On the ontology of handedness

The photograph above is a selfie that I took with a right-handed friend, or its mirror image. Are there any clues in the image to say whether it is mirrored or not? Unless you are familiar with the place (Kumpula Botanic Garden in Helsinki), it is quite impossible to say.

One can try to guess, of course. Did I take the selfie with my right or left hand? I am lefthanded, but with a GoPro it is easy to take the selfie with whichever hand happens to be in better direction for the image. On the left (or maybe it is actually right?) there is a small sign on the ground: if it was bigger and its text would be readable, then it would be quite easily tell whether it is a mirrored or not. But nature doesn't seem to have left and right, and while this photograph also has many human cultural elements in it there is nothing that would definitely tell if it is a mirror image or original.

How to even define 'left' and 'right'? You learn them when somebody shows you that this is your right hand and this is the left one. But that is not a definition. So is there any way to define them without having a reference to any particular asymmetric object such as one's body or the Earth? Chiral concepts such as 'clockwise' and 'north' don't help because either they already require that you know the difference between 'right' and 'left', or you have to use some object such as Earth as a reference.

Kant and Wittgenstein

The question of handedness has been discussed by philosophers like Immanuel Kant and (1724–1804) and Ludwig Wittgenstein (1889–1951).

Kant asked one to take a look at one's hands. When looking one's right hand in a mirror one sees a left hand. And yet even though your hand is identical with its mirror image you cannot replace one with another. You cannot put right hand glove to your left hand (see Kant's Prolegomena §13).

Above, there is a two-dimensional illustration of two hands mirrored by a line. Line is one-dimensional object. This analogical to a three-dimensional object being mirrored by a two-dimensional plane, like in the case when you are watching yourself in a mirror. Now, if you print the image on a paper amd cut either one of the hands out, you can move it on the other one by turning it round in three-dimensional space.

Ludwig Wittgenstein's answer to Kant is based on this. He wrote: 'A right-hand glove could be put on the left hand, if it could be turned round in four-dimensional space' (Tractatus 6.36111).

That would mean that if only difference between two objects is their handedness, there is no real difference at all. You just need one more dimension to turn it round. But is that a real solution? Doesn't it seem that Wittgenstein just moves the problem to another dimension? For four-dimensional objects one needs a five-dimensional space, for five-dimensional ones a six-dimensional space, and so on, ad infinitum.

Scientific solution

Nevertheless, there is a way to define 'right' and 'left' without any reference to other chiral concepts nor to particular asymmetric objects. However, instead of philosophy, we need some science. The method was revealed by physicist Chien-Shiung Wu in 1958. Just follow the instructions to try yourself:

1. Cool the atoms of cobalt-60 to near absolute zero.
2. Line up their nuclear axes with a powerful magnetic field.
3. Count the numbers of electrons flung out by the two ends of the axes.
4. The end that flings out the most electrons is the end that we call 'south'.
5. It is now possible to label the ends of the magnetic axis of the field used for lining up the nuclei.
6. This in turn can be used for labeling the ends of a magnetic needle.
7. Put such a needle above a wire in which the current moves away from you.
8. The north pole of this needle will point in the direction we call 'left'.

What Wu did was that she demonstrated asymmetry in a physical phenomenon. Prior to her experiments, Wolfgang Pauli, another famous physicist, was sure that she would fail. He said: 'I do not believe that the Lord is a weak left-hander, and I am ready to bet a very high sum that the experiments will give symmetric results.' I don't know how much Pauli lost but if we believe him, even God is left-handed (although I don't understand what would make lefthandedness more asymmetrical than righthandedness)!

Handedness in everyday life

While modern physics has succeeded to solve the problem about right and left, it might still be better to skip cobalt-60 if you want to explain the difference to a child, for instance. In everyday life, handedness remains a cultural thing and not something that you can find in the nature.

Here is another photo that might be a mirror image or not. It is taken on one of the roads to Teide on the island of Tenerife. Knowing that it is taken in Spain probably helps in guessing whether it is mirrored or not. But still, all the hints are cultural. There is nothing in the nature that can tell it unless we have access to laboratory where we can cool cobalt-60 atoms to near absolute zero temperature.

References

Gardner, Martin (1991). The Ozma problem and the fall of parity. In James Van Cleve & Robert E. Frederick (eds). The philosophy of right and left. Incongruent counterparts and the nature of space, pp. 75-95. Kluwer, Dordrecht.

Kant, Immanuel. Prolegomena : eli, Johdatus mihin tahansa metafysiikkaan, joka vastaisuudessa voi käydä tieteestä. 254 p. Gaudeamus, Helsinki.

Van Cleve, James (1991). Introduction to the arguments of 1770 and 1783. In James Van Cleve & Robert E. Frederick (eds). The philosophy of right and left. Incongruent counterparts and the nature of space, ss. 15-26. Kluwer, Dordrecht.

Wittgenstein, Ludwig (1933/1996). Tractatus logico-philosophicus. 88 p. WSOY, Juva.

Apart from the books listed above there was a university course that greatly influenced the writing of this article:

Himanka, Juha (1999). Johdatus fenomenologiaan (Introduction to phenomenology). Lecture course, University of Helsinki, Department of Philosophy.

Are the images mirrored?

And in case you were still thinking: both photographs of this article are mirrored (the author image is not).

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