<div dir="ltr"><div><div><div><div><div><div><div><div>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.<br><br></div>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".<br><br></div>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. <br><br>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.<br><br></div>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). <br><br>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.<br><br></div>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.<br><br></div>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.<br><br></div>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.<br><br></div>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. <br><br></div>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.</div><div class="gmail_extra"><br><div class="gmail_quote">2016-11-30 8:46 GMT+01:00 Karl Javorszky <span dir="ltr"><<a href="mailto:karl.javorszky@gmail.com" target="_blank">karl.javorszky@gmail.com</a>></span>:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><span class="im HOEnZb"><p dir="ltr">Topology</p>
<p dir="ltr">The session so far has raised the points: meta-communication, subject-matter, order, spaces.</p>
<p dir="ltr">a.) Meta-communication</p>
<p dir="ltr">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.</p>
<p dir="ltr">b.) Subject-matter</p>
<p dir="ltr">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.</p>
<p dir="ltr">c.) Order</p>
<p dir="ltr">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.</p>
<p dir="ltr">d.) Spaces</p>
<p dir="ltr">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.</p>
</span><div class="HOEnZb"><div class="h5"><div class="gmail_extra"><br><div class="gmail_quote">2016. nov. 29. 15:15 ezt írta ("Karl Javorszky" <<a href="mailto:karl.javorszky@gmail.com" target="_blank">karl.javorszky@gmail.com</a>>):<br type="attribution"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><p dir="ltr">Topology<br></p>
<p dir="ltr">The session so far has raised the points: meta-communication, subject-matter, order, spaces.<br></p>
<p dir="ltr">a.) Meta-communication</p>
<p dir="ltr">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.<br></p>
<p dir="ltr">b.) Subject-matter</p>
<p dir="ltr">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.<br></p>
<p dir="ltr">c.) Order</p>
<p dir="ltr">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.<br></p>
<p dir="ltr">d.) Spaces</p>
<p dir="ltr">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.</p>
<div class="gmail_extra"><br><div class="gmail_quote">2016. nov. 25. 14:44 ezt írta ( <<a href="mailto:tozziarturo@libero.it" target="_blank">tozziarturo@libero.it</a>>):<br type="attribution"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div><p style="margin-top:0px" dir="ltr">Dear Joseph, <br> 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. <br> 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. <br> 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<br> <a href="https://link.springer.com/article/10.1007/s10773-016-2998-7" target="_blank">https://link.springer.com/arti<wbr>cle/10.1007/s10773-016-2998-7</a></p>
<p dir="ltr">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. <br><br><br><br></p>
<div id="m_6796094262707843539m_449244164563425182m_4166931447349316921mail-app-auto-default-signature">
<p dir="ltr">--<br> Inviato da Libero Mail per Android</p>
</div>venerdì, 25 novembre 2016, 00:28PM +01:00 da Joseph Brenner <a href="mailto:joe.brenner@bluewin.ch" target="_blank">joe.brenner@bluewin.ch</a>:<br><br><blockquote id="m_6796094262707843539m_449244164563425182m_4166931447349316921mail-app-auto-quote" style="border-left:1px solid #85af31;margin:0px 0px 0px 10px;padding:0px 0px 0px 10px" cite="http://14800735500000025323">
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<div><font face="Arial" size="2">Dear All,</font></div>
<div><font face="Arial" size="2"></font> </div>
<div><font face="Arial" size="2">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.</font></div>
<div><font face="Arial" size="2"></font> </div>
<div><font face="Arial" size="2">In Pedro's note of 2016.11.24 there is the
following:</font></div>
<div><font face="Arial" size="2"></font> </div>
<div><font face="Arial" size="2">"<font face="Times New Roman" size="3">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."</font></font></div>
<div><font face="Arial" size="2"></font> </div>
<div><font face="Arial" size="2">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.</font></div>
<div><font face="Arial" size="2"></font> </div>
<div><font face="Arial" size="2">Best wishes,</font></div>
<div><font face="Arial" size="2"></font> </div>
<div><font face="Arial" size="2">Joseph</font></div>
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