We are inundated with the Logic of Matter. The technological successes of modern science provide support for this type of reasoning. Absorbing the logic of our environment, we indiscriminately apply this way of understanding reality to other modes of existence – sometimes accurately, sometimes not. If this type of reasoning works with Matter, why not the rest – goes the liminal1 thinking.
Absolutism is a feature of Material Logic. While appropriate for the seemingly objective Material Realms, absolutism is an ineffectual way of conceptualizing the subjective Verbal Realm of words and ideas. While mathematical propositions are true or false, verbal propositions, due to the innate ambiguity of transmission, obey the true-false postulate – true in some circumstances, false in others. Verbal truths are generally relative to context, i.e. provisional, rather than absolute.
The prior article illustrated why scientific realism is best understood as a conceptual metaphor rather than evaluated as true or false. The notion that there are absolute truths, whether scientific realism or any other theory, derives from Matter’s Set Logic. If inappropriate, what is the alternative?
Both Attention and Fractals are based in feedback loops. As such, we can employ Fractal Logic to better understand the Intentional behavior associated with Attention. The many qualitative differences between these two types of logic, i.e. Fractals and Sets, places living and non-living matter in distinctly different sets.
The remainder of the article both explores the differences between traditional set logic and fractal logic, and the implications for living systems. In particular, we examine the nature of the answer in both systems. Definitive predictions of Set Logic versus pattern identification of Fractal Logic.
The intelligentsia regularly attempts to map Matter’s precise set logic onto verbal constructs. Rather than one size fits all, it is of crucial importance to find (or develop) the right map for the job. The set mapping is inappropriate due to our ability to interact with the environment – our immaterial component – our interactive feedback loops. Also based in feedback loops, fractal logic provides a far better map of our verbal realm.
This form of logic is based in the behavior of fractals. The laws and logic of both fractals and sets are derived from mathematical deduction. However, Fractal Logic and Set Logic have some fundamental differences. They do not even belong to the same set.
Fractal Logic ≠ Set Logic
While sets are based upon lines, fractals contain no lines – only complex, unquantifiable, replicating patterns. Hence, the phrase: ‘fractalization of the boundary line’.
Ultimately, Set Logic applies to Matter, while Fractal Logic is more applicable to Life.
Set Logic -> Matter
Fractal Logic -> Life
Let us explore these ideas and their implications in more detail.
Living and Material Logic are not equivalent. There is a fundamental difference between living and inanimate matter that has a direct and qualitative influence upon the logic of each system. This diversity is not esoteric or even hard to understand. It should be celebrated – taught to our children and our children’s children.
Living Matter via Attention is constantly engaging in Interactive Feedback Loops with environmental information, both internal and external. Life employs an iterative process, i.e. an algorithm, to first evaluate and then adjust to circumstances, then reevaluate and readjust, forever and ever amen.
Or until the organism and its cells suddenly degenerate into inanimate matter – losing all sense of unity and purpose – disintegrating all of a sudden from a unified whole to a heap of disinterested atoms and molecules – all going their merry way without regard for the rest – with whom they had spent such intimate time together. No loyalty whatsoever.
Why? No Interactive Feedback Loops to keep them in check – bind them as a unit. Non-living Matter simply does not engage with environmental information, except in a reactive way – pushed here and there by every little force, no matter how small – an instantaneous tit for tat. Can’t help himself. He was born that way.
Because of this quality, Matter is a Set kind of guy. Everything fits in a precise box. It is what it is, nothing more or less. Electrons are electrons, each the exact same precise amount of mass and energy. No fluctuations since the beginning of time. Sort of boring, if you ask me. Also holds true of photons, molecules, quarks and neutrons. Exactly the same from the moment of the Big Bang onwards. Talk about monotonous.
Not only that. The interactions between these so-called elementary particles have also been identical. As a group, electrons always behave in the exact same way when faced with identical conditions – no variation whatsoever – perfectly predictable – as are all the rest of those exactly identical material forms. No surprises ever.
Nothing like those unpredictable life forms. Can never tell what they might do. It’s those damn feedback loops. Each iteration of the feedback process provides an opportunity for a choice.
Despite the possibility of decision-making, all living systems, including humans, are on autopilot a majority of the time. Considering the many opportunities, it is rare when they actually interfere with the program. This is good, actually very important, as Nature has taken millions, if not hundreds of millions, even billion of years to set up these internal programs. Unless there is a really good reason, it is better not to mess with the routine. But sometimes, just sometimes, it is necessary to step in and assert oneself into the biological flow – proactively taking action to prevent disaster.
It is these tiny decisions that occur regularly throughout the day for all living systems that throw all the material predictions off course – the proverbial monkey wrench in the machine. Attention’s iterative process enables choice, which in turn introduces unpredictability into an otherwise predictable system.
Living systems are neither completely random, nor are they predictable, nor do they exert complete conscious control over their behavior. Rather their behavior is probabilistic. Not accidental, haphazard, or arbitrary, but filled with propensity. They move with distinct purpose, whether to procure sustenance, avoid enemies, or write a book. Each step comes with parameters – mean, range, and trends. While possessing a limited range of motion, the potential for variation is vast – especially one small guided step at a time – like turning an ocean liner around.
Matter has no Attention, no interactive feedback loops, and subsequently no ability to guide its behavior. Accordingly, the set-based logic of Matter can be broken into true and false – and it has been. It is either an electron or it is not. No in-betweens. In other words, it is possible to make absolute determinations regarding the behavior of elementary particles (example: modern technology). This scientific fact indicates that absolute truths exist in the Material Realms (at least for all practical purposes – not concerned about the edges). Indeed, scientists have uncovered mathematical laws that have governed material behavior since the beginning of time – or at least since the Big Bang – I guess it’s the same.
While Matter is a straightforward, cause-effect kind of guy, Life engages in interactive feedback loops that disrupt the natural mechanistic flow. Rather than the certainty of Matter’s set-based logic, Life requires a different kind of logic – a type of reasoning that encompasses open feedback loops.
Scientists have nailed down the completely predictable behavior of Matter and Computers. Due to this unqualified success, the intelligentsia inappropriately applies Matter’s either-or, true-false, set-based Logic to living systems. Philosophers and material scientists are especially prone to this fatal flaw. As a group, they have this misguided intention to determine the absolute truth or falsehood of verbal constructs. This is certainly an honorable endeavor. But they don’t check their results against real life experience. Or worse, they disavow the importance of the experiential against the logical. Ah well, such are word-addicted humans.
Is there a better alternative? If Set Logic is the best we have, no need to jump trains. However, its absolutism seems to fall short when it comes to living systems. We suggest that Fractal Logic is more appropriate – better suited for the job – reveals more underlying patterns – revelatory, and instructive.
As with living systems, fractals are also based in iterative feedback loops. These feedback loops are the bane of material systems – introduces too much uncertainty. However Life and Fractals are compatible in this regard. Is this rapport superficial? Or will it lead to a long-term relationship?
What does Fractal Logic even mean? What are its features? To understand the logic, let’s examine the innate nature of a fractal.
Mandelbrot is the undisputed father of fractals. He developed some iterative, recursive equations that exhibit some amazing qualities. Mandelbrot’s equations look relatively simple, consisting only of a single variable and a single constant.
He examined what happened when he changed the constant in the equation. He employed a computer to perform the iterations. After a sufficient number of iterations, the recursive function either approached a definitive result or not depending upon the value of original constant.
Recursive functions are reflexive in that they refer back to themselves in a repetitive cycle. In other words, current results play a part in the following results. These so-called Reflexive Equations engage in a type of feedback loop. A computer is required to do the computations due to the vast number of repetitions of the algorithmic process.
The traditional Regular equations that characterize Material Behavior are never recursive. Because there are no reflexive feedback loops, the results are definitive and singular. As such, answers can be visualized in a clear-cut manner. On the most basic level, the equation for a circle can be visualized as a curved line that is equidistant from the center. Regardless of how much it is magnified, it remains a line with the exact same curvature.
In contrast, visualizations of the results of Mandelbrot’s Reflexive Equation are fractalized. In a famous set of pictures, the boundary line reveals a fabulously intricate structure. Patterns replicate themselves in smaller or larger frames. More amazing still, each time these lines are magnified, the visualization reveals a different type of fractal structure. The following illustration provides an example of a fractalized boundary line.
What’s the significance?
Set logic has three states: inside the box, outside the box, and the line between inside and outside. The boundary line is well defined and continuous – no cracks or breaks to allow uncertainty to sneak through. Either-or; Yes or no; win or lose; absolutely true or false.
Fractal Logic also has three states: inside, outside and fractalized line divides the two. Continuous lines do not divide inside from outside in the visualization of Mandelbrot’s fractal equation. Rather the boundary between inside and outside is fractalized.
Fractalized? Patterns that replicate themselves on large and small levels replace the distinctive lines that characterize non-Reflexive functions.
Absolute determinations are impossible in this fuzzy area. Results in this in-between state must be evaluated on a case-by-case basis.
This fuzziness is one reason that Mandelbrot’s fractals generated such an uproar in the scientific and mathematical communities. Accustomed to definitive mathematical results for centuries, scientists were horrified by this newcomer – hoping against hope that it was a mere curiosity with no real applications. After all, Matter was obedient to their Regular, i.e. non-Reflexive Equations, why not the rest of existence, especially Life.
If this rookie applies to any feature of reality, it would certainly undermine their elevated sense of self-importance. In their almost mystic quest to discover the unified field theory that links all the fundamental forces of nature, Physicists really believe they are unlocking the fundamental secrets of the Universe. They are – to the material Universe – not the living universe, or should I say Poly-verse.
How they wish that they could bring Life under the sway of their deterministic Regular equations – the ones that obey set theory, the ones that generate distinct unbroken lines – not the ones that refer back to themselves and generate those confounding fractal lines – impossible to generate any useful approximations in times of uncertainty. Damn fractals. What use do they have anyway?
The futility of their quest for unification is somewhat pathetic, as it is tinged with the arrogance that they know better than the rest. Time always tames hubris. Nothing divine, just a mathematical principle named ergodicity (a topic we deal with in the next article).
While fractals do not have any lines, they do have patterns that replicate themselves on small and large levels and in-between. Unfortunately replicating patterns are hard to identify or quantify – much more difficult than fitting an equation to the precise measurements regarding Matter’s behavior. What number or equation can encapsulate any of Mandelbrot’s intricately filigreed fractals? Although visually obvious, these patterns are mathematically opaque.
Further the application of these patterns is a bit fuzzy. Yikes! Certainty is overthrown.
This discussion has highlighted two types of equations. Let’s summarize their differences. Matter’s Regular Equations obey traditional set theory. This type of equation generates distinct lines and results can be approximated to any degree of accuracy.
Mandelbrot’s Fractal Equation does not generate lines and approximations are next to impossible. Rather than sets, Mandelbrot’s Equation generates fractalized boundary lines. Fractal structures are patterns that replicate themselves on many levels from small to large.
What’s the point – the significance? Does Fractal Logic have any real world applications? We suggest yes – especially to Life’s Realm of Attention.
We have been exploring some fundamental differences between Set Logic and Fractal Logic. The first is associated with definitive lines that divide inside from outside. The second is associated with fractalized lines that result in fuzzy boundaries. Matter’s Regular Equations are based in the Logic of Sets, while Mandelbrot’s Equation reveals the Logic of Fractals.
Mandelbrot’s Equation belongs to a more general set of recursive functions. As this type of equation is self-referential by definition, we have deemed them Reflexive Equations. Rather than Set Logic, Reflexive Equations are more akin to Fractal Logic.
Our two distinct types of logic, i.e. Set and Fractal, with their two types of equations, i.e. Regular and Reflexive, reveal qualitative differences between living and inanimate matter. The Set Logic of Regular Equations aligns with the Material Realms, while the Fractal Logic of Reflexive equations has more affinity for Life’s Realm of Attention. Let us see why.
Life via Attention employs a reflexive function, i.e. an algorithm, to digest data. (This process is a key feature of the Attention Realm.) Reflexive functions, like Mandelbrot’s equation, tend to have fractalized boundary lines. Life’s reflexive algorithm, i.e., the Living Algorithm, also generates fractal patterns. This fractalization makes it virtually impossible to predict whether a boundary point will be inside or outside the set without examining the data very carefully.
The inability of Reflexive Equations to make absolute determinations in all cases disables the absolute truths of Material Logic. The boundaries are entirely too unpredictable to make sweeping statements. Rather than definitive, the results are sometimes inside the box and other times outside the box. In Mandelbrot’s case, sometimes the answers proceed to a limit (determinate) and other times they do not (indeterminate).
Despite the fractalization of the boundary lines, it is possible to make determinations of relative truth. Each of the fractal lines surrounds areas that lie firmly within the territory. It is not that we can’t determine truth; just determinations must be done on a case-by-case basis. And then the lines are still fuzzy. Due the fractal nature of Life’s recursive algorithm, generalizations are very dangerous – true in one part on the line – false in the other.
Due to the iterative, recursive nature of our verbal experience, no verbal construct is absolutely true all the time. However, some verbal constructs are true some of the time. They apply in particular situations, but not all.
Let us return to our original question, the one that inspired this part of the book: ‘Is Choice true or false?’ The question itself is founded in and generated by the Absolutism of Matter’s Set Logic. Choice is, of course, a central feature of the ‘monitor and adjust’ interactive feedback loops that living systems regularly employ to both survive and thrive. As such, a more appropriate question in this realm of Fractal Logic becomes: When does choice apply and when not? To what extent does it apply?
Even the notion of ‘absolute free will’ is a mental construct that derives from Set Logic. Contemporary psychologists are in agreement that our capacity for decision-making is limited – very narrow parameters. Driven by primal emotions, we are certainly buffeted around. Yet we can guide the course of our small ship through these turbulent waters more or less successfully.
Success, itself is relative – dependent upon numerous conditions. Short term or long term – physical, spiritual or psychological? Success for the species, the individual or the family? And how about the trade-offs? One wins and another suffers. A man gets a high-paying promotion that takes him away from his wife and children. Go to college or get a job?
The assessment of success is highly subjective and strongly debated. Rather than an unbroken, definitive line, the boundary between inside and outside is fractalized. Definite behavioral patterns can be identified that replicate themselves on large and small levels. However, the definitive predictions of Matter’s Set based logic are unattainable regarding Life’s intentional behavior. Period. Forever and ever. Amen.
Our ongoing interactive feedback loops void this possibility. No matter how many of us there are.
This analysis indicates that the absolutism of Matter’s either-or Logic is a poor tool with which to evaluate the success of living choice. Fractal Logic provides a far more better model. The question is not: Is choice true or false? But rather: under what circumstances is choice true or false?
This analysis does not just apply to choice, but instead to virtually all of the verbal constructs that we employ to understand our world. Due to fractalization, our abstractions are true in certain circumstances, false in others – no absolute truths. Due to Attention’s reflexive process that is unique to living matter, the innate nature of the Realm of Attention is fractalized and only contains contextual truths.
Containing no feedback loops, our physical Universe is filled with absolute truths. The many Regular Equations of calculus with their definitive results are realizations of these non-fractalized processes. Disallowing self-reflection from its mathematical tool set, the Material Realms are also firmly rooted in absolutely permanent relations between absolutely defined essences.
Perfect definitions are a necessary requirement of absolutism of any variety, whether religious or philosophical or scientific. It is essential to have perfectly defined entities to determine whether a proposition is absolutely true or false. While possible with inanimate matter, these absolutely unassailable definitions are impossible when it comes to our intentional behavior. Too many factors and too many reflexive loops.
Reiterating the chapter’s overriding theme: While appropriate for the physical world, the absolutism of Material Logic is inappropriate for the fractalized boundary lines of Life’s reflexive processes. The following section provides another example of misapplying Matter’s Absolutism to Life.
Matter’s set-based Logic leads to the notion that existence is dominated by absolute truths. Governed by deterministic mathematical laws, the Material Realms stand as a testament to truth of this proposition. While tempting, it is inappropriate to apply absolutism to the Fractal Logic of the Living Realm. Based in open feedback loops, Attention’s regular iterations muddy the waters of causation, hence determinism and absolutism.
Matter’s Absolutism ≠ Life’s Fractalization
Just as Material Logic is misapplied to Living Systems with regards to verbal truth, it is also misapplied to the related notion of Identity.
Material Identity ≠ Living Identity
Material Identity is definitely content based. Is it an electron or not? Anti-matter or not? A field or not? And so forth ad infinitum. A significant feature of the scientific quest is to accurately label identity. Once we know what the thing really is, we also know its properties, its permanent qualities, e.g. how it always responds in such and such a circumstance.
Material Identity = Content-based
While identifying absolute content is an accurate approach for the Material Realms, it is entirely inappropriate for the Living Realm of Attention. This immaterial realm is in constant transition. Nothing remains the same in the Flux of Life and Death.
Living Identity ≠ Content-based
For one, the actual physical content of every living system is constantly changing – not permanent in any way whatsoever. Every life form from single cells to multi-cellular organisms are constantly recycling actual substance and rearranging structure. Even a paramecium has the ability to learn from experience – entailing a reorganization of structure.
Although composed of an ever-changing composition of molecules, electrons and such, we still possess a physical identity, albeit dynamic. Don, that’s my Person, has brown hair, blue eyes, is about 5’ 10” tall, and so forth. My friends can easily recognize me when I arrive at Tai Chi Practice even though my hair is not a brown as it used to be nor am I quite the same height any more. Every living thing has a distinct though changing physical identity, however only as long as it lives.
Despite this physicality, Living systems are better characterized by their interlocking, interrelated, interdependent processes. While Life’s material content is ever changing, living processes are relatively constant. Procure food, consume, digest, eat, digest – over and over again for as long as we live. Responding to cues from Body’s digestive system, Mind directs the muscles and such to perform the appropriate actions. All living systems perform this Mind-Body dance. Non-living systems Not.
The Cell/Body has many of these interlocking systems, from elimination to respiration. Each system is best characterized by these regular dynamic, imprecise processes. While content, e.g. type of cells and molecules, is identified, the content illuminates process, not vice versa. Function determines Form, not vice versa. The digestion system’s function, i.e. providing energy, determines its form, the processes and molecules necessary for completion of its duties.
Hence in terms of a relatively stable identity, we are better characterized by our regular processes, our many systems, than by our ever changing content. Put simply, Living identity is process-based.
Living Identity = Process-based
Note: it is easy to confuse content and process. For instance, appearance, e.g. face hair color, etc, is frequently associated with identity. Yet this seemingly permanent content, our Body, is most frequently experienced as a process. We generally experience material content via living process.
While objectified as in a photo, the image’s potency lies in its ability to evoke the experiences, e.g. smiles and laughter, that were associated with the moment. The physical content is just the vehicle that brings us to the living processes, the experiences. With appearances acting as a trigger, we remember the emotions associated with our experiences. Witness the unsettling appearance of that same physical content after death.
While consisting of a revolving door of molecules, Life engages in the same ongoing time-tested processes while alive – all day long every day. In fact, once the processes of an organic system cease, death follows. The molecules disband and move on. They never die.
The particles/bodies of the Material Realms are not bound to processes. Instead, Material Identity determines the Processes. Atoms engage in specific kinds of predictable processes, but are not determined by them. Very different from Life, where Living Processes determine Physical Identity.
Matter’s identity is content-based; Life’s identity is process-based. One more in the long list of differences between living and inanimate matter. Are these differences merely emergent features of Matter? Or could it be that Life has an immaterial component based upon its relationship to information? Could this immaterial relationship include the interaction between Attention’s mental energy and data streams via the Living Algorithm? Do you have a better explanation?
Seeing the beautiful vegetal patterns generated by Mandelbrot’s famous equation, many have made the claim that fractals reveal the secret of Life in terms of self-replicating patterns. I agree. However, there are also significant differences between the two systems, i.e. mathematical and living, which should be acknowledged – not ignored.
Life has her own mathematics, which is based in the Living Algorithm. Both Mandelbrot’s Fractal Equation and Life’s Living Algorithm are Reflexive Equations, i.e. based in feedback loops. Due to this affinity, they share a similar logic. We have shown how this so-called Fractal Logic is more appropriate for living systems than is the absolutist set-based logic of Matter. In particular, fractalized boundary lines disable the absolute truths that many attribute to verbal constructs.
However, always another ‘however’, we must remember that the relationship between living systems and fractals is metaphorical in nature, as are all abstractions. As such the fit between model and reality is not perfect, never is. Let’s examine the mathematics of the two equations to see where the fractal metaphor breaks down with regards Life. In so doing, we will discover where the fractal metaphor falls short when it comes to living systems.
Let us compare and contrast Mandelbrot’s Fractal Equation with Attention’s Living Algorithm. Although they are both Reflexive (recursive) Equations, the first is deterministic and static, while the second is open and dynamic. Quite a difference! Let’s check out the details and the significance.
Mandelbrot’s Reflexive Equations (the ones that generated the fractal patterns) are closed – no external input. Despite being closed to the outside, small differences in the initial conditions, i.e. the constant, can still yield diametrically opposed results – limit or no limit – the equivalent of distinct destination or lost – directed or aimless. No precise lines identify which points are inside and outside of the destination set.
Despite the complexity of the results (no demarcation lines), Mandelbrot’s fractal equations are still deterministic. The initial conditions always yield the exact same result. With no external input, there is no variation in the output.
Even more complex is the reflexive equation that Attention employs to interact with data streams – the Living Algorithm (LA). While Mandelbrot’s fractal equations are closed, the LA is open to external input. With each iteration of the LA’s computational process, new information enters the system. As an open, reflexive equation, the LA is not deterministic. Due to this freedom, the LA’s mathematical system is qualitatively different from the absolute determinism of Material Equations or Mandelbrot’s Fractal Equations.
Material Equations & Fractal Equations = Deterministic
Living Algorithm = Not Deterministic
Yet the LA defines the Living Realm of Attention. What does this freedom mean? If the mathematics can’t predict results, what’s the point? Not a specialist in material events, the LA instead identifies processes and their features. This is appropriate as even Life’s identity is based in process, rather than content, as a subsequent section illustrates.
Rather than illuminating a process, Mandelbrot’s equation reveals the results of an event, i.e. which constant is chosen for the iterative sequence. On the most basic level, the result is binary – limit or no limit (determinate or indeterminate). On a secondary level, the answer can also have a speed, the speed at which it approaches the limit. Some sequences are faster and others are slower. This variation accounts for the beautiful colors that are associated with the fractal patterns.
Gorgeous but so what? Not sure. I don’t know if anyone has uncovered any real utility to these static fractal patterns. Certainly don’t hear much about it in the literature.
In contrast, the Living Algorithm reveals two fractal patterns that dominate the rhythms of Attention. Rather than revealing static, deterministic results, as do the other two functions, the LA’s computational iterations identify two dynamic processes that are replicated on the very small time frames, e.g. the blinking of an eye, to the very large, e.g. an entire lifetime of mastery – one’s life work or even the Pulse of a Chinese dynasty.
The Pulse is one of the fractal patterns that we are referencing. Reflecting our Attention span, the Pulse is everywhere that there are living systems. It has some distinct characteristics that shape the form of our awareness, e.g. a distinct beginning and end; and a peak of awareness that is negatively impacted by interruptions – disproportionately so.
The other mathematical pattern that replicates on the large and small levels is what we have chosen to call the Triple Pulse. This fractal process is related to our need for sleep, rest and variation in a theme.
Natural selection has chosen to take advantage of both of these mathematical processes. Appropriate biological systems evolved to exploit the potentials of the LA’s mathematical system, i.e. Data Stream Dynamics (DSD). For example, both Posner’s Attention Model and Dement’s Opponent Process Model for the biology of sleep have a strong metaphoric relationship with the mathematical processes of DSD. Both of these models are also intimately related to a complex of biological systems in many species.
In summary, there is a huge difference between our two Reflexive Functions. Mandelbrot’s Fractal Equation reveals the deterministic results of particular events. The Living Algorithm reveals the fuzzy shape of living processes associated with Attention. There is even a bigger difference between our two types of logic. Matter’s Set-Based Logic is Absolutist, true or false in all cases. Fractal Logic is particular, with truth evaluated on a case-by-case basis. Further, Fractal Logic is based in replicating patterns. The LA’s Pulse and Triple Pulse are examples of these replicating patterns as applied to Attention.
What is the significance of these differences?
The logic of the system determines the nature of the answer. Matter’s Set Logic enables precise predictions of specific results. The Fractal Logic of recursive functions, e.g. Mandelbrot’s equation and Life’s Living Algorithm, enables the identification of patterns.
To apply Set Logic’s precision to Attention’s interactive feedback loops is misguided foolishness. Doomed to failure, this quest will never be able to reveal the underlying mechanisms that shape an organism’s intentional behavior. Rather than precise predictions, the best we can hope for is to identify the natural rhythms of Attention.
1 Liminal: the border between conscious and subconscious cognition