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Monday, July 11, 2005

chiral up!

Lately, LI has been enjoying Chris McManus’ book Left Hand, Right Hand: The Origins of Asymmetry in Brains, Bodies, Atoms and Cultures. We love an omnium gatherum, of which this is a superior instance. Also, handedness is naturally of interest to the philosophically minded. It comes as no surprise (although, actually, it did come as a surprise) that one of the great pioneers in the study of the problem of handedness was Immanuel Kant. Kant thought that the dispute over absolute or relative space – the dispute between Newton and Leibnitz – could be resolved by considering right and left. Kant was, as always, right (a word etymologically connected, as all handedness researchers assure us, to the superstitious reverence accorded to the right hand, just as superstition accords ill luck to the left – the left is “cack-handed”), although as always, he was also wrong.

In 1768, Kant wrote a little essay entitled Von dem ersten Grunde des Unterschiedes der Gegenden im Raum (usually translated as On the basis of differences between regions in space) about absolute and relative space. You will remember that Leibniz’ argument against absolute space capitalized on the anxiety caused by the loss of discernability – L.’s idea being that one region of absolute space would be absolutely identical to another. This would mess up the cosmic bookkeeping of God himself. Kant’s first theory about space (he changed his mind later, when he wrote the Critique of Pure Reason) sought to find the answer in the dispute between Newton and Leibniz in considering incongruent counterparts: the left hand and the right hand are the most “at hand” examples. The metaphysical dimension of the problem would be on the way to logical solution if we could find some fundamentally right handed spatial object – something asymmetrical to which all parties could refer.

Now, as McManus notes, the problem of transforming a one dimensional shape on a plane facing one way into its incongruent counterpart facing the other way has been solved by the trick of assuming another dimension, in which the first object can be flipped. What is the medium of that third dimension?

Remember, the argument is ultimately about discernability. Here’s how McManus puts it:

“If space could be described adequately in terms solely of the relationships between objects, as Leibniz…argued, then objects that are different could be distinguished by different interrelationships of their components. [in other words, the differences would be expressed by internal configuration -- LI]. … That, though, is not the case with my own right and left hand. All of the angles and lengths are the same in my two hands, yet still the hands are indisputably different. I cannot put my right glove on my left hand or my right shoe on my left foot [although I can try, as I discovered a few days ago, trying to put a right sandal on the left foot of the squirming two year old son of a friend of mine. The child, being an inveterate Kantian, baulked-LI]… For Kant, the conclusion is inescapable: there must be something against which right and left can be compared – and that could only be space itself: “Our considerations … make it clear that differences, and true differences at that, can be found in the constitution of bodies: these differences relate exclusively to absolute and original space.’ Even empty space must have some absolute structure against which it can be said that our right hand is not the same as our left.”

Kant’s paper has created a sub-industry. Pooley’s paper, here, defends the Leibniz-ian view, modified by contemporary physics, against Kant.

“I will side with most—although admittedly not all—philosophers in defending an account of incongruent counterparts according to which they are intrinsically identical.3 Moreover, I will defend a relational account of handedness according to which the difference between incongruent counterparts is grounded in their relations to each other and to other material objects. Kant thought that there were reasons to reject such an account. Initially he concluded that the difference between left and right hands did indeed come down to a difference in their relational attributes, but that these involved relations to “universal space as a unity” (Kant,
1992 [1768]: 365). Not long after reaching this conclusion, he also rejected this substantivalist account of handedness. Instead he now believed that the difference between incongruent counterparts was fundamentally incomprehensible: that it could only be grasped in perception, through a “pure intuition,” and not by any “characteristic marks intelligible to the mind through speech” (Kant, 1992 [1770]: 396).”

We will return to handedness in another post But we should include, here, the most wonderful bit of Kant’s essay. Like Condorcet and Locke, Kant liked the Enlightenment notion of an imaginary problem (which has become, as philosophers have grown into thinking of themselves as scientists without portfolio, into “thought experiments’). This is Kant’s

“ . . imagine that the first created thing was a human hand. That human
hand would have to be either a right hand or a left hand. The action of the creative cause in producing the one would have of necessity to be different from the action of the creative cause producing the counterpart.”

Has Borges somewhere taken up this absurdly beautiful idea? LI, at least, finds it ravishing, and would like to worship that unknown God that created, as his first magic trick in the as yet uncreated universe, a human hand.

Of course, this might actually have been God's first trick in all earnest -- given the handedness of the electrons.

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