by Rik Smits
The way our bodies are constructed fits neatly within this general rule. The difference between our fronts and backs, or between our top and bottom halves, is significant and profound, just as in all other vertebrates, but the difference between left and right can barely be seen at all externally. On both sides we have an eye, a hand, a foot and a great deal else, and body parts of which we have only one, such as noses, navels, penises and vaginas, with all that goes with them, are right in the middle and themselves more or less symmetrical. The only exception is the parting in our hair. Plus natural blemishes such as birthmarks and warts, but then that’s what makes them blemishes.
Nevertheless, it’s because of the incompleteness of this apparent symmetry that we can tell left and right apart at all. If we were perfectly symmetrical, we would have no way of distinguishing between that which lies to our left and that which lies to our right. Our own mirror image, for example, would be exactly the same as our real-world image, so we would be unable to tell the difference between our actual appearance and the way we look in the mirror. As a result we would simply not notice that our image had been reversed. Nor would we notice if the entire world around us suddenly switched, as happened to Lewis Carroll’s Alice when she stepped through the looking-glass. Any experience we perceived on our left side would in no way differ from the same experience to our right. So we’d be able to see that a d and a b were each other’s mirror image if they were written next to each other on a piece of paper, but we’d never be able to explain how a d should be written. Freud’s childhood memory of having to work out which was his writing hand illustrates the point perfectly. When he no longer knew which was which, he made himself extra-asymmetrical by putting his writing hand to work.
The fact that children have so much more difficulty telling right from left could have to do with the fact that adults are less symmetrical than children. Like the rest of our bodies, our brains grow during childhood, not only in size but internally. Their structure changes.
The brain of a newborn baby is to some extent comparable to a recently built office block. The basic facilities are in place but as yet it’s unfurnished. On completion of the structure, all the rooms are interchangeable concrete spaces, but within a few months every part of the building has been occupied by one department or another. The third floor, for example, may have become the financial heart of the company, while the canteen is on the first floor; the left side of the fifth floor houses public relations and to the right of the lift are the sales staff. In the process, cupboards have been moved several times, desks turned around, extra lamps brought in. Things that didn’t appear in the initial plan for the layout have turned out to work better in practice. The way a building ends up is therefore determined partly by the initial blueprint and partly by a learning process, by trial and error.
In the same way, parts of our brains are furnished according to a standard plan that’s anchored in the genes of every new world citizen, while others develop according to a learning process generated by the external influences operating upon the child. Over the years a vast number of new connections are made between neurons and a good many existing connections disappear, so that ultimately a set of circuits emerges that can get us through adult life successfully.
In this sense the development of the human brain does not differ greatly from that of other mammals. Their brains too are incomplete at birth; they too need to experience the world before they fully reach adult-hood. In humans the process is longer and more complex, but there’s something else as well, something quite special. Human brains differ from those of other mammals in the size of the upper, outer layer, the cerebral cortex. It’s there that the so-called higher functions are located, including things we regard as typically human. In other mammals the cerebral cortex is symmetrical, consisting of two roughly identical halves connected by a broad bundle of axons called the corpus callosum. Only in humans, or at the very least in humans far more than in any other animal, some parts of the cortex that specialize in specific tasks are found on one side only. As a result the two halves of the brain, though largely identical at birth, eventually come to feature significant differences. They may look symmetrical, but adult human brains work asymmetrically to some extent. Many functions that have to do with speech are generally found in the left half, as are arithmetical skills, while the right half tends to be engaged with the final processing of visual and spatial sensations. The right side of the brain commands the databank of faces that ensures we don’t simply walk past family, friends and colleagues on the street without noticing them. People also somehow become able to control one hand better than the other. Because of this typically human process of one-sided specialization, known as lateralization, the brains of adults are far less symmetrical than those of small children.
16
Why a Running Rabbit Doesn’t Tear
Itself Apart
Although it’s harder for us to tell left from right than, for example, top from bottom, we can recognize mirror-image likenesses between left and right much more easily than other symmetries. That’s only logical. Your life may depend on it, whereas in emergencies chance symmetries between top and bottom or front and back are merely a distraction. What happens off to our left requires a reaction that’s a neat reversal of the way we react to precisely the same event to our right, whereas what happens in front of us demands a totally different reaction from what happens behind us.
Our sensitivity to left–right symmetry is clearly visible in the things we make. Traditionally, cathedrals and other large, official buildings are symmetrical when seen from the front, just as we are, but when looked at from the side there’s no symmetry between the front and back halves. Such buildings, intended to be seen mainly from the front, have to radiate certainty and authority. The sense of repose evoked in us by symmetry helps them to achieve this. The same does not apply to fairytale castles, which, from Neuschwanstein in Bavaria to the Queen’s castle in the Walt Disney film Snow White and the Seven Dwarfs (1937), are intended to create romantic tension, an enjoyable sense of mystery and adventure. They are therefore anything but symmetrical.
Friezes and decorative paintings often feature some form of left– right symmetry, but only rarely do we see a mirroring of top and bottom, the way riverbanks are reflected in the water. Clearly we are particularly sensitive to left–right symmetry, but how we detect it is another question, one we can answer only in part.
By and large our visual system consists of the retina deep within each eye, the visual cortex and the optic nerve that connects the two. The visual cortex is at the back of the brain, so although we look with our eyes, we see with the backs of our heads. The eyes appear to be connected crossways to the left and right halves of the visual cortex, in the same way that many other body parts are controlled by the opposite half of the brain, but it only seems that way. In reality the system is more refined: the right half of the brain processes information coming from the left half of the field of vision, which falls on the right half of the retina of each eye, while the left half of the brain deals with information from the left half of each retina, which comes from the right half of the visual field. The result is that the right half of the brain processes everything that happens on the left side of whatever we’re looking at, and vice versa.
At first sight the lower of these two patterns by Bela Julesz looks symmetrical, the other asymmetrical. In fact they are the same, except that one is perpendicular to the other. If you turn this book through 90 degrees, the symmetry will move to the other pattern. We immediately notice left–right symmetry but are less likely to spot top–bottom symmetry.
Neuschwanstein, the fairytale castle built by the romantic but shy King Ludwig ii of Bavaria in the second half of the nineteenth century in ‘the genuine style of the old German knightly fortresses’, as he wrote to Richard Wagner, ‘with the winds of heaven blowing around it’.
This may strike us as an unnecessarily complicated way of going about thing
s, but the evolutionary advantage it confers is easy to recognize. Eyes have to be exposed to the outside world, otherwise they would see nothing, but this makes them more vulnerable than the brain, which is stored safely away in the skull. The layout of our visual system ensures that even if one eye is put out of action completely, we can still use our entire visual cortex, since each eye serves both halves of the brain. A one-eyed person has a larger blind angle than normal and can no longer see depth – this applies only to the handful of species that have two eyes facing forwards – but in all other respects their visual faculties remain just as good as anyone else’s. Were both eyes connected in their entirety to one cerebral hemisphere or the other, the loss of one eye would partially or entirely disable half our visual brain capacity.
All mammals have the same mishap-resistant set-up, but not all vertebrates. Pigeons, for example, have a system in which each eye is connected exclusively with one half of the brain.
This raises the question of how our visual system manages to recognize left–right symmetry. We cannot say for certain. A number of suggestions have been made, the most credible being an idea put forward by Bela Julesz, a researcher at Bell Laboratories in America, in about 1970. His theory, which builds on earlier work by the Austrian physicist and philosopher Ernst Mach, goes roughly as follows.
The visual cortex of each cerebral hemisphere includes among other things an area in which information coming from the eye is ‘pictured’ before being processed further. We will call this area the projection screen, even though that’s a misleading term in some ways, since of course no one is actually looking. To put it rather simplistically, the stimulation of the projection screen area by signals from the retina is the first phase of the process we call seeing.
The visual system, in broad outline. Light entering from the left of the visual field travels to the right side of the retina in both eyes, and from there signals travel to the right side of the primary visual cortex at the back of the head.
If we look at the centre of a shape that has left–right symmetry, then one half of it is pictured by both eyes in the left side of the visual cortex and the other half in the right side. To recognize symmetry we have to compare every point on the left half of the projection screen with its corresponding point on the right. This is made possible by the corpus callosum, a broad bundle of some 150 million axons that connects the two halves of the brain. If almost all the points we compare are stimulated in the same way, then we know we’re looking at something symmetrical.
Julesz produced symmetrical patterns that provide quite strong evidence that the detection of symmetry does indeed essentially work this way. If, after identifying symmetry, we then focus not on the middle of the pattern but on some other point to the left or right, we are suddenly unable to see the symmetry any longer. What’s left is an unstructured jumble of black and white squares.
It seems a sound argument, but there is one serious snag. How come we’re capable of making comparisons of this kind? The answer is by no means obvious.
The same symmetrical Julesz pattern as before. If we focus on an imaginary line between the two arrows, we suddenly cease to see any symmetry.
Seeing is an involuntary process, which cannot be switched off even if we deprive ourselves of sight by shutting our eyes. Anyone who has ever sunbathed on a beach knows that we can’t ignore the light that penetrates our eyelids. Everything that gets through to our eyes from whatever is happening in front of us is sent to the visual cortex, which puts together as coherent an image as possible, whether we want it to or not. This is not to say that we are conscious of everything we see. On the contrary, most of the signals that reach us are dismissed as unimportant after passing through an initial stage in the process. Sometimes they get stored away in the memory, but often they are immediately forgotten.
The degree of relentless diligence the visual cortex exhibits in processing images at lightning speed all day long without our noticing is demonstrated by the reflex reactions we are capable of having to things in our visual field. A fly or a drop of fat from a frying pan heading straight for an eye makes us close the eyelid with remarkable speed. If we notice it at all, it’s not until afterwards. We would never be able to react consciously as quickly as that. Everyone knows the feeling of having seen ‘something’ but not being able to say quite what it was. It’s a popu lar feature of detective novels.
Seeing consists of a great deal more than simply the depicting of im pulses on the projection screens of the primary visual cortex. It’s impor tant to remember that on each projection screen, images from each eye relate to only one half of the field of vision. First the data from both eyes has to be compared and combined, so that a coherent half-image is created (one that has depth as a result of the slight difference in the angle of vision between the two eyes). Then those two half-images have to be linked together into the one, seamless, complete image that we experience.
Seeing symmetry is as involuntary as the act of seeing itself, so it’s reasonable to assume it’s an integral part of the process of comparison and splicing together of half-images. In other words it’s apparently here that mirroring enters into the process in some way. But this presents a significant problem, since everything suggests that we do not use mirroring in interpreting signals coming from the retina. If we did, we’d become severely disorientated. It would be like living in a crazy fair-ground attraction.
Imagine what would happen if the splicing together of the two half-images, in other words the integration of images in the two halves of the brain, involved mirroring. A rabbit running past would appear to run back towards where it came from as soon as it passed the centre of our field of vision. This is clearly not the way it works. If it were, not only would we hardly ever catch any rabbits, but we’d also be terribly accident-prone. It’s even less likely that the mirroring takes place as we compare versions of the same half-image from our left and right eyes, in other words within one and the same cerebral hemisphere. If it did, then a rabbit that according to our left eye was running from left to right would be running in precisely the opposite direction according to our right eye. This would also make it completely impossible for us to detect symmetry, since after mirroring, none of the points in the image from one eye would coincide with its counterpart in the image from the other eye. Seeing depth, a capacity that relies on slight differences in position of the same impulse on the two retinas, would be impossible as well.
So again we find ourselves confronted with a paradox. To see symmetry we must apply a process of mirroring, but that would make it impossible for us to see anything properly. Fortunately, Julesz came up with a solution. He looked at the vast majority of animal species that do not have both their eyes on the front of their heads but one on each side. Looking sideways, they are forced to create mirror images, and they need to do this at the stage when they’re interpreting the half-images from their left and right eyes. It goes like this.
If a butterfly flies past the left side of a rabbit from its back to its front, then the image moves across the retina of the rabbit’s left eye ‘from nose to ear’. If the butterfly passes to the right of the rabbit, then the right eye experiences precisely the same thing. Nothing unusual in that, it would seem. But when they arrive at the projection screen in the rabbit’s brain, the two movements, which were in the same direction, appear to run counter to one another. To allow the rabbit to experience the actual direction of movement in both cases, a correction has to take place somewhere, and it must take the form of mirroring. It becomes clear how important this is if we have the rabbit move as well, running so that the world moves in relation to its eyes. If the animal interpreted the images coming from its two eyes without mirroring, then it would be torn apart inside by the firm conviction that one half of its body was running backwards at the same speed as the other half was moving forwards.
Parallel eyes on the front of the head are the exception, and they may be a fairly recent evolutionary phenomenon. I
f we go far enough back in time, at least a few tens of millions of years, then we come to our own distant ancestors, who like the rabbit had eyes on the sides of their heads. They must have had a visual system suited to such an arrangement, and here may lie the explanation for our sensitivity to symmetry. We mainly function according to a visual system that is relatively new and does not involve mirroring. Although it is adapted to our parallel, front-facing eyes, Julesz argued that it still contains echoes of characteristics of the much older system that did involve mirroring. It’s possible that this system is so old that rather than being located in the cerebral cortex it’s lodged in the brain stem, which is far more ancient in evolutionary terms – a legacy of the immeasurably deep past in which we still communed with crocodiles, and a feature that now proves fantastically useful. Julesz’s theory is an admirable attempt to find a solution to the mystery of how we recognize symmetry, but it’s probably not the final word on the subject. It has too many weak points for that. For example, the mirroring capacity of animals with eyes on the sides of their heads neutralizes an apparent contradiction between partial images within one half of the visual field, whereas the detection of symmetry concerns the connection between the two halves of the field of vision. Furthermore, the fact that we cease to experience the symmetry of Julesz’s patterns if we focus on a point well away from the axis of symmetry proves that mirroring to detect symmetry has nothing to do with the way rabbits see. To rabbits, butterflies travel in the correct direction even if they are at the very edge of the field of vision, quite apart from the fact that sideways-eyed creatures like the rabbit have no more to gain than we do from a process of mirroring the two halves of the visual field.