“Wow! And wow again! Experimental evidence supports the importance of naps for the humans that I embody. And these results are reflected in the behavior patterns of the Alga’s Triple Pulse!” Life was obviously excited from her most recent session with the Living Algorithm.
“What was the intriguing chain of reasoning that led to that conclusion? In our initial encounters we explored the patterns of correspondence between Alga’s Triple Pulse and the regular Sleep that many of my creatures require. In the Sleep Deprivation study, the Author provided experimental evidence suggesting that the Triple Pulse model is associated with the alternation of Consciousness and Sleep. In a closer examination of the mathematics of this model, we saw that the measures of time were both relative and elastic. Accordingly, the Triple Pulse model could apply equally to sleep at night and naps during the day. If the model does apply, then we can make the following statement: Just as adequate sleep at night maximizes our cognitive abilities during the subsequent day, a shorter nap should enhance our cognitive performance for the ensuing hours. Experimental evidence verified this prediction. The scientific literature was clear. Naps improve cognitive performance.”
“The mathematical mechanisms of Alga’s Triple Pulse again dovetail with the experimental findings regarding my behavior. Thus far, the behavior of Alga’s Triple Pulse parallels the behavior of the living systems I embody in four different ways: Interruptions, Sleep Deprivation, Sleep Necessity, and now Naps. Further, each of these phenomena has been verified experimentally. Amazing!” Life was getting carried away with excitement over how compatible she and the Living Algorithm were. Life expressed gratitude to the powers that be for introducing her to the Living Algorithm. "Could Alga really be the mathematics that will unlock the code to my matrix?"
To tame her runaway emotions Life sat down to meditate. This process raised more tantalizing questions – of course. “Are these intriguing correspondences between our behavioral reality and Alga’s Triple Pulse just a long string of coincidences? Have our perceptions been tricked again - seeing unlikely patterns of correspondence between unlike phenomenon - pure mathematics and behavioral reality? Or could these diverse forms of the human behavior that I embody have some kind of integral correspondence to the mechanisms of the Triple Pulse? If they do, is the correspondence merely metaphorical? Or is there a cause-effect correlation between the two types of facts, mathematical and behavioral? If there is a causal connection, could it be based upon the way we digest information? Who knows? Certainly not me.”
“Ommm? Could Alga’s Active Pulse really be associated with our ability to think and her Rest Pulse be associated with sleep or naps? Experimental correspondences suggest that this is so. No disagreements or contradictions, so far, at least. Alga’s mathematics indicates that the Rest Pulse refreshes the Active Pulse. The implication is clear. The unconscious state associated with sleep of any duration refreshes our ability to think, which, of course, improves our cognitive performance.”
“Why is this so? In the Sleep Necessity article we saw that sleep has nothing to do with resting our brain, as the neural networks associated with cognition are particularly active during sleep. Could the refreshment that sleep seems to provide for consciousness be just some kind of statistical artifact? Or could it be that our subconscious takes that time to digest information that our consciousness has ingested? Is it possible that our mind can get stuffed with too much information and needs time to file it in its proper place? Could the Rest Pulse provide the necessary empty space to finish digesting leftovers? Could sleep provide subconscious processes the essential time to finish the day’s business? Could this be one of the codes to my living matrix?”
Both refreshed and perplexed by her meditation, Life couldn’t wait for her next session with the Living Algorithm. She was hoping for some preliminary answers to her questions. “What was our next topic? Oh right. Alga mumbled something about The Triple Pulse & the 10-minute Rule. I wonder what that’s going to be about?”
To remain in our mythological world, read on.
Alga: “Well, what do you think?”
Life: “Impressive. Your amazingly flexible system mimics yet another feature of the human behavior that I embody. It seems that shifting from one thought modality to another might refresh attention, just as shifting from one number to another refreshes your ability to generate pulses.”
Alga: “I definitely need a regular change of numerical scenery, if I am to generate anything of significance. I can do a lot with a little. For instance, if I am fed a simple sequence of 1s, I generate the beautifully contoured Pulse of Attention. But even I have my limits. If the 1s continue for too long, I begin spitting out 0s – just flat lines with no interest to anyone.”
Life: “The Author links this feature of your behavior with cognitive science’s 10-minute rule. This rule suggests that the audience’s attention naturally fades after 10 minutes unless it is refreshed with new material. To combat this natural tendency, lecturers, and even musicians, introduce variety into their presentations.”
Alga: “I, too, fade out permanently unless my material, my data streams, go through regular alternations.”
Life: “Because of our similarities in this regard, we seem to be compatible in yet another area of human behavior. If our behavioral correspondences have any validity, your mathematical model suggests that shifting thought modalities should refresh the attention of my humans. Although the experimental evidence supporting this proposition is weak, there are many cultural instances which seem to reflect the necessity of regularly shifting focus to refresh attention – for instance coffee breaks, intermissions, or even the breaks between innings in baseball.”
Alga: “I am glad that my system is illuminating your system.”
Life: “Our processes are so similar that it is uncanny. As you can see, your system is becoming more interesting to me with our successive interactions. In fact, my intellectual excitement tempts me to overlook some troublesome details, which can lead to big problems down the road.”
Alga: “Speak up. What's bothering you? Let me attempt to address your objections. Festering emotions only turn into infectious boils, which can bring nefarious consequences.”
Life: “The correspondences between our systems seem to make a lot of sense. Your Active Pulse corresponds with Consciousness and the Rest Pulse with Sleep. Yet, how could your relatively simple mathematical model have any connection with these complex constructs that are dear to me? It seems unbelievable. I’m tempted to reject this fantastic idea out-of-hand. It simply doesn’t fit into any of those sophisticated boxes that I employ to organize the Universe.”
Living Algorithm: “I understand your skepticism. Our correspondences seem equally impossible to me. After all, we are of the same generation – trained to organize the world with the same mental constructs. To keep things in perspective there are a few aspects of this investigation that I try to keep in mind.
“First, I remind myself that these fantastic theories, as you call them, are an attempt to make sense of the patterns of correspondence between my mathematics and empirical data, including experimental findings, regarding human behavior. In other words, theory does not lead the investigation. Theory follows facts. Theory attempts to make sense of our perceived congruencies that occur in so many diverse areas.”
Life: “In this sense, the Author is offering his wild theories as a plausible explanation for our empirically based patterns of correspondence. He is not creating his theory independent of fact.”
Alga: “Exactly. In fact, he never proposed any theories until he had some solid empirical evidence that supported his perceptions. Further, the Author is equally stunned by the direction that the investigation has taken. His tentative explanations have become more definitive with each successive study. The correspondences between my mathematical model and human behavior are refined rather than rejected or contradicted.”
Life: “You said that were other things to keep in mind.”
Alga: “Another feature that must be remembered is the innate nature of the relationship between mathematics and words. On the simplest level, when words are employed mathematically they are stripped of connotation and become pure denotation (definition). Specifically, the key words of our investigation (conscious, unconscious, and even attention) have so many extraneous meanings that it would be impossible to list them. However, when we use these concepts in these studies, they have a specific definition. Further this denotation is limited, defined and refined by experimental findings.
“For instance, the word 'consciousness' means a million things to a million different people. Volumes have been written about this mysterious core concept. We each have a common sense notion of what consciousness means. Scientists in the field of anesthesia are currently attempting to how identify when a sedated patient is conscious or not. In this study, the word consciousness is employed to turn myriad findings into a core concept. This core concept is fused by the interaction between Living Algorithm mathematics and empirical findings.
Because of the original association of the Triple Pulse with the alternation of waking and sleeping, the Active Pulse has always been associated with ‘Consciousness’. Our initial investigation into sleep deprivation linked Active Pulse ‘Consciousness’ to testable cognitive abilities. The Author generalized this concept into the ability to think. Then because of the 10-minute rule, he further associated the Pulse of 1s with the ability to pay attention.
But the use of any of these ambiguous words must always be tempered by mathematical and experimental facts. Caution must be taken when entering upon any speculation that is not grounded in facts. Making speculations with inherently ambiguous words that have no factual foundation has little meaning.
“Of course, there are inherent dangers with associating a mathematical construct with a familiar word that has so many connotations. However, the Author has deliberately chosen this familiar approach to terminology, rather than creating confusing technical jargon that only specialists can remember.
“Further, Physics set the precedent in this regard. The words – energy, work, power, and momentum – had and have multiple common sense meanings that don’t accord with the tightly defined mathematical constructs of dynamics. Plus in general, mathematical constructs, such as energy, are defined by equations rather than words. In fact, defining these concepts with words frequently confuses the mathematical meaning. Mathematicians and Physicists attempt to stay close to their mathematical derivations and equations, only employing verbal understanding to communicate with the non-algebraic world. In similar fashion, caution must be maintained when extending the mathematical results and correspondences of my mathematical System to the real world. It is essential to avoid straying too far from the facts when entering upon theoretical speculation.”
Life: “Let’s see if I can apply these ideas to our correspondences. In the sleep deprivation study we noticed patterns of correspondence between the mathematical behavior of the Triple Pulse and human behavior regarding sleep loss. Specifically, interruptions to both the Rest Pulse and Sleep had a negative impact upon the ideal conditions of the ensuing Active Pulse and the ensuing day’s cognitive abilities. The next study on sleep necessity confirmed these correspondences. Without a Rest Pulse, there was no more Active Pulse. Similarly without Sleep, humans die. These studies showed that when humans have enough sleep that their cognitive abilities are unimpaired. In the next study we showed that sleep in the form of naps actually enhances our ability to think. The correspondences are clear. A Rest Pulse refreshes the Active Pulse, just as sleep refreshes our waking state. Staying close to our results, the waking state is associated with our testable cognitive abilities.
“These congruent results led us to associate the Rest Pulse of 0s with the state of unconscious sleep and the Active Pulse of 1s with the waking state of consciousness. This association does not mean that the Rest Pulse is the Unconscious State, or that the Active Pulse is the Conscious State. It only means that the relationship between the Rest Pulse and the Active Pulse is the same in certain specific regards as the relationship between sleep and our cognitive abilities.
“To refine understanding of the relationship between the Active and Rest Pulse, the Author returned to the mathematics of the Triple Pulse. He noted that if any two distinct numbers are substituted for the 1s and 0s in the Triple Pulse data stream, the results are the same. For instance, you, the Living Algorithm, generate the same Triple Pulse whether you digest an uninterrupted sequence of 1s and 0s, or 100s and -5s, or any other alternating number pair. We had previously associated the Active Pulse of 1s with consciousness and the Rest Pulse of 0s with sleep. But due to this mathematical freedom, we extended the association to thought modalities. In other words, if these correspondences are accurate, shifting thought modalities should refresh our cognitive abilities just as does sleep.
“Cognitive science’s 10-minute rule combined with Dr. Medina’s Core Concept teaching method is an example of this phenomenon. Cognitive research has found that students have about a 10-minute attention span when listening to a lecture. To get around this innate cognitive limitation, Dr. Medina broke his presentations into 10-minute segments, each with its own core concept. This approach proved successful. In other words by regularly shifting thought modalities, Dr. Medina was able to refresh his audience’s attention span. The Author noted that coffee and lunch breaks, acting as shifts in thought modalities, might also refresh our ability to do work.
“The successful application of the Triple Pulse model in this regard led us to extend our associations. Instead of just applying to sleep and the waking state, the model seems to apply to any shift in thought modality. Again, it is the relationship that seems to apply, not the constructs. The relationship between the Active and Rest Pulse seems to be the same as the relationship between different thought modalities, whether it be different core concepts or waking and sleeping. Shifting thought modalities seems to refresh our cognitive abilities, or in the 10-minute rule, our ability to pay attention.”
Alga: “Good explanation. I particularly liked your shift in emphasis from construct to relationship. In other words, the Active Pulse and the Rest Pulse are incidental to the study. However their relationship is significant, in that it that parallels your behavior. Did this discussion address your questions?”
Life: “Definitely. I could sense that I, and perhaps the Author also, was beginning to confuse the symbol for reality. This conscious articulation of boundary has allowed me to better differentiate the two. Because of our innate tendency to merge conceptualization and actuality, we need to regularly deconstruct the results of our coming interactions.”
Alga: “Great idea. I, too, have a tendency to confuse my mathematical abstractions for the real world, when they are just metaphors – a symbol of reality. The precision of the mathematical metaphor enables researchers to make testable predictions. The results of experimentation further refine the applicability of this symbol, but the mathematics remains a metaphor.”
Life: “It’s comforting that we are on the same page. Like any couple, we coincide in many areas, but are fundamentally different and unique beings. Recognizing this feature will make our relationship even stronger.
Alga: “Whoa! We covered some deep material today.”
Life: “Definitely. I need a break to digest these insights. See you next time.”
Another date between Life and the Living Algorithm, and still no fights or even any disagreements. Instead, the Living Algorithm’s Triple Pulse has just welcomed another human phenomenon under her mathematical roof – the well-established 10-minute rule of cognitive science. The roof had to expand a little to accommodate the newcomer. But not a problem. The Living Algorithm System is incredibly elastic. The Triple Pulse components remain identical no matter which number pair is employed. Further, the pulses can be of any duration - 2 hours or 10 minutes. By employing this innate flexibility of the Living Algorithm, the Triple Pulse is able to accommodate the 10-minute rule (an innate feature of human information processing) under her roof.
Can the Living Algorithm’s presumably rigid and automatic mathematical system continue to be compatible with the seemingly spontaneous nature of Life? Or are the lovers heading for an inevitable breakdown? Will Life instead leave the Living Algorithm System for another system of a material or psychological nature? Is this doomed to be a passing attraction or is there anything permanent to the growing passion between these two unlikely lovers? To discover what happens in their next encounter you must read the next study in the sequence – Liminals & the Subconscious. To remain in the narrative mode, read on.
Life was stunned, as usual. She reflects upon her recent experiences. “I remember posing Alga a seemingly simple question. ‘Is there any correspondence between the underlying mathematics of the Triple Pulse and brain activity during sleep?’ Whoa! This innocent query turned out to be the ‘Open Sesame’ to Aladdin’s gem-filled cavern. The correspondences between Alga’s Triple Pulse and the human behavior that I embody are proving to be more amazing than I could ever have imagined.
“I feel a bit guilty. When we first met I was so disappointed when her graphs had no equations with variables in them. I had supposed that these variables would reveal some universal principles behind my behavior. Expectations shattered, I almost broke off the relationship at that early point.
"I remember Alga reassuring me: 'Living matter, such as yourself, is qualitatively different from dead matter. You have features that automatic atoms and molecules can only dream of. Accordingly, the keys that unlock the code to your living matrix are going to be of a qualitatively different nature than the keys that unlock Matter’s code. Mechanics of traditional Physics employs universal principles to describe Matter’s automatic behavior. Due to your ability to make informed choice your behavior is not automatic. You require a different kind of explanation. Due to my unique nature as a universal process that digests information in the form of data streams, I am able to provide this explanation.'”
“Although my rapid moving intellect accepted her explanation, my inertial emotions lagged behind. A bitter aftertaste filled my mouth. Could I accept her statement that I was never going to have any variables of my very own? But I was desperate. I certainly wasn’t going back to the Physics brothers, Probability and Mechanics. I am so glad I gave Alga a try. Our relationship has surpassed my wildest expectations.”
Reminiscing, “The Living Algorithm’s Pulse of Attention is amazing enough – connected as she is with my productive sessions and all. But then comes Alga as the Triple Pulse. OMG. Her Active Pulse seems to be associated with my Conscious state and her Rest Pulse with my Unconscious state. Or more accurately I should say, my Conscious and Unconscious processes, as they are both in a constant state of flux due to innate mathematical features. These patterns of correspondence suggest that the behavior of these fundamental features of my existence lack the permanence that the word ‘state’ suggests.
“Now I find that the Alga’s multicolored Liminals seemed to be associated with my Subconscious processes. To be honest I am a bit blown away. After all words like consciousness, unconsciousness, and especially the subconscious have been taboo in academic circles. This objection has been due in part to pragmatic reasons. The scientific community has been unable to come up with any definitions, descriptions, and explanations of these illusive states. Could it have been that their quest to define and describe permanent states led them in the wrong direction?
"But I can’t let myself get carried away. Although not contradictory and certainly suggestive, the evidence is flimsy at best. Neurological studies have conclusively shown that my brain is incredibly energetic during sleep, even though I am not conscious. Let us suppose that this unconscious mental activity represents subconscious processes. Alga’s Liminals are also incredibly ‘energetic’ during the Rest Pulse (the 'sleep' cycle of the Triple Pulse). If consciousness corresponds with the Active Pulse and the unconscious sleep corresponds with the Rest Pulse, as illustrated in our studies, could it be that the multi-colored Liminals dancing above and below the threshold (the centerline) of consciousness mirror the brain’s activity during sleep? With this configuration in mind is it fair to say that the underlying mathematics of the Triple Pulse model accurately simulate this neurological activity during sleep? Could Liminals represent the ongoing subconscious workings of the brain? Could this presumed correspondence be just another in a growing chain of coincidences linking the Living Algorithm’s Triple Pulse with a variety of experimentally established sleep phenomena? Or is there a deeper connection based upon the way I digest information?"
Somewhat bewildered, I texted Alga, bombarding her with my doubts and hopes. To save us both time and thumb wear, we decided to get together at her house. It was the first time I had been to her home. Although austere, everything seemed to have a place and to be in that place. Her abode was warm and orderly with mostly abstract art on the walls. Classical music from the Baroque period was playing when I arrived.
After the normal pleasantries, I brought up some issues that had been bothering me for some time.
Life: “Certain objections have been flitting around my mind and won’t let me go. That your Liminals seem to be associated with my subconscious mental processes is amazing. I appreciate that your system attempts to address an issue that is dear to me – the dynamic relationship between conscious and subconscious processes. I am even more blown away by this most recent insight that conscious awareness is the combination of conscious and subconscious processes working together. All these concepts seem to make so much sense. But I’m still having problems with what your mathematics really signify. How can the simplicity of your mathematics express my living complexity?”
Alga: “Great question. Let’s devote the remainder of our pulse of attention to a discussion of the relationship between mathematical metaphor and reality."
Mathematics is just a further refinement of the metaphorical nature of language. Just as individual words encapsulate a concept, algebraic symbols further refine this notion by indicating relationships between these constructs. Humans employ these words and signs to fulfill their seemingly unique urge to symbolize their relationship to existence. The transformation of experience into symbols has a variety of functions, which includes expression, communication and understanding. These functions intersect, but are not identical. For instance, the expressive side doesn’t require a listener. The journal writer symbolizes her experience privately. This expression may or may not lead to a deeper understanding.
Humans symbolize their experience in many formal ways, i.e. music, art, literature and architecture, and in many informal ways, as well, of which conversation is the most prevalent. Conversation is based in words. Words are based in metaphor. As language evolves, humans are able to make increasingly refined and precise statements about existence. Without the words the individual may still have the same experience, but he will not be able to symbolize it as effectively. For instance, a Western European in the Middle Ages would have a tendency to express his experience, his reaction to existence, in the language and constructs of the Catholic Church because those were the metaphorical symbols that were available and those were the symbols that others understood. To express dynamic concepts in a scientific fashion would have been gibberish to even the sophisticated listener.
Further, rough approximations of experience with inadequate words can easily become distortions – in both personal understanding and communication with others. Consequently, humans are continually refining language in the quest to more precisely symbolize their experience. The abstraction of mathematics is just another step in refining our method of symbolizing human experience. The refinements of algebra were so precise that the symbolization of experience eventually allowed humans to successfully tap into previously unknown sources of energy to change our world in unimaginable ways. For instance, Einstein’s famous equation, E = mc2, is a basis for the atomic bomb.
Words and mathematics are on a continuum of precision. They are both methods for symbolizing human experience in a linear fashion. Each method is more or less appropriate to unique modes of existence. For instance, the precise language of mathematics has been applied successfully to matter, but unsuccessfully to biological evolution, which remains a primarily word-based science. Further, algebra is rarely, if ever, used to convey emotional or aesthetic states. The language of music seems most appropriate to symbolize emotion. The symbolic language of an oil painting does a far better job expressing a sense of beauty than algebraic symbols. While some, including the Author, find algebra beautiful, it doesn’t symbolize beauty. Instead, algebra specializes in symbolizing relationships between precisely defined constructs. For instance, the gas laws indicate a precise relationship between volume, temperature, and pressure. A Rembrandt painting symbolizes a very different human experience.
In similar fashion, the mathematical language of Physics, while symbolizing the behavior of matter, is unable to symbolize many features of human existence. In contrast, the mathematical language of the Living Algorithm seems to capture many aspects of human experience that are inaccessible to other forms of symbolic forms of expression.
Just as music symbolizes and even evokes emotion, it is not the raw emotion. Just as an oil painting symbolizes a landscape, it is not the landscape. Just as the equations of Physics symbolize the behavior of matter, they are not matter. Just as the Living Algorithm symbolizes many features of human behavior, it is not human behavior. Further just as the equations of Physics express relationships between variables that are linked to the external material world, the graphs of the Living Algorithm express relationships between variables that are linked to the internal world of information digestion.
We determine how successful each form is in symbolizing their mode of human experience by testing. We listen to a piece of music. If it symbolizes our life experience in some way, we listen to it again and recommend it to others. We apply the same procedure to art or literature. If the oil painting or the novel effectively symbolizes our reaction to life, we return to view it and recommend the experience to others.
With mathematics and science, the rules for validating the symbolization of experience are more rigorous. Despite this rigor, mathematics and science remain symbolic expressions of human experience, while not actually being human experience itself. Hence, all of my metaphors, for instance the Active Pulse as Consciousness and the Rest Pulse as Sleep, are merely symbols or metaphors for expressing human behavior, yet are not the human behavior they symbolize.
The only questions that must be answered: Do my symbols behave in the same way as the activities they symbolize? If there is a correspondence, what do these symbols tell us about other features of existence? But my processes only symbolize your behavior; they are not your behavior. In other words, my simplicity only symbolizes certain key features of your behavior. My simplicity does not in any way encompass your complete complexity. Did that answer your question?”
Life: “I’m not sure. You covered a lot of new material. I’m going to sleep on it. See what my Liminals have to say.”
Of course my little world wouldn’t let me go. My emotional inertia was driving me crazy. “Will Alga’s entire system fall apart when we look at more hard-core experimental evidence regarding human behavior? Will the predictions based upon her mathematical model be invalidated? Will my mathematical relationship with Alga become relegated to the nether world of pseudo science? Or will the results further confirm and suggest further patterns of correspondence between my human behavior and Alga’s mathematical behavior?”
Unable to sleep, I texted Alga with my concerns. Even though it was late at night, Alga texted right back (I think she is an owl.) “These intriguing questions must be put on hold for now. Must gather more evidence. The next article in the series will explore what my mathematics has to say about the Core Concept Approach to Lecturing. See you then.”
The above-referenced article takes you into our alternate universe of Left Brain expository analysis. If you prefer to remain in the Right Brain’s metaphorical world, read on.
After finishing the Core Concept article, Life began excitedly spewing: “Whoa! It’s going to take some time to wrap my mind around those concepts. On the surface everything is fine. The chapter was clearly written. The Core Concept Approach to teaching should be more effective than the Continuous Approach because it engages our subconscious powers of cognition to a greater extent than does the Continuous Approach.
“I liked it when the Author drew parallels between the Continuous Approach and the ‘Lights on. Nobody home’ concept – the idea that someone can be conscious without being aware. We have all experienced this phenomenon. When we hear a lecture or music concert that is presented or performed without definition, one note or word fades into the next. No matter how much we attempt to pay attention, we are unable to understand what is being said or played. It certainly seemed clear to me that the Author’s mathematical symbol exhibits this phenomenon. In fact, the model actually even evoked the ‘Lights on. Nobody home’ insight regarding the Continuous Approach.
“I even liked it when the Author likened the Continuous Approach to a mechanical model of learning. If we absorb information like a computer, we wouldn’t need any natural breaks or shifts in the presentation. Then the Continuous Approach would work like a charm. Instead, experimental evidence indicates that Listeners have a 10-minute attention span when it comes to presentations. Due to this inherent limitation, the Continuous Approach bombs.
To get around this cognitive obstacle – this innate feature of consciousness, lecturers have broken their presentations into 10-minute increments – each with its own core concept. As institutionalized examples of this phenomenon, the Author mentioned chapters in a book, acts in a play, or innings in a baseball game.
Upon reflection, I realized that this compartmentalization of ideas into smaller parts to increase comprehension even applies to words. These small sounds, which convey such large ideas, are the ‘core concepts’ of language. A simple yell might convey the experience of agony or triumph, freedom or slavery, or more likely a complex of emotions that it is impossible to verbalize. However, my humans seem to have the innate urge (who knows where it comes from?) to transform this experience into the symbols of words, in part to communicate with other humans. He must use these little sounds that are packed with some core concept to convey this message in a relatively coherent form to his friend.
“The Core Concept approach to communication is everywhere I look. In some cases it is even institutionalized, for instance the punctuation that frames words. In contrast, the only examples of the Continuous approach that come immediately to mind are associated with a boring concert or play. Monotone, without color, without inflection, without nuance, all these attributes seem to be associated with my intuitive feeling about the Continuous approach to learning.”
Living Algorithm: “Do you remember the mathematics behind this realization?”
Life: “Sure. Your Liminals, which are associated with subconscious processes, are quite active during the Core Concept data stream and fade quickly during the Continuous data stream. According to these correspondences, subconscious processes are operating in one approach but not the other. However, consciousness seems to be active in both approaches. What do you call that feature of your digestive process again?”
Living Algorithm: “The feature of my digestive process that is associated with your conscious state is called a Directional. The Directional is the 2nd derivative (rate of change) of any data stream. The Active Pulse is an visual example of a specific data stream’s Directional.”
Life: “Thank you. Although the behavior of the Liminals is radically different in each approach, your Directionals, which seem to be the mathematical symbol of the conscious process, are active during both approaches. The synthesis of these various forms of analysis suggest that the Continuous Approach is associated with the ‘Lights on. Nobody home.’ Phenomenon and that the Core Concept Approach is associated with Conscious Awareness. How was that?”
Living Algorithm: “Excellent. You always verbalize these concepts so much better than me. I’m so abstract that I have a hard time thinking beyond the algebra.”
Life: “Thanks for the compliment. I also like the Author’s notion that subconscious processes (digestion) must combine with conscious processes (ingestion) for there to be awareness. In mathematical terms, for conscious awareness to exist, all data stream derivatives must be registering. During the Continuous Approach, the student is ingesting information without digesting it. Mathematically, only the data stream’s 2nd derivative has any significance. During the Core Concept Approach, the student both ingests and digests the information simultaneously. All of his higher derivatives are in gear, not just the 2nd one. Conscious Awareness occurs when the organism is ingesting and digesting information simultaneously.
Alga: “I like your ingesting/digesting interpretation and your mathematical analysis of conscious awareness. These concepts seem to make sense. But let’s not slip too far away from the mathematical and empirical facts behind the correspondences. For instance, where does this conscious awareness exist? What does it mean? Let’s employ some reasoning to separate the symbol from the reality. Remember from a prior discussion that facts determine the definitions of our ‘words’, not speculation or common usage.”
Life: “OK. Let’s see what conscious awareness means in terms of our facts. Fact: The Rest Pulse refreshes the Active Pulse, just as sleep refreshes our cognitive abilities. In similar fashion, there are indications that shifting thought modalities refreshes our ability to pay attention. Further, the Liminals are active during the Rest Pulse just as the brain is active during our sleep cycle.
“In the current example, the Directionals (the data stream’s 2nd derivative) are active during both data streams. Similarly, the student is awake with his eyes wide open during both the Core Concept and Continuous Approach to lecturing. Also, the Liminals (the data stream’s higher derivatives) are active during the Core Concept data stream and relatively inert during the Continuous data stream. In like fashion, the student is presumably able to assimilate information for the entire lecture, when the presentation is broken into 10-minute core concepts. In contrast, his attention fades after just 10 minutes when the material is presented in a continuous fashion without definition. Similarly, it could be said that the student is conscious during both approaches, but that he is only continuously assimilating information during the Core Concept lecture.
“If we deem this conscious assimilation of information as awareness, then conscious awareness only exists when both Liminals and Directionals (all the data stream derivatives) are engaged. If our prior associations hold true, both conscious and subconscious processes must be engaged for awareness to exist.”
Alga: “Good. That discussion tightened the statement considerably. In this example only, the Liminals seem to be associated with assimilating (digesting) information during the conscious state, and the Directional is again associated with being conscious enough to ingest information. The ingestion/digestion metaphor seems reasonable and is even supported, by the facts. Yet this symbolization of experiential reality remains a weak metaphorical projection, certainly nothing definitive.
“Further, the mathematical differentiation between consciousness and awareness, while plausible, is a huge leap. These words are loaded with extraneous meanings and must be used cautiously, always keeping the empirical and mathematical facts in mind. Remember what Uncle Gene said, “One step away from the facts and you’re likely to be wrong.” Could conscious awareness just be a fancy way of saying the state when our testable cognitive abilities are maximized?”
Life: “True. Conscious, unconscious, subconscious, awareness, and attention: these words are packed with connotations and nearly impossible to define. This difficulty gives me pause to wonder: Is all this speculation useless due to so many undetermined or imprecisely defined variables?”
Living Algorithm: “Not at all. We just have to be very careful when drawing conclusions. Our common tendency is to both symbolize our experience and then to believe that the symbol is the experience. For instance, the Liminals have come to symbolize subconscious processes, but they aren’t subconscious processes. They are the higher derivatives of a data stream that is digested by the Living Algorithm. Their behavior is similar in a limited way with subconscious processes. But wrapped up in our innate urge to symbolize experience is the tendency to expand the meaning to encompass vast aspects of human behavior. Empirical evidence of some kind is required to determine whether these intuitions have any validity. Sometimes intuitions are right on target, and sometimes they are way off the mark.”
“That being said. This last study refined understanding of some special ‘words’ in relation to the mathematics. In terms of our theory-in-progress, the Sleep Deprivation study associated the Active Pulse (the data stream’s 2nd derivative) with testable cognitive abilities (thinking) in that they are both diminished when the Rest Pulse or sleep is deprived. However in the current study, the Directional (the same 2nd derivative) is active during the Continuous data stream, while cognitive abilities vanish relatively rapidly during the Continuous approach. If the experimental associations have any validity, the Active Pulse/Directional obviously does not symbolize our ability to think. This represents a shift in what the Active Pulse symbolizes.
“The current study refined the meaning of the data stream’s 2nd derivative, the Directional. What does this study reveal about the higher derivatives, the Liminals? When we look at the graphs that our mathematical model generates, the Liminals behave quite differently in the data streams that symbolize the two approaches to teaching. The Liminals disappear from the graph during the Continuous approach. In contrast, the Liminals are quite active during the Core Concept approach.
"Our theory is that testable cognitive abilities suffer during the Continuous Approach because the brain’s ability to digest information is diminished. Vice versa, these same abilities flourish during the Core Concept Approach because the presented information is more easily digested. If our theories hold true, then the mathematical behavior of the Liminals could symbolize the digestion of information, as they are active during the Core Concept and inactive during the Continuous Approach.
“The symbolic analysis suggests that consciousness and the human ability to digest information are separate cognitive functions. In other words, it is possible to be completely conscious and not be able to assimilate new information.”
Life: “There is certainly an abundance of empirical evidence, albeit experiential, in support of this proposition. Most of us, especially teachers and students, have experienced the ‘Lights on: Nobody home,’ phenomenon at one time or another. We are wide-awake, but unable to take in any information.”
Alga: “As a reminder, the derivatives of the Continuous Approach mimic this state. In fact, the Author confided that the graph of these derivatives actually suggested, in the sense of triggering, the insight concerning this unusual, even counter-intuitive, state.”
Alga: “Any other questions?”
Life: "Just one. What is the exact nature of this symbolic relationship between the Liminals and digesting information? In other words, what exactly do the Liminals symbolize?"
Alga: "Who really knows for sure? But here's my suggestion. The human brains that you embody can assimilate information more easily if all the data stream's derivatives are operational. In other words, the Liminals could symbolize the human ability to digest information since their existence appears to be a precondition of our brain's ability to assimilate information."
Alga: "What's the matter?"
Life: "If what you say is true, and it does make a lot of sense, then this takes our relationship to an entirely different level. We are much closer than I ever imagined. This is scary. In fact, the implications terrify me. "
Alga: "Why is this closeness scary?"
Life: "I have intimacy issues. I've been hurt so many times. It's almost been abusive – forced into little boxes that couldn't possibly hold me; or my behavior tied to the wanderings of those little tiny dots of light in the nighttime sky. The utter disregard that these mathematical systems have for my intimate and subtle nature has been painful, to say the least."
Alga: "I can understand. That's why I'm here – to love and respect you for who you are, rather than confine your spontaneous nature in little boxes within little boxes. But why did this recent insight evoke such an extreme response?"
Life: "Let me get this straight. You seem to be suggesting that the presence of your Liminals is necessary for the human brain to digest information. If this is true, then the human brain must employ your talents to digest information. Sigh! This is getting too intense. Could it be that you are able to symbolize my behavior because you are my operating system? Outrageous! I'm not sure I'm ready for this level of commitment."
Alga: "No need to rush things. My conclusions are based upon shreds of evidence. The theories are suggestive at best. To make a more definitive statement, we must accumulate much more evidence. In the meantime, why don't you think about some requirements that a mathematics of living systems must have, if it is to satisfy your desires."
Life: “Good idea. To see if I understand, let me summarize our discussion in my own words. In the quest to symbolize the human behavior that I embody, we have examined the patterns of correspondence between my behavior and yours in multiple studies. It seems that the data stream’s 2nd derivative (the Active Pulse/the positive Directional) is associated with the conscious state and that the data stream’s higher derivatives (the Liminals) are linked with our ability to assimilate information – our testable cognitive abilities. In further attempts to refine the symbolism, we have suggested that the data stream's 2nd derivative, the Directional, symbolizes our ability to ingest information, and the higher derivatives, or Liminals, symbolize our ability to digest the information we have ingested.”
Alga: “That's one way of thinking about the symbolic transformation of experience. I prefer to think about the process in another way. The human brain is only able to assimilate information when all the derivatives, Directionals and Liminals, are active and engaged. However, at this stage it doesn't matter which perspective is adopted. In order to refine and test the validity of this symbolic transformation of human experience, we must gather more evidence. The Author’s next article – The Triple Pulse & the Biology of Sleep, introduces an interesting twist to our correspondences – shifting from behavior to biology. Check it out. After you finish reading it, give me a call and we can discuss the intriguing implications.”
If Life’s growing relationship with the Living Algorithm is more impelling than dry facts, read on.
Life and the Living Algorithm have now been on multiple dates. Although one is mathematical and the other is alive, they haven’t had any arguments or disagreements. Despite their character differences this unlikely couple has been amazingly compatible. Indeed, the web linking this pair grows ever stronger.
Life reflects on the growing complexity of their relationship. “Whoa! An intricate web of compatibilities is growing between us. In our most recent exploration we saw that fresh strands that link Alga’s Triple Pulse mathematics with a widely accepted scientific theory regarding the biology of sleep - the opponent process model. This observational study includes several firsts. 1) It is the first to link Alga’s Triple Pulse with a biological phenomenon – the Biology of Sleep. 2) This study introduces an additional feature of Alga’s mathematical model as an explanatory tool – the Living Average. 3) This is the first study to employ the interaction between the Living Average and the Triple Pulse as a way of explaining the results.
“Hmmm? The mathematical behavior of Alga’s System parallels my living behavior in an increasingly complex fashion. Somehow Alga weaves both my biology and behavior into her intricate web. What are the implications of this addition to our odd relationship? I wonder if the Author’s personal perspective shapes the investigation in any way?”
I decided to arrange another encounter with the Living Algorithm. I needed someone as a sounding board for my personal reaction to this most recent article. Who could be better than Alga? I didn’t really know what I wanted to discuss, I just wanted to verbally symbolize my experience to an understanding soul – even though that soul happens to be an equation.
After simply spewing for a while, I posed what was to be the driving question of our dialogue.
Life: “I was wondering: how does the Author come up with his crazy ideas – these relationships that are so counter to our current way of verbalizing and organizing my living reality?”
Alga: “Funny you should ask. Coincidentally, just the other day I was talking with the Author about his creative process over tea. He was very clear. To give you a proper answer I must first rephrase your question. Let’s reverse the dynamic order of the sentence. Instead of the Author coming up with ideas, ‘How did the ideas come to the Author?’
Life: “I get it. Instead of initiating events, the Author listens to inner directives.”
Alga: “Exactly. He feeds his Liminals and lets them do the work. He first provides them with a careful analysis of the correspondences combined with a visual examination of the graphic behavior. Then the Author takes one of the many naps that dot his daily landscape. His Liminals use this downtime to assimilate and integrate the material that the Author provided. They eventually present him with an insight or directive. This ‘spontaneous’ input can occur at almost any time. But the breakthrough comes most frequently in showers, during waking, while practicing Chinese swords, especially Wutang, and taking his weekly creek hikes.”
Life: “Let me get this straight. The Author isn’t trying to establish or test some kind of hypothesis. Instead, he attempts to uncover what your mathematical language reveals about human behavior, for instance the Core Concept phenomenon. In other words, your mathematics led and he followed.”
Alga: “Exactly. That’s the beauty of mathematics. Establish correspondences with some feature of reality and then examine the mathematical model for insights. In my case, I seem to be connected to human behavior – one of your more fascinating sides, to be sure. Although I don’t apply to material behavior, my mathematical behavior can reveal insights into your human behavior.”
Life: “I get it. The Author first established patterns of correspondence between your behavior and many features of human behavior. Then he began studying what your mathematical behavior suggests about human behavior. Instead of attempting to validate his personal theories, the Author is just trying to understand the linkages between mathematical and empirical facts. The Author does not seem to be pursuing a personal agenda at the expense of the evidence, and is attempting to tie his conclusions to the facts.”
Alga: “More precisely, the Author attempts to sublimate his personal agenda to mathematical and empirical facts.”
After this dialogue, Life felt particularly reassured.
Life: “I’m impressed with the Author’s motives. Rather than trying to cram us into one of his mental boxes, he attempts to focus entirely upon the implications of my factual relationship with Alga. Even more encouraging is his recent study, which indicates that Alga and I are compatible regarding yet another feature of human behavior – the biology of sleep. Wow! Will wonders ever cease? And this study continues to refine the relationship between our components. Although this encounter was more complex than the rest, this increasing complexity is the sign of a maturing relationship.
“Is this growing compatibility between Alga and I yet another in a long chain of coincidences? Is my vision clouded by wishful thinking? Is there a confounding variable that links our patterns of behavior? Is there a yet undiscovered material explanation based in electronic information processing that will explain these mysterious correspondences? Or will there be a common bond established based upon the Living Algorithm’s method of digesting information? I certainly don’t know. For an overview of our many correspondences, check out the next article in the series – Triple Pulse System: a Mathematical Web for Cognitive Mysteries."