[ExI] isaac's number

spike spike66 at att.net
Wed Aug 2 16:04:01 UTC 2017



From: extropy-chat [mailto:extropy-chat-bounces at lists.extropy.org] On Behalf Of John Clark
Sent: Wednesday, August 02, 2017 6:00 AM
To: ExI chat list <extropy-chat at lists.extropy.org>
Subject: Re: [ExI] isaac's number


On Tue, Aug 1, 2017 at 2:10 PM, spike <spike66 at att.net <mailto:spike66 at att.net> > wrote:


>>...Woolhouse's 11/144 = .076388889, equal to my Monte Carlo solution to about a part per million.

​ ​

Correction, my sim gives .0763889013, but I found a much faster way to do the calc by generating only three points and calculating an area.



>…That my friend is impressive! 



John as much as I would like to soak up that sentiment, I can’t claim credit.  The really impressive feat was the closed form solution found by Woolhouse.  I went thru that Woolhouse page BillK found, estimated the probability that I would eeeeeever discover a closed form solution to that problem and every single time that probability came out to way less than 0.07639.  I would be generous to estimate my probability of discovering 11/144 at less than a part per thousand.


I have been learning of all the cool stuff Wesley Woolhouse did back in the 1800s.  I note that he was one of Billk’s countrymen.  Considering my interests in probability theory, I am astonished that I haven’t found his work before now, or rather I used some of his results without knowing where they came from.  BillK thanks for finding this, me lad.



>…Do you have a hardware random number generator on your computer? I didn't know software pseudorandom

​ ​ones were that good…


Nah I just use the rand() function in Excel VBA and my son uses the JavaScript Random(B1,B2); function.  I don’t know JavaScript, but I have used the VBA rand() for over half my life and found it to be acceptable.  Its limits are easy enough to discover: make a script which plots a point on a graph and put down 10k points.  Your eye can easily spot the flaws.  I think VBA uses a 32 bit seed, but I am not an expert at these matters.  John, you are the guy I would have asked on that: is there a way to stack the rand() function in Excel to create the equivalent of a 64 bit randomizer?




​>…Maybe they have hardware ones built into microprocessor chips these days.


 >…John K Clark




I don’t know John.  I need to learn up on this, figure out how the rand() function works in VBA.  Oh for a thousand lifetimes, a million.  I would squander most of them digging around in the astonishing mathematical toybox this universe has given us as a priceless gift.






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