natural multi-state computing

NATURAL MULTI-STATE COMPUTING(Engineering Evolution: Simple Machines and Beyond)

Marcus Abundis1

AbstractThis essay covers adaptive logic in humans and other agents, and complements a related ‘general theory of meaning’ (Abundis, 2016). It names informational roles needed for minimal adaptation as a direct experience, versus the ‘reasoning by analogy’ typical of artificial intelligence. It shows how levers, as a computational trope (adaptive template), typify meaningful adaptive traits for many agents, and later afford the advent of simple machines. To develop the model: 1) Three lever classes are shown to compel a natural informatics in diverse agents. 2) Those lever classes are next deconstructed to convey a ‘scalable creativity’. 3) That creative logic is then shown as entailing three entropically generative computational roles. 4) Lastly, that adaptive logic is used to model tool creation. Thus, the analysis frames systemic creativity (natural disruptions and evolution) in various roles (discrete, continuous, and bifurcation) for many agents, on diverse levels, to depict a ‘general adaptive intelligence’ (16 pages, 6,600 words). Keywords: adaptive logic, evolution, information theory, theory of meaning, information science, functionalism, levers, simple machines, kinematics, entropy, computation.

INTRODUCTION

Human evolution is now often sustained by simple machines that frame much of our reality. From crude hand axes to self-driving cars, space ships, and hyperloops, our ‘tools’ drive a vast cultural ecology. This adaptive mechanics arose from the fact that early humans had few purpose-built tools (fangs, claws, etc.) to use on the evolutionary landscape. For example, basic traits allowed us to survive along with other early agents. But human adaptation now entails language, information, sociability, intelligence, and the like, as major adaptive leaps. A core question thus arises: How is our unique adaptive creativity explained, despite a shared primitive origin? Answering this one issue is key to understanding humanity’s unique evolutionary past, its present, and its future.

Despite a deeply creative modern informatics, humanity’s earliest adaptations lie in primitive mechanics. This study thus seeks to tie our modern informatics to early mechanical roles. To develop that ‘bridge’ this analysis begins with a necessarily primitive part of human prehistory.

MODEL DEVELOPMENT – Computational (Lever) Emergence

Early human adaptation (post-genomic, pre-cognitive) is perforce mechanical, often arising via ‘levers’. Levers (Figure 1) offer a means for exploiting environs and have many forms (Figures 2 and 3). But this critical levered role does not explain the many adaptations now seen among humans and other agents. As such, we must see how and why levers exist in diverse adaptive roles, how levers afford the rise of simple machines, and how they also implicate informational wherewithal or an adaptive general intelligence.

Organizational Behavior (GFTP), Graduate School of Business, Stanford University (March 2011).1

� 5 April 2017 – M. Abundis1

To detail that adaptive logic this paper names: 1) three lever classes, 2) transitions in lever classes, and 3) additive and divisive facets that enlarge lever functions and afford simple machines. The model thus names various recombinant or computational roles, using a lever, to typify diverse emergent/disruptive functional traits, but especially as seen among humans.

Figure 1: Standard Lever Classes. Each lever system has distinct functional traits or meaningful L, F, and E roles. Modern levers now arise as common tools: Class 1 – claw hammer, pliers, scissors, shears, oar, shovel, and pry bar; Class 2 – wheelbarrow, nutcracker, bottle opener, and hinged door; Class 3 – tongs, tweezers, broom, rake, spoon, fishing pole, and baseball bat. Below, L, F, and E (a triune Set) depict a lever’s systemic Aesthetic Elements.

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Figure 2: Class 1 Levers in Diverse Roles. A plant’s movement toward sunlight (left) is afforded by a Class 1 lever driven by molecular action potentials. Complex cranial movements, human or other, on top of a spine (right) also depict a Class 1 lever. Further, a plant’s cellular body echoes spinal vertebrae, where both entail compound Class 1 levers. This meaningful levered reality exists for many species in various forms, often typified as skeletal systems.

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While this study targets human adaptivity, many of the points raised here apply to other agents. A shared core exists as we are born to a world where levers abound. Whether as annelid, arachnid, arthropod, or anthropoid, this levered base is clear. Thus, when humans later evolve, basic lever functioning need not be invented but need only be acted upon. As such, levers mark a general cognitive artifact (Harris, 2016 ) relevant to many agents, along with an innate functional logic


or operative rules of ‘What it means to be/have a lever.’ Any agent’s first adaptive task is thus simply to see how levers work within set parametric bounds (e.g., fingers, limbs, etc.). This ‘need to discover’ drives each newborn to explore motor skills, priming (programing) a phenomenal/empiric (meaning-full) base. In this direct experiential manner agents first come to know what a ‘lever’ means, with interacting L, F, and E elements. This early priming instinct affords a functional intuition that enables pro tem survival for agents, where the only practical alternative is summary demise.

While many functions may actually typify an adaptive agent’s basic input-output system (life BIOS), this study focuses on levers as they are behaviorally and adaptively explicit, are nearly universal, afford a broad functional intuition, and naturally underlie the advent of simple machines and beyond, as soon seen.

To continue this adaptive analysis, despite a levered core developmental differences quickly divide humans from other agents (heterochrony, branching events). Parametric variety in the number, simplicity, and complexity of levers within each agent, and in diverse roles and contexts, places all agents on unique paths as a fated subjective edict. For example, complex or versatile levers, like a human hand, require more coordinated effort/logic. Humans then test and display lever agility via play, sports, dance, and the like, as selectable skill (or intuitive) differences. Also, as humans hold few purpose-built tools our need to discover lasts into adulthood (neoteny), an enduring adaptive trait of curiosity arises. Psycho-logical curiosity in some form likely drove early human migrations and the Upper Paleolithic Revolution, seen in cave art, jewelry, and other symbolic expressions.

Figure 3: Hominid Levers. Skeletal systems (endo/exo) entail many simple and complex levers in meeting various functional needs. But lever diversity can also cloud one’s sense of levers. For example, the ways in which Aesthetic Elements (L, F, and E) are explicit/direct (shown here) versus ambiguous or implicit (Figure 2, left), or simple versus compound (right: bicep-tricep pairing; Figure 2, right) show mixed causal/functional roles for many levers.

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Next, as we expand our symbolic repertoire (representative gestures, sounds, and artifacts) the chance to make everything abstract or symbolic arises, driving an early selectable meta-physics as general and social knowledge (cognition). Hence, from an early and mildly abstract need to


explore levered roles, modern human artifacts, culture, society, psychology, and the like, follow – in toto yielding (or ‘computing’) a cultural ecology that depicts humanity’s adaptive essence.

This brief narrative enfolds eons of evolution, omitting many details. But studying that level of detail is not the aim, which is, rather, to name primitive meaningful roles that bridge to a modern informatics – as an extensible adaptive logic. As such, key points to emphasize here are:• Universal: Levers (core artifact) sustain diverse agents in many roles, implying a natural (core)

informatics and generalizability. This focus on levers does not exclude other core roles. • Logical: ‘What it means to be/have a lever’ has innate operative rules, derived over millennia

of natural selection. Levered agency and rules are de facto extant. Hence . . .• Durable: Levers are select-ably useful and resilient, implying a type of survival logic. Agents

or ‘models’ lacking durability (survival logic, effective life BIOS, etc.) are necessarily extinct. • Differentiated: Not all agents/levers express survival logic equally, a subjective edict exits for

all agents, in each role, where ‘a difference’ between agents implies a possible adaptive gain. • Intelligent: Agent survival logic perforce typifies a manner of intelligence, even as minimal

adaptivity, or in exhibiting far-richer cognition and creativity. • Normalized: The above sum to a cultural ecology for each agent. Cultural ecology is first seen

as basic survival, but is later refined and expanded via agent-group tendencies. Normalization still has degrees of differentiability, driven by: genomics (internal variation), curiosity (behavioral variation), and environmental happenstance (material variation).

In this synopsis, nature’s invention of levers is ‘a given’ tied to the advent of life. ‘Why and how nature should invent levers (or life)?’ is an interesting question, worthy of study, but it is not explored here. Instead, we focus on the ensuing extensible adaptive logic that is afforded by the presence of levers. Also, the pervasiveness of levers means that an agent’s direct experience is necessarily a type of functionally directed experience, due to nature’s pre-existing lever roles.

The above naming of adaptive logic as ‘select-able survival’ (from mechanical, intuitive, and cognitive skills), even if true, is vague. It leaves further detail buried in the past and cannot bridge to a modern informatics. But this minimal view offers a way to distill adaptive facets needed to construct that bridge. If we examine this levered core, lower-order detail arises. To see that deeper logical detail I continue the analysis.

LEVER DE-CONSTRUCTION – Mechanical Advantage → Computational Adaptation

Three lever classes are detailed above in step 1 (Figures 1 - 3). This sets a starting point in modeling general adaptive intelligence. To next study lever transitions (step 2), those levers are deconstructed. This second step details the ‘what, why, and how’ of lever adaptivity, and thus, a lever’s extensible adaptive logic.

To begin lever deconstruction, all levers offer a functional mechanical advantage (MA) via aesthetic triune Sets (L, F, and E ≈ Lever Aesthetic). MA computation is shown in Figure 4 for a Class 1 lever, and Figure 5 shows a continuum of MA roles for Class 1 ➔ Class 2 ➔ Class 3 levers.

In considering L, F, and E, and lever MA, three basic adaptive/computational roles are seen.


• #1 – The Order of L, F, and E defines a Lever Class with three states: L-F-E, F-L-E, and F-E-L. All possible orders are herein named Order Entropy. Order Entropy is adaptive as ‘jumps in Order’ (➔) mark major-scale (disruptive) functional changes, shown in Figures 1, 5, and 6, as Class 1 ➔ 2 ➔ 3 jumps.

• #2 – Within an Order, fixed Values for L, F, and E define an Aesthetic Set (X). Thus, conversely, ‘shifts’ (⧻) in L, F, or E alter lever functioning. Shifting Element Values = Value Entropy. Value Entropy is adaptive as it marks minor-scale (gradual) functional changes, shown in Figures 4, 5, and 6. Alternatively, for a non-adaptive role . . .

• #0 – Signal Entropy (Shannon, 1948) from Aesthetic Sets (X) marks discrete ‘noise-free’ lever work. Signal Entropy has Set Order, Values, and Elements. A Set’s computational/functional direct-ness (or aesthetic invariability) makes Signal Entropy non-adaptive. Instead, it produces ‘directed signals’ (functioning) that convey meaningfully targeted messages or roles. Signal Entropy underlies the well-established domain of information theory, which emphasizes the practical transmission of ‘signal Sets’ in a noise-free manner.

Figure 4: Systemic Mechanical Advantage (MA) – Class 1. As L shifts (⧻) toward F, MA grows and lessens the E needed as work. MA growth is shown as a sloping dashed line: L is a vari-able Aesthetic Element, F is static, and E is a dependent Element. Order (L-F-E) thus ‘computes’ a range of useful L Values via L ⧻ F shifts, or select-able Value Entropy (dashed line ‘hash marks’). Within Value Entropy, a Set of L-F-E values (X) defines one specific lever, and yields discrete signals (Signal Entropy) as that lever works. Any variation in L, F, or E (Aesthetic Set 1X) amidst the conduct of that work adds ‘noise’, or presents lever instability.

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In summary, Order and Value Entropy mark two select-able ‘adaptive types’ or adjacent possibilities (Kauffman, 2000) that generatively (variably) alter or ‘re-create’ MA lever functions. Also, Order and Value Entropy’s innate variability means they seem ‘noisy’. Alternatively, Signal Entropy conveys specific MA lever functions, in part, by avoiding Order Entropy, Value Entropy, and other Entropic ‘noise’. Signal Entropy is therefore shown in direct relation to other entropic types, thus suggesting a ‘general entropic map’ as a way to model adaptive logic. The resulting ‘general adaptive bridge’ is shown in Figures 6 and 7.


Thus far the study names three lever classes (step 1), and three lever rules (step 2): #0 Signal Entropy, #1 Value Entropy, and #2 Order Entropy, both of which apply to all levers. But this ‘lever deconstruction’ holds more detail. For example, close study of Figure 5 shows that zero points [5] ‘break’ lever Order, where no MA is possible. This break is a natural part of the transition between lever Orders. These zero points are easily overlooked as we often think of levers in discrete (Signal Entropy) roles, and not as part of a logical continuum as shown in Figure 5. Further, notions of Order and Value Entropy are also atypical, again, due to levers often being seen as functionally discrete (aesthetically invariable) roles.

Figure 5: Systemic Mechanical Advantage (MA) – natural multi-state computing. One: three Lever Classes lie across the top, where the Order of L, F, and E ‘compute’ a Class. Two: within a Class, shifting L-E Values compute MA (heavy dashed line). Three: each Class holds a specific range of possible Values, shown as Value Entropy [1]. Four: a fixed Aesthetic (value) Set [2] then computes a targeted lever role, or Aesthetic Habit [3]. Five: working that Set computes Signal Entropy [4]. Six: now returning to the top, ‘Order transits’ (L transits F and E) [5] alter ‘What it means to be a Lever’, therein computing new Orders, or Order Entropy [6]. Seven: each transit also computes a critical ‘zero point’ [5] where distinct ‘not-lever’ roles arise.

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Those zero points mean that two ‘not-levers’ lie within the continuum, as: L/F-E, and F-L+E (Figure 8). As we wish to detail all logical aspects of that continuum, the not-levers mean a ‘rule #3’ is needed to cover those functional gaps – which requires further analysis. Also, some readers may balk at the idea of adaptive logic typified by three basic rules and simple lever graphs. Thus, the analysis next enlarges on Value Entropy and Order Entropy, and names a fourth Element Entropy rule.

• Value Variation – In Figure 4, as L nears F, E lessens due to a growing MA (dashed line): rule #2 Value Entropy. L does not pass F as that sets a new Class: rule #1 Order Entropy. Next, fixed


Values X name an Aesthetic Set, and working that Set produces Signal Entropy X: rule #0. Any change in L’s Value of Order during that work adds noise to Signal Entropy. These four traits thus point to a simple adaptive logic (vari-able L), while also framing signal-and-noise within Shannon information theory – all shown as Value (L) Variation. Alternatively, we can say Value Variation names a ‘useful noise’ beyond Signal Entropy, and affords testable/noisy adaptive options. Lastly, only L variation is noted here but any Aesthetic Value (F and E) can be varied, and would equally alter a lever’s functioning.

Beyond this basic mechanical view, Value Variation also helps to define native intelligence. For example, a newborn testing its environs naturally encounters diverse Loads, inciting varied Efforts, as direct adaptive (L-E) learning or simple trial-and-error. In later higher-order tool use, value variation points to subtle L-E learning differences in tool geometry, size, and position. For example, a claw hammer’s slot or a pliers’ hinge offers a range of useful Values, in the tool’s placement during use. Working that hammer or pliers then conveys Signal Entropy, and if the tool happens to slip during use, noise arises.

Value Variation also underlies many basic informational notions. Vari-able sounds afford language (e.g., International Phonetic Alphabet), where variable qualities (direction, distance, loudness, pitch, etc.) further convey ‘urgent-or-other’ meaning. Writing employs variable markings as fonts, symbols, equations, books, and so on. Computers use variable magnetic spots in reading binary digits (bits) that drive functions (Table 1). Mathematical and musical notation use numbers and notes as normalized vari-able elements (hereafter valuation) to present operative or use-full roles. Lastly, the neural nets and backpropagation (‘deep learning’) that underlie much of current artificial intelligence (Le Cun et al, 2015) are essentially Value Variation schemes.

In general, variation, as entropy of any sort, underpins adaptive logic for many reasons: A. If we see levers as ‘logical’, part of this logic is that variation be bounded if reliable levers

are to arise – noise-free Signal Entropy or recurrent discrete Sets are a rule #0 requisite. B. But aesthetic vari-ability helps if subtly altered/optimized roles are needed. Thus, generative

Value Entropy (‘vari-able and select-able’ L positions) marks a ‘next’ subtle adaptive logic. C. Also, the granularity of that variability fixes how closely an agent can target events to which

it is adapting. Value granularity (gradual-ness) thus further refines subtle adaptive logic. D. Lastly, L position (Value) is noted above but L, F, and E hold many likely vari-ables: L can

vary in density/shape, or F may vary in mass and height, or F may roll or pivot. Any variant that affords a new function, expands adaptive logic. Thus, Generic Entropy or general variant ‘noise’ implies many functional/logical possibilities for levers (Figure 6).

The above detailing of entropic types naturally bridges Signal Entropy and Generic Entropy. Each type holds a facet of adaptive logic that applies to diverse informational roles, as already suggested. Further, the range of likely L, F, and E values named here means that Figures 4 and 5 show only minimal cases, where myriad adaptive levers are actually possible. Lastly, we have not yet detailed compound levers, the above noted Order Variation/Entropy, in a computational role.


Figure 6: Five Entropic Types – general map. Lever MA roles are shown as entropic types: Signal, Value, Order, Element, and Generic Entropy. Each type has an innate functional logic that makes it meaningful. Signal Entropy (non-adaptive) is shown alongside noisy-but-meaningful (adaptive): Value + Order + Element + Generic Entropy ≈ ‘noise’, as variably generative options. These types imply many possible MA roles beyond the one MA line shown here, with Signal Entropy (X) as a discrete ‘narrowly defined’ case. The map thus conveys a signal-and-noise (adaptive) continuum.

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• Order Variation – Order variation details jumps across lever classes, named as rule #1: L-F-E, F-L-E, and F-E-L. Jumps in order occur when L transits a Fulcrum or Effort point (Figure 5 [5]), and are disruptive as they offer new Valuative options (rule #2), as a new Order (rule #1). Likewise, inventing a new tool (via Order Variation, see Figure 1’s note) disrupts ‘What it means to be an adaptive Human’, which differs from the daily Valuative use of existing tools. Order Variation (ordination) thus marks a new adaptive logic beyond basic valuation.

Order Variation’s disruptive role is natural. For example, the Sun crossing Earth’s equator (mid-point) sharply alters weather patterns. For levers, joints show Order Variation in a bicep-tricep pair and elbow (Figure 3, right). This presents a dual-use Class 1-3 Fulcrum, as a natural F jump, or a compound lever. This joint role means that humans can then project (intuitively/psycho-logically scale) ‘joint artifacts’ as an idea of ‘holding’ a rock or stick. Joint-ing a rock amplifies that internal compound lever as a ‘hand axe’ – for a type of compound or scale-able adaptive logic.

Joint roles typify ordination as they expand the ways in which we ‘play on Order’. For example, testing a ‘held’ rock or stick stirs new learning. Sticks (trebly compound levers) let us beat, spear, prod, stab, whip, etc., at low risk and greater adaptive gain. But more co-ordinated logic/effort is needed as not all of us have equal skill in spear or rock throwing (select-able differences). Lever scale-ability (or co-ordination) marks a new learning style, where trial-and-error, training, and rehearsal (e.g., Olympic Games) help to optimize functions. Human trial-and-error generatively mimics the trial-and-error innate to evolution, as both produce new functions. A more-basic form of trial-and-error was noted earlier in a newborn agent’s L-E (vari-able L) functional priming.


Figure 7: Signal-and-Noise Continuum – general bridge. Figure 6 is herein reduced to computational traits. ‘Pure Signals’ (right: a Shannon signal) target specific functions, while ‘Pure Noise’ (left) is a source of (as yet undefined) functional possibilities. Both are non-adaptive, each is highly recurrent in its own way: Pure Noise is wholly unbound (open, function-less), and Pure Signal is well-bounded (closed, functionally invariant). Value Entropy, Order Entropy, and Element Entropy (middle) thus mark an Interpretive (entropy) System that transitions between ‘noise’ and ‘signal’, as a general adaptive bridge. That transition implies a type of ‘informational work’ generatively deriving adaptive options (creativity). Missing in this bridge are details on Selection Dynamics (lower right) or the entropic reduction needed to define functional optimums, as required by natural selection (Abundis, 2017).

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Scale-able compound levers imply tool use logic. We intuitively export internal levers to image(ine) new external compound functions. Ordination as tool use is key to human adaptation, overawing our lack of purpose-built tools. Ancestors with no tool use ‘ideas’ were likely first to die. This psycho-logical (projective) role then affords a scale-able worldview of ‘useful’ and ‘not useful’ things. This early human metaphysics sees ‘better maps’ as offering better adaptive habits. We start with rocks and sticks but our repertoire grows to entail all tools named in Figure 1’s note, and beyond. Lastly, everything seen here still typifies a lever. All Elements (L, F, and E), in all Classes, are extant and known. Scale-able ordination (rule #1) is thus mildly disruptive, as compared to subtly vari-able or gradual valuation (rule #2).

As further examples, language also employs ordination. The words cat, act, and tac alter order to convey unique meaning from identical Aesthetic Elements (a, c, and t). Also, the role of word order in the structure of language is well know as ‘syntax’. Phonetics and numerics equally rely on meaningful ordination. Other ordinate roles show in music (chords), humor (puns, jokes), fables (poems, novels), sports (game strategy), chemistry, physics, engineering, and so on. This scale-able ‘play on Order’ drives much of human entertainment, science, trade, etc.

Despite the striking adaptivity afforded by ordination (rule #1 scale-ability) and valuation (rule #2 vari-ability), a full computational story is not yet told (missing rule #3, or element novelty). For example, IT also uses ordination where ordered 1s and 0s trigger ASCII functions (Table 1).


But less well known are the other Elements (hexadecimal, octal, etc.) that have equal functions. This points to two issues: 1) how do new Aesthetic Elements arise, and 2) how are new Elements useful? This suggest a third (missing) computational rule and a third adaptive logic – Element Variation.

Table 1: Functional ASCII (2013) Codes. Discrete 1s and 0s (bits, left) typify Aesthetic Elements, where ‘play on Order’ (ordination) drives ASCII functions (right). But the middle columns use new Elements (3, 5, E, #, etc.) to mark identical roles. Together, all columns show a simple-to-complex continuum of ‘higher-order’ roles. The entire table is thus a logical ordering-of-orders, of related Aesthetic Elements, and which details meaningful ASCII metadata.

Figure 8: MA Breaks amid Classes – element variation. In Class 1, if L meets F Class 1 order ‘breaks’ and a not-lever emerges [1]. A similar event occurs in Class 2, when Class 2 breaks [2]. These logical disrupts mark new Raw Elements (right) of: L/F (loaded fulcrum or Incline), and L+E (loaded effort or Axial-Radial).

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• Element Variation – So far non-adaptive signal Sets (rule #0), adaptive jumps across Classes (#1 ordination), and adaptive shifts within a Class (#2 valuation) are covered. Zero points amid Classes are now detailed as an adaptive rule #3 (element novelty).

Binary Octal Decimal Hexadecimal HTML ASCII Functions/(base 2, 8-bit bytes) (base 8) (base 10) (base 16) Code Commands

00000000 000 0 0 n/a NUL (null) ∅00000001 001 1 1 n/a SOH (start of heading)11101001 351 233 E9 é é (accent acute e)01000000 100 64 40 @ @ (at sign)01000001 101 65 41 A A (capital a)


Zero points arise in Figure 8 (⦿) where [1] L joins F, and thus, L cannot be lifted, and [2] L joins E, and E directly affects L. These points offer zero MA as a ‘break’ or acute disruption. But these disruptions also convey Element Variation as they ‘compute’ new elements. New elements have no System, Set, Value, or Order (they have a null Aesthetic) and are thus functionally un-defined ‘Raw Elements’. For example . . .

At [1] L-E functioning is null (E is ‘orphaned’) and L/F and a fallen plank remain. This computes an Incline Element (Figure 8, right), where E must re-orient if a new function is to arise. Element Variation (elementation) requires valuation and ordination applied to a Raw Element, via trial-and-error (or a third ‘adaptive type’). As such, Inclines later come to typify wedges and ramps (via elementation), or two new functions are eventually named. Also, as with levers, many types of wedges and ramps are possible, again due to Generic Entropy (Figure 6), where no one ‘ideal’ or Platonic Form exists.

As background, six classic simple machines are defined: lever, wedge, incline plane, wheel, pulley, and screw. Hence, three simple machines (lever, wedge, and incline plane) now have a simple explanation of their existence.

Inclines have four true facets: 1) as noted, they later re-orient to wedges and ramps, 2) that also ‘lift loads’, but in more-primitive ways, 3) Inclines entail a plank (primitive Plane), as do levers, and 4) a Plane’s orientation in a wedge or ramp ‘directionally implicates’ a new aesthetic role for E, lessening the trial-and-error needed to convey new functions. In toto, two actual Raw Elements thus devolve at [1], an Incline and a Plane, where an Incline = Fulcrum + Plane.

At [2] MA functioning is also null (L-E is ‘direct’), and F-P-(L+E) remain. This computes an Axial/Radial role or a joint artifact, so two Raw Elements again arise: A and R (Figure 8, right). ‘Joints’ first arose in studying compound levers. To expand further on joint roles, a fist is a natural Axial-Radial hammer. An Axial-Radial hammer joined to a stone becomes a hand axe, or ‘big teeth’ as incisor-wedge and molar-hammer. Next, tying a stone wedge (Incline) to a stick (Plane) amplifies that hammer/axe – such that a cascade of vari-able leaps (sledgehammer, broadax, pickax, etc.) can then unfold as part of an agent’s scale-able cognition or adaptive logic. Lastly, the mere presence of a Plane again ‘directionally implicates’ a new role for E by forcing a Radial angle.

In even-more primitive ways Axial-Radial roles also typify atomic nuclei (A) and electron ‘orbits’ (R). Atomic A and R are adaptively undefined as they precede anything we can call adaptive logic. But this atomic comparative also hints at a broader (intuitive) framing for quantum mechanics and ‘symmetry breaking’ as entropic roles (Josephson, 2016), with Figure 7 as a template. In a similar manner, Inclines and Planes also implicate functionally undefined (Raw) gravitational elements, prior to the advent of adaptive logic. They are first seen as hills, mountains, plains, etc., but come to greatly influence later agent adaptations.

Thus, this more-primitive lever analysis (deconstruction) names a suite of Aesthetic Elements – Load, Effort, Fulcrum, Incline, Plane, Axis, and Radius – as general non-adaptive/adaptive roles, or Archetypal Forms. The innate ‘meaning’ of an Elemental Form comes to be known only through interaction with other elements. Those Archetypal Forms later sustain an ‘interactive’


modern informatics of ‘simple machines and beyond’, as soon shown. Lastly, in considering Axial-Radial roles, A-R hammers are oddly omitted from the list of classic simple machines, while A-R also afford many simple machines, such as diverse levers, wheels, pulleys, and screws.

In summary, Element Variation (elementation) has basic divisions [1] and additions [2] computing new (Raw) Elements. Those Elements then require a third adaptive logic, beyond systemic ordination (rule #1) and valuation (rule #2), as element ordination and valuation, or a ‘rule #3’. Raw Elements are discretely produced, sensed, and tested by adaptive agents (or natural selection) to derive new functions. That interactive context creates an Aesthetic meaning for each Element, as new or existing roles. The trial-and-error involved here is the least intuitive (more cognitive) of the trial-and-error roles named, although fundamental intuition as ‘curiosity’ about ‘some function’ is as present as before – where basic survival remains a compelling motive.

Still, elementation suggests an ‘autonomous’ adaptive logic, where the creation of ‘man made things’ departs sharply from ‘evolution by natural selection’. Thus, as a distinctly human cognitive ecology arises, but one still based on extant Elemental Forms. Those Forms are not seen here as presenting an exhaustive list as they only cover ‘lever analysis’, where other cores roles may still exist.

Elementation holds vast creative potential. Raw Elements mark a generative material expansion, enlarging the logical possibilities for systemic ordination and valuation. Elementation has four facets: 1) An element with distinct traits is discretely produced and sensed. 2) That element interacts with other elements in a regular manner. 3) Assessed regularities then define how well-known (use-full) the element is. 4) Lastly, diverse elements are brought together in testable systems of vari-able and scale-able roles – as select-able expressions of adaptive logic.

Finally, what conveys a signal or noise for one agent differs from what other agents see as signal-and-noise, again, due to natural parametric variety (subjective edict). Elementation thus ‘aesthetically binds’ all Elements and Systems, which, in turn, binds an agent’s subjective sensorium/rationale (Hutter, 2012). Subjective/aesthetic binding further frames an agent’s adaptive ‘freewill’ (as physiological ‘affordance’). Lastly, natural binding also appears in nature’s innate ‘invention of levers’, and other natural binding roles arising as Selection Dynamics (Abundis, 2017).

I next explore this adaptive logic in the human advent of simple machines and beyond.

SIMPLE MACHINES – and beyond . . .

As brief review – a general role was named as ‘L, F, and E ≈ Lever Aesthetic’. Exploring that general Lever Aesthetic shows three lever Classes and three computational traits. Those traits are seen as: #1 mildly disruptive jumps (scale-able ordination), #2 gradual shifts (vari-able valuation), and #3 acutely disruptive breaks (novel elementation). Within those Classes, roles, and traits five entropic types are also named as: Signal, Value, Order, Element, and Generic Entropy, for a signal-and-noise continuum. Lastly, Archetypal Forms are detailed – Load, Effort,


Fulcrum, Incline, Plane, Axis, and Radius – as equally non-adaptive and adaptive elements. This section now applies the above ‘presumed intelligence’ to detail the advent of simple machines and more.

Figure 9: Fulcrum Variation. Two Fulcrum types exist: a Radial-F (left ‘roller’, also Figure 2) seen in plants, worms, etc.; and an Axial-F (left, dot on triangle; also Figure 3) seen in skeletal systems. A Radial-Fulcrum has three degrees of freedom (‘noisy’: horizontal, lateral, and vertical; a ‘search’ role), which is versatile but unstable. It thus requires more-coordinated Effort to realize work (‘inefficient’). Axial-Fulcrums have one degree of freedom (stable: vertical, ‘direct’ work) and need less coordinated Effort. Next, an Axial-Radial generalized joint (right) arises if A-F joins R-F. This differs from the earlier joint analysis as it has one infinite degree of freedom of ‘endless rotation’ as a proto-wheel or a limitless serial lever/centrifuge, with gravitational implications – therein creating a new Habitual Radial (HR) element.

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Figures 9-11 give a facile-but-specific account of the advent of simple machines. These models of adaptive expansion reach even further as air/water Screws (Figure 11) imply the advent of ‘buoyant’ aircraft (air-Planes) and boats (hydro-Planes). Also, a Habitual-Radial (Figure 9) joining an Incline alters Effort, such that a gravitational sense of adaptive braking and acceleration arises. Elemental play on Value and Order (rules: #3, #2, and #1) holds seemingly endless potential, further renewing and enlarging humanity’s cultural ecology. Lastly, each machine shown here entails specific aesthetic traits (as employed Elements) that allow us to know a ‘functional meaning’ for the thing (wheel, pulley, etc.) being depicted.

Figure 10: Habitual Radial (HR) Variation. Following from Figure 9, -A- (left) typifies HR as an evolving serial lever. Next, -B- shows HR as a realized pulley (HR joins with two side Planes), and -C- shows a serial lever as an early segmented spoke wheel. Lastly, in -D- multiple serial Levers cross (join) other serial Levers as interlaced spokes. These levered-levers add vertical and lateral strength, reduce overall HR weight, and are typical to bicycle wheels.

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Missing from this account are the numerous aesthetic variants that are ‘selected from’ to convey useless, useful, or optimal traits (select-able differentiation). This paper only covers generative


entropy as presenting basic ‘logical adaptive options’. It does not detail the ensuing trial-and-error or entropic reduction of those options as needed to find optimal functions. For example, in a universe of all possible levers Figures 5 and 6 would show many Xs; each X being innately functional, and with no one targeted adaptation in mind. But natural selection demands that all agent’s answer ‘To what end?’ is a lever used, and it must be the best possible lever in the role. Thus, entropic reduction or Selection Dynamics is as-vital-as, but must follow, generative entropy. Study of Selection Dynamics exceeds the paper’s focus and is instead addressed elsewhere (Abundis, 2017).

Figure 11: Incline/Wedge Variation. -A- shows an Incline as F + P (from Figure 8). In -B-, a Radius joins an Incline to produce a Cone. Then, in -C- a Wedge joins the face of that Cone to produce a Screw. Next, -D- shows a Wedge joining an Incline, then expanded with a Plane, to produce a prototypical Airfoil -E-. Lastly, in -F- the Airfoil joins a Screw to produce an air or water screw (propellers).

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CONCLUSIONAny attempt to model ‘general adaptive logic’ requires a firm starting point if an empiric answer is needed. But vastly diverse agent roles, types, and contexts makes naming a practical starting point tricky. Still, as seen here, levers offer a good base due to their near universal nature. Levers appear in many agents and scale up-and-down in more-complex and more-simple roles. They also hold discrete-and-continuous computation and bifurcations (base adaptations), or innate ‘natural multi-state computing’ as part of that direct practical experience. Discrete-and-continuous roles then echo facets of quantum mechanics (discrete particles, continuous waves, wave collapse ≈ Signal Entropy, electron shifts ≈ Value Entropy, etc.), and bifurcations mark branching events seen in evolution and chaos theory. As also seen, levers underlie the advent of simple machines and beyond. This all implies a universal key lies within the foregoing lever meta-analysis. Lastly, this view of a ‘functionally directed-direct’ evolutionary experience contrasts sharply with abstract notions of general intelligence (Mirza et al, 2017; Baroni et al, 2017) currently seen in artificial intelligence.

Models of basic mechanical logic date to Archimedes, Franz Reuleaux, and others. But such kinematic views do not detail aesthetic creativity, and ignore the psycho-logical origination of invented devices. Also, the computational rules named here apply to many informational roles, while the same is not easily said for all mechanical logic. Lastly, levers are used here only as a trope (aesthetic template) in order to detail a larger ‘theory of meaning’, where that theory has


implications beyond basic kinematics. As such, the model posits a direct experiential link between classic Signal Entropy and the generation of ‘meaningful adaptive functions’. Such a common sense view of information represents an advance in the general modeling of information theory (Shanon and Weaver, 1949; Floridi, 2017).

Indeed, in more practical (less theoretic) terms, humanity long ago found a meaning-full mechanical-cum-psychological internal habit – driven by natural selection. With no other clear adaptive path, informational logic then became a fortuitous ‘adaptive crutch’. We have since extended that adaptive logic to a psychological-cum-mechanical external inventiveness that surpasses other agents. Human creativity grows such that it even bothers us. Endless innovation and related resource demands seem to disturb the Natural Order, in turn, risking our own survival. But an evolutionary fight – that we did not start – demands we see how far and to what end human adaptivity can grow. In the face of our assured evolutionary terminus we must see ‘For how long might an ultimate death be denied?’

The required optimization of our human creative potential demands that we ponder all risks and benefits, not blindly marching on. But such optimization is essentially a psycho-logical task evoking a mental wherewithal that surpasses anything we have exhibited to date. It is unclear if or how we will come to master this next adaptive challenge.

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