In 1800 a 12-year-old boy emerged from a forest in southern France, where he had apparently lived alone for seven years. His case was taken up by a young Paris doctor who set out to see if the boy could be civilized. In this week’s episode of the Futility Closet podcast we’ll explore the strange, sad story of Victor of Aveyron and the mysteries of child development.
We’ll also consider the nature of art and puzzle over the relationship between salmon and trees.
A cab was involved in a hit and run accident at night. Two cab companies, the Green and the Blue, operate in the city. 85% of the cabs in the city are Green and 15% are Blue.
A witness identified the cab as Blue. The court tested the reliability of the witness under the same circumstances that existed on the night of the accident and concluded that the witness correctly identified each one of the two colors 80% of the time and failed 20% of the time.
What is the probability that the cab involved in the accident was Blue rather than Green knowing that this witness identified it as Blue?
Psychologists Amos Tversky and Daniel Kahneman offered this problem to study subjects in 1972. The right answer is about 41 percent:
Most subjects estimated the probability at more than 50 percent, some more than 80 percent.
Tversky and Kahneman call this the representativeness heuristic: When we rely on representativeness to make a judgment, we tend to judge wrongly because the fact that a thing is more representative doesn’t make it more likely.
(Amos Tversky and Daniel Kahneman, “Evidential Impact of Base Rates,” No. TR-4, Stanford University Department of Psychology, 1981.)
This is bewildering: This diamond isn’t moving, and its luminance and texture are unchanging. Yet when it’s surrounded with very thin edge strips whose luminance changes with respect to the background, the whole diamond seems to move. Using the controls at the bottom, you can even direct the illusion to send the diamond drifting “up,” “down,” “left,” or “right.” But it ain’t moving.
See the paper below for details.
(Oliver J. Flynn and Arthur G. Shapiro, “The Perpetual Diamond: Contrast Reversals Along Thin Edges Create the Appearance of Motion in Objects,” i-Perception 9:6 [2018], 2041669518815708.)
(Thanks, Sanford.)
In 1976 psychologist Harry McGurk discovered that seeing a person speak affects our impression of the sound we hear. Faced with conflicting information, the brain seems to make its “best guess” as to what it’s perceiving. In some cases a third sound is produced: When the syllables /ba-ba/ are spoken over the lip movements /ga-ga/, the perception is /da-da/.
This casts doubt on the assumption that the senses operate separately and can be studied in isolation. Psychologists and philosophers are still considering the implications.
(Harry McGurk and John MacDonald, “Hearing Lips and Seeing Voices,” Nature 264:5588 [1976], 746.)
In David Hayes and Tatiana Shubin’s Mathematical Adventures (2004), University of California-Davis mathematician Don Chakerian describes a method used in antiquity for solving an equation in one unknown. He illustrates it with a problem from Daboll’s Schoolmaster’s Assistant (1800):
A, B, and C built a house which cost $500, of which A paid a certain sum, B paid 10 dollars more than A, and C paid as much as A and B both; how much did each man pay?
We’ll make two guesses as to how much A paid, check them, and plug the “errors” into a formula to get the right answer. First, suppose A pays $80. That means that B pays $90 and C pays $170, giving a total of $340. That’s 500 – 340 = $160 short of the goal, so our guess of $80 yields an “error” of $160. As a second guess, suppose that A pays $150. In that case B pays $160, C pays $310, and the total is now $620. This time the “error” is 500 – 620 = -$120. The false position method (technically here the double false position method) offers this formula for finding the right answer:
In this case it gives
When A pays $120 then B pays $130, C pays 250, and together they pay $500, so this solution works.
This is hardly the most efficient way to solve a simple linear equation given the tools we have today, but it served for centuries. In his Ground of Artes of 1542, Robert Recorde offered a rule:
Gesse at this woorke as happe doth leade.
By chaunce to truthe you may procede.
And firste woorke by the question,
Although no truthe therein be don.
Suche falsehode is so good a grounde,
That truth by it will soone be founde.
From many bate to many mo,
From to fewe take to fewe also.
With to much ioyne to fewe againe,
To to fewe adde to manye plaine.
In crossewaies multiplye contrary kinde,
All truthe by falsehode for to fynde.
From Ed Southall’s Twitter feed, a polygon name builder:
A 55-sided figure is a pentacontapentagon; one with 79 sides is a heptacontaenneagon. A system exists to go even higher: A figure with 9,000 sides is an enakischiliagon, and one with a million is a megagon.
René Descartes suggested the 1,000-sided chiliagon as an example of a thing that can be considered without being explicitly imagined; one “does not imagine the thousand sides or see them as if they were present.” So the intellect is not dependent on imagination.
From Lewis Carroll’s diary, Feb. 5, 1856:
Varied the lesson at the school with a story, introducing a number of sums to be worked out. I also worked for them the puzzle of writing the answer to an addition sum, when only one of the five rows have been written: this … astonished them not a little.
He had started by writing an arbitrary number:
21879
Then he asked the students to call out a second five-digit number. Carroll added a third, the students shouted a fourth, and Carroll added a fifth and immediately wrote the sum:
21879 62593 37406 82527 + 17472 221877
How did he do this?
In 1954 a social psychologist started a war between two teams of fifth graders at an Oklahoma summer camp. He wanted to investigate the sources of human conflict and how people might overcome them. In this week’s episode of the Futility Closet podcast we’ll review the Robbers Cave Experiment and examine its evolving reputation.
We’ll also dredge up a Dalek and puzzle over a hazardous job.
Last August, researchers at Rome University produced tiny portraits of Albert Einstein and Charles Darwin by modifying E. coli cells to respond to light patterns. Bacteria that received more light would swim faster, so over time they tended to concentrate in the darker parts of a negative image.
Lead author Giacomo Frangipane said in a statement, “Much like pedestrians who slow down their walking speed when they encounter a crowd, or cars that are stuck in traffic, swimming bacteria will spend more time in slower regions than in faster ones.”
Using the same technique, they created a (tiny) version of the Mona Lisa.
