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by
Jim Holt
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February 26 - March 24, 2019
Our mental powers, it is argued, must outstrip those of any computer, because a computer is just a logical system running on hardware and our minds can arrive at truths that are beyond the reach of a logical system.
Gödel himself drew a different moral. If time travel is possible, he submitted, then time itself is impossible. A past that can be revisited has not really passed. And the fact that the actual universe is expanding, rather than rotating, is irrelevant. Time, like God, is either necessary or nothing; if it disappears in one possible universe, it is undermined in every possible universe, including our own.
When you’re an adult, as Fran Lebowitz once observed, Christmas seems to come every five minutes.
The past and the future might be equally real, but—for reasons traceable, oddly enough, to the second law of thermodynamics—we cannot “remember” events in the future, only ones in the past. Memories accumulate in one temporal direction and not in the other.
“Time is nature’s way to keep everything from happening all at once.”
“Time is a great teacher, but unfortunately it kills all its pupils.”
haaa
“Some people believe that psychology is just being replaced by brain imaging, but I don’t think that’s the case at all,” Dehaene said. “We need psychology to refine our idea of what the imagery is going to show us. That’s why we do behavioral experiments, see patients. It’s the confrontation of all these different methods that creates knowledge.”
The fundamental problem with learning mathematics is that while the number sense may be genetic, exact calculation requires cultural tools—symbols and algorithms—that have been around for only a few thousand years and must therefore be absorbed by areas of the brain that evolved for other purposes. The process is made easier when what we are learning harmonizes with built-in circuitry. If we can’t change the architecture of our brains, we can at least adapt our teaching methods to the constraints it imposes.
What this means is that if the play has already had n performances at the point in its run when you happen to see it, you can be 95 percent sure that it has no more than 39 × n performances to go and no fewer than n ÷ 39. (This is a matter of elementary arithmetic: the upper limit keeps you out of the first 2.5 percent of the total audience, and the lower limit keeps you out of the last 2.5 percent.) With nothing more than the Copernican principle and a grade school calculation, you can come up with a 95 percent confidence interval for the longevity of something like a Broadway play. That is
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Woody Allen’s character in the film Hannah and Her Sisters is similarly given to suicidal thoughts, but he is pulled back from the brink when he goes to a revival cinema and sees the Marx Brothers, in Duck Soup, playing on the helmets of the soldiers of Freedonia like a xylophone.
If there were only finitely many primes, then, by multiplying them all together and adding 1, you would get a new number that could not be divided by any prime at all, which is impossible. (This new number would leave a remainder of 1 if it was divided by any of the numbers on the supposedly finite list of primes; so it would have to be either a prime number itself or divisible by some prime that was not on the original list. In either case, the original finite list of primes must be incomplete. So no finite list can encompass all the primes.
“If a twentieth part of the cost and pains were spent in measures for the improvement of the human race that is spent on the improvements of the breed of horses and cattle, what a galaxy of genius might we not create!” he wrote in an 1864 magazine article, his opening eugenic salvo. (It was two decades later that he coined the actual word “eugenics,” from the Greek for “wellborn.”)
It was Galton who coined the phrase “nature versus nurture,” which still reverberates in debates today. (It was probably suggested by Shakespeare’s Tempest, in which Prospero laments that his adopted son, Caliban, is “A devil, a born devil, on whose nature / Nurture can never stick.”) What made him so sure that nature dominated nurture in determining a person’s talent and temperament? The idea first arose in his mind at Cambridge, where he noticed that the top students had relatives who had also excelled there; surely, he reasoned, such runs of family success were not a matter of mere chance.
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All told, there were some sixty thousand court-ordered sterilizations of Americans judged eugenically unfit. Large numbers were also forcibly sterilized in Canada, Sweden, Norway, and Switzerland (although not, notably, in Britain).
Both these techniques can be subsumed under “negative” eugenics, because the genes screened against are those associated with diseases or, potentially, with other conditions the parents might regard as undesirable, like low IQ, obesity, same-sex preference, or baldness.
Thomas Jefferson wrote in his seventy-sixth year that contemplating the truths of mathematics helped him to “beguile the wearisomeness of declining life.” To Bertrand Russell—who rather melodramatically claimed, in his autobiography, that it was his desire to know more of mathematics that kept him from committing suicide—the beauty of mathematics was “cold and austere, like that of sculpture … sublimely pure, and capable of a stern perfection.”
Aristotle, at the outset of On the Heavens, declared that “the three dimensions are all there are.” Why? Because, he argued in a somewhat mystical vein, the number 3 comprises beginning, middle, and end; therefore, it is perfect and complete.
Some maps need four colors: that much is patent. What the four-color conjecture asserts is that there is no possible map that needs more than four colors. What would it mean to “resolve” this conjecture?
To make matters a little less abstract, you might pretend that we live in a world with an infinite number of people. Now consider all the possible clubs (sets of people) that might exist in this world. The least exclusive of these clubs—the universal club—will be the one of which absolutely everyone is a member. The most exclusive—the null club—will be the one that has no members at all. In between these two extremes will lie an infinity of other clubs, some with lots of members, some with few. How big is this infinity? Is there any way of matching up clubs and people one to one, thereby
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And if he was sometimes in over his head, it is because he chose to wade through the deepest waters.
The notion of Ada Lovelace as the inventor of computer programming appeals to the imagination because it contains two improbabilities and an irony. Improbability one: that computer programming, that seemingly masculine preserve, could have been invented by a woman. Improbability two: that the first program could have been written more than a century before a real computer came into existence. Irony: that this ur-programmer could have sprung from the loins of Lord Byron, who would have loathed anything having to do with a computer.
Psychologists distinguish two broad types of intelligence. “Fluid” intelligence is one’s ability to solve abstract problems, like logic puzzles. “Crystallized” intelligence is one’s store of information about the world, including learned shortcuts for making inferences about it. (As one might guess, fluid intelligence tends to decline with age, while the crystallized variety tends to increase, up to a point.)
This raises a prospect that has exhilarated many of the digerati. Perhaps the Internet can serve not merely as a supplement to memory but as a replacement for it. “I’ve almost given up making an effort to remember anything,” says Clive Thompson, a writer for Wired, “because I can instantly retrieve the information online.” David Brooks, in his New York Times column, writes, “I had thought that the magic of the information age was that it allowed us to know more, but then I realized the magic of the information age is that it allows us to know less. It provides us with external cognitive
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We know that creativity is empirically correlated with mood-swing disorders. A couple of decades ago, Harvard researchers found that people showing “exceptional creativity”—which they put at less than 1 percent of the population—were more likely to suffer from manic depression or to be near-relatives of manic-depressives. As for the psychological mechanisms behind creative genius, those remain pretty much a mystery.
The final moments before universal annihilation would release an infinite amount of energy, Tipler reasoned, and that could drive an infinite amount of computation, which would produce an infinite number of thoughts—a subjective eternity. Everyone who ever existed would be “resurrected” in an orgy of virtual reality, which would correspond pretty neatly to what religious believers have in mind when they talk about heaven. Thus, while the physical cosmos would come to an abrupt end in the big crunch, the mental cosmos would go on forever.
To become a type 3 civilization, one powerful enough to engineer a stable wormhole leading to a new universe, we would have to gain control of our entire galaxy. That means colonizing something like a billion habitable planets. But if this is what the future is going to look like, then almost all the intelligent observers who will ever exist will live in one of these billion colonies. So, how come we find ourselves sitting on the home planet at the very beginning of the process? The odds against being in such an unusual situation—the very earliest people, the equivalent of Adam and Eve—are a
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!
Still, we ought to be excited that we’re living in the first generation in the history of humanity that might be able to answer the question, how will the universe end? “It amazes me,” Lawrence Krauss said, “that, sitting in a place on the edge of nowhere in a not especially interesting time in the history of the universe, we can, on the basis of simple laws of physics, draw conclusions about the future of life and the cosmos. That’s something we should relish, regardless of whether we’re here for a long time or not.”
The number of Planck times that make up a human lifetime is very, very much more than the number of human lifetimes that make up the age of the universe. “People talk about the ephemeral nature of existence,” the physicist Roger Penrose has commented, “but [on such a scale] it can be seen that we are not ephemeral at all—we live more or less as long as the Universe itself!”
A decade earlier, Carter had baptized the much-debated “anthropic principle,” which purports to explain why the laws of physics look the way they do: if they were any different, life could not have emerged, and hence we would not be here to observe them. We find ourselves living in this particular universe, in other words, because alternative universes are uncongenial to intelligent life.
The third argument, that your posthumous nonexistence is no more to be feared than your prenatal nonexistence, also collapses on close inspection. As Nagel observed, there is an important asymmetry between the two abysses that temporally flank your life. The time after you die is time of which your death deprives you. You might have lived longer. But you could not possibly have existed in the time before your birth. Had you been conceived earlier than you actually were, you would have had a different genetic identity. In other words, you would not be you.
Overconfidence is nearly universal. But is it distributed equally? Evidently not. In a 1999 paper in the Journal of Personality and Social Psychology, David A. Dunning and Justin Kruger drew a poignant conclusion from their research: The most incompetent people have the most inflated notion of their abilities. “Not only do they reach erroneous conclusions and make unfortunate choices,” the two psychologists observed, “but their incompetence robs them of the ability to realize it.”
In 1991, Erdős found himself befuddled when the Parade magazine columnist Marilyn vos Savant published a probability puzzle called the Monty Hall problem, named after the original emcee of the TV game show Let’s Make a Deal. It goes like this. There are three doors onstage, labeled A, B, and C. Behind one of them is a sports car; behind the other two are goats. You get to choose one of the doors and keep whatever is behind it. Let’s suppose you choose door A. Now, instead of showing you what’s behind it, Monty Hall slyly opens door B and reveals … a goat. He then offers you the option of
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The most overconfident judgment in history might turn out to be cogito, ergo sum.
And where there is information, says the panpsychist, there is consciousness. In David Chalmers’s slogan, “Experience is information from the inside; physics is information from the outside.”
(For those who want to understand the weaknesses in the standard arguments for God’s existence, the best source I know remains the atheist philosopher J. L. Mackie’s 1982 book, The Miracle of Theism.)
(Dawkins coined the term “meme” three decades ago to refer to bits of culture that, he holds, reproduce and compete the way genes do.)
The American philosopher Donald Davidson, whose influence in the Anglophone philosophical world was unsurpassed, put the point succinctly: “Nothing can count as a reason for holding a belief except another belief.”
We may be happier thinking that we are really good at what we do even if that is a delusion. (The people with the truest understanding of their own abilities, research suggests, tend to be depressives.)
Indeed, much of what we call poetry consists of trite or false ideas dressed up in sublime language—ideas like “beauty is truth, truth beauty,” which is beautiful but untrue. (Oscar Wilde, in his dialogue “The Decay of Lying,” suggests that the proper aim of art is “the telling of beautiful untrue things.”)
The paradigm here is Sir John Falstaff, the greatest comic genius literature has to offer. In a dark Shakespearean world of politics and war, statecraft and treachery, Falstaff stands as a beacon of freedom.
