Transcript • Metaphor: an Intermezzo
January 9, 2012 • 12:24PM

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In these dangerous times, beyond which it is possible that the human species may not survive, it is essential to have a powerful imagination. This is not to fantasize in order to mentally escape our current situation, but rather to have the strength to envision the future which could be, a future worth fighting for. The human mind, unlike the brains of animals, is capable of going beyond the senses, of forming new conceptions of things yet to be, and of bringing them about. We have covered many future-oriented projects on this website, such as NAWAPA, the SDE, maglev rail, Arctic development, fusion-powered travel to Mars, and, eventually, matter-antimatter reactions.

How does the human mind create something new that didn’t exist before? How do we go from an investigation of the already-existing, to see something new? The answer to this question, is: metaphor, the key to discovery. Obviously, economic progress is impossible without scientific discovery, but while many would like to think of metaphor as a means to an end, as the tool by which we achieve progress, it is itself the goal. We’ll get to that, but first: what is metaphor?

Lyndon LaRouche has defined the meaning of the term “metaphor” in a recent writing, The Strategic Situation Now. He writes: metaphor “does not refer to a particular, explicitly direct object, or set of objects; it refers, to an implied simultaneity among a very special quality of several, indirectly related objects.”

He urges the reader to: “Consider the case of such an apparent characteristic of such a shadow-like object cast as such a pair, or, more. In such cases we are able to conceptualize the specific effect which accounts for the generation of the shadow of such a pair-wise, or comparable shadow; but we do not “see” the relevant sort of linkage.”

Let’s investigate this “implied simultaneity among a very special quality of several, indirectly related objects,” and let’s do that from the standpoint of projections. An object is concealed behind this screen, and you are seeing its projected shadow on the screen. What do you think the hidden object’s shape is? Here’s the shadow of another object. Based on this shadow, what do you think it looks like? Now, what would you say, if I told you that in both projections, you were seeing the same object, just from a different angle? Can you guess its shape? The viewpoints are unified in the actual shape of the object.

With access to only one of the two original projected viewpoints, it would have been impossible to determine the shape of the unseen object. By using them together, it became possible. Let’s now move to a higher example, Kepler’s investigation of the orbits of Mars and the Earth in the first work of modern science, his New Astronomy.


In his 1609 work, The New Astronomy, Johannes Kepler made use of two different viewpoints when he investigated the motion of the earth. Since we are standing on the earth, it makes it very difficult to see where it is, in astronomical terms. To look at the location of the earth, astronomers watched it indirectly, from the sun. You can look at the perceived location of the sun at dawn or at dusk, by looking at which stars are behind the sun. The sun’s location changes through the year, moving through the twelve constellations that make up the zodiac. Now, when we see the sun, it must see the earth in the exact opposite direction. This means that we can construct a map of the perceived motion of the earth, from the sun’s point of view. Note that although we observe the direction, we do not know the distance. Using only these direction observations, we can’t tell whether the earth moves in a circle, in an oval, or perhaps in an even more bizarre shape. With only the direction, it’s impossible to determine the shape of the orbit.

Copernican astronomers before Kepler, favoring simplicity, said that the earth moved at a constant speed in a circle around a point near the sun, although not the sun itself. Using the best measurements available, this hypothesis did match the data of perceived sun directions.

But Kepler, who at this point in his investigations had already shown from his study of Mars, that that planet did not move in a circle with a uniformity of motion, was seeking for a physical hypothesis of planetary motion, not a mathematical-geometric one. He believed the sun caused the motion of the planets, and that they were driven them more quickly when they were closer to the sun. But if the other astronomers were right, and the earth moved uniformly, in total defiance of the sun’s power, then Kepler’s hypothesis would go up in smoke. Therefore, he needed to know more about the earth’s orbit. How could he discover more?

Before we get to the answer, I need to ask you to perform an experiment. So, first, close or cover one of your eyes, and then keep your head totally still. Just move your eye in its socket. Look around the room, but don’t move head move at all -- just your eye. Now turn your head, and look somewhere else in the room. Do the same thing: keep your head still; move only your eye. Notice whether objects around you seem closer or further away. Okay, now, without moving your head, just open your other eye. Do you feel like you just put on 3d glasses? Using your two eyes together changes the richness of sight.

To get a similar effect, to add a “second eye” for his astronomy, Kepler decided to make Mars his observatory! Every approximately 686 earth days, he knew that Mars returned to the same position in its orbit. By using observations of the sun and Mars from earth on these days, he could reverse them, to watch the earth from the viewpoint of both the sun and Mars, at the same time! This parallax, this second view, allowed Kepler to measure the earth orbit much more precisely, and show that it, too, moved non-uniformly. This opened up the way for a universal cause of motion, governing all the planets physically, including the earth.

In this example, like the earlier example of the object behind the screen, Kepler used two different projections, a simultaneity between the two indirectly related perceptions, to discover something that neither could discern individually, by uniting them in his mind.

An Impossible Unification

While Kepler’s use of parallax shows the combining of two different perceptions, the resulting object of thought, an orbit, still lies in the field of vision. Like our earlier object hidden behind the screens, even if we couldn’t see it directly, it existed in the domain of possible visual perceptions, in visual space: it could have been seen, given the right viewpoint. But what if the unification of differing projections simply cannot be made in this way? What if the projections can’t be unified? We’ll take this up with another example from Kepler’s New Astronomy: his vicarious hypothesis.

Now, as we get into this model, as a preliminary note, astronomers before Kepler, recognizing that the planets seemed to change their speeds, had introduced the mathematical equant into their work – it is an imaginary point around which the planet would be seen to move uniformly. In this example, if the grey equant point was watching the planet, the planet would seem to rotate around at a perfectly constant speed. To make this easier to see, I’m showing eight different positions on the orbit -- they always appear the same angle apart from each other from the equant’s point of view, even though the actual speeds change. Now, you can see lines indicating the direction the sun would see the planets – the eight locations, always equally far apart in time, appear to change more or less as the speed of the planet increases and decreases. On the right, the distance between observations is large -- the planet moves much farther in one eighth of its year near the sun, then it does at the left when it is far from the sun. The perihelial apparent speed is how fast the planet appears to move, from the sun’s point of view when it is closest to the sun, and the aphelial apparent speed is how fast it appears to move when it is furthest from the sun. Here, the shaded-in angles give a measure for the apparent speeds.

So for Kepler to investigate the orbit of Mars, he had to pull together observations. In order to watch Mars from a stable position, Kepler set up another observatory, this time on the sun. He pulled together a dozen high-quality observations made when the sun, the earth and Mars were aligned, allowing Mars to be watched from the viewpoint of the sun. As you see here, the direction the earth sees Mars, is the same direction that the sun sees Mars: they’re all in a row. This alignment is called opposition.

With these observations, Kepler worked out the best possible model using the circular orbit and equant-controlled motion of his predecessors. He called this model his vicarious hypothesis, which you see here, creating the motion of Mars. And, now, eight different positions are displayed at once. Now, this strange name is because Kepler didn’t believe in circles and imaginary points causing the planets to move: the real, physical principle of motion could at best live vicariously through such a mathematical model. Now, this model that he made – this vicarious hypothesis – it was an amazing success. All twelve opposition observations were predicted perfectly (within observational error) by the model, something that no other astronomer had ever come close to achieving.

So, let’s examine this model. When we look at it, we see that it includes an implied distance between the sun and the center of the Mars orbit, seen here. Kepler didn’t get this distance directly, by measuring distances, but only indirectly, by seeing where he ought to put the center of the orbit to make the observations work out as best he could.

Kepler wanted to test whether the distance was correct. To do this, he used a different kind of perception, a second kind of view. You see, astronomical directions have latitude and longitude, just like position on the earth. His vicarious hypothesis had only used longitude, like moving around the equator. (In astronomy, this equator is called the ecliptic.) What if Kepler also brought in latitude, motion north and south of the ecliptic? Well, by doing that, Kepler was able to measure the distance of Mars from the sun, at its closest and furthest points on its orbit. He did this by creating triangles with the sun, earth, and Mars, and using the angle Mars traveled above or below the ecliptic plane to calculate the distance from Mars to the sun. Using these distances, he could find the center, and thus measure the real distance between the center of the Mars orbit and the sun.

Now look at this distance: it does not agree with the distance in the vicarious hypothesis. Let’s see what happens if we adjust the vicarious hypothesis to take into account the real physical distance as measured by the latitudes. The red orbit with the red center is being split, into a second, orange orbit with an orange center. This orange center is the right distance from the sun, to agree with the latitude-measurement of distance. Remember, the original vicarious hypothesis gave the correct longitudes, the correct directions of the planets perfectly. But, as we the center of the orbit is moved to agree with the measured distance, the directions change. Kepler calculated the maximum difference, and found that here at this position, the difference was eight minutes of arc, where there are sixty minutes in one degree of angle. That is, there is an 8’ difference between the red position, corresponding to the original vicarious hypothesis, and the orange position that took into account the distance from latitudes. So, this eight minutes: if you wanted to measure that amount of angle in the sky, it is the same width as if you’d held a pencil lead out at arm’s length. This is a tiny difference, but it was definitely observable with instruments available in Kepler’s day.

Kepler called these eight minutes “the key to a new astronomy,” because it was simply impossible to unify the different observations of longitude and latitude with this model: longitude alone created a model that gave correct longitude directions, but had an incorrect distance. Latitudes gave us a correct distance that upset the perfect longitude directions given by the model, by up to 8’. The two types of observations simply cannot be reconciled in this model. Here, the unification of the two kinds of simultaneous perceptions, is impossible!

In this case, this failure was Kepler’s goal, this was the metaphor he created. The only unification, the only resolution, lay outside sense-based modeling. The abstract shape of a circular orbit, and the angular rotation of the equant would have to give way to something unseen, and, indeed unseeable: they must give way to Kepler’s hypothesis of universal physical gravitation, and the power of the sun to cause the motion of the planets.

Like the previous examples of combining different viewpoints, knowledge only comes from combining the different evidence of two different perceptions. But this time, the resolution does not exist in the domain of any viewpoint, since it cannot be “seen” at all!

Metaphor, in a Different Sense

To probe further, what happens when the two view-points are not even view at all? We combine sight and sound every day, when we associate sounds and appearances with objects around us. If you hear a purring sound, and you see it’s coming from the direction of a cat, there’s no mystery involved. We usually don’t even realize the extent to which we combine our senses to create a single experienced world: for example, taste and smell are remarkably connected, something you might notice if you have a cold blocking your nose – you’ll notice that foods seem to taste differently, because smell has changed.

The field of chemistry has included almost all the senses: substances are described by appearance, texture, mass, and (when it’s safe), even their smell and their taste. The unification is the distinct personality of the substance, but not in one sense: you can’t measure what “color” something tastes like, or quantify how “curved” it smells.

What if a sight and sound were fundamentally irreconcilable? In Kepler’s next major work, his Harmonies of the World, he uses both the harmonies of vision (in the form of the Platonic solids) and the harmonies of hearing (in the form of the musical scale he constructed from the divisions of the circle), to develop the orbits of the planetary system as a whole. The visual harmonies were seen in the ordering of Platonic solids that lay between the orbits of the planets. If each planetary orbit were a sphere, the solids would give the spacings between the spheres. The harmonies of sound are “heard” in the fastest and slowest speeds of the planets, as their motions would be “perceived” or “heard” by the sun.

As an example, Saturn’s fastest and slowest speeds, as seen by the sun — its perihelial and aphelial apparent speeds, are in a ratio of 4:5. This ratio of speeds (apparent speeds), if expressed by sound, as in the cutting of a string into a 4/5 ratio, is precisely what we call a major third.

Here we have what Kepler called the “hard” scale, made from the aphelial and perihelial motions of the planets.

This itself is a combination of imagined senses, since the sun cannot hear planets (there is no sound), yet the visual perceived motion is considered from a musical (or auditory) point of view. But, the distances and speeds from the visual solids, and speeds required for musical harmony, contradict each other.

The Platonic solid distances determine the orbits only incompletely (they don’t give us a clue to the thickness of the spheres, which give the shape of the ellipses), and the musical harmonies alone also fall short. They have no general structure to give to the planets without the solids, and the internal contradictions of perfect tuning can only be resolved by the goal of the composition in which the intervals are sounded.

For example, if we ascend a major third three times ((audio)), we would musically reach the same note as if we ascended an octave ((audio)). Yet, taking the ratio of the major third three times, gives us 64/125, which is not equal to ½, the ratio of the octave. To choose the “correct” tuning of the higher note, you have to look at it in the context of a piece of music, not as a single sound. Can you think of the composition of which the motion of a single planet plays a part?

The perception of the musical harmonies is itself a contradictory union: the visual apparent motions are heard by the sun.

So how can sight and hearing be unified? Unlike in chemistry, they cannot be unified in anything like a perceptual substance or an object, but only in an intention, an intention which has as its shadows, the harmonies of the two distinct sense-perceptions. This is seen in the role of the sun as conductor. The apparent speeds of the planets, as seen by the sun, the basis of Kepler’s musical harmonies, are not characteristics of the planets themselves: they simply don’t exist without the sun as observer. That is, planets do not have apparent speeds, unless they are being observed. The harmonies Kepler discovered don’t exist in the planets, or in their motions, but only in the organizing intention, only from the sun. The principle at play here cannot be found in the perceptions themselves, but they must be unified into an entirety before they have any meaning. Kepler’s unification, his discovery, is a becoming rather than a being: it is a metaphorical unification, in the scientific sense of “metaphorical.”

Now let’s take another example from astronomy: the Crab Nebula. Our absurdly small array of astronomical telescopes includes a variety of different types: visual light, radio waves, infrared, xrays, gamma emissions, and ultraviolet among them. When we view this single astronomical marvel with four different instruments, we get these different views:

Now, unlike the previous combinations of perceptions, there is no single perceptual space in which these measurements are unified. We are no longer even looking at the form of an object or the location of a planet, but rather at conflicting types of activity.

What do these different views suggest to you?

Where does the unification of these paradoxically different projections exist? How will it be formed, as a single idea? And will that unification be the final answer? This is the domain of the human mind: unlike animal brains, our conceptions are not limited by our senses. We use our senses as tools, like telescopes, spectrometers, and voltmeters, but they do not define the reality of what we experience. The fact that they are built into our physical bodies as standard equipment is definitely convenient, but they have no qualitative claim to superiority over our extended electromagnetic (you might say “external”) instruments. Although our basic senses are embedded in the body we directly control, they no more represent our minds than do the oscilloscope of an electrical engineer or the spectroscope of the chemist.

The measurements we make, using these tools, are projections, not reality. A bird has a measurable length, but did you ever see 12 centimeters fly from tree to tree? Imagine a physicist studying life. While a living frog has projections, or images, such as length, mass, and electrical conductivity, none of these are life – none of these are the frog. We can’t measure the human individual by the built-in senses. The reality of the human soul lies outside the body altogether, and we are most at home, most ourselves, not in our bodies, but when we are using our minds to make new discoveries. True discoveries involve the creation of a new thought through the process of metaphor – an actual existence that cannot be found within the entire domain of perceptible reality.

This metaphorical domain is the truest reality of the human experience. This development of new ideas – true human creativity, is not a change or shift from one mental state to another, higher one. Instead, it is the state. For human life, this process is our substance.

Our goal must not be a particular state of physical economic predicates, such as energy production or standard of living, although these are essential. The goal is the guiding self-conception of the human species. A culture based upon this metaphor-based view of the human individual – of discovery – is itself the future towards which we must aim.

So let’s do it. Unlike many journeys, this one is completed as soon as we are on the right path. But, since being on the right path is itself the goal, we will never reach a destination at which we can safely rest. Cultures that do not progress, die, because they cease to be human.

The human individual is not a collection of sensory impressions, and the goal of life is not to seek out pleasure while avoiding discomfort. We are what we do, and the enormous crisis of thermonuclear war we currently face gives us one last chance: embrace the human destiny of mirroring the universe through a continued series of developments, or go extinct like an animal species that has not evolved to move forward with the rest of the biosphere. It’s our choice: let’s make the right one.

For more on Kepler, see: