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“If you’ve ever run an experiment, you know scientific truth doesn’t pop out of the clouds blowing a flaming trumpet at you. Data is messy, and inference is hard.”
― How Not to Be Wrong: The Power of Mathematical Thinking
― How Not to Be Wrong: The Power of Mathematical Thinking
“What can I say? Mathematics is a way not to be wrong, but it isn't a way not to be wrong about everything. (Sorry, no refunds!) Wrongness is like original sin; we are born to it and it remains always with us, and constant vigilance is necessary if we mean to restrict its sphere of influence over our actions. There is real danger that, by strengthening our abilities to analyze some questions mathematically, we acquire a general confidence in our beliefs, which extends unjustifiably to those things we're still wrong about. We become like those pious people who, over time, accumulate a sense of their own virtuousness so powerful as to make them believe the bad things they do are virtuous too.
I'll do my best to resist the temptation. But watch me carefully.”
― How Not to Be Wrong: The Power of Mathematical Thinking
I'll do my best to resist the temptation. But watch me carefully.”
― How Not to Be Wrong: The Power of Mathematical Thinking
“That’s how the Law of Large Numbers works: not by balancing out what’s already happened, but by diluting what’s already happened with new data, until the past is so proportionally negligible that it can safely be forgotten.”
― How Not to Be Wrong: The Power of Mathematical Thinking
― How Not to Be Wrong: The Power of Mathematical Thinking
“torturing the data until it confesses,”
― How Not to Be Wrong: The Power of Mathematical Thinking
― How Not to Be Wrong: The Power of Mathematical Thinking
“Outsiders sometimes have an impression that mathematics consists of applying more and more powerful tools to dig deeper and deeper into the unknown, like tunnelers blasting through the rock with ever more powerful explosives. And that's one way to do it. But Grothendieck, who remade much of pure mathematics in his own image in the 1960's and 70's, had a different view: "The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration...the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it...yet it finally surrounds the resistant substance."
The unknown is a stone in the sea, which obstructs our progress. We can try to pack dynamite in the crevices of rock, detonate it, and repeat until the rock breaks apart, as Buffon did with his complicated computations in calculus. Or you can take a more contemplative approach, allowing your level of understanding gradually and gently to rise, until after a time what appeared as an obstacle is overtopped by the calm water, and is gone. Mathematics as currently practiced is a delicate interplay between monastic contemplation and blowing stuff up with dynamite.”
― How Not to Be Wrong: The Power of Mathematical Thinking
The unknown is a stone in the sea, which obstructs our progress. We can try to pack dynamite in the crevices of rock, detonate it, and repeat until the rock breaks apart, as Buffon did with his complicated computations in calculus. Or you can take a more contemplative approach, allowing your level of understanding gradually and gently to rise, until after a time what appeared as an obstacle is overtopped by the calm water, and is gone. Mathematics as currently practiced is a delicate interplay between monastic contemplation and blowing stuff up with dynamite.”
― How Not to Be Wrong: The Power of Mathematical Thinking
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