From Typographical Twigs to Allegorical Branches

By the end of 2023, I had suspended the idea of visualising the main philosophical branches of Objectivism and instead attempted to represent the various salient points they articulated.

But perhaps an apt representation of the branches should be the starting point.

A purely typographic solution may not be the most appropriate. As visual and spatial creatures, we are more immediately resonant with 3D objects than type. Moreover, dressing-up type into objects falls between two extremes, being neither clear type nor object.

Pursuing the opposite route may be more suitable. Creating familiar objects that convey each of the five branches of Objectivism within the same scene. This would not be a static image but a 3D model that could be interacted with.

The question is what five objects would be most appropriate for the scene?

Candidate objects to be revealed next month…

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A Return To Trichotomies & A Wholly Typographic Solution?

On second thought, the division of the axioms into twin pairs, whilst a neat explanation of their relationship, does not seem to extend to deeper layers. However, a pattern of threes does appear to be maintained: the first is the fundamental (the more metaphysical), the second is the detail that explains it (the more epistemological) and the third is the general conclusion (the more axiological, its value).

Meanwhile, I have had a further re-evaluation. As I am dealing with concepts it may be preferable to dispense with abstract shapes and use only words. I am considering an entirely typographic solution to convey the structure of Objectivism. 

More words on this next month…

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Tetrad, Not Trinity?

I'm wondering whether two pairs of twins run through the structure of Objectivism (rather than the previously considered trichotomies).

The tetrad idea derives from John Galt’s speech: 

To exist is to be something, as distinguished from the nothing of non-existence, it is to be an entity of a specific nature made of specific attributes. Centuries ago, the man who was—no matter what his errors—the greatest of your philosophers, has stated the formula defining the concept of existence and the rule of all knowledge: A is A. A thing is itself. You have never grasped the meaning of his statement. I am here to complete it: Existence is Identity, Consciousness is Identification.  

Adapting ‘pairs of twins’ into a 3D model, within a golden epistemological spiral, occasions a set of four sphere of decreasing golden ratio, each at right-angles, pairs facing each other across the origin. 

Front view

Top view

But does this quaternary continue down through successive spiral rotations? Watch this space…

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Structure Of Objectivism: Re-Setting The Table?

Over the last few years I’ve been proposing the construction of a model to represent and convey the structure of Objectivism. However, on reviewing the very basis on which this model would be built — the table of 27 statements set out back in October 2021’s blogpost — I am not convinced that it is as logically sound as I once thought. Seeing that this table is the very basis for all subsequent work it is crucial that the series of sequential statements it contains is airtight when looking through the rigorous lens of propositional logic. 

Additionally, the table (or tables) should be able to somehow incorporate a certain amount of flexibility within the sequence, dependent on context, otherwise it risks being Rationalistic (a valid accusation that this project risks anyway). 

Over the next few months I'll aim towards offering a tighter table… 

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A Place To Be

Last month’s animated model (Epistemology Churning Metaphysical Milk Into Axiological Butter) seems to be fairly apt for all levels. The next step is to arrange these spheres appropriately into a set of nine. Utilising interactivity, only one sphere/level would be active at a time and the ‘game’ would be to focus upon the active epistemological element and be able to ‘drive’ it around all nine spheres.

I’m also toying with the madcap idea of introducing initial randomness and even allowing for the geometric spiral shapes to morph into something more interesting, more inhabitable like isles or little planets, adding to the pleasure of the experience, making it less abstract (yet without losing the underlying structure). 

More dizziness next month… 

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Epistemology Churning Metaphysical Milk Into Axiological Butter

The idea that I'm working on here is to convey how learning (epistemology) about fundamental reality (metaphysics) actively generates choices to how we deal with that reality (ethics/axiology).

• The inner white–bright ball of energy spiralling around represents epistemology. 
• The initial grey cloudiness of the container sphere represents metaphysics.
• The black spiral which results (from epistemology's work) represents axiology. 

As the inner white ball moves upwards, illuminating all it touches, it orders the greyness into a distinct black/white spiral form. It then descends down the spiral to be ready to take on the next learning task. 

If you know what side your bread is buttered, you'll tune in next month… 

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Interplay

How Existence, Identity, Consciousness are integrated: visual demonstration via interactivity 

I’m becoming more aware that user interactivity could be key in showing how the three metaphysical axioms define one another. 

A 3D model ought to start with Existence yet display nothing but a ‘grey-noise’ until the viewer initiates action. This could be as little as moving a cursor which would temporarily create a clearing in the middle of the fuzzy greyness — a potential space for Consciousness. A further, specific action would unveil something else, something more solid — Identity. 

Therefore, what I ought to be pursuing is something more akin to an interactive game than a mere 3D model. A game which rewards the user with clarity and beauty once the correct (epistemological) path forward has been found. 

Less fuzzy greyness next month… 

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Park Or Pursue?

I’m currently not sure whether or not to continue pursuing a visualisation of the structure of Objectivism. If I did continue I’d be tempted to investigate a radical break with the geometric shapes that I have been using up until now. I’m thinking about making it less abstract and more allegorical. 

If I decide to pursue the project, we’ll meet again in a month's time, at the start of 2026. If not, I hope that you will have found something of value within these blogposts. 

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Three Phases, Three Arrangements

 

The nine levels are divided into threes: 

• Levels 1–2–3 are circumscribed by metaphysics (the ‘grey-noise’ sphere)
• Levels 4–5–6 are circumscribed by epistemology (the lighter coloured sphere)
• Levels 7–8–9 are circumscribed by axiology (the darker coloured sphere) 

As each level develops from the previous level, the primary is still metaphysical (existence).

Less circumlocution next month…

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One Model, Three Viewpoints

Clicking to one of three viewpoints in the prospective 3D model would be a better option. That would even be the case if the cameras for metaphysics and axiology were in the same place, the animation itself would be rewound to either display Existence (‘grey-noise’) or Identity (a black/white split). 

I still think that Consciousness (Identity refracted in a ‘crystal ball’) — the epistemological camera — ought to see things from 90°, from the top, and the viewer would experience ‘travelling there’ in order to convey a change of location. 

Let's travel on to next month…

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One Model, Two Viewpoints

 Top

Front

Last month’s animation isn’t very suited to a 3D model, which is what I’m ultimately interested in.  

Here is another model, seen from two perspectives; from the front and from above (unfortunately the animations don't always sync perfectly). 

The unusual difference between the two is that the top view looks through ‘the crystal ball of Consciousness’ which affects what is seen underneath it. 

These two perspectives try to convey something of the difference between an objective and subjective viewpoint, yet both viewpoints work together in the same overall model.

Perhaps a real 3D model for next month…

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Automated Axioms?

 

This animation conveys ‘the mechanics’ which integrate and reciprocate axiomatic concepts: metaphysical concepts (like existence exists) separating out into the other two main philosophical branches: proto–axiological concepts (identity: A is A) and proto-epistemological concepts (consciousness as he process of identifying that which exists). The former is relatively passive, the latter is active. However the axiological does effect the epistemological — the active white ‘prediction ball’ switches to ‘prediction-error’ black once it identifies its surrounds. Both branches contribute to the generation of the subsequent metaphysical concept, in this case revealing the existence of entity (entities exist as identifiable similarities).   

I think that ‘mechanics’ hinted at are somewhat appropriate: passive/active/neutral seems to be a useful way in differentiation the three main philosophical branches and their related concepts. 

However, it is a different approach to last month’s model. Here the route from one conceptual level to another is linear (the epistemological and axiological don’t contain subsequent nested pairs). 

I wonder if there is a way of combining these two approaches as I still think that including alternative hierarchies has its merits. Perhaps that’ll be the assignment for next month…

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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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