How you use your attention in waking life has definite effects in your dreaming life.  The following is my distillation of some insights from anthroposophy in this regard, which I offer as one way of looking at this phenomenon, specifically around the issue of video games and dreaming.  This post should provide an appropriate background if necessary.

If people are comfortable with the terms, we can talk about how the astral body (the subtle body that allows something outside to become something for us inwardly; i.e. the sense-body, which we share with animals) gains its content in large part by reflecting itself off of the etheric body (the less subtle body that keeps your body from becoming a corpse, which we share with the plant realm).

When you spend hours of time focusing your senses on particular stimuli (i.e. a video game) your are patterning your etheric body through physiological repetitions: the movements of your eyes, hands, breathing, etc., and more importantly in the endocrine responses and other physiological changes that go along with the particular game experience.  Knowing why this is important needs a little background first.

When you go to sleep, and you are no longer imposing your astral body on your etheric (i.e. choosing where to direct your attention and what sensations you will seek and avoid) your etheric body starts to “digest” all this activity that happened during the day.  This digestion is like a reverse-engineering, it is a sort of inversion of the processes that occurred during the day because of what you did while you were awake.

From this perspective, what sleeping is has to do with the way the astral body (along with the “I” or “ego) detach from the physical and etheric bodies (although not completely, which is what death is).  Dreaming occurs when the astral and ego dip back into the etheric a little, but not all the way back into the physical (in which case you wake up).

Because the content of the astral body is primarily supplied by reflecting itself off of the activity of the etheric body, what the etheric body is doing changes what becomes available as sensations for the astral body.  This is true all of the time, but there is a difference in this relation when awake and when asleep, and when dreaming (and also lucid dreaming) as well.

In waking life the etheric and physical bodies are directed, even “used” (or used up!) by the astral and ego, and the close links between these two groups means that almost all sensations (via the astral body, directed more or less by the ego) are directly linked to purely physical events or etheric processes (hunger, elimination, and so forth are the most obvious).

But when sleeping the astral and ego are no longer directing the show back in the physical and etheric bodies; the etheric body is free to do its work of getting everything ready for the next day (repairing tissues, cleaning the blood, glycolosis in the liver, etc.).  The wisdom of the physical and etheric bodies is such that a lot of this building-up activity happens earlier in the night.  This can be seen as an esoteric “reason” for why non-REM sleep is greater earlier in the night and REM sleep increases later.

The point is that how you structure your attention during the day (and what activities you therefore engage your etheric body in) has definite effects during sleep.  Much of the effects can be dealt with by your etheric body in non-REM sleep, but it can’t do it all in one sleep cycle, so when your astral body and ego dip back down into the etheric body (resulting in a dream), and the astral body uses the etheric body to reflect itself to the ego (for conscious experience), whatever the etheric body is doing at the time changes (to continue the metaphor) the shape of the mirror, which modifies the reflected image of the astral body to the ego.  In other words, some dreams (most, actually) are the kind where the astral body is having to deal with what is leftover in the breaking down of patterns that got imprinted on the etheric body during the day.  You literally then “dream your body-processes”.

But your astral body is a sense-making body; it builds sensory images, or what is poorly referred to in cognitive science as “representations” (it is way more than representing; it is creating, synthesizing, organizing, filtering, elevating, discarding…).  So when your astral body dips into the etheric and uses it to “see” itself, it forms sensations (in the dream) out of the etheric activity that is going on at that time.  Basically your astral body gets to peek in on the activity of the etheric body and turn it into imagery.  This is why it can be really hard to predict what dream images actually form on the basis of day-waking activity.  The more structured and repetitive the attention in daily life, the more likely the dream imagery will be a working through (a digestion) of this activity, a dismantling of it, a “dealing with” it.  The term “images” means visual images, yes, but is also much wider in scope: sensory images can include all senses, it is also the feeling of what an experience is “like”.

The astral body has its own patterns (protocols for avoidance of and seeking for particular sensations cascades).  And it will generate imagery that is derivative of the day-waking sensation patterns.  If the astral body meets the etheric body, which is digesting the patterns associated with playing a video game in waking life, the astral body is more likely to generate sensory images in the dream that fit that activity, and this MAY take the form of actual game imagery, but may not.  The root is not the image itself but the activity upon which it rests in the etheric body; many possible images can be formed when the astral body meets the etheric in a dream (this is why any book that claims to be able to interpret your dreams by telling you what each symbol means is likely false; this is, however, an issue that needs a separate discussion).

The upshot of all this is that you can utilize the relationship between the physical, etheric, astral, and ego bodies in skillful ways.  To begin with you can simply see for yourself how structuring your attention in the day can change your dream life.  In more extreme cases you can even see the effects of this _before_ sleep onset.  If you play a game for three hours just before bed, then when you get into bed you will likely find that as soon as you relax the conscious focusing your attention, game imagery will fill your mind without your bidding.  You may even find it very difficult to NOT experience the continuation of game imagery as you are lying in bed, trying to fall asleep.  Whereas normally you may be able to direct your attention in a focused way to this and then that idea or sensation, now you have to spend all that effort just to not experience game imagery, and it creeps back in as soon as you relax your attention at all.  You have created a pattern in your etheric and astral bodies that continues without any effort now on your part; now you have to “deal with” the consequences of this patterning.  This is important because there is a whole lot of other things that could occupy your attention, but they are literally drowned out by the large amplitude of the patterns in the etheric and astral.  All that is subtle (other aspects of your day that might present opportunities for deeper reflection) still takes place, but you don’t notice it anymore.  You have to work through the biggest and most obvious stuff first, and because you just sat down for three hours of really focused time, concentrating on a game, you essentially have told your etheric and astral bodies that this must be super-important!

These effects continue during sleep, but the difference here is that what can potentially occur during sleep is even more subtle than what happens during the day when sensations are linked so strongly to whatever the physical body is doing.  This is where the “spiritual” realms come to the fore, and THIS is what makes a difference for people interested in spiritual development, and who also happen to play games (I am one of these people — Skyrim, oh, Skyrim!).  A real tension is set up between being able to utilize sleep as a sacred space for spiritual work and the day-waking desire for fun and escape.

But recognizing this means that we can take steps to be wiser about how we structure our attention, rather than simply letting the physical world and your etheric needs lead our attention around, so that our astral body and ego spend all their time reacting and playing catch-up with the world.  Meditation is the archetypal training for this, and is superior to video games by orders of magnitude in the sense of its ability to create a free capacity for directed attention.  We can sensitize ourselves to the effects of the habits we have around structured attention in the day by monitoring our dream life, which then is like a tableau upon which our spiritual work of the day gets played out in sensory images.  Recognizing this link opens the door to more subtle and complex and transpersonal use of dreams and sleep life, which can be of great use for those on a path of self-development.

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In aesthetic epistemology, notions of “reality” are replaced by “patterns in process.”  ”Things” are (ontologically) patterned processes.  We mistake the nature of the universe when we presume that “things,” to be, must “be” from the bottom up: on the basis of some “substance,” which THEN interacts in processes to yield what we experience (the first coherent expression of this began with the atoms in the void hypothesis of Leucippus and Democritus in Ancient Greece).  We assume that it is silly to speak of patterns of process without some kind of “thing” that we can point to as an indicator that the process is proceeding.  Because of the way our senses are involved in cognition, we tend to count as “real” only what can be made apparent to us through our senses (or their extensions via instruments). This is a huge presumption on our part.  What if we tried to conceive of “substance” as a secondary phenomenon?  What if process (thing-less process) is more primary?  In this view, things are precipitates (momentary nodes, relatively ‘still’ areas of patterned processes) of higher-order relations… not relations between THINGS but relations qua the activity of relating.  This may sound abstract, but this is because we are trained to think of reality in terms of substances (sub-stances: the “underneath-standings,” the bits from out of which a universe gets built).

The best example of one way that this can look is given in the field of mathematics.  Mathematics has no atoms, not even metaphorical atoms; it is entirely substanceless.  Rather, mathematics has, at its base, processes and their relations.  Even numbers aren’t the basis of mathematics, where numbers would form the “things” that various logical operations “apply to.”  Rather, the numbers themselves fall out of, are like precipitates out of, the field of logical relations themselves.  The drama around this showed up millennia ago in the Pythagorean school.  The Pythagoreans thought that the primal ground of the universe was number (specifically, whole numbers and their ratios). All being owed itself to number, which formed the ontological core of the universe.  But they quickly ran into something that seemed to defy their understanding of what was meant by the very concept of number in the relationship between the diagonal of a square and its side.  Indeed, the (possibly apocryphal) story is that Hippasus of Metapontum, a Pythagorean, when he announced to his fellows on a boat ride of his discovery that the ratio of a side of a square to its diagonal was incommensurable, was thrown overboard and drowned in order to try to keep this information from spreading.

Today we have a shorthand for this concept: we say that if the length of the side of the square is unit in length, then the length of the diagonal has a length of the square root of .  But in this shorthand we gloss over some very profound potential insights.  First of all, we must note that the “number” is formed by a ratio between the sides of a square and the diagonal.  It is more correct to say that  ”is” a process rather than a number.  This is embedded in the very form of the number itself: it is irrational, meaning that is it literally incalculable.  The number requires an infinite number of digits to express, and there is no ratio of whole numbers that yields the number.  For this reason we create a shorthand to indicate the process of this ratio: the square root sign.  But we get lulled by this sign into treating the process as a still fact, a “bit” to be used in calculation.  This is, of course, very helpful, because it allows us to work at a more abstract level with the process of the  relation; we literally abstract (draw out) the symbol from the process in order to use it, but in doing so often forget all the activity that is embedded in the symbol.

The important thing to note is that it is not only square roots which are at their root processes; ALL numbers are like this.  To say it directly: all numbers are becomings, patterns of relations. All the arbitrary symbols that designate numbers are a short-hand by which these processes can be “fixed” and thus more easily manipulated.  Even the number “” is short for an ongoingness, a never-ending process, expressed in decimals as the infinite number of zeros that follow the decimal point: . Mathematicians are the people who have chosen as their profession the re-enlivening of the fixed symbols back into their process-nature, so that they can form new, free, creative relations with other relations, which can then be symbolized and fixed into new symbols that can be of use in calculation, closing the circle.

Why is this all important?  It shows an example of how it is possible to think relationally in an exact way.  One of the big fears of moving away from a substance ontology is the feeling that without some kind of static anchor, we lose predictability, control, precision, and clarity.  If approached wisely, a process reality need not result in any such occurrences.  Indeed, just the opposite is true: embracing patterns of processes as the deepest ontological level of the universe can yield far greater precision and clarity — but it is a precision and clarity that can only be had by doing the hard work of training or attention to move in resonance with the patterns that make up the “things” of the world.  We always fail at this, and at some point we give up and “fix” a process with the use of a symbol.  The symbol thus represents the cessation of the process.  But just as we have the capacity to form symbols, so too we have the capacity to render what became abstracted and fixed (through our activity!) back towards its process-nature.  What has precipitated can be dissolved.  We can both fix and render back into solution.

Together these two tendencies form a basic polarity, a pattern, that describes the unfolding of other patterns; it is a meta-pattern.  It illuminates how other processes happen.  The symbolizing, fixing, cessation pole can be archetypally described as centric, while the re-enlivening, dissolving, rendering back into motion of the complementary pole is archetypally peripheral.  This polarity forms a sort of primal archetypal recursive unity.  The universe can be thought of as the play of this polarity in all its endlessness; the continual unfolding of the tension between centers and peripheries, at all levels.  There are no true “things” here, only relations between patterns in process.

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Abstract

This essay outlines connections between the Elemental Cycle as an archetype of transformation, transdisciplinarity, and  cybernetics.  A number of questions are addressed: the nature and importance of connecting these fields, an examination of resources and the dominant disciplinary discourses for the associated fields, and a critical examination of my assumptions, beliefs, and position.

Introduction

How often do we find ourselves in a position of not being able to see something unless it is first pointed out to us?  This happens all the time with the visual and other physical senses, but of course also occurs in our thinking; certain concepts seem to hide in plain sight, and unless we are cued into where and how to look for (or to think about) them, they slide on by as a part of the undifferentiated background of conceptual life.  Usually we are introduced to these sorts of concepts just like we are to new people, through a third party who is already familiar with each of us: “Seth, I’d like you to meet Recursion; Recursion, this is Seth.”  Often with this sort of introduction comes an experience: “Oh hello Recursion!  You know, I feel like you must hang out at some of the same coffee-shops as I do, but we’ve never been formally introduced.”  And so a relationship begins with a concept, and just as with human beings, you can become more intimate and familiar, get into fights, seek new levels of understanding, and go on adventures.

I was introduced to the Elemental Cycle over 10 years ago: an archetypal pattern of the process of transformation, situated in the four alchemical elements of Earth, Water, Air, and Fire, and we have been journeying together ever since.  This pattern seemed like the kind of concept (although archetypes are much more than merely conceptual) that Goethe called an “open secret”—invisible to cursory examination, but completely out in the open and obvious once you know how to recognize it, and have some familiarity with its style.

Phrased more simply, the Elemental Cycle concerns how transformation occurs.  What I’m interested in is the extent to which there are lawful patterns that describe how transformation really happens in the world, both in personal experience of one’s own transformation and as a way of describing more ‘objective’ processes that do not explicitly have to do with humans.  Are there patterns to transformation, or does transformation occur through a wide variety of processes which have little or no relationship to each other?  How do we know that transformation is occurring, or has occurred?

My feeling about this can be made clear through a metaphor.  There are many paths up a mountain, and if you ask each person to describe the specific details that they observed on their way, you’ll get a unique description from each person.  This is complicated by the fact that even if two people travel the very same path, they will likely pay attention to different features and give diverse accounts.  Nevertheless, with some probing you can find certain aspects which begin to coincide and link from story to story; for example, the fact that no matter what path you take, an overall directionality is apparent: from low to high elevation.  Other patterns exist, but this serves to illustrate the point that even though “transformation” can happen in an extremely wide variety of contexts and through a number of seemingly diverse processes, it is my understanding that certain patterns continually inform how transformation unfolds.  In particular, my research has brought me to an understanding of some of these patterns, which, borrowing from the language and tradition of alchemy (where everything is about transformation) I call Earth, Water, Air and Fire.  These four elements are manifestations of the archetype of the pattern of transformation.  Each element describes one qualitative stage of the process through which any transforming situation unfolds, and they fit together in a cycle (or rather, a vortex, which is always a spiral), moving from an initial (often unconscious) Fire, onwards to Earth to Water to Air, then to Fire again, and back to what we could call a New Earth.  The details of each elemental stage and the building up of the underlying theory constituted the subject of my master’s thesis.

Future inquiry needs to explore more fully the application of this archetypal metaphor to human transformation.  Central to this inquiry is simply the desire to become more familiar and fluent with how the pattern works, where it works (and where it doesn’t), and the extent to which consciousness of the pattern can be of practical help in regards to work that attempts to bring about, make efficient, or to simply understand transformative processes.  The Elemental Cycle has clear potential applications in therapy, counseling, spiritual practice, dialogue and communication, planning, management, education, personal growth, and scientific realms; as an archetype it necessarily crosses boundaries such as these with ease.  The linking factors between all these areas are processes in human consciousness.  As there is almost no published literature that deals with this particular way of dealing with the elements and transformation, my work will be primarily to remedy this gap, and to make the strongest case for the applicability of the Elemental Cycle through specific examination of transformative situations.

I believe this work is important for a number of reasons.  My experience with the Elemental Cycle has shown me that it can be a reliable guide for the deepening of consciousness around transformative processes.  It helps clarify and complexify understanding, it responds flexibly to a variety of situations and can be applied across scales, and it actively helps lead one through transformations by providing contact with and context within an archetypal, lawful, process that transcends the potentially limiting and blinding nature of personal (subjective) patterns of thinking, feeling, and behaving.  This kind of understanding and approach to transformation, which has transpersonal roots and implications, and which builds on a view of the human being and cosmos that is normally ignored by the majority of academic discourse (as it lies outside any academic discipline), is simply missing in the literature.  By studying the application of the Elemental Cycle, and framing it through the more modern languages of transdisciplinarity, complexity theory, cybernetics, and general systems theory, I hope to provide a strong foundation for its theoretical basis and practical potential.  Ultimately, I aim at bringing to a larger audience an entryway into a different way of thinking and perceiving, which can adaptively move between self and other, operates fluidly on multiple levels, includes the full complexity of the human being, and which recognizes and employs the transpersonal.  This way of thinking is compatible with the three principles underlying the paradigm of complexity laid out by Edgar Morin (2008): 1)  the dialogic, which “allows us to maintain duality at the heart of unity, [associating] two terms that are at the same time complementary and antagonistic” (Morin, 2008, p. 49), 2) organizational recursion, where “the products and the effects are at the same time causes and producers of what produces them” (Morin, 2008, p. 49), and 3) the holographic principle, where “the part [is] in the whole, [and] the whole is in the part” (Morin, 2008, p. 50).

This inquiry has always presented me with a number of difficulties (but many more successes and insights).  First of all, what I’m after is very, very difficult to work with directly, because of its intrinsically wily nature.  Archetypes cannot be pinned down and captured like a butterfly on an etymologist’s display board.  You can’t even capture transformation by pinning down each successive stage of the caterpillar-to-butterfly process; you only end up with the death of the very thing under scrutiny (this is a manifestation of an Earth-type approach to transformation).  Working with an archetype–particularly an archetype of transformation–requires a different way of working. (A treatment of what I mean by the word archetype follows the discussion of Jung below.)

Transdisciplinarity

Transdisciplinarity, luckily, has run into and attempted to deal with many of the very same problems that I face in my inquiry.  Basarab Nicolescu, one of the founders of transdisciplinarity, points out that disciplinary processes of knowledge creation—the dominant mode through which most knowledge in the Western world has been constructed for the past few centuries—is only one arrow shot from the bow of knowledge (Nicolescu, 2008, p. 3), the others are multi-disciplinarity, inter-disciplinarity, and finally transdisciplinarity. Disciplines have a tendency to form specialized knowledge on the basis of assumptions and methodologies which are unique to the individual discipline.  Indeed, many disciplines are initially formed in and by the very process of distinguishing themselves from other disciplines in just this way.  While allowing for extremely specialized forms of knowledge, such disciplinarity can lead practitioners into the situation, described by Brue Wilshire (1990), in which “missing is any sense that anything is missing” (Wilshire, 1990, p. 12).

Disciplines keep their purity by engaging in what Wilshire calls veiled purification rituals: “the refusal to mix a stance with other views (and evidence) which are palpably relevant to it.  Mary Daly calls it methodolotry.  Each field’s formalism defines and guards its boundaries” (Wilshire, 1990, p. 161). Lewis Gordon (2006) identifies a similar pattern:

The emergence of disciplines has often led to the forgetting of their impetus in living human subjects and their crucial role in both the maintenance and transformation of knowledge-producing practices.  The results are special kinds of decadence.  One such kind is disciplinary decadence. Disciplinary decadence is the ontologizing or reification of a discipline.” (Gordon, 2006, p. 4)

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Form and Content

Understanding change is a very difficult task. No aspect of our world, either experienced outwardly through our senses or inwardly through our feelings and thoughts, seems exempt from the paradoxical rule that the only constant is change. It is possible to examine the way change occurs at many levels. At the “lowest” level of examining change, we generally tend to focus on what can be called the “content.” The particular identified content (we’ll see in a minute why it is important to note that this content is “identified”) depends upon the arena in which the transformation is being studied. Generally, however, the content is the “thing” that is undergoing change, and is usually the overt focus of our attention. For example, in a chemical situation, the content would be the physical elements, such as hydrogen and oxygen in electrolysis. In a therapeutic setting, the “thing” might be one’s thoughts and feelings (in psychology), one’s bones (in chiropractics), or a family system (in family therapy).

The content level is always present; it is always a part of the way that we encounter change. Yet in addition to looking at the content-level, we can also examine change in a different way: we can examine patterns of change. That is, we can place our attention on the way that changes in content unfold, and seek to identify similarities and differences in such patterns in order to get a deeper understanding of the “rules” that inform what happens at the content level. Paying attention to this level of change is paying attention to the process of change, rather than just its results.

This way of examining change takes place one level removed from the content level, and can thus be understood as a “higher” level. It is more abstract than the first, and because it provides the contextual rules that inform the unfolding of the processes as they appear at the content level, we can call this second level that of “Form”, or even better, “Forming”. This is spelled with a capital “F” to distinguish it from “form”, in the sense of a static outer shape or configuration. A given quadrilateral has a definite individual form, and there are an infinite number of quadrilaterals, such as the square and trapezoid. But every possible quadrilateral shares the same Form. This is the same relation between a set and an element in formal logic. The Form is a way of indicating patterns of becoming shared by forms.

When examining the facts of change, we are talking about the content level; when examining the how of change (the process), we are talking about the Form(ing) level. In daily life, it is usually much easier to become aware of the content level than the Form level; we must actually practice to become awake to the context and patterns that operate on the level of Form. There is an important reason for this, but it takes a little unraveling, having to do with thinking and feeling.

Further down the rabbit hole:

• Blow your mind with epistemology and ontology!
• Reality, Process, and Mathematics
• Thinking about thinking about feedback
• Notes on the roots of epistemology in recursion
• An Esoteric Guide to Spencer Brown’s Laws of Form #4

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Introduction

About 100 years ago the birth of quantum theory changed forever how humans perceive the universe… sort of.  Certainly “quantum physics” is a phrase found far outside the boundaries of physics classrooms, and has even achieved a fairly wide popularity through movies such as What the Bleep and works like Fritjof Capra’s Tao of Physics.  Does this mean, for the average person who has at least been introduced to some basic ideas from quantum mechanics, that reality will never be the same?  Or do ideas from quantum mechanics (QM) remain something of a curiosity—fascinating and mind-boggling but so far removed from ‘normal’ everyday experience as to be essentially irrelevant?

Take a moment and ponder this question for yourself.  Can you remember how you were affected when you first heard of electron tunneling, the EPR paradox, entanglement, the uncertainty principle, or more likely, Schrodinger’s cat?  Did your view of the world change?  A more relevant question might be: how do you know?  Perhaps the next time you looked at the shimmer of a butterfly’s wings or the more prosaic spectrum reflected off a thin layer of oil on pavement you gave an intellectual nod to the underlying quantum mechanical principles which give rise to these phenomena… and then went on about your day just like it was 1904 (the year before Einstein’s four seminal papers revolutionized the world of physics—many other worlds are still playing catch up).

Now, quantum mechanics is, without a doubt, one of the best theories ever produced by human minds.  The effects of QM are likewise undeniable in their scope, and have reached every corner of the Earth, influencing the course of the 20th century immeasurably, mostly through the various technologies it has made possible (from computers and just about everything electronic—transistors, anyone?—to advances in medicine, communications, manufacturing, and more).  But the problem here is that relatively only a very few individuals need to understand principles of QM for all of this to be possible, while the rest of us can simply make or use the resulting technologies without ever changing our epistemology.  My cell phone works just fine whether I understand how it works, just as I can see my computer screen perfectly well, even though if I wish to understand how this is possible, a number of quantum principles are required.  Heck, even the scientists who understand and apply the principles of QM in new and ingenious ways aren’t required to change their epistemology—the fundamental assumptions upon which their knowledge and actions are based—they can simply use the principles logically to predict future experiments.

But this leads us to an interesting point—aptly made by one of the greatest physicists of all time, Richard Feynman, who said: “I think I can safely say that nobody understands quantum mechanics” (Feynman, 1965).  Now if someone who has won the Nobel Prize in physics for developing quantum electrodynamics doesn’t understand his own field, what hope do we have that its principles can precipitate an epistemological shift at all, let alone do so for your average person?  Let’s take a look at why Feynman can say something like this—and mean it—because this will help throw some light on the issue.

Part 1: Why we don’t understand quantum mechanics

Rather than being facetious, Feynman is attempting to point out a subtle but important issue that arises when we try to understanding QM: the way the world works on a quantum scale is nothing like how it appears to us on an everyday scale.  The entirety of our daily experience occurs in ways that belie the existence of the laws operative at the quantum level.  In other words, we don’t experience the principles of quantum mechanics at work in anydirect way, nor can we, because all our sensory and conceptual tools have evolved to deal with the vastly larger scale on which human experience plays out (although this very point is increasingly in debate).

Humans seem to experientially occupy a meso-scale realm between the quantum and the relativistic.  We are the peanut butter and jelly sandwiched between two infinite slices of bread: one infinitely large, the other infinitely small.  Yet our uncanny ability to think logically (and therefore mathematically) has led us to formulate theories of these other realms which are not otherwise accessible to our thinking.  This is to say that the closest we can get toreally understanding the quantum (or alternatively, relativistic) scales of the universe is by virtue of the logic of the maths that describe such scales.

Humans don’t do so well when we are forced to understand something solely in terms of its logical relations; we want, and perhaps need something more visceral in the experience of understanding, something we can relate to.  But this is just the problem: as soon as we try to think about what it is like for the universe to have the strange relations that the mathematics of QM implies, our thoughts simply fail its principles; we can’t do them justice through the way we normally experience the world.

“What it is like” is a question that has embedded within it a particular kind of epistemology—one thoroughly embedded within and adapted to the ‘normal’ scale of human experience.  As soon as we attempt to step outside the formal logical relations embodied in the mathematics in order to translate or understand what the relations really mean or signify for our experience of the universe, we necessarily dispose of (at least some of) the very elements we are trying to keep intact.  Quantum ‘weirdness’ is quantum weirdness; translating it into terms, images, or metaphors that can be understood by your average person (although, if Feynman is right, it doesn’t matter at all who you are) makes the quantum weirdness into normal weirdness, capable of being dealt with through all the normal epistemological modes we have been using to deal with the ‘normal’, Newtonian scale of things.

Feynman’s unequivocal statement is a stark wake-up call: we can manipulate the mathematical symbols in accordance with the rules which allow us to properly predict the results of experiments (no test of QM has ever failed to uphold these rules… yet), but we simply are not built in such a way as to be able to understand what these rules mean, because questions of meaning necessarily fall within the scale of experiences that are actually available to human consciousness.  In other words, you can’t imagine the impossible, because if you can it has already been subjected to the rules and limitations embedded in the epistemology underlying your imagination (regardless of whether these have any reality outside your imagination).  Only the unimagined is truly impossible, lying outside the realm of consciousness altogether.

Okay, fine.  We don’t understand the meaning of quantum mechanics in situ; we can simply calculate results of quantum-scale experiments and use them to our benefit, and that’s the end of the story… or is it?

Part 2: Why we do understand quantum mechanics

The “Copenhagen” interpretation of QM, spearheaded by Niels Bohr, invites us to make statements about ‘reality’ only when an actual experiment has been performed, and then we are only allowed to say what occurred as a result of the experiment.  This is because questions about the universe that are not actually answered experimentally are meaningless questions (this has been characterized as the “shut up and calculate” approach by David Mermin).  Why?  Because reality is something only by virtue of the particular questions we ask of it; i.e. the experiments we perform.  Outside the context of such experiments, we must simply be silent, because the answer to a question depends on how you ask it.  Ask it one way, you get one answer; ask it another way, you get a completely different answer.

Now, human as he was, Bohr couldn’t help but extrapolate this view into a full-fledged principle called complementarity.  This principle states that the universe can exhibit multiple, seemingly contradictory manifestations, but not simultaneously.  Actual experiments determine whether reality will be one way or the other.  Unfortunately for Bohr, making this statement violates the very principle he is attempting to uphold: he is making a generalizationabout how the universe really operates, but doing so without an actual experiment.  Indeed, the principle of complementarity itself, by its own formulation, cannot come from experiment, but must be an interpretation of at least two experiments whose results are contradictory.  This is to say that Bohr, and those who insist that physics doesn’t deal with ontological questions (“Shhhh! Back to your calculators!”), are simply deluding themselves.  This is okay, because it also simply means that such people are human after all.

So Bohr, the foremost champion of keeping our thinking and language clean with respect to attempts at ‘interpreting’ QM nevertheless does so himself.  He extrapolates from the mathematics and arrives at a principle, strange as it may be to ‘normal’ experience, that is at least understandable there: how I approach the world plays a not insignificant role in how the world appears to me.

But here we are presented with the complementary side to the coin presented in part 1: the possibility that we can approach the world in such a way as to draw out aspects of the world which would otherwise be unavailable to us.  Specifically, maybe it is possible that the realm of quantum mechanics can be approached not solely mathematically, but in other ways as well—perhaps in ways that allow us to experience it more directly than at first seems possible.  Approaching it in such a way reveals something different than would be the case if one stuck fervently to the pure logical formulations of the underlying principles, but this does not necessarily mean that the resulting understanding is simply “wrong” or irrelevant.

There is room for hope here, on at least two fronts.  The first front has roots in what is known as “the measurement problem” in quantum physics.  The rules of QM have no implicit scale of operation: the laws can apply to systems of any size (although we can only do approximations for even the smallest systems because of the infinite complexity involved: for example, calculating the influences on a single electron would ultimately require taking into account every other electron in the universe; this would make one very late for dinner).  In other words, there does not seem to be in the rules of QM itself any place where, when looking at a system of just slightly larger size, it apologetically shrugs at the experimenter and says “Sorry, chap, I get real tired at scales over a few nanometers; can’t you just use Newton’s stuff from here on up?”  No, if there are any limitations, they seem to be ours; we give up long before the math does.

Given this situation, the previous argument that we don’t experience things on a quantum scale and thus can never really understand QM may have a tiny loophole: presumably the whole world operates by the principles of quantum mechanics, including sensory and conceptual tools we use to experience the world.  Now, granted, this is an arguable point: it may be that there is no inherent connection between the underlying quantum mechanical rules on which our thinking processes are based and our ability to understand those rules.  Perhaps the ability to think about QM is an emergent property that, while relying for its very existence on quantum mechanical processes, is far enough removed from them as to completely miss them when they pass by on the street.

This may not be as big a problem as it first appears, however.  ALL thinking is removed from its foundations, considered physically.  Nevertheless, we have evolved to a point where we can understand quite a lot about these very foundations, an understanding owed to an advancement in thinking and to an extension of perception.  To say that our experience is somehow ultimately limited to a very particular scale (between a tiny speck of dust and the distant horizon, between a fraction of a second and many years) because these scales are the only ones directly amenable to experience is likely to be simply wrong.

Human ingenuity has provided us with tools that extend both our conceptual capacities (QM not the least among these), as well as our sensual capacities (both through application of technologies as well as through the ability toself-transform—more about this in a minute).  It is the combination of conceptual and perceptual capacities that gives us hope in regards to our ability to understand, in a non-trivialized way, the principles of quantum mechanics.

When I first had a chance to look through a good telescope at the planet Saturn, I was struck by how much it looked… exactly like someone cut out a tiny picture of the planet from an astronomy book and pasted it at the end of the telescope.  It was an odd experience: to see something in person for the first time that looked so much like itself that it seemed fake; it was just too real to be, well, real.  Now, if I didn’t know that Saturn was millions and millions of miles away, I would have ‘trusted my senses’ which were telling me that the image was a tiny cutout about four feet away from my eyeball.  This would be a case of my thinking becoming subject to my perception.  But because I did have prior concepts about Saturn, in this case my thinking modified my perception, so that ultimately the combination of the two (where knowing takes place) allowed me to have a much more accurate visual sense of its true distance and size.

The point is that both thinking and perception are fluid and malleable; they mutually modify each other to create a space in which new knowing can happen that otherwise would be inaccessible, as was probably the situation in the famous (and at least partly apocryphal ) case of those who looked through Galileo’s telescope without ‘seeing’ the moons of Jupiter.

This, then, is the second front of attack: we human beings are capable of real and radical change and evolution, both in our thinking and in our perception.  The ideas of quantum mechanics have been around only for a century, an insignificantly tiny portion of the span of human development as a whole.  Yet even in that time our understanding has advanced considerably, and not just through “sheer logical manipulation”.  It takes human creativity to suggest places that look promising for exploration in the quantum tunnels (if you’ll forgive the pun).  Physicists even speak of a sort of quasi-magical ‘intuition’ that is both innate and capable of being developed which suggests how to think about things in new ways that lead to interesting insights, experiments, and theories.  Feynman was something of a master at this.

Inconclusion

Now let’s put this all together, or at least overlap things a bit.  Humans seem primed by instinct to deal with Newtonian scale events, which occupy the vast bulk of our lives.  But we are also primed with the capacity to change our capacities through a variety of means, both externally and internally.  We have been thinking about thinking for at least two or three millennia, and have arguably made considerable progress with how we understand our understanding.  That techniques for modifying understanding (esoteric technologies, we could call them) can produce experiences that lie far outside normal scales of everyday life seems to give testament to the human ability of overcoming our ‘built-in’ limitations. Perhaps the numerous accounts of trans-personal experiences (among which experiences of the infinitely large and the infinitely small in both space and time are not the least important) are possible precisely because of QM?  Maybe these types of experiences could even be considered just as ‘direct’ in regards to the quantum mechanical realm as an experience of throwing a baseball is with regards to the Newtonian realm?

We have also extended our outer sensory capacities through various technological means, which has opened up whole new worlds to experience.  With corresponding changes in our conceptual abilities, human beings seem capable of moving past the Newtonian scales that otherwise bind our experience.  As an example, even if we personally have never seen them, we can easily imagine a whole realm of germs, parasites, and viruses that cannot be seen with the naked eye, and what’s more, we actually live our lives with this realm partly in mind.

It doesn’t seem like we have evolved to understand QM, even if we have evolved with and even because of QM, at least in part.  But sewn into the very fabric of this tapestry is the thread of its own unraveling: evolution isn’t over, and may indeed be speeding up and changing course in ways we have barely begun to imagine.  It seems much too hasty to declare that our present inability to directly understand the science of QM will remain true for even the relatively close future.

The whole history of humanity shows us, over and over again, how human understanding has changed and adapted with the types of sensations, environments, and capacities that are both unconsciously encountered and consciously developed.  Quantum mechanics is so recent we have barely (collectively, that is) sat down next to it at the bar, let alone asked it out in a date.  How could we be expected to know what it would be like if we moved in together, not to mention that out of the corner of our eye we keep seeing sexy string theory (or mysterious M-theory) throwing meaningful glances our way?   Perhaps Feynman would agree with the uncertainty (and thus openness) of our future; his statement was in the present tense, after all.

Human epistemologies are adaptive and flexible.  They are also capable of reorganization on the basis of intent, at least to some extent.  It may be that the appearance of present limits to understanding are temporary, or at least amenable to shifts.  New ways of experiencing the universe, both conceptually and perceptually, provide the opportunity to explore new modes of knowing, which do not necessarily retain the limits imposed upon us by our innate biology.  Our biology, in a sense, can be extended; our consciousness can be extended as well.  Some curious fellows seem to have been exploring this kind of extension for thousands of years, but the rise of technological methods for extending perceptual capacities (and the corresponding conceptual advances) have created a completely new situation in this respect with regards to experiences available to the average person.

The extent to which humans can embody and enact new epistemologies on the basis of changing perceptual and cognitive resources is unknown.  But it does seem that a dynamic set of possibilities lies between the two extremes, allowing at least a partial ability by which humans create situations that lead to significant changes in the way we conceptualize and interact with the world.  Quantum mechanics may very well contribute to such a shifting.  The situation, like a quantum wave-function, is continuing to evolve through a vast array of superpositions.  Maybe once we get to first base the wave-function will collapse and we’ll have a picture of where the relationship is headed; for now, though, it looks like we’re still flirting at the bar.

References

Feynman, R. P. (1965). The character of physical law. Cambridge,: M.I.T. Press.

http://bedejournal.blogspot.com/2006/11/who-refused-to-look-through-galileos.html

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This question is a touchstone for the modern human dilemma, and it’s all about consciousness.

I’ve recently been in some discussions around transitioning to being vegetarian/mostly vegan.  Part of the discussions revolve around the available evidence for the state of affairs with respect to our food production.  Two heavy-hitting potential sources for perspective can be found readily on the YouTube: the movie Earthlings (http://www.youtube.com/watch?v=UeSA2j4oiDA), and a video lecture presentation by Gary Yourofsky (http://www.youtube.com/watch?v=es6U00LMmC4).

Watching these sorts of things is not fun, and people know it.  We intuitively know that when we expand our awareness and broaden our perspective, we cannot remain the same.  HOW we don’t remain the same is up to us, there is no script given to us by the universe telling us unequivocally how to act.  The apprehension around this feeling of inevitable change (which is completely understandable), can deter us from seeking new knowledge and perspectives that are different than whatever perspectives we currently entertain, and which are already integrated into our daily lifestyles, choices and self-image.

In the face of this apprehension, when presented with an opportunity to entertain an alternative perspective, the following kind of thought might occur:

“Ok, so I will think about it…watching it that is. And how do you know that there is not an intended bias put in that distorts the situation? There are horrible examples of almost everything (parenting, professors, sanitation…) but that doesn’t mean it is ALL like that.”

This is quite true: a few bad apples don’t spoil the whole bunch, and everyone is biased. There is quite overtly an intended bias in the lecture/films. This is, indeed, the point: they are biased towards treating animals decently, towards environmentally sound choices, and towards developing the “humane” part of the human being. In other words, being biased towards knowledge (vs. ignorance), towards compassion, and towards care for the world is something very different than a bias towards maximizing corporate profit, for reduction of knowledge (systemic practices of hiding the nature of the processes by which our food is created), and for reduction of ethical considerations around food choices.

This difference should be pretty clear. There is always distortion; that is the nature of being a human. But because that is a given, we have the ability to take a second-order view: we can’t eliminate distortion (doing so would itself be a distortion), but we can become active curators of the processes by which our views get distorted. By entering into these admittedly subtle processes, rather than ignoring them, we can gain some measure of freedom.  This is essentially saying that the question is–quite centrally–an epistemological one.

This is one of the most basic psychological principles: what you DON’T know about yourself influences you more deeply and directly than what you DO know about yourself. Just like individual therapy was created to help humans take an active stake in self-knowing, so that we can have more freedom in the way we conceive of ourselves, and just as family therapy (systems-oriented therapy) took that to the next level and showed how it is not enough to have self-knowledge (because the family system is always more than individuals and individual dynamics), so too there is a burgeoning field of ecotherapy, in which the next logical step is taken, towards recognition that individuals and family systems are embedded in, and co-evolve with, even larger contexts (and spiritual psychology takes that beyond the Earth to even higher realms).

Each expansion is accompanied by greater awareness of the systemic connections between levels, so that what at first seemed totally individual (“what I want for lunch”) becomes inextricably connected to all the other systems, and not in a vague, wishy-washy way, but by virtue of various streams of evidential data and shared experiences. So, the very true fact that “it is not ALL like that” simply means that if we don’t want to be supporters of the places where it IS like that, we need to become aware of the myriad elements of the particular systems in which we partake, so that they are no longer part of an unconscious or semi-conscious “given” context for our actions, but become available consciously as one of a possible number of other contexts in which we can act (and create!).

The entire world is already paying the increasing price for the lack of this work (global climate change being a major example). The weird key is that it is the individual human being (always in larger contexts, but still individual) who represents the capacity for the world to wake up to itself, to see itself as a whole, and to begin to evolve in less systemically destructive ways. So human beings have a particular responsibility to develop just this capacity to see–as individuals–beyond their individuality, to hold in consciousness the various polarities necessitated by life, to recognize the connections between all the various living and non-living systems, and how this all calls for the creation of new ethical distinctions that, when acted upon, help create a better world for the whole, rather than just some few parts.

The time for ignorance is quickly coming to an end; human systems are too globally interconnected, too vast and dehumanized in their processes, to let them continue without better guidance. Knowingly choosing an answer to the question “what’s for lunch?” is exactly what this guidance looks like on an everyday basis. If humans don’t begin to collectively (as individuals!) ask that question in some form, then the fate of the world will be given over by default to exactly the same kinds of unconscious or semi-conscious processes that are behind the vast majority of the world’s problems. The world itself is in need of a kind of therapy, but it is human beings who are the only ones capable of both being the therapists and the clients in this situation. We have to create the therapy and administer it to ourselves, on behalf of the world. We can’t sit the ducks, polar bears, bees and amoeba down in the chair and explain to them what they need to do to change so that the world can evolve together in a more peaceful and healthy manner. We can only do this to ourselves–not ourselves as individuals only, but also as representatives of the rest of the entire world that can’t speak for itself without our help. This calls on human beings to undertake a path towards wakeful compassion that extends our individuality beyond the walls of our skin, beyond the walls of our limited mental representations of self, so that we become facilitators of ways of being that are systemically, integrally wise.

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http://vimeo.com/10929373

This is a great interview with Professor Andrew Pickering, University of Exeter, author of The Cybernetic Brain: Sketches of Another Future.

• Brain as performative organ, and an organ of adaptation.  Not a representational, thought-based organ.
• Work spanned out into adaptive systems everywhere, beyond just the brain (even into spirituality).
• “We don’t have to be in the world in the way that most of us are today…”
• “I understand cybernetics as a very different paradigm from modern science and modern engineering.  It’s a different way of going on the world.”
• Ontological theater: the decentered dance of agency.
• Gordon Pask: from control to conversation.  Open-ended interactions, allow for novelty, creativity, diversity.
• Cybernetics quite saturated with spiritual elements.  British cyberneticians often associated with spiritual ideas and practices, including seances, speaking to the dead and that sort of thing.
• Cybernetic vision: endless becoming, endless surprises… performatively.  One class of surprises is spiritual.
• Cybernetics sees our own selves as capable of surprising performances as well.
• Rethinking the “self” — undermining the modern (reified, centralized, limited) self…

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(New readers will want to start with the first installment.)

We ended the last installment by discussing the esoteric nature of the injunction.  We continue this exploration, and bring this series to a close.

LoF p. 81

• In the command “let the crossing be to the state indicated by the token” we at once make the token doubly meaningful, first as an instruction to cross, secondly as an indicator (and thus a name) of where the crossing has taken us. It was an open question, before obeying this command, whether the token would carry an indication at all. But the command determines without ambiguity the state to which the crossing is made and thus, without ambiguity, the indication which the token will henceforth carry.

This re-affirms that the mark has both a first and second-order character: it names the state of its content (its indication), and it is an instruction (its injunction) to mark that name, to make that distinction which yields that state. Thus every mark is both an indication and an injunction.  It is an indication of a content and an injunction on how to get there.

LoF p. 82

• We may consider how far, in ordinary life, we must observe the spirit rather than the letter of an injunction, and must develop the habitual capacity to interpret any injunction we receive by screening it against other indications of what we ought to do. In mathematics we have to unlearn this habit in favour of accepting an injunction literally and at once. This is why an author of mathematics must take such great pains to make his injunctions mutually permissive. Otherwise these pains, which rightly rest with the author, will fall with sickening import upon the reader, who, by virtue of his relationship with respect to the author, may be in no position to accept them.)

All this actually relates to the task of the esoteric teacher, who recognizes that the way in which injunctions are presented (their context) has a quite prominent role to play in affecting the ability of the pupil to take them up.  Thus a key aspect of esoteric teaching necessarily involves extensive caveats, personalizations, modifiers, generalizers, and specifiers.  It is relational through and through.

In discussing the nature of the primal injunction, “draw a distinction”, GSB notes that

LoF p. 84

• We have here reached a place so primitive that active and passive, as well as a number of other more peripheral opposites, have long since condensed together, and almost any form of words will suggest more categories than there really are.

All this indicates the primal nature of the WILL, its irreducible ontology.  All that “is” flows from WILL.  But we have seen also that this will is not alone: it is accompanied, in a complex unity, with both a thinking and a feeling, taken in their most primordial sense.

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(New readers will want to start with the first installment.)

We ended the last installment with a recognition that the Laws of Form naturally led GSB to an understanding of both the necessity and importance of the realm of imaginary numbers.  We will continue this elaboration.

You are likely familiar with the paradoxical sentence: “This sentence is false.”  Is it false or true?  The answer is yes, and it depends on when you ask me.  It was this kind of paradox that drove Russell and Whitehead into creating their Theory of Logical Types, which was designed specifically to prevent this kind of thing from simply ever coming up in the first place.  GSB is not so limited, and understands the importance of formally including paradox in his calculus.  So how does he deal with this?

He points out that we are driven to a higher order of logic, one that includes re-entry. In the first Esalen lecture, GSB states that

• “This has been totally overlooked in mathematics, that i is in an oscillatory state. Because in order to get over this paradox of x-squared equals minus one, we see that we can’t use any ordinary form of unity so we invent in mathematics another form of unity and we-call it i, which is the root that satisfies that equation.”

Let me continue quoting him at length, because his own dialogical presentation is quite apt:

• It is really an oscillation defining time; but it is the first time, and, therefore, being the first time, the oscillations are without duration, so the wave has no shape at all. Just as the space of the first distinction has no size, no shape, no quality other than being states. This is one of the things that tend to upset people. It is part of the mathematical discipline that what is not allowed is forbidden. That is to say, what you don’t introduce, you can’t use. And until you have introduced shape, size, duration, whatever, distance, you can’t use it.
• In the beginning of Laws of Form, we defined states without any concept of distance, size, shape–only of difference. Therefore the states in Laws of Form have no size, shape, anything else. They are neither close together nor far apart, like the heavenly states. There is just no quality of that kind that has been introduced. It’s not needed.
• The same with the first time. The first time is measured by an oscillation between states. The first state, or space, is measured by a distinction between states. There is no state for a distinction to be made in. If a distinction could be made, then it would create a space. That is why it appears in a distinct world that there is space.
• Space is only an appearance. It is what would be if there could be a distinction.
• Similarly, when we get eventually to the creation of time, time is what there would be if there could be an oscillation between states. Even in the latest physics, a thing is no more than its measure. A space is how it is measured; similarly, time is how it is measured. The measure of time is change. The only change we can produce–when we have only two states–the only change we can produce is the crossing from one to another. If we produce an expression, like the ordinary expressions in the algebra, we have to make the crossing. We have to do something about it. We have to operate from the outside. If we produce that cross that feeds into itself, now we don’t have to do any thing. It is a clock, just as an ordinary distinction is a rule. A rule makes or defines space, and a clock defines time. In making our first distinction all that we have done is introduce the idea of distinction. We have introduced nothing else. No idea of size, shape, distance, and so on. They do not exist, not here. They can be constructed, and they will be, but not yet. They are what happens when you feed the concept back into itself enough times.
• Again, when you first construct time, all that you are defining is a state that, if it is one state, it is another. Just like a clock, if it is tick, therefore it is tock. But this time is the most primitive of all times, because the intervals are neither short nor long; they have no duration, Just as these states have no size.

All we need to add is that when he says “In making our first distinction all that we have done is introduce the idea of distinction. We have introduced nothing else.” we can recognize something of the complexity of what this idea of distinction is, and how it acts.

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(New readers will want to start with the first installment.)

We ended the last installment having come to realize something of the esoteric significance of the taijitu, or yin-yang, form, in something of an extended tangent. We return now to the text.

GSB himself seemed to understand the importance of the Laws of Form, even if there were some of these more subtle specifics which were not apparent to him (or at least which he did not explicitly recognize).  Having reached this point (literally we are still on page 1 of LoF), the vast majority of the rest of the work in LoF is seen to be secondary.  Yet there are many valuable indications which deserve connection to esoteric principles, and the point of this exploration is to show that such connections are not arbitrary. So, to return to the actual content of LoF now, after this long but foundational detour, we can note that he says:

LoF p. 5

• Let any token [of the mark] be intended as an instruction to cross the boundary of the first distinction.

That is, every mark is an invitation to cross it; every distinction is a call to make that distinction, not to simply point it out, but also to DO it, to MAKE the distinction.  In other words, the whole thing is ACTIVE, not passive, it is not descriptive but PRESCRIPTIVE.  Of course, the esoteric significance of this should be obvious, because precisely what distinguishes esoteric work from, say, philosophy or other disciplines, is that it is, at its roots, injunctive.  That mathematics is the discipline most closely allied to esoteric work in this respect only serves to strengthen the indication that mathematics is the most spiritual of academic disciplines.

Now, if you don’t know, GSB uses LoF to show how, starting from one single form, he can build an entire logical calculus, including (but not limited to) the Boolean Algebra.  In fact, the way he came upon the LoF was precisely through asking himself the question “what is the basic arithmetic upon which the Boolean Algebra is based?” (Esalen conference, session two).

He uses the token of the form, the upside-down and backwards “L” as an operator to do this work.  The whole of the logical calculus in LoF is built out of the way that this form works with itself, and he notes that the two “primitive equations” upon which everything else is based take the form:

LoF p.11

He calls the first primitive equation number, and the second (where a form is inside itself, which equals the unmarked state) order.  Why is this important?  Because we can note that these two principles, upon which everything that is to follow in LoF is based, is nothing other than the embodiment, in form, of the principle of the N and N+1 orders discussed as the key to the whole thing in the first place.

To state it another way, these two primitive equations work because they embody exactly what would be required of them if they were to work (to take a GSB type of phrasing).  More directly, they embody the principle of the creation of the cross and the crossing of the cross.  Together, these two equations express the principles required to yield all the complexity necessary for any ontology: this means they have, together, a horizontal and vertical direction, or a breadth and depth, a distinguishing and a unifying nature.  The first equation is horizontal: it serves to open up all the later logical space in LoF.  The second equation is vertical: it serves to unify across levels, or to create more levels.  You can see that this is just what is implied in the levels N and N+1: the level N is what it is by virtue of its containing everything else that is at level N, while the level N+1 is precisely the activity of the unification of everything in level N.  N is the content, N+1 is the activity by which anything in N gets to be in N in the first place, vs. at any other level (say, N-1).  The reason for calling these levels N and N+1, vs. actually counting them from some starting point should be obvious: they are recursive with each other; there can never be some absolute destination “N” that could serve to begin the counting.  We can only ever count from where we actually begin.

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