[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.
spike
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