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?”


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:


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.]


  1. “Most participants will agree that the top line appears longer than the bottom one”

    That rather depends on the culture from which they come, it seems. Not everyone perceives things the same way an American does.

  2. I’m not sure why analysis of this type needs to be called philosophy – any discipline requiring precision, including practical subjects such as Engineering, needs to be clear on the meaning of the concepts used otherwise much time will be wasted.

    However I was struck by the opening sentence: “Analytic philosophy has been enormously influential in part because it has been an enormous philosophical success”. This reminded me of a similar statement I’ve read quite recently. Here it is. In Back to Big Thinking on March 21 2013 Hilary Lawson wrote “A century of analytic philosophy is hard pushed to find a single clarification that has been of any real value to another discipline”.

    That sounds like diametrical opposition. There was some support for Hilary’s position at the time but almost no comment on this post so far, although I presume that these opening words have been read by hundreds of people, many of them professional philosophers. Is that the end of the debate?

  3. DiscoveredJoys

    We have been misled by our language.

    Hmm. I’m reminded of E-Prime (see Wikipedia) which is a prescriptive version of the English language that excludes all forms of the verb to be. It is said that E-Prime communicates the speaker’s experience rather than judgment, making it harder for the writer or reader to confuse opinion with fact.

    I wonder how much philosophical thought could be expressed in E-Prime?

  4. Steve, do you have any particular study in mind? I ask because your proposal sounds almost like the Sapir-Whorf hypothesis, which has been largely abandoned.

    K, although it’s been a few months since I read Lawson’s article, I recall being sympathetic to the underlying inspiration, but completely at odds with its conclusions. To use just one example, the distinction between speaker’s meaning and sentence meaning did its part in creating the modern subfield of linguistics known as pragmatics. The boundary between philosophy of mind and cognitive science is particularly porous, and so you’re going to find many instances of cross-fertilization. Not long ago, I was perusing an article written by a computer scientist which attempted to formalize an aspect of speech act theory.

  5. DJ, I hadn’t heard of E’, thanks.

    It always struck me as very strange that certain historically important subfields that investigate the use of language (including general semantics and semiotics) are not at all discussed in analytic philosophy of language. This is in spite of the fact that these fields owe a great deal to philosophers: general semantics to Wittgenstein and Pierce, semiotics to Pierce and Locke.

    [On first blush,] I’m not sure we have any excuses for not just shifting over to E’, so long as we think it has a better handle on the logical form of sentences. It is commonly asserted that ‘is’ serves various functions, doing different sorts of things with ontology. Hence, it is said that we would be better off if we used a different word for each function. And from the third-person perspective, this is probably right.

    But the problem is that we’re not expert third-persons. Thoughts are often confused or indeterminate. Indeterminate thoughts are altogether not truth-apt, and hence deserve to be corrected. But you can’t correct an error that goes unsaid. Yet E’ would force us to shut up about any thought which was ontologically ambiguous. Hence, many thoughts would go unsaid. And we would be impoverished as a result.

    To mandate E’ for the purposes of clarifying thought is like an expert potter banning clay, out of spite for its formlessness.

  6. Jim P Houston

    Rather than anything to do with Saphir-Whorf , Steve’s point may be the one touched on in the Cognition and Culture page you link to – that as per Segall et al (1966) culturally influenced differences in visual experience during formative years affect how people see Müller-Lyer images with people in some ‘less carpentered’ societies, such as that of the Kalahari hunter-gatherers, being pretty much immune to the illusion. So perhaps how we see things such as M-L is not linguistically relative but still culturally so?

  7. Ah, Jim, not so fast! Simon Barthelme’s point at C&C was actually that the contribution of culture is indirect at best. It is more plausible to think that the most direct influence during the formative years is exposure to parts of the physical environment.

  8. Jim P Houston

    Ah, yes, ‘culturally relative’ was a misleading way of putting it – the more plausible thought was what I (and perhaps Steve) had in mind.

    Btw, I’ve just been reading about the ‘hollow-mask’: apparently drunkenness can reduce susceptibility to it – there’s a thought if you find analytic philosophy isn’t (un)doing the trick for you. 😛

  9. Jim P Houston

    Back to the Müller-Lyer, I read that in the cross-cultural tests the arrowheads and tails were separated from the line segments and coloured differently allowing the experimenter to unambiguously identify what’s length was in question…

  10. Fair enough. Coloring is perhaps a better idea than line thickening.

    But — since you’re looking at illusions, what do you think of Figure 3? Do you still think one is longer than the other?

  11. A further profitable line of investigation is the extent to which animals are subject to the same optical illusions as we are (in which case we can rule out cultural influences and level of drunkenness).

    Research (Nature Sept 2010) indicates that male bowerbirds arrange objects in their bower in ascending order of size to create a forced perspective illusion which further impresses the female. However getting a bowerbird’s opinion on whether one line is longer than another would require some thoughtful experimental design.

  12. That sense perception is fallible is not new; things are not as they seem. In contrast, the ability to describe something that does not refer to a tangible entity is a good argument for metaphysics. In this regard, some in new physics, based on non-locality, or signal-less communication at a distance, are positing that the fundamentals of nature may be transcendent. Charles Robert Richer who won a Noble Prize saw the future of science in metaphysics saying, “Greetings then to the new science which is going to change the orientation of human thought.” Presently philosophy and old science are as hostile to metaphysics as orthodox religion is to immanence.

    Ancient philosophers knew the seed sounds that were equally divided between alphabet and number. Theoretical computing is based on Panini’s work from 2500 years ago. If analyses of language is not based on fundamentals it is stymied in attempting to clarify what is real and what is illusion. Concepts that represent what is fundamental can be expected to become concrete over time, not necessarily tangible, instead being understood as hidden forces. Making concepts defunct has to be based on something other than their not being within the current frame of reference.

    Whatever the relevance of analytical philosophy after one hundred years, it is unlikely that it will be relevant in 2500 years.

  13. Jim P Houston

    Hi Ben,

    Using different colours for the tails and arrows and separating them from the segments may be a better idea for the purposes of avoiding linguistic confusion yes. The rationale behind your re-drawing seems to be rendering the L-M so that whether the subject thinks the length of A or B is at issue the answer will come out the same. If it ‘works’ it doesn’t seem to avoid confusion as such but stop any confusion from affecting the answer given – you get the same answer whatever question is thought to be asked but you are leaving it ambiguous as to what question is being asked.

    I do think the result of the redrawing is interesting though – for me the illusion doesn’t seem to arise in fig.3, my initial reaction was just that it was somehow ‘odd’. I find the thickened lines interfere with me seeing the tailed line as if I were looking down at the corner of a room.

  14. “(“If a tree falls in the forest, and no-one is around, do air molecules vibrate?”), then the answer is an obvious “yes”.”

    “If a tree falls…”, is a Buddhist Koan. Neither answer, yes or no, is correct or incorrect. Whichever answer you give the smiling and serene Buddhist monk who poses the question, will be wrong. And he will smugly dispense his eastern wisdom, condescendingly point out how you could not be correct. The idea of a Koan is to show you how unenlightened your intuitive thought is, and help lead you towards enlightenment.

    “A new distinction has helped us to resolve an old problem.”

    You’re not allowed to change the question to suit your solution. Which is a lot like paring down a square peg until it fits a round hole.

    “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”

    No, this is neither a paradox nor is it absurd. And this is a serious question in science, though it seems patently absurd. If there is no human observer, does an event happen at all. The answer is the anthropocentric event does not occur. This is a serious question, because in quantum physics the results of our analysis is that a particle is in one single place when we measure/observe it, but the result strongly indicates the particle is in many places before the observation is made. Everyone knows the Schrödinger’s cat experiment – it sounds like an obvious absurdity, but when you do a possible experiment, one that uses electrons instead of cats (electrons through a double slit – look it up on wikipedia), then there is no other plausible explanation than that the electron is in many places, even crossing paths with itself, before it reaches the screen where it can be said to be definitely in one single position.

    So, if a Buddhist monk asked as a Koan, “If a cat is in a sealed box, and a poisonous gas is released, but no one can see, is the cat alive or dead?”. And the answer, consistent with contemporary scientific knowledge, is that the cat is neither alive nor dead, but in a superposition of two states; both being simultaneously alive and dead. Physicists do not understand this either. In the Many Worlds interpretation – which is taken seriously – when you open the box, the universe splits in two, in one universe the cat will be dead, in the other it will be alive. For its’ preposterousness it’s worse than Buddhism. It also means, in many universes Ben is a woman, and even in some universes we’re all cats. Many physicists dislike the idea, not because they can find anything wrong with it, more because it’s obviously horrific.

    The arrow heads drawing is a Müller-Lyer distortion illusion. More interesting is a Penrose impossible triangle. It’s classed as an optical illusion but there is something much deeper in it. The triangle appears impossible, but there is no specific point where the inconsistency that makes the triangle impossible manifests itself – the corners are self consistent. It’s the kind of thing Russell would wish didn’t exist, because as well as being mathematical peculiarities, they exist in language and cannot be removed – unless you intend reducing language to grunting and pointing – it would be the only way to achieve an absolute consistency.

    Another Buddhist Koan is “What is the sound of one hand clapping?”. It seems an absurd statement but it is trickier than it looks. It’s very much like a Penrose impossible triangle. You can’t win with the monk. If you say it doesn’t make a sound, he will gracefully move one hand in a clapping gesture and say “It is the wind” – or air molecules vibrating. If you try that one, the monk will say “But a clap is a very definite sound” – which it is. Possibly the most satisfying answer would be to sit in silence, then in a fast and very unexpected gesture use one hand to clap the monk very hard in his smug face, and say “That?”…..And if the monk doesn’t get it the first time, repeat the action as many times as is necessary.

    In terms of linguistic analysis, the ancient Buddhist monks were not behind Russell – it’s the other way around. The linguistic paradoxes are irresolvable. The consistency is limited to short ranges – and this is how language evolved; it just needs enough consistency not to sound like gibberish. As cavemen confected it, they didn’t think through all the logical implications. From the point of view of a person standing on earth, the earth is flat, but from outer space it’s obviously not flat. And this is also why, paradoxically a circle in maths can be regarded as a one dimensional shape and not two dimensional. On a small enough scale, like the earth, the edge of the circle appears flat. At a small enough scale, the curvature of a circle is infinitesimal. Or to put it another way, if you’re standing on the edge of a large enough circle, it will appear to you that you are standing on a straight line, but if you follow the straight line, you will eventually come back to the point you started from. like the earth, the edge of the circle appears flat.

  15. “If a tree falls…”, is a Buddhist Koan. Neither answer, yes or no, is correct or incorrect.

    Perhaps that’s the intention, but it’s wrong all the same. Of course, there might be further conversational goals that the monk wants to achieve, but these goals will have to be achieved by other means. “Winning”, here, is not the task — the aim is to give a true answer. Some people are content with being confused, and best of luck to them. The task is not to discipline confused people into accepting true beliefs.

    Still, there are indeed better examples of what you want to say. e.g., unlike the Locke/Zen case, it does seem like GE Moore’s commonsense “refutation” of skepticism was guilty of changing the subject. In some loose sense, the context has been altered. But the Moore/Descartes case is very different from the Locke/Zen case. That’s because the Moore/Descartes case involves pitting a fully articulated theory against a fully articulated theory.

    You’re not allowed to change the question to suit your solution.

    Okay, but the question is the same as it ever was. Grammatically, nothing has changed. The words are the same, the structure of the sentence is the same.

    If anything, the whole language has been slightly altered, so that the answer can be made visible. But this happens all the time, albeit with less dramatic effects (because concepts don’t tend to have general sufficiency conditions). That’s not arguing to a conclusion, it is just what happens when you are set to the task of thinking inside of a living language.

    You may be right about quantum business. When people ask what the electron is up to, I say I mind my own business. All the same, that’s a different subject, and the fact that we accept that the domain of subatomic physics is strange does not by itself give us warrant to draw out similar inferences about the rest of the actual world. (Though there is a whole industry of woo dedicated to showing that macro-level events are beholden to explanation in terms of quantum physics, I don’t think we ought to be emulating them.)

  16. Hi BLS, glancing back and forth between fig.1 and fig.3, I get the illusion every time with fig.1 but not at all with fig.3…I’m not sure why the thickening of the lines seems to affect it so much.

    Re the whole bit with the tree falling in the forest, I don’t see why the answer isn’t just “yes” on both counts?

    My naive interpretation of what the word “sound” means is something like ‘that which can be heard’. On this view, the paradox seems somewhat silly–the answers are clearly “yes” and “yes”.

    In order to arrive at your own answers (no and then yes), “sound” would have to mean something like ‘that which is heard’. However, I don’t see any reason to render it this last way.

  17. Thanks all for posting!

    Dregs, when you suggest that the naive reading is “can be heard”, you’re giving a novel interpretation that doesn’t fit the primary/secondary qualities distinction. And there’s nothing wrong with your proposal — it’s perfectly defensible. Kantian, even. So your answers to the prompt fit, given your definition.

    The only worry one might have is that the answer might not do justice to the initial clash of intuitions. In the first place, we’re all supposed to feel tugged in both directions — we’re supposed to think, “The tree makes a sound, and the tree doesn’t make a sound”. I assume you felt that way, at one point or other (though we’ve both grown out of it).

    One way of sorting through that internal conflict is to just make an easy distinction, King Solomon style, giving as much credit to the ‘no’ intuition as to the ‘yes’ intuition. That’s what results in the distinction between primary and secondary qualities. The only attraction of making this move is that we get to keep just as many of our intuitions as we started out with.

    But “I want to save an intuition” is never by itself a minimal reason to adopt some belief. An intuition has all the evidentiary weight of a feather. If I defended the primary/secondary qualities distinction, it would be in terms of articulated beliefs. e.g.: (a) I recognize my own actual imminent first-person experiences as being worthy of distinction, (b) that these experiences have a productive role in how I structure my explanations, and (c) I don’t acknowledge any deep conflict between your proposal and the primary/secondary qualities distinction.

  18. A) if you want to reduce the importance of the thickness of the line, then make the lines *thinner*. Grab your paint program of choice and use a brush size of only 1 or 2 pixels.

    B) Or you can avoid the linguistic confusion by asking *which line is longer*. If people tend the answer that the shorter line appears longer, then tada, illusion demonstrated just as effectively, despite linguistic clarity. Not a problem unless some people who have “trouble” interpreting perspective aren’t fooled, and then have to deal with the ambiguity of (segment) or (segment + arrowhead)

  19. (a) won’t work. The lines were made thicker to eliminate the ambiguity between whole line and line segment. Making them any thinner would re-introduce the ambiguity.

    (b) is true, and common practice, it seems. e.g., some experiments ask people to focus, effectively, only on the line segment, not the whole line.

    So, at best, the use of the distinction will only help us understand the causes of (Fig 1), not eliminate the illusion from that figure. Language is powerful, but not that powerful. No, the illusion can only be eliminated in one sense: if we recreate the illustration in such a way that the ambiguity does not arise (as in Fig. 3), the illusion disappears (to my eye, anyway).

  20. There’s a decent literature on ‘adjustable’ Muller-Lyer illusions. This is an approach where the separation of the arrow-heads and the length of the joining line can be adjusted until apparent parity is achieved. This technique allows one to quantify how big the illusion is for different viewers and thus do some robust science on the phenomenon.
    One on-line example that works well is available at:

    Fun to try. Go for the ‘short’ trial option (20 attempts then you’re given the results properly analaysed statistically).

    For me, the business of ‘optional delusions’ (as a friend delights in calling such phenomena) is enormoulsly rich in revealing the limitations present at what can seem a very simple level of comprehension. Consciousness is an illusion, alright.

  21. Sorry – that web address for adjustable Muller-Lyer missed out above:


  22. Great link, and great test!

    One pattern I noticed is that the more time that passed, the more inaccurate my answers became.

  23. I always hated the tree-in-the-forest thing, human -centric, what do they mean ‘no-one’. If a tree falls and NOTHING is around does it make a sound? If nothing is around, the tree wouldn’t likely be there. If a tree is around there are plenty of critters that are not considered a ‘someone’, or a ‘no-one’ by absence, that have ear drums. So the answer is ‘yes’.