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 σύνθεσιςσύν “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.

_______

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.”
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13 Responses to Vision: the Master Metaphor

  1. ramblingperfectionist says:

    :) I find myself more than a little amused at the tone in “Two frames of reference, one hopes, can refer to the same object — they are constrained by reality! ” , after that whole thing on Google Reader when I tried to defend “simple truth”.

    Isn’t it possible that the dominance of vision metaphors is just because most of the raw information that we consciously process is via this one sense? Just a theory.

    I have another proposition. What if you’ve simply stretched your metaphor a bit too far? What if a grand theory, whenever it is found, provides both scope and resolution? That would be something worth discovering, and I’d always assumed (computational feasibility aside) that that’s what people were looking for in a GUT. I know I’m providing no proof for this, but honestly, your argument by analogy can’t claim to have much value as a proof either. (Although it was quite interesting in its own right.)

  2. Han says:

    I wasn’t actually trying to prove anything. Nonreductionism is a philosophical position, rather than a falsifiable theory or axiom. It’s sort of like the different interpretations of QM. All of them give the same numerical results, and cannot be disambiguated be experiment (yet). We’re quite free to pick whichever interpretation suits us. (I like the Copenhagen interpretation, and intensely dislike Many-Worlds. :)

    Like I said, a unification theory is devoutly to be wished for. Even failed efforts produce insights. The lens metaphor (partly) describes knowledge as it is currently, not as if will be in the ideal future. (This is like the difference between Thomas Kuhn and Karl Popper.) If scope and resolution begin to co-vary, then of course we can abandon our faulty metaphors. In any case the visual one breaks down even now — later on maybe I’ll talk about how time doesn’t always map neatly into a visual metaphor.

    But the ‘resolution’ issue is very interesting. I’d recommend reading the Laughlin PNAS paper for details. Basically, computational feasibility is central to theory, and not some side issue. This is a philosophical position one can take: a truth that cannot be explicitly accessed cannot in any sense be said to exist. Asserting that macrobiology is an intractable extension of microbiology is somewhat useless in any case. Especially because solid state physics and chemistry show us that ad hoc new laws can help us when ab initio methods fail. And ironically, the stronger the theory gets, the more susceptible it is to the work of Godel and Church. (Have you read Godel Escher Bach? Great stuff.)

    As for simple truth, we might consider the early Wittgensteinian approach — the “universe is all that is the case”. Logical positivists start with something like this, equating reality with it. But in an earlier post I staked out my position — I hold that truths are distinct from reality as experienced. Truth-bearing sentences are a subset of possible utterances, which in turn are a subset of possible experiences. Common experience offers the possibility of rendering different frames comparable, rather than isolated. But being commensurable is different from being consistent. Quantum mechanics and classical mechanics are commensurable, but not consistent in the limit.

    The example of yellow perception points to interesting possibilities. Differences in neural make-up might produces striking differences in ‘qualia’, which in turn result in different ‘simple’ truths. What disambiguates them?

    So…what do you think are the simplest (non-tautological) truths?

    (Thanks for the pointed comments!)

    • ramblingperfectionist says:

      I’ve always found Copenhagen awkward, and thought Many Worlds was just too cool not to be true.

      The thing about computational feasibility is that it’s changing quite rapidly, isn’t it? Moore’s Law for now, which isn’t exactly bad, and better if we somehoe get closer to quantum computing. But yes, this will still be subject to the scope/resolution issues, except for when we are fortunate enough to have the sort of theories where terms cancel out simply/obviously enough when aggregated. (OK now that I’ve written that, no longer sure if it means what I was thinking of, but I’ll let you figure it out Or ignore.)

      The simplest truths are always the ones that seem tautological, aren’t they? Complexity is just a measure of how many times and into how many parts you have to break down a statement’s parts and their interactions until you get it in terms of tautologies. Although I might be using tautology in a colloquial, “obviously true” sense here than the strict logical definition “things that are by definition true”.

      • Han says:

        I think reading about incompleteness helps. It’s a theoretical problem that is independent of computational power per se.

        So if you agree that tautologies are the only simple truths, then the problem of truth from perception and observation remains. Definitions are outside of logic itself, and that’s where half the arguments over truth happen.

        As for QM — I don’t like unobservables, so infinite universes seems a bit much.

      • ramblingperfectionist says:

        I’ve read (most of) GEB and have some (very) basic idea of incompleteness, and I know it’s not related to computational power. That wasn’t really what I meant, because I gathered that incompleteness isn’t the only thing you were talking about, either. Or does the entire scope/resolution problem reduce to it?

        I take the sort of arguments where you don’t know whether you’re talking about “the variation of pressure that propagates through matter as a wave” or “the sensation excited in the ear when the air or other medium is set in motion” as trivially resolved when people are arguing in good faith, because once you strip away the connotations and clarify what you’re referring to, I can’t see why anyone should care what letters on a page or a series of sounds “actually” are. I understand I’m not in the majority here, though.

  3. asafoetida says:

    This might strike you as a digression, but i always felt that the dominance of visual metaphors is a reflection (argh) of our overreliance on sight as opposed to other means of sensory perception, especially tactile, when it comes to survival.
    Steven Pinker attributes this phenomenon to our evolution as diurnal creatures, and among other things, to the presence of nocturnal predators during the process.

    Explanations of behavior that are derived from evolutionary psychology are extremely tempting, but in some cases appear suspicious because of how convenient they are. In fact, they lie right before our eyes. I am willing to assimilate this one, however, because of the amount of evidence in its favour. The fear of the dark aspect of existence is all too palpable to be ignored. One might even say that it has to be seen to be believed.

  4. Han says:

    I suppose that’s a plausible story for the origin of the centrality of visual thinking. But the issue with evolutionary psychology is that the explanations are always plausible, but rarely verifiable or falsifiable. Richard Lewontin mentions that in explaining everything, sometimes evolution ends up explaining nothing. It may be true that our current state is our evolutionary inheritance, but without the details of the manifestation, it’s more of an assertion than an explanation.

  5. Han says:

    @ramblingperfectionist: Incompleteness suggests in very strong formal terms that the stronger and more consistent a formal systems, gets, the more susceptible it is to the following: one will always be able to produce a statement that is undecidable within that system. The undecidability is theoretical, rather than a technical problem. The speed of the computation doesn’t enter into the problem. It leads to a situation where any finite formal system cannot be both complete and internally consistent. This is a hard limit on the validity testing approach to truth, but is not related to the scope/resolution thing exactly.

    The computability issue is a separate one (that may relate to polynomial time and other NP type issues) but Laughlin discusses it in the paper I cited:

    “No computer existing, or that will ever exist, can break this barrier because it is a catastrophe of dimension. If the amount of computer memory required to
    represent the quantum wavefunction of one particle is N then the amount required to represent the wavefunction of k particles is N^k.”

    In physics you can’t solve problems bigger than the 2 body problem exactly. We use approximations, but they become increasingly susceptible to chaos as we get further from the current (already known) state of the system. You can always replace “wavefunction” with whatever theory of “everything” currently holds sway. On this basis Laughlin says that simply asserting that ab initio calculations are possible “in principle” is pretty weak sauce. I say it in the following way: information that has not been expressed does not in any sense exist. So saying that science “can” explain something “in principle but not in practice” is not itself science, this is an article of faith. We only know what science has explained. And what science explains is only ever real in practice.

    (There were some papers that treated reductionism from the standpoint of scope and resolution — that’s where I got the metaphorical idea. I’ll link to them as soon as I find them.)

  6. Han says:

    This is it. I think it’s work in progress, but it’s accessible and interesting, and has useful quotes and citations: http://arxiv.org/PS_cache/nlin/pdf/0609/0609011v1.pdf

  7. Pingback: Macroeconomics and Metaphors « Random Variable

  8. slehar says:

    Another interesting posting! I love analysis at this lofty abstract level!
    As for the epistemological question of what it is that we can know with any certainty to be true, my own thoughts on the matter can be found here: The Boundaries of Human Knowledge. (Chapter 1)

    http://cns-alumni.bu.edu/~slehar/webstuff/book2/Boundaries.html

    Chapter 2 proposes an answer to your question of why vision seems to dominate mental imagery. I propose an answer through *amodal perception*, an invisible structural understanding of the world which is not actually visual as such, but is a modality-independent structural model of reality that we easily mistake for reality itself. See p. 26 Sensory Confluence in the Amodal Percept:

    “we do not perceive different amodal structures for each sensory modality separately, but rather all of the different sensory modalities share the same amodal structural framework. When we hold a baseball in our hand, the tactile texture of the ball sensed through the skin of our palm is experienced on the very same spherical surface as is the color and brightness that we perceive visually. The hardness or irregularity of the ground that we feel underfoot are experienced as properties of the very same amodally perceived ground that carries the color and brightness that we perceive visually. In other words, the spatial structure that is our amodal experience of the world is the common ground, or lingua franca, that unites all sensory experience in a modality- independent structural representation of the world, and that amodal structure represents our perceptual and cognitive understanding of the world.”

    In *my* world view, reification is no longer a “fallacy of ambiguity”, it is the constructive, or generative aspect of perception which, like a guided hallucination, generates the three-dimensional image of our experience based on the two-dimensional retinal input. It is the very font of the creative process in perception, art, and mathematics.

    • Han says:

      Lots more food for thought! So…are you saying the “image registration” idea is not a problem? That the amodal structures solve that issue?

      • slehar says:

        No, you are right about the mosaic of knowledge and the gaps between known fields, and I agree that there is no guarantee we can ever put it all together in our minds. But if we ever CAN, then it would be through the amodal structure, which, I propose, is the way we understand that which we *HAVE* been able to put together into a coherent picture. So the amodal structure is our best bet in trying to put it all together, which is novel because most people don’t know about amodal perception, and anything that they perceive amodally, they believe to be the actual object itself. For example you only see the exposed near surfaces of objects, but you perceive their solid volumes and hidden rear surfaces very vividly, and most people mistake that amodal percept to be the objective object itself, that underlies the exposed-surface sensory *experience* of the object. Once you recognize that you cannot see the world directly, out where it lies, and you understand that solid structures are constructs in your mind, then you see that our understanding comes from those solid-seeming structures. Sensation “paints” the exposed surfaces with vivid modal color, perception fills-in the 3-D volume percept amodally by perceptual reification.

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