More on this book
Community
Kindle Notes & Highlights
Speed, of course, equals distance divided by time. Evidently, the faster you go in your car, the shorter your ruler must become and the slower your clock must tick relative to mine; that is the only way we can continue to agree on the speed of light.
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.
It has been estimated that by the age of eight, one has subjectively lived two-thirds of one’s life.
As the mathematician Hermann Weyl memorably put it, “The objective world simply is; it does not happen.”
It is also pretty clear that the nature of memory has something to do with the feeling that we are moving in time. 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.
In general, things that have been around for a long time will likely be around for a lot longer. Conversely, things of recent origin likely won’t be. Both of these conclusions flow from the “Copernican principle,” which says, in essence, you’re not special
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 fairly amazing.
(In addition to being clean and gentle, pure mathematics is cheap: all its practitioners need is chalk and a little travel money. It is also open and transparent, because there are no inventions to patent.)
In his 1940 book A Mathematician’s Apology—justly hailed by David Foster Wallace as “the most lucid English prose work ever on math”—Hardy argued that the point of mathematics was the same as the point of art: the creation of intrinsic beauty.
The intellectual habit of grappling with a problem by ascending to higher and higher levels of generality
“Of the people we knew, we alone moved to France and survived,” Mandelbrot writes, adding that many of their neighbors in the Warsaw ghetto “had been detained by their precious china, or inability to sell their Bösendorfer concert grand piano.”
The man who detected this flaw was a classicist and mathematician called Percy Heawood—or “Pussy” Heawood by his friends, owing to his catlike whiskers.
He set his slow-running watch just once a year, on Christmas Day, and then for the following year did the necessary calculations in his head when he needed to know the time. “No, it’s not two hours fast,” he once insisted to a colleague, “it’s ten hours slow!”
Can mysticism play a genuine role in the attainment of mathematical knowledge, especially knowledge of the infinite? Here the authors, confirmed secularists as they are, are less certain. “We trust rational thought more than mystical inspiration,” they say. The same, though, could be said of the French mathematicians who were supposedly surpassed by the Russians. One is left with the impression that mysticism in mathematics has at least a degree of pragmatic truth; that is, it works.
And rightly: for it is to him who masters our minds by the force of truth, not to those who enslave them by violence, that we owe our reverence.”
“Je vois plus que jamais qu’il ne faut juger de rien sur sa grandeur apparente. O Dieu! qui avez donné une intelligence à des substances qui paraissent si méprisables, l’infiniment petit vous coûte autant que l’infiniment grand.” (I see more than ever that one should judge nothing by its apparent size. O God! who has given intelligence to such contemptible-seeming beings, the infinitely small costs you as little as the infinitely large.)
Augusta Ada Byron, who became by marriage the Countess of Lovelace, is widely supposed to have produced the first specimen of what would later be called computer programming. In her lifetime, she was deemed a mathematical prodigy, the Enchantress of Numbers.
With the coming of the computer age, Ada’s posthumous renown expanded to new proportions. She has been hailed as a technological visionary; credited with the invention of binary arithmetic; made into the cult goddess of cyber feminism.
But there are also skeptics who maintain that computers are having the opposite effect on us: they are making us less happy, and perhaps even stupider.
“bad habits can be ingrained in our neurons as easily as good ones.”
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.
We can burden these servants and liberate ourselves.”
“geniuses are wonks.” They work hard; they immerse themselves in their genre.
What makes Poincaré such a compelling case is that his breakthroughs tended to come in moments of sudden illumination.
It is the connection between memory and creativity, perhaps, that should make us most wary of the web. “As our use of the Web makes it harder for us to lock information into our biological memory, we’re forced to rely more and more on the Net’s capacious and easily searchable artificial memory,” Carr observes.
But conscious manipulation of externally stored information is not enough to yield the deepest of creative breakthroughs: this is what the example of Poincaré suggests. Human memory, unlike machine memory, is dynamic. Through some process we only crudely understand—Poincaré himself saw it as the collision and locking together of ideas into stable combinations—novel patterns are unconsciously detected, novel analogies discovered. And this is the process that Google, by seducing us into using it as a memory prosthesis, threatens to subvert.
It’s that the web may be an enemy of creativity. Which is why Woody Allen might be wise in avoiding it altogether.
The fact that our universe appears to be fine-tuned to engender life is not a matter of luck. Rather, it is a consequence of the “anthropic principle”: if our universe weren’t the way it is, we wouldn’t be here to observe it.
In the postmodern era, we are told, aesthetics must take over where experiment leaves off.
Because string theory does not deign to be tested directly, its beauty must be the warrant of its truth.
The closest thing to an enduring mark of beauty is simplicity;
The initiators of the dual revolution a century ago—Einstein, Bohr, Schrödinger, Heisenberg—were deep thinkers, or “seers.”
theology, if it’s relevant, has to be consistent with science.
We could be doomed to endless stagnation—thinking the same patterns of thoughts over and over again,
Broadly speaking, philosophy has three concerns: how the world hangs together (metaphysics), how our beliefs can be justified (epistemology), and how to live (ethics).
Roko’s basilisk,
Look up
The most incompetent people have the most inflated notion of their abilities.
Overconfidence may decrease with competence, but other studies show that it increases with knowledgeability; that is, the more specialized information you have about something, the more likely you are to be overconfident in your judgments about it. Overconfidence also tends to rise with the complexity of the problem.
high levels of confidence are usually associated with high levels of overconfidence.
The doctrine that the stuff of the world is fundamentally mind stuff goes by the name of panpsychism.
Of course, the rock doesn’t exert itself as a result of all this “thinking.” Why should it? Its existence, unlike ours, doesn’t depend on the struggle to survive and self-replicate. It is indifferent to the prospect of being pulverized. If you are poetically inclined, you might think of the rock as a purely contemplative being. And you might draw the moral that the universe is, and always has been, saturated with mind, even though we snobbish Darwinian-replicating latecomers are too blinkered to notice.
Is there an important distinction between failing to do this and walking away from the drowning child?
