by Dennis Small

I am sure you are all familiar with the case of the guys who went hunting, the three professionals: one was a doctor, the other was a lawyer, and the third was a mathematician, specifically a mathematical probability theorist. They went hunting for geese.

So the doctor gets out there, and he’s the first man up. Now he’s a doctor; he may be a skilled surgeon, but he really doesn’t know a whole lot about shooting. So he picks up the shotgun: Blam! It’s about ten yards to the right of the target. “Damn. Missed.”

Then the lawyer comes up and says: “No problem, I can do this.” He pulls the shotgun up and: Blam! Ten yards to the left. “Damn. Missed.”

Finally the mathematical probability theorist stands up. And he shouts: “Got ’em!”

I’m assuming you had a delayed reaction here; and that’s what’s interesting, because that’s how the mind works (as we’ll come to later). This is proof of how humor actually functions: It is mental activity, not anything specific that is said. After all, who could imagine that the two words “Got ’em,” could be funny? What is funny in saying the words “Got ’em?” Is there anything funny about the words “Got ’em?” Not particularly.

What is it that makes it funny?

To actually get at the underlying, epistemological issues behind this, the fundamental philosophical questions, we are going to need to briefly review a few salient points about the concept of time-reversal. Because, as you may have noticed, what was actually humorous here, was the totality of the joke as viewed retrospectively from the punch line. There was nothing particularly funny about the course of the joke itself. The humorous thing comes in, as your mind recapitulates everything that it has just walked through, after the conclusion. The conclusion isn’t funny. None of the points along the way are funny. The whole thing strung together isn’t funny. What is funny, the humor, is what is unsaid, which is the mental activity of recapitulating what you have just walked through, from the standpoint of the unexpected conclusion. Which is why the delay factor is of some interest in this, in how it works. Because it is your mind retracing its own steps: that is “time-reversal.”

Let me tell you what I don’t mean by time-reversal, and what I do mean by it.

If you look at Lyndon LaRouche’s writings on the issue of time-reversal,1 you will note that the phrase he actually uses is “time-reversed causality.” You may have noticed also that, over the last several years, LaRouche has stopped using the word “negentropy,” and instead has insisted on using the expression “not-entropy,” or “not-entropic,” or “anti-entropic.” He has explained that the reason for this, is that the word “negentropy” triggers an association in the mind of people who have read Norbert Wiener and so forth, of a concept of entropy going backwards: in other words, simple entropy in reversed time. And that is not what LaRouche means by “not-entropic”—he is not talking simply about taking entropy, and standing it on its head, or taking a video clip of something that is entropic, and playing the reel backwards, that kind of time-reversal.

What he is talking about with “not-entropy” is something completely different. He is talking about a different process of development, which is completely contrary to the concept of the physical universe as described in “entropy.” And he has deliberately chosen to use the phrase “not-entropy,” or “anti-entropy,” to force the individual, each of us, to create in our own minds a positive concept, which cannot be reached by simply trying to explain it negatively in relationship to entropy.

Now the question of “time-reversal” is similar. Time reversal is not the arrow of time which marches along chronologically, like a metronome (1, 2, 3, 4,...), going in the opposite direction. It is not a linear concept of time, put in reverse. That is not what we are talking about; we are talking about something completely different.

We are talking about a concept of time that actually functions at two levels simultaneously—two different types of time. We are talking about the time of that which is created, of the phenomena which occur, as in a chronological time; simultaneously considered with the time of that which creates them, that is, of the hypothesis relative to the theorem-lattice2 which it has created. The time of the hypothesis is everywhere present in every moment of the development of the theorem-lattice. As the causal factor, it is equally present at points A, B, C, D, E, or F, in what is otherwise chronological time.

So, the time of the hypothesis is in that sense eternal, relative to the entirety of the time of that which it has created.

Let us look at the matter this way. Leibniz says the following, on the subject of time and space:

Space is an order of coexistences, as time is an order of successions.3

“Space is an order of coexistences.” In other words, Leibniz is saying that the physical universe is not composed of physical objects banging around in space. Rather, space is actually relative; there is no distinction, there is no way of cleanly separating out space and the material objects “in” it. There is no three-dimensional, empty spatial Cartesian coordinate system, within which material bodies are banging around. Rather, Leibniz says, space is an order of coexistences—it is the way that coexistence is ordered. It is an ordering of physical space-time. And he says similarly, “time is an order of successions.”

In his 1714 Letter to Remond, Leibniz says:

Space, time, extension, and motion are not things, but well-founded modes of our consideration.... The source of our difficulties with the composition of the continuum, comes from the fact that we think of matter and space as substances. Whereas, in themselves, material things are merely well-regulated phenomena. And space is exactly the same as the order of coexistence, as time is the order of existence which is not simultaneous.4

So time is not the clicking off of the clock or the metronome. The only thing that time is, says Leibniz, is the order of existence which is not simultaneous. So already, in Leibniz, we have a completely relativistic concept of time and space. But to more thoroughly grasp the concept of time-reversed causality, we have to go back to Plato’s solution to the paradox, or the apparent paradox, of the One and the Many.

Do not think of a One as the aggregation or assembling of a Many, to get a picture of the totality. That is not the idea. Rather, think of a One as the causal singular concept which uniquely explains, or causes, all of the specific things, or Many, which are created. You want to think of the One as the hypothesis, which is at a different level of existence, a higher level of existence, than all of the particularities of the phenomena which it is explaining. So, you have a multiplicity of phenomena, either of experiences or of material objects, if you care to view it that way, which produce these experiences. And the concept of a One, is that hypothesis which, through mental action, you create and which is the causal explanation of the Many. The One functions or exists at a totally different level than the Many. You cannot get to the One through any aggregation of the Many.

Similarly, you cannot have a concept of time as it relates to the One, within the same general bounded universe of the Many. You are talking about two completely different levels of existence.

This is what LaRouche frequently refers to in terms of the idea of a theorem-lattice, and then the hypothesis which creates a succession of such theorem-lattices. Within the realm of the specific theorem-lattice, or that which is created, you have what could be called chronological time, time which is clicked off like a metronome. This time seems to march fairly regularly forward—from past through present into the future—through that time as it exists within the world of the created.

However, if you look at that exact same process from the standpoint of the hypothesis which created the theorem-lattice, then you are looking at a concept of time which applies to the totality of that which has been created (the Many). And the time of the hypothesis is, on the one hand, eternal, or everywhere present within the time of the many, but it is also simultaneous. It is neither before nor after; it is neither later nor earlier; it is simultaneous and eternal at the same time. It affects all parts of that which is changing, but it is that which does not change through all change.

One of the most useful examples of this conceptual issue, is the famous Heraclitus question: Can you step in the same river twice? If you view “the river” as your sensory experience of whatever the river is made up of—the water, the pebbles, the bank, and so forth—it is clearly the case that you cannot possibly step in the same river twice. If you define “the river” as what you are experiencing, what you experience one minute when you stick your toe in, and then you come back a minute later or even a half second later, and you stick your toe in again, it’s a completely different river. Nothing is the same; everything has changed. The water has gone by; the pebbles have moved a little bit; the wind is blowing differently. Everything is pure change. So what is it, then, that allows us to say “this is a river.” What is it that makes it a One, a Unity?

We are clearly forming a mental concept, a construct, a hypothesis, which is a One, relative to the Many which we are perceiving. That One is somehow unchangeable through all change.

The same thing applies to human identity. You say the word “I.” But what do you mean by “I”? Do you mean the “I” that you perceived at the moment that you began to utter that one-syllable word; or the “I” when you finished enunciating that one syllable word? Because everything has changed inbetween. You’ve moved a little bit; all of your atoms and molecules have moved; everything around you has moved; your internal, somatic experience of yourself has changed; you are probably a little hungrier than you were the instant before; you may be more thirsty; hotter or colder. Everything has changed; nothing is the same. So what, then, gives you the right to say “I”?

It’s an interesting question. What is identity? What is that One which is the same throughout all change? This is the concept of the One and the Many, and it starkly poses the issue of two distinct levels of time which exist simultaneously.

To quote directly from LaRouche on this subject:

Given: a series of events, each and all consistent with a specific theorem-lattice. These events are located in time and place. The relevant theorems are determined by an underlying hypothesis. In what part of that span of time and place, does that hypothesis exist? The hypothesis never changes during any part of that span of space-time; it exists, “simultaneously,” in all the places and times defined by that theorem-lattice, but is confined to none of them. Meanwhile, that hypothesis is the necessary and sufficient cause for the selection of all of the theorems adopted as propositions for the occurrence of the events. In this respect, as sufficient and necessary cause, the hypothesis has the form of the Good....

Thus, rather than the “Dr. Dolittle Push-me/Pull-me,” fairy-tale myth of mechanistic causality, commonly taught in schools today, we must have the sense of efficient relationship among past, present and future, as implicit in the Platonic notions of hypothesis and Good. If one says, from this latter standpoint, that the future shapes the present, or that the present shapes the past and future, it is only in the Platonic sense of hypothesis and Good, that such an efficient role of time is to be premised. It is through the relatively timeless hypothesis which shapes past, present, and future, that these three aspects of a continuing process behave as if they might be efficiently interactive at all times. They do not interact directly, of course!5

So, this is no simplistic, reductionist idea of time, such as: “Oh, yes, the future acts on the present and the past.” That is not what is happening. LaRouche emphasizes that it acts “as if” that were the case, and the reason that is so, is because what is actually acting efficiently in the past, the present, and the future of the chronological time of the created theorem-lattice, is a different order of time, that of the hypothesis, which is eternal or timeless relative to the past, present, and future of that which is created.

This brings us of necessity to Plato’s presentation of knowledge and the Good, in his famous discussion of the “Divided Line.” It is necessary to briefly review this, in order to address our next topic: Nicolaus of Cusa on the issue of how you know what you know, on time-reversal, and on the relationship of all of this to the all-important issue of jokes.

Plato presents his discussion of the “Divided Line” in Book VI of the Republic dialogue. The basic point that Plato makes is, that knowledge works by a process of successive development of new, overall concepts, or Ones, which explain the Many which are the objects of mental experience. The way that the mind works is, that it takes as its raw material, first, the simple perceptions that come from the visible world, the images produced by sensible objects. And from those perceptions, those images, the mind constructs a hypothesis, an explanation, a single, unique One, of what it is that is producing all of those sense perceptions. And this is what Plato describes as the process of hypothesis formation.

Plato goes on to explain that the mind works to see, in the world of the intelligible, much as the eye sees in the world of the visible. The visible world is illuminated by the sun; the intelligible world, the world of ideas or of thought, is illuminated by the Good. He says: Think of the Good as akin to the sun, which illuminates everything around it, but is not that which it illuminates.

Plato then explains that we form an initial hypothesis about the nature of even an object—because hypothesis formation is involved even in the humble task of conceiving of an object as such, and calling it an object. For example, a river: that is a hypothesis; you are saying that there is some Unity there. Or, when you say “I,” the implicit assumption of using that word is that there is such a thing as a Unity, there is such a thing as an “I.” There is a One, which doesn’t change throughout all of its specific manifestations.

Plato elaborates, saying that, in the world of the intelligible, the first objects of the understanding, or the first class of intelligible things, are those concepts that come from the physical world. But the mind then constructs an actual universal object, distinct from the specific things which it is observing. This is what he calls a thought-object, or a Form, or Idea. And the mind forms such a hypothesis, or Idea, in the world of the intelligible, regarding that which it is observing, that which it is taking as its object of thought.

Plato then describes the way the mind, in addition to constructing specific hypotheses to explain specific things, clearly demonstrates a capability of developing an ongoing series of such hypotheses, and that capability, which itself produces hypotheses, is a higher hypothesis. So, you have a whole nest of hypotheses, which is produced by a higher hypothesis. And then, too, the ordered set of these higher hypotheses, is in turn produced by a mental faculty, which is hypothesizing the higher hypotheses. So, you are talking about a level of causality existing at a higher level than the simple objects which are perceived. Plato is getting at the idea that, if you simply describe the world in terms of the space and the time of that which is created and apparently exists around us, you are missing the essential point. What you have to do is to look behind this, to the causal hypothesis which has created that array, and which leads you to a different concept of space and to a different concept of time.

This raises the crucial question of metric or measurement. How do you measure these distinctions, or these differences in space or in time?

LaRouche argues that, if the chronological time of the created, that is to say, the time of the theorem-lattice as such, is not the same as the time of the hypothesis which created it, and other theorem-lattices, then that difference has to be measurable:

Time is not an absolute, but only the name conveniently assigned to the experience of change.6

This is very similar to Leibniz’s formulation. The time of the hypothesis, the way you measure time in the domain of the hypothesis, of the One, is different from the measurement of time in the lattice itself. The time of the hypothesis enfolds within it, includes within it, that which then becomes unfolded as the time of the lattice.

This issue of enfolding and unfolding appears in many theological writings, including those of Nicolaus of Cusa. For example, Cusa explains that God enfolds within himself the totality of the created physical universe which He unfolds. But that unfolding, simply observed as an unfolding, is not in fact the enfolded totality which is within God. In other words, God and the physical universe He creates are not the same thing. You cannot say “God equals the entire universe”—which is the pantheist view. You are talking about two completely different levels of existence, of Creator and the created.

What LaRouche stresses, and this gets to the heart of the matter, is that, if you are talking about two different ways of measuring time, of two different ways of conceiving of it; if it does not function as a single, strictly chronological, metronomic time; then you have to be able to measure the difference, in some sort of an experiment, between what the perceived results would be based on the linear or the chronological time of the created lattice, and the measurement of time from the standpoint of the hypothesis.

This is the same issue posed by C.F. Gauss, Bernhard Riemann, and others in their study of curvature. Take the case of a plane surface. The metric, or the unit of measurement, on a Euclidean plane surface is, as we have all been taught, that “the shortest distance between two points is a straight line.” A related, axiomatic feature of this metric applied to a plane surface, is that the sum of the internal angles of all triangles adds up to 180 degrees.

That is fine and good, so long as you are on a flat surface. But what if we are not on a flat surface, but, say, on a spherical surface, which of course has curvature?

If that were the case, how would the distinction manifest itself? Well, it would show up in the fact that the shortest distance between two points on a sphere, for instance, is not a Euclidean straight line, but is actually measured by an arc of the great circle cutting the sphere at those two points. Thus, in the case of a spherical triangle, the sum of the internal angles does not add up to 180 degrees. And the shortest distance is the one which connects two points by the geodesic, that is, the shortest distance on a curved surface, which in this case corresponds to an arc of the great circle which goes through the center of the sphere.

So even in this very simple example of different curvatures, there is a difference of metric: your unit of measurement in one geometry (a flat Euclidean surface), is different than your unit of measurement in a spherical geometry. You don’t measure with the same units, because your unit of measurement in one case is itself already curved. The same principle holds in the more complex case of surfaces of changing (i.e., non-constant) curvature—which more closely reflect the nature of the real physical universe.

The same issue of metric applies to time. And, LaRouche argues that, if this is in fact the case, the difference betwen the two metrics is of necessity measurable. We can’t simply assert that there is the simple chronological time of the Many, and that there is also the time of the causal One which produces the Many; this distinction must be measurable:

The measurable impact of “time-reversal” must necessarily lie within the conceptual bounds of the crucial discovery at the center of Riemann’s habilitation dissertation. In other words, applying those methods of C.F. Gauss’s general principles of curved surfaces (which Riemann incorporated in the method of his own discovery), there must be a measurable difference in the implied curvature of physical space-time, reflecting the action of time-reversal upon the function as otherwise determined. [“Time-Reversal,” p. 39]