[math-fun] N-athlon proposal and the Rain Man
I’ve been absent from math-fun for a while, but from a quick glance at recent posts I see mention of N-athlons and visual estimation of shapes. Strangely, these combine in a new, untested, race that involves parked cars. The idea is to have the runners shout out the N-fold symmetry of the parked car hubcaps as they are passing them. You’d have to space the runners, so they cannot hear each other. But I think you get the idea: to get a good time you can’t afford to stop and count spokes (or whatever) to determine N. For example, you can train your eye/brain to determine if there is a line of bilateral symmetry, and then the existence or non-existence of an equivalent line orthogonal to that. Now you are dealing with N congruent to 0 or 2 mod 4, and for N not too large (<20) the ball-park-estimate part of your brain should be able to quickly arrive at say, 18 (don’t ask me why, but they exist). In the movie Rain Man, the title character was able to count objects almost instantaneously, up to the hundreds. Such people would do very well in my proposed race, and without clever tricks … or so you would think. Although it’s been a long time since I saw that movie, I clearly recall that when he was counting the number of spilled matches on the floor he verbalized 62,62,62,62 … 248 (please correct me if I got the numbers wrong). So it seems the Rain Man was able to directly see the factorization! Alternative hypothesis: he really liked 62 as a unit, and it was a lucky accident that it came out even. -Veit
VE: "I clearly recall that when he was counting the number of spilled matches on the floor he verbalized 62,62,62,62 … 248 (please correct me if I got the numbers wrong)." From quotegeek: Raymond: 82, 82, 82. Charlie: 82 what? Raymond: Toothpicks. Charlie: There’s a lot more than 82 toothpicks, Ray. Raymond: 246 total. Charlie: How many? Sally Dibbs: 250. Charlie: Pretty close. Sally Dibbs: There’s four left in the box. I have to say, it was this part more than anything else in the movie that ruined for me the credibility of the Raymond Babbitt character.
On 2018-08-01 16:48, Hans Havermann wrote:
VE: "I clearly recall that when he was counting the number of spilled matches on the floor he verbalized 62,62,62,62 … 248 (please correct me if I got the numbers wrong)."
From quotegeek:
Raymond: 82, 82, 82. Charlie: 82 what? Raymond: Toothpicks. Charlie: There’s a lot more than 82 toothpicks, Ray. Raymond: 246 total. Charlie: How many? Sally Dibbs: 250. Charlie: Pretty close. Sally Dibbs: There’s four left in the box.
I have to say, it was this part more than anything else in the movie that ruined for me the credibility of the Raymond Babbitt character.
Because 82 isn't prime? I believe this skill (the ability to see large numbers, exactly, instantly) is either (1) not so rare, or (2) based explicitly on observations by Oliver Sacks of twin savants who were able to identify the number of matches dropped on the floor (possibly by prime factorization of the random skill) or (3) Oliver Sacks was mistaken. If you search for Oliver Sacks twin savants prime you'll find many articles on this. I just randomly read a one-page letter in J Autism Dev Disord from 2007, which quotes the Sacks essay (from The Man who Mistook his Wife for a Hat), and says they instantly ("in a fraction of a second") identified 111 matches dropped on the floor, and quotes Treffert 2007 for other instances of people apparently possessing this same skill. (Another quote of the essay reports that the twins said "37" three times, which doesn't appear consistent with "in a fraction of a second", unless, of course the fraction is > 1). I have no idea how credible any of this is, but I'm just not sure that the particular scene you cite should have (instantly :-) ruined the credibility of the character. There's a lot of scepticism about Sacks' claim that the twins could identify 12 and 20 digit primes "by sight" or by feel or by smell, although he confirmed their skill with 6 digit primes (instantaneous) and 10 digit primes (which apparently required more thought). The very fact that it took them longer to "recognize" larger numbers as primes makes me sceptical of the claim that there was something on the surface that allowed them to recognize the numbers as primes without doing any calculation. But, in any case, from my very sketchy reading, it seems that there's much less scepticism about the claim of visually identifying the exact number of matches (or toothpicks) on a floor.
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MG: "I have no idea how credible any of this is, but I'm just not sure that the particular scene you cite should have (instantly :-) ruined the credibility of the character." It's in my skeptical nature. I don't even believe that a box of 250 toothpicks will necessarily contain 250 toothpicks. That at least would be an easy one to demonstrate or counterexample. The matter of a hearsay human ability without the benefit of a rigorous laboratory test, well, not so much.
Rain Man musings ... A splatter of even 25 toothpicks is likely to contain ambiguities, where, because of overlaps, the image is insufficient to distinguish each toothpick. I've been skeptical of Sach's "prime twins" ever since reading about them. With concerted effort, you might be able to memorize a coded table of six-digit primes. (Coding as 100K hex digits.) Recognizing 10-digit primes accurately is very hard to credit. The twins could fake it by memorizing a hundred 10-digit primes. More interestingly-- the film-maker may have thought his audience would recognize that 246 is exactly 4 short of 250. [fifty year old memory below - details unreliable] I recall reading a WSJ article ~1970 (google can't find it -- have they digitized that far back?) about a counting fad that started in New York. Someone purchased a box of 100 paper clips. When they opened the box, it seemed short, so they counted and found ~70. Their story went viral, and sparked a fad of counting: sheets in a ream of paper, etc. A surprising number of "short count" cases turned up, enough to suggest that some manufacturers were deliberately cheating. The NY attorney general became involved. It was decided that (true) average counts were allowable if the deviation wasn't too big. Some makers routinely overfilled by 5-10%. Rich ---- Quoting Hans Havermann <gladhobo@bell.net>:
MG: "I have no idea how credible any of this is, but I'm just not sure that the particular scene you cite should have (instantly :-) ruined the credibility of the character."
It's in my skeptical nature. I don't even believe that a box of 250 toothpicks will necessarily contain 250 toothpicks. That at least would be an easy one to demonstrate or counterexample. The matter of a hearsay human ability without the benefit of a rigorous laboratory test, well, not so much.
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On Thu, Aug 2, 2018 at 3:31 PM, <rcs@xmission.com> wrote:
[fifty year old memory below - details unreliable] I recall reading a WSJ article ~1970 (google can't find it -- have they digitized that far back?) about a counting fad that started in New York. Someone purchased a box of 100 paper clips. When they opened the box, it seemed short, so they counted and found ~70. Their story went viral, and sparked a fad of counting: sheets in a ream of paper, etc. A surprising number of "short count" cases turned up, enough to suggest that some manufacturers were deliberately cheating. The NY attorney general became involved. It was decided that (true) average counts were allowable if the deviation wasn't too big. Some makers routinely overfilled by 5-10%.
There's an anecdote about a town in the old west where a shopkeeper gets a fancy spring scale and adjusts it so it overestimates the weight. The shopkeeper later complains that the miller is shortchanging him on flour. The miller says, "I don't have a spring scale. I just put the five-pound bag of sugar I bought from you on one side of a balance and fill the other side with flour." Cereal boxes and potato chip bags say "sold by weight, not by volume" on the packaging to avoid accusations of underfilling. -- Mike Stay - metaweta@gmail.com http://www.math.ucr.edu/~mike http://reperiendi.wordpress.com
I wouldn't have believed flash anzan were possible either: https://www.youtube.com/watch?v=JawF0cv50Lk&t=37s https://www.youtube.com/watch?v=7ktpme4xcoQ https://www.youtube.com/watch?v=LN2hnfsHZCE&t=1m2s Or computing square roots to four decimal places of square roots of six-digit numbers as fast as he can type them: https://www.youtube.com/watch?v=ktFX7Lkr4rk&t=1m28s Or multiplying two 8-digit numbers in your head in 20 seconds: https://www.youtube.com/watch?v=fIrJjaMiLrs&t=18s Maybe there are some primality tests you can train yourself to do quickly? On Thu, Aug 2, 2018 at 3:31 PM, <rcs@xmission.com> wrote:
Rain Man musings ...
A splatter of even 25 toothpicks is likely to contain ambiguities, where, because of overlaps, the image is insufficient to distinguish each toothpick.
I've been skeptical of Sach's "prime twins" ever since reading about them. With concerted effort, you might be able to memorize a coded table of six-digit primes. (Coding as 100K hex digits.) Recognizing 10-digit primes accurately is very hard to credit. The twins could fake it by memorizing a hundred 10-digit primes.
More interestingly-- the film-maker may have thought his audience would recognize that 246 is exactly 4 short of 250.
[fifty year old memory below - details unreliable] I recall reading a WSJ article ~1970 (google can't find it -- have they digitized that far back?) about a counting fad that started in New York. Someone purchased a box of 100 paper clips. When they opened the box, it seemed short, so they counted and found ~70. Their story went viral, and sparked a fad of counting: sheets in a ream of paper, etc. A surprising number of "short count" cases turned up, enough to suggest that some manufacturers were deliberately cheating. The NY attorney general became involved. It was decided that (true) average counts were allowable if the deviation wasn't too big. Some makers routinely overfilled by 5-10%.
Rich
----
Quoting Hans Havermann <gladhobo@bell.net>:
MG: "I have no idea how credible any of this is, but I'm just not sure that the particular scene you cite should have (instantly :-) ruined the credibility of the character."
It's in my skeptical nature. I don't even believe that a box of 250 toothpicks will necessarily contain 250 toothpicks. That at least would be an easy one to demonstrate or counterexample. The matter of a hearsay human ability without the benefit of a rigorous laboratory test, well, not so much.
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-- Mike Stay - metaweta@gmail.com http://www.math.ucr.edu/~mike http://reperiendi.wordpress.com
RCS: "[fifty year old memory below - details unreliable] I recall reading a WSJ article ~1970 (google can't find it -- have they digitized that far back?) about a counting fad that started in New York... I found a Teamster article that referenced the WSJ one. I've pieced it together from snippet views but not all of the text was snippeted so I've had to trust Google's text bridging, and my own word-guesses where some near-the-binding text wasn't visible. Caveat emptor. Cheating of Consumer Becoming Commonplace [The International Teamster, vol. 72-73, 1975] Merchants and manufacturers - worried about profits, costs and competitors - have begun deliberately cheating American consumers. The victimizing has become so flagrant that the Wall Street Journal, which usually confines its news coverage to items of interest to corporate businessmen and coupon clippers, felt obliged to publish a front-page story recently documenting the short-changing. Alert consumer advocates are discovering the cheating in the most unexpected places. Most often it amounts to simple shorting of a product. At this point, the cheating is confined largely to metropolitan areas where every shaving helps to preserve extra profit margins for the merchant. A man in Miami, Fla., for example, purchased a bottle of vitamin tablets at a drugstore. When he looked inside the bottle later, it was obvious there were not 100 tablets in the bottle as stated on the label. A count showed the total to be 90 vitamin pills - a 10 per cent cut. The vitamin buyer pursued the shortage and was told by the manufacturer that the short bottle was caused by malfunctioning electronic production equipment. The consumer, Art Merrill, was quoted by the Journal as saying that he then began to count everything he purchased. Time after time he came up with short counts. Further probing has discovered boxes advertised as containing 100 screws, for instance, but actually containing only 60. A most common short-changing is in the area of cough drops and patent medicines. Aspirin, prescription drugs, electronic parts, paper clips, carbon paper, facial tissue, etc., were all checked by Merrill and friends. On the average, they found products anywhere from l0 to 30 per cent short of the amount advertised. "Few people," noted the Journal, "go to such lengths to make sure they are getting their money's worth. If they do stumble across a case of short-counting, most consumers forget it, figuring the loss is too small to complain about." But magnify the short counts by thousands upon thousands of consumers and the petty theft adds up to a hefty hidden profit - "rake-off" if you will - for the merchant and manufacturer. Fred Tucker, chief of New York State's Bureau of Weights and Measures, has estimated that the total loss to American consumers from short-counting amounted to between $2.5 million and $3 million in 1973. The practice has ballooned during 1974. The Journal told its readers: "A recent survey conducted by this newspaper confirms that short-counting may be so widespread as to represent a considerable drain on already-strained consumer budgets." The Journal survey counted more than 500 products selected at random. They ranged from office supplies to housewares, medicines and foodstuffs. It was found that about 41 per cent of the packages contained less than claimed, 48 per cent held advertised amounts, and 11 per cent provided more than promised. Of the four categories checked in the Journal's survey, office supplies led all others in short counts. Some 53 per cent of the items were short. One package of 100 paperclips, for example, held only 91. Other products counted were envelopes, index cards, thumbtacks, stenographer pads, staples and paper. About 40 per cent of foodstuffs checked by the Journal fell short. Only 43 packs of artificial sweetener turned up in a box of 50. A flagrant cheat was a package of 8 frozen lobster tails which somehow managed to produce only 6 tails. Housewares, the Journal found, were packaged more accurately. Only about a third of the products checked were shorted with facial tissues being almost chronically short by 10 to 15 per cent. Low-count products for sale in the marketplace are there because those who make and peddle them know there is small chance of being confronted with the deceit. Government officials charged with detecting such violations work under an enormous handicap. It is virtually impossible to check every bottle or package of merchandise offered for sale across the land. Another factor that slows enforcement is consumer apathy. Officials are quick to say they receive only a handful of complaints a year about short counts. It is almost as though the consumer is unaware of the thievery. Still another element is the attitude of the retail merchant himself. Many of them consider shorting their customers a way to recoup losses from pilferage. One hardware store manager admitted to the Journal that nails are one of his most "profitable" items. He was quoted: "Say I have a box of 100 nails on the shelf. One day a guy will need 10 and we'll charge him two cents apiece. Then we'll reseal the box. The next day a builder will come in and want box of 100. We take down the box of 90 and charge him for a full box. Why not?" Art Merrill, the consumer advocate whose investigations eventually led to the Journal story on short-counting, says that pharmacists have begun to short prescriptions to long-time customers. Merrill advises medicine purchasers to count their pills on the spot when paying for their prescriptions. He explains, "If you go home first and then come back, you haven't got a chance." Undoubtedly a lot of the short-counts are the result of factory count-devices that fail to function properly - because of maladjustment. But naturally, the Journal survey revealed, short-counts are a deliberate attack on the shopper's pocketbook.
participants (5)
-
Hans Havermann -
Michael Greenwald -
Mike Stay -
rcs@xmission.com -
Veit Elser