Dear All,
Thanks to Pedro for his remarks about our collaboration which now
extends some 16 years. At that time, I was terminating a job as senior
systems analyst with the IAEA and took up again a question I was
addressing after doing my PhD in psychology and statistics. The
question was: “How is the transfer of information engineered the other
way around in genetics?”
The “to” direction (from the DNA into the organism) was well
understood. The DNA is a sequence and some biochemical mechanisms copy
its information content into something which is not a sequence. For
those in the data processing trade, contents are indexed either
sequentially or category-based. We have a data transfer from a
sequence into a category-based collection and – in the ovaries and
testes – from a non-sequenced collection into a sequence again.
Having counted the number of distinguishable logical states of a
collection, while it is sequenced, and again while it is commutative,
one finds on comparing the results that a very funny intertwined
relation exists. This is the main accounting trick Nature uses to copy
from and to between sequences and commutative collections. The
comparison of the two functions shows that if the cardinality of the
set is below 32 or above 97, there are more sequential states to the
collection than distinct logical states of the same collection if
treated as commutative; and of course the other way around, too. This
play with the real content of our concepts behind “how many”, “what
kind” and “where” allows Nature to shrink and expand at will.
The disagreement with Pedro is a long-standing one and relates to his
results of the evaluation of the number of logical states a
commutative set of n objects can be in. My proposition is that the
number of distinct logical states of a commutative set of n objects
agrees to the number of partitions of n raised to the power of the
logarithm of the number of partitions of n. No one has yet given a
proof that this is erroneous, nor have I heard of anyone saying his
opinion about the correct result. So I stand to my intertwined
functions and would of course prefer people saying that their results
disagree, and not that my results are a miscalculation. No problem
with the calculation. One may reject the idea that the copying must
allow for as big a disc space as the size of the data set one wants to
copy. We see in genetics copying happening to and fro, therefore there
must be a size allowing the process to take place, once in “to”, once
in “from” direction. There must be excess possibilities (disc space)
at least as many or more than the set contains, if the set copies from
the organism to the DNA and also if the set copies from the DNA to the
organism. Now a set that needs more (or less) disc space both ways of
copying in dependence of the size of the chunks transmitted does have
some funny characteristics. The basic flip Nature uses is that it
treats the assembly concurrently as a commutative set of twice 67
units and as a sequenced set of thrice 45 units, and this relates to
(has the consequences of) a reading of the assembly in a 12 based
sequence. The graphs showing this interrelation are available on the
web.
The discussion in 2011 is far advanced on these starting points.
Presently we deal with the machine-ready translation table of the main
trick in 2 or 3 dimensions. That the numbers (as dimensionless natural
numbers counting the number of distinct logical states) don’t match in
the 0th or 1st dimension has been already discussed (see above). Now
we unfold from the numbers themselves two planes and two Euclid spaces
(which can be merged into one accounting-wise, while losing the
accounting exactitude of either the place coordinates or the amount).
Unfolding from the planes the spaces and folding from the spaces the
planes is no big deal, because they are all logically the same.
Genetics boils down to a play of combinatorics on
{a,b,a+b,b-a,b-2a,2b-3a,a-2b,2a-3b}.
The jump in abstraction from sperm to sequence and woman to
commutative collection is maybe for some a step too far. Clarifying
the accounting procedures behind a sequence being logically equivalent
to a commutative collection (in quite many respects) and while the
logical equivalence is maintained (the organism lives) remaining
equivalent in both of its readings may help getting a solidly rational
view of the process. If it is rational, which we hope it is, it must
be suited by its intrinsic properties to a discussion originating in
a+b=c. The sad fact is that we humans do have to dig that deep in our
fundamental ideas about rationalism and causality until we arrive to
that point where we can notice that we took the wrong turn. This wrong
turn was the cavalier attitude towards the small details relating to
the subtle differences between 3+4 and 5+2. Once one uses the
contrast, the concept of additions gains a much wider scope of
applications and many processes can be brought into that which we can
reckon rationally by doing additions.
2011/1/27, joe.bren...@bluewin.ch <joe.bren...@bluewin.ch>:
>
>
>
>
> Dear Krassimir and All,
> Please let me direct your attention to the following in Soeren's last note,
> as well as Pedro's comment on Karl's system and Logic of Distinctions:
> ".... severe limitations to " a view of information theory as a universal
> glue, a universal predicate, a universal code .... the problem of feeling
> consciousness, perception and qualia, meaning and language as prerequisites
> for any kind of information science"
>
> I see no reason why the necessary qualitative aspects of information cannot
> exist in concert with the universal quantitative ones, giving each the
> proper emphasis depending on conditions. The Logic in Reality (LIR) of which
> some of you are aware is a logic of overlaps or interactive complements, a
> Logic of /Non-Distinctions/ that complements Karl's logic. I suggest both
> are necessary to organize and explicate the qualitative-quantitative complex
> of information, which co-exist and are never clearly one or the other part
> of the time.
> Thus, and this may be new to you Krassimir, in my approach it is not
> necessary to have "a frame in which the concepts will not be contradictory"
> ! In my logic, contradictory and conflicting concepts of information,
> exactly like the properties of information itself, co-evolve and illuminate
> one another, allowing the emergence of new ones.
> Best wishes,
> Joseph
>
>
>
>
>
> ----Ursprüngliche Nachricht----
>
> Von: mar...@foibg.com
>
> Datum: 27.01.2011 15:37
>
> An: "Pedro C. Marijuan"<pcmarijuan.i...@aragon.es>, <fis@listas.unizar.es>
>
> Betreff: Re: [Fis] comments & next session
>
>
>
>
>
>
>
> Dear Pedro and FIS
> colleagues,
>
>
> In Russian literature there exists
> an collective “author” Kuzma Prutkov , i.e. a group of writers who have used
> this common name to publish sentences.
>
>
>
> One of Kuzma Prutkov’s sentence is
> “Нельзя обнять небъятного!”, or in English “It is impossible to embrace the
> infinite”.
>
>
>
> What I mean? It is impossible to
> have only one information theory to cover all information phenomena.
>
>
>
> Because of this we need to have
> philosophical paradigm which will unite all particular information
> theories.
>
>
>
> I think we need to clear what a theory
> will discuss in given moment. This way we will have a frame in which the
> concepts will be not contradictory.
>
>
>
> How such frames can be drawn is
> topic just of the common philosophical paradigm.
>
>
>
> Friendly regards
>
>
>
> Krassimir
>
>
>
>
>
> P.S. Many thanks to all who became
> members of the ITA 2011 GIT Int. Conference Committees.
>
> The updated Call for Papers is
> published for the FIS society at:
>
>
>
> http://www.ithea.org/fis
>
>
>
>
>
>
>
>
>
>
>
>
> From:Pedro C. Marijuan
> Sent: Thursday, January 27, 2011 3:34 PM
> To:fis@listas.unizar.es
> Subject: [Fis] comments & next session
>
> Dear
> FIS colleagues,
>
> I found very intriguing the "fast & furious" messages
> of past days. One of the main triggers, I think, was Karl's response to
> Joseph's
> requests on his info theory... The logic of distinctions that Karl worked
> out
> years ago was in my view an outstanding contribution (the use of
> multidimensional partitions in set theory). Unfortunately he linked it to
> very
> idiosyncratic notions on cellular dynamics between DNA and cytoplasm, and he
> also miscalculated the number of multidimensional partitions. These are
> nontrivial matters that he has to solve or that we can discuss (necessarily
> in
> face to face exchanges!!), at least for me to accept any of his further
> developments. But let me insist that his "logic of distinctions" is highly
> original and very elegant.
>
> Then, among the many other exchanges (Jerry,
> Loet, Gavin, John, Bob...) my contention is that most of them were insisting
> in
> the predominance of some disciplinary orientation versus the competing ones.
> Jerry put it in a very clear way: "The abstract symbol systems of Dalton,
> Lavoisier, and Coulomb underly the foundations of thermodynamics as well as
> the
> Shannon theory of information as well as our concept of such abstractions as
> “energy” and “entropy.” These symbol systems are now firmly embedded in the
> logic of scientific communications..."
>
> Thus, was the exciting discussion
> basically a rhetorical contest between disciplinary orientations (where
> unfortunately neuroscience was missing)? Yes and No. Let me interpret it in
> favor of what I argued about the undefinability of information, and the
> possibility to establish a number of info conceptions after reliance on some
> particular disciplinary narrative. If we accept that undefinability, we can
> start to discuss in a different and more productive way: about conditions
> and
> procedures to establish the most elegant and economic general approach to
> information GIVEN THE DISCIPLINARY CONTENTS OF OUR TIME.
>
> Thus the past
> discussion on "intelligence and information" was very strategic (entering a
> new
> focus in our discussions), as can be the coming session, on the historical
> background of modern science. What kind of "info theory" and what
> conceptions of
> information could be framed or were present in the medieval world? How were
> they
> "recombining" their knowledge? Our presenter Dr. James Hannam (James in
> our friendly list) has recently written a very successful book. "God's
> Philosophers: How the Medieval World Laid the Foundations of Modern Science"
> in Icon Books (2009), which has been translated to several languages and has
> been shortlisted for the Royal Society Science Book Prize 2010 (and is now
> out
> in paperback). The "official" announcement of the session will be made in a
> few
> days.
>
> Information science is different, and fascinating, as it contains
> so many tricks and labyrinthine paths!
>
> best
>
> ---Pedro
>
> --
> -------------------------------------------------
> Pedro C. Marijuán
> Grupo de Bioinformación / Bioinformation Group
> Instituto Aragonés de Ciencias de la Salud
> Avda. Gómez Laguna, 25, Pl. 11ª
> 50009 Zaragoza, Spain
> Telf: 34 976 71 3526 (& 6818) Fax: 34 976 71 5554
> pcmarijuan.i...@aragon.es
> http://sites.google.com/site/pedrocmarijuan/
> -------------------------------------------------
>
>
>
>
> _______________________________________________
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>
>
>
>
>
>
>
>
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