How to see (4)

escher200Drawing hands
Laurence Goldstein

Imagine a picture P1 of the right hand of the artist MC Escher emerging from a shirt cuff. The hand is resting on a sheet of paper, and a pen held between thumb and forefinger is being used to draw a picture on the sheet. That picture, P2, almost complete, is of a left hand. So the latter is a picture of a picture of a hand; it is not a picture of a real hand, but of a drawn hand. But wait….. that left hand is shown drawing a right hand, so the latter picture cannot be the picture of a real hand but is the picture of a picture of a picture of a real hand, P3. And is identical to P1 which, as we originally claimed, is a picture of a real hand. Contradiction. Or is it? Can the picture right hand simultaneously be P1, P3, P5, P7, ad inf., and the picture left hand simultaneously be P2, P4, P6, P8, ad inf.?

We are, of course, talking about Escher’s 1948 lithograph “Drawing Hands”. There is, as Norwood Russell Hanson said, more to seeing than meets the eyeball. Do observers who naïvely saw “Drawing Hands” as two drawn hands, now (after accepting the above analysis) see it differently as a pair of infinite superimpositions of picture hands, even though what meets their eyeballs is the same?

Awakening the sense
Ray Tallis

Philosophy neither tints the lenses nor sharpens the acuity of the eye. It can, however, help us to see differently by inviting us to “untake” the for granted. Things that are invisible because they are obvious may become visible through being put into question.
That cup over there has not particularly attracted my attention: when I am not using it, it is invisible through irrelevance; when I am using it, it dissolves into the flow of my activities. But when I look at it now with the disinterested, but not uninterested, gaze of the philosopher, lo and behold it becomes a focus of mystery. For example, I believe that it is independent of me, so how can I be aware of it? By what means is that thing over there experienced by me over here if I and it are in no way bound to one another? If it is not independent of me, then the world is more peculiar than I had thought: it is not, it seems, a place in which my body is an object among other objects, externally related to them. Suddenly we see that we are seeing and cannot see how this is possible. The most bored glance is a mystery.

By roughening up the smooth surface of the taken for granted with questions, the philosopher awakens a sense of possibility that requires of us that we should entertain new ways of seeing. The evidence for this is the wonderful history of philosophy which has godfathered inquiries into the material world, our place into it, and our knowledge of it, by which we have been immeasurably enriched.

Laurence Goldstein’s latest (co-authored) book is an introduction to the philosophy of logic: Logic (Continuum Press)
Ray Tallis is the author of The Kingdom of Infinite Space (Atlantic)

For previous articles in this series, see here, here and here.

  1. Laurence,
    Aren’t both hands, in fact, right hands?
    “Can the picture right hand simultaneously be P1, P3, P5, P7, ad inf., and the picture left hand simultaneously be P2, P4, P6, P8, ad inf.?”
    Of course they are. In each case you’re giving the hand an infinite number of different names. You can probably do what you did above with any two things with a reflexive relation, e.g.
    A is the brother of B
    A is the brother of (the brother of (the brother of B)) etc.

  2. Sorry, I meant a symmetric relation.

  3. Ray,
    “By what means is that thing over there experienced by me over here if I and it are in no way bound to one another?”
    You’ve made the decision that if something is independent of you you shouldn’t be aware of it. Why? What do you mean by independent? For that matter, what do you mean by aware? In the latter case, if you mean “experienced by,” then I’d have to give the rather ordinary answer from optics, viz. light waves reflected from the object to our eyes, etc.
    I don’t really feel convinced of the things you’re saying, but a slight extension of it might have some possibilities for me, e.g. I look at my unmoving hand. It is a part of my body and hence me. Yet the only way I’m aware of it at this moment is by looking at it. It doesn’t feel any more a part of me than your cup. Consider further: What if the hand is prosthetic? I see it on the rest of my limb. Is it part of me? In fact, there would probably be a greater awareness of the false hand on my limb than a real one.

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