It has become commonplace to conclude that humans are simply irrational—more Homer Simpson than Mr. Spock, more Alfred E. Neuman than John von Neumann#1427•
A smartphone and a case cost $110 in total. The phone costs $100 more than the case. How much does the case cost?
It takes 8 printers 8 minutes to print 8 brochures. How long would it take 24 printers to print 24 brochures?
On a field there is a patch of weeds. Every day the patch doubles in size. It takes 30 days for the patch to cover the whole field. How long did it take for the patch to cover half the field?#2843•
The answer to the first problem is $5. If you're like most people, you guessed $10. But if that were right, the phone would cost $110 ($100 more than the case), and the total for the pair would be $120.
The answer to the second question is 8 minutes. It takes a printer 8 minutes to print a brochure, so as long as there are as many printers as there are brochures and they are working simultaneously, the time it takes to print the brochures is the same.
The answer to the third problem is 29 days. If the weed patch doubles every day, then by working backwards from when the field was completely covered, we may infer that it was half covered the day before.#2833•
And the third problem, the one with the weed patch, is not a trick question but taps a real cognitive infirmity. Human intuition doesn't grasp exponential (geometric) growth, namely something that rises at a rising rate, proportional to how large it already is, such as compound interest, economic growth, and the spread of a contagious disease#2834•
People's insensitivity to this lucrative but esoteric information pinpoints the cognitive weakness at the heart of the puzzle: we confuse probability with propensity. A propensity is the disposition of an object to act in certain ways. Intuitions about propensities are a major part of our mental models of the world.
People sense that bent branches tend to spring back, that kudu may tire easily, that porcupines usually leave tracks with two padprints.
A propensity cannot be perceived directly (either the branch sprang back or it didn't), but it can be inferred by scrutinizing the physical makeup of an object and working through the laws of cause and effect.
A drier branch may snap, a kudu has more stamina in the rainy season, a porcupine has two proximal pads which leave padprints when the ground is soft but not necessarily when it is hard.#2894•
Intuitive probability is driven by imaginability: the easier something is to visualize, the likelier it seems. This entraps us into what Tversky and Kahneman call the conjunction fallacy, in which a conjunction is more intuitively probable than either of its elements.#2895•
Unlike the selection task, where people make errors when the problem is abstract ("If P then Q") and get it right when it is couched in certain real-life scenarios, here everyone agrees with the abstract law "prob(A and B) ≤ prob(A)" but are upended when it is made concrete.#2890•
"A man needs a little madness or else he never dares cut the rope and be free," said Zorba the Greek.#2975•
The psychologist David Myers has said that the essence of monotheistic belief is: (1) There is a God and (2) it's not me (and it's also not you).6 The secular equivalent is: (1) There is objective truth and (2) I don't know it (and neither do you). The same epistemic humility applies to the rationality that leads to truth.#2978•
"Ambition must be made to counteract ambition," wrote James Madison about the checks and balances in a democratic government, and that is how other institutions steer communities of biased and ambition-addled people toward disinterested truth. Examples include the adversarial system in law, peer review in science, editing and fact-checking in journalism, academic freedom in universities, and freedom of speech in the public sphere.#2979•
Stoppard's professor may have been misled by David Hume's famous argument that "reason is, and ought only to be the slave of the passions, and can never pretend to any other office than to serve and obey them." Hume, one of the hardest-headed philosophers in the history of Western thought, was not advising his readers to shoot from the hip, live for the moment, or fall head over heels for Mr.
Wrong.
He was making the logical point that reason is the means to an end, and cannot tell you what the end should be, or even that you must pursue it.#2971•
By "passions" he was referring to the source of those ends: the likes, wants, drives, emotions, and feelings wired into us, without which reason would have no goals to figure out how to attain. It's the distinction between thinking and wanting, between believing something you hold to be true and desiring something you wish to bring about.
His point was closer to "There's no disputing tastes" than "If it feels good, do it." It is neither rational nor irrational to prefer chocolate ripple to maple walnut.
And it is in no way irrational to keep a garden, fall in love, care for stray dogs, party like it's 1999, or dance beneath the diamond sky with one hand waving free.#2970•
In 1969 Richard Nixon reportedly ordered nuclear-armed bombers to fly recklessly close to the USSR to scare them into pressuring their North Vietnamese ally to negotiate an end to the Vietnam War#2972•