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).
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.
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.
- 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.