[ExI] tumbling pyramids again

spike spike66 at att.net
Fri Feb 17 00:34:10 UTC 2017



-----Original Message-----
From: extropy-chat [mailto:extropy-chat-bounces at lists.extropy.org] On Behalf
Of BillK
Sent: Thursday, February 16, 2017 4:20 PM
To: ExI chat list <extropy-chat at lists.extropy.org>
Subject: Re: [ExI] tumbling pyramids again

On 16 February 2017 at 23:42, spike  wrote:
>
>>...Hi BillK, note the next sentence right after the part you quoted:
>
...
>
>>... OK, I am arguing that this tumbling pyramid question might be a case 
> where we can come up with guesses on h to make square-down = .2, but 
> in the end we must admit we will just have to make some and try it.  
> We might find it is material-dependent, but we don't know.





>...When I consider all the many different types of multi-sided dice that
are in use, it seems logical that all the faces should be the same shape and
all the angles and sides should be equal. Then it doesn't matter how you
throw the die or how it hits the surface or which face hits the surface
first. I think that if you tried to use a pyramid die you might encounter
some difficulty in persuading the other players that it was a fair die. :)

>...BillK
_______________________________________________


Eh... BillK, the question isn't about creating a device with five equal
probability outcomes.  That is easy: that triangular prism device, or a
simple spinner.  The question is to figure out with equations and theories
what the dimensions of such a device would be.  I have three possible
answers: h = 1.41, h = 1.58 and h = 1.675 but I disagree with the reasoning
behind that last one.

The next question is if the device would be material-dependent, and if so,
what characteristics of materials would favor the square base and which
would favor the triangular faces, and why.

I haven't even gotten to applications yet, but let me suggest one.  Imagine
these devices with reflective surfaces with a range of h values.  Imagine
them being hurled out over some flat surface and some of them land
square-down and some triangle down.  In that h range, the higher h units
would be more likely to land triangle down, lower h more likely square-down.

OK now imagine a light shining directly down from above.  The square-down
devices reflect the light four ways, but the triangle-down devices reflect
it only two ways.  The signal return could be detected remotely, which would
indicate the range of h predominant in that sample.  If you run off to the
patent office with the idea, say nice things about me.

spike




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