John D. Barrow
DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA
First email: Friday, 4 October 2013 17:48:11
Dear Prof. Dr. John Barrow:
The depth and breadth of your work is simply amazing, truly a gift to this world. However, your Millennium Mathematics Project places your feet firmly on the ground.
I am grateful. So, with your mind in search of meaning throughout
the cosmos and your deep understanding of nature of God, I write
with great respect.
I have two simple questions:
1. Can we take the Planck Length and multiply it by 2, and then each
result by 2, until we are near the edges of the Observable Universe?
2. Does it mean anything? Our students thought it was a very neat
and orderly way of looking at the universe.
I do not have answers to these two very naive questions.
After we went through the 202-to-205 notations, I told the kids that
I would continue doing research and report in. My first attempt to get
some help was to write up a Wiki article, but that was kicked off the site
as “original research” which for Wikipedia editors means there were
no scholarly, published, first-hand references of any one using base-2
notation from the Planck Length to the Observable Universe.
It all started when our high school geometry teacher asked me,
“Uncle Bruce, will you take my five classes and introduce them to
the Platonic solids?” I did. We especially looked at nested geometries,
when the question was asked, “How far in can we go?” That required
a review of Zeno and Max Planck and the Planck Length.
It wasn’t long before we just went the other direction! We were quite
surprised to learn that there were so few base-2 notations from the
smallest to largest measurements of a length.
In our little exercise, simple geometries and number were necessarily
related. We could see how we could begin tiling the universe with
a simple tetrahedral-octahedral chain, increasingly nested from
about the tenth to the 205th notation.
Might it be of some interest to you and the MMP?
PS. We are well aware of Kees Boeke’s work from 1957 and
the Powers of Ten with Phyllis and Phil Morrison and the Huang
twins’ wonderful scale. Base-10 is not granular enough and
has no inherent geometry, albeit we realize that ours is instantiated.
PPS. If you would like to see more, I have been writing it up as
we go along so people could follow the path of our thinking:
1. Rough, working draft, possible start of an article
2. The article rejected by Wikipedia
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