Dement’s ‘opponent process’ model provides a widely accepted mechanism for the biology of sleep. Are there any patterns of correspondence between the biology of sleep and the mathematics of the Triple Pulse? Prior articles have established linkages between human behavior and the Living Algorithm's mathematical system. Thus far in our investigation, experimental results have not provided any contradictory evidence. What will our first foray into the links between biology and mathematics bring? To answer this question let's first examine the current biological model for sleep.
To avoid the distortion that comes from interpretation we will again quote directly from Dr. Medina’s brain rules – the highly respected book that transmits recent discoveries of mainstream science to the educated public.
According to Medina, Dement, the father of sleep research, and Kleitman, a fellow researcher, made significant discoveries that introduced a new paradigm into the field. It is called the ‘opponent process’ model. Rather than a peaceful transfer of power between our waking and sleep states, the two states are “locked in vicious, biological combat”. There is an ongoing
“pitched battle between two powerful and opposing drives, each made of legions of brain cells and biochemicals with very different agendas. Though localized in the head, the theater of operations for these armies engulfs every corner of the body.”
The conflict has a few strange features.
“First, these two opposing forces are not only engaged during the night, while we sleep, but also during the day, while we are awake. Second, they are doomed to a combat schedule in which each army sequentially wins one battle, then promptly loses the next battle, then quickly wins the next and so on, cycling through this win/loss column every day and every night. The third strange thing is that no one army ever claims final victory in this war. This incessant engagement results in the cyclical waking and sleeping experiences all humans encounter every day (and night) of our lives.”
This conclusion is counterintuitive. Common sense would instead simply suggest that our system gets tired and needs sleep to rest from the day’s activities. Or perhaps we might reason that the light of the sun wakes us up; and the dark of the night puts us to sleep. The data suggests otherwise. Exhaustion is merely a byproduct of this internal battle rather than a reaction to either the day/night cycle or the daily output of energy. In other words the sleep wake cycle is not triggered by external factors, but is instead an internal biological mechanism. Further this mechanism is a battle between two forces, rather than a cooperative effort. Once again the findings of science violate common sense.
What is the mechanism behind this biological conflict?
“One of Kleitman’s and Dement’s greatest contributions was to show that this nearly automatic rhythm occurs as a result of the continuous conflict between two opposing forces.”
What are these opposing forces composed of? And what are they called?
“One army is composed of neurons, hormones, and various other chemicals that do everything in their power to keep you awake. This army is called the circadian arousal system ‘process C'. If this army had its way, it would make you stay up all the time. Fortunately it is opposed by an equally powerful army. Also made up of brain cells, hormones, and various chemicals. These combatants do everything in their power to put you to sleep. They are termed the homeostatic sleep drive 'process S'. If this army had its way, you would go to sleep and never wake up. It is a strange and paradoxical war. The longer one army controls the field, the more likely it is to lose the battle.” (brain rules, pp 153-55)
This is the current understanding of the scientific community regarding the biology of sleep.
Let's summarize our findings. For decades the powerful scientific community has studied sleep extensively. In the process they have developed a consensus regarding sleep's biological component. They call it the ‘opponent process’ model. Although scientists in many disciplines have employed all the sophisticated technology at their disposal – brain scanners, electronic imaging, and such – they are still mystified by the underlying mechanisms of this widely recognized process. Could this be because they are searching for a material explanation, when a mathematical one is required?
How does Dement’s 'opponent process' model, a widely accepted scientific theory regarding the biology of sleep, correspond with the mathematics of the Triple Pulse? Are there any similarities whatsoever, or just a mish-mash of suggestive patterns with no real substance? Just an imaginary dragon that we might see in swirling clouds?
To answer these questions we must evoke yet another innate mathematical feature of the Living Algorithm.
The Living Algorithm’s sole function is digesting data streams. This digestive process reveals the data stream's ongoing rates of change (the derivatives). Similarly, a car's velocity and acceleration are also rates of change. The Triple Pulse is the result when the Living Algorithm digests a specific data stream consisting of a string of 120 1s, followed by a string of 120 0s, and then another string of 120 1s. The Triple Pulse (the green area) is the visualization of the 2nd derivative of this data stream. The Liminals (the other colored areas) are the higher derivatives (the rates of change) of what we call the Triple Pulse data stream.
Note: the horizontal x-axis indicates how many times the Living Algorithm process has been repeated (iterated). Hence it consists of whole numbers only – no partial iterations. This is a purely mathematical process. As such, the vertical y-axis indicates relative values, i.e. more or less. In other words, the data stream's acceleration is greatest at the peak of the Pulse and becomes smaller with each subsequent iteration. In similar fashion, the same mathematical ellipse can be applied to planetary motion, where the values are enormous, or to a student's homework assignment, where the picture fits upon a page. Because the number strings consists of 0s and 1s, these relative values are between 0 and 1.
We have introduced the higher derivatives of a data stream. But we have yet to meet the data stream's 1st derivative. It is called the Living Average. We can liken the Living Average to the temperature gauge of our system of information digestion.
Let's inspect the Living Average (the 1st derivative) of the same data stream that produces the Triple Pulse. In this particular case, the data stream begins with a string of 1s. The Living Average starts at 0. As each successive 1 enters the system the Living Average, the data stream's 1st derivative, begins to rise. Similarly, the temperature rises as heat enters a room. As the number of 1s in the system increases, the Living Average approaches 1. We call this value 'practical' one. The Living Average’s progress from 0 to 1 is shown in the graph at right.
After this point as long as 1s are added to the system, the Living Average remains in the state of 1 indefinitely. In like fashion, a poorly insulated room might reach an equilibrium point where additional heat does not increase the temperature, but just maintains the temperature. If, however, the composition of the data stream shifts from 1s, to a string of 0s, the result is quite different. The Living Average immediately begins falling from the peak. After a sufficient number of 0s have been added to this mathematical system, the Living Algorithm reaches practical 0. In parallel fashion, after the heat is turned off, a room's temperature falls, eventually reaching equilibrium with the outside.
At this point, the data stream's composition shifts again, from 0s to a string of 1s. With this shift, the Living Average’s cycle repeats itself, growing from 0 to 1. Similarly, when the heat is turned on again, the temperature rises again. It is evident the alternation of a string of 1s with a string of 0s keeps the Living Average in a constant state of change. Without the alternation, the Living Average 'stagnates' at either 1 or 0.
Note: the identical data stream generates both the graph of the Living Average (the data stream's 1st derivative – shown above) and that of the classic Triple Pulse (the 2nd derivative – shown at right).
Repetition for retention, hence assimilation: these graphs visualize processes that are pure mathematics. As such, they represent mathematical patterns generated when the Living Algorithm digests the Triple Pulse data stream. To exhibit the parallels between Dement's sleep biology model and our mathematical model, let us employ Dement's military metaphor to characterize the relationship between the Triple Pulse data stream (the alternation of 1 strings and 0 strings) and the Living Average (the data stream's 1st derivative). In other words, we can describe this particular mathematical process as a battle between the 1s and 0s.
The stream of 1s corresponds with Process C (the multitude of biological processes that want to keep us Conscious). The stream of 0s corresponds with process S (the multitude of biological processes that drive us to Sleep). The Living Average indicates the ongoing progress of the battle between these two opposing forces. This value is a gauge of the state in the battle. For instance, when the Living Average is closer to 1, the army of 1s is winning. When the Living Average reaches 1, the army of 1s has won the battle, but not the war, as we shall see.
The Living Average (the data stream's 1st derivative) begins at 0 (the beginning of the day). This indicates that the 0s have won the battle. The army of 1s (Process C) assert themselves in the attempt to change the Living Average from 0 to 1. Eventually the 1s win the battle – as they have changed the Living Average to 1 (the end of the day). At this point the army of 0s (Process S) take over and begin attempting to change the Living Average back to 0. Eventually the 0s win the battle with the 1s, as the Living Average returns to 0. Now, the 1s reawaken from their sleep and begin reasserting control again. At the point that the 1s completely win the battle, the 0s reassert themselves again. This process continues ad infinitum.
From this conceptual perspective, this is a mysterious process. Why would the 1s give up control after completely annihilating the 0s and vice versa? The 1s are on the verge of total victory, when they relinquish control to the vanquished opponent. In terms of winning and losing, this strategy makes no sense. The simplistic view of this mathematical process as a battle between 1s and 0s doesn't explain anything and leads to greater confusion.
We’ve established that Dement's ‘opponent process’ model and the Living Algorithm's mathematical model exhibit symmetrical patterns. For a deeper understanding of this mysterious process, let us tweak the mathematical model to see what it has to reveal about the mechanisms behind Dement's model. What would happen if one of Dement's armies were able to win the war – vanquish his opponent forever? It is obvious what would happen if Process Sleep (the army of 0s) won the war. We would remain in the unconscious state of sleep permanently. Inevitably we would enter a coma and die.
It is not so obvious what would happen if Process Consciousness (the army of 1s) won the war. Process C, our circadian arousal system, wants to keep us up awake forever. What's wrong with that? Most of us would love to enjoy continuous consciousness rather than enter a state akin to death for one third of every day. In fact, this is one of the mysteries of cognitive science. Why must humans enter a state of mini-hibernation every 24 hours, especially since it makes us vulnerable to our predators? What evolutionary mechanism conjured up this bizarre behavior?
Let us employ a data stream consisting of an endless string of 1s to represent/symbolize what happens when the army of 1s (Process C) wins the war. In other words, there is no more army of 0s (Process S) to fight for supremacy. Process C (the army of 1s) reigns supreme and we never have to sleep.
When the Living Algorithm digests a data stream consisting solely of 1s, the 1st derivative (the Living Average) rises from 0 to 1 and then flatlines. Similarly, the higher derivatives generate pulses and then flatline at 0. In other words, the rates of change (the derivatives) are minimized when the content of the data stream remains the same. In like fashion, a data stream's derivatives are minimized when its content is random. The graph at right illustrates this mathematical phenomenon.
This is a visual representation of the derivatives of a data stream consisting of 360 1's. The horizontal x-axis indicates the number of times the Living Algorithm process is repeated (the iterations). The vertical y-axis indicates the relative sizes of these rates of change (the data stream derivatives). After the initial 120 1's, all the derivatives fade to 0. In other words, the Living Algorithm's information system 'stagnates' if either of the armies wins the war, not just the battle. Stagnates might be a mild descriptor, as the flatlining is more reminiscent of what we see on a hospital's machines after the signs of vitality shut down and the patient dies.
Alternately, the regular alternation of a string of 1s and a string of 0s refreshes the successive pulses. This refreshment maximizes the dimensions of the data stream derivatives. The benefit of alternating numerical strings is not winning or losing the battle (as visualized by the Living Average). Rather than vanquish the opponent, the benefit of the alternation between 1s and 0s is simply to maximize the dimensions of the data stream's rates of change. Rather than adversarial, the 1s and 0s are in a cooperative relationship to maximize change in the Living Algorithm's mathematical system. Another way of stating the same phenomenon, the alternation of number strings prevents 'stagnation' in the information system.
What are the implications of this curious mathematical phenomenon regarding the biology of sleep? Do the biological processes that are conceptualized via Dement's 'opponent process' model maximize change, thereby prevent stagnation? If so, what kind of change are we talking about?
Before suggesting answers to these questions, let us take a step back to understand the greater purpose of this article - the meta-perspective, as it were. It seems that there are distinct patterns of correspondence between the Living Algorithm's mathematical model and Dement's 'opponent' process model. Dement's model is an attempt to conceptualize the patterns of empirical data regarding the biology of sleep. Our mathematical model is an attempt to symbolize Dement's model with numerical relationships. Both models are generated to better understand the underlying mechanisms behind the patterns of empirical data. However, both models are abstractions – one mathematical, the other conceptual. Cognitive science has shown that the relationship between abstraction and reality is inherently metaphorical in nature.
This is true of all scientific theory. Although the mathematical models of the hard sciences provide a nearly perfect fit with hard empirical data, the understanding of this relationship is still metaphorical in nature. In his book QED, Richard Feynman, one of the kings of subatomic physics, takes this a step further. Although physicists done an excellent job at fitting a mathematical system with the empirical data, Feynman suggests that they don't really know what's going on in the world of electrons and photons. The mathematical fit is more important than a theoretical model for the scientific community.
"I have pointed out these things [the bizarre behavior of subatomic particles] because the more you see how strangely Nature behaves, the harder it is to make a model that explains how even the simplest phenomenon actually work. So theoretical physics has given up on that." (p. 82, QED)
Comparing the patterns of the 2 models with those of the empirical data is certainly informative. However, the real power behind this form of analysis lies in a different direction. Pattern recognition is only the 1st stage. It acts as a preliminary filter. If the patterns don't coincide, the investigation ends. Coinciding patterns inspire further investigation into the relationship between the model and the process. However, the congruence doesn't prove that there is any connection – any causal relationship – between the model and reality. For instance, just because all hard drug users started out on milk, we don't infer that milk leads to drug use. The motivation behind drinking milk is nourishment, while humans employ drugs to alter their state of consciousness. Because the underlying logic behind the two activities is completely different, we reject the association out of hand.
Examining the underlying logic behind the model and the facts is the second stage in the verification process. Because milk is not an intoxicant, one does not compare it with intoxicating drugs. The final step towards scientific acceptance is when the underlying logic behind the model provides explanatory power for the empirical data. For example, because the underlying logic behind Dement's 'opponent process' model provides the best current explanation for the biology of sleep, the scientific community has embraced it as the standard.
We've already established that the Living Algorithm's mathematical patterns are similar to the biological patterns of sleep as revealed by Dement's conceptual model. We can now proceed to the second stage. The following discussion examines the underlying logic behind both systems. Our model has an advantage because it is mathematical. The underlying logic behind mathematical systems is crystal clear, as it is based upon deduction. This is why scientists are ever searching for mathematical equivalents.
In contrast, Dement's conceptual model is based in inferential logic. Dement's 'opponent process' model is based upon a familiar army metaphor but has no mathematical foundation. Ultimately, we suggest that the underlying mathematical logic of the Living Algorithm provides a greater explanatory power for the empirical data associated with the biology of sleep than does the underlying military logic behind Dement's 'opponent process' model.
More importantly, the Living Algorithm's mathematical model links the biology of sleep with a multitude of other unexplained cognitive phenomena (some of which are included in the diagram below). This universality is one of the strengths of mathematics. Mathematical patterns can be analyzed independently of empirical data to see what they reveal about the underlying nature of reality. In contrast, Dement's 'opponent process' model, while effective, is limited to the biology of sleep.
Dement's model, as mentioned, is limited to the biology of sleep. In contrast, the Living Algorithm's mathematical model exhibits patterns of correspondence with a multitude of diverse phenomena. To gain insight into the potential meaning of the connection between the 2 models, let us examine some prior results, specifically the patterns of correspondence between the Triple Pulse and Sleep Deprivation.
As is evident, the Triple Pulse consists of 3 pulses (green). The positive pulses are called Active Pulses and the negative pulse is called the Rest Pulse. The Active Pulse is generated when the Living Algorithm digests a string of 120 1s. The army of 1s generates a Living Average that corresponds with Process Consciousness. The Rest Pulse is generated by a string of 120 0s. The army of 0s generates a Living Average that corresponds with Process Sleep. In other words, the same army of 1s that generates the Active Pulse is also associated with Process Consciousness. Similarly, the same army of 0s that generates the Rest Pulse is associated with Process Sleep.
More specifically and more significantly, the relationship between the army of 1s and the army of 0s mimics the warring relationship between Processes C and S, as well as the mysterious relationship between our cognitive abilities (thinking) and sleep. The relationship between the army of 1s and 0s is exhibited by the Living Algorithm's information digestion process. The Living Algorithm digests the same data stream composed of the army of 1s and army of 0s. The data stream's 1st derivative, the Living Average, mimics the warring relationship between Processes C and S, while the 2nd derivative, the Triple Pulse, mimics the sleep/thought relationship. Could it be that the underlying logic of the data stream's 2nd derivative applies equally to the relationship between Processes C and S?
As previously illustrated, the alternation of numerical values (the army of 1s and the army of 0s) refreshes the potentials of the Living Algorithm's mathematical system. Without the alternation, the Pulses disappear. If the content of the data stream doesn't change periodically, the data stream's rates of change (the derivatives) flatline. The information system stagnates. How does this strictly mathematical process apply to Dement's model for the biology of sleep?
In our Sleep Deprivation study, we saw that the Rest Pulse of 0s refreshes the Active Pulse of 1s, just as sufficient sleep refreshes our testable cognitive abilities. As such, the Rest Pulse is associated with the state of sleep, while the Active Pulse is associated with our ability to think - our cognitive abilities. Without the Rest Pulse, the Living Algorithm's information model flatlines - stagnates. Without sleep, humans die. Could it be that Process Sleep was designed to prevent cognitive stagnation? Is it possible that Process S is necessary to refresh our cognitive abilities? Without Process S, does Process C lead inevitably to mental stagnation and death?
The relationship between the Active and Rest Pulses, the 2nd derivative, seems to correspond with the relationship between our testable cognitive abilities and Sleep. When the Rest Pulse is interrupted, the subsequent Active Pulse loses size. This loss in size parallels the loss in cognitive abilities. If the relative lack of data stream derivatives symbolizes stagnation, the presence of these same derivatives could indicate vitality/energy. Instead of symbolizing our cognitive abilities, the relative size of the Active Pulse could instead symbolize the mental energy that is required to employ our cognitive abilities.
The underlying logic behind this interpretation of the correspondences between Living Algorithm mathematics and empirical reality makes more sense. It seems more reasonable that our cognitive abilities are hard-wired into our biology – in this case, our neurological system. More specifically, our cognitive abilities are directly related to the structure of our neural networks. Further the findings of cognitive science have shown that timed repetitions are required to reconfigure these neural networks.
In other words, it takes a time investment to cause an effect, in this case a permanent change in the underlying structure of our Mind. Because of the necessity of this time investment, the neural networks that are associated with our cognitive abilities are relatively stable. They change slowly, over time. In this sense, our cognitive abilities are a relatively stable set of tools that we develop gradually.
Because of this relative stability, sleep loss on a night-to-night basis would not exert an appreciable effect upon our cognitive abilities. Then why does sleep loss correspond with a fall in our cognitive performance? It takes energy to do work. The carpenter's tools do not build a cabinet. Neither do our cognitive abilities solve a problem. The carpenter must have energy to employ his hammer and saw in a constructive fashion. Similarly, we must have sufficient energy to utilize our cognitive tools/neural networks most efficiently.
We suggest that this energy has a mental, as well as physical, component. No matter how well rested our mind is, if our body is in pain, our cognitive performance suffers as well. Similarly, no matter how fit the carpenter is, he is likely to make mistakes if he has not slept the night before. Sleep loss equals mind loss. His cognitive abilities are diminished and so is his physical performance.
In other words, energy is required to effectively employ Mind's tool, our neural networks/cognitive abilities. The energy does not seem to be physical in nature. Or at least, cognitive scientists from around the globe have yet to find a biochemical interaction that explains the mysterious loss of mental performance from sleep deprivation. Let us take an alternate approach and assume that mental energy is required to energize our neural networks – take advantage of our cognitive abilities. Because sleep loss impacts our mental energy, our cognitive performance also falls.
With these parallels in mind, let us entertain the possibility that the higher data stream derivatives, such as the Active and Rest Pulse, symbolize how much mental vitality/energy that is available. Without mental energy, our cognitive abilities can't be utilized. Mental vitality is required to employ our cognitive tools to do the work of digesting and assimilating environmental information that is required for survival.
In other words, as the derivatives flatline, our mental energy vanishes. Alternately, active derivatives indicate that mental energy is available. Derivatives up; Mental Energy up; and vice versa.
Does this supposition make any sense? To find out, let us apply this understanding to our biological sleep system. We will describe the Living Algorithm's mathematical process alongside the biological C & S Processes associated with sleep. In this way we can uncover if the assumption has any explanatory power. Are the parallels meaningless? Or does the underlying logic behind the mathematical process lead us to a deeper understanding behind the mysterious relationship between the C & S processes?
At the beginning of the information digestion process or when we awaken from sleep, the army of 1s (Process C) seizes control. The data stream's Living Average begins at 0 and then climbs steadily until it reaches 'practical' 1. Process C (the 1 generator) can claim total victory at this point – having totally vanquished Process S (the 0 generator). However, if Process C remains in control, the Living Average and the other derivatives stagnate. In terms of our supposition, our mental vitality vanishes and with it the ability to digest environmental information. Our article on the Necessity of Sleep certainly supports this interpretation. Without sleep we die.
At the point of total victory, all the data stream derivatives have begun to flatline and the System has lost its vitality. To refresh the System's vitality, the content of the data stream must change. Initiating a stream of 0s (Process S) fulfills this purpose. This change refreshes the vitality of the System, information or biological. The string of 0s (Process S) changes the Living Average from 1 back to 0. After the army of 0s (Process S) has converted the Living Average to their side, they have won this battle. For the System to avoid stagnation, another shift in the data stream's content is in order. Changing to a stream of 1s (Process C) serves this function. After the respective data streams of 1s or 0s have converted the System back to their side, they have finished their task. It is the alternation of the '1' string and the '0' string that refreshes the System's vitality (the data stream derivatives), thereby avoiding stagnation.
It is evident that the purpose of utilizing alternating number strings (Processes C and S) could be viewed as maximizing mental vitality rather than defeating an ‘opponent’. To refresh the System's vitality, the stream of 1s and 0s alternate. This process is reminiscent of the alternation of yin and yang. This is not a war of destruction between 2 opposing forces. This is cooperation between two forces that is designed to prevent stagnation and maximize potentials.
Does this analysis provide a deeper understanding of our biological sleep system? Could it be that the longer Process Consciousness controls the field, the more likely it is that the biological system will lose mental vitality and stagnate? Could it be that the biological mechanisms behind Process Sleep refresh our mental vitality and with it our cognitive ability to digest and assimilate information? Could it be that the "opponent process' model is not a battle for supremacy, but a biological mechanism designed to maximize our mental vitality? The indications certainly point in this direction.
Instead of viewing these number strings as armies of battling soldiers, we can also view them as armies of workers, each with a different task. The task of the workforce of 1s is to raise the Living Average (grey) from 0 to 1. Similarly, the task of the workforce of 0s is to return the Living Average from 1 to 0. After the 1s have completed their task, the 0s take over, and vice versa.
In this mathematical sense, each number is a bundle of information that works to change the Living Average to their side. Work requires energy. As such, each number acts as a bundle of information energy.
At the point of victory, the workforce of 1s (Process C) has reached the limits of their ability to change the Living Average. The workforce of 1s has completed their job of raising the Living Average from 0 to 1. There is no more work for the 1s to do. There is nowhere else to go but down. In other words, when the Living Average equals the value of the number/data bit, the data is doing no more work.
Requoting brain rules: “It is a strange and paradoxical war. The longer one army controls the field, the more likely it is to lose the battle.” The longer the 1s cycle controls the field; the more likely they are to lose the battle to the 0s. Or in less aggressive terms, the longer the 1s control the field; the more likely it is that they have completed their task. Similarly, the longer the 0s control the field the more likely it is that they have completed their task. Each number defers to the other once they have completed their task.
This analysis, of course, raises new questions. Instead of a battle between opposing armies, it seems that the biology of sleep could be better likened to a cooperative relationship between 2 work forces with complementary tasks. After finishing their part of the job, one labor force passes it off to the other, and vice versa. What are these complementary tasks? What are the respective functions of Processes C and S? Let us offer some preliminary suggestions in this regard.
In our original study on interruptions to a productive session, the string of 1s symbolized the mental energy of Attention. The current set of sleep-related studies validated and extended this association. Instead of applying only to a 2-hour session, the string of 1s seems to symbolize the Conscious Attention of our waking day. When the Living Algorithm digests this same string of 1s, the result is the Pulse of Attention, i.e. the Active Pulse.
The Active Pulse is the 2nd derivative of a data stream consisting of 1s. In an earlier section, we suggested that the value of the data stream derivatives is associated with energy. Due to the associations with Attention, this Pulse could symbolize a pulse of fresh mental energy. Under this way of thinking, this fresh mental energy is only generated while we are conscious, i.e. when Process C is dominant.
It seems a reasonable assumption that the function of this mental energy is to digest environmental information. While Process C is dominant, we generate 1s of Attention/mental energy to organize our existence. This entails reversing the entropy of the material world. We employ this mental energy to digest fresh information with the aim of fulfilling potentials. Once this information is assimilated, we can utilize the knowledge to obtain food for sustenance and seek out reproductive partners for the continuation of the species. Under this way of thinking, the task of Process Consciousness (the Attention generator) is to digest and organize fresh environmental information.
Prior studies suggest that the string of 1s symbolizes Attention. These same studies suggest that the string of 0s symbolizes Sleep, i.e. lack of Attention. Fresh mental energy enters the system via Attention while we are conscious – while Process C is in ascendance. Alternately, no more mental energy enters the system when Attention is turned off during sleep – while Process S in charge. In other words, the Attention's mental energy is on while we are conscious and off we are asleep.
Why couldn't Process Conscious continue forever? Why is Process Sleep necessary? Is the mental energy used up during awake time and requires the downtime of sleep for regeneration? Our common sense suggests that mental energy is a commodity like gas, i.e. an entity that can be consumed. We use up our biological energy during our active day. Nighttime provides an opportunity to rest our weary bones and rejuvenate our body with sustenance. In similar fashion, it makes sense that we use up our finite store of mental energy during the day and replenish it while we are sleeping. Our mathematical model does not support this interpretation, nor do the current findings regarding sleep.
The correspondences between our mathematical model and empirical reality suggests that the mental energy of Attention is not physically based, but is instead due to the rhythmic cycle of information digestion. The Living Algorithm's Triple Pulse reveals the mechanisms behind this process. The efficient employment of this mental energy maximizes our ability to pay Attention. While biophysical energy is necessary for the bodily functions that support our mental capabilities, the real secret to mental energy is efficiency. How information is digested gives rise to the mental energy of Attention, not biochemical mechanisms.
According to our suppositions, if Attention is maintained for too long, mental energy stagnates, as revealed by our mathematical model. If Attention is not maintained for long enough due to interruptions, mental energy does not reach its full potentials. (We explored these mathematical features in the Interruption and Sleep Necessity studies.)
To maximize the mental energy of Attention, it must be sustained for an ideal duration: not too long, not too short, but just right. From this perspective, the content of the data stream is secondary to the manner in which it is digested.
According to our model, there is one last feature that inhibits the ideal potentials of the mental energy of Attention - insufficient or interrupted downtime. When the Living Algorithm digests a string of 0s after the string of 1s, the Rest Pulse is the result. This is the same army of 0s that corresponds with Process Sleep. This Rest Pulse is required to refresh the potentials of the corresponding Active Pulse. If the Rest Pulse is abbreviated or interrupted, the ideal potentials of the Pulse are diminished. This suggests that if our sleep (downtime) is insufficient or interrupted that our mental energy is diminished even it is not interrupted.
In other words, timing plays a huge role in determining the amount of mental energy available to ignite our cognitive abilities. The duration of Attention and Downtime must be just right to maximize our mental energy. If either is interrupted or shortened, the ideal potentials of our mental energy suffers.
If the task of Process C/the Active Pulse is to invest fresh mental energy into environmental information, what is the task of Process S/the Rest Pulse? We surmise that the mental energy of Attention is not completely consumed during consciousness. While Process S is dominant, we generate 0s. This means that no fresh mental energy enters our information digestion system. This gives us time to digest the mental energy that is leftover from the day.
In other words, the mental energy of Attention begins the information digestion process while we are conscious (Process C) and the leftover energy finishes the digestion process while we are asleep (Process S). These speculations are developed more fully in future articles.
The mathematical behavior of the Triple Pulse parallels Dement's universally accepted ‘opponent process’ model. Further, the underlying logic behind Living Algorithm mathematics provides a plausible explanation for this biological process that has mystified the scientific community. This essentially exact symmetry between the ‘opponent process’ model and the Triple Pulse model suggests some tantalizing possibilities.
Number strings that alternate periodically prevent 'stagnation' and maximize the 'vitality' of the Living Algorithm system. Further it is scientific 'fact' that the periodic alternation of sleep and consciousness maximizes our cognitive abilities, in the sense that sleep deprivation degrades our mental performance – 'sleep loss equals mind loss'.
The inference is clear. The periodic alternation of the biological Processes C and S could also refresh our cognitive system.
Of course, optimizing the working of our cognitive system provides an evolutionary advantage that furthers our chance of survival individually, and as a species.
Is it possible that the body employs a biological system based upon Living Algorithm's information digestion system? The evidence certainly points this way. Could our biological sleep system have evolved to prevent 'stagnation' and maximize the 'vitality' of our cognitive system? It is certainly conceivable that the periodic alteration of Processes C and S could maximize our mental vitality, hence our cognitive abilities. In other words, it seems plausible that Process S could have evolved to force the human organism to sleep in order to naturally replenish the awake cycle. A complete sleep cycle certainly refreshes our ability to think clearly, at least according to contemporary findings in cognitive science. The biology has asserted itself as a way of assisting the organism to do what is best for survival.
It seems apparent that Triple Pulse mathematics was a determining factor in the necessity for sleep to refresh consciousness. It seems equally plausible that the biological cycle of Process C and S evolved to take advantage of this process. However, this internal biology evolved under another force, as well – that of the 24-hour day and night cycle – the light-dark cycle of the Sun’s revolution about the Earth. (Thank you, Ptolemy.) It makes sense that these internal mechanisms would simultaneously adapt to the regularity of the 24 hours as well as the mathematical pulses. As such, it is not surprising that the C and S processes have a 24-hour cycle.
It seems that Triple Pulse mathematics may have been a driving force in the evolutionary formation of these bodily processes. However, these biological processes now have a life of their own and function independently. As an example, the urge for justice drives the creation of laws. But then the laws take precedence over justice, if merely for practical reasons. There are still consequences for violating mathematical principles (diminished mental performance), but the biological mechanisms become a force in their own right.
In summary, the theory behind the Triple Pulse model provides a plausible and powerful explanation for the necessity of the everyday occurrence of human sleep – previously a mystery. Further the human body has evolved a biological mechanism (the 'opponent process' model with battling C and S processes) seemingly based upon Triple Pulse mathematics. Note that the mechanism is so important that it encompasses an integrated system of ‘neurons, hormones, and various other chemicals’ that ‘engulfs every corner of the body’. This biological mechanism, which mirrors the mathematical processes of the Living Algorithm, could easily have evolved to maximize the potentials of consciousness – a tool that is required for survival.
This raises some interesting questions. Do Triple Pulse thresholds trigger the C and S processes? For instance, could internal biology initiate the C process and turn off the S process when the Active Pulse drops below a threshold? And vice versa, could this same internal biology also initiate the S process and turn off the C process when the Rest Pulse drops below a threshold? Or, is this alternation of processes instead triggered when the simpler Living Average has reached a practical maximum or minimum? In general, does the need to refresh consciousness with unconsciousness determine the threshold that catalyzes a change in the processes associated with the biology of sleep?
It seems that the behavior and underlying logic of Living Algorithm mathematics parallels and provides an plausible explanation for both the relationship between sleep deprivation and thinking (our testable cognitive abilities) and Dement's model for the biological of sleep. What are the implications of this intriguing synergy of mathematics, thought and biology? For a summary, consolidation and extensions of our findings regarding the Triple Pulse model and multiple sleep-related phenomena, check out the next article in the series – Triple Pulse System: a Mathematical Net for Cognitive Mysteries.
If you are interested in the Author’s process of discovery relative to this article, check out Moving in the Dark.
To see what Life thinks about this article, return to our metaphorical universe by following this link – Life amazed at growing web of compatibility.