Thank you for joining me here. I’m glad someone other than me finds this kinda stuff interesting….though maybe I should count those chickens after I hatch this section.
The premise of this section is to show that even the most widely accepted manifestation of binary structure –the pattern of 1’s and 0’s that make up a digital program– breaks down upon closer inspection and is not really binary at all. We will eventually take that understanding out of the virtual and back to the real reality to address our binary assumptions we make about that too. But first, a simple illustration that just came to me this morning.
My primary job is to deliver food to a wide variety of folks in the northeast US. The invoices for these deliveries are assigned serial numbers that mark their place chronologically in the order that they are generated. As an example , I’ll take this opportunity to plug my favorite customer in all the territories I cover: Nori’s Village Market in Saranac Lake, New York.
The invoice number for their delivery today was 000304621.The 000s at the beginning of our serial numbers have been there as long as I’ve worked for this company. I don’t know if the first order 24 years ago was 000000001, or if it has always been a six-digit number with 000 at the front, or if the Y2K scare convinced a programmer to be VERY proactive in projecting room for future growth. In any case, if we are lucky enough to survive and fill our 100,000,000th order someday, by Jove, our software will be ready for it.
So the 000s serve a purpose –a far fetched one, but a purpose: they hold the place in the serial sequence for the invoice numbers to grow to seven, eight and nine digits. This is the context chosen by the programmer to account for future needs. These 000s do not change the numerical value of the invoice number; you could take them away, or give it four 0’s, or four hundred, or four hundred billion if you don’t mind using reams of paper to print one invoice. No matter what, the position of the Nori’s order in the sequence of our order history is #304,621.
But the 0 between the 3 and 4 is a completely different beast. Take that 0 away, or add three more, or move it to a different location in the number, and the numerical value changes. In this case, the 0 is a digit with specific value in a decimal system, as it is in the number 10, or 101, or 1001 etc.
So you can see the difference between two uses of 0: one has numerical value, the other is simply a symbol that says “there is no digit here.” It represents the null set from which a context is chosen to give the digits their proper significance.
To demonstrate the importance of context to this significance –and to illustrate the change that occurs when we jump from numerical context (ie linguistic, analog) to digital– let’s say I’m sitting at a desk and write “10101” on a piece of paper. Looking at what I’ve done numerically, we see the number 10,101. Its context is defined as a five-digit number, surrounded by a null set in which I chose to write no numbers in order to express 10,101 clearly. The 0’s are digits that are significant to the numerical value, and we are so accustomed to seeing numbers written this way that it doesn’t occur to us to consider the digit-less space that surrounds it, so we don’t question the context at all. Pretty straight forward.
But take it out of the linguistic context of seeing it as a number, and look at it instead as an extremely simple digital code. Now the 0’s no longer have a value unto themselves as one of ten possible integers –they are “not-1’s” inserted to show specific distance between 1’s. If we don’t consider the malleability of context, this difference isn’t immediately apparent, and 0 appears to have a binary relationship with 1.
But now let’s say I get up from this desk, walk 20 feet to the left of it and sit at another desk, and write a “1” over there. Mathematically speaking, in terms of our 10,101, the relationship between them is a complete mystery; there are not enough known (or knowable) facts to connect what one must conclude to be two separate numbers that require some external creative force in order to interact with each other (and I’m going to suggest, albeit prematurely, that this is perfectly symbolic of the awkwardness with which language handles apparently separate phenomena, and why we almost must see “God” as external to us while viewing Creation through the binary filter).
As manifestations of digital code, however, the 1 and 10101 have a pre-existing, self-sustaining relationship: they are finite sets of 1’s, surrounded in all two-dimensional directions by non-1’s. Independent of specific context, there is a relationship between these sets of 1’s that is fixed and unchanging: they are connected by empty space. Try to keep this in the back of your mind as I steer our attention away from it.
Now here is where context becomes crucial. As the author of these codes, I can look at them separately as two distinct manifestations, drawing dotted lines around them (dotted, that is, to show that I have chosen these boundaries; there is no natural separation between them). It is appropriate to say now that they have no local significance to each other (a major concept we will use abundantly later) and that lack of significance defines their relationship within those chosen contexts, without really affecting their relationship as part of the whole.
Or I could just as well draw a single dotted line around both and call this the context of my digital program. Now the not-1 space between the lone 1 and the 10101 is not being ignored, and it will fill up with 0’s that define the distance between them. the result is a digital code that looks like “1[twenty feet worth of 0’s]10101.”
(Let’s keep this simple but make it more tangible. I’m not a musician, so I hope I’m not mangling the elegant language of music, but let’s say the 1 represents a one second blast of a B flat note from a trumpet, and 0 is the quiet space between notes. In the first context, where 1 and 10101 are distinct codes, an MP3 player reproducing them would treat the first B-flat note as Track 1, followed immediately by Track 2, a note-silence-note-silence-note sequence. In the context of one integrated program, however, it would be one track comprised of a single note followed by maybe 20 minutes of silence, then the three note sequence. Very different output, all because of a change in context that had no effect on the position of the digits relative to each other.)
The ability to select a specific context and focus on it to the exclusion of all that surrounds it: I will call this “selective attention.” It is not exclusive to human beings, but certainly our degree of refinement of selective attention is unique in our world.
It is understandable that an observer with selective attention looking at this code on paper or hearing it manifested as music would conclude that there is a binary relationship between the 1 and the 0, the sound and the silence. But this viewpoint can only be maintained by ignoring the whole picture of reality surrounding our chosen context — the non-1 that permeates the boundaries of this context, existing in the form of silence before and after the music plays as well as the spaces between notes. Context appears to give it the same kind of value that the 0 has in 304,621, but in reality it is more analogous to the 000 in 000304621 –it is holding space for the non-1 that pre-exists the creation of the program.
As you can see, we’ve now introduced the dimension of time. This is the proper context for any digital program manifested as music or a movie or words on a computer screen, because now we have a series of digital codes encountered sequentially by the device reading them. One could say that, whereas our simple codes were two-dimensional as static representations on paper, these blueprints for virtual reality exist in three-dimensions, the third being the depth provided by time sequence. The digital device that manifests their images and sounds is programmed to have a very precise selective attention, and if your MP3 player had the capacity to reflect on its sensory input, it would probably also perceive your music as a series of binary programs instructing it as to exactly what sounds to make exactly when.
But again, I hope it is clear that these songs exist in a sensory field of pre- and post-existing silence, and the space between notes is held by this very same silence. You could say that each 1 in a digital program marks a precise point where/when a sculptor carves into a block represented by 0, or an artist adds 1-paint to a 0-easel –most definitely not, to re-evoke Berry, where two opposing forces of sound and silence collide and do battle. We should be starting to see that 0 is the entire background for the program, not merely a component of it.
Now let us make the jump from virtual reality to reality itself. The most advanced digital computer program in the world is still a stick figure drawing compared to the four-dimensional, multisensory masterpiece that is every moment of life itself to every sentient being. And yet, if you look at the world on the sub-atomic level (as human beings are privileged to do thanks to our mastery of selective attention), you see a jambalaya of finite 1’s making up electrons and the soupy quantum sub-sub-structures of protons and neutrons, all connected by relatively vast amounts of non-1. Without diving into the abyss of knowledge regarding quantum physics (which I am intellectually unable to permeate anyway), my limited reading on the subject has revealed one fact that is very germain to this discussion: we are filled with an awful lot of emptiness. Whereas selective attention once led us to believe that the essential structure of our physical world resembled elaborate stacks of cannonballs interacting with each other as solid units, we are now seeing that every atom in the universe consists mostly of empty space.
So inwardly, by shrinking our selective attention down to an adequate level, we see the presence of “non-1” in everything. And outwardly, we know every attempt to make a product of selective attention into an absolute breaks down with the question, “What is beyond that?” –or “What is the background of your chosen context?” This forces a perpetual re-evaluation of the context to keep it concurrent with reality, and the context becomes ever-larger until the mind that chooses the context reaches a snapping point and gives up trying to contain the uncontainable, and is left with the unfathomable truth that the background of everything is infinite.
It is at this point, of course, that the designations of “inward” and “outward” lose all meaning, for infinity does not extend outward nor inward from a finite point. The same must be said of “background” and “context,” lest we slip back into a dualistic viewpoint and forget that, no matter what context we choose, there is null (non-1) space within it that permeates the boundaries of our selective attention. And that contextual space is one and the same as the extracontextual space, the primordial silence from which the music of existence is orchestrated.
Difficult as it is to compute with the way our minds work, it is a sound logical conclusion that, just as the 1 and the 0 in digital code symbolize a relationship between a thing with a boundary and a boundless field that transcends and includes it (a monism of 0, you could say), so is everything in the universe part of a boundless field that transcends and includes it. Far from validating dualism, the digital model actually becomes a perfect illustration for how dualism is swallowed whole by the greater reality reported by mystics for millennia.
From this, we can deduce that the universe is either infinite in its manifested state (this is generally regarded as the conclusion of pantheism), or a vast 1/non-1 pattern surrounded by the infinite non-1 of unmanifested background (more aptly described as “panentheism”).
I’m not concerned about the difference; seems like the splitting of some ultrafine hairs. Either way, we have laid the groundwork to see that everything in the universe –from the most basic building blocks in the cells of your body to the farthest clusters of galaxies imaginable– is not (to borrow Wendell Berry’s idea) made of two discrete parts glued together, but is a single mystery, an intricate, integrated whole of two blended complementary components: finite “stuff” with distinguishable parameters in space-time (1’s, or “dust”), and a transcendent, omnipresent element (0’s, or “breath”) that cannot be contained by selective attention and is common to all. Binary opposition stops being so oppositional, and starts feeling more like the intimate relationship between Creation and Creator, Taoist and Tao.
So what are the implications of the breakdown of binary code into a non-dual relationship of finite and infinite? They are many and varied, and I think this is the best point to merge back into the main thread of discussion for Part 3 so those who skipped this section won’t miss out.