Kaspar Guttman's mastery of fractional percentage increases
June 20, 2021 6:45 AM Subscribe
Rewatched The Maltese Falcon for the 200th time, spoiler alert if you haven't seen it.
So, at the end, as Guttman is coming to terms with the fact that the whole San Francisco gambit has been a red herring, and that if he still wants the dingus he has to go to Istanbul immediately, he says:
If *I* were to figure out a percentage increase I'd take the difference between the ending and starting values (18 - 17 = 1), then divide that number by the starting value and make it into a percentage by multiplying by 100. (1/17 = 0.05882352941, or 5.88%) I did that with a calculator, obviously. In my head I could get to, "Uh, just under 6?" with pencil and paper I could get to 5.88.
But Guttman is doing it in fractions, in his head. And he is clearly doing it to show (as a character!) that he is a smart, refined, educated fellow. He knows some formula, an algorithm, that he uses to get to the answer, and he IS a smart guy, so he does it quickly. But he's not a mathematical savant!
Certainly, back in 1941, when the only way to do this sort of math was manually, people were just better at it. And maybe this is one of those things that is just EASIER with fractions.
At any rate: how does he do it? More to the point, since it is a MOVIE, and the truest answer is "that's what was written in the script", how would someone quickly and mentally determine that adding one more year to a 17 year investment is a 5 and 15/17ths percent increase?
So, at the end, as Guttman is coming to terms with the fact that the whole San Francisco gambit has been a red herring, and that if he still wants the dingus he has to go to Istanbul immediately, he says:
Seventeen years I've wanted that item, and have been trying to get it. If we must spend another year on the quest...well, sir, it will be an additional expenditure in time of only...five and fifteen-seventeenths percent.... and as he is saying this he is clearly doing the calculation in his head. How?
If *I* were to figure out a percentage increase I'd take the difference between the ending and starting values (18 - 17 = 1), then divide that number by the starting value and make it into a percentage by multiplying by 100. (1/17 = 0.05882352941, or 5.88%) I did that with a calculator, obviously. In my head I could get to, "Uh, just under 6?" with pencil and paper I could get to 5.88.
But Guttman is doing it in fractions, in his head. And he is clearly doing it to show (as a character!) that he is a smart, refined, educated fellow. He knows some formula, an algorithm, that he uses to get to the answer, and he IS a smart guy, so he does it quickly. But he's not a mathematical savant!
Certainly, back in 1941, when the only way to do this sort of math was manually, people were just better at it. And maybe this is one of those things that is just EASIER with fractions.
At any rate: how does he do it? More to the point, since it is a MOVIE, and the truest answer is "that's what was written in the script", how would someone quickly and mentally determine that adding one more year to a 17 year investment is a 5 and 15/17ths percent increase?
Best answer: Along the same lines as madcaptenor: he's calculating 100/17 (that is, 100 percent times 1 additional year divided by 17 years already spent). 17 goes into 100 5 times, with a remainder of 15 (or 17 * 5 = 85 = 100 -15). So 100/17 is equivalent to 5 + 15/17, or "five and fifteen-seventeenths percent".
posted by firechicago at 7:25 AM on June 20, 2021 [9 favorites]
posted by firechicago at 7:25 AM on June 20, 2021 [9 favorites]
1/17=x/100 (this is a “formula” that will get you a percentage)
17x=100 (cross-multiply, that is, you’re multiplying the top of one side times the bottom of the other, google can explain why this works if you need)
X=100/17
Then finish as firechicago demonstrated. You wouldn’t go from decimals to fractions, you would just leave it as a fraction before you even get to that step.
All that said, I couldn’t have thought of all those steps on the spot, but with a little time to think through it, that’s how I’d do it.
posted by Night_owl at 8:40 AM on June 20, 2021 [2 favorites]
17x=100 (cross-multiply, that is, you’re multiplying the top of one side times the bottom of the other, google can explain why this works if you need)
X=100/17
Then finish as firechicago demonstrated. You wouldn’t go from decimals to fractions, you would just leave it as a fraction before you even get to that step.
All that said, I couldn’t have thought of all those steps on the spot, but with a little time to think through it, that’s how I’d do it.
posted by Night_owl at 8:40 AM on June 20, 2021 [2 favorites]
Also, I would say that just doing this stuff a lot makes it tons faster and after a while there are some answers you just know. My son was into "number sense" competitions which involve doing stuff like this or even a lot more complicated in your head, no scratch paper, are not allowed to change your answers, and under strict time pressure. He can answer any of the types of math questions he studied just off the top of his head no problem.
Learning the methods and then practicing them a lot makes it seem easy
posted by RustyBrooks at 9:44 AM on June 20, 2021 [3 favorites]
Learning the methods and then practicing them a lot makes it seem easy
posted by RustyBrooks at 9:44 AM on June 20, 2021 [3 favorites]
Certainly, back in 1941, when the only way to do this sort of math was manually, people were just better at it. And maybe this is one of those things that is just EASIER with fractions.
I think these are both true, and I'd add a third related point: in the world before electronic calculators, I believe, quotient-and-remainder was the expected form of answer to an integer division problem (unless there was some reason to prefer a decimal, which requires more work). Today, influenced by calculators and computers, we're more likely to think of decimals as the expected form, and perhaps to be blind to the alternative.
posted by aws17576 at 12:50 PM on June 20, 2021 [3 favorites]
I think these are both true, and I'd add a third related point: in the world before electronic calculators, I believe, quotient-and-remainder was the expected form of answer to an integer division problem (unless there was some reason to prefer a decimal, which requires more work). Today, influenced by calculators and computers, we're more likely to think of decimals as the expected form, and perhaps to be blind to the alternative.
posted by aws17576 at 12:50 PM on June 20, 2021 [3 favorites]
It was probably more valuable to be practised at it in those days. My grandfather's education ended at age 12 but he had a talent for mental arithmetic that was praised and encouraged by his his grade school teachers. When he joined the British army at the outset of WWII, this ability was noted and it got him a position as an artillery captain. He ended up running an Italian POW camp in North Africa before returning home to take a management position at city hall. It seems to me that a keen sense for numbers was the sort of skill that could help you transcend class barriers.
posted by bonobothegreat at 3:06 PM on June 20, 2021 [1 favorite]
posted by bonobothegreat at 3:06 PM on June 20, 2021 [1 favorite]
The way you do it is, you guesstimate it to as close as possible, then fling out a number with confidence and before anyone else has a chance to check it, you've moved on. The impression that you knew the number sticks with everyone.
My point is, I never thought to take Guttman's arithmetic was valid. I always assumed throwing out the number was a magic trick, done for the wow factor. That it is a precise number just makes it sound more certain but like much about Guttman, is mostly schtick. I'm 89.63% certain of this.
posted by From Bklyn at 1:57 AM on June 21, 2021 [1 favorite]
My point is, I never thought to take Guttman's arithmetic was valid. I always assumed throwing out the number was a magic trick, done for the wow factor. That it is a precise number just makes it sound more certain but like much about Guttman, is mostly schtick. I'm 89.63% certain of this.
posted by From Bklyn at 1:57 AM on June 21, 2021 [1 favorite]
I think the easiest way to think of it is that he is trying to find out “what percent of 17 years is one year”. So he divides 100 percent by 17. The simplest way to do it is to note that 100/20 is 5, the difference between 20 and 17 is 3, and 3 x 5 is 15.
So as an example if he’d been looking for 23 years he could note that 100/25 is 4, and 4 x 2 is 8, to come up with an increase of “four and eight twenty-thirds percent”.
posted by lsy at 9:36 AM on June 21, 2021 [2 favorites]
So as an example if he’d been looking for 23 years he could note that 100/25 is 4, and 4 x 2 is 8, to come up with an increase of “four and eight twenty-thirds percent”.
posted by lsy at 9:36 AM on June 21, 2021 [2 favorites]
John Huston basically used the novel as the script, so technically Dashiell Hammett did the math when he wrote the book and presumably had plenty of time to do the math. Sydney Greenstreet just had to read the line as Kasper Gutman, and he did great.
posted by kirkaracha at 2:51 PM on June 21, 2021
posted by kirkaracha at 2:51 PM on June 21, 2021
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posted by madcaptenor at 6:47 AM on June 20, 2021 [2 favorites]