Orthogonality

6[anonymous]

4[anonymous]

3Viliam

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It follows that quantity of avocations correlates positively with winning Nobel Prizes, despite the time these hobbies take time away from one's specialization.

An alternative explanation is that there are factors that both allow having hobbies and increase the probability of winning a Nobel Prize. Things like "having lots of free time" and "not having to worry about various problems".

It is true that hobbies and specialization compete against each other for time and attention. But there are also other things that compete with both hobbies and specialization; and if you succeed to eliminate them (e.g. by being rich, having a spouse that takes care of everything, or living an ascetic life), it provides more space to both.

TL;DR: I used to think the best way to get really good at skill si was to specialize by investing lots of time ti into si. I was wrong. Investing lots of time ti into si works only as a first-order approximation. Once ti becomes large, investing in some other tj≠i produces greater real-world performance pi than continued investment in ti.

I like to think of intelligence as a vector s={s1,s2,…,sn} where each si≥0 is a skill level in a different skill. I think of general intelligence g as the Euclidean norm g=√∑ni=1s2i.

I use the Euclidean norm instead of the straight sum ∑ni=1si because

generality of experience equals generality of transference. Suppose you are exposed to a novel situation requiring skill sn+1=0. You have no experience at sn+1 so you must borrow from your most similar skill. The wider a variety of skills you have, more similar your most similar skill will be to sn+1.The best way to increase your general intelligence g is to invest time tw into your weakest skill sw.

If your invested time ts for your strongest skill is already high then investments in tw can also increase the real world performance of your strongest skill faster than investments in ts.Suppose you want to increase p1, your real world performance at s1. ∂p1∂t1>0. Investing time t1 into s1 always results in increasing p1. But eventually you will hit diminishing returns. For every ϵ>0 there exists a δ∈R such that if t>δ then ∂s1∂t1<ϵ.

limt1→∞∂p1∂t1=limt1→∞∂s1∂t1=0

Here's where things get interesting. "All non-trivial abstractions, to some degree, are leaky" and a system is only as secure as its weakest link; cracking a system tends to happen on an overlooked layer of abstraction. All real world applications of skill are non-trivial abstractions. Therefore performance in one skill occasionally leaks over to improve performance of adjacent skills. Your real-world performance at p1 leaks over from adjacent skills sj≠1∈s on rungs above and below s1 on the ladder of abstraction.

These adjacent skills increase your real world performance on p1 by a quantity independent of s1. Since limt1→∞∂s1∂t1=0, there will inevitably come a time when increasing t1 increases s1 less than increasing ti≠1.

It follows that quantity of avocations correlates positively with winning Nobel Prizes, despite the time these hobbies take away from one's specialization.

When I want to improve my ability to write machine learning algorithms, my first instinct is to study machine learning. But in practice, it's often more profitable to do something seemingly unrelated, like learning about music theory. I find it hard to follow this strategy because it is so counterintuitive.