Dear Stan,
In your last posting, you said:
> SS: Of course, the origin of the genetic system is arguably the most
>outstanding problem facing natural science. It seems that, other than the
>(to me) unconvincing RNA World idea, there is no compelling model of it.
The model that the RNA (together with the DNA) is a sequence and that the
genetic mechanism copies the information from a sequence (the dna/rna) into
a nonsequenced assembly (the living organism) and from there (by means of
the ovaries and the testes) back into a sequence is a quite compelling
model.
The term "information" has been shown in this chatroom to mean the cuts that
segregate, separate and distinguish summands;
The term "sequence" has been defined by Peano;
The term "nonsequenced /=commutative/assembly" is indeed hairy, as there
exists no definition for multidimensional partitions, although this is what
it means;
The term "copies" means a filter restriction on a set of entries into a
database (a restricted, in optimal case, bijective map between two
enumerations).
So, we can say:
Genetic information management can be modelled by assuming that
The information (the pattern of cuts on intervals)
In a sequence
Gets copied into
The information (the pattern of cuts on several intervals)
In a commutative assembly
And from there back.
A mathematician would never go near or touch something that has no
definition. Contrary to a psychologist, who has a quite different attitude
towards things undefined.
Even, if a logical entity behaves in a fashion that it is not possible to
say by rational words what it is, we can count its differing subtypes. In
the Middle Ages, they maybe counted different aspects of witchcraft or
aurification. It is legitimate to count differing appearances of a thing
even if we do not know what the thing is; as long as we can distinguish two
different kinds of that something. And that we can distinguish two differing
multidimensional partitions (e.g. sociograms) is an obvious truth.
By counting distinguishable appearances of a logical entity we do not know
the exact nature of, we can establish its logical width, domain, complexity.
In the present case, we only need to know how many different kinds of
multidimensional partitions exist, not what they are in reality.
In reality, and this answers the other question in the post:
>I know of no scientific principle that allows
>for ANY analogous entity in nature,
>save humans, to store its structural information
>digitally on a specific kind of molecular template.
What one means by the term "multidimensional partitions" appears to be the
cut pattern on the set. We have spoken about the cuts separating two similar
units generating the basis of our present counting system, N. They are
thought as unit as we think the unit to be of unit properties, that is,
alike to any other unit.
We overlook the existence of the diversity of the cuts. If we think the cuts
as extremely unit like as we think the units unit like, there remains no
space for the diversity property of the opposite of the similarity.
We end up like a partial judge who listens only to the one side. Yes, our
counting system is based on similarity. So what is it opposed to? Who
represents the interests of those who are defined irrelevant?
The cuts have differing heights and numbers. We should not force them to be
in the same - similarity based - logical picture as that they are the
enemies of. The cut is the mortal enemy of the continuation, and it succeeds
in discontinuing our perception. (We do not go, after all, as consequently
to the end in asserting similarity as to say that everything is one and
without any interruption.)
We do accept the existence and the relevance of the cuts, but we really do
not recognise their legal right to be there and to be counted in their own
facon d'etre.
Once you start co-employing the cut patterns alongside the texture, the
mechanism will become apparent, by which only such sequences can exist,
where the cut pattern agrees to the cut pattern on the heap of textile. The
key element in the mechanism is the individuating power of the symbols
employed, and that boils down again to diversity, that is how diverse are
the logical units we use to describe the world with.
It is a long and detail-rich seminar one needs in order to re-educate
himself on using diversity alongside similarity. The FIS chatroom may not be
in its intention such, so we cannot go more in details here. But please let
me keep the chance to maintain the belief that the model - compelling to me
- that our logic has heretofore not been sufficiently complex to describe
the most basic method of densifying information, namely that of writing and
rewriting it from a sequence into a commutative assembly and back, by
employing symbols that individuate in differing extents. We can increase the
complexity of our logic by co-employing the heretofore neglected aspect of
the properties of the cuts and their patterns. This makes the counting
system itself more exact as a self-referencing instrument by the factor of
0.3E-96; it allows size-independent logical and numerical statements; it
generates numerically comparable levels and densities of logical truth; it
connects the units of the counting levels "logical relation" and "object";
it employs logical archetypes with properties that are enumerated in a
numbering system, of which the basic units are the fillup limits of the
electron layers.
So, there are quite many and well-founded arguments for assuming that indeed
there appears to exist a logical answer to the great question of natural
science, how genetics functions, and that this is a model to which
reasonable and sober people can say this is a convincing, say compelling
model.
Thank you for the opportunity to advertise the
sequential-commutative-sequential mantra, which is identical to the
similar-diverse-similar mantra.
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