January 24, 2015 § Leave a comment
There’s a perennial question about how much achievement something depends on talent, and how much on hard work. Perhaps genius (or even garden variety exceptional performance) is written into someone’s genes, or perhaps what separated Einstein from his peers had more to do with his work ethic than his IQ.
Evidence points in both directions. On the one hand, most high performers, whatever their field, emphasize how important hard work – rather than ‘just talent’ – is to their achievements (e.g. Terrence Tao, Will Smith, Ira Glass, Thomas Edison). Some, like Malcolm Gladwell, talk about a ‘10000 hour rule‘ as the required hard work before one can truly excel. Perhaps the main proponent of the ‘Arbeit uber alles’ approach is Erikson’s work on deliberate practice. On the other hand, there are lots of instances where innate physical or mental characteristics play an important role: the average height of NBA players is 6’7″, Intelligence (albeit imperfectly measured by IQ) seems to predict lots of things (including various intellectual achievements) – and it appears to remain predictive even into the very high range.
So perhaps it is a mix. But the precise mechanism of the mix could be important; how do innate talents and amount of training relate to one another when it comes to achievement? Could some maths help?
A Growth-mindset model
Here’s one suggestion, implied by Uri Baum:
Performance = Talent + Practice intensity x Time practising[ref]Perhaps even better would be to use a time integral here, as likely practice intensity will vary over time. But multiplication is simpler, and simplicity is better than precision for toy models.[/ref]
On this sort of model, talent counts, but as time passes, practice matters more. Unlike talent – a static given – one can grow a stock of practice over time, and time invested in practice and hard work has a rich return on performance (c.f. Hamming’s remarks). An attractive corollary is that if one can improve one’s practice intensity, be that through more focused training, deliberate practice, better learning styles, etc. this acts as a multiplier – working smarter, as well as working harder may be a stronger determinant of success than talent.
If so, extraordinary talent may be a curse – it could let us coast. Bram suggests there might be a mechanism where if we select for exceptional achievement, we select for people with varying mixes of raw talent and hard work. The group which skew more towards the latter may overtake those skewing to the former former over time: those who skew towards more practice time and intensity will be able to grow faster, whilst those who mainly got to where they were ‘just’ on their talent may find they are hitting a wall unless they can improve how they develop. « Read the rest of this entry »
January 16, 2015 § Leave a comment
Many outcomes of interest have pretty good predictors. It seems that height correlates to performance in basketball (the average height in the NBA is around 6’7″). Faster serves in tennis improve one’s likelihood of winning. IQ scores are known to predict a slew of factors, from income, to chance of being imprisoned, to lifespan.
What’s interesting is what happens to these relationships ‘out on the tail’: extreme outliers of a given predictor are seldom similarly extreme outliers on the outcome it predicts, and vice versa. Although 6’7″ is very tall, it lies within a couple of standard deviations of the median US adult male height – there are many thousands of US men taller than the average NBA player, yet are not in the NBA. Although elite tennis players have very fast serves, if you look at the players serving the fastest serves ever recorded, they aren’t the very best players of their time. It is harder to look at the IQ case due to test ceilings, but again there seems to be some divergence near the top: the very highest earners tend to be very smart, but their intelligence is not in step with their income (their cognitive ability is around +3 to +4 SD above the mean, yet their wealth is much higher than this).[ref]Given income isn’t normally distributed, using SDs might be misleading. But non-parametric ranking to get a similar picture: if Bill Gates is ~+4SD in intelligence, despite being the richest man in america, he is ‘merely’ in the smartest tens of thousands. Looking the other way, one might look at the generally modest achievements of people in high-IQ societies, but there are worries about adverse selection.[/ref]
The trend seems to be that even when two factors are correlated, their tails diverge: the fastest servers are good tennis players, but not the very best (and the very best players serve fast, but not the very fastest); the very richest tend to be smart, but not the very smartest (and vice versa). Why? « Read the rest of this entry »