8. The Triple Pulse &
the Importance of Naps


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Tantalizing Questions

The Triple Pulse and naps? Naps are a curious phenomenon. Why sleep in the middle of a productive day? Why waste precious awake time in a state that is akin to death? The importance of naps? Could that oblivion, which only seems appropriate to the middle of the night, have anything to do with the quality and quantity of a work session? What could the Living Algorithm's Triple Pulse (a mathematical model) possibly have to say about naps (a behavioral reality)?

The Living Algorithm’s mathematical behavior mimics Human Behavior regarding Sleep & Interruptions.

Thus far in our investigation, the Living Algorithm’s mathematical system has exhibited remarkable patterns of correspondence with 3 significant aspects of human behavior – 1) the effects of interruptions on a productive session, 2) the effects of sleep deprivation on cognitive abilities, and 3) the necessity of sleep. In other words, the behavior of the Living Algorithm’s primary transformations, the Pulse of Attention and the Triple Pulse, mimic human behavior.

Cognitive Abilities and Sleep linked with the Living Algorithm’s Active and Rest Pulses.

If the linkages between this mathematical behavior and cognitive behavior have any validity, then the Living Algorithm’s Active Pulse of 1s is linked with our cognitive abilities; and the Rest Pulse of 0s is associated with sleeping. The empirical evidence in support of these corresponding patterns is suggestive, rather than definitive. But, the experimental findings tend to be very encouraging and do not contradict these perceived relationships.

What does Living Algorithm Mathematics say about Naps?

We will now investigate a related area of correspondence: the relationship between the experimental evidence regarding naps and the Living Algorithm’s Triple Pulse. Will the experimental evidence dispel these presumed connections between the behavior of the Living Algorithm System and cognitive behavior? Will contradictory facts emerge? Or will the facts further confirm the links between the Living Algorithm’s mathematical reality and our cognitive reality?

Triple Pulse Model: Elasticity of Time Increments

This article begins by developing the mathematical facts behind the Living Algorithm’s Triple Pulse. We then explore the experimental evidence regarding naps. The article concludes by examining the parallels between these two disparate methods. Let's begin the discussion by revisiting our mathematical model.

Triple Pulse: Elasticity of Time

In prior articles we explored the patterns of correspondence between the Triple Pulse mathematical model and our cognitive behavior. We believe that the Triple Pulse model can be applied to an even wider range of cognitive behaviors. This wide-ranging applicability is due to the mathematical model’s flexibility regarding the relative measures of time. As we shall see, in our model time is elastic.

Relativity of Session Duration

Let's discuss the relativity of time increments regarding the mathematical model. Thus far in our investigation of the correspondences between our mathematical model and behavior, we’ve been talking in terms of minutes and hours. The mathematics does not depend upon any particular measure of time. The particular measure of time is dependent upon the behavioral reality under investigation. Our mathematical formula is an abstraction that, because of its relativity, can be applied to any data stream of interest. The relevant point here is that the abstract mathematics possesses a flexibility that allows it to digest data from any number of time-related scenarios.

The Pulse of Attention can be associated with any time duration.

In the initial experiment we imagined the Pulse of Attention to be a 2-hour productive session that was divided into 'one-minute' intervals. In the second experiment we imagined the Triple Pulse to be 3 eight-hour pulses, each divided into 'four-minute' intervals. These time designations are applied in an elastic manner. For instance, the '5-minute' interruptions in the Attention Pulse were relative to a '2 hour' session. If the session is '8 hours' long, these '5-minute' intervals are stretched to become '20-minute' intervals. In a similar manner, the Pulse of Attention need not be measured exclusively in terms of hours. The Pulse might be much longer, or could be as little as 10 minutes, or even shorter. These time increments are elastic in the sense that they are based entirely upon the behavior that the mathematics is intended to model.

Due to time flexibility, Triple Pulse behavior applies to both Naps & Night Sleep.

Thus Triple Pulse mathematics could easily apply to much shorter sleep cycles. The relative behavior of the model remains the same no matter which behavior is modeled. Regardless of the time frame we use, a Rest Pulse is essential to renew the ideal potentials of the subsequent Active Pulse. Accordingly, the conclusions regarding the necessity of sleep could be applied almost straight across the board to naps. Will scientific analysis and testing empirically validate patterns of correspondence between the Triple Pulse and naps?

Prior Results

Uninterrupted 1s: No Breaks

The Triple Pulse mathematics is straightforward. An Active Pulse of 1s fades out naturally and permanently, unless it is refreshed by a Rest Pulse of 0s. The graphs at the right illustrate this innate feature of the Triple Pulse. An uninterrupted sequence of 360 1s generates the top graph. The Active Pulse fades out naturally and permanently even though the data stream of 1s continue. Without a break of 0s in the data stream, the pulse 'disappears'. With a break of 0s the pulse reappears naturally. The bottom graph is the ideal Triple Pulse – a visual illustration of this mathematical mechanism. Instead of 360 1s, an alternating sequence of 120 1s, 120 0s, and 120 1s generates the three pulses. Mathematically, a Rest Pulse of 0s is necessary to refresh the Active Pulse.

Triple Pulse prediction: Naps should refresh cognitive abilities and performance.

In the previous study we associated the Active Pulse with being awake. We could also associate this same Active Pulse with a 2-hour work session that begins our day. Instead of being associated with our sleep cycle, the Rest Pulse could be associated with a short catnap. Is it possible, that a catnap could refresh our ability to think clearly just as well as a good night’s sleep? Could a nap refresh our ability to work, just as sleep refreshes our ability to think? If naps correspond with the Triple Pulse, the prediction is clear. Naps should enhance our mental performance, just as completely as does our nighttime slumber.

Experimental Facts regarding Naps

To test this Triple Pulse prediction, let’s explore the current scientific understanding regarding naps.

21st century science: Naps improve performance

Experimental results are very clear about the advantage of naps. We again rely on Dr. Medina brain rules:

"At first, scientists didn't believe that the nap zone existed except as an artifact of sleep deprivation. That has changed. … We know it is not related to a big lunch …. It appears, rather, to be a part of our evolutionary history. Some scientists think that a long sleep at night and a short nap during midday represent human sleep behavior at its most natural. … One NASA study showed that a 26-minute nap improved a pilot's performance by more than 34 percent. Another study showed that a 45-minute nap produced a similar boost in cognitive performance lasting more than six hours. Still other researchers demonstrated that a 30-minute nap taken prior to staying up all night can prevent a significant loss of performance during that night." (brain rules, pp 159-160)

It is evident that naps are not required due to sleep deprivation or even to digest a big lunch. It is equally evident that naps enhance mental performance. If naps do indeed augment our cognitive abilities, it seems evident why naps would be "part of our evolutionary history". We hypothesize that our ancestors, who had a natural inclination to nap, were rewarded with enhanced mental potentials. In this sense, naps provide an evolutionary advantage in the area of cognitive abilities.

Why do Naps enhance Cognitive Performance?

Although studies indicate the power of naps to refresh our cognition, they don’t answer the question of why naps perform this important function. How does science explain this unusual phenomenon? Recall that science has no idea why we must sleep, nor why sleep deprivation has a negative impact on mental performance. They are equally perplexed about the importance of naps.

Science's tentative explanation for naps.

Dr. Medina proposes a theory held by some scientists. It has to do with the 'opponent process' model of biological sleep developed by William Dement. (We will elaborate on this model in much more detail in an ensuing article called the Triple Pulse & Biological Sleep.) According to Dement’s model, there are two opposing biological armies involved in the tension between sleep and activity. These forces reach a stalemate in the afternoon. They hypothesize that this state leads towards exhaustion. It presumably requires a greater amount of energy to balance these opposing forces as the tension grows.

Incomplete Scientific Understanding

Although this model could have something to do with why we take afternoon naps, it certainly doesn't explain why naptime has a positive influence on cognitive performance. Clearly, the current scientific understanding regarding the beneficial nature of naps remains incomplete. With the current scientific understanding of naps in perspective, let's revisit our earlier analysis regarding the Triple Pulse's theoretical prediction concerning naps.

Experiments validate Triple Pulse correspondence w/Naps

The above-cited experimental evidence clearly corresponds with our prediction based upon Triple Pulse mathematics: naps should improve cognitive ability. The model suggests that naps and sleep improve mental performance because they conform to the same pattern. The break in thinking provided by naps and sleep somehow refreshes our ability to think, which improves our testable cognitive performance. Of course, any improvement in cognitive abilities provides an evolutionary advantage.

Could Naps/Sleep provide the downtime required to digest Information?

Experimental results: Naps clear short-term memory storage for more information

The above-cited experimental findings clearly suggest that naps improve our cognitive abilities. Recent scientific evidence confirms Dr. Medina’s statements and sheds further light on the importance of naps. The AARP Bulletin January-February 2013 states:

“A midafternoon nap can help improve mood, memory, alertness and learning – and it won’t interfere with your nighttime zzz’s, according to New York’s Weill Cornell Medical Center.” (pp. 12)

The AARP Bulletin goes on to provide scientific evidence that the effectiveness of naps can be observed in a variety of time frames:

“Naps come in different lengths. Researchers at the University of California, Berkeley, find that a 90-minute siesta clears the brain’s short-term memory storage center and makes room for new information. Snoozing for 20 minutes improves alertness and performance without leaving you feeling groggy. … Even a six-minute micro-nap may help improve memory according to a German study.” (pp. 12-14)

The scientific evidence is instructive. Naps of whatever duration are incredibly effective at boosting our cognitive performance in a variety of areas. The reasons for these empirical results, however, continue to be unclear. In other words, why do naps boost cognitive performance? What exactly is the mind up to during a nap?

Implication: Opportunity to clear short-term memory storage

The Berkeley researchers, mentioned above, suggested that a 90-minute nap  “clears the brain’s short-term memory storage center and makes room for new information.” The immediate implication of this interpretation is clear. The human brain has a limited amount of short-term memory storage. The downtime of a nap provides our neural networks with an opportunity to clear this storage center and make way for new material. This raises a significant question. What does ‘clearing the brain’s short-term memory storage center’ mean?

Is clearing memory storage the same as digesting residual information?

Clearly some organizational system must be at work here. Either the brain discards short-term memories like a computer empties the trash, or the brain somehow organizes and stores this information. Could the nature of this organizing process be akin to the digestive process? Does the brain integrate information the way the body integrates sustenance?

Does sleep provide an opportunity to integrate information?

The stomach needs a break between meals to completely digest the food that has been ingested. Could a backlog of undigested or partially digested information accumulate while we are conscious? Is the nap an opportunity for the mental integration of the recently ingested data stream? If so, doesn’t it seem probable that the nap’s close relative, nighttime slumber, similarly provides such an opportunity?

Why do humans need down-time to clear short-term memory storage?

Why does our brain need some downtime to digest the constant flow of environmental information that occurs while we are awake? Could our brain require a break from consciousness to digest this residue of information? Is it possible that the unconscious state of sleep, whether a six-minute catnap or a full 8 hours of slumber, provides this opportunity?

Reasons for downtime not found in continuous processing of a computer

The empirical data suggests that the reason(s) for this significant behavior cannot be found in our contemporary understanding of the functioning of the electronic computer. The human mind may be a flurry of electrical activity, but it does not behave like any electronic system that we know of. The Living Algorithm’s information digestion model is distinctly different from electronic information processing. Computers don’t need downtime to process information. Our digital machines can operate all day and night without missing a beat.

Evidence indicates that the Brain requires downtime.

If our brains process information in an electronic fashion, we should not require the downtime of sleep to refresh our cognitive abilities. All the experimental evidence suggests otherwise. It appears that the unique organization of electrical activity in the brain cannot be continuous, but requires downtime.

Summary, Questions & Links

Triple Pulse behavior mimics human behavior regarding Naps.

Experimental evidence supports the importance of naps in refreshing human cognition. These results are reflected in the behavior patterns of the Living Algorithm’s Triple Pulse. What was the intriguing chain of reasoning that led to that conclusion?

Logical Chain linking Triple Pulse & the Importance of Naps

In our initial investigations, we explored the patterns of correspondence between the Living Algorithm’s Triple Pulse and the regular nighttime slumber that humans require. Our cognitive behavior regarding sleep deprivation, as demonstrated by empirical evidence, closely corresponds with the behavior of the Triple Pulse’s mathematical model. In a closer examination of the mathematics of the model, we saw that the measures of time are relative, and therefore elastic.

We applied this new understanding of the Triple Pulse’s increased flexibility regarding time increments to naps. We inferred that naps should increase mental performance, as does nighttime slumber. If the correspondences continue to hold, the midday 'rest' cycle should refresh our cognitive abilities. Experimental evidence verified this prediction. The scientific literature is clear. Naps improve cognitive performance. The mathematical behavior of the Living Algorithm’s Triple Pulse again dovetails with experimental findings regarding human behavior.

Could a Rest Pulse refresh our ability to think?

These results raise more tantalizing questions – of course. Could the Living Algorithm’s Active Pulse really be associated with our cognitive abilities? Could the Rest Pulse be associated with sleep and naps? Experimental correspondences suggest that this is so. We are further encouraged by the fact that no contradictory evidence has arisen as of yet. The Living Algorithm’s mathematics indicates that the Rest Pulse is necessary to refresh the Active Pulse. The implication is clear. The unconscious state, associated with sleep of any duration, refreshes our ability to think. The result is improved cognitive performance.

Could sleep provide time to digest information?

Why is this so? The Sleep Necessity article exhibited that sleep has nothing to do with resting our brain. The neural networks associated with cognition are, in fact, particularly active during sleep. What is the nature of this refreshment that sleep seems to provide for consciousness? Could it be that our subconscious takes that time to digest information that our brain has ingested while we are awake? Is it possible that our mind needs time to organize data, and perhaps file it in its proper place(s)? Could sleep provide the essential downtime for the subconscious to complete a mathematical digestion process? Could the Living Algorithm’s mathematical behavior enable this digestion process to unfold?

Tantalizing Questions regarding nature of intriguing Correspondences

Thus far, the mathematical behavior of the Living Algorithm’s Triple Pulse parallels human behavior in 3 different ways: Sleep Deprivation, Sleep Necessity, and Naps. Further, the scientific community has experimentally verified a relationship between sleep and our cognitive abilities in each of these 3 phenomena.

Are these intriguing correspondences between human behavior and the behavior of the Living Algorithm’s Triple Pulse just a growing string of coincidences – some kind of bizarre statistical anomaly? Have our perceptions been tricked again by another set of experiments that seem to point to a connection between pure mathematics and behavioral reality? If there is a connection, is the nature of the correspondence a cause-effect correlation? If there is a causal connection, could it be based upon the mathematical nature of the way we digest information?

Link to more Evidence

To begin to address these questions, we must gather more evidence. An earlier article on the necessity of sleep evoked a question that has yet to be addressed. Namely, why is there so much brain activity during sleep? Does the Living Algorithm System reveal anything about this counter intuitive phenomenon? If so, what? To find out, read the next article in the series – Liminals & the Subconscious.

To better assimilate this unusual information, we recommend reading our allegorical perspective – Life & Living Algorithm agree on the Importance of Naps.

For the Author’s relationship to naps, check out Naps: Personal History.

For the logical sequence behind this article, read Naps: Logic.


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