Losing your illusions

Analytic philosophy has been enormously influential in part because it has been an enormous philosophical success. Consider the following example. Suppose it were argued that God must exist, because we can meaningfully refer to Him, and reference can only work so long as a person refers to something real. Once upon a time, something like that argument struck people as a pretty powerful argument. But today, the analytic philosopher may answer: “We have been misled by our language. When we speak of God, we are merely asserting that some thing fits a certain description, and not actually referring to anything.” That is the upshot of Russell’s theory of descriptions, and it did its part in helping to disarm a potent metaphysical illusion.

Sometimes progress in philosophy occurs in something like this way. Questions are not resolutely answered, once and for all — instead, sometimes an answer is proposed which is sufficiently motivating that good-faith informed parties stop asking the incipient question. Consider, for instance, the old paradox, “If a tree falls in the forest, and no-one is around, does it make a sound?” If you make a distinction between primary and secondary qualities, then the answer is plainly “No”: for while sounds are observer-dependent facts, the vibration of molecules would happen whether or not anyone was present. If you rephrase the question in terms of the primary qualities (“If a tree falls in the forest, and no-one is around, do air molecules vibrate?”), then the answer is an obvious “yes”. A new distinction has helped us to resolve an old problem. It is a dead (falsidical) paradox: something that seems internally inconsistent, but which just turns into a flat-out absurdity when put under close scrutiny.

Interesting as those examples are, it is also possible that linguistic analysis can help us resolve perceptual illusions. Consider the image below (the Muller Lyer illusion, taken from the Institut Nicod‘s great Cognition and Culture lab). Now answer: “Which line is longer?”

mullerlyer-illusia

Fig. 1. Which line is longer?

Most participants will agree that the top line appears longer than the bottom one, despite the fact that they are ostensibly the same length. It is an illusion.

Illusions are supposed to be irresolvable conflicts between how things seem to you. For example, a mirage is an illusion, because if you stand in one place, then no matter how you present the stimuli to yourself, it will look as though a cloudy water puddle is hovering there somewhere in the distance. The mirage will persist regardless of how you examine it or think about it. There is no linguistic-mental switch you can flip inside your brain to make the mirage go away. Analytic philosophers can’t help you with that. (Similarly, I hold out no hopes that an analytic philosopher’s armchair musings will help to figure out the direction of spin for this restless ballerina.)

However, as a matter of linguistic analysis, it is not unambiguously true that the lines are the same length in the Muller-Lyer illusion. Oftentimes, the concept of a “line” is not operationally defined. Is a line just whatever sits horizontally? Or is a line whatever is distinctively horizontal (i.e., whatever is horizontal, such that it is segmented away from the arrowhead on each end)? Let’s call the former a “whole line”, and the latter a “line segment”. Of the two construals, it seems to me that it is best to interpret a line as meaning “the whole line”, because that is just the simplest reading (i.e., it doesn’t rely on arbitrary judgments about “what counts as distinctive”). But at the end of the day, both of those interpretations are plausible readings of the meaning of ‘line’, but we’re not told which definition we ought to be looking for.

I don’t know about you, but when I concentrate on framing the question in terms of whole lines, the perceptual illusion outright disappears. When asked, “Is one horizontal-line longer than the other?”, my eyes focus on the white space between the horizontal lines, and my mind frames the two lines as a vibrant ‘equals sign’ that happens to be bookended by some arrowheads in my peripheral vision. So the answer to the question is a clear “No”. By contrast, when asked, “Is one line-segment longer than the other?”, my eyes focus on the points at the intersection of each arrowhead, and compare them. And the answer is a modest “Yes, they seem to be different lengths” — which is consistent with the illusion as it has been commonly represented.

Now for the interesting part.

Out of curiosity, I measured both lines according to both definitions (as whole lines and as line segments). In the picture below, the innermost vertical blue guidelines map onto the ends of the line segments, while the outermost vertical blue guidelines map onto the edges of the bottom line:

Screen Shot 2013-04-28 at 6.12.15 PM

Fig 2. Line segments identical, whole lines different.

Once I did this, I came up with a disturbing realization: the whole lines in the picture I took from the Institut Nicod really are different lengths! As you can see, the very tips of the bottom whole line fail to align with the inner corner of the top arrow.

As a matter of fact, the bottom whole line is longer than the top whole line. This is bizarre, since the take-home message of the illusion is usually supposed to be that the lines are equal in length. But even when I was concentrating on the whole lines (looking at the white space between them, manifesting an image of the equals sign), I didn’t detect that the bottom line was longer, and probably would not have even noticed it had it not been for the fact that I had drawn vertical blue guidelines in (Fig.2). Still, when people bring up the Muller Lyer illusion, this is not the kind of illusion that they have in mind.

(As an aside: this is not just a problem with the image chosen from Institut Nicod. Many iterations of the illusion face the same or similar infelicities. For example, in the three bottom arrows image on this Wikipedia image, you will see that a vertical dotted guideline is drawn which compares whole lines to line segments. This can be demonstrated by looking at the blue guidelines I superimposed on the image here.)

Can the illusion be redrawn, such that it avoids the linguistic confusion? Maybe. At the moment, though, I’m not entirely sure. Here is an unsatisfying reconstruction of the Nicod image, where both line segment and whole line are of identical length for both the top arrow and the bottom one:

mullerlyer-illusia2

Fig 3. Now the two lines are truly equal (both as whole lines and as segments).

Unfortunately, when it comes to Fig. 3., I find that I’m no longer able to confidently state that one line looks longer than the other. At least at the moment, the illusion has disappeared.

Part of the problem may be that I had to thicken the arrowheads of the topmost line in order to keep them equal, both as segments and as wholes. Unfortunately, the line thickening may have muddied the illusion. Another part of the problem is that, at this point, I’ve stared at Muller-Lyer illusions for so long today that I am starting to question my own objectivity in being able to judge lines properly.

[Edit 4/30: Suppose that other people are like me, and do not detect any illusion in (Fig. 3). One might naturally wonder why that might be.

Of course, there are scientific explanations of the phenomenon that don’t rely on anything quite like analytic philosophy. (e.g., you might reasonably think that the difference is that our eyes are primed to see in three dimensions, and that since the thicker arrows appear to be closer to the eye than the thin ones, it disposes the mind to interpret the top line as visually equal to the bottom one. No linguistic analysis there.) But another possibility is that our vision of the line segment is perceptually contaminated by our vision of the whole line, owing to the gestalt properties of visual perception. This idea, or something like it, already exists in the literature in the form of assimilation theory. If so, then we observers really do profit from making an analytic distinction between whole lines and line segments in order to help diagnose the causal mechanisms responsible for this particular illusion — albeit, not to make it disappear.

Anyway. If this were a perfect post, I would conclude by saying that linguistic analysis can help us shed light on at least some perceptual illusions, and not just dismantle paradoxes. Mind you, at the moment, I don’t know if this conclusion is actually true. (It does not bode well that the assimilation theory does not seem very useful in diagnosing any other illusions.) But if it did, it would be just one more sense in which analytic philosophy can help us to cope with our illusions, if not lose them outright.]

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