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An Instruction Manual for Concept Art

Henry Flynt

(c) Henry A. Flynt, Jr. 1993

A counting stand consists of two quarter-inch thick rods, displayed vertically at eye level with a one-inch separation. Forty-four inches behind the stand is a black wall. The viewer stands 14 to 16 inches in front of the counting stand and looks past the rods at the wall.

[see the illustration]

A typical result is that you transitorily see three rods. (The apparent breadth of the display doubles.) If the rods are of different colors (left--yellow; right--blue), either yellow or blue can be seen in the center. There can be a middle rod with a stable composite color, but instead of being green, it will be whitened green, or chalky.

Many number/position variants can be seen. The middle rod can be a fusion (Siamese twins) of the two outer rods. Four rods can be seen. In both of these cases, with four distinct stripes, the colors can repeat (yybb) or alternate (ybyb). The left rod of the three can vanish, leaving two rods of the same color shifted one inch to the right. If the two rods are stainless steel, both outer rods can vanish, so that only one (center) rod is seen. (In a further variant of this last effect, one can see three rods, but the bottoms of the outer rods vanish.)

Yet another complication is that two middle rods can be separate at the bottom and grow together as they rise.

Visitors to my exhibit are asked not to touch the counting stands; I make an exception for myself. When I try to touch a middle rod that looks like the right rod with my forefinger, in most cases my forefinger hits the right rod. If I sustain the doubling of the rod while my finger enters my field of vision, then my finger doubles.

When the yellow rod is present in the left middle position and I try to touch it, my forefinger splits, and the left scopic finger passes through the left middle (yellow) rod. (While the side of the right scopic finger may hit the blue rod.) With practice, I can see my forefinger and the left middle rod interpenetrate.

Mathematical logicians of the early twentieth century raised the question of a state of the world which falsifies arithmetic as a throwaway remark. In From Mathematics to Philosophy (1974), p. 26, Hao Wang acknowledged that elementary arithmetic would be falsified if it were "misapplied" to pieces of cloud. In Constructive Mathematics (1951), p. 70, Reuben L. Goodstein had made a similar throwaway remark:

A world in which objects appeared and disappeared spontaneously would be a world in which our common arithmetic would find no application, just as our language would find no part to play in a world which disrupted the familiar coincidences of visual, audile and tactile experiences.

From my point of view, it is a waste of time to respond to these remarks. (For Wang to have chosen pieces of cloud as his example of transitory entities was especially clumsy and shallow.) I shall proceed directly to expound the intricately nuanced lessons of the counting stands.

Approaching a counting stand, common sense tells us that we are concerned with two material rods. Such a common-sense statement as this is at the base of physical science, since science can conceptualize the rods, and bring apparatus to bear on them: only after you common-sensically and conatively find the rods, the apparatus, and your own "impulsion" (motivation, choice-making, imagination, etc.).

After the attempt to vindicate common sense as the metaphysics of substantiality collapsed, modern empiricist philosophers acknowledged that awareness "finds" or embraces sense-contents, not material bodies. That is, for consciousness, material bodies cannot be anything but pragmatically favored conjectures. As long as visitors do not touch the counting stand, their perception or knowledge that there are two material rods approximately in front of them depends entirely on a visual impression. One concludes a material body from a visual impression because one already has a fully formed conceptualization of the world one is encountering, prior to any particular perception. One already "knows" what a material rod is; and because one continues to see two distinct rods as one's vantage-point in the room changes, one has no hesitation in interpreting the scopic rods as material bodies. In other words, perception of the rods as material bodies is confirmed, even if one never handles them, by abstract visual invariance of the rods' number and color as one's vantage-point changes. (Although, of course, number and color are only approximately invariant; it is easy to find vantage-points such that one rod hides the other, or such that their shades change.)

One expects that tactile exploration would find the same rods that vision finds--both in respect to number and to position. Looking at a rod and grasping it at the same time, one perceives not a scopic rod and a tactile rod which are incomparable, but rather a material body.[1] To repeat, one perceives a material body. This is an interpretation--it could not appear in perception without a pre-conceived theory of material bodies. Psychology says that perception organizes the object-gestalt (the presumptively material rod) intermodally (i.e. intersensorily). In the act of perception, there is an inversion in which the sensuous contents (sights, touches) are alienated in the experience-world, to become mere supports of the material body (that body being given to perception, yet being totally pre-conceived and conjectural).

Even though one has this fully formed conceptualization of a material body, any attempt to codify this conceptualization in propositions will quickly become foolishness. How does a material body occupy its position in absolute space[2] ? How does it get from one instant of time to the next?--by persistence, or by re-creation? ("The yellow rod now is the yellow rod back in the past"; then what is the obvious estrangement between the present rod and the bygone one?) When the body's position in space varies from one instant to the next, how is its material identity sustained?

At one time, these were questions for metaphysics. Proving to be futile, they were abandoned. A new method arose, Baconian science, which soon cloaked itself with an ideology of empiricism. Today, we are indoctrinated to translate the questions of the previous paragraph into questions which physics might seek to answer at the most advanced level.[3] But knowing proceeds here on a cyclic path which never reaches any autonomous evidence or identically true experience. It is through acts of perception which are excluded in physics that one finds, first, the laboratory, then the door, then the doorknob--wills the opening of the door, a juncture incomprehensible to physics--enters the laboratory, and "finds" the material rods. One uses one's common-sense pre-conceptions to find the material rods in absolute space; then, centuries later, one concocts some recondite fantasy such as geometrodynamics to substantiate that material bodies can be in absolute space.[4] Geometrodynamics--unlike the presence of a material rod in the room--cannot be tested relative to sensuous contents at all.

Let me call the common-sense rods one is supposed to find the normative rods. There are two normative rods. But when I view the counting stand, I transitorily, and in response to my intent, see three rods, or four, or only one. If we are restricted to a vocabulary of normative rods, then perception proves that

2 = 3

for example. (Since the three rods I observe are only allowed to be the two I am supposed to find. I have to crush my perception to my pre-conception.)

On the other hand, we may turn to a language of apparitions. This is an extremely difficult step.[5] One borrows the language of common-sense objects to describe apparitions; but common-sense objects are just what apparitions are not. In this study, I am concerned with sense-specific apparitions or sensuous contents--the very contents which perception overruns to organize an object-gestalt. An extraordinary analytical procedure is involved. I disconnect a level of interpretation of the sensorium which previously was automatic. The act of perception had alienated the rod-sight (and rod-touch, if any) to favor the material body, a conceptual conclusion. Now I regain the rod-sight and rod-touch.

Apparitions can be terms in a language without being analytically reduced to sense-specific contents (sights, auditions, touches, smells). That is how one reports a dream, for example: as if one had been present with objects. That approach will not be involved in this study.

To begin with, then, we are concerned with visual-apparitional rods or scopic rods. Let us now bring in the logic of plurality. Over an extended period of time, the viewer faces a set of scopic rods. The things in the set which are counted are scopic rods. The set varies instantaneously in number, position, color--and even object-composition, as when one sees Siamese-twin rods. There is an interaction of voluntary control of the image and involuntary alteration of the image.

Abstracting to the cardinality of the set, excluding the Siamese twins and half-vanished rods, we have a set of scopic objects whose count varies momentarily from one to four without any material change in the object-zone. In a process which is probably related to non-deceptive autosuggestion, you learn to find a particular illusion and hold it. If the focus of your eyes determines the image, this focus stabilizes only when you intend the image. Knowing what you want to see selects the focus--not the other way around.

The situation is so far beyond any ever pondered by scientific civilization[6] that at the present time, I only propose to familiarize us with the situation "phenomenologically." To codify an arithmetic for sets of external things which appear and vanish--interactively with awareness but without being fantasized or hallucinated--is a task for a much later stage. Such an arithmetic would of course have to be cross-related to whatever arithmetic would reflect the Necker-cube rationales which I treated in "The Apprehension of Plurality." Since one doesn't see more than four rods at a counting stand, for example, the phenomenon is not unconstrained.

The cardinality of the set, we find, is produced between personal awareness and the object-zone. It is between personal awareness and the object-zone that the world-mirage occurs; personal awareness palpably conditions the clinical objectivity which one finds.

If I fix a point in the visual field mentally without an image to anchor it to[7] (the farthest left of the field; the exact center of the field?), then the location of the scopic rods relative to that point undergoes instantaneous or continuous changes. As I said, it is possible to see three rods and then have the leftmost rod (or both the leftmost and rightmost) vanish. When the leftmost of the three vanishes, it looks as if the normative pair of rods jumps one inch to the right.

One might argue that it is not fair to codify arithmetic so that it mimicks things-in-the-world. (Except that children are taught arithmetic with blocks.[8] ) Arithmetic, it is said, concerns celestial abstractions. These abstractions have the identity-character of rocks (or wooden blocks), except that instead of being fixed for a year or two, they are fixed for eternity. (The numbers are made out of nothing and they remain fixed forever--what a marvelous building material that would make.) It might be argued that I am unfairly substituting for an arithmetical situation a situation whose logic can only be understood physically. Very well, let us consider the set of scopic rods as a situation in physics--a situation observed visually, as astronomy observed the sky for most of its history. We have instantaneous division of bodies, instantaneous change of position, two bodies interpenetrating to occupy the same place at the same time, etc. It may be objected that this is still unfair, since I have not included tactile evidence in concluding what I observe. Very well, let us bring in tactile evidence. Now we find, as I said, that I see that I have two right forefingers (do I only feel one forefinger?), and that I see the leftmost finger pass through another body (like a ghost) while I feel the rightmost finger hit the side of the rightmost rod. We have all of the empirical pieces of physics, but having chosen to view the whole through an "abnormality," the pieces do not support the notion of a physical universe.

The same remarks pertain to a different zone of conceptualization: common sense--and objecthood as one of its categories. When you try to touch the presumably phantom rod, usually you feel a solid rod. On the other hand, it is possible, although rare, to follow your finger as it visually passes through a copy of the yellow rod, feeling no tactile resistance. The common-sense object disintegrates at the level of its intermodal organization in perception.

Husserl forthrightly addressed this juncture in Ideas--as he would have to do to propound "phenomenology" seriously. "The world-order is not guaranteed by things-in-themselves; that would be superstition. The world-order is guaranteed by regularity of the collation of sensations. Admittedly, there are junctures, called illusions, where the regular collations fail." But, Husserl says, these failures actually prove the rule: because they precisely fit into a much broader total collation. (In this case, the neurophysiological doctrine of vision as a stereographic camera; and binocular competition.) But again, this orthodoxy takes a cyclic path which never reaches any autonomous evidence or identically true experience. Husserl's "broader collation"--arcane and conceptual--rests on nothing but the narrow collation provided the narrow collation is well-behaved. (When the perception-of-the-moment agrees with the norm, in other words.)

To Husserl, the counting stand proves that (when the flaws of your neural apparatus are triggered) you can see a rod which isn't there. (Again, do we have a vocabulary for apparition or not? Husserl needs to say that an appearance can be palpable as an appearance without matching objective reality. Incidentally, that returns us to the intractable problem of objective reality. But without the distinctions, Husserl has said "here is a rod which isn't here"--asserting an inconsistency.)

My perspective turns the argument upside down. Husserl's sure-enough, God-honest material rods are an incoherent cultural fiction. Science can propound all the conceptual models it wishes about the retina, the optic nerve, the visual cortex, binocular refraction. Everything that science says to explain the abnormality involves immensely circuitous "models" such that one has to abandon the standpoint of the living viewer to prove them out.

In turn, conative implementation of the theories requires acting in the life-world--as guided by the vernacular theory called common sense. And yet science must pretend to hold common sense in contempt. A compilation of common sense's manifest tenets finds it to be pervasively inconsistent.

So the models rest on incoherent circuitousness and conceptualization.

The forefinger passes through the rod; and the rods instantaneously change position in the field of vision--without any force being imposed in the object-zone. Having chosen to view the whole through an abnormality, the occurrences do not crystalize as a physical world. Husserl's faith in conformism rests on the assurrance that there is a wider collation, a vastly more circuitous and conceptualized[9] collation, which explains these junctures away. But we only have here a classic case of the protocol of rationalization. Each of the endless surprises for the theory is reconciled with the initial strategy by a qualification added for its benefit. But my position is that the doctrine of objecthood was elementally in the wrong epistemologically before it ever looked at any occurrence. Thus, I refuse to humor its protocol of rationalization.

Only after we have allowed Husserl to have his say can we name the viewer's perception at the counting stand. It is an "illusion," or an "anomaly": the abnormal rods. You have a crystallized peception which does not match the God-honest object. Again, Husserl needs to say that an appearance can be palpable as an appearance without matching objective reality. The perception at the counting stand is the wrong answer; but, then, it is an abnormality. (If we said that it is abnormal for a horse to have four legs, would that guarantee that no horse really has four legs?)

Again, experiences at the counting stand expose that one arrives at any perception carrying a fully pre-conceived metaphysics of the life-world. Given the counting stand, you "request" of your own perceptions that vision and touch should always agree that there are two rods atop it. You already have a fully conceptualized theory of what you should sense and what it signifies. You carry a fully elaborated doctrine of material bodies with you. Perceiving is a ceaseless gymnastics of twisting the rush of sensations into this doctrine.

Normally, you would not maintain the middle rod; rather, you would pigeon-hole it into the theory which says that there are two material rods. You would seize on cues to discredit the middle rod (such as inability to stabilize the total image even when you hold your gaze steady). When your senses do not provide the requested answer, you become an intellectual opponent of your senses. You try to argue them down.

One has to consider accepting all experiences, perceptions, or sensations without treating them as evidences of realities. Then a common-sense world or a physical universe could not be found. That motivates my terminology of grading. One grades the scopic rods, taking the greater variability of the rod in the middle as a proof that it possesses less reality than the outer rods. (But it's not that easy. The distance between the real rods changes when the middle rod disappears!)

Of course, my offer of a new integration is not a proof that material bodies don't exist. The value of the counting stands is to introduce you to situations in which direct perception and doing diverge from the normative preconceptions, and actually belie them. These situations motivate the richer and more subtle integration which I offer. As far as a comprehensive exposition of this integration is concerned, my work of the last three decades is only a beginning.


The counting stand had an unexpected result. In Wittgenstein's Tractatus, there is a passage asserting that it is logically impossible for a surface area to be uniformly colored by two different colors at the same time. Let me quote the entire passage, omitting the section numbers.

For example, the simultaneous presence of two colours at the same place in the visual field is impossible, in fact logically impossible, since it is ruled out by the logical structure of color.

Let us think of how this contradiction appears in physics: more or less as follows--a particle cannot have two velocities at the same time; that is to say, it cannot be in two places at the same time; that is to say, particles that are in different places at the same time canot be identical.

(It is clear that the logical product of two elementary propositions can neither be a tautology nor a contradiction. The statement that a point in the visual field has two different colours at the same time is a contradiction.)

Tractatus Logico-Philosophicus, p. 145

Wittgenstein felt so strongly on this issue that he made it almost the entire topic of "Some Remarks on Logical Form" (1929).

But now we have the counting stand with yellow and blue rods--and the middle rod. There are moments when I see that the middle rod is blue all over and yellow all over at the same time.[10] Once again, then, anomalous perception has provided an apparition which violates logical possibility.

As I noted when discussing such junctures in general, in "Introduction to the Logic of Contradictions," the experience is not at all a mere "convention." For me, it was entirely unexpected that the component colors could be in the same place without mixing. Moreover, the perception is uncanny: you instinctively feel that you shouldn't be seeing it. I now have a rather extensive list of such perceptions. They are highly diverse qualitatively. Let me extrapolate, and propose that every inconsistent observational description could be given a non-vacuous semantics through "irregular" perception.



Henry Flynt, Blueprint for a Higher Civilization (Milan, 1975)

Henry Flynt, "The Apprehension of Plurality," in Io #41: Being = Space X Action (l989)

Henry Flynt, Paradoxes of Common Sense (1988, unpublished)

Henry Flynt, Introduction to the Logic of Contradictions (1981/1992; unpublished)

Henry Flynt, Superseding Scientific Apprehension of the Inanimate World (1990, unpublished)

Reuben L. Goodstein, Constructive Mathematics (1951)

Adolf Grünbaum, "Relativity and the Atomicity of Becoming," The Review of Metaphysics, 1950, pp. 143-186

Adolf Grünbaum, "A Consistent Conception of the Extended Linear Continuum as an Aggregate of Unextended Elements," Philosophy of Science, 1952, pp. 288-306

Adolf Grünbaum, Modern Science and Zeno's Paradoxes (1967)

Hao Wang, From Mathematics to Philosophy (1974)

Ludwig Wittgenstein, Tractatus Logico-Philosophicus (London, 1961)

Ludwig Wittgenstein, "Some Remarks on Logical Form," Knowledge, Experience, and Realism (Johnson Reprint Corp., 1964)


[1] Just as, when one taps the floor with a stick, one perceives the floor in the end of the stick.--Even though anatomically this is absurd.

[2] Absolute space: the space which is supposedly homogeneous independently of vantage-points.

[3] Classic examples are Adolf Grünbaum's treatments of Zeno's paradoxes. See the References.

[4] One has to take care not to be betrayed by the rotation of fads. Geometrodynamics, treated respectfully in the Seventies, has now more or less been discarded as charlatanism.

[5] One issue. If I see a red patch here, could I be mistaken? How close are the terms to meaning the apparitions?

[6] Again, the only precedent is Wang's clumsy example of pieces of cloud.

[7] Since the display attempts to eliminate "data" not involved in the illusion.

[8] Wooden blocks, of course, cannot express properties involving "very large" pluralities.

[9] The layperson accepts physics blindly because it has overrun his or her life. The layperson has no idea what physics actually says. Try to explain any idea of physics to a filling-station attendant or a dishwasher and you will be told that you are insane. For example, when a suspended object is released, it passes through an infinite number of different speeds before reaching any positive speed. Does the filling-station attendant wish to show me each of the infinite number of different sub-positive speeds? If one believes the orthodoxy, science's explanation of the infinitely small was utterly wrong throughout the entire classical modern period--until Cantor straightened it out with his notion of different sizes of infinity. Even the experts were utterly wrong about the most basic things until a century ago. That is how far physics is from being straightforward.

[10] Neurophuysiologically, it is as if you are stacking the binocular information.