[Fis] Very Small Details

[Karl Javorszky]

Learned Friends,



*Taking encouragement* from Pedro’s positive judgement of the style some
basic problems of epistemology and number theory have been presented to
you, this person again reaches for the lute and sings one more strophe of
the song about diversity as opposed to similarity.

*To the comments* so far on the Ten Principles and the Simple Question:

·       *“ … information must make a difference to the promotion of any
dissipative structure. (Here we arrive in physics!)” [Stan, cited by
Pedro];*

·       *"eventually Nature itself is a pattern emerging from the relation
between universal numbers; some playing the role of environment for
others." [Bruno, cited by Pedro];*

are both very well put statements which say the same as what this person
tries to show by pointing to

a) natural numbers,

b) pairs of natural numbers,

c) cohorts of logical primitives,

d) patterns of movements of ad hoc task forces, teams of logical primitives
(aka cycles), when the cohort reacts to periodic changes,

e) differences in the readings of patterns of movements of cycles within
cohorts, namely:

1) spatially related (counted in identical units),

2) qualitatively related (counted in units of diversity).

Yes, we indeed do talk about the same deep structure, even if the surface
structures appear different. Such is the usual lay of matters in
linguistics.

*Once again, a restatement of what has been said is in order*

1) We cannot avoid constructing *a logic which is taking place in the
physical world*. We may happen to accidentally, *en passant,* explain e.g.
molecular geometry, like it accidentally happened with gravitation and some
properties of magnetism, in the course of our proceedings while we try to
catch, trap and tame Information;

2) *Information takes place in our head*, as Krassimir keeps pointing out,
like the phases of the Moon or the seasons take place in our head. It is an
anthropomorphic projection of the magic-mythical kind to say that the Moon
influences or regulates the spawning patterns of some fish. The Moon is a
big chunk of rock and does nothing, no influencing, no regulating, because
inanimate objects do not do anything.

Thomas Aquinas says the same in his own words as Newton says, in the words
of: “Be relieved, objects do not hunt you, they have no own free will,
neither heavenly, nor satanic. They stay where they are and if they are
moved, they keep moving in one and the same direction by their own obedient
nature, which means that things have no free will, specifically cannot be
possessed by Satan”. That was the socio-culturally revolutionary message
which made Newton beloved and famous, one of Fathers of Science.)

The effect of the Moon is that it is a summand in the algorithms
establishing the coordinates of that point, where the *vertical *axis *C*
(gravitation, similarity, sorting order: *a+b*), hits the *horizontal *plane
(qualitative differences, diversity, 2 sorting orders: *b-2a, a-2b*). One
may be sure there are some Institutes in Germany or Switzerland, where a
huge pendulum slowly draws circles around that point where it would point
at if the gravity of the Moon was not mixing up with the gravity of the
Earth. (There used to be such a pendulum in Budapest in the late 19th
century.) Some fish and some mammalians put such cycles to use as
metronomes.

As we see a pizza with a slice already eaten, we *think* that it would look
like a complete circle if it was still in its integrity, and we *imagine *that
part which is missing. Both the whole pizza (which is the *expectation*)
and the missing part (which is the *information*) are created in our head.
That, what is actually the case is the actually existing remainder of the
partly eaten pizza.

*But information is actually there in the physical world*

Apparently, anticipation and pleasure/disappointment resulting from the
comparison of perception with expectation is a faculty naturally born to
humans. Therefore, there must exist in Nature something which can be
otherwise than expected. Usually, we are happy that things are so as
expected; at times we are happy to experience something outside of the
usual. We are prepared to deal with both, and with mixtures of old and new,
same and different. We would not be prepared to react to such stimuli, if
such stimuli were not present in the environment. Both ends of the
describing dimension ‘same – otherwise’ do have physical realisations, from
the interplay of which we have learnt during evolution to process the
stimuli accordingly (being adapted to a world that is same and different in
the same moment and place, and across time and space.)

*The Original Sin*

Fitting to the Ten Principles, let this sub-prophet also climb a suitably
small to medium sized hill and declare in stentorian equations that we have
grown callous, sinful, disrespecting the Deeper Meaning of the Eternal
Truth of *a=a*, and have therefore lost our way to Informia (that Atlantis,
where the wise centaurs live, who are stitched together: *a *parts human, *b
*parts horse, usually in the discreet disguise of logical primitives.)

We may have sworn falsely and declared untruthfully that we follow the
rules and consequences of *a+b=c,* but in reality, we did not do so. We
have so far only and exclusively used that historically accepted reading of
*a+b=c*, which had been written by the victorious *c, *which states that
there are *no* *cuts *between agglomerations of lower level symbols, never
have been any such, and that such abominations be never ever talked about
or even mentioned again. A fine work of *damnatio memoriae* of the late cut
that formerly separated *a, b. *This is callous, because the cut is still
alive and kicking, as the left side of *a+b=c *shows.

The cavalier attitude towards cuts, (and the cursed superstition that the
goals legitimise the means: that we can do anything in order to arrive at a
world where everything is as we wish it; we say: as it should be), has led
us to the present unholy state of affairs. The more one idealises his
rules, the more one lives in self-created Utopia. This erroneous idolatry
of similarity, and our deeply felt revulsion against all that are not as we
imagine them, they should be, these false prejudices have led us astray! We
have lost our way in the dark. The sub-prophet cries out: thou shalt
recognise reality! Diversity is a fact of life! I say unto you: We should
truly not have dropped the cuts (Separator symbols, Parentheses of
differing strengths, like e.g. /,[,{,(,/*,//:, etc.), completely ignoring
them, pretending that they make no difference. We have to deal with
diversity also, if we address biologic phenomena.

*Repent and Recount!*

Counting the parentheses separating the continuities – as opposed to the
traditional method of counting the continuities, backgrounding the
separators -, appears to be, comparing the algorithms used, unfortunately
much less intuitive than the traditional way. (One would need 17 fingers on
each hand for a start, about 6 or 7 hands, the premium version would be 8
hands, and a memory very astute.)

Using the diversity algorithm for calculating unrelated occurrences is a
possible task, but the procedure takes some dedication till one has learnt
it. Better at first to use the overall extents (upper limits) and then find
something to count, where the occurrences are related.

*The difference that makes a difference*

In fact, the slack between the *f1(n) *and *f2(n)*, similar and diverse, is
really not that big. The deviation of one to the other is by factors of
about *(1,-3.2,1,3.4,1,-q)*, where *q *grows from 1 to ∞ as *n > 97,
*specifically
with* n > 135. *That there are three equivalence points (at *n=1, 32, 97)*
and two maxima (near *n=11,67*) is quite practical, if one wants to
discuss, how many different linear line-ups are possible when compared to
the maximal number of subdivisions into groups carrying different symbols.
The idea that one can make more than *3 *times more sequences of elements
than one can create distinct groups among the elements, if the elements
count *6x11, *but one can make more than *3 *times more distinct groups
among the elements than one can make distinct sequences among the elements,
if the elements count *66, *this clickety-clock interplay can nicely
explain how information is compressed. It tends to get complicated in some
of the details, though.

The point to make here is, that a 300% increase in information transmission
efficiency when one switches *from:* reading his 67 fingers one after the
other *to:* watching the fingers being dent to any of *d *distinct
different degrees, regardless of the how-many-eth of the fingers they are,
sounds very nice if one plays with fingers and amino acids, which do the
trick with *3x4* and *64 → 21*, but let us keep the perspective: these
are *indeed
very, very small *differences. In the most efficient variant, on *n=66*, we
compare 5.4E92 with 1.9E93. Relative to the bigger, the smaller is about
28% of it. Regarding both together, their difference is a minuscule part in
the order of magnitude of 3.4E-91%.

The original sin, of *neglecting the cuts while counting*, is sinful not so
much in the *extent *of having measured wrongly and given false testimony
when announcing the results of the measurement, by having neglected to use *two
*measuring rods in order to come near any sensible degree of precision,
because, after all having been said and done, and measured, a measurement
inexactitude (the extent of the inner incongruence of the numbering system)
of about 3.4E-91% is *really not* *that a great difference*; the original
sin lies rather in *neglecting the principle *of diversity and similarity
being both equally present and legitimate in our life and indeed in the
physical, chemical and biological world we live in.

The importance of the principle comes to light if we consider what we have
counted and compared. One can manipulate 66 objects in astoundingly
manifold ways, almost as creatively as Nature does, if one sees them once
as *6x11* sequenced individuals and once as one whole group of *66 *being
subdivided into subgroups. The upper limits count all possible distinct
sequences and commutative structures imaginable on *n *elements. Among
these there are some in which the elements are *related *to each other, and
also those in which the elements are *not related* to each other. The
elements, of which the interplay we investigate, are surely *related *to
each other (some say ‘adjacent’ if they mean “there is a Zusammenhang among
the Sachverhalte”).

*Enter cycles, harbingers of redemption*

Cycles are a sure sign that heavenly forgiveness exists. Cycles allow us to
find and use an interface which connects *sequenced *and *commutative *symbols;
they are in fact actually such an interface and Rosetta stone. The corpus
of a cycle contains members which are *sequenced *among each other; these
are furthermore concurrently sharing the *commutative *symbol of
appurtenance to that specific cycle. If we speak in words of cycles,
whatever we say will be interpretable as well as a statement regarding
sequences and as well as a statement regarding subgroups that are different
to some other subgroups. The manoeuvres of the logical primitives during
periodic reorganisations allow recognising that the corpora of cycles are
consisting of a relatively small number of elements, and that these
elements are related to each other in very many ways, across different
cycles, too. The interplay of *“there can be no <such> sequences, because
there are not enough <such> commutative structures that can be related”*
and *“there can be no <such> commutative structures, because there are not
enough <such> sequences that can be related”* can go full throttle if the
elements are *adjacent* to each other, occasionally, periodically,
regularly, predictably; if the elements are deeply related to each other.
(The words following *“there can be no …”* are containing information,
because they describe that part of the pizza which has already been eaten.)

*Many roads lead to Informia*

There are more than a dozen different intellectual pathways leading to the
idea which is signified by the value *3.14.* Similarly, there will be many
different ways of establishing the working mechanism of the system which is
signified by the principle *n! (=, >, ~, <, ~, >, >>) n? f(n),* where *n? *is
a cousin to *n! *and yields the maximal number of distinct collections of
concurrent overlapping partitions on a collection of *n *elements.

The proposal of using *two *chopsticks for measuring something complex,
where the two chopsticks are *very-very-very* *(repeat 91 times)* *slightly*
out of whack respective to each other (and agree with each other at
*n=1,32,97*) opens up a wholly new world of epistemology, therefore of
logic, therefore of number theory, therefore of physics, chemistry and
physiology. In psychology, we know the instincts of imprinting and of
curiosity. The former feeds the brain with endorphins if everything is like
expected, the latter brings forth gratifications for the brain if there is
diversity in the perception (*varietas delectat*). The interplay between
similar and different is a basic fact of life. If our generation decides to
call it ‘information’, so be it. The surprise element of the spectacle is
caused by our having separated the two aspects beforehand and now we are
coloured surprised as we see how they interact if left free in their
natural habitat, among other mental products. The difference between
similar and diverse is not man-made. It has always been a part and parcel
of our thinking, because our ancestors have adapted to periodic,
predictable changes affecting the habitat, recognising eternal periodic
changes against a background of continuity, and recognising the continuity
against a background of eternal periodic changes. Our neurology uses the
compromises between similar and diverse, even though our thinking prefers
to handle impressions on their basis of similarity, predominantly a
cultural achievement. Our culture has had, so far, no means to address the
subject-matter of how much a group can be diverse and still stay one group,
in any formal way or depth, because not even Euclid, Archimedes, Euler or
Gauss could have reasonably dreamed of writing up all the possible cycles
among logical primitives that are related to each other, and systematically
investigate and categorise the patterns appearing, because scientists in
earlier times had not had computers.

*What we do in this chatroom* is strictly spoken not a work on an
invention, because we do not invent anything basically new in the
subject-matter itself. What we do here is rather comparable to the work of
archaeologists: we uncover fundaments of cultures, on the shoulders of
which we stand. Like the work of archaeologists is tremendously furthered
by the assistance of magneto-interferometers mounted on drones, the work of
epistemology is advanced tremendously by the availability of access to
industrial methods of generating true statements, sieving the lot and
fishing for tell-tale patterns, which lead to insights. One such is that
the combinatorics of *6x11 *can arrive at creating semantic differences by
using its being syntactically different to that of *66. *Although the slack
is rather small in relative terms, it allows loopholes, crooks, hooks,
nozzles, weaving patterns and knots, and the creating and tying up of loose
ends, specifically if one thinks in terms of units aggregated from lower
level units. Nature knows how to aggregate into *3x4, 64, 21, etc.*, that
is: into logical units of such sizes, on which she can perform the
accounting tricks she evidently performs. Here, in this chatroom we are at
the task of reverse engineering Nature, by figuring out, how she deals with
information. Information being the deviation between what can be the case
and what is the case, we have had to find one more small detail in the fine
prints to the general agreement of *a=a*, and lo behold! indeed who resides
and hides in the small details: in our case, our charming Information.

PS: the upper limits *n?, n!* are discussed in oeis.org/A242615.
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