Monday, November 12, 2007

Great minds (warning... math terms folllow)

The question was posed to me on Saturday... should the frequency of great minds in history being getting higher, or slowing down?

Assumption #1: As society progresses, the scope of the problems faced by great minds become exponentially more complex.

Assumption #2: At the same time, previous advances increase both the probability of great minds being afforded a chance to dwell on these problems (rather than say, hunting for food)... previous advances provide resources to help great minds solve the increasingly complex problems (say, learning from a teacher, rather than teaching themselves algebra and physics).

What is the shape of the line marking efficacy of resources in aiding to find new solutions? Assumption#3: I'm inclined to believe the benefit of new technologies will be best described by an exponentially decreasing trend (i.e. the wheel helped more than the internet - or oral communication more than written com., more than radio, more than TV, and so on.). Enter Calc 2... if the trend is convergent, it's sum (or integral to time=now) has a horizontal asymptote, and there's a limit to human progress (but not necessarily a limit to knowledge... just a point we can't pass); if the trend is divergent... there is no limit to what society can do.
*clearly, the points are opinions... but you get the idea

Assumption #4: Humans are evolving at a negligible rate... the distribution of cognitive capacity today is basically equal to that of humans one thousand years ago, there are just a lot more of us. (I'm talking natural ability... clearly we have more teaching and resources, see assumption 2)

So the question is... Which is currently more powerful, the benefits of our previous advances, or the increasing complexity of our current problems?

Sorry for all the maths... I just can't help myself. I expect zero comments on this post :-)

2 Comments:

Blogger charlie said...

I was thinking about this a while ago. If our functional lifespans don't get longer then our rate of innovation will decrease eventually. Longer times spent studying to understand the current state. We'll have to hand things over to artificial intelligence and hope that they don't phase us out like HAL. In addition deeper knowledge means we'll have to specialize early so any genius types that might make a big advance may be shut off in a field that they aren't destined to push forward. My thoughts are still fuzzy on this one but I think I'm close to being able to crystallize it into a solid theory.

8:04 PM  
Blogger charlie said...

You might like Slate's articles on genetically inherited intelligence.
http://www.slate.com/id/2178122/entry/2178123/

8:06 PM  

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