To my mind, the key point is that practice must be something other than misery. That which makes us actively and persistently miserable we strive to avoid just as soon as we can.
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Replying to @MathPrinceps @stevenstrogatz and
The world abounds in persons who practiced math sedulously in their youth, found the experience actively miserable, and chose subsequently to have nothing whatever to do with the subject in any of its forms.
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Replying to @MathPrinceps @stevenstrogatz and
The half-life for the decay of those skills attained by practice of this sort is not long; typically a year or two suffices to efface them pretty completely. (Indeed, in many cases the half-life is best measured in weeks.)
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Replying to @MathPrinceps @stevenstrogatz and
And once they have been effaced, the obvious question becomes: what was the point of all that practice?
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Replying to @MathPrinceps @stevenstrogatz and
No skill has value unless it is retained, and no skill is retained unless its exercise benefits the user. It is therefore an essential part of the transmission of skills to make their exercise gratifying to those to whom we would transmit them.
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Replying to @MathPrinceps @stevenstrogatz and
Failing in the discharge of this obligation is failing in all respects.
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Replying to @MathPrinceps @stevenstrogatz and
It is certainly true that effort is needed to acquire skill, and that skill is needed for successful performance of complex tasks. But not all exertion is miserable, nor need it be.
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Replying to @MathPrinceps @stevenstrogatz and
The notion that suffering ennobles is pernicious. Merely because a form of practice is onerous does not make it valuable.
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Replying to @MathPrinceps @stevenstrogatz and
A key question, typically sadly neglected, is: what practice regimen is optimal? In professional and Olympic sports, systematic attempts to answer this question have led to vast improvements in outcomes.
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Replying to @MathPrinceps @stevenstrogatz and
Certainly not all forms of practice are equally beneficial, and excess practice of the wrong sort can be harmful. So one may reasonably question the wisdom of advising practice without specifying what sort of practice is advisable.
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Only experiment can determine what practice regimen is optimal, but it seems clear that the search should be guided by the experience and intuition of experts (who, after all, have acquired their expertise through practice of a presumably more-nearly-optimal sort.)
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Replying to @MathPrinceps @stevenstrogatz and
But experts have very little incentive to grapple seriously with this question. And so we have a sort of tragedy of the commons: it's to the advantage of every individual expert to imagine this work to be somebody else's job -- with the result that no one even attempts to do it.
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Replying to @MathPrinceps @stevenstrogatz and
And with experts ignoring the job, it falls to those whose expertise is scant -- who, unsurprisingly, achieve poor results.
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