12. Attention Capacity & Sleep Biology



The Physics of Attention is based upon a Math/Fact matrix. Prior articles exhibited some preliminary evidence that validated the matrix. Each new pattern of correspondence between the LA’s mathematical system and empirical evidence strengthens the web. The current article employs this network to begin developing the theory behind the physics.

The combination of evidence and explanatory power provide validation for a theory. The LA’s mathematical system links five experimentally verified phenomena under one roof. These phenomena remain cognitive mysteries. This article employs the underlying logic of the LA system to provide a plausible explanation for these five mysteries. A mathematical model has two advantages in this regard: 1) precise deductive logic and 2) universality, i.e. application of the same logic to seemingly unrelated phenomena.

One of the variables in the Physics of Attention is our Capacity for Attention, which determines cognitive performance. Our first four studies indicate that Data Stream Acceleration in the LA system corresponds with the Capacity for Attention.

In order to model the sleep/awake cycle, we chose a number string of 1s to model Conscious Attention and System C in Dement’s biology of sleep and number string of 0s to model Sleep, i.e. lack of Attention, and System S. The acceleration of this data stream of alternating number strings is the Triple Pulse. Tampering with the data stream in any way diminished the ideal potentials of the acceleration. Similarly tampering with the Sleep/Wake cycle diminishes our cognitive performance, which is a function of Attention Capacity. The inference is straightforward. Evolution chose to enforce this sleep/awake cycle with Dement’s alternation of Process C and S to enhance our all-important Capacity for Attention. 

We can also explain these correspondences in dynamical terms – the Physics of Attention's interaction with Information. Mathematically the alternation of number strings is the most powerful as it produces the most work. Each of the alternating number strings works to change the System’s state as indicated by the data stream’s velocity to its value. Our theory postulates that the work of Conscious Attention as enforced by Process C is to digest and assimilate new information that comes in the form of data streams. In complementary fashion, the work of Sleep as enforced by Process S is to complete the digestion process. The downtime enables the system to complete the integration process. Further leftover energy from the Conscious cycle powers the Sleep cycle. The mathematical logic of the LA system supports this interpretation.

Section Headings


Explanatory Power: Mathematical Advantages

Data Stream Acceleration & the Capacity for Attention

Attention Capacity applied to Sleep Biology

LA Model: Conscious Attention, Capacity for Attention

Maximizing our Capacity for Attention

Numerical Energy works to change Living Average to its Side

The Complementary Tasks of Process Sleep and Process Conscious

Play of Mathematical and Biological Forms

Answers inspire more Questions. .


The following 5 phenomena remain cognitive mysteries: 1) the harm of interruptions to a productive session, 2) the harm of sleep deprivation to cognitive performance, 3) the necessity of sleep, 4) the benefit of naps to cognitive performance, and 5) the biological systems that force us to sleep. The LA’s mathematical system links these experimentally verified phenomena under one roof. Could the underlying logic of the LA system provide explanatory power?

What is the current understanding regarding these 5 phenomena? The scientific community has conclusively established their existence. Four of these scientific factoids remain isolated mysteries. Only one (the biology of sleep) has a model – Dement’s opponent process model. Although the model describes the What of biological sleep, it does not even come close to touching the Why behind the mysterious process.

Dement's Military metaphor poor fit with sleep bio

Biologists typically employ the battling army metaphor to better understand the biology of sleep. The military metaphor breaks down almost immediately. The underlying logic of battling armies only bears a slight resemblance to Dement’s model. Armies, rarely if ever, relinquish the field upon vanquishing their opponent. As such, the logic of the military map provides a poor description of the territory.

Material metaphor poor fit with living behavior

Similarly the logic of material behavior is frequently mapped onto living behavior. These misguided attempts lead us in the wrong direction, as these maps do not accurately describe the territory. As such, these models provide little explanatory power – no why behind the what.

LA’s math logic better fit, hence more potential explanatory power

We hope to convince you that our mathematical model provides a better description of this territory. As such, the mapping of the LA’s mathematical logic onto biological logic provides the potential for greater explanatory power – a plausible why behind the what. To persuade you of the truth of these propositions, this article employs the mathematical logic of the LA system to provide a plausible explanation for our 5 phenomena.

Explanatory Power: Mathematical Advantages

Current article: Begins Development of Math/Fact Matrix

Before delving into our topic, let us take a step back to better understand the greater purpose of this book - the meta-perspective, as it were. As mentioned in the introduction, a Math/Fact matrix gave birth to our Theory of Attention. The express intent of this work is to both provide supporting evidence for this fertile matrix and to also begin developing its child – a comprehensive theory of Attention. Previous chapters focused upon exhibiting patterns of correspondence. The current chapter consolidates our findings to initiate theory development. To further bolster the crucial matrix, we also refine and extend its components.

2 sources of validation for Math/Fact Matrix: Correspondences & Explanatory power

Validation of the Math/Fact Matrix comes from at least two directions: 1) correspondences with living reality, of which we have seen several, and 2) explanatory power. The first establishes a connection between the mathematical system and empirical phenomena. The second employs the LA’s mathematical logic to attain a better understanding of the underlying causes of the phenomena.

Basis of explanatory power? Map describes territory

What is the basis of explanatory power? To facilitate understanding, we apply the logical structure of a metaphor that we understand to mysterious phenomena. The familiar is mapped onto the unfamiliar. The quality of the fit determines the potential for explanatory power. However, the fit between model and phenomena is never exact due to the metaphorical nature of the relationship.

All Models are Metaphorical Abstractions

Cognitive science has shown that the relationship between abstraction and reality is inherently metaphorical in nature. This is true of all theory, scientific or otherwise. Words, mathematics, and models are merely abstractions designed to describe empirical, experimental, and experiential reality. Rather than reality, these metaphorical abstractions are merely maps that assist us to navigate the territory.

Even math models metaphorical

The mathematical models of the hard sciences provide a nearly perfect fit with hard empirical data. Yet the relationship remains metaphorical in nature. The equations provide a map of reality, but are not reality.

Feynman Quote: Subatomics Mathematics: excellent fit: no explanatory power

Even the best match between model and data does not guarantee explanatory power. In his book QED, Richard Feynman, a demi-god of subatomic physics, states this position very clearly with regard to the Subatomic Realm. Although physicists have done an excellent job fitting a mathematical system with empirical data, Feynman suggests that they don't really know what's going on in the world of electrons and photons. For the scientific community, the mathematical fit is even more important than a theoretical model.

"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)

Dement’s model: excellent fit, but no explanatory power

Although physicists can accurately describe the data, they don’t understand why subatomics behave the way they do. In similar fashion, Dement’s opponent process model provides an excellent description of the data regarding the biology of sleep. However, the military metaphor provides little explanatory power. As such, biologists still seek a reason behind this mysterious process. Despite the excellent fit, they are still perplexed by the question: Why did evolutionary forces choose biological mechanisms that force us to sleep?

Model/Data fit does not guarantee causality

It is evident that even a perfect map does not guarantee an explanation. An exact correlation doesn't even prove that there is a 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.

Confounding Variable Info digestion a confounding variable?

There can always be a confounding variable that is not accounted for. Despite an exact correlation between milk use and heroin use, there could be psychological, environmental or even genetic factors that lead to addiction. Is it possible that the process of information digestion by living systems is a confounding variable regarding sleep-related phenomena? Is this why exclusively physical explanations provide very little understanding of the unconscious downtime that dominates our existence?

3) Does Model’s Underlying Logic provide Explanatory Power?

The final step towards scientific acceptance is when the underlying logic behind the model provides explanatory power for the empirical data. Even though Newton’s equations accurately described gravity, it took Einstein a few centuries to prove why they worked.  Even though Dement's 'opponent process' model fits the data, it doesn’t explain why it fits. In contrast, the LA’s mathematical system provides a cogent explanation, as we shall see.

Advantage of Mathematics: Underlying Logic is Crystal Clear.

Mathematical models, such as the LA’s, have a few advantages. First, 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.

Magic of Mathematics: Universality, logic links diverse phenomena

Another strength of mathematical models is universality. Mathematical patterns can be analyzed independently of empirical data to see what they reveal about the underlying nature of reality. The logic of a Math/Fact matrix can be extended to seemingly unrelated phenomena. This is the magic of the mathematical matrix.

LA Math links sleep biology + multitude of phenomena

For instance, 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). In the remainder of the article, we will illustrate how the same logic applies to each phenomenon. In contrast, Dement's 'opponent process' model, while effective, is limited to the biology of sleep.

Data Stream Acceleration & the Capacity for Attention

LA’s mathematical model links five mysteries, 4 cognitive and 1 biological. Is there some kind of causality behind the correspondences or are the linkages due to a confounding variable? Will the exact logical precision of mathematic provide explanatory power or will be just as confused as ever? Will the universality of mathematics link our five mysteries or will they remain isolated phenomena?

For stability: must identify and refine variables

A shaky foundation results in an unstable structure. In order to provide a firm foundation for our explanations, we must first clearly identify and refine our variables. With that end in mind, let us review some results.

Sleep Deprivation Study: Active Pulse associated with cognitive abilities

In our Sleep Deprivation Study, the relationship between the LA’s Active and Rest Pulses seems to correspond with the relationship between our testable cognitive performance and Sleep. When the Rest Pulse is interrupted or shortened, the subsequent Active Pulse loses size. Similarly, when Sleep is interrupted or shortened, our cognitive performance suffers. In other words, the Active Pulse’s loss in size parallels a loss in cognitive performance.

Does Active Pulse ≈ Cognitive Abilities?

What are the implications? Does this correspondence imply that the Active Pulse signifies our cognitive abilities?

Rather than variable, Cognitive Abilities relatively fixed, change slowly

Probably not. Rather than varying according to external circumstance, it seems more reasonable to assume 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. This neural structure changes relatively slowly. According to the findings of cognitive science, regular repetitions over time are required to reconfigure our neural networks.

Neural Networks/Cognitive Abilities: Stable

In other words, it takes a time investment to generate 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 over a lifetime.

Cognitive abilities: a constant, don’t change over night

Because of this relative stability, sleep loss on a night-to-night basis would not exert an appreciable effect upon our cognitive abilities. Depending upon circumstances, we might not be able access our mental talents as well, but they probably haven’t changed appreciably. In the daily context, it seems safe to assume that our cognitive abilities are a constant.

Cognitive Abilities = a Tool that requires Human

As such, our mental abilities are just the tool, not the agent. The carpenter's tools do not build a cabinet. Neither do our cognitive abilities solve a problem. Both types of tools, physical and mental, require a human to employ their capabilities.

Human must have both physical energy & mental Attention to effectively utilize tools

Further this human must have both sufficient physical energy and mental Attention for the task. The carpenter must have enough energy and focus to employ his hammer and saw in a constructive fashion. Similarly, we must have enough physical energy and mental focus to effectively utilize our cognitive tools.

Conscious Attention crucial component

It seems that Attention is required to effectively employ our physical and mental tools, i.e. the cognitive abilities embedded in our neural networks. In other words, Conscious Attention is an essential part of the tool utilizing equation. No matter how much energy we have, we can’t employ either type of tool, while we are sleeping, i.e. no Attention.

Conscious Attention = Constant: Cycle binary: On or off, 1 or 0

There is yet another consideration. Conscious Attention, as with our cognitive skills, seems to be relatively fixed. Although we might be a bit groggy upon waking, it seems that we are either awake or asleep – very little in-between. It even seems safe to characterize the sleep/wake cycle as a binary relationship. Consciousness is either on or off, either a 1 or 0.

Capacity for Attention = Variable

Despite the relative consistency of Consciousness, our ability to focus Attention seems to vary considerably. For instance, it is difficult to focus upon a boring lecture or a repetitive task. Conversely, a lively conversation or interesting work captures our Attention. Further, our focus even seems to exhibit a distinct pulse-like behavior, rising and falling over time. This phenomenon is so prevalent that it has a name – an Attention span. Finally sleep deprivation has negative impact upon our ability to focus, as witnessed by the decline in our cognitive performance. Let us call this variable our Capacity for Attention.

Why is Attention Capacity variable? What factors influence?

Why does our ability to focus vary so much? What factors influence our Capacity for Attention? For instance, why does a carpenter’s performance suffer if he has not slept much the night before? Why does ‘sleep loss equal mind loss’: as Dr. Medina states so succinctly? What is mind loss? Why does sleep loss correspond with a fall in our cognitive performance?

Lack of energy? Probably Not. Sleep-related phenomena unrelated to lack of energy

It is tempting to relate this mind loss to the lack of available energy. Because we are tired from a poor night’s sleep, we are unable to access our talents as readily. Yet none of the sleep-related phenomena that we have examined thus far have been connected with the lack of available energy. For instance, our brain activity during unconscious sleep and consciousness is relatively equivalent. Although our body rests while we sleep, our brain is not resting and is instead quite active. Due to the relative consistency of brain activity waking or sleeping, depleted physical energy does not seem to be the probable cause of diminished cognitive performance.

Compromised Attention compromises our ability to employ tools

However, unfocused or dispersed Attention is a possible candidate. Those with fragmented Attention are unable to employ time and tools as efficiently as those with focused Attention. For instance, an army that is led by a focused leader can exert a considerable harm upon its opponents, while the same army, if overcome by fear, can be routed, dispersed and then easily defeated by the same opponents. The power of concentrated Attention can be qualitatively different than dispersed Attention of the same size, e.g. a laser vs. sunlight on a cloudy day. It seems that if our capacity for Attention is compromised then this would certainly compromise our ability to employ tools.

Capacity for Attention compromised by variety of factors, unrelated to physical energy

Our capacity for Attention can be compromised by a variety of factors, including intoxication, emotional arousal, interruptions or even sleep deprivation. These factors are not necessarily related to physical energy. We might have plenty of physical energy when intoxicated, emotionally aroused, interrupted, or sleep deprived. Plus too much energy, as in the case of those with Attention deficit disorder, can also prevent us from concentrating our Attention. Yet when our capacity for Attention is compromised (unfocussed), we are unable to use our physical and mental tools as effectively.

Potential Physical factors for Intoxication & Emotions, not sleep deprivation

The negative impact of both intoxication and emotional arousal upon the focus of our Attention can be blamed upon confounding bio-chemicals, e.g. alcohol. This could also be true of interruptions and sleep deprivation. However scientists have yet to find these detrimental molecules. If the cause is not physical, what could it be? Is it possible that our capacity for Attention is influenced by the way we digest the information contained in data streams? The Theory of Attention based upon the LA’s Math/Fact matrix certainly affirms this position.

Positive Correlation between Attention Capacity & Cognitive Performance

Despite its variability, the Capacity for Attention is incredibly important for our existence. It seems reasonable to say that there is a positive correlation between our capacity for mental attention and our ability to employ our tools, physical or mental. More directly, Attention Capacity Up à Cognitive Performance Up; Attention Capacity Down à Cognitive Performance Down. In other words, maximizing our capacity for attention simultaneous maximizes our cognitive capabilities and vice versa.

Correspondence Applied to 4 Prior Studies

Let us see if this presumed correlation applies to our prior studies. 1) If interruptions compromise our capacity for attention, this could certainly exert a negative impact upon the ideal potentials of a creative session. 2 & 3) If sleep or naps somehow augment or even maximize our capacity for attention, this would certainly have a positive influence upon our cognitive performance. 4) If sleep interruptions or shortening diminish our capacity for attention, this would certainly diminish our cognitive performance.

Could LA’s Active Pulse model Attention Capacity?

In each of these four studies, the Active/Creative Pulse effectively models our Attention Capacity in these varying relationships with creative sessions and sleep. Rather than our fixed cognitive abilities (our mental toolkit), could the Active Pulse model our variable Capacity for Attention?

Generalizing: Data Stream Acceleration models Attention Capacity

Recall that the Active Pulse is the acceleration (the 2nd derivative) of a data stream composed of 1s. An uninterrupted Active Pulse indicates that our Attention Capacity is at a maximum. Tampering with this data stream diminishes the acceleration’s ideal dimensions, which indicates that our ideal focus is also compromised. Generalizing to data streams in general, let us entertain the possibility that the size of a data stream’s acceleration corresponds with the size of our Attention Capacity.

DS Acceleration up; Attention Capacity up; and vice versa.

Under this assumption, if a data stream’s acceleration flat-lines, our Attention Capacity should also vanish. Alternately, a lively acceleration should indicate a vibrant Attention Capacity. Data Stream Acceleration up; Attention Capacity up; and vice versa.

If correlation true, Evolutionary forces would choose to maximize Data Stream Acceleration

Attention is required to employ the tools, mental and physical, that maximize our chances of survival. As our Attention Capacity rises, so does our ability to employ any tool, whether physical or mental. Conversely, without sufficient mental focus, our cognitive abilities can't be utilized. If indeed data stream acceleration does indeed correspond with our capacity for Attention, it would seem that evolutionary forces would certainly choose biological systems that maximize DS acceleration. Could Dement’s biology of sleep be one of those systems?

Attention Capacity applied to Sleep Biology

Explanatory Power for Sleep Biology?

Does this hypothesized correlation provide any explanatory power for Dement’s opponent process model for the biology of sleep? To find out, let us describe the Living Algorithm's mathematical process alongside the biological C & S Processes associated with sleep. Are the parallels meaningless? Or does the underlying logic behind the mathematical process lead us to a deeper understanding of the mysterious relationship between the C & S processes?

Let term ‘Vitality’ refer to relative size of DS Acceleration & Attention Capacity

For convenience in communication in the following discussion, let us employ the term vitality in association with the size of both DS Acceleration and Attention Capacity. More specifically, a high vitality data stream system is one in which the DS Acceleration is lively, and a high vitality biological system is one in which the Capacity for Attention is high. Conversely a low vitality system, mathematical or biological, is one in which these components are inactive or small.

If the army of 1s (Process C) remains in control for too long, Attention Capacity vanishes. Vitality at a minimum

At the beginning of the LA’s 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 (the 1st derivative) and the acceleration (the 2nd derivative) stagnate. In terms of our supposition, our Attention Capacity should also vanish and with it our cognitive performance. At the moment of total victory, the vitality of both systems is at a minimum.

Number String of 0s (Process S) refreshes vitality

To refresh the ability to focus, the content of the data stream must change. Initiating a number string 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.

Alternating streams of 1s & 0s (Process C & S)  maximizes System's vitality.

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 periodic alternation of the '1' string and the '0' string (Process C and S) that refreshes the System's vitality, thereby avoiding stagnation.

Cooperation to maximize potentials – Not a war of destruction

It is evident that the purpose of utilizing alternating number strings (Processes C and S) could be viewed as maximizing our capacity for attention rather than defeating an ‘opponent’. To refresh the System's vitality, the stream of 1s and 0s (Processes C and S) alternate – a process reminiscent of the alternation of yin and yang. Rather than a war of destruction between 2 opposing forces, this process represents cooperation between two forces that is designed to prevent stagnation and maximize vitality.

Do Process Consciousness & Process Sleep alternate to maximize mental vitality?

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 – our capacity for Attention? The indications certainly point in this direction.

LA Model: Conscious Attention, Capacity for Attention

Let us review and cement our understanding.

String of 1s symbolizes Conscious Attention & generates the Pulse of Attention.

In our original study on interruptions to a productive session, the number string of 1s modeled 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 could also represent the Conscious Attention of our waking day. When Living Algorithm digests this same number string of 1s, the result is the Pulse of Attention, i.e. the Active Pulse, the data stream’s acceleration.

String of 0s models Sleep & generates the Rest Pulse.

In parallel fashion, we chose a number string of 0s to model our Sleep cycle, the state of no Attention. When it follows the number string of 1s, the number string of 0s generates the Rest Pulse, the acceleration of this portion of the data stream.

Alternation of String of 1s & 0s models Sleep/Awake cycle & generates Triple Pulse.

The alternation of these number strings of 1s and 0s models the Sleep/Awake cycle. According to LA mathematics, the acceleration of this data stream is the Triple Pulse, the alternation of the Active Pulse and Rest Pulse.

Active Pulse models Attention Capacity while Awake

While the number string of 1s represents the mental energy of Conscious Attention, the Active Pulse (the data stream’s acceleration) models our Capacity for Attention – our ability to concentrate/focus, but only during the awake cycle.

Rest Pulse models Absence of Attention Capacity while Asleep

In parallel fashion, the Rest Pulse models our lack of capacity for Attention during the Sleep cycle, when Process S dominates.

Triple Pulse models Attention Capacity during Sleep/Wake cycle

Taken together, the Triple Pulse models our capacity for Attention during the Sleep/Awake cycle, i.e. when Process S alternates with Process C.

Maximizing our Capacity for Attention

Capacity for Attention enables to utilize tools

I believe it is safe to say that virtually everyone would agree that our Capacity for Attention is a key component in the quality of our performance. Concentrated focus enables us to employ any of our tools, whether physical or mental, more effectively.

Attention Capacity correlated with Quality of Life

Besides the ability to effectively utilize tools, we suggest that this variable plays a significant role in determining the quality of life. Why? Our Attention Capacity is intimately related to our capacity for appreciating all that existence has to offer: The ability to focus is the root of inspiration, sex and ecstasy as well as the simple enjoyment of the sensual delights.

How can we maximize Attention Capacity?

How can we maximize our ability to focus our Attention – to concentrate? What does LA’s mathematical logic teach us about our Capacity for Attention?

DS Acceleration ≈ Capacity for Attention

Let us begin this exploration with one assumption: 1) Data stream acceleration is associated with our Capacity for Attention. With this assumption in mind, let us see what we can learn from the LA system.

Rather than biochemical, Mental Energy Efficiency maximizes Attention Capacity

Our studies indicate that how we employ our Attention determines our capacity for Attention. The efficient employment of the mental energy of Attention maximizes our ability to pay Attention and vice versa. Biophysical energy is certainly necessary for the bodily functions that support our mental capabilities. However, the real secret to our capacity to concentrate and focus does not lie in biochemical mechanisms, but rather in the efficient use of our mental energy.

Efficient Use of Attention maximizes Capacity for Attention

According to our suppositions, if Attention is maintained for too long, our Capacity for Attention stagnates. If Attention is not maintained for long enough due to interruptions, our Capacity for Attention does not reach its full potentials. (We explored these mathematical features in the Interruption and Sleep Necessity studies.)

To maximize our Capacity for Attention, we must sustain our focus for an ideal duration: not too long, not too short, but just right – the Goldilocks effect. From this perspective, the content of the data stream is secondary to the duration of our Attention.

Insufficient downtime also inhibits Pulse's ideal potentials

According to our model, there is one last feature that inhibits the ideal potentials of our Capacity for 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 Attention Capacity is diminished even if our Attention is not interrupted.

Duration of Downtime & Attention must be just right to maximize Mental Energy.

In other words, timing plays a huge role in determining the strength of the Attention Capacity that is required to take advantage of our cognitive abilities and maximize the quality of our lives. The duration of Attention and Downtime must be just right to maximize our Capacity for Attention. If either is interrupted or shortened, the ideal potentials of our mental focus suffers.

Not discounting nutrition, exercise & emotions, stressing efficient use of Attention

We are not discounting the importance of nutrition, exercise, and emotional regulation as factors that influence our ability to sustain focus. However, we suggest that the efficient use of Attention’s mental energy is of equal importance in promoting mental vitality. The factors that we have enumerated all play a part. These include the necessity of sustaining Attention for sufficient duration to maximize our capacity for Attention, the necessity of downtime to refresh this mental vitality, and the harm of interruptions. In general, we must aim for the balance point – not too long, not too short, instead just right – the Goldilocks effect.

Numerical Energy works to change Living Average to its Side

Info Dynamics applied to Sleep Biology

In the preceding discussion, we noted that the mathematical behavior of data stream acceleration in the LA system parallels our Capacity for Attention. We then employed this pattern of correspondence to provide a plausible explanation for Dement’s opponent process model. Let us examine this mysterious process from yet another perspective – the dynamics of information. Is it possible that the biology of sleep evolved to maximize our capacity for digesting and integrating information?

Application of DSD Constructs, work & power

We have made multiple references to LA’s mathematical system – Data Stream Dynamics (DS Dynamics). However we have yet to reveal her magic. Let us take advantage of this unique opportunity to provide a cursory introduction into the exquisite explanatory power of this dynamical system regarding the flow of information. By utilizing dynamical constructs such as work and power, we will be able to better understand the implicit logic underlying Dement’s model for the biology of sleep.

Number Strings of 1s and 0s as armies of workers, rather than battling soldiers

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 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.

Numbers are a Bundle of Information Energy that works to change the Living Average to their side.

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 point of victory, Work force of 1s has finished their job.

At the point of victory, the workforce of 1s 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 string, the data stream is doing no more work.

The longer a workforce has controlled the field; the more likely they have finished their task.

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 respective tasks.

What is Advantage?

What is the advantage of this courteous mathematical relationship? If our correspondences between the LA System and empirical reality are accurate, why would evolutionary forces choose this numerical strategy?

Number String Alternation maximizes Power of Info System

Periodic and regular alternation of number strings maximizes the amount of numerical work performed by the data stream. The work consists of changing the state of the LA System (the Living Average) from one number to another. As it performs the most concentrated work in the shortest amount time, alternating number strings is the most powerful type of data stream.

Random & Too Constant Least Powerful DS

In contrast, a random data stream performs very little work over the same period of time, and certainly no concentrated work. A number string that persists for too long ceases to perform any work at all. These types of data streams (random and over-extended) are the least powerful.

DS Power corresponds with Acceleration

The power of a data stream corresponds with its acceleration. When a number string continues for too long, the acceleration flat-lines at 0 – reminiscent of the vital signs of a moribund patient. In contrast, the regular alternation of data strings invigorates/maximizes the dimensions of the acceleration. In the LA’s mathematical system, the most powerful data streams are those that consist of alternating number strings.

The Complementary Tasks of Process Sleep and Process Conscious

Rather than battle, a cooperative relationship between 2 workforces.

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. This analysis, of course, raises new questions.

What are the complementary tasks?

What are these complementary tasks? Mathematically, it concerns the work of transforming the System’s value from one number to another. What does this mathematical process signify with regard to the sleep/wake cycle? What are the respective functions of Processes C and S if viewed under the light of our correspondences? Let us offer some preliminary suggestions in this regard.

Math: Alternation of Number Strings produces most work

We have represented Conscious Attention, when Process C is dominant, with a number string of 1s (on). Alternately, we have represented Sleep, i.e. lack of Attention, when Process S is dominant, with a number string of 0s (off). As mentioned, the alternation of number strings, in this case Consciousness (1) and Sleep (0), also Processes C & S, is the most powerful and efficient type of data stream in that it produces the most work.

Task of Attention’s Mental Energy?

According to our model, the fresh mental energy of Attention is only generated while we are conscious, i.e. when Process C is dominant. What is the Attention’s task?

Task of Attention, the mental energy generator, Process C: accumulate & assimilate Fresh Information.

Our Theory of Attention postulates that the function of the mental energy of Attention is to digest fresh environmental information. While Process C is dominant, we employ Attention’s mental energy to accumulate information that is relevant to the task of fulfilling potentials, e.g. survival. 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 Consciousness (the mental energy generator) is to digest and organize fresh environmental information.

Process C digests: Process S assimilates/integrates?

If the task of Consciousness is to digest information, what is the complementary task of the sleep cycle? Our theory postulates that the downtime of sleep is required to finish the information digestion cycle?

Complete shutdown of Process S required to finish information absorption cycle

Under this way of thinking, during the ascendancy of Process C, we convert (digest) the information contained in data streams into a more useful form, and simultaneously begin the absorption (integration) process. As long as we are taking in new information, we can’t complete the assimilation cycle. Our information system requires a complete shutdown to finish integrating the fresh information into our neural networks. Process S enforces this function, by turning off Attention – our information accumulator. During the ascendancy of Process S, we finish absorbing the information accumulated while we are awake.

Process S: no more mental energy 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, Attention's mental energy is ‘on’ while we are conscious, and ‘off’ when we are asleep.

Why couldn't Process Conscious continue forever?

Why couldn't Conscious continue forever? Why is Sleep necessary? Is a finite amount mental energy used up during awake time and requires the downtime of sleep for regeneration?

Common Sense: Replenish Mental Energy with Sleep

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.

Science & LA Math Model do not support this Common Sense

Although seemingly true, the current findings regarding sleep do not support this interpretation, nor does our mathematical model. While true regarding our physical energy, our brain is incredibly active while we sleep. This nighttime phenomenon continues to mystify the scientific community.

LA Mathematics: Maximizes ability to digest and integrate information

LA mathematics provides a plausible explanation. Rather than replenishing our mental energy, our mathematical model suggests that leftover mental energy from the day powers our cognitive processes while we sleep. Let’s examine the process in more detail.

Task of Process S to provide downtime to digest leftover mental energy

While Process S is dominant, Attention is off. This means that no more fresh mental energy enters our information digestion system. If Attention’s fresh mental energy enters the system during Process C, where does the energy that drives Process S come from? According to our mathematical model, the mental energy of Attention is not completely consumed during consciousness. This leftover mental energy from Process C drives Process S. In such a way, Process C and Process S are mutually interdependent processes, as shown in the following diagram.

Attention begins the Information Digestion Process; Sleep finishes it.

In other words, Attention’s mental energy begins digesting information while we are conscious (Process C). However, it can’t complete the process, and the leftover energy finishes the digestion process while we are asleep (Process S). These speculations are developed more fully in future articles.

Digestive System parallels Information System

Our Theory of Attention maintains that living systems require both food and information for nourishment. Further, Life has the two systems, one that digests food and one that digests info. These two systems have many parallels.

Two Processes: Digestion/Absorption & Necessity of Downtime to complete process

Just like our info system, our food digestive system consists of two processes – digestion and absorption. The biological system first digests food, i.e. breaks it into smaller, useable, parts. These tiny morsels are then absorbed to nourish the cells that make up our organism. The digestive system requires downtime to finish the absorption process, as does our information system.

Digestion System Logic ≈ Information System Logic ≈ LA Math ≈ Sleep Biology Logic

 It seems that the underlying logic of the digestive system is quite similar to the proposed underlying logic of our information system, which is similar to the logic of LA’s math system, which could reveal the underlying logic of the interaction between the C and S processes of Dement’s process model – the biology of sleep. The logical parallels are striking. Could these affinities between the diverse systems be another coincidence? Or could there be some causal mechanisms that link the systems?

Digestion System Logic ≈ Info System Logic ≈ LA Math ≈ Sleep Biology Logic

Play of Mathematical and Biological Forms

Exact parallel suggests Biological Forms mimic Mathematical Forms

Our mathematical model 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.

Could Biological Forms have evolved to take advantage of the Living Algorithm System?

Number strings that alternate periodically prevent 'stagnation' and maximize the 'vitality' of the Living Algorithm system. Further it is a 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'.

Periodic Alternation of Processes C & S refresh our cognitive system

The inference is clear. The periodic alternation of the biological Processes C and S could also refresh our cognitive system.

Optimizing Cognition provides Evolutionary Advantage

Of course, optimizing the working of our cognitive system provides an evolutionary advantage that furthers our chance of survival individually, and as a species.

It seems that our biological sleep system could 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 LA mathematics provides a plausible mechanism behind the necessity of sleep to refresh consciousness. It seems equally plausible that the biological cycle of Process C and S evolved to take advantage of this process. Is it possible that the body employs a biological system that evolved to take advantage of the Living Algorithm's information digestion system? The evidence certainly points this way.

Biology also adapts to earth's 24 hour revolution

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. 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 circadian cycle.

Although math-driven, Biological mechanisms take precedence

LA 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.

Triple Pulse: a plausible and powerful mathematical explanation for the biology of sleep

In summary, the theory behind the LA’s Math/Fact matrix 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 LA 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 LA’s mathematical processes, could easily have evolved to maximize the potentials of consciousness – a tool that maximizes the chances of survival.

Answers inspire more Questions

Implications of mix of math/cognition/biology?

It seems that the behavior and underlying logic of LA mathematics parallels and provides an plausible explanation for both the negative impact of sleep deprivation upon our testable cognitive abilities and Dement's model for biological sleep. What are the implications of this intriguing mix of mathematics, cognition and biology?

Link between DS Acceleration & Attention? Any More evidence?

While providing some insights into the underlying logic of our Math/Fact matrix regarding sleep-related phenomena, this discussion also raises new questions? Why is DS acceleration in LA’s system associated with our capacity for Attention? Could it be that Attention is attracted to acceleration? Does the mathematical logic of the system provide any insight? Is there any other evidence that indicates the truth of our propositions? Ensuing articles illustrate that the internal logic of the LA’s mathematical system (DSD) is similar to the internal logic of both psychology’s 10-minute rule and Dr. Medina’s award-winning core-concept teaching method. Read on for details.


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