X=4, Y=5, and the seductiveness of that trap was demonstrated earlier in this thread.Neither interpretation is what the lede was actually trying to say, which demonstrates the shortcomings of how it was written.The lede gave us X<=4, but we needed the full 3<=X<=4 in order to comprehend the intended meaning. Without knowing either the answer to "X = at least ?" or "Y=?," we can't relate the other variables to "Z = at least 9" other than "Z = at least Y," which we could have predicted with certainty from the previous day's story anyway (barring unforeseen resurrections). Or, we could have deduced that "Y is at most 9," but there would be little point.If readers had recalled from the previous day that Y=6, they could have solved for X and figured out what the lede was supposed to mean. Or they could have read the rest of the story to figure out what the lede meant, which is what our copy desk had to do to fix the lede.But readers shouldn't have to do that. The lede of a hard news story is supposed to comprehensibly synopsize the most important facts that are being reported, not deliver a nonsensical, misleading puzzle.[ November 11, 2003: Message edited by: SeaRaven ]

Dyslexic · **Posted:** Tue Nov 11, 2003 12:44 pm

So, what you are saying is that the lede makes sense mathematically, but is too abstract to be in a newspaper. I agree.

SeaRaven · **Posted:** Tue Nov 11, 2003 1:28 pm

Iâ€™m saying that the lede is unclear about what itâ€™s trying to say and that it tricks many readers into a false understanding of whatâ€™s being reported.It offers three variables but not enough information to construct an adequate equation system (or weak inequality system) for determining useful solutions to all three variables, although it pretends to be a complete and soluble system. Few readers will think in those terms in trying to comprehend the lede, but that is the logic behind the inherent confusion.Itâ€™s possible, as you showed, to derive algerbraic identities from the given information, but thatâ€™s not really a mathematical solution. It still leaves the reader with an unnecessarily wide range of possible answers to the question: â€œHow many people were killed?â€The writer knew that the answer was â€œat least three, possibly four.â€™â€™ Thatâ€™s what was missing from the lede: a simple statement of the essential fact that had prompted the writing of the story.[ November 11, 2003: Message edited by: SeaRaven ]

majorbabs · **Posted:** Tue Nov 11, 2003 6:09 pm

There are just way too many math majors on this board. But thanks for the education. I feel like I've just been through senior algebra -- again -- but without the cute guy who sat next to me. Blanp? Are you there?

Phillip Blanchard · **Posted:** Tue Nov 11, 2003 6:13 pm

<blockquote>quote:<hr>Originally posted by majorbabs:
There are just way too many math majors on this board. But thanks for the education. I feel like I've just been through senior algebra -- again -- but without the cute guy who sat next to me. Blanp? Are you there?<hr></blockquote>Like I made it to "senior algebra."

jjmoney62 · **Posted:** Tue Nov 11, 2003 7:20 pm

Math majors can be such geeks.That's why I'm only a math minor.And I've got to say, that convoluted algebra combined with the Middle East is mind-numbingly numbing.

SeaRaven · **Posted:** Tue Nov 11, 2003 7:52 pm

You're quite right, jj. I'll return to lampooning the job listings for a while.

ADKbrown · **Posted:** Wed Nov 12, 2003 6:08 pm

<blockquote>quote:<hr>Originally posted by Dyslexic:
Given:
x = Number of Palestinians killed on Saturday = {0..4},
The total number of Palestinians killed = {9..infinity} ... <hr></blockquote>But there could not have been an infinite number of Palestinians killed (not that Sharon isn't trying his best). The story said only five were killed (or six, depending on the write-thru) on the first day and as many as four on the second day. So it's at most nine (or 10) and at least five (or six).[ November 12, 2003: Message edited by: ADKbrown ]

SeaRaven · **Posted:** Thu Nov 13, 2003 3:01 am

I had my fingers crossed when I said I was done with this thread. Which explains the quality of the typing.One more time, with less math:(If A and B, then C)If exactly 6 apples were in the bowl,
and we added at least 3,
there are now at least 9.
= VALID CONCLUSIONIf exactly 6 apples were in the bowl,
and we added as many as 4,
there are now as many as 10.
= VALID CONCLUSIONIf exactly 6 apples were in the bowl,
and we added as many as 4,
there are now at least 9.
= INVALID CONCLUSIONMoreover, the lede didnâ€™t even tell us how many apples were initially in the bowl. Worse still, it led many readers, as we have seen in this thread, to conclude that there were 5, although the true number was 6. Another dimension of the problem in the lede is that the word â€œbringingâ€ strongly implies that a legitimate arithmetical operation is taking place, as in â€œSosa hit 3 home runs Saturday, bringing his season total to 48.â€ However, the figure in the lede that â€œbroughtâ€ the running total to â€œat least 9â€ was not logically capable of doing so.The lede contained two valid figures that were certainly worth reporting, but it tried to connect them in an illogical and confusing way.OK. Carry on.p.s. -- MS Word spellchecker wants me to change â€œless mathâ€ to â€œfewer maths.â€---[ November 13, 2003: Message edited by: SeaRaven ]

SeaRaven · **Posted:** Thu Nov 13, 2003 4:22 am

I just noticed something. Although itâ€™s wildly unlikely that anyone besides John Ashcroft is still listening, my definition of Z should have been either:X+Y=Z;
Z lies somewhere in a range of whole numbers from 9 to infinity. Or:
X+Y>=Z;
Z is given as 9.But not:
X+Y>=Z;
Z is given as a range of whole numbers from 9 to infinity.See why?(Itâ€™s just a technical correction of a typo and doesnâ€™t affect the analysis.)

Phillip Blanchard · **Posted:** Thu Nov 13, 2003 5:30 am

Mary has three apples.Q. How many apples does Mary have?

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