The Great Red Spot (or, When Can a Thing be Said to Exist?)

Consider the Great Red Spot of Jupiter. It is a storm that has been around for two centuries. It’s a vortex big enough to contain two or three planets the size of the Earth. But is it a thing?

What does it mean to say that a thing exists? In what sense are plastic cups or rocks things? And are living things also ‘things’ in the same sense? To work towards a better understanding of ‘existence’, let us examine our intuition about the properties of things. A thing has a location in space and time, and a boundary that separates it from all that it is not. A thing can move around and morph its shape and size, but it retains some degree of integrity, so that as it undergoes transformations, it can still be recognized as the same thing. An apple remains the same apple as it decays, changes shape, and rolls around, until it crumbles and decays.  These changes can be quite dramatic. When a caterpillar becomes a butterfly, we say that it has changed, and not that some new flappy thing mysteriously replaced the creepy-crawly that was there a few days before.

Another property of a thing that we might propose is that it is always composed of the same stuff. The atoms and molecules in a rock do not change much. You could make a little etching on the rock, and then find it later on, confident that you had found the same thing.

But I think this kind of material consistency is the exception rather than the rule for many of the things we are interested in. Let’s go back to the Great Red Spot. Surely it is a thing? It has been around since long before you or I were born. Astronomers are readily able to identify it and talk about its shape and location. But a storm like the Great Red Spot does not generally retain all the material contained in it. Stuff comes in, stuff goes out. Back on Earth, we know that a storm can pick up gas molecules, water, houses, people and cows, and dump them elsewhere. Perhaps some molecules stick around with it for the duration of its destructive dance, but plenty of others just hitch a ride for a little while.

A storm is a process. And it is also a thing. It has position, velocity, shape and size, but it does not have a constant configuration of atoms and molecules. In this it is like a wave. There’s a lot you can learn about wave motion from a rope or a string. If you tie one end of a rope to a stationary object, you can send a wave along it by making the right sort of up-and-down shake on the other end.

I recommend playing around with this handy web applet that let’s you send waves along a virtual rope. And here’s a picture of some scientists doing the real thing in a classroom:

What I’d like to draw your attention to is the fact that when a wave moves horizontally along a rope, the particles in the rope do not move horizontally. If they did move horizontally, the rope would eventually break! In fact, they move up and down. What moves along the horizontal direction is the movement itself. If we want to consider the wave a thing, we have to concede that it is not made up of a specific set of particles. It is a process, and the particles are just the medium by which the process flows.

What applies to waves also applies to human beings. The oldest particles in your body have been with you for perhaps seven years. The body is not a constant set of particles, it is a wave, a travelling pattern, a Great Spot whirling around the surface of the Earth. And in a sense, you already knew this. You take in food, air and water every day, and yet you maintain the same weight. (Well, more or less the same weight.) Cells die and are replaced by new ones that are made up of the matter you ingest. You are what you eat.

I like the way Richard Feynman gets this point across. ”So what is this mind of ours: what are these atoms with consciousness? Last week’s potatoes! They now can remember what was going on in my mind a year ago—a mind which has long ago been replaced. To note that the thing I call my individuality is only a pattern or dance, that is what it means when one discovers how long it takes for the atoms of the brain to be replaced by other atoms. The atoms come into my brain, dance a dance, and then go out—there are always new atoms, but always doing the same dance, remembering what the dance was yesterday.”

So we are not what we are made of. We are what we do.

When we realize that all things are also processes, the concept of existence can take on a new meaning. Perhaps we should shift our focus from the idea that existence is about things. What exists is what is happening. No process goes on forever, and thus we can’t really speak of the things that exist for all time and in all places. Things, people, societies, ideas… these are all dancing patterns, and when the dancing stops, only stillness remains.

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Notes:

• I began thinking about the ‘wave’ nature of human beings when I read an article from the Edge Foundation by Tor Nørretranders.  ”I have changed my mind about my body. I used to think of it as a kind of hardware on which my mental and behavioral software was running. Now, I primarily think of my body as software. [...] 98 percent of the atoms in the body are replaced every year. 98 percent! Water molecules stays in your body for two weeks (and for an even shorter time in a hot climate), the atoms in your bones stays there for a few months. Some atoms stay for years. But almost not one single atom stay with you in your body from cradle to grave.”

• All the matter in us and around us was produced inside the furnaces of stars. If you believe in modern science, the phrase “we are stardust” is not a metaphor! But of course, we are more that just stardust. We are waves that use stardust as a medium for propagation.

• If you use a spring instead of a rope, you can see two types of wave motion: transverse and longitudinal. Transverse waves are like the ones on a rope, with the particles moving in a up-and-down direction. In longitudinal waves, the particles do move back-and-forth in the horizontal direction, but still do not travel with the wave.

• Wave-particle duality suggests that at a very fundamental level, the distinction between particle and wave can be blurry. Also, condensed matter physicists often find it useful to characterize the systems they study in terms of “quasiparticles“. You could go as far as saying that the a particle can be redefined as a type of phenomenon or interaction, rather than a thing. From here we can question the meaning of the word “fundamental”, perhaps be opposing it with the word “useful”. More on this later.

Vision: the Master Metaphor

Human beings frequently conceptualize experience and understanding in terms of visual metaphors. These metaphors pervade our discourse: we ‘illuminate’, ‘shed light on’, and ‘dispel shadows’. When you think you understand, you often say “I see.” In IIT Bombay lingo, after explaining something you’d ask “Chamka kya?” (Did it shine?)

Art is believed to reveal a kind of truth: Hamlet declares that the “purpose of playing” is to hold “the mirror up to nature.” Ignorance is our inability to see through the darkness. St Paul says “now we see but a poor reflection as in a mirror; then we shall see face to face. Now I know in part; then I shall know fully, even as I am fully known.”

I can’t be sure why visual metaphors appear to dominate, rather than tactile or auditory ones. Neuroscience and history (evolutionary, cultural and linguistic) may one day shed some light on the origins and workings of this phenomenon. George Lakoff and Rafael E. Núñez , in their book Where Mathematics Comes From, go as far as suggesting that logic itself — seemingly alienated from human experience — is born of a kind of visual logic that manifests itself in the vision-behavior nexus. Perhaps this nexus is a substrate for ‘self-evident’ truths. Regardless of the origins of visual thinking, in general discourse it provides us with powerful analogies with which to structure our discussion of metaphor and the ‘axes’ of human understanding.

If art holds a mirror up to nature, science holds up lenses and prisms. Lenses symbolize observation, and prisms symbolize analysis and synthesis. I’ll talk about prisms first, and them move to lenses, which afford us extended, systematic metaphors.

A prism serves to break up a beam of light into its constituent spectrum, and can also (re)combine spectral components. The choice of prism material and shape depends on the spectral band of the radiation being investigated. In their role as dispersers, prisms analyze light. The word “analysis” is a transcription of the ancient Greek ἀνάλυσις: analusis, “a breaking up”, from ana- “up, throughout” and lysis “a loosening”. Chemical analysis can be seen as set of prisms by which the composition of a substance is revealed through ‘dispersion’. The role of prisms in recombination can symbolize the complementary process, synthesis, which come from the ancient Greek σύνθεσις, σύν “with” and θέσις “placing”, and means a combination of two or more entities that together form something new. Prisms combine red and green light, for instance, to yield yellow light.

Lenses can magnify images, bringing otherwise invisible objects into focus, so that we can better analyze their structure, composition and behavior. But lenses also warp and distort. Further, there is no single lens that can be used to capture all possible images. You cannot use a microscope to study the stars. This is not a technical difficulty. The scope of a lens and its resolution do not co-vary — you cannot simultaneously apprehend a square mile of territory and view it at one micron resolution. Similarly, you cannot simultaneously study an object at the quantum mechanical level and at the Google Street View level. A single device does not have a little knob with which to arbitrarily increase resolution while maintaining the size of the frame. To zoom in to a point is to discard more and more of the area around that point.

We build up our understanding of an object or process by employing multiple lenses. This raises the possibility of discontinuities in the picture we construct from the multiple views. Since any single device cannot simultaneously and smoothly vary its focus, scope and resolution across the whole range of human perception, we resort to the use of multiple devices. If the operating ranges of the devices overlap, it becomes possible to construct a composite image. This is one of the ways a panoramic photograph can be constructed. Multiple photos are stitched together.

Let us ground these metaphors in a specific example. DNA was discovered is 1869 by investigating pus in bandages with a microscope. In 1919 its composition was revealed by chemical analyses. By 1928 biochemists had established that DNA is a carrier of genetic information. It’s structure was determined in 1953 using X-ray diffraction, a technique previously used in crystallography. All of these views were integrated (‘stitched together’) with the glue of mathematics and shrewd deduction. And this beautifully synthesized view is still in no sense complete — though the human genome project has given us the complete sequence of base pairs (in a handful of people),  the nature of the “code” has not been cracked — it appears that a wider scope incorporating cellular and chemical context needs to be supplied: the burgeoning field of epigenetics appears to be orders of magnitude more complex than genetics. It seems that learning to read the ‘Book of Life’ is much harder than transcribing it, and may involve looking at some of the other books in the Library of Life. Chemistry, biology and physics were the lenses used to uncover what we know about DNA. Each field has its own scope, resolution and focus, and the process of stitching together the ‘image’ requires ingenious puzzle-solving abilities. And the puzzle pieces often fail to fit perfectly together! Even in the (literal) case of photography and imaging, image registration — the alignment of images to form composites — is a task that is far from straightforward. “Registration is necessary in order to be able to compare or integrate the data obtained from [...] different measurements.” If you’re going to plan out a journey using two overlapping maps that have different scales and distortions, you’d better be careful about how and where they align.

What applies to image registration applies to all fields of human inquiry. Consider the world of physics. Popularizers of science (as opposed to actual scientists) will often have you believe that physics is — or will soon become — a unified view of the universe. A Grand Theory of Everything is supposedly within grasp. The following diagram illustrates the pre-unification state of physics. I’ve mapped out the subdomains of physics on axes of length (somewhat precise) and speed (not precise at all).

The subdomains of physics in relation to length scale and speed. (Click to embiggen.)

I’ve based this image on this handy visualization and other similar diagrams, but I want to draw attention to the white spaces, which are caricatures of the ‘holes’ in physics — they occur not just at the margins of our furthest perceptual reach, but in ‘central’ regions, as well. Quantum field theory unifies (registers) quantum mechanics with some relativistic concepts. But it cannot incorporate the effects of gravity, hence the quantum gravity (black?) hole. The most elegant example of ‘theory registration’ is the equivalence of classical/Newtonian mechanics with relativistic/Einsteinian physics. If the velocity term affecting the Lorentz factor is sufficiently low, Einsteinian physics reduces to Newtonian physics as a limiting case. The mathematics to show this is simple and unambiguous.

Showing the equivalence of quantum mechanics and classical physics, on the other hand, has not been clearly established yet. Many physicists assert that classical physics exists as a special case of quantum mechanics in the limit of very large numbers of particles. (In a sense this is obviously true if we conflate the theory with the reality. However, as a general rule of thumb, scaling up the number of elements in a theoretical system rarely yields results that correspond with experiment. More is different.) This assertion is known as the correspondence principle, but it is not quite a proven statement. Unlike in the case of relativity, no universally agreed upon mathematical procedure can show classical mechanics as the limiting case of quantum mechanics. To go back to the image registration metaphor, this would be like having a discontinuity in the stitched-up panoramic photo that we declare non-existent by fiat! Objects that span the classical-quantum divide — perhaps DNA molecules and carbon nanotubes — currently fall into conceptual no man’s land. But you are free to believe that one day a Grand Unification Theory will fill in all the holes in physics. Perhaps then the mosaic-like quality of our current understanding — riddled with discontinuities — will disappear?

I am not convinced that a Theory of Everything in physics will satisfy our general curiosity. Many of the most interesting problems we face have nothing to do with physics. I am drawn to a philosophical position among scientists – non-reductionism or emergence — that holds that grand unification may not be possible, and further, that even if it were possible, would not answer important questions about observable phenomena, even within physics. In other words, a Theory of Everything would explain very little of consequence.

This is the region where all the action is. And physics has not filled up all the holes.

In the picture above, I’ve highlighted the region that concerns most human beings. It is the region of the universe we live in — where genes, cells, brains, computers, and societies are much more ‘fundamental’ to our existence than quarks or galactic superclusters. This is the region of the map where physics per se is rarely able give us any useful information. Chemistry, biology, psychology, sociology and economics… these fields deal with phenomena that show no sign of revealing their mysteries to the physicists’ particle accelerators or radio telescopes. The scope and resolution of the physicists’ (conceptual) lenses simply won’t suffice. The truths we collect in these domains are multifaceted, inconsistent, and often nonmathematical. The ‘theory registration’ problems are therefore particularly acute.

Or rather, the alignment of various theories would be an acute problem if that were the primary goal of human inquiry. Accounting for quantum gravity, mathematizing the transition from quantum to classical — these sorts of goals are laudable, and when successful, frequently provide new insight into observable phenomena or suggest phenomena hitherto unobserved. But the unification program may sometimes be nothing more than papering over tiny gaps between the tiles of a mosaic — gaps that are only visible if you are looking for them (as opposed to using the mosaic of lenses to solve problems). Grand Unification seems often to be an aesthetic principle rather than a self-evident necessity of the universe. There is no reason a priori to assume that all domains of human understanding are mutually consistent. This search for consistency sends physicists looking for increasingly obscure regions of time and energy — the first few seconds of the universe, or deep inside the Large Hadron Collider. If your panoramic view of the sky has vast regions of empty space,  is it really important to find (or more often, create) phenomena that suggest disambiguating alignment procedures? Is it not sufficient that the telescope (theory) pointing in one direction sees (accounts for) the stars (observations) in its field of view, as long as there are other telescopes and microscopes for other stars or minuscule particles? If a star and a quark can never in any real sense be seen to interact, do we really need a theoretical bridge between astrophysics and QFT? What use would it serve?

I do not want to suggest that attempts at reductionist unification in the sciences are misguided or pointless. My aim is to demonstrate what human knowledge looks like as is, not as it should be or can be. Currently, human knowledge looks very much like a patchwork quilt of theories, ad hoc rules, stories, speculations and observations. A collage rather than a ‘veridical’ photograph. For this reason the truths that physicists have thus far described as universal are rarely universally useful — they have meaning and force only when viewed within the lens that gave rise to them. Quantum electrodynamics may be ‘universally’ true, but how it can be put to work in clinical psychology is far from clear.

Vision offers another interesting metaphor. If we see human knowledge as a fixed collage — one in which, say, quantum mechanics is the only lens for physics below the nanoscale, and neoclassical economics is the only lens for understanding the flow of money and labour — then we are in danger of reification: turning abstractions into reality. We can inoculate ourselves against premature ossification by remembering that lenses are not objective generators of truth. They require someone to look through them. They require an observer, who is always viewing things from a particular frame of reference, and asking particular questions. We don’t really need the principle of relativity to arrive at the realization that there are multiple frames of reference, and none of them are privileged. If we cling to a single frame of reference, we often make errors in measurement, such as parallax. Different frames of reference give us different views, and moving between them gives us a better sense of the object or process. (This introduces the problem of image registration to neuroscience. Shifting between different viewpoints, how does an individual brain/mind make mappings between mappings? Metamappings?)

I spent a few impressionable years being dazzled by postmodernism, mainly because it tends to stress the possibility of multiple viewpoints and the absence of a central, fundamental frame of reference, or “grand narrative” in postmodernese. But the postmodern theorists go too far — they jump from this observation to an unjustified assertion that all frames of reference are mutually incommensurable — ‘hermetically sealed’. But surely no viewpoint is totally isolated from all others? Frames of reference need not be irreducibly incommensurable or mutually unintelligible. Two frames of reference, one hopes, can refer to the same object — they are constrained by reality! For all the supposed incommensurability of human knowledge systems and cultures, the common frame of human behavior offers us a wide, overlapping region for interaction. Our toolboxes may contain very different lenses and prisms, but surely we can bring them to bear on the same situation? We can and do act together in the world in ways that allow us to align our theories and frames of reference, even if these alignments are contingent, provisional or ephemeral. Our lenses may create idiosycratic distortions, but we are more than our lenses. We are also our deeds, and our deeds interact even when our ideas do not. Shared praxes can align our axes.

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Notes

• All metaphors break down eventually. Similarly, human vision breaks down at the size scale of the wavelength of visible photons. It makes little sense to visualize particles that are altered radically by interaction with a photon. A physics professor in IIT advised that we stop trying to visualize quantum mechanical systems. In many cases one has to ‘see’ an electron as nothing more than an abstract phenomenon governed by an equation. The process of disanalogy will become useful when we want to investigate the limits of our language, and the limits of our understanding. More on that later.
• When red and green light arrive at the eye, humans see yellow light. There is no purely physics-based explanation for this. ‘Objectively’ yellow light has a frequency ranging from  570–580 nm, but mixing red and green light does not yield new wavelengths. The yellowness of the mixture has to do with the way human color vision works. Thus what we see depends not only on what is ‘out there’, but what is ‘in here’ too.

Further Reading

Anderson, P.W. (1972). “More is Different“. Science 177 (4047): 393–396.

A classic paper explaining emergent phenomena in terms of symmetry breaking. Quote: “At each stage entirely new laws, concepts, and generalizations are necessary, requiring inspiration and creativity to just as great a degree as the previous one. Psychology is not applied biology, nor is biology applied chemistry.”

Laughlin, R. B. (2005). A Different Universe: Reinventing Physics from the Bottom Down. Basic Books. ISBN 978-0-465-03828-2.

Nobel Laureate Robert Laughlin makes a strong case for non-reductionism and emergence in relatively simple language.

Laughlin, R.B, and Pines, D. (2000) “The Theory of Everything” PNAS 97, 27-32

A thorough critique of Theories of Everything, complete with examples from physics. Quote: “We have succeeded in reducing all of ordinary physical behavior to a simple, correct Theory of Everything only to discover that it has revealed exactly nothing about many things of great importance.”

Truth, Validity and Usefulness

There are three closely related — but in my opinion distinct — concepts that ought to be closely scrutinized before discussing metaphor proper. (The post is long but I hope you will bear with me: making the points I wanted to make took many more words than I had anticipated.)

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Truth is the most difficult topic to do any justice to, especially if we start with the supposition that no truth is self-evident. Truth is a topic that has been flogged to death in academic philosophy, but it is far too important to surrender to philosophers. At the outset, let me just say that I subscribe to the view that truth is an attribute of statements about the world, and not of the world itself. Rainfall is a process in the world — it is neither true nor false. It just is. But a human statement about rain, such as “It is raining” can be either true or false (or undetermined, if you are in a windowless room). Truth is an aspect of communication. (Can animals lie? I’m sure they can intentionally mislead, but I don’t know if we should call this lying.)

How do we assess the truth of a statement? There is no foolproof formula or algorithm. The truth of statements about directly observable events is determined by corroboration. If you say it is raining, then I can go check. End of story. (At least, for most people. Ludwig Wittgenstein, for instance, refused to acknowledge that there was in fact no unicorn in the room, much to Bertrand Russell’s exasperation.) Most people trust their senses, especially when they receive multiple corroborations. This is usually adequate evidence to convince themselves that what their senses throw at them is not a private hallucination. Madness, after all, is a minority of one. (Is the world a collective hallucination then? This is a much stranger question, and one we’d better ignore for now.)

As soon as we get to unobservable events, the trouble begins. If you tell me that it rained in Boston, Massachusetts on August 13th, 1947 at 2:53 pm, I will have to use indirect methods to assess the truth of your statement. I might, say, consult newspaper archives looking for weather reports. But I will then need to place some faith in the newspaper’s accuracy, transforming the question of the truth of your statement about rain into an investigation of the trustworthiness of archived newspapers. We often decide on the truth of a statement based on the trustworthiness of the source. If you know someone who is a pathological liar, you take what s/he says with a grain of salt, until you can confirm what they say. Conversely, if you know a scrupulously honest person, you may believe whatever s/he says without seeking confirmation. Note that the liar could be telling the truth, and Honest Abe could be lying or simply mistaken. Without the ability to confirm statements using our own senses, we are at the mercy of other people.

The truth of a statement is often established using an appeal to authority. This is the typical technique of religious fundamentalists. But scriptural literalists are not the only people who appeal to a higher authority. Everyone does this, and it starts early. Children often ask “Who said so?” We implicitly evaluate what is said by finding out who originally said it. The value of a statement is displaced and relocated in the personality of its first proponent. Popularizers of science frequently refer to the statements of famous scientists. These are the ‘facts’ that Science — usually a disembodied entity — has ‘shown’. One seldom hears about the conceptual or theoretical framework within which the statement makes sense. The authority of a particular scientist may be tested via the systematized extrapolations of confirmation-via-the-senses that we call experiments, but very few nonscientists engage in this kind of activity. Most people are unable or unwilling to confirm statements by scientists and other public authority figures. Society places trust in some people (for reasons that are far from obvious) and individuals often just inherit this trust, even if they have the resources to test it themselves. I imagine most people assume that any statement being widely touted as the Truth would be subject to minute examination by persons more qualified and motivated than themselves. Alas…

Other ‘authorities’ we frequently appeal to: parents, teachers, politicians, philosophers, social ‘scientists’, priests, medical doctors, astrologers, and even journalists. There is also depersonalized tradition –”It’s true because this is what we’ve always believed”.  Another authority is aesthetics (“Beauty is truth, truth beauty” — a particularly pernicious obscurer of truth, even, or perhaps especially, for scientists. Perhaps more on this in a future post.) But the most mischievous authority we appeal to is ‘common sense’. What on earth is it? It has something to do with reasonableness, and rationality, and sensitivity to ‘evidence’, but beyond words that are themselves vague I can say very little.

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Pinched from SMBC

I can, however, say something about validity, which is related to logic and therefore by association, to the popular perception of rationality. Validity — for the purposes of this blog at least — means logical consistency. We often conflate validity with truth. Many true statements also happen to be valid, in that they are consistent with other truths, and can be related to them using the algorithmic processes of logic. (We can include formal mathematics in the term ‘logic’ here, although there are those who might argue that logic should be seen as a subset of mathematics, not the other way round.)

Consider the sort of ‘truth’ arrived at by syllogisms such as the following:

Major premise: All humans are mortal.

Minor premise: All Greeks are human.

Conclusion: All Greeks are mortal.

The conclusion is valid because logic has been applied correctly, and it is also true. Why is it also true? Because the major and minor premises are both true to begin with. This is not always the case. Consider:

Major premise: All ducks have feathers.

Minor premise: All basketball players are ducks.

Conclusion: All basketball players have feathers.

It is important to recognize that the conclusion is valid. Logic has not been violated. But I hope everyone can agree that the conclusion lacks truthiness. The minor premise is absurd. I’ve picked a silly example, but you can easily imagine that things get murky very quickly if the premises sound sophisticated, plausible and/or ‘reasonable’. Logic is an internally consistent system that, if used correctly, will always give you valid results. Like a computer program, it’s Garbage In Garbage Out. (Logically consistent garbage, of course.) The truth lies elsewhere.

Wittgenstein asserted that statements that can be deduced by logical deduction are tautological — empty of meaning. Meaning and truth lie in what we put into the logic machine. We can put true statements (arrived at using the vague rules of thumb hinted at above) into a logic machine and crank out new true statements. I use the machine metaphor consciously: it is not very hard to get a computer to perform logical deductions, because it all boils down to rule-based symbol manipulation. Douglas Hoftstadter demonstrates this very vividly in Gödel, Escher, Bach (a strange, entertaining book whose fundamental argument eludes me). Doing a derivation in mathematics or physics resembles this algorithmic process. It’s all symbol-manipulation — moving around x’s and y’s using the laws of algebra and calculus (with much assistance from intuition and clever tricks, without which we would get nowhere). The meaning of a mathematical symbol lies elsewhere. The variables in formulae must (eventually) be mapped to observables in the world — this fundamental act of naming and associating is not done within mathematics or logic. Variable x can take on any value you give it. What value you give it depends on the problem at hand. (Even if we somehow had access to all true axioms and a sufficiently powerful logical system, we would still face a problem. Gödel used formal mathematics/logic to subvert itself, yielding his notorious incompleteness theorems. One of the interpretations of the first theorem is that there will always exist statements expressed in a mathematical system whose validity cannot be tested, even in principle, however powerful and consistent the system happens to be. Hofstadter uses an effective metaphor. Imagine that a mathematical system is like a phonograph. Playing a record establishes its validity. There will always be one record that carries a frequency that will destroy the player. You can try building a new, stronger phonograph, but you will always be able to make a new record that can destroy it.)

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And now let us cease this academic chatter about truth and validity, and come to the problem at hand. The third leg of our tripod is usefulness. Statements (and systems of statements) are not merely true or valid. They can also be useful. Newton’s laws allow us to make precise predictions about the movements of bodies both terrestrial and heavenly. We are offered “better living through chemistry”. And quantum mechanics, for all its alleged conceptual incoherence, is the fertile soil from which spring all the wonders of the electronic age. Clearly there are statements that have power. Note that I am not concerned with subjective value here. You may hate iPods, railway trains, or vitamin C tablets, but you should be able to acknowledge the efficacy of chemistry, physics or engineering as tools for achieving the goals of its practitioners.

You might argue that the power of science comes from its truth. But we must also admit to ourselves that there are powerful, world-changing statements that are not true, or whose truth has not yet been definitively assessed. Questionable beliefs and superstitions have power in that they influence the way people behave. These effects may not be as well understood as phenomena involving inanimate matter, but people regularly find ways to deploy them reliably. Think of proselytizers, PR companies, or politicians.

Many of the statements born out of religious and spiritual tradition do not hold up to scientific standards of truth and validity, but even scientists are capable of recognizing the power of allegedly false beliefs in helping people cope with pain, anxiety, and poor health — and also in spreading hatred, conflict and ignorance. But even truth and validity do not always co-occur. The Schrödinger equation is true and useful, but it cannot be derived from other more “fundamental” principles. (Heuristic  derivations are used as didactic aids.) Physics and chemistry are littered with examples of ad hoc rules that do not simply flow logically from first principles. They may be consistent with other rules, but their validity was not the basis for their acceptance into the cannon of true theories. Validity is often discovered after the fact of a true discovery. This was the case with Newton’s calculus. Mathematicians in the 19th century lamented the fact that calculus was on shaky foundations (fluxions, anyone?), and proceeded to place calculus on more firm, rigorous foundations. I have often wondered whether the “foundation” metaphor is even appropriate here, given that calculus was already being used to great effect despite the untrustworthiness of its moorings, since the 17 century. (I intend to return to the metaphor of foundations and fundamentals at a later date.) Richard Feynman described mathematics as coming in two varieties: Greek and Babylonian. The Greeks were concerned with deriving all truths from a small set of self-evident axioms. The practical Babylonians, on the other hand, used intuition and heuristics, working out new truths from other truths that happened to be adjacent to the problem at hand. (I recommend reading the full Feynman quote on p. 46 or watching the lecture.)

I am not trying to knock rigor, however. The pursuit of rigor yields many discoveries that are interesting in their own right. And mathematical ideas that are valid and well-formed can sit around for decades before someone discovers a use for them. This was the case with non-Euclidean geometry, which was born of an attempt to prove (or validate) Euclid’s fifth postulate using the other four. The method known as proof by contradiction was employed, but no contradiction was forthcoming, so seemingly unearthly geometries — in which parallel lines intersected well before infinity! — lurked in mathematicians’ closets. Such geometries were dusted off and dragged into the daylight when Einstein announced to the world that spacetime is curved.

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Usefulness, truth and validity can be used in concert to get us out of philosophical black holes. You might agonize over the question: “If logic establishes truth, then what established the truth of logic?” Worse, you might arrive at some kind of sophomoric nihilism, based on nothing more than the discovery that contrary to hope or expectation, truths are rarely well-founded or absolute. But if we remind ourselves that logic persists in human society because it serves us well, then questions about the validity of validity-establishing systems or the truth of truth-discovering systems lose their fearful circularity. They are still circular — and going around in circles may not be as pointless as it first appears — but the discomfort is gone. With these three ways of measuring, we can perhaps resolve the apparent dichotomy between theory and application. Truth and validity have their uses. And perhaps usefulness is a truth of its own. Each aspect supports the other, but they can and do exist independently of each other.

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Truth, validity and usefulness can also be deployed in less-than-admirable ways. In a debate, you might complain that a truth held axiomatically is ‘invalid’, or that a valid argument is ‘useless’. And all this can be done even if your opponent has stated clearly that he means to establish one thing — truth, validity or usefulness — and not all three simultaneously. This is the debating equivalent of the three-card monte. Point-scoring debates can evolve into genuine opportunities for learning and progress if we cooperate with our partner (no longer an opponent) by accepting premises provisionally, recapitulating arguments, suggesting truth-testing rubrics, or imagining the uses of ideas or techniques. A shared goal can make communication much more interesting; the sharp tools of science and logic can then be made subordinate to a particular orientation, rather than simply being used to shred particular statements or churn out valid-but-useless ones.

Usefulness can breathe life into truth and validity. Truth can shine a light on the workings of power, and confer meaning to validity. And validity gives us a way to be cautious about alleged truths or attributions of usefulness. The truth-validity-usefulness triad gives us a kind of Instrumental Reason with which to explore the world and ourselves. Investigating their complex dynamic — separable but interpenetrating — is the key.

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The post is already too long, so I’ll just end with an image of how these three concepts often get tangled together with related and important concepts that are not always relevant.

Extraneous values can often obscure Truth, Validity and Usefulness

Axis? Praxis?

What is the nature of metaphor? What constitutes an effective analogy? What is distinctive about the analogies used in science and mathematics? Can scientific metaphor enrich the wider world of discourse? And how do we deploy metaphor and analogy to achieve our goals? These are some of the questions I’d like to explore in this blog. My aim is not necessarily to answer them, but to explore them, and to see what arises from discussing them.

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I have a habit of juxtaposing words in nonsensical ways, for the “sound-sex” of it, as Stephen Fry invites us to do. For instance, well before I had an inkling of what “dialectical materialism” meant, I twisted the phrase into “analectic immaterialism”. Half the fun is then deciding what such a collision of words might mean. (Analectical immaterialism, if you’re curious, came to suggest a quasi-mystical political philosophy that combines Confucius with postmodernism.) “Axis, Praxis” was another lexical copulation of this sort. (For the full effect, introduce a gentle pause between the words, half way between colon and semicolon, and emphasize “Praxis” with the zeal of a Marxist and/or Evangelical preacher. I’ll explain why in a moment.)

Assuming you and I have the same kind of graph paper, I can communicate to you the coordinates of rectangle ABCD, and if all goes well, your rectangle should be very much like my own. But what we do with these rectangles depends on praxis!

“Axis, Praxis” refers to the relationship between the ways we arrange our information (axis), and the ways we then use this information (praxis). The word axis comes from the Latin for axle, and is most familiar to us in the system of perpendicular lines bequeathed to us by René Descartes: the ‘x axis’ and the ‘y axis’. Coordinate systems such as the Cartesian one (there are quite a few) allow us to associate numbers with geometry. The intuitive conceptual clarity of vision (our primary sensory modality) is fused with the precision and reliability of algebra (our most lucid ‘modality’ for reckoning with unknowns). The technical uses of the word are not crucial here: in the title of this blog “axis” is a shorthand for any system used to order information. An axis is a spine: it gives structure to the amorphous perceptions, inferences and opinions that constitute the flesh of an informational organism. As is evident from a piece of graph paper, axes act together to frame a picture, rendering tangible the relationships between the picture’s parts: we can then measure distances, angles, and degrees of curvature. And in measuring them precisely, we can communicate them unambiguously. But for a given object or process, there is in general no unique set of axes that is always and everywhere recommended. Before solving physics problems we are always warned to choose our axes carefully. (And as we all know, not labeling them can have dire consequences.) The choice of coordinate axes is often more art than science, and depends on what we intend to do with the information thus represented. Which brings us to praxis.

Having ordered our information, what do we do with it? “Praxis” comes from the Greek for “to do” or “to act”. I could have used the somewhat less interesting cognate “practice”, but “praxis” has a certain piquancy.  This may have something to do with the almost paradoxical fact that two historically antagonistic modes of thinking/acting employ the term. In Marxist thought, praxis came to mean the deployment of theory in the service of political or socioeconomic change. It was Marx, after all, who said  ”philosophers have only interpreted the world in various ways; the point is to change it.” The other stream of thought that uses the term “praxis” is Christian theology — none other than Marx’s opium of the masses. Praxis is the practice of faith. Preceding Marx by over a thousand years, the Byzantine theologian Saint Maximus the Confessor said that ”theology without action is the theology of demons.” In modern times, liberation theologists – influenced by socialism’s emancipatory ideals –  used the term to express how the Gospel of Jesus Christ is to be lived in the world. So praxis is all about action — the kind that can bring about revolutions: internal/spiritual or external/political (and perhaps — as a dialectical synthesis – both). From the point of view of strict dictionary definition, “praxis” is not very different from “practice”. But its connotation of world-changing, soul-saving deeds gives “praxis” a vitality that is missing from “practice”, which conjures up the quotidian repetitiveness of “piano practice” or “football practice”. (We can ask a speculative question about praxis: history has given us religious and political praxis, so what might scientific praxis look like? Would it be distinct from ‘the’ scientific method?)

So “Axis, Praxis” is about ordering the world in order to act in the world. The two processes are intertwined, because our actions determine what we know and how we (can) represent it, and our knowledge determines what we (can) do. This is vague enough to sounds a tad ambitious: it just might entail talking about all of human knowledge and behaviour (?!). But my goal is not to explain (or even list) all our axes of knowing and our praxes of change. I want to survey the space, look at illustrative examples, and see if anything interesting emerges from a view that is by necessity wide and fuzzy. In parallel, I want to see if nontechnical discussions have anything to gain from scientific language and metaphor. Can science offer axes around which to orient our day-to-day praxis?

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(Feel free to regularly bombard the commentspace with suggestion, criticism, argument, execration, refutation, and refudiation, as well as complaint of a stylistic, typographical, or grammatical nature. Nitpicking welcome. And I’m not the best proofreader in the world.)