[Fis] The Limits

Fri Mar 1 14:00:02 CET 2019

Dear colleagues,

Limits also need a collaborative effort. Just in the last contributions, we
saw Pedro approach the same subject from the biologists’, Bruno from the
mathematician-philosopher’s side, Stan giving an overview. The term ‘limit’
is applied, if I understand the positions clearly, referring once to
thresholds within, and twice to boundaries delimiting the inside from the
outside.

The proposal is to return to the linguistic analysis of what we all say.
Pedro agrees that symbols which are applied concurrently on objects can
create a model of a living organism, quasi as a temporal cross-section of
the processes in an organism. In the contemporary context – let me thank
Michel Petitjean, who has advised me to take care with the word
‘commutative’, as it refers to concepts that have their own connotations
and definitions in mathematics -, it is possible to say ‘the liver contains
x1 mg Fe/g tissue and y1 mg K/g and z1 mg Ca/g, while the lungs contain x2mg
Fe/g tissue and y2mg K/g and z2mg Ca/g and the muscles contain x3mg Fe/g
tissue and y3mg K/g and z3mg Ca/g”, while it is not reasonable to say
“liver is 1st, muscles are 2nd and lungs are 3rd”, because these objects
are contemporary. Insofar the word ‘mixture’ describes an assembly, in
which the elements have no fixed spatial order or sequence, the organism is
a contemporary mixture, and in amateur-speak commutative (because one has
learnt that if the position of an element in an expression is of no
relevance, then the ability to be anywhere is called being commutative).
One could continue the list of nutrients and constituents across more
organs, the principle is clear: more than one statement can be true with
regard to one element. These statements make the elements distinguishable,
irrespective of where they are, and even more irrespective of the sequence
in which we recite their properties. (We generalise into *n* organs and
substitute mg/g value ranges into colors. ‘Of *n* balls, *r* are colored
*red*, *b* are colored *blue*, *g* are colored *green’*, observations: 1.)
blue, red and green balls are distinguishable, 2. The question is
meaningful to ask: ‘How many are *{red+blue, blue+green, …*?’)

As opposed to the commutative (contemporary, like a mixture), the sequenced
assembly, of which the finest example is our DNA, is such, that it is not
possible to say “element *i* is on position *i1* and concurrently on
position *i2* and *i3*”. This is a different way of piling true statement
above each other. Each element is unique with regard to its place, but is
seen as being without any private, distinguishing marks, once lifted off
its place. It is actually the imagined place of the element what we count,
not the element itself, that being without any marks. The element is
actually defined by “That, which is *i *places away from *no-place*,
otherwise nondescript.”

Now we have arrived at having *two* counting backgrounds, once with regard
to the how-ness of elements, irrespective of places, and once with regard
to the where-ness of elements, irrespective of their how-ness.

We relate the *how-ness* of elements to their *where-ness* by means of
using their common *how-many-ness*. Having a fixed number of elements, we
discuss, how many variants of how-ness are possible for so many elements,
and compare this to the results we find as we investigate, how many
where-ness these same elements can produce. The results are indeed
startling, and can be studied in detail in oeis.org/A242615.

We are used to having a mental grid of evenly spaced intervals as the
background, like a millimetre paper. In such a system, the undeniable
existence of limits, thresholds, equivalence ranges and delineations, which
comes by itself, appears indeed puzzling. The proposal is to use *two *kinds
of millimetre paper, which deviate slightly with respect to one another. If
we use the basic unit of 1 million logical relations and scale, how many
actual units are needed to produce so many combinatorial varieties, we
shall get two, slightly differing kinds of millimetre papers (background
graph papers).

Once we overlay the equally patterned web grid with one more web grid,
which is a slightly deviating non-equally patterned grid, we see
magnifications and shrinkage, separated by two slices of almost sharp
agreements of the scales. Which of the two background grids is
well-proportioned and which is distorting, is of course n undecidable
epistemological, oftentimes livid, at times explosive discussion among the
two principles which depict “number of distinct logical relations possible
among *n *elements” in two, slightly different ways. There are always more
variations of space for the things being varied, except if the things
number between 33 and 96, in which case there are more variations of things
possible in the moment than variants of space exist to accommodate the
variations. The conclusion is, that the world is both contemporary and
sequential. Hence the necessity for the cycles.

The overlap of two, equally valid, counting scales, number lines, while
counting leads to a great number of limits, thresholds, equivalence ranges
and many other phaenomena, among which logical archetypes, that is: types
of agglomerations of logical variants for which there is no logical space
to be in.

The delineation to the outside, and with it, the recognition, for which
kinds of logical sentences the method of counting *consistently* is
helpful, and for which not, has been addressed following a very fine
tradition by Bruno and by Stan here. If I understand their exposes
correctly, the moral of the story is: we can recognise, which systems are
rational, if we had built the system rationally, and this system itself is
a definition of what can be expressed by it rationally. This is a
time-honoured result of thinking, and agrees to what The Great W said about
not wasting time talking nonsense, and what is not a nonsense is anyway
nothing news, as it cannot be anything new. What we can reasonably say, we
could have said it all, long ago before now, we were just too much occupied
with other business to talk about it before. It is not the fault of
tautologically true sentences that they had not been explicated sooner:
they had always been there. It is just us, who had not thought it possible
till now.

The good news is, that there is a light at the end of the tunnel (vision).
It appears possible to give a step-by-step introduction to the algorithmic
grasp of the term ‘information’. Information is in a fashion an answer to
the question: ‘How many steps yet to the limit?’. This can be utilised, so
there is reason to keep working on encircling the biest.

Karl

Am Mi., 27. Feb. 2019 um 16:22 Uhr schrieb Stanley N Salthe <
ssalthe en binghamton.edu>:

> Here I reply to Pedro's challenge to arrange three well-known Principles
> into a Subsumptive Hierarchy.
>
> GODEL:  The first incompleteness theorem states that no consistent system
> of axioms whose theorems can be listed by an effective procedure is capable
> of proving all truths about the arithmetic of the natural numbers.
>
>        SNS:  Logic. You need a more encompassing system to demonstrate
> consistency of a system of axioms. This invites use of the subsumptive
> hierarchy; {{ }}.
>
> CHURCH-TURING:  Computation:  A function on the natural numbers is
> computable by a human being following an algorithm if and only if it is
> computable by a Turing machine.
>
>         SNS: Mechanicism.
>
> HEISENBERG:  Measurement.   The position and also the velocity of an
> object cannot both be measured exactly, at the same time.
>
>        SNS: Measurement is physical and disturbs the measured, changing it.
>
>
> Thus, in the subsumptive hierarchy:
>
> { logic --> { mechanicism projected onto material world --> { contingency
> in material world }}}
>
>
> STAN
>
> On Tue, Feb 26, 2019 at 3:15 PM Pedro C. Marijuan <
> pcmarijuan.iacs en aragon.es> wrote:
>
>> See the red color and big font below ("fundamental principles: Godel,
>> etc. ")
>>
>> El 26/02/2019 a las 21:09, Stanley N Salthe escribió:
>>
>> Pedro -- Sorry, but I don't see the Three Principles in this message.
>> Could you please resend them? Thank you.
>>
>> STAN
>>
>>
>> On Tue, Feb 26, 2019 at 8:26 AM Pedro C. Marijuan <
>> pcmarijuan.iacs en aragon.es> wrote:
>>
>>> Yes, Stan, they are below. I repeat herein, see the context in the
>>> message.
>>> *"inevitably reappears later on in strange but fundamental principles:
>>> Godel, Heisenberg, Church-Turing... They basically consist in limits of
>>> thought..."*
>>> Perhaps you can post in the list a composite with the response to the
>>> principles too
>>> --Pedro
>>>
>>>
>>>
>>> El 26/02/2019 a las 14:08, Stanley N Salthe escribió:
>>>
>>> Pedro -- Thanks, but ... I don't see the "three principles below". Can
>>> you repost?
>>> Also, please advance this discussion to the list (I just forgot).
>>>
>>> STAN
>>>
>>> On Tue, Feb 26, 2019 at 7:55 AM Pedro C. Marijuan <
>>> pcmarijuan.iacs en aragon.es> wrote:
>>>
>>>> OK Stan, but how would you put in hierarchical ordering those three
>>>> principles below?
>>>> By the way, you have not posted to the list (only to me).
>>>> Best--Pedro
>>>>
>>>> El 25/02/2019 a las 21:15, Stanley N Salthe escribió:
>>>>
>>>> Pedro -- Regarding limits, I again advance a litany of limitations as
>>>> shown in hierarchical form (using the subsumptive hierarchy format),
>>>> suggesting how limitations and biases are piled upon us.
>>>>
>>>>  (physico-chemical {biological {animal {mammalian {primate {human
>>>> {languaged }}}}}}
>>>>
>>>> Of course, each level opens up new, increasingly limited, opportunities
>>>> for new explorations.
>>>>
>>>> STAN
>>>>
>>>>
>>>>
>>>> On Mon, Feb 25, 2019 at 1:42 PM Pedro C. Marijuan <
>>>> pcmarijuan.iacs en aragon.es> wrote:
>>>>
>>>>> Dear Karl and FIS Colleagues,
>>>>>
>>>>> Your message has made me think a couple of subjects. First, I have
>>>>> acknowledged several times, both publicly and privately, that your approach
>>>>> to estimating the multidimensional partitions on limited sets (the limit of
>>>>> distinctions when multiple qualities are piled upon elements of finite
>>>>> sets) is highly original and may find application in different fields. I
>>>>> think particularly in hippocampus' space/time organization of our spike
>>>>> sequences into binding percepts; probably in fields of physics too. But on
>>>>> the other hand, I have always disagreed on your (over)extension to DNA
>>>>> triplets, which has received a strong emphasis from your part ... Well, it
>>>>> is my personal opinion, and it may be quite wrong, of course.
>>>>>
>>>>> Anyhow, the above has taken me to the next reflection, somehow
>>>>> outlandish, that concerns "limits". I have some vague memories of a
>>>>> reflection in C.Booker (2004; or was it in Bonnet 2006?) on why we are not
>>>>> conscious of our own limitations and incur in quite many idiosyncratic
>>>>> biases, which are so well captured in narratives. I will try to put it in a
>>>>> more conceptual way: our thinking limitations do not let us establish the
>>>>> limits of our thought. It has individual consequences in our terrible
>>>>> inclination to overextend paradigms, but also a more "abstract", collective
>>>>> lack of final anchors. There is a false closure attempted that fails,*
>>>>> and inevitably reappears later on in strange but fundamental principles:
>>>>> Godel, Heisenberg, Church-Turing... *They basically consist in limits
>>>>> of thought put to the foundations of universalistic disciplines. In other
>>>>> more restricted fields, particularistic ones, those principles do not
>>>>> appear, or better, they are not needed. In the case of information science,
>>>>> which in my view is also universalistic, that kind of principled limit is
>>>>> needed too. Once properly established, or at least intuited, we could
>>>>> better discuss on the kinds of general theories that may be comprehended
>>>>> within a really multifarious enterprise such as info science.
>>>>>
>>>>> I will appreciate hearing opinions on these baseless comments.
>>>>>
>>>>> Best--Pedro
>>>>>
>>>>>
>>>>>
>>>>> El 19/02/2019 a las 12:08, Karl Javorszky escribió:
>>>>>
>>>>> Dear Pedro,
>>>>>
>>>>> please allow me to raise a dissenting voice to the content of
>>>>> following citation:
>>>>>
>>>>> *“…On the other hand, no general theory for large non-equilibrium
>>>>> systems exists.  The legendary Hungarian mathematician John Von Neuman once
>>>>> referred to the theory of non-equilibrium systems as the “theory of
>>>>> non-elephants” meaning there could be no unique theory of such a vast area
>>>>> of science.” *(Per Bak, How Nature Works)
>>>>> In fact, the theory has been brought to you since some 24 years, as a
>>>>> sequence of suggestions, proposals, models, initiatives, encouragements,
>>>>> requests and so forth,  that observing the interaction between sequences
>>>>> and mixtures  is opening up a new door to a completely fresh view of the
>>>>> interrelations among the parts of the world. The principles deducted from
>>>>> models that employ such elements which are distinguishable and concurrently
>>>>> both contemporaneously and sequentially labeled (as opposed to all models
>>>>> known hereto, which each use elements that are indistinguishable and either
>>>>> sequential or contemporary), these principles are valid and actually at
>>>>> work in Nature, on all echelles, from the subatomar to the galactic .
>>>>>
>>>>> I include the abstract I submitted to IS4SI, as part of the FIS track,
>>>>> and hope that the colleagues will participate in bringing recgnition to the
>>>>> collaborative work that has gon on in this FIS chatroom since 1997. The
>>>>> abstract describes, in the form of a general theory, large non-equilibrium
>>>>> systems. By including that part of the world, which is not the case, the
>>>>> theory encompasses elephants and non-elephants concurrently.
>>>>>
>>>>> Karl
>>>>>
>>>>>
>>>>> --
>>>>> -------------------------------------------------
>>>>> Pedro C. Marijuán
>>>>> Grupo de Bioinformación / Bioinformation Group
>>>>> pcmarijuan.iacs en aragon.eshttp://sites.google.com/site/pedrocmarijuan/
>>>>> -------------------------------------------------
>>>>>
>>>>>
>>>>>
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>>>>
>>>> --
>>>> -------------------------------------------------
>>>> Pedro C. Marijuán
>>>> Grupo de Bioinformación / Bioinformation Group
>>>> pcmarijuan.iacs en aragon.eshttp://sites.google.com/site/pedrocmarijuan/
>>>> -------------------------------------------------
>>>>
>>>>
>>> --
>>> -------------------------------------------------
>>> Pedro C. Marijuán
>>> Grupo de Bioinformación / Bioinformation Group
>>> pcmarijuan.iacs en aragon.eshttp://sites.google.com/site/pedrocmarijuan/
>>> -------------------------------------------------
>>>
>>>
>> --
>> -------------------------------------------------
>> Pedro C. Marijuán
>> Grupo de Bioinformación / Bioinformation Group
>> pcmarijuan.iacs en aragon.eshttp://sites.google.com/site/pedrocmarijuan/
>> -------------------------------------------------
>>
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