ZIG, ZIR & their Zebra


Excerpt from a chapter in Zann Gill’s forthcoming book What Daedalus Told Darwin.


Debates about defining life, and about the origin and evolution of life, may have their roots in our assumption that a purely material explanation will suffice, which is questioned by this thought experiment about the origin and evolution of life.

Suppose, you’re ZIG (A in the diagram), a “Zebra Image Generator” with a computer screen. You can generate and represent images, but you’ve never seen a zebra and have no idea what a zebra looks like, so you cannot assess whether the images you generate look like zebras or not. You collaborate with ZIR (B in the diagram), a “Zebra Image Recognizer.” She assesses whether each image you generate looks more or less like a zebra than your previous image and informs you by varying the relative loudness of her alarm. This is a simple diagram of a feedback look. Artist M.C, Escher represents that concept with two hands, each drawing the other.


As ZIG, you represent the process of random mutation. ZIR represents environmental selection. Whether the two of you as a team can invent a zebra image or not addresses the question of whether evolution proceeds solely through random mutation and environmental selection, or whether some other mechanism was needed to complement your ability to generate, and ZIR’s to recognize.

How hard is your zebra-drawing task, and how long will it take? Life might be inevitable, but still take a long time. Or it might be accidental, but happen very quickly.

When all information is present, all alternatives that can potentially be developed using that information are equally probable. By selecting options, and discarding other options, ZIR sacrifices “possibility,” and the information associated with that possibility, in favor of less information and greater definition toward a zebra image.

escher_handIn this thought experiment a zebra image emerges through epigenesis (development through differentiation of an initially undifferentiated entity as more and more pixels on your screen collaborate to represent a zebra. You and ZIR illustrate how life may have emerged as small components aggregated, collaborated, and integrated their skills until they achieved sufficient complexity to become alive. Inventing an image of a zebra starts without the use of structural categories (such as body, legs or head), and without neutral forms that can gradually become more and more differentiated.

The monitor has only a grid of pixels that can represent zebras, stripes, or any other image, an undifferentiated matrix that starts a neutral gray with black and colored, off and on pixels, randomly and evenly distributed. This undifferentiated matrix has no affinity with any zebra components. But out of this matrix any of them can evolve — all is possible.



John Conway invented the cellular automaton called the Game of Life. The global rules for Conway’s Game of Life look like a tic-tac-toe game.

Each pixel on the computer screen can be either on or off. When a dot on the screen in the Game of Life goes on, it’s called a “birth.” When it goes off, it’s a “death.” Whether it goes on or off depends upon the condition of its eight neighboring pixels. If two neighbors are on (alive), it stays as it is, either on or off. If three are on, it lights up, whether or not it was lit in the previous instant. In all other cases it goes dark. Slight variation in the rules can give widely differing results.

Imagine a grid of light bulbs, which can be only on or off (1 or 0, “yes” or “no”). But, because they are so tiny, and there are so many of them, they can approximate shades of gray, as do the dots in a newspaper photograph. Similarly, on a computer monitor or television screen, the image is created by a grid of tiny dots (pixels), each of which may be on or off. If the mind perceived only the dots, we would not recognize the image. It is our ability to perceive coherence and to “connect the dots” that allows us to recognize a picture. Though the picture is digital, our ability to recognize and interpret interim results is analog, like our ability to “see shades of gray.”

In 1971, John H. Conway designed the cellular automaton called the “Game of Life,” which can be programmed onto a computer and displayed on a screen. This “board game” is played out in a discontinuous series of states on the screen of the computer monitor.

The global rules for Conway’s Game of Life look like a tic-tac-toe game.


Each pixel on the computer screen can be either on or off. When a pixel on the screen in the Game of Life goes on, it’s called a “birth.” When it goes off, it’s a “death.” Whether it goes on or off depends upon the condition of its eight neighboring pixels. If two neighbors are on (alive), it stays as it is, either on or off. If three are on, it lights up, whether or not it was lit in the previous instant. In all other cases it goes dark. Slight variation in the rules can give widely differing results.

Each “cell,” or pixel on the grid, computes its state in the next instant, given the state of its nearest neighbors in the behaviors vary accordingly. From this one principle, slight variation in the rules can give widely differing results.

A cellular automaton evolves over time. Each cell has criteria for decision-making on the fly, rather than a goal. It uses these criteria to detect whether its light should be on or off in the next iteration of its world.

Pixels in the zebra image that ZIG and ZIR will draw are linked through the global action of uniform rules. A discontinuity or perturbation in ZIG’s matrix triggers the invention process. The trigger could be a “seed pattern,” or another discontinuity in the matrix of dots. In this metaphorical scenario our two characters, ZIG and ZIR, collaborate to draw zebra using cellular automata as their tool. They show how a global pattern arises through local response to global uniform rules.

As ZIG and ZIR carry out their thought experiment to invent a zebra image, our traditional fixation on goals might allow us to notice only the final zebra image. But through the process of gradually approximating a zebra, many images are generated along the way. These interim images would be discarded if ZIR recognized only zebras. The origin of life, its evolution, and the creative process in general seem to share five attributes. Both

  • start inventing from uncertainty;
  • establish decision-making criteria without goals;
  • tolerate ambiguity;
  • recognize patterns in partial data; and
  • interpret interim results.

These five attributes characterize a third option to explain evolution. An hypothesis for how life originated and evolved emerges as life itself emerged and became alive. Both hypotheses about evolution, and evolution itself, gradually converge on their outcome over time. Criteria for becoming alive differ from the goal of being alive because criteria define becoming alive as a process, whereas goals only allow us to assess life’s outcomes as objects after-the-fact.

The origin of life, and its evolution, both qualify elegantly as “ill-structured problems.” But from our perspective, to call them “ill-structured” is misleading. Such problems are “ill-structured” before-the-fact, “structured-in-process” (i.e. self-organizing), and “highly structured” after-the-fact. Where the interpreter sits relative to the timeline of the process makes all the difference.

Through the “big picture” of ZIR’s perception of an image evolving, we ask the same questions of ZIG and ZIR as they try to invent a zebra image that origin of life theorists might ask:

What was the first zebra image like?

Gray. Very gray, as it flickered between not being a zebra and becoming a zebra.

Who was the first ancestor of that image?

That ancestral image emerged from uncertain gray, from neither black nor white. It’s hard to define precisely when it started to become a zebra image.

Where did that zebra image begin?


On neutral ground, emerging gradually from foggy grayness to clarity. Where? is both the context for the origin of life and the big screen on which ZIG and ZIR collaborate to invent a zebra image. A trigger in the undifferentiated matrix must unbalance stasis to start evolution.

How did an image of a zebra invent itself?

A little gaming is the ticket here, as in the games of Twenty Questions, chess, the uniform rules of cellular automata, and the Prisoner’s Dilemma. ZIG knows nothing about extinct species, so inventing a Tasmanian Tiger image by accident as a route into zebra stripiness is unlikely. The Tasmanian tiger, of which the last known died in 1936, was compared to both tigers and wolves because of its appearance, but it was actually a marsupial, showing how little appearance sometimes reveals. The Tasmanian tiger (technically known as a thylacine) has been proposed as a candidate for cloning. Interesting, but a digression from ZIG’s current focus on inventing a zebra image.

Nor would inventing an image of the extinct Quagga, of whom the last died in 1883, be on track to a zebra image. Once considered a species distinct from the zebra, the Quagga was only recently reclassified as a variation of the southern plains zebra. But our thought experiment concerns only the invention of a zebra image, a zebra look-alike, so these genetic details are irrelevant.

QuaggaWhich great debates are about inventing an image of a zebra?

Debates about local decision-making and global structure, targets of selection in evolution, open systems versus closed, predictability versus unpredictability, the how-much-time and information debates, and the concept of co-evolution are represented by this thought experiment about ZIG and ZIR and their image of a zebra.

Where is the boundary between “not being a zebra” and “being a zebra”?

That’s hard to say. We cannot predict in advance where on the spectrum from non-zebraness to zebraness ZIR will exclaim, “Aha! That’s a zebra.” Maybe it’s like the question, When did non-life come to life?

What evidence exists to claim any given image could possibly become an image of a zebra?

That’s a matter of opinion. ZIR’s opinion. Or yours, OR mine. Or the opinion of the zebra image itself.

What if?. . .

A zebra image inventing itself, with a little help from its friends ZIG and ZIR, may resemble how life originated itself with a little help from its environment, evolving by choosing promising directions to pursue.

In the game of Twenty Questions, one player, ZIR, thinks of a word. The other, ZIG, must guess what it is in less than twenty questions, which can be answered by “yes” or “no.” There’s a goal: to guess the word “zebra” that was chosen at the outset of the game. Each image ZIG generates is like a question in the Game of Twenty Questions. And, as in Twenty Questions, each of ZIR’s responses is independent of the previous response, related only to the goal, the zebra image. All previous answers remain valid as ZIG and ZIR progress toward a pre-determined goal.

“No” can be analog, a guide, indicating that ZIG is off track and should readjust. Or “no” can be digital, shutting off a path and demanding backtracking to start again. ZIR gives ZIG only the first type of “no” answers, “You were closer with your last image – don’t continue this,” or “This is better than your last try.” As in Darwinian evolution, ZIR (playing the role of the environment) can only assess what ZIG has already done. She cannot tell ZIG how to generate anything new.

Twenty Questions requires digital answers: Is it an animal? “Yes” or “no” either selects or rejects each proposition. For this analytic approach, ZIR sits outside, looking down on ZIG’s screen with a God’s eye view. If ZIR sees “the big picture,” which no individual pixel sees, and knows what each individual pixel must do to play its part in that big picture, then ZIR can respond to each individual pixel with its own personal alarm. Problem solved. No invention is necessary; each pixel follows instructions.

But in evolution there is no such overview.

ZIG, by guessing, and recognizing the successes in his guesses, gradually approximates a solution. ZIR assesses the whole image at each interim step. As ZIG and ZIR invent a zebra image, the “correct” answer is not absolute. Each answer is assessed relative to the previous. Though pixel states are digital (on or off), ZIG and ZIR’s thinking processes are analog: ZIG amplifies aspects that “seem to work” and diminishes aspects that “don’t seem to work.”

Each move is determined relative to the previous move (question or image). This move brings the collaborating pixels closer or further from a zebra image. In the game of Twenty Questions, where previous answers remain valid. In chess previous answers are lost, and become irrelevant, as the board changes. The current state of the board summarizes all relevant history in the game.

Chess-playing computer programs illustrate how criteria for decision-making supersede goals. The program does not know the form of its goal, checkmate. So it cannot be pre-programmed to “reduce the difference” between its present state and this unknown goal state. Instead, it uses criteria for decision-making to choose between alternative lines of play. Early computer chess programs tended to compute decision trees forking from alternative moves. Capacity for whole pattern recognition, to fill out possibilities implied in partial patterns, was a harder problem.

Suppose one pixel is out of order and permanently “off,” so that it must be part of the zebra’s black stripe. If one of ZIG’s pixel “light bulbs” burns out, this trigger determines that there will (certainly) be no white zebra stripe crossing that spot. This trigger introduces a bias. What counts is not this trigger but the fact that ZIR recognizes it as a trigger that causes a reaction that shifts complete neutrality toward a possible image of a zebra.
0zebrastripesOnce ZIG accidentally generates stripiness, and ZIR signals that stripiness is an attribute of zebraness, ZIG still has an infinite range of options for “the other color,” and drives ZIR crazy with his experimenting until he finally recognizes that he must stick with white.

ZIG, ZIR, and their pixels invent a zebra image by distinguishing between mental uncertainty and actual possibility. They start in the uncertain gray between the definite extremes of black and white to make inferential, abductive leaps toward possible zebra images. ZIG and ZIR are uncertain as they design and interpret the zebra images that they collaboratively generate.

Maximum uncertainty sits in the middle of the spectrum, where it is equally possible that the image may, or may not, become a zebra. But actual possibility relates to mental uncertainty in an interesting way. Certainty exists only at two opposite ends of the spectrum — when ZIR’s alarm does not go off at all (definitely no zebra here), and when it goes full blast (definitely a zebra). For the entire spectrum between those two extremes, some actual possibility (maybe this image might become an image of a zebra) is correlated with some mental uncertainty (maybe ZIR thinks this image could become a zebra).

Related Topic:

       The APR Hypothesis: autonomy + pattern recognition


I thank physicist Erich Harth who originally inspired this thought experiment and encouraged this work. Alth0ugh we normally think of metaphors as linking objects, this thought experiment is a process metaphor that explores an emergent model for the creative process and its analog in evolution: suppose the origin and evolution of life and mind exemplify epigenesis — starting generic, differentiating, self-organizing and gradually becoming more specific (as a spore or egg differentiates to produce an organism).

  1. Harth. 1976. “Visual Perception: A Dynamic Theory” Biol. Cybernetics. NY: Springer Verlag. 22.169-180.

_______. 1982. Windows on the Mind. N.Y.: Morrow.

_______. 2005. The Creative Loop: How the Brain Makes a Mind. N.Y.: Helix Books.

I’m indebted to Scott Turner for his probing analysis and logical gap-finding in the ZIG-ZIR thought experiment. He was the critic who prompted me to ponder whether I was indeed caught in a Platonic trap (I think not). His concerns led ZIR to make friends with QIR in order to get out of her fix  (QIR was excluded fromthis excerpt. Read the chapter in the book What Daedalus told Darwin for the full story).

Image Credits: Giulio Zanni. Zebra Herd in Tanzania.
Steve Bloom. Zebra herd in Botswana.