Dear FIS,
in a parallel chatroom, in the course of a discussion, I had written up the current formulation of my
research subject. Maybe, a portion of it could be of interest for FIS, as a definition of
information evolves quite naturally from additions.
... the question, responding to which I propose the answer "so", would
be:
"How does theoretical genetics conceptualise the transmission of information from and into the
DNA?"
The answer, again, is today in the following formulation:
"While conducting the addition 1+1=2 we actively neglect an aspect of the term "1+1"
by maintaining that for all practical purposes 1+1 is indeed the same as 2. We disregard by this
social convention /agreement, definition/ a very slight logical difference, which resides in the
obvious difference that is there between 1+1 on one hand and 2 on the other hand. We disregard an
information by using the uniformity of the summands. Information is that what we neglect as we
conduct an addition.
In a closed system (like mathematics), no parts of it can be discharged, disregarded, wished away.
We may ignore the difference (the information) of 1+1, but this cavalier attitude to logical
exactitude does carry a price. The result is not quite exact, even if we say/insist that it is by
definition exact.
The numeric extent of the logical inexactitude is indeed extremely small but adds up, like rounding
errors can keep adding up, until, in an idealised assembly, 136 units are counted. Then, it becomes
unclear whether the rounding error we commit by treating a set consisting of parts as if it was in
one piece /that is, conducting additions with no regard to the information content in the summands
which we throw away/ adds up to a whole unit.
The same inexactitude governs also theoretical genetics, the mechanism by which the brain packages
and unpacks information by way of the memory, and generally quite many more basic facts of Nature
which have so far been beyond our understanding".
So, summarising, I keep saying that:
a) the operation of addition is usually presented as being more exact than it is in reality;
b) the operation of addition emphasises the uniformity of the units;
c) the units have also a dissimilarity property (which is the basis for information);
d) evolving a measure (function) for dissimilarity involves one in determining the properties of a
maximally structured set;
c) comparing a maximally structured set's possible states once with regard to the uniformity, once
with regard to the diversity of the subsets leads one to numerical discrepancies;
d) these discrepancies appear to have a fundamental importance within mathematics and of course in
all applications where mathematics is in use;
e) the key point being rigid (linear) neighbourhood relations.
Hope you like the "information is that what we disregard as we conduct an addition" bit of
it.
Best
Karl
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Received on Thu Jan 12 18:09:43 2006
