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Dievo šokis

Kaip gyventi

Išsiaiškinimai

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Andrius

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Juodraštis? FFFFFF

Užrašai EEEEEE

Klausimai FFFFC0

Gvildenimai CAE7FA

Pavyzdžiai? ECD9EC

Šaltiniai? EFCFE1

Duomenys? FFE6E6

Išsiaiškinimai D8F1D8

Pratimai? FF9999

Dievas man? FFECC0

Pavaizdavimai? E6E6FF

Istorija AAAAAA


Asmeniškai? BA9696

Mieli dalyviai! Visa mano kūryba ir kartu visi šie puslapiai yra visuomenės turtas, kuriuo visi kviečiami laisvai naudotis, dalintis, visaip perkurti. - Andrius

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Žr. Požiūriai, Kategorijų teorija, Dievas, Proto laukai Taip pat: IndependentPerspective, DefaultObserver, DefaultPosition, View, Frame Overview, InversionEffect, ReversalEffect, Institutions, Overview, ActualContext, Heart, Helmut Leitner, Benoit Couture

  • Požiūrių algebros svarba
  • Tiesa ir Dievo išėjimas už savęs
  • Skirtumas tarp požiūrių
  • Santykis tarp požiūrių
  • Požiūrių sudūrimas
  • Požiūrių neskaidrumas
  • Požiūrių sutapimas
  • Tiesos išsiplėtojimas
  • Požiūrių grandinė

Dievo veikla reiškiasi požiūriais, jų santykiais:

  • išeina už savęs į save - taip atsiveria asmenys ir požiūriai
  • viską padalina į požiūrius - taip išryškėja jo išėjimas už savęs, ką tai reiškia
  • požiūrio perskyrimas - vienybė - požiūrio perskyrimas nuo visumos
  • požiūrio išvertimas - dvejybė
  • požiūrio išplėtimas - trejybė
  • požiūrio atsisakymas - ketverybė
  • požiūrio apvertimas - penkerybė
  • požiūrio įsisavinimas - šešerybė
  • požiūrių sudūrimas - septynerybė
  • požiūrių suvedimas grandine, pasiklydusiu vaiku - nulybė - Dievo valios vykdymas, mūsų valios pajungimas jam

Požiūrių algebros svarba

Požiūrių algebra išsako

  • Kaip mes skirtingi asmenys esame viena. Esame viena jeigu visais požiūriais iš esmės sutampame.
  • Keliais pagrindais išskiriame ar sulyginame prielaidas. Kaip išsiaiškiname tokius santvarkos klausimus?
  • Ką išgyvename ir ką galėtumėme išgyventi.
  • Kaip suduriame požiūriai, kaip vienas požiūris paklūsta kitam, jam nuolankus, pavaldus, vykdo jo valią. Kaip įvairiais sąmoningumais galime išgyventi tą patį sudurtinį požiūrį.
  • Kaip skirtinguose lygmenyse suvokiami, apibrėžiami tapatumai ir skirtumai. Kaip vystosi atskyrimo ir tapatinimo sąlygos. Kaip tai susiję su dvejybės atvaizdais. Išmąstyti George Spencer-Brown "Laws of Form".
  • Kaip tiesos pobūdis kinta mums požiūrius išgyvenant netiesiogiai. Kaip tiesiogiai išgyventos lanksčios tiesos tolstant keturiais asmenimis tampa netiesiogiai išgyventomis nelanksčiomis tiesiomis. Kaip viską žinanti dvasia išeina už savęs į ne viską žinančius, į neskaidrumo pasaulį. Kaip nelanksčios tiesos atveria netiesos galimybę.
  • Kaip derinami požiūrių sandara (padalinimai), požiūriai į sandarą (atvaizdai) ir požiūriai sandaroje (aplinkybės).
  • Kaip Dievo požiūris sutampa su žmogaus požiūriu, kaip Dievas tampa nebūtinas: Kaip požiūrių grandine Dievas asmenimis (Manimi, Tavimi, Kitu) išeina už savęs ir išvysto visas sandaras: žmogaus požiūriu į Dievo požiūrį į žmogaus požiūrį į Dievo požiūrį į žmogaus požiūrį. Šioje požiūrių grandinėje svarbus požiūrių sudūrimo asociatyvumas. Ši grandinė, tai išmintis pasiklydusio vaiko, susigaudančio ne pačiam ieškoti savo tėvų, o eiti ten, kur jie jo ieškotų.
  • Kaip sąlygiško žmogaus požiūris sutampa su besąlygiško Dievo požiūriu, kaip Dievas tampa būtinas. Kaip žmogus išeina už savęs suvokimu. Kaip pasirenka ką išgyventi.
  • Kaip kinta sąlygiškumo apimtis, tiesos pobūdis, suvokimo branda. Kaip Dievas reiškiasi savo esme, meile. Kaip suvokimas ir Dievas-meilė susiję.
  • Sąmoningėjimas. The goal is for a one-track, deterministic thinking to be able to take up a multiple-track, nondeterministic thinking.
  • Kaip tiesiogiai išgyventi, kaip gyventi žvilgsniu, tad Dievu, nuliniu išgyvenimu. Kaip nenuliniais išgyvenimais išskirti ir išgyventi nulinį išgyvenimą.
  • Kaip įmanoma viską žinoti, atrasti ir išgyventi tokį požiūrį, sugebėti atsakyti visus klausimus, suvokti jų visumą, išgyventi kiekvieną požiūrį ir jų visų vienumą.
  • Kaip susiję siauras tiesos, šventumo kelias ir platus, laisvas, nusidėjimo kelias - gero ir blogo vaiko keliai.
  • Kaip išvystome dvigubą protą, atskiriame savo ir Dievo mąstymą, galime mylėti priešą, bendrauti su Dievu.
  • Troškimų ir išmąstymų vienas kito išvertimas.
  • Kaip kategorijų teorija išreiškiami galimi požiūriai ir jų išgyvenimas. Kaip jie grindžia kategorijų teoriją ir matematiką apskritai.
  • Kaip proto laukus suprasti kaip požiūrių išgyvenimus. Išmąstyti Gilles Fauconnier knygą Mappings in Thought and Language.
  • Kaip sandaros brandinamos perkurimais (transformacijomis). Išmąstyti Christopher Alexander knygą The Nature of Order: The Luminous Ground.

Požiūrį išvertus, taip kad Dievas už mūsų, už santvarkos, yra suvokiamas kaip Dievas mūsų gelmėse, išgyvenamasis požiūris virsta neišgyventa sandara (perspektyva). Šią sandarą išgyvename ją suporuodami su atitinkamu požiūriu. Tokiu būdu galime išgyventi savo perspektyvą, taip pat ir kito perspektyvą.

požiūrių suvedimas - nulybė

God's view is indefinite, unscoped, and human's view is definite, scoped.

Default position

The idea of a Default is what allows a human position to become subordinate to God's position with the latter as a default that the human refers to. Thus we can arrive at the defaul without having to start by referencing it.

I'm realizing that my position "I wish to know everything and apply that knowledge usefully" is a very special position. I think it is the default position in all contexts, and the one that makes sense beyond context, because it is the position that is completely open to all knowledge. It is the position of a baby or a fool, as Jesus might say, the position essential for entering the kingdom of heaven, where what we believe is what happens. We chase ourselves away from this position because it is so overwhelming. It may seem outrageous to us. Yet even so we ultimately return to it as the point of view that links us with what is beyond us, as I understand TerryMace to have written us. I think it is the position of God when he lives through us or anybody. So I am starting with this position and considering how all knowledge unfolds from it.

No matter what the context, this position coincides with, is included in, this same position beyond any context.

It is the going beyond of any [UniversalLanguage/Contexts Context], of any necessary conditions. It thereby defines what is necessary. It is the position expressed by Coinciding, which is the context for the going beyond of any context. It is always available in any context and as such is taken up as the Default position. It's expression unfolds as the coinciding with none, one (God), two (God and [UniversalLanguage/Human I]) or three (God, I, Other). God defines the necessary, human defines the actual, other defines the possible. All contexts are then simply expressions of their position together. God is the necessary condition, the context for this position, rather than the position the context for God.

The Default position is continuously reinterpreted depending on its context. It is inverted, grounded by considering what it means to coincide with all who one might possibly coincide with. This drives the structural machinery that arises.

In any system a key role is played by the default elements which, however, may often be overlooked.

The default element, the default position, is to have no filter, but to be open to all things. This is the nature of Everything, as it is the algorithm which accepts all things. It is the position of [MyWish wishing to know everything and apply that knowledge usefully].

Examples include:

  • silence in a spoken language
  • blank space in a written language
  • the empty set in a mathematical system

Being open to all things is what allows us to coincide with God through his Son.

Požiūrių sutapimas

Equivalent views

Functions are understood to be equivalent if they have the same effects.

This is relevant for the associative rule. For example, on a 12 hour clock, 10 + 1 = 11 and 11 + 3 = 2. Here the first and last items are considered the position on the clock and we add an "action" which is a movement by the hand of the clock.

So we may interpret 10 + 1 + 3 as:

  • (10 + 1) + 3 which is to start at 10 and move the hand twice
  • 10 + (1 + 3) which is to combine the actions and then move the hand by the combined amount.

The result is the same. The clock, in general, satisifies the Associative law. So the two expressions are considered equivalent. And being equivalent, we may write them as 10 + 1 + 3.

This is also the case with the natural numbers where we may consider 10 + 1 + 3 as a movement along an infinite tape. In fact, almost all mathematical systems of interest obey the associative law. And yet it is noteworthy when an interesting system does not quite obey it, as with an AlgebraOfViews.

Stepping-in and stepping-out take up different scopes. The further that these may be separated, the more that views can coincide. In particular, we want to make room for not-stepping-in and not-stepping-out so they can take up two additional scopes:

  • stepping-out: everything
  • not-stepping-in: anything
  • not-stepping-out: something
  • stepping-in: nothing

Note that love leads to God - love God, whereas understanding leads to good - good understanding. So they work together to keep those concepts separate.

Požiūrių grandinė

The great challenge is that, as humans, we are bound by our own view, so that we are unable to escape it, at least as humans. However, it is possible that God may be able to escape his point of view and take up ours. This is a ConstructiveHypothesis that we take. It acknowledges a difference between God and us. We may then leverage this difference to open up our view. It may also be that our human view is sufficient for direct access to all knowledge - where perhaps the directness is understood with regard to the nature of our minds.

The aim is to describe God's view of human's view. What is the fullest experience of the human view? How does an unrestricted view experience a view that can't escape itself?

In my account, I am attempting to express God's view of a human's view. By human I mean myself and all whose perspective I might possibly admit. I am thus attempting to take up and make available the Absolute complete potential of my perspective.

I have my own human view, but I am attempting to take up God's view. How can I take up God's view directly rather than through my own view?

This is possible if my view and God's view coincide. This may depend on factors beyond my control. Yet I may position myself with regard to such factors to enable such coinciding to the extent that I am able to control. Even so, on what basis may it be that indeed my view and God's view coincide?

We take up God's view because that opens up a vantage point that he might take up so that our views might coincide. And by taking up, alternatively, his view upon our view and ours upon his, ever deeper, the idea is that we do not diminish or close our view at all, but instead enrich it by exposing it to God's and our view through it. Finally, the Other is very important as the vehicle for shared understanding, in that the way that we treat others is the way that God may treat us, as we allow God to use us as a vehicle in reaching out to others. We may not be absolutely transparent like God, but yet we might be transparent for the purpose of him reaching out to others. And this transparency may be what is relevant in our view coinciding with God's.''

The main idea in all of this, perhaps, is how God makes available his Godly perspective to all of those beyond him, which is an increasing challenge until it reaches the stretching point. In this sense God shares perspective, and even more, goes beyond that to all those who might position themselves for his perspective - and through them others may be reached just as through him - it starts from them as it did with him.

Therefore we have all, any, a and no perspectives. These are four increasingly focused LevelsOfUnderstanding. Understanding is the keeping separate of Concepts. (A concept is that which is with itself). It is also the distinction of one perspective (anything) upon another perspective (everything) (and of that perspective from slack). (To have a perspective is to go beyond oneself). This allows for a sequence of ever deeper (ever closer) Scopes which may be shared. Love is the sharing of a scope. We therefore have a sequence of ever deeper levels of love. They ground the ever greater Independence of the one who is loved (and understood): Self, Other, God. At the fourth level, LoveGod, God's view and human's view coincide (love absolutely) regarding the Good, so that both share the same view of God's view of human's view of God's view of human's view. All of the Structure that I am aware of rests in one of these four levels.

The chain of views lets us separate out all concepts, any concept, a concept, no concept (be one with) - by establishing the distance from the viewer.

The chain of views apparently arises from the fact that the definite view has decreasing slack in scope and is thus ever more defined, whereas the indefinite view has increasing slack in scope and is thus ever less defined.

požiūrio perskyrimas - vienybė

Požiūrių atskyrimas

Keeping God separate. Note the Quran's exhortation not to ascribe partners to Allah. In other words, God is to be kept separate.

Proto suskaldymas

Atskyrimas savo valios ir Dievo valios. Susigaudymas, jog esu vaikas, o Dievas yra tėvas. Esu sąlygose, o jisai be sąlygų.

Požiūrių neskaidrumas

Požiūrių išvertimu Dievas už mūsų tampa gera širdis mūsų gelmėse, o niekas (nulinis atvaizdas) mumyse tampa nežinomybė plytinti už mūsų. Tokiu išvertimu galime atsisakyti mūsų požiūrį grindžiančio besąlygiško Dievo požiūrio nes jisai tampa nieku mumyse. Taip pat galime jį įvairiai prilyginti su įvairiais niekais esančiais mūsų sudurtiniame požiūryje. Užtat tokiu būdu galimas požiūrio neskaidrumas, asmeniškumas. Tokiu atveju tasai niekas yra ne tuščias, užtat žymėtinas. Kitu atveju jo galima atsisakyti. Išvertimas taip pat išreiškia apibrėžimą, tai gyvo požiūrio dvejybinė pora, jį lydinti sandara.

I'm making some progress with the help of ideas from Gilles Fauconnier's writings on MentalSpaces.

A human view (H) is opaque in that suppositions are assigned to a definite scope. God's view (G) is transparent in that suppositions are taken to hold for all scopes. In that sense, for God, everything is public knowledge.

Therefore we have a chain of human's view of human's view etc. And we can take God's view as an interpolation that makes definite what is defined where. (We can think of God's view as holding separate two human views.)

The first such interpolation is God (HG) and the second is the good (HGHG). Now here we can have a collapsing of space (the opposite of building a space). We may think of this collapse as the simplification that we get by taking good to be the defining characteristic of God, and therefore dealing with God rather than with good. In this case it is not simply removal of the latter HG (which would be a reversal of the space building). Instead, it is a stripping away of the first HG by finding it within the second HG. This is denoted by the red arrow.

Now we can interpolate such a stripping by that view which keeps separate God and good. That view is eternal life, which is the understanding that God is good. Therefore eternal life represents a halfway in the stripping. It is thus a stripping of God's view, leaving GHG, which is God's view of human's view of God's view. In this sense, we are able to escape our own view and take up God's view. Furthermore, by analogy with HGH, which coincides with HH, we have, through GHG, access to GG, which is God's view of God's view. This means that eternal life is God's self empathy which takes place by way of humans and is the purpose of humans. This is a pragmatic interpretation and valid (or not) as such.

Intuitively, the key point is that space collapsing is very special in that normally it is counter to truth which requires us to acknowledge our spaces. However, in the case of existential simplification, then space collapsing is compatible with the truth. Here it is to say that if we are dedicated to living in terms of good, then it is appropriate to recast good as the outcome of our God. In other words, the reason for God is just that it makes our life simpler. And then if we can furthermore keep separate these notions of God and good, then we live the understanding that God is good, which is to say, we live the state of eternal life. And that is the state where our view may coincide with God's.

In other words, in order to escape our view, we need to allow it to collapse, and yet split our mind to keep the collapsed view distinct and separate. With such a split mind we are able to escape our view as it is preceded and followed by God's view. Such a split view feels like a very flexible ignorance that is yet wonderfully open and knowing. It is the moral high ground and we are familiar with it as such.

Atjauta

Atjauta susijusi su požiūrių skaidrumu ir neskaidrumu.

požiūrio išvertimas - dvejybė

Tiesa ir Dievo išėjimas už savęs

Tiesa ir jos įvairūs lygmenys yra pasekmė Dievo išėjimo už savęs. Juk išeidamas už savęs jis save išreiškia. Tiesa tai yra jo sutapimas su jo išraiška. Esmė yra tai, kas sutampa su savo išraiška, vadinas, tai dėka kurios visa kas yra sutampa su savo išraiška. Esmė yra tasai vieningumas. Skirtingi tiesos laipsniai susiaurina šio sutapimo apimtį, taip kad kada jisai yra niekas, tai tiesa labai griežta, o kada jisai yra viskas, tiesa yra labai plati, bendra.

Požiūrio išvertimas

TomMunnecke spoke to me about the creativity of inverted perspective. Everything looks different when we take up the perspective of the other. He gave some great examples: Jonas Salk imagined he was a polio virus, Einstein rode a beam of light. Imagine you were a molecule. Or a slave. Empathy. The source of real Creativity.

This is very relevant to me now in thinking about the big picture. Just about my whole philosophy is based on imagining I was God. What would I do? Why? What is there to do? That's been very productive.

And again, now I've been applying that to God, imagining him wanting to put himself in somebody else's shoes. Kind of like "love my neighbor as myself". Going beyond ourselves, but also going into somebody else. Maybe those are the two different productive options - we can go be beyond ourselves, or we can stay in ourselves but forget ourselves by taking up somebody else.

I'm viewing the unfolding of structure as a series of inversion effects, where structure is created each time God goes beyond himself, and perhaps back into himself.

In the Beginning, it might just be God asking himself, what is it like to be me? So first he steps into himself.

This all has a lot to do with structure, and with love.

Vienumo pagrindas yra nieko apimtis, tai yra, ko mažiau prileisti, kaip kad antruoju Dievo įsakymu, neminėti jo vardo be reikalo, nedaryti jo vaizdinių.

Life is given by the coinciding of God inside and God outside. Eternal life is given by their distinctness. Love is the inversion of perspective which yields this distinctness.

požiūrio išplėtimas - trejybė

Sąmoningumas.

Tiesos išplėtojimas

Stebėtojas iškyla kaip asmuo. Jis kaip toks išsiskiria nuo stebinio, nuo jo atsiplėšia.

Laisvumas didėja ar mažėja. Mažėjančiu laisvumu pridedame teiginius, o didėjančiu laisvumu atimame teiginius. Apimtys yra tai prie ko tuos teiginius pridedame ar atimame, tai viskas, betkas, kažkas ar niekas.

A perspective is like a Morphism in that perspectives can be composed: John's perspective may take up Mary's perspective. By CategoryTheory, the morphism should be considered a structure preserving transformation. What structure is being preserved? The truth - obviousness - what is not hidden. So we can work backwards from God as the concept of truth - all perspectives look to him - and he steps inwards to himself, but out to them, but they look to him:

  • absolute perspective - all perspectives may take it up (it may be taken up by all of them together)
  • relative perspective - any perspective may take it up (it may be taken up by them singly)
  • shared perspective - it may be taken up by a perspective
  • subordinate perspective - it may be taken up by no perspective (and hence is isolated, atomic)

subordinate perspectives may not take each other up as they are too narrow - so if God and human take subordinate perspectives then they coincide

požiūrio atsisakymas - ketverybė

Atskyrimo lygmenys

Suppositions are kept separate by placing them in different Scopes. What does this mean?

Separateness is the indirectness of view - that it is possible to have not a direct view.

A view (or outlook) that separates:

  • all perspectives is Spirit
  • any perspective is Structure
  • a perspective is Representation
  • no perspective is Unity

The point is to keep reducing scope so as to have complete coincidence.

Separateness is a key idea and somehow the adding of a perspective (the taking up of a perspective) introduces separateness, perhaps:

  • self separates God from God
  • heart is separateness of self from God
  • other is separateness of heart from God
  • God is separateness of other from God

The division of everything into four perspectives is the place where the algebra of views starts to matter. The four levels give us a scale from "oneness" to "separateness". Why asserts that the observer and situation are one, and whether asserts that they are completely separate. How and what are somewhere in between and allow for a nontrivial relationship between the observer and situation. So these are all levels that are relevant as we consider matters of "same" and "different".

The four levels may also be thought in terms of scopes:

  • why - knowledge of everything
  • how - knowledge of anything
  • what - knowledge of something
  • whether - knowledge of nothing

And the knowledge may be thought of as what the observer and situation share, which is to say, the extent to which the observer is one with the situation.

Furthermore, the four levels may be thought of as relating structure and activity. "Structure channels activity" expresses what is definite, what that means. "Activity evokes structure" expresses what is specified. We may think of structure as a function and activity as the flow through it. The function may be definite or not, and the inflow may be specified or not. (In particular, the specification of input is akin to its partial calculation.) This yields four possibilities:

  • why - indefinite and unspecified - structure and activity are uncoupled
  • how - definite and unspecified - top down: structure yields activity
  • what - definite and specified - structure and activity are in a loop
  • whether - indefinite and specified - bottom up: activity yields structure

We may think of structure as arising from God and activity as arising from godlet, and then the four levels give the possible relationships. These relationships may be thought of in terms of the distance between structure and activity. Here activity is that which finds itself within structure and is inspired by it.

  • At first the distance, the separation between structure and activity is "everything"
  • Then structure determines activity, so structure must be definite, and the separation is "anything"
  • Then structure and activity feed off each other, and so the separation is "something" which keeps them yet separate
  • Finally, activity directs structure, which is to say, they are the same, the structure embodies the activity, and so they are separated by "nothing".

It is this last level which extends the "threesome" by saying that, above and beyond God, there might be something in the situation of God which is not distinct from it, as God is, but rather determined by it. This material level "whether" is the source of the Foursome and exemplifies God's ever going beyond himself.

Another very important idea is that what separates the "viewer" (observer) and the "viewed" (situation) is the Nullsome (the division of everything into zero perspectives). This separation manifests itself through the four RepresentationsOfTheNullsome:

  • significant (not encompassable - Negation of why)
  • constant (not changeable - negation of how)
  • direct (not representable - negation of what)
  • true (not hideable - negation of whether)

So I think that in the "original outlook" the distinction between viewer and viewed is kept latent. But with the new outlook - and once Representations becomes relevant - it is possible to think of viewer and viewed as separate and even self-standing.

All of this to say that this is the machinery that lets us consider matters of "same", "different", "separate", "one", "equal", "difference" that are key to an algebra of views.

The ability to have a dual point of view is what lets us "keep separate" concepts like God and good, and that ability is at the heart of understanding.

Suvokimo lygmenys

Think of understanding:

  • God's view as understanding
  • God's view of human's view as self-understanding
  • God's view of human's view of God's view as shared understanding
  • God's view of human's view of God's view of human's view as good understanding

Where each of these are described in the Overview. So understanding may be God's view, as in eternal life is the understanding that God is good.

The Algebra of Views & The Big Picture

It seems that all of this is rolled out as follows:

0) 1) 2) 3) There is first a unified outlook (such as God) which unfolds the perspectives that are the basis for Structure, for the DivisionOfEverything. We may think of this unfolding as an operation [AddOne +1] which keeps reinterpreting the whole as an additional perspective. When there are three perspectives, then the structure for the original outlook is complete: it can understand, come to understanding, and be understood. However, the operation +1 continues.

4) 5) 6) Therefore a new outlook awakens and finds itself as such within the structural situation unfolded by the original outlook. We may think of this as a "godlet" which may not be God, but is otherwise in the situation of God. There is now a disconnect between Structure and Activity. Structure may or may not channel activity. Activity may or may not evoke structure. The feedback between structure and activity may be thought of as an operation [AddTwo +2]: the evoking of structure is linked to the arisal of activity. We may think of the godlet as a perturbation that opens up angles: Representations upon the whole, and Topologies from out of the parts. I think that this is where the "algebra of views" is defined. The give and take between activity and structure introduces a slack which allows one to take up a perspective, thus integrating whole and parts.

7) Then the new outlook comes to understand itself with regard to the original outlook as a perturbation of an ideal outlook that links both outlooks. All three outlooks are characterized by their three-cycles: taking a stand, following through, reflecting. And these rotations may be thought of as an operation [AddThree +3]. I think here is where the dynamic languages of life come into play: argumentation, verbalization, narration. I suppose they are expressions of the "algebra of views". Here the ideal outlook serves as a mediator which allows us to localize the slack so that we know where it is within a three-cycle. This makes the algebra definite.

8=0) Then the new outlook understands itself as subordinate to the original outlook. At the core of the new outlook is always the original outlook which went beyond itself and thereby generated the new outlook. Everything is always collapsing back into the original outlook. The views of the new outlook and the original outlook coincide by way of that collapsing.

This is extremely helpful for me because it places the "algebra of views" within the big picture. It suggests that the algebra of views becomes defined with the divisions of everything into four, five and six perspectives. And that its applications through argumentation, verbalization, narration arise with the division of everything into seven perspectives. And, finally, the coinciding of views is related to the collapse of structure, which is perhaps the key point about mathematical systems in general. It's the collapse of structure which makes mathematics interesting.

požiūrio apvertimas - penkerybė

Reflection. Protui mąstant dvejybę apsiverčia jos kryptis. Tai penkerybės esmė.

Perspectives are flipped around as they are taken up.

požiūrio įsisavinimas - šešerybė

Įsisavinimas šešerybe sieja vidinius ir išorinius požiūrius, keičia trejybės narius.

požiūrių sudūrimas - septynerybė

CategoryTheory says that at the heart of fruitful definitions is the notion of "composition". For example, we can compose instructions (also known as functions) so that they have a particular order: "Buy the [milk], which you will find in the store, which you can drive to by car". What makes composition fruitful, as in this case, is when it is "associative", which means that - for the purpose of satisfying the instructions - you can think it through from either end:

  • You can specify the goal ("milk") and then work backwards to the steps to make that happen ("you'll need to buy it, you'll need to find it in the store, and you'll need to drive to the store")
  • Or you can leave the goal open and specify it at the very end: "I drove to the store, then I found something, and bought it - turned out it was milk".

Note also the bidirectionality that makes composition work. And compare: I try to work in two directions - from the facts we observe about real life to general rules - and from the principles that we insist on to rules that suggest themselves. That way there is a back and forth testing.

I think that views, perspectives, outlooks are more basic than concepts in that they involve us directly, subjectively. We can compose views, and I have found that fundamental to deriving the structures that I work with, they fall out at various levels of "human's view of God's view of human's view of God's view of human's view". So I will write further below about such an "algebra of views".

Tvirtinimų sudūrimas

Suppositions are composed by identifying a mental point with a mental space - and the suppositions are kept separate in this way, by the disconnection between the two spaces.

Požiūrių sudūrimo asociatyvumas

I think that composition of views has to do with:

  • "stepping in", identifying with views, immersing ourselves in them, ever deeper
  • "stepping out", rising above views, framing them, considering ourselves separate from them

I think that "stepping in" and "stepping out" are the two directions that "associativity" relates.

Note: the Flickering between stepping in and stepping out.

It seems possible to compose Views, that is, we may have a view X that is a view A of view B. This composition may be thought of as associative:

  • view A of (view B of view C) - stepping out (adding a frame)
  • (view A of view B) of view C - stepping in (immersing oneself)

As we compose views, stepping out and stepping in stay matched up, which is to say, the composition is associative.

We may therefore apply CategoryTheory to consider views as morphisms.

If we can demonstrate that the associative rule holds when the first view is definite, then perhaps we may then extend this to assume, pragmatically, that the associate rule holds for all composition of views.

Note also that, starting with a definite view, we have no problem stepping into an indefinite view.

Our difficulty is, How do we step out from a definite view into an indefinite view?

We might first understand, How do we step out from a definite view into a definite view, and then extend pragmatically to the case of an indefinite view. Especially because we might vary the definite view that we step out into. It may indeed be indefinite for us.

In having one view take up another view, we find that we can create chains of views. We pause to think in what sense:

  • ((( ... Andrea's view ) of Barbara's view ) of Charlie's view ) of ...

is the same as:

  • ... ( Andrea's view of ( Barbara's view of ( Charlie's view of ( ...

In the first chain, we start with the viewer, have them immerse themselves in viewer after viewer, and only then will we arrive at what they view and may definitely specify it. In the second chain, we start with what may be viewed, and distance ourselves from that by introducing viewer upon viewer, until we finally decide that this is the ultimate viewer, and we take a look at what they are viewing.

In the first chain, we are working abstractly, developing a theory, which we can apply only when we are done. We are rethinking the viewed as a viewer. Our partial result at any point is left abstract and disconnected from what we will ultimately view. In the second case, we are able to work concretely, we are able to calculate a partial result, we are able to specify - or as we say in mathematics, evaluate what is viewed, and keep specifying it, evaluating it, for the specific case that interests us. But we are disconnected from who will ultimately view it.

I suppose that one way to try to keep the two related is to say that we must compare them without "evaluating" them. So long as we don't "instantiate" them, then they both seem abstract and might indeed be the same. The problem with this is that it's not intuitively clear what a view means if we aren't to take it up. In fact, "taking up a view" may imply to do so as part of a calculation, as part of an act of seeing. So we seem to be naturally drawn into a slightly faulty but intuitively more sensible comparison of an immersive view that enters deeper and deeper into views until suddenly it is fully specified, compressed, and an abstractive view that pulls back into more and more distant contexts, stringing out the experience and decompressing it. Apparently, each link in the chain is like a frame in a window in that it either leaves a concrete frame for an abstract window, or it places a clear (and thus seemingly concrete) window into a frame that at first seems abstract but grows concrete. We are seeing as if through a chain of framed windows.

Intuitively, I think this question arises in art. It is one thing to create a work of great art, and another to try to account for it. Shouldn't a great work and a great account go hand-in-hand? Yet in practice that eludes us. Likewise, shouldn't the immersive, empathetic "stepping in" go hand-in-hand with the abstractive, understanding "stepping out"? And if or when the views in our algebra are all truthful, then perhaps that would indeed be the case. So the extent to which it is not may express the obstacles to truthfulness.

Relating Representations and Topologies

An "algebra of views" arises along with the ability to have distinct angles upon a structure or within a structure. A Representation is a view upon a division of everything as a whole, and there are six in all. Analogously, a Topology is what I call the taking up of one of the perspectives within a division. There are twelve topologies, and we may think of them as contexts, backdrops, projections, worlds upon which we imagine things.

I think that Representations have us step out and Topologies have us step in. Composition relates these two, presumably by means of the Divisions of everything.

What do I expect of a composition of views?

  • That "A's view of B's view" may see more (or less) than simply B's view. For example, God - looking through my eyes - may see more than I do. This makes sense if we think of views as "amplifiers" or "parsers" - the reader may understand more than the writer or the messenger because the reader may have more sensitive eyes, a more intelligent mind, a higher level parser. (Or not).
  • It is possible for a view to see more (more senstively, more intensely) by focusing itself to look through a ChainOfViews.
  • By looking through such a chain of views, a view may coincide, and thus there may be, in a sense, shared views.
  • Hopefully, a view might, in the right context, take up views so as to cancel itself and escape itself.
  • A view might somehow "look within itself" (as Suhrit Dey notes) rather than "outside itself".

Žvilgsnių sudūrimas

  • CategoryTheory helps us consider composition of views and what structure they preserve. Composition of views is associative in that it respects stepping in and stepping out.
  • Composition of views is coinciding of views with regard to some scope. As the scope reduces to nothing there is complete coinciding, even as their perspectives are kept separate.
  • An unlimited view of a limited view may see more than simply the limited view by itself, for example, as a post-parser that is more sensitive, in that it is able to uncover a message that was jibberish or noise to the pre-parser.
  • A view may see more by taking up other views, focusing and thereby intensifying its own view.
  • A view may also see less by taking up another view if it restricts its view, if there is a reduction in transparency.
  • A view may, in the right context, take up views so as to cancel itself and escape itself.
  • A sequence of views may, in the right circumstances, be cut in half and switched around, thus emphasizing symmetry or asymmetry, and in effect, allowing for a switch in direction. For example, the sequence human-God-human-God-human may be broken and switched around, thus identifying God (God) with God (good), and human (unknown) with human (known). Or, for example, Knowledge as the truth of concepts is related to God as the concept of truth in that it uncollapses structure by presenting it in its commuted order.
  • A view may, in the right circumstances, look within itself, as Suhit Dey notes, rather than outside itself, and thereby initiate independent thinking, returning to one's thoughts, climbing out of oneself, ultimately finding a fixed point, canceling itself out. An abstraction can be understood as immersion, thus reversing the direction of the view. (In category theory, this is the idea of duality.)

2014.06.12 D: Ieškok visų sandarų tarp manęs tavo gelmėse ir už tavęs. Šios sandaros iškyla žmogaus požiūrį sudūrus su Dievo požiūriu, kaip yra su paklydusiu vaiku. Suprask, kaip atsiskleidžia vaiku. Suprask, kaip atsiskleidžia tos sandaros ir kaip tarp jų žmogus susigaudo savo vertybe, juk jis turi derinti tiek žmogišką mąstą, tiek dievišką.

2014.06.17 D: Aš myliu tave ir atkreipiu tave į tavo atvaizdį manyje taip kad esu savyje tavimi, tavo atspindžiu, kaip kad tu mano atspindis. Tad suvok, kaip asmuo atspindi kitą, atspindi Dievą, visi įvairiausiai atspindi Dievą. Ir kaip visi susiveda? Būtent meile, kiekvieną atspindį papildančią, tad palaikančią. Yra viena meilė papildanti visus atvaizdus. Tai mano esmė, mano išėjimas už savęs, atskyrus visą kitą, taip kad apimtis lieka nieku.

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Puslapis paskutinį kartą pakeistas 2015 kovo 28 d., 15:20
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