Infinity at the Barber Shop

Infinity at the Barber Shop

I remember as a boy of eight, going to the barber shop with my two brothers. Of course, I went to the same barber shop at an earlier age than that, but when I was eight I had a Eureka moment.

Two perfumed Sicilians with dyed black hair ran the barber shop in a shopping centre. It was a longish rectangular room, about seven metres wide, with walls of mirrors running along each side.

When I climbed up onto the barber chair, I was 2½ metres away from the nearest wall of mirrors, and as the barber began cutting my hair, I noticed in that nearest mirror the reflection of the other wall of mirrors, 4½ metres behind me.

Strange to say, I could see myself in a series of reflections, cast back and forth: first on the wall behind us; then on the wall closest to us, only smaller; then on the wall behind us, but smaller still; then on the wall closest to us, even smaller.

I remember thinking at the time, “this series of reflections goes on … forever. I am seeing myself front and back practically disappear into the distance. So this is what it’s like to look at infinity. But … I wonder … how can infinity be contained within the walls of the barber shop?”

I asked a friend of mine, the engineer Darius Nikanpour, if he would kindly figure out by how much the image in the mirror is reduced each time. Based on the dimensions of the barber shop and the distance of the barber chair from the nearest mirror, he came up with the following estimate of the reduction factors: 1, then 1/6.6 (meaning, the original image of 1 is reduced by a factor of 6.6), then 1/12.2 (the original image of 1 is reduced by a factor of 12.2), then 1/17.8 (the original image of 1 is reduced by a factor of 17.8), etc. Darius confirmed this would go on to infinity.

He also provided the schematic above with calculations, to make things easier for me to understand.

Ever since this time, I have been fascinated by the play of light on mirrors, bubbles and bodies of water, as if it revealed a reality without limits, somewhere beyond.

 

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