Complexity and the Ten-Thousand-Hour Rule
Forty years ago, in a paper in American Scientist, Herbert Simon and William Chase drew one of the most famous conclusions in the study of expertise:
There are no instant experts in chess—certainly no instant masters or grandmasters. There appears not to be on record any case (including Bobby Fischer) where a person reached grandmaster level with less than about a decade’s intense preoccupation with the game. We would estimate, very roughly, that a master has spent perhaps 10,000 to 50,000 hours staring at chess positions…
In the years that followed, an entire field within psychology grew up devoted to elaborating on Simon and Chase’s observation—and researchers, time and again, reached the same conclusion: it takes a lot of practice to be good at complex tasks. After Simon and Chase’s paper, for example, the psychologist John Hayes looked at seventy-six famous classical composers and found that, in almost every case, those composers did not create their greatest work until they had been composing for at least ten years. (The sole exceptions: Shostakovich and Paganini, who took nine years, and Erik Satie, who took eight.)
This is the scholarly tradition I was referring to in my book “Outliers,” when I wrote about the “ten-thousand-hour rule.” No one succeeds at a high level without innate talent, I wrote: “achievement is talent plus preparation.” But the ten-thousand-hour research reminds us that “the closer psychologists look at the careers of the gifted, the smaller the role innate talent seems to play and the bigger the role preparation seems to play.” In cognitively demanding fields, there are no naturals. Nobody walks into an operating room, straight out of a surgical rotation, and does world-class neurosurgery. And second—and more crucially for the theme of Outliers—the amount of practice necessary for exceptional performance is so extensive that people who end up on top need help. They invariably have access to lucky breaks or privileges or conditions that make all those years of practice possible. As examples, I focussed on the countless hours the Beatles spent playing strip clubs in Hamburg and the privileged, early access Bill Gates and Bill Joy got to computers in the nineteen-seventies. “He has talent by the truckload,” I wrote of Joy. “But that’s not the only consideration. It never is.”
Continue reading at http://www.newyorker.com/online/blogs/sportingscene/2013/08/psychology-ten-thousand-hour-rule-complexity.html
km/h.
km/h.
km/h
h
h
[2]
h
, in descending powers of 
and the value of this term.
since it is the seventh term (recall 
)
(independent of 
(Ans)
(use GC invNorm function!)
(3 s.f.)
is out of the set 
says!)
(6 d.p.)
; 
(months)
![\displaystyle\begin{array}{rcl}S_n&=&1.005^n(100)+1.005^{n-1}(100)+\cdots+1.005(100)\\ &=&\frac{a(r^n-1)}{r-1}\\ &=&\frac{1.005(100)[1.005^n-1]}{1.005-1}\\ &=&\frac{100.5(1.005^n-1)}{0.005}\\ &=&20100(1.005^n-1) \end{array}](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle%5Cbegin%7Barray%7D%7Brcl%7DS_n%26%3D%261.005%5En%28100%29%2B1.005%5E%7Bn-1%7D%28100%29%2B%5Ccdots%2B1.005%28100%29%5C%5C++++%26%3D%26%5Cfrac%7Ba%28r%5En-1%29%7D%7Br-1%7D%5C%5C++++%26%3D%26%5Cfrac%7B1.005%28100%29%5B1.005%5En-1%5D%7D%7B1.005-1%7D%5C%5C++++%26%3D%26%5Cfrac%7B100.5%281.005%5En-1%29%7D%7B0.005%7D%5C%5C++++%26%3D%2620100%281.005%5En-1%29++++%5Cend%7Barray%7D&bg=ffffff&fg=1a1a1a&s=0&c=20201002)
months (inclusive of Jan 2001 !!!)![\displaystyle S_n=\frac{(1+x/100)(100)[(1+x/100)^n-1]}{(1+x/100)-1}=4900](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+S_n%3D%5Cfrac%7B%281%2Bx%2F100%29%28100%29%5B%281%2Bx%2F100%29%5En-1%5D%7D%7B%281%2Bx%2F100%29-1%7D%3D4900&bg=ffffff&fg=1a1a1a&s=0&c=20201002)
and using GC, we get
is
(from part ii)
Mathtuition88 