Essay contest: Is reality digital or analog?

It's an interesting topic, but if you look at the challenge questions, most of them raise issues with the idea that reality is digital. But from the little I know, modern quantum theory is analog. The polarization state of a photon is expressed as a point on a unit circle. That's analog. It takes an infinite number of decimal places to precisely express the state of the photon. In that sense, it represents an infinite amount of information.

But the paradox is that if you try to store information in the photon state and then read it out, you can only store 1 bit. How much sense does that make, that you have a state that takes an infinite amount of information to represent, but in practice you can only store one bit? Why would there be such an infinitely information-hungry infrastructure, to support such limited, information-poor storage?

To put it in terms people around here might appreciate, imagine if Google required an infinitely large cloud computer to store just one bit. They wouldn't stay in business long. That's no way to run a universe.