It's just math. https://en.wikipedia.org/wiki/Central_limit_theorem
When you add random variables, you add their means and variances and the sum tends to a Gaussian curve. When you multiply instead of add, the same thing happens when you take the log of the distributions. On Fri, Jun 15, 2018 at 11:05 PM Steve Richfield via AGI <agi@agi.topicbox.com> wrote: > > Matt, > > Yours is a remarkable posting - with SO much crammed into just two > paragraphs. Several disciplines would benefit if you were to write this in > more bite-sized pieces spread over several pages, with explanations mixed in. > Or, perhaps, I have simply missed a VERY important article? > > Steve > > On 10:29AM, Fri, Jun 15, 2018 Matt Mahoney via AGI <agi@agi.topicbox.com> > wrote: >> >> On Thu, Jun 14, 2018 at 10:40 PM Steve Richfield via AGI >> <agi@agi.topicbox.com> wrote: >> > >> > In the space of real world "problems", I suspect the distribution of >> > difficulty follows the Zipf function, like pretty much everything else >> > does. >> >> A Zipf distribution is a power law distribution. The reason that power >> law distributions are so common over different domains (for example, >> wealth distribution or population of cities) is the same reason that >> Gaussian normal distributions are common. When you add a large set of >> small random variables, the result is Gaussian by the central limit >> theorem. When you multiply instead of add, you get a power law >> distribution, which is the exponential of a Gaussian. It happens >> whenever small random variations are in proportion to the magnitude of >> the variable. >> >> So yes, the distribution of problem difficulty over broad domains is >> Zipf or power law. It is why intelligence (as measured by problem >> solving ability) is proportional to the log of computing power. The >> value of intelligent systems grows linearly while their power grows >> exponentially by Moore's law. >> >> -- >> -- Matt Mahoney, mattmahone...@gmail.com > > Artificial General Intelligence List / AGI / see discussions + participants + > delivery options Permalink -- -- Matt Mahoney, mattmahone...@gmail.com ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/T5ada390c367596a4-M59fb087d9a0d7d0ed251b173 Delivery options: https://agi.topicbox.com/groups
