Alan N. Shapiro, Technologist and Futurist

co-author: Alexis Clancy

We need a new technique that augments the inheritance mechanism of Object-Orientation.

In addition to inheritance, we will have analogies or resemblance between the software instance and the “blueprint” software classes which furnish the possibilities of what the instance can do.

The highest-order analogy, defining the base of operations of this subsystem, is the idea of the software instance having a choice, having existentialist freedom, rather than being determined by available template attributes and data.

Choice is inaugurated by Incompleteness.

Incompleteness is inaugurated by Choice.

Choice is inaugurated by the Möbius Twist and the Aleph Operator.

Incompleteness is at the foundation of the architecture of a radicalized Object-Oriented class inheritance hierarchy.

Whereas Descartes and Leibniz (before Deleuze wrote about Leibniz) in the 17^th century wanted to deduce a system of knowledge starting from a few certainties (an axiom-based system), WE WILL START WITH INCOMPLETENESS (integrated at an axiomatic level).

The Aleph Operator operates on a playing field where choice is offered to the instance.

Create the Möbius Twist on the “50 Yard Line” (American Football) of the playing field.

Create two types of Incompleteness: the Gap and the Jump.

These are two potentials, both operated on by the Aleph Operator.

The Gap and the Jump both cross the playing field on which Incompleteness becomes visible; they generate two collapsed waveforms.

The energies of the potentials (the Gap and the Jump) relate to the energy of the event to be roused into awakeness, leaving the Epsilon Energy attributable only to the Aleph Operator.

Plus a little bit of Epsilon Energy is required to keep the two events of the Gap and the Jump separate when they materialize into Euclidean space-time.

The Möbius Twist is realized by unrealized choice.

In a given quantum potential field, a (semantic) horizon can be drawn yielding an “up” or a “down.”

Ultimately and absolutely there is no way of knowing whether, on realization, “up” or “down” will be yielded, so the potential field offers both.

In relation to itself, the potential field is complete and entire, so there is an interval where “up” meets down.

This is how the half-twist – the Möbius Twist – is generated in the model.

A potential component can either be “up” or “down,”  it cannot be both – this is how the “gap” and the “jump” are respectively rendered according to a general rule.

This general rule carries with it a follow-on rule: opposing components cannot be in the same place within the model in a given frame.

In our frame, there exists, within the field, three further fields which lie outside of our understanding: the two “gaps” and the “jump.”

These elements are strictly analogous to Incompleteness: I (Alexis) call this “Topographical Incompleteness.”

If we decide to populate the “gaps” with some other, smaller potential, we will find the same thing within the frame again – more pairs of “gaps” – in a sense self-similar or “Fractal Incompleteness.”

This technology of resemblance to be realized on the basis of the new mathematics provides an answer to the question of how do we deal with the problem of complexity.

Within the existing computing paradigm, in order to deal with a complex problem, we break down the problem into smaller, more manageable parts.

This is essentially the Cartesian Method.

But it is impossible to apply the Cartesian Method to quantum-mechanical generalized complementarities like the wave-particle duality or the Heisenberg Uncertainty Principle.

Whereas the Cartesian method may work for mechanical systems, it cannot be of much use when we aspire to the creation of something that is living.

The more correct approach corresponding to a breakthrough into 21st century science is to identify relationships of similarity, to find SAMPLES or PATTERNS that capture something of the vitality and complexity of the whole without breaking it down in a reductionist way.

With further respect to the Möbius Twist in the frame, I (Alexis) imagine an observer looking at this Twist and trying to reason it.

Reason fails at the point that it contemplates the mystery of choice – not the choice that exists in the mind of the observer (a concept that is a veritable can o’ worms in a theological/philosophical sense), but more so that a choice is presented to the observer.

When this concept is removed from reasoning, what is left is the Möbius Twist in the frame put there by some “thing” or, more to the point, by some mathematical Operator.

So I (Alexis) simply invent a mathematical Operator and designate a symbol for it.

I call it the “Aleph Operator” and adopt the Hebrew Aleph – א – as its symbol.

Aleph is the first letter of the Hebrew Alphabet and also represents the number 1.

This Operator operates on a frame/field where choice is offered.

The Operator creates a Möbius Twist somewhere in the field, also generating the the two types of Incompleteness – the “Gap” Incompleteness and the “Jump” Incompleteness.

Another reason for adopting the א is that, graphically, it looks like a Möbius Twist.

DESIGN:

Based on the C++ Object Model (see the work of Stanley B. Lippman who worked at AT&T Bell Laboratories and Walt Disney Feature Animation), implement a working Object-Oriented Inheritance Mechanism.

Create the framework of a Resemblance Technology, parallel to the Inheritance Mechanism.

We need a coded class for an Incompleteness Channel.

Program the Möbius Twist.

Program the Aleph Operator.

Program an “ideal type” circumstance where the instantiated instance chooses in a entirely free way who it is and what it wants to do rather than being governed like a slavedog by preprogrammed attributes and data.

Create the playing field class with specified area boundaries.

Program the type of Incompleteness that is the Gap.

Program the type of Incompleteness that is the Jump.

Program how the Gap crosses the playing field where Incompleteness has appeared from the mysterious tall cornfields beyond the left outfield fence (see the baseball film “Field of Dreams”).

Program how the Gap then generates a collapsed waveform.

Program how the Jump crosses this same playing field.

Program how the Jump then generates a collapsed waveform.

Program the effect of Epsilon Energy on keeping the Gap and the Jump separated as they reappear in the Euclidean space-normal dimension.

Continuing the image-metaphor of “Field of Dreams,” this would be the moment when the spectators who are sitting on the benches behind the first base line stop being mere spectators and join in with the vintage baseball players who have come forth from their ghost-like Existenz in the cornfields and who are now playing super-sharp pepper practice in preparation for the first pitch of today’s Sunday doubleheader – Cy Young himself on the mound in game one – in which the heretofore spectators will also now be participants.

At that moment, a relationship of resemblance – the software object as SAMPLE or PATTERN of the systemic whole – emerges from the dark shadows of the netherworld or afterlife into the light of day.

The long night’s journey into day — is over.