You are about to enter a Twilight Zone of contradiction and paradox, where the boundaries between “real” and “not real” are blurred. We will travel to strange, seemingly incomprehensible places, only to discover we have arrived home. I begin our journey with an invitation: “Let’s Play!”

Digital Logic

Let’s begin with the digits that compose our modern world.

Our virtual world, a dreamscape projected through a screen, is anchored in electrical processes and material hardware that follow the dictates of the physical world and logical laws. Microchips containing a staggering number of electrical “switches” that are knitted together in quick changing patterns of electrical circuits are the basis of cyberspace. Each of these switches, or bits, possess only two possibilities: either “on” or “off”, which typically are assigned a digital value of 1 or 0.

Pictures, music, images, broadcasts, streaming, data—just about all forms of information and electronic communication—are now digitalized. This process is accomplished by segmenting analog signals, such as sound or light waves, which are continuous, into the tiniest of discrete bits of information, and converting letters, numbers, and other forms of information into a bit string. The binary format, either 1 or 0, allows for easy transmission, manipulation, and storage of information. Our digitalized world is organized by machines that can, at lightning speed, conduct huge calculations with bits composed of the binary, either 1 or 0.

This binary, either-or structure presupposes an assumption that a bit cannot be “on” and “off”, “0” and “1”, simultaneously. This assumption is so obvious, so basic to our understanding of how things exist in the world that it constitutes a fundamental law of logic: the Law of Non-Contradiction. This Law states that it is impossible for something to be A (i.e., “on” or “1”) and not-A  (i.e., “off” or “0”) at the same time. This is considered a first principle of logic upon which all else rests.  

Cosmic Logic

The cosmos, surprisingly, defies our logical sensibilities. Quantum mechanics, which is the fundamental physical process that constitutes everything in the universe, is based on the seeming impossibility that something can simultaneously be A AND not-A. So, for example, in quantum mechanics, light can be both a wave AND a particle; we just don’t know which until we look.

Efforts are underway to construct a computer with exponentially greater power than current computers that exploits the logic-befuddling quantum properties that something can be simultaneously A and not-A. These properties include quantum entanglement and spooky action at a distance. When particles are quantum entangled, the effects on one particle will instantaneously affect the others—even if they are located at opposite ends of the cosmos. These instantaneous effects over such great distances cannot be explained by our current understanding of the physical universe; spooky action at a distance is the phrase used to describe this.1

Quantum mechanics not only is revolutionizing computing, it also has shattered our assumptions about reality. Obvious principles of logic—overturned. Entanglement of particles with mutual, instantaneous influence across unimaginable distances—inexplicable. The world hangs suspended, particle AND wave, “0” AND “1” awaiting interaction with a macroscopic system— such as us—to give it form. We cannot assume a “gods eye” position of observing, measuring, and understanding the workings of the universe independent of our own place, time, and actions in it. The ground beneath our feet is unstable.

Playful Logic

Another AND subverts the seemingly obvious Law of Non-Contradiction: play. Playing is no simple matter, as it requires sophisticated communication abilities. A dog that playfully nips another must communicate, “This nip is not really a nip”, otherwise the nip could precipitate a fight rather than a playful response. This is typically communicated by exaggerated movements of some kind, such as paws out, head lowered, tail wagging, and galumphing about. These are metacommunicative messages that signal: The nip (A) is not really a nip (not-A).2

These metacommunications entail distancing from the ongoing stream of messages; stepping outside the stream to signal how these messages should be interpreted. Play requires self-referential awareness of being “the one doing the signaling,” as well as awareness of the other as the “one to whom the signals are meant” (and who, also, is “one who signals”).The player acts “as if” the bite is real and must have “double knowledge”: being able to tell the difference between the actual and pretend bite at the same time. It is both “real” and “not real.”

Play engenders a deeper kind of knowing; both a cognitive double knowledge of “as if,” and a social entanglement with another, forged in mutually sharing that a “bite is not a bite.” For these reasons, play is often used as a marker for assessing the relative cognitive and social capacities among species. It is also considered a nascent form of a much more sophisticated mental ability: representation.


“This is not a pipe.”

Representation consists of an object or referent (A) that is re-presented by a sign or symbol (not-A). The re-presentation is both A, as it acts “as if” it were A, AND not-A, because it stands in place of A. Representations can take many forms, from images, to words, numbers, and sounds. Untethered from reality, existing in its own created reality, a representation affords leeway from the represented, allowing us to play with it in symbolic ways, exploring novel, strange, fantastic, comical possibilities.

We easily can, and do, become swept into the represented reality without realizing that it is an “as if” one. We lead a “double life.” Magritte, a 20th century French painter, humorously points this out in his painting, “This is not a pipe.” We initially are confused by the painting because we immediately assume, it is a pipe. But it is, AND is not, a pipe. The painting amuses because it playfully exposes our taken-for-granted double life. We dwell within a representational world as strange, peculiar, and bizarre as quantum mechanics.3

Paradoxical Power of AND

While representation is not the real thing itself, it does, paradoxically, enable us to grasp reality in a more fundamental way. Quantum mechanics, for example, affords an exceedingly precise understanding of the cosmos, which is understood through mathematics, perhaps the most abstract and detached of all forms of representation. Indeed, quantum mechanics is an abstract mathematical reality whose representational fidelity to reality is tested, empirically, in extraordinarily complex and abstract ways. We are a like blind man, probing the world with a mathematical stick. The same can be said for language, art, and music—all of which, in themselves, are not “real”— but it is specifically their “as if” quality that affords us the ability to “see” with greater depth and clarity.

Logical contradictions and paradox, ironically, empower us. Thus do we catch a glimmer of the dizzying hall of mirrors that comprise ourselves and the cosmos that we inhabit.




  1. “Quantum weirdness”, which includes “spooky action”, prompts many unfounded, far-fetched inferences, such as the universe is animated by spirits, ghosts, or supernatural forces. “Spooky action” is simply a colorful term coined by Einstein to denote that these actions defy our current knowledge. It is not an invitation to identify “spooks”.
  2. This A AND not-A analysis of play was offered by Gregory Bateson, who was one of the great minds of the 20th century. His influence is wide and deep. His work, begun in the 1940’s, initiated a wave of research on animal communication and play that continues to this day; he is considered to be one of the founders of cognitive science; was instrumental in creation of the discipline of family therapy; and offered fruitful perspectives for reconsidering hypnosis, drug addiction, and schizophrenia. His approach was groundbreaking, emphasizing systems, relationships, patterns, networks, and contextual influence—it is the foundation for contemporary research on ecology and climate change. His influence is certainly greater that his wife, Margret Mead, whose renown greatly outshines his in cultural memory. His work has had a profound influence on my thinking.
  3. See Abracadabra!