Branches Branching: Alternative Hierarchies?

 

I don’t think that last month’s blogpost was the last word on a visualisation for the structure of Objectivism. A major concern is that the animated model was too linear. Peikoff, in his lecture (Understanding Objectivism — Lecture five, “The Hierarchy of Objectivism”) talks about the hierarchical structure requiring some room for contextual re-arranging: 

The rationalist hates the idea of options; he wants everything to be like geometry. An empiricist hates anything that isn’t an option; he wants any order of any kind as he feels. The key to Objectivism here is a logically necessary structure in principle, plus many options in detail and application.  

Well, a visualised structure has to be somewhat geometrical, yet it doesn’t have to be such a geometrically fixed model as presented last month. 

One interesting aspect of using a loxodrome spiral with two reciprocal ‘golden’ shapes (as seen more smoothly in last August’s Metaphysical Axioms Animated) is that the spiral could continue in a loop so that the contained shapes may alternate between being ‘dominant’ and ‘subservient’. 

This would usher in a contextual choice “in detail and application” which moves the model away from an over-rationalistic linearity. 

More integrated irregularity next month…

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Spiralling Through Hewn Lunes

 

Spiralling through the first nine lunes, each representing a concept within the structure of Objectivism — a colourful journey!

Is this the final model? Perhaps conceptual labels will be added next month…

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Lune Hewn

 

This is a 120° segment of a sphere ~ a lune ~ viewed frontally and slightly from above (the heart-shape is unintended).

 

It is similar to the lunes posted back in October 2022, yet with another spherical lune hewn out at the bottom. 

This form satisfies a number of requirements for representing concepts I think. However it needs to be seen in relation to other smaller lunes, housed in the hewn-out space and allowed to rotate around the centre.

More lunacy next month…

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Cooking Concepts

 

Let’s start with the first three fundamental ingredients: 

• Existence 
• Identity 
• Consciousness 

Unpack each one, give it a rinse, then lay them out together on the metaphysical cutting board.

Now we must decide on what type of dish to create in order to bring out the full flavours. Certainly not a lazy mix of all three, that would make them indistinguishable from each other. Not three completely separate courses, because it’s the combination and contrasts which give them each their appeal. 

Anyway, our task in the kitchen is to represent them (not recreate them), so we need a bowl (a containing frame on a blank page). I prefer a round bowl so that baking is as even as possible.

Some sort of axiom pie seems apt, for with a pie there’s a definite outside and inside. We’re baking it from the “Objectivist Cookbook” so we know that Consciousness should be the filling (otherwise we would serve up the primacy of Consciousness — a sickly fare). 

But what should form the pie’s outer crust? 

What about a crust made in two equal halves of those two ‘external ingredients’, so all three ingredients can be in contact with each other; thus Consciousness would be half within Existence, half within Identity? 

I don’t think so because Existence and Identity would seem too separated.

What about Existence as the whole outer crust, with Identity as the ‘between layer’ (inner crust), both containing Consciousness? 

It’s more apt as Existence and Identity are corollaries, two sides of the same coin, while Identity (via identification) is a bridge that Consciousness needs to grasp the reality of Existence.

We'll see what comes out of the oven next month…

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Simmering…

I’m still not sure whether a visual representation of the structure of Objectivism is feasible or would inevitably be over-rationalistic. After all how can such profound concepts like Existence, Identity and Consciousness be conveyed by a mere doodle on a page? 

On the other hand, even if it ultimately falls short, some visuals are more apt at representing these metaphysical axioms than others. This series of blogposts have demonstrated a few different ways in which the task can be attempted — some more successfully than others, yet none being fully satisfactory so far. 

I still think I can get closer. This project is simmering away, I hope to be able to bring it nearer the to boil next month…

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Convoluted Convergence

 

Moving on from overlapping tori, here are overlapping spiral shells (a cut-away). It’s so convoluted a form that it requires at least two images from different perspectives to tell what’s going on, but even then it’s a tricky shape to envisage. 

Back to the drawing-board I think! 

More thoughts next month…

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Golden Horn Torus

 

A 3D model of the three metaphysical axioms: two overlapping ‘golden ratio’ horn tori (one black, one white) within a (grey) container sphere (cross section). 

The intention is to match the 3D model to the schematic of the three axiom (November's blog).    

 

But is this visual structure apt? More thoughts next month…

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Horn Torus

 

An animated 3D version isn’t quite there yet, still far off on the horizon. However, it would be somewhat based upon the above standard horn torus (albeit with ‘golden ratio’ proportions).

Something more ‘golden’ next month…

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Tortuous Tori

 

Moving on from last month’s ‘back to basics’, I’m currently thinking about a torus (with zero radius hole) which duplicates when it deforms. The resulting semi-overlapping tori pair expand and contract in a similar way yet at opposite locations, creating interesting spaces in-between.

The above image is a cross-section: a grey containing sphere, one black and one white torus (both sliced-through vertically, like a doughnut halved upon a plate). These tori are thick at one place, thin at another — hence the cross-sectioned big and little circles.

The labels for the three metaphysical axioms have been tentatively added, although I don’t think the aptness of these can’t be fully assessed until demonstrated in an animated 3D version — something on the horizon for next month…

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Back To Basics

 

Aiming at the simplest, most essential graphic representation of the three metaphysical axioms has resulted in an animation which I'm happier with. 

Existence as flat grey to gradients of grey, contrasted with Identity as black/white differentiation, works. 

Consciousness emerging from Identity as an active process, then turning over (from 2D into 3D) so that it can be seen ‘inside-out’ seems promising.

I'm concerned about the obvious use of the yin-yang shape and its association with mysticism, however I couldn't come up with a better form. 

 

There is certainly room for improvement and development, more next month…

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Critique of Current Model

It is not a satisfactory model. 

It is confusing rather than clear. 
It relies too heavily upon animation.
Indeed it doesn't work as a physical object or mechanism — there is a complete lack of natural cause and effect.
Unless stated, it is far from obvious that shapes represent metaphysical axioms.

 
Specific points to address: 

• The only vaguely apt upshot are the two ‘golden’ black & white spheres within the spiral, within the (half) container sphere of greyness (or grey-noise). However, even that set of objects is an overblown way of conveying Identity. All that's needed is a zoom-in to the grey-noise and show a black sphere surrounded by white or white sphere surrounded by black. Furthermore, Identity doesn't grow out of greyness (a grey sphere), it just is, like Existence. 
• The Consciousness sphere is unconvincing, not radical enough and seems to emerge magically, without causation. 
• Consciousness's split, echoing Identity's split, has more sense than the former, yet the process should be more immediate and no account is given of the context of a moving body (let alone the Free Energy Principle). 
• The emergence of Entity is lazy. It ought to combine Identity with Consciousness in a more convincing way. 

What can be salvaged, ameliorated is scheduled for next month…

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Metaphysical Axioms Animated

This is an animated version of last month's key stages in the relationship between the three metaphysical axioms of Existence, Identity and Consciousness. 

A fourth metaphysical axiom, Entity, emerges at the end which effectively begins the cycle again. 

Much called for clarity on this is earmarked for next month…

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Inversion Of The Sphere Of Consciousness

 

A sphere of Consciousness may be useful after all. It may evolve within the paradigm of Identity, growing from next to nothing… 

As an informational sphere it flips its surrounds into contrasts where it is able to. 

Once done, it tries to verify that the outside state stays the same, it expects it to stay the same… 

(new small white inner circle as prediction; new larger (black) inner circle as prediction error)

If not (a prediction error) it inverts its contents  — hiding its bounds in so doing.

Above, without the ‘process’ spirals. The upper pair of nested spheres (the prior) would fade-out leaving just the three metaphysical axioms: Existence (grey), Identity (black), Consciousness (the white prediction error forming ‘current experience’ within Identity). 

An animation of this is on the cards for next month…

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Spiral Comes Between The Dynamic Duo

 

Following on from using two spheres to represent (the processes of) Identity formation and another two spheres to convey the process of Consciousness, the above ‘storyboard’ animation hints at a spherical duo which might also generate or hew-out a spiral.

Stay tuned for next month's exciting episode…

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Dynamic Duo?

I wonder if it might be more appropriate to represent certain concepts with two circles/spheres rather than one?  

Existence is just one thing — everything. 

Yet a dynamic duo of using two circles/spheres could help to convey the idea that Identity involves difference. 

Furthermore, another pair assists in revealing Consciousness as being a process between prediction and prediction-error.  

More adventures with the ‘dynamic duo’ idea next month…

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Elevating The Primacy of Existence

 

I think the above animation for the structure of Objectivism is an improvement on last month's because it firmly re-establishes “the primacy of existence” — indeed, the primacy of metaphysics at each stage. 

• Metaphysics is always the containing sphere.
• Epistemology is here always shown as the darker, larger sphere.
• Axiology (Ethics/Politics/Æsthetics) is here always shown as the brighter, smaller sphere.

It is just a bare-bones, 2-D animation. I haven't abandoned the reciprocal nature of each sphere's growth/shrinkage, nor the possibility of using loxodromic spirals on a 3-D model — I've kept the new arrangement as simple and as essential as possible for now. 

There are nine sets of conceptual trichotomies, passing through nine stages/levels.

For easy reference, here is a replicate of the tables (from February's blogpost): 

Metaphysics	Metaphysical  Angle	Epistemological  Angle	Axiological Angle
1 Axioms	1 Existence   exists.	2 Consciousness  is the process of identifying that which exists.	3 Identity  is what defines an existent (the difference  that makes a difference).
2 Correlates	4 Entities  exist as identifiable similarities.	5 Action  is how entities behave together as processes in accordance with their attributes.	6 Causality is the law of identity applied to the action of entities.
3 Inference	7 Volition Inserts Self  as a result of the choice to focus/evade (autopoiesis).	8 Validity of the Senses in that they are causal evidence of a difference making a difference.	9 Objective Reality as absolute  (primacy of existence).

Epistemology	Metaphysical  Angle	Epistemological  Angle	Axiological Angle
4 Integrals	10 Sensation  as undifferentiated awareness of objective reality.	11 Perception  as groups of sensations becoming causally identified as entities in the present.	12 Conception as the volitional categorisation of percepts into particular relationships.
5 Formation	13 Mind-Body Integration harmonises consciousness with existence.	14 Differentiation  & Integration of percepts into concepts.	15 Man-Made from Metaphysical  conveys that choice-contingent concepts are hewn from given percepts.
6 Integration	16 Cognitive Objectivity when concepts are aligned with reality.	17 Logic  as method of developing knowledge through non‐contradictory identification.	18 Rationality  as man’s only true means  of knowledge.

Axiology	Metaphysical  Angle	Epistemological  Angle	Axiological Angle
7 Ethics	19 Reason  as man’s means of survival.	20 One’s Own Life  as the ultimate measure of value  (reason, purpose,  self-esteem).	21 Virtue of Selfishness with man as an end in himself (pursuing rational  self-interest).
8 Politics	22 Happiness  as the aspired condition  of man  (via rational self-interest).	23 Individual Rights (freedom from coercion) entails enforcement  by governmental agency.	24 Capitalism  as the only moral system (in which happiness may be fully realised).
9 Æsthetics	25 Art  as the concretisation of metaphysical ideas.	26 Romanticism  as the supreme conceptual school of art.	27 Æsthetics  Are Objective when evaluated within the appropriate, holistic context.

More meat on the bones perhaps next month…

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