Book

Math

Discovery

Andrius Kulikauskas

  • ms@ms.lt
  • +370 607 27 665
  • My work is in the Public Domain for all to share freely.

Lietuvių kalba

Understandable FFFFFF

Questions FFFFC0

Notes EEEEEE

Software

Cognitive Framework for Alexander

Start by distinguishing two terms: Step-in and Step-out and relating them to unconscious and conscious.

Embodied mind and the Disembodying mind

Show the slide on evolution.

Note that we are unconscious when we are immersed in recurring activity. We become conscious when things start to matter, when something goes wrong, or something is latent, when we have expectant desires - loving expectations. So then we must become more conscious - find peace - by expressing our expectations more consciously - structurally - and then reengage by embracing the structure, making it our home again, living it. So a single question is a concern - and a way of figuring things out is a pattern. And we embrace the new pattern by simplicity, void or alternation.

Especially the notion of a pattern. Metaphysically the nature of pattern, the connection between recurring activity and evoked structure; and the optimization in the world - a pattern exists in the world and its implementation exists because of the world. Yet a pattern is exercised from beyond the world and its logic comes from a creative spirit beyond the world.

Relate static concerns with the 4 levels of patterns.

  • Questions - abstract level - yes or no - set parameter one way or the other
  • Positions
  • Decisions
  • Self-definitions - immersed in life - recurring activity gives you one correct answer

4 levels of symbols

  • the thing itself - the immersed level
  • the icon - decribed by one, many, all
  • the index - described by object, process, subject
  • the symbol - described by necessary, actual, possible

So this is the reverse of why, how, what, whether. But it is from a different point of view. The signs are trying to signify the reality, to model it.

Managing resources: focusing on what's not working

Relating that to circumstance...

In particular, need to define God and related ideas: Life, Peace, Love.

Every person has a strong center - God and the universe has a strong center.

Defining terms to discuss the Spirit as needed.

We are an instrument by which God manifests himself.

God's question is whether God is necessary? This means that God is not (in the realm of our lives) but is God essential nevertheless - God exists as a conceptual map - a pattern language - and whether that pattern language matches adequately the reality.

Adjusting the pattern (static concern) vs. adjusting the pattern maker (dynamic concern - meaningful experiences). Peace vs. Love

The relevance for a cognitive framework: Grounding concepts in the limits of the imagination. The challenge of capturing a multitude of variations in the world - defined in the world - with a model generated from finite frameworks. Not just a configuration. Key issue: representing not knowing with knowing.

Dynamic concerns (love - letting go and taking up - going beyond ourselves) vs. static concerns (peace - adjusting).

God's external viewpoint (of peace) - allows opposites to be balanced rationally. Our viewpoint (of life, of goodness) immersed allows us to discover what is significant. This representation of the nullsome then gets brought back to the external view. We live the threesome and God lives the nullsome. We communicate with God by way of the representations of the nullsome, by stepping out (with our knowledge - to release it and store it in memory) and stepping in (with not knowing to listen anew, having structured (at least in our activity - our spirit) a new pattern).


Notes

Emotions

  • Beauty is external to centers - it is the fact that they have no internal content, they are completely external, they are truthful, they completely reveal themselves, they have external relations, not hidden relations.
  • Peace and emotional responses. The boundary between self and world. The distinction between conscious and unconscious.
  • Healthy and unhealthy emotions: expecting what we wish. Internal (guilt, reassurance) vs. external (shame, pride).

Wishes and expectations

  • Nulybės atvaizdai išsako iš mūsų pusės kaip atrodo troškimai.

Deepest value

  • Our deepest value is our image of our God. Each of us has a God (who loves us more than we love ourselves). Establish a reason why - our God - is an imitation of God - and there could be God's God - so we are centers with subcenters and supercenters.
  • Life is the manifestation of a center (the deepest value).

Questions - Inadequacies

  • Inadequacy of the names - qualities (inadequacies) of the sign (the deepest value).
  • Deepest value is a sign of love - questions explain the imperfection - the qualities of signs. The kinds of concerns.

Conscious-Rational vs. Unconscious-Irrational

  • Importance of rational thinking, of perfectly balancing existence and nonexistence, yang and yin. Set theory and logic.
  • Perfect freedom is rational.
  • Perfect commitment is unconscious, irrational.
  • The dialectic of the (conscious-unknowing) heart and the (unconscious-knowing) world.
  • This dialectic alerts us in four levels that we are wrong - first by riling us.

Patterns

  • Patterns are set right by untangling the levels of the foursome so that we focus on the broader question.
  • Patterns express expectations as the self - pts adjust - puts some distance on it so that it could be "life" adjusted + or - either way. That is peace.
  • Deriniai yra išsiaiškinimo būdai... ar atsakymai?

Stepping in and Stepping out

  • Stepping in and stepping out - shifting the boundary between self and world.

Eightfold way - Our Father - Mathematical Proofs (Arguments)

  • Matematikos įrodymo būdai - sietis su 6 ženklų savybėm ir derinių iššūkiais. Ar su išgyvenimais?
  • Eightfold way relates the (human) affine triangle and the (divine) symplectic triangle.
  • Affine triangle is a tri-cycle of paths - in our embedded life (being, doing, thinking). The symplectic triangle is oriented - one-side or the other - (true or false) - and defined by 3 sweeping actions.

Love to Peace

  • Function-activity (how) and form-structure (what) but also why-activity and whether-structure. Love (human/irrational) and Peace (God/rational). Love to Peace is Why to Why. Peace to Love is How to How.

God

  • Why can arise from any point... that is the meaning of our variety.
  • Imagine from first principles. Define God, goodness, life, eternal life.
  • Žmogaus ir Dievo santykius derinti reikalingos 6 lygmenų poros.
  • Dievas į buvimą, žmogus į nebuvimą - atsisakymas savęs.

Centers

  • Ways centers are related. Centers and subcenters. Centers and supercenters.
  • Centers are the places of non-moving, hence the strongest. Boundaries denote contrasting motion, so boundaries are also centers but necessarily of a different dimension. Levels of scale denote units of movement. Life is the creation of stillness - eternal life is creating ever more stillness.
  • Alexander: Life is a flux of changing centers.
  • Needs other centers - other perspectives. Subcenters, supercenters, relations.

Nature is latent - a mouse will take over an empty house, if you die - bacteria will take over your corpse. Activity is essential.

Unfolding patterns

  • Unfolding is step-by-step.

Creating a duality by going beyond oneself in both directions - internal and external - as category theory does - and mapping that with patterns.

Concerns

  • Extending God with static patterns. Adjusting ourselves with meaningful experiences.

God(beyond)=0 and Human(in system)=3 (+3=consciousness) and between them is 1-stepping out and 2 stepping-in. Compare with representations where we have unmarked opposites and marked opposites.

Buvimas remiasi pažymėta priešingybe - esame Dievas - esame. Dievas pažymėtas gerumu, tai gyvenimas. Nebuvimas remiasi tobulomis priešingybėmis (nebuvimas ir buvimas tolygūs) - tai amžinas gyvenimas? Tai svarbu Dievo įrodymui.

Aplinkybė duoda žmogui suprasti nebuvimą.

Semiotinis kvadratas: Wishing -> not knowing, Knowing->Not wishing. Žmogus: Knowing->Not Knowing, Dievas: Wishing->Not Wishing. Žmogus išeina už savęs per aplinkybę ir nulybę - per būklę, ko nėra, ir per nebuvimą jame. Dievas išeina už savo išėjimą už savęs.

  • Nemylintis-neprasmingas, neramus-nepastovus, neužtikrintas-netiesus, neužtikrintas-netiesus, nesavarankiškas-neakivaizdus.

Dievas savo atžvilgiu yra - ir mūsų atžvilgiu yra:

  • mylintis - prasmingas
  • ramus - pastovus
  • užtikrintas - betarpiškas
  • savarankiškas - akivaizdus

Kas nesavarankiškas gali būti išreikštas kitais. Susieti su savo tiesos teorija.

Aleksandro išsiaiškinimo būdus moksliškai apžvelgti.

Lygmenų poros turi duality.

Nulybė yra tai kas už mūsų, o aplinkybės yra mūsų - sandaros žymės.

4 layers - let go of the self, put some distance on it.

How do things come to matter

  • Kaip ima rūpėti: Kaip atsiranda neramumas ir kaip jisai išrišamas ir įprasminamas.

Step out

  • Kodėl: aplinkybėmis iškyla tikslas rasti kodėl - find the purpose - atrasti ramybę
  • Find the purpose - the purpose is the stillness - the center - the source of peace

Step in

  • Kaip: taikyti meno taisykles - principles of life - evoke, support life

6 questions are related to meaningful experiences, with mathematical methods of proof, the gradation, Our Father, the eightfold way.

(Was: Exists - possible - desirable) instead should be: exists - desirable - possible. (But compare with the doubts.)

Paskui trejybės nariu išeiname už savęs į ramybę paskiromis aplinkybėmis. Grįžtame trejybe. Aštuongubas kelias išplečia šešerybę (6+3=1):

  • Dievas. Kaip TAIP. Kaip mums gyventi savo vertybe? Link with God:
    • Morphism - įmanoma/sprendimas - teesie šventas...,
    • induction - pageidaujama/pavyzdys - teateinie tavo karalystė...
    • algorithm construction - yra/priežastis - teesie tavo valia...
  • Gerumas. Kodėl NE. Kodėl negyvename savo vertybe? Trikdžiai: Three-cycle:
    • substitution - neįmanoma/susitelkti - kasdieninės mūsų duonos...
    • examination of cases - nepageidaujama/pataisyti - atleisk mums mūsų kaltes...
    • construction - nėra/tapti jautriam - neleisk mūsų gundyti...

Derinys yra ženklų.

  • Viskas-simboliai, betkas-indeksai, kažkas-ikonai, niekas-taškučiai (daugybė paskirų)
  • Klausimai/derinimai, nuostatos/jėgos, sprendimas/derinys, veikla/savęs-apibrėžimas
  • <= praplėsti požiūrio apimtį

Ženklas (širdis) - turinys (pasaulis)

Ženklų savybes palyginti su rūpesčiais ir branda.

Medis M, seka (token) S, tinklas (mikrosavybės) T.

Visuma, ryšiai, apimtis, reiškinio visuma.

  • plačiai taikomas - patogus - lankstus SM - galima pertvarkyti
  • skiria jėgas - nesavanaudiškas - pakitus TM
  • judus - laisvas - gali atpalaiduoti ST
  • esminis sprendimas - amžinas - įsimintinas SM
  • jėgas derina - pilnas - reikšmingas MT
  • tinkinimas - tisklus - tikslingas TS

He doesn't say there are 15 - he says it could be different - but I make the case that there are 12+3.

Troškimas - Dievo būklė.

Dievas yra tai kas už mūsų. Užtat nulybėje nėra jokio požiūrio.

Healthy concerns have us apply a pattern abstractly, through potential and actual recurring activity, to step outside of our situation, as if into an extra dimension of new possibility, where we locate a sense of peace and balance. From this optimal vantage point we resolve our tensions by establishing the pattern concretely, as material structure, and stepping back into our situation, where we become sensitive to new tensions.

We thus develop circumstances for an ever more central sense of peace, and an ever greater sensitivity to life, to the natural tensions and concerns ever forming at the periphery. We describe a system of six concerns which patterns address and which provide various "names" for aspects of this Quality Without a Name.

We relate the 15 properties of life to 4 planes of being stepped out, being stepped in, and moving to and from these states. 3 general properties (strong centers, strong boundaries, levels of scale) get expressed in these planes as 12 specific properties. We derive these 12 properties and relate them to cognitive linguistics.

  • Seek connection with visualizations and how they link the conscious and the unconscious.

Add ideas about Centers - and relate to patterns. And in a world of centers - we are participating in levels and metalevels - and God's point of view is important. A transparency as a center - relation to centers within it and centers it is within. Also, it relates to the importance of changes in ourselves. Unfolding whole - structure preserving transformations. Need to be able to take it all down and put it back up again. Level and Metalevel - Human and God. Deepest value (our center) and investigatory questions that sharpen it.

Salingaros's three laws: select the origin so as to minimize entropy (level), alternate - simplest rhythm (metalevel view), levels of scale = e (level and metalevel)

Heuristics - Ways of figuring things out

Extra

  • Define wishes: self-sufficiency, certainty, peace, love. Body, mind, heart (expectations), will (values). We are creatures of knowing, God is not knowing.
  • Conscious mind ruling the unconscious mind: visualizations.
  • Conscious mind - divisions of everything: twosome, threesome, foursome.
  • Six representations (wholes).

Exploring the Nature of Order Generating Rules, Macintosh & Romme


Making it a science. I add some possibilities:

  • Trying to define the principles of life mathematically in terms of the Mandelbrot set.
  • Identifying the purposes of art, and the rules of art, relating them and also with the 15 principles.
  • Defining peace as the core, neutral emotion at the heart of our emotional life.
  • Objective about the reasons for modern architecture - squalor - people spending time outdoors, not indoors - independent thinkers crushed by villagers

Main points

  • patterns: approximating the unknown (waiting) with the known (expecting)
  • static concerns in the world (patterns - recurring activity) - dynamic concerns in us (meaningful experiences - one-time activity - creating and adjusting patterns)
  • 12 properties of life: in terms of 12 circumstances: three-cycle vs. logic of negations
  • peace: stepping-out (peace - conscious - impartially, rationally balancing) and stepping-in (love - unconscious - going beyond oneself - favoring the unconscious)
  • ways of adjusting a pattern: the names for peace - types of signs and their qualities

Life and peace (wholeness).

Will describe:

  • Wholeness (peace) and Life (agitation - commotion).
  • Attempts to name the Quality without a name - are signs of agitation, that we are riled, that we have a feeling of caring.
  • Properties of life are how (and where) we find a purpose - stillness - center by which we can step-out (of the threesome) into the nullsome (let go of our point of view) and ultimately into peace. And the same properties of life are how we step-in.
  • The process of applying patterns is one of stepping-out (from being riled (by activity) into peace by embracing the truth of the heart) and then stepping-in (by creating structure).
  • Patterns are coherence amongst the four levels.

I add to this:

  • Dynamic concerns - by which we take up one of the 6 challenges - what is or what is not - and choose the truth of the conscious (unknown) over the truth of the unconscious (known).
  • Static concerns - by which we establish the pattern.

Questions

  • How to define the qualities of signs? Signs mediate the relationship of the activity with its creator - thing, icon, index, symbol.
  • Define the four-level nature of patterns.
  • Define how patterns are applied.
  • Relate how God goes beyond himself (wishes) and how we go beyond ourselves (representations of the nullsome - by way of the circumstances).
  • Describe how we go beyond ourselves by listening for peace - and how this affects existing patterns.
  • Describe how we go back into the world with God by applying patterns anew.
  • Describe what happens if we go back into the world without peace.

More questions

  • What is the relevance of the negation of the levels of the foursome by the representations of the nullsome?
  • What is the role of the representations of the nullsome? Coherence of the threesomes makes for coherence of the nullsome. Similarly, coherence of the properties of signs. This makes for coherence of the spirit.

Stillness of nothing - significance, stillness of something - constancy, stillness of anything - direct, stillness of everything - truth.

Stillness is a sign of peace - centers have stillness - Stillness has four forms. Smaller stillness should serve the greater stillness.

Significance... Constancy is the icon of peace. Directness is the index of peace. Truth is the symbol of peace.

Thus these are levels

Similarly, every pattern is simply an imperfect approximation of peace.

The sign of peace is stillness. Every pattern aligns , a sign of that peace. Stillness is the sign of peace, and we experience stillness as centers. Every pattern has four stillness...

It is a sign of the peace.

Our deepest value is not peace but simply a sign of that peace.

Problem of deepest value

The twelve purposes explain where we see them - but in each case we can look for the corresponding nullsome, which is THE purpose.

The twelve rules of art - the principles of life - explain how we manifest the spirit of a pattern that we are applying - we live its activity and thereby apply its structure through these principles.

Patterns: 4 levels - relate with the 4 representations of the threesome.

Rationality.

Identify the purpose with a circumstance, then through us identifies it with a representation of the nullsome. Empathize back in.

Note dynamic concerns are the representations of the threesome derived from truth (in positive and negative forms).

Note that dynamic concerns can thus be stored in memory.

Dialectic of the heart and the world

There are four levels of properties - broadest to narrowest. We are riled - we "care" - we have loving expectation or hating expectation - if we focus on the narrow rather than the broader. We need to flip that around. The properties of life show this vividly - so roughness, gradient, nonseparateness should never be a concern - let them happen naturally - whereas simplicity, the void, alternation should always be the first concern - you can't go wrong by being devoted to them.

Try to connect 6 pairs of these levels with the challenges for patterns (and the names of peace).

Our concerns and God's concern: our maturity

Relate to person (deepest value) and God.

Pattern language for our personal growth - 12 questions - and we need to ground in reality - what we care about, our deepest value - not abstractions

And building blocks for our growth - self-identity transformations.

Alexander-Extra


Naujausi pakeitimai


Puslapis paskutinį kartą pakeistas 2017 spalio 20 d., 02:09
Tweet