Looking-Glass Images

Perception of Mirror Images (Frame 11)

Consider this: why does a mirror exchange left and right but not top and bottom? Why could we say that it seems that gravity is not affected by the reflection but directions of right and left are inverted?

The answer: A mirror actually changes neither. The top remains at the top, and the right actually remains on the right. What is actually changed is what is front and back. When you look into the mirror through your own 1st person view and just see your reflection looking back at you, this is not very obvious to realize at first. Our intuition however interprets the mirror image as a rotation about a vertical axis rather, hence the belief that mirrors exchange left and right. This is because we commonly see humans "pivot" or rotate about a vertical axis to create an image similar to one seen in a mirror, but not invert themselves to create such an image. However, if we were to stand behind someone else and to the side of them, seeing both them and their reflection from a third-person point of view, we would realize that their face in the real world and in the reflection seem to be the same distance from the plane of the mirror along with the back of their head. In other words, their face is closest to the mirror on both sides and the back of their head is farther away.

Through the Looking Glass (Frame 12 and 13)

The above illustrations from Lewis Carroll's Through the Looking Glass, and What Alice Found There can illustrate the concepts behind mirror images. Note that in the picture on the right, Alice has her right arm raised. The picture on the left, which is of the reversed "Looking-Glass world" (perhaps indicated by the appearance of a strange face on the clock), has Alice with her same right arm raised on the left. The second picture is actually the image of the first if it were rotated about a vertical axis rather than a reflected image.

Lewis Carroll was the pen name of Charles Lutwidge Dodgeson. As an Oxford mathematician, this would be a strange error for him to make. The illustrations however, were not drawn by him, but by John Tenniel, who was blind in one eye (thank you Wikipedia). Could this error have been due to the limitations of his sight?

It turns out that the error is actually assuming the second picture is a reflection. Note that the title states Through the Looking Glass, meaning the picture is of Alice traveling through the mirror rather than being reflected by it. If Alice were to have been reflected by the mirror and her reflection were to appear in the second picture where she is supposed to exist on the other side of the mirror, then it would have been named more appropriately In the Looking Glass

An image in the looking glass would then be more similar to this picture, a mirror image of the second picture, in that the extended arm is now on the right.

So rather it seems that Lewis Carroll and John Tenniel were not incorrect in their illustrations and descriptions in this book. It might be curious to point out that the book itself was published in 1872, which coincides with the time period of the 1860s and 1870s when the 3D tetrahedral structure of carbon bonding and the position of atoms in space and their spatial orientation was being pondered and developed by scientists such as Stanislao Cannizzaro, Emmanuele Paterno, Adolf Lieben, J.H. van't Hoff, and Hermann Kolbe. Of course the emergence of the 3D tetrahedral view of carbon bonding then led to the possible chirality characteristic of carbon.

Looking-glass milk (Frame 14)

What is perhaps most curious about Through the Looking Glass is the quote "Perhaps looking-glass milk isn't good to drink." Through the Looking Glass was published in 1872, around the same time as a new discovery of a substance present in meat that seemed to be identical to lactic acid found in milk, except that both of these substances rotated polarized light in opposite directions. This substance was referred to as sarcolactic acid. The discovery of the relationship and comparison of these two acids actually helped reform the 3D structural theory of atoms and it caused scientists to suggest the tetrahedral structure of carbon bonding in space in 1874, then giving rise to the theory of stereoisomerism and chirality. Perhaps Carroll was aware of the contemporary developments in chemistry because of his acquaintance with the chemist Augustus Vernon Harcourt and Sir Benjamin Collins Brodie and thus referenced this in his work.

Here is a 3D image of lactic acid. The chiral carbon is circled. As you can see it has 4 different substituents bonded to it: a hydrogen (-H), a methyl group (-CH3) , an alcohol group (-OH), and a carboxylic acid group (-COOH).

For further information, follow this link: E. Heilbronner, J.D. Dunitz, Reflections on Symmetry, 1993, p. 86 external link: http://www.pnas.org/content/93/25/14260.abstract

Previous Page: Counting_Dewar_Isomers

Following Page: Chirality_&_Mirrors