[Fis] NEW DISCUSSION SESSION--TOPOLOGICAL BRAIN

[Karl Javorszky]

Thank you for the excellent discussion on a central issue of epistemology.
The assertion that topology is a primitive ancestor to mathematics needs to
be clarified.

The assertion maintains, that animals possess an ability of spatial
orientation which they use intelligently. This ability is shown also by
human children, e.g. as they play hide-and-seek. The child hiding considers
the perspective from which the seeker will be seeing him, and hides behind
something that obstructs the view from that angle. This shows that the
child has a well-functioning set of algorithms which point out in a mental
map his position and the path of the seeker. The child has a knowledge of
places, in Greek "topos" and "logos", for "space" and "study".

As a parallel usage of the established word "topology" appears
inconvenient, one may speak of "toposcopy" when watching the places of
things. The child has a toposcopic knowledge of the world as it finds home
from a discovery around the garden. This ability predates its ability to
count.

The ability to be oriented in space predates the ability to build abstract
concepts. Animals remain at a level of intellectual capacity that allows
them to navigate their surroundings and match place and quality attributes,
that is: animals know how to match what and where. Children acquire during
maturing the ability to recognise the idea of a thing behind the perception
of the thing. Then they learn to distinguish among ideas that represent
alike objects. The next step is to be able to assign the fingers of the
hand to the ideas such distinguished. Mathematics start there.

What children and animals have and use before they learn to abstract into
enumerable mental creations is a faculty of no small complexity. They
create an inner map, in which they know their position. They also know the
position of an attractor, be it food, entertaintment or partner. The
toposcopic level of brain functions determines the configuration of a
spatial map and furnishes it with objects, movables and stables, and the
position of the own perspective (the ego).

This archaic, instinctive, pre-mathematical level of thinking must have its
rules, otherwise it would not function. These rules must be simple,
self-evident and applicable in all fields of Physics and Chemistry, where
life is possible.  The rules are detectable, because they root in logic and
reason. The rules may be hard to detect, because, as Wittgenstein puts it:
one cannot see the eye one looks with, fish do not see the water. We
function by these rules and are such in an uneasy position questioning our
fundamental axioms, investigating the self-evident.

The rules have to do with places and objects in places. Now we imagine a
lot of things and let them occupy places. It is immediately obvious that
this is a complicated task if one orders more than a few objects according
to several, different aspects.

We introduce the terms: collection, ordered collection, well-ordered and
extremely well ordered. As a collection we take the natural numbers, in
their form of a+b=c. This set is ordered, as its elements can be compared
to each other and a sequence among the elements can be established. We call
the collection well-ordered, if every aspect that can create a sequence
among the elements is in usage, determining the places of elements in
sequences. A well-ordered collection can not be globally and locally stable
at the same time. In most parts and at most times, it is in a quasi-stable
state. The instabilities coming from contradictions among the implications
of differing orders regarding the position of elements will appear in many
forms of discontinuities. We call the collection extremely well-ordered, if
the discontinuities, which appear as consequence of praemisses which are no
more compatible to each other, in their turn cause such alterations in the
positions of the elements that henceforth the praemisses are again
compatible to each other. The extremely well-ordered collection maintains a
loop of consequences becoming causes while changes in spatial
configurations take place. In the well-ordered collection there is a
continuous conflict, out of which loops that maintain stability can evolve.

The mechanism is easy to recreate on one's own computer. Nothing more than
a few hours of programming is required to understand and to be able to use
the toposcope. Its main ideas are known under "cyclic permutations". It is
important to visualise that elements change places during a reorder. The
movement between "previously correct, now behind me", "presently here, not
yet all stable" and "correct in future, not yet there" has many gradations
and many places. Patterns evolve by themselves, as properties of natural
numbers.

There is a simple set of numeric facts that build the backbone of spatial
orientation. The archaic knowledge shared by animals and children is based
on a simple set of algorithms. These algorithms predetermine the connection
between where and what. The toposcopic brain utilises the numeric facts,
like the liver utilises the chemical facts.

The layer of interpretations of the world that is a pre-human, animal,
instinctive knowledge about spatial orientation needs no learning, because
it is based on facts. The facts are not, where it will condense and what it
will look like, but rather the facts are that there will be a region where
it will condense and it will have a specific property to it. The patterns
of movements of elements during changes in order in a well-ordered
collection create a basic sceleton of thinking. To see the patterns here
referred to, it is necessary to order a collection and then order it some
more until it becomes well-ordered, and watch the conflicts that are
immanent to order, namely its alternatives and its background.  This is
simple, archaic and instructive.

2016-11-30 8:46 GMT+01:00 Karl Javorszky <karl.javorszky at gmail.com>:

> Topology
>
> The session so far has raised the points: meta-communication,
> subject-matter, order, spaces.
>
> a.)     Meta-communication
>
> Gordana’s summary explicates the need to have a system of references that
> FIS can use to discuss whatever it wishes to discuss, be it the equivalence
> between energy and information or the concept of space in the human brain.
> Whatever the personal background, interests or intellectual creations of
> the members of FIS, we each have been taught addition, multiplication,
> division and the like. We also know how to read a map and remember well
> where we had put a thing as we are going to retrieve it. When discussing
> the intricate, philosophical points which are common to all formulations of
> this session, it may be helpful to use such words and procedures that are
> well-known to each one of us, while describing what we do while we use
> topology.
>
> b.)    Subject-matter
>
> Topology is managed by much older structures of the central nervous system
> than those that manage speech, counting, abstract ideas. Animals and small
> children remember their way to food and other attractions. Children
> discover and use topology far before they can count. Topology is a
> primitive ancestor to mathematics; its ideas and methods are archaic and
> may appear as lacking in refinement and intelligence.
>
> c.)     Order
>
> There is no need to discuss whether Nature is well-ordered or not. Our
> brain is surely extremely well ordered, otherwise we had seizures, tics,
> disintegrative features. In discussing topology we can make use of the
> condition that everything we investigate is extremely well ordered. We may
> not be able to understand Nature, but we may get an idea about how our
> brain functions, in its capacity as an extremely well ordered system. We
> can make a half-step towards modelling artificial intelligence by
> understanding at first, how artificial instincts, and their conflicts, can
> be modelled. Animals apparently utilise a different layer of reality of the
> world while building up their orientation in it to that which humans
> perceive as important. The path of understanding how primitive instincts
> work begins with a half-step of dumbing down. It is no more interesting,
> how many they are, now we only look at where it is relative to how it
> appears, compared with the others.
>
> d.)    Spaces
>
> Out of sequences, planes naturally evolve. Whether out of the planes
> spaces can be constructed, depends on the kinds of planes and of common
> axes. Now the natural numbers come in handy, as we can demonstrate to each
> other on natural numbers, how in a well-ordered collection the actual
> mechanism of place changes creates by itself two rectangular, Euclidean,
> spaces. These can be merged into one common space, but in that, there are
> four variants of every certainty coming from the position within the
> sequence. Furthermore, all these spaces are transcended by two planes. The
> discussion about an oriented entity in a space of n dimensions can be given
> a frame, placed into a context that is neutral and shared as a common
> knowledge by all members of FIS.
>
> 2016. nov. 29. 15:15 ezt írta ("Karl Javorszky" <karl.javorszky at gmail.com
> >):
>
>> Topology
>>
>> The session so far has raised the points: meta-communication,
>> subject-matter, order, spaces.
>>
>> a.)     Meta-communication
>>
>> Gordana’s summary explicates the need to have a system of references that
>> FIS can use to discuss whatever it wishes to discuss, be it the equivalence
>> between energy and information or the concept of space in the human brain.
>> Whatever the personal background, interests or intellectual creations of
>> the members of FIS, we each have been taught addition, multiplication,
>> division and the like. We also know how to read a map and remember well
>> where we had put a thing as we are going to retrieve it. When discussing
>> the intricate, philosophical points which are common to all formulations of
>> this session, it may be helpful to use such words and procedures that are
>> well-known to each one of us, while describing what we do while we use
>> topology.
>>
>> b.)    Subject-matter
>>
>> Topology is managed by much older structures of the central nervous
>> system than those that manage speech, counting, abstract ideas. Animals and
>> small children remember their way to food and other attractions. Children
>> discover and use topology far before they can count. Topology is a
>> primitive ancestor to mathematics; its ideas and methods are archaic and
>> may appear as lacking in refinement and intelligence.
>>
>> c.)     Order
>>
>> There is no need to discuss whether Nature is well-ordered or not. Our
>> brain is surely extremely well ordered, otherwise we had seizures, tics,
>> disintegrative features. In discussing topology we can make use of the
>> condition that everything we investigate is extremely well ordered. We may
>> not be able to understand Nature, but we may get an idea about how our
>> brain functions, in its capacity as an extremely well ordered system. We
>> can make a half-step towards modelling artificial intelligence by
>> understanding at first, how artificial instincts, and their conflicts, can
>> be modelled. Animals apparently utilise a different layer of reality of the
>> world while building up their orientation in it to that which humans
>> perceive as important. The path of understanding how primitive instincts
>> work begins with a half-step of dumbing down. It is no more interesting,
>> how many they are, now we only look at where it is relative to how it
>> appears, compared with the others.
>>
>> d.)    Spaces
>>
>> Out of sequences, planes naturally evolve. Whether out of the planes
>> spaces can be constructed, depends on the kinds of planes and of common
>> axes. Now the natural numbers come in handy, as we can demonstrate to each
>> other on natural numbers, how in a well-ordered collection the actual
>> mechanism of place changes creates by itself two rectangular, Euclidean,
>> spaces. These can be merged into one common space, but in that, there are
>> four variants of every certainty coming from the position within the
>> sequence. Furthermore, all these spaces are transcended by two planes. The
>> discussion about an oriented entity in a space of n dimensions can be given
>> a frame, placed into a context that is neutral and shared as a common
>> knowledge by all members of FIS.
>>
>> 2016. nov. 25. 14:44 ezt írta ( <tozziarturo at libero.it>):
>>
>>> Dear Joseph,
>>> The Borsuk-Ulam theorem looks like a translucent glass sphere between a
>>> light source and our eyes: we watch two lights on the sphere surface
>>> instead of one. But the two lights are not just images, they are also real
>>> with observable properties, such as intensity and diameter.
>>> Until the sphere lies between your eyes and the light source, the lights
>>> you can see are two (and it is valid also for every objective observer),
>>> it's not just a trick of your imagination or a Kantian a priori.
>>> Therefore, the link between topology and energy/information is very
>>> strong.  If we just think the facts and the events of the world in terms of
>>> projections, we are able to quantitatively elucidate puzzling and
>>> counterintuitive phenomena, such as, for example,  quantum entanglement
>>> https://link.springer.com/article/10.1007/s10773-016-2998-7
>>>
>>> Therefore, the 'eternal' discussio­n of whether geometry­ or energy
>>> (call it dynamics, informational entropy, or whatsoever)­ is more
>>> fundamental ­in the universe, does not stand anymore: both geometry and
>>> energy describe the same phenomena, although with different languages.  In
>>> physical terms, we could say that geometry and energy are 'dual' theories,
>>> e.g., they are interchangeable in the description of real facts and
>>> events.
>>>
>>>
>>>
>>> --
>>> Inviato da Libero Mail per Android
>>> venerdì, 25 novembre 2016, 00:28PM +01:00 da Joseph Brenner
>>> joe.brenner at bluewin.ch:
>>>
>>> Dear All,
>>>
>>> Pedro should be thanked already for this new Session, even as we welcome
>>> Andrew and Alexander. The depth of your work facilitates rigorous
>>> discussion of serious philosophical as well as scientific issues.
>>>
>>> In Pedro's note of 2016.11.24 there is the following:
>>>
>>> "Somehow, the projection of brain "metastable dynamics" (Fingelkurts)
>>> to higher dimensionalities could provide new integrative possibilities for
>>> information processing. And that marriage between topology and dynamics
>>> would also pave the way to new evolutionary discussions on the emergence of
>>> the "imagined present" of our minds."
>>>
>>> What Pedro calls here "the marriage between topology and dynamics"
>>> reminds one of the 'eternal' discussion of whether geometry or energy
>>> (dynamics) is more fundamental in the universe. I just suggest that there
>>> are alternative terms to focus on and describe the interaction between
>>> topology and dynamics that are more - dynamic, and make an emergence a more
>>> logical consequence of that interaction.
>>>
>>> Best wishes,
>>>
>>> Joseph
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