Re: [Fis] Re: gravity and symmetry

At 10.18 6/3/03 +0100, you wrote:
>Dear Pedro and FIS colleagues,
>I have not read Smolin's book, but you can find find similar issues and much
>more in my preprint "How we count or is it possible that two times two is not
>equal to four." You can read this preprint at the following address:
>
>http://www.mathpreprints.com/math/Preprints/
>Sincerely,
>Mark Burgin

Dear Mark and FIS colleagues,

Many thanks for the reference (I could finally locate the paper after some
search in the site). The subject you treat looks quite relevant:
'non-Diophantine' arithmetics', like the well-known non-Euclidean
geometries. To the novice, it is amazing that the topic has transpired so
little into general scientific circles. Counting and natural numbers, as
you say, are taken as the last refuge of undiscussed mathematical 'truth'.

You mention several cases in economics, and another physicist (Zeldovich),
concurring on the idea that "fundamental problems of modern physics are
dependent on our ways of counting" (I had already mentioned Penrose and
Smolin, later on I have found in the web a very exciting paper by Smolin
and Stuart Kauffman more or less close to the idea:
http://www.edge.org/3rd_culture/smolin/smolin_p1.html). But in any case, I
think it is in the biology of the cell where the best cases of non-regular
arithmetics can be found. When cells 'count' through their receptors, or
better throughout their signaling systems, the non-Diophantine arithmetics
appears to be the general rule. For instance, a very recent paper in Nature
on toxicology addresses this very issue: (Calabrese and Baldwin, 2003,
Nature 421, 691-2) rather than lineal responses with or without thresholds,
an 'hormetic model' is followed in most, most cases (like an U-shaped
curve, but very asymmetric). Apart from my tentative application of Karl�s
partitions to signaling systems, that I think is meaningful, your new
arithmetics could also work there...

all the best

Pedro

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Received on Mon Mar 10 12:07:20 2003