My GP (family doctor) referred me for physiotherapy but the surgery doesn't have a physio of its own, so the receptionist held a card in front of me with a list of about ten and told me to choose which I wanted. This is the zeitgeist: consumer/patient/customer choice.
I wasn't really in a position to make an informed choice, but I pointed: "I'll take that one".
My choice is communicated somewhere - it's not important where - so this can be nicely modelled by the Shannon communication channel. Each time a patient chooses a physio, we have a message selected from 10 possible messages, and, if each physio is equally popular, the message conveys log2(10) = 3.32 bits.
What I'm thinking, is that choice is needed for information. In 'the difference that makes a difference", implicit in the 'difference' (#1 in the phrase), is a choice of one the alternatives. It is tied up somehow with intention.
Can a difference without a choice makes a difference?
But in my example I wasn't really making a choice, or rather there was no information in my choice. If we'd gone a layer up, there was no selection. The apparent 3.32 bits of information was spurious.
This needs working through further.