FIS colleagues:
The recent contributions, each in his way, encourage systemic thinking. The
best
thread, for me, to demonstrate on what number theory can contribute to this
discussion, is to comment on Aleks Jakulin's text. As Aleks writes anyway in a
very broad perspective, I hope other contributions feel also mirrored.
Aleks:
> Let's focus on the level of a (possibly compound) system, composed of
> components, which are themselves composed from molecules.
We discuss a set composed of subsets, which are themselves composed from units
we consider for purposes of this discussion to be the unit.
Aleks:
> there
> can be sub-corporate entities that cut in the intermediate space between
> the corporation as a whole and an individual employee.
The perspective of our investigations is focused on subsets - as opposed to
the
whole of the set and to the individual unit.
Aleks:
> So evolution takes place at many levels. The key realization is that one
> level sits on top of other levels.
The set includes subsets. Subsets can also include smaller subsets.
Aleks:
> You cannot survive under an x-ray
> machine because your cells are dependent on stable molecules and atoms.
An over-determination of places of parts of an assembly (e.g. by synchronising
their movements due to the effects of a radiation) is not conductive for
biologic processes.
Aleks:
> A culture that consumes its people in wars, or expends its best people
> without letting them reproduce (e.g., through an overextended education
> that interferes with reproduction), is a dying one.
The quality of a set as described in a temporal cross-section (in this moment
there are x people in reproductive age, y people are not available for
reproduction, z people have sufficient circumstances to reproduce, etc.)
has an
intimate (according to some, causal, logical) relation with the probability
spread re prediction about the set's future state (if it is so now, then it is
probable to a% that it shall be in state k in time t from now, to b% that it
shall be in state w in time t from now, etc.)
Aleks:
> I was merely trying to concoct a physicalist theory of meaning in terms
> of Stan's hierarchies: the higher level is the 'meaning' of the lower
> level, and the lower level is the 'fact' to a higher level.
The description of the set in terms of its subsets will always have an
arbitrary touch in it, if there are several "layers" of subsets. Specifically
so, if the segmentation of the set into subsets happens several times
concurrently. Given some properties of a subset, its included subsets have
also
some predictable properties. The properties of subsets of a subset depend
heavily on the properties of the mother subset.
Aleks:
> This way one
> avoids the recursive self-referential loop (What is A to A? What is the
> feeling of feeling cold? What is the meaning of meaning?),
There are two languages which describe a set: one details the proportions of
subsets among each other, the other details the properties of individuals.
They
are of course cross-referencing each other (the more specific properties
subsets have, the more individualised are the objects each.) The meaning of a
fact is its description in the other language. (Cold is that electrical
pattern
which accompanies this bunch of biochemical properties. Understanding is that
bunch of biochemical properties which accompanies the reproduction of some
electrical patterns which were predictable and predicted.)
Aleks:
>Of course, the thinking is not complete and perfect,
As thinking it is complete and perfect. As a part of a to-and-fro, of
predictably stable bijective relations between feeling and thinking, (between
the representation of a <thing> as a biochemical mixture and the
representation
of the same <thing> as an electrical discharge pattern, that is, congruent
relations between commutative and sequential arrangements of the arguments
of a
logical sentence referring to the same logical entity), it is not complete and
perfect.
Aleks:
> but if one
> accepts that thinking is essentially a web of constructs,
thereby we accept the Wittgenstein set of logical relations
Aleks:
> we can discuss
> different theories of meaning: all of them are oversimplified, but some
> we might like better than the others.
The theory of meaning being presently arrived at in this very FIS jam
session/workshop does not strike me as being oversimplified.
>
> > The social system has developed, for example, a juridical system
> > which tries to prevent people from perishing when they are weak.
The
> > dynamics of philosophies ("your philosophy will perish")
are in important
> > ways different from the dynamics at the level of species. These
> > in the dynamics provide us with room for generating a
knowledge-based
> > economy. Scientific knowledge is often based on counter-factuals
and
> > counter-intuitive by nature.
>
> I agree that the dynamics is different, but still I find it similar
> enough so that the same explanatory metaphors can be used. I have seen
> my share of technologies and methodologies that have perished, a great
> many of dead ends. And there too are means of protecting and saving the
> weak, like the web archive [http://www.archive.org], and various
> sanctuaries for old software
> [http://www.woundedmoon.org/win32_freeware.html]
and old computer games
> [http://www.the-underdogs.org/].
Nevertheless, a lot unnamed things have
> perished, and I'm sure this is the case of philosophy as well. Beware
> the trap: if you can remember it, it hasn't perished yet.
>
> > Thus, the natural ("biological") order of things is a
dangerous
> > argument at the level of society because one risks to
> > throw away the child with the bathing water (i.e., culture).
> > The differences between "biological" evolution and
cultural evolution
are to
> > be celebrated if we wish to understand how a knowledge-based
subdynamics can
> > counteract upon the "natural" order of things.
The concept of evolution is the counterconcept to entropy. What one considers
natural, is culturally dependent. In number theory, the natural numbers are
the
most natural we can get. They do have, naturally, natural properties, and this
is what number theory sings and dances about. There are very natural
densities,
agglomerations, probabilities which allow simulating evolution. May we
respectfully offer the properties of natural numbers to find common ground in
the discussion of how properties of systems and sub-systems evolve? Let us use
mathematics to help to figure out what the normal flow of matters is.
Aleks:
> I write "biological"
> > deliberately between quotation marks because the biological
sciences are
> > part and parcel of this culture.
Which culture? The culture at the cafeteria of a TU and of that of a
psychology
institute are quite different. The belief in the predictability of reality
sets
the two populations apart.
Aleks:
> Agreed. But naturalistic approaches do speak of co-evolution between
> culture and population, so the workers in the area are well aware of the
> problem. The devices, however, are at a lower level,
Newton has turned up the philosophy of science by saying it remains idle or
keeps rolling. This excludes all that breathes and eats and reproduces. Since
then, biology has been treated offside or in cabaretistic ways (occult
calculations, planetary biorhythms, etc.). There is much basic re-education
necessary to make absolvents of TUs understand the way one counts in
psychology. It is not the devices which are at a low level. Often it is the
ability of the researcher to look thru the microscope /having persuaded
himself
that there might be something worth looking at/ and to recognise the
extraordinary that is to be encouraged, rather than the engineering of the
microscope.
Aleks:
> It's the same as the interface between chemistry and biology,
> or between psychology and sociology.
The contrast can be emphasised by biology vs. mechanics. The basic axioms re
"stable state", "predictable state" are quite different.
Aleks:
> While chemistry and biology, psychology and sociology peacefully
> coexist, humanists and naturalists keep throwing insults at one another.
They speak in different grammars: one in a sequential grid (the Wittgenstein
set), the other in distance-torsion-structures (what Wittgenstein says is
outside his set). This frustrates.
Aleks:
> Most naturalists don't take the time to understand philosophy and just
> ridicule it and dismiss it in their naive overconfidence; most humanists
> fear the one-sided uninformed brashness of naturalists, and then employ
> scare tactics. I guess the problem is in the competition between
> psychology and cognitive neuroscience, and between sociology and
> evolutionary psychology. With the escalated temper at both sides, there
> is rarely an opportunity to exchange ideas.
> Aleks
All the better that there is FIS.
Karl
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Received on Mon May 16 10:54:02 2005
