I emailed back and forth with Leslie a lot about this, when I first read his paper. There is an earlier analysis of the same phenomenon by different people (the arbiter problem) which I discovered later.
At first, I had trouble to believe it, and tried to find counterexamples, until I realized that the composition of continuous functions is continuous. I still wonder sometimes whether an infinite composition of continuous functions has to be continuous (limit of a sequence) if it represents some real world evolving process. Can it produce a discontinuity in the limit?
Anyway, Buridan’s principle informs our consensus process in Intercoin Protocol[1] [2] — it is why the consensus groups are always of a bounded finite size, so we don’t approach the errors in Buridan’s priciple (I think this is also called unstable problems).
Right. So now the question is -- are you able to give a physical example of physical (continuous) processes which can create a discontinuous output from a continuous initial state, in a finite amount of time? I think this is a sort of Zeno's paradox...
No. The coin could land on its side, for instance, and stay there.
Consider a pencil that is placed almost vertically, and then later drops to a horizontal position. There is a period where it is "unsure" where to go, and the more perfectly balanced it starts out, the longer this period is (assuming no wind etc.)
At first, I had trouble to believe it, and tried to find counterexamples, until I realized that the composition of continuous functions is continuous. I still wonder sometimes whether an infinite composition of continuous functions has to be continuous (limit of a sequence) if it represents some real world evolving process. Can it produce a discontinuity in the limit?
Anyway, Buridan’s principle informs our consensus process in Intercoin Protocol[1] [2] — it is why the consensus groups are always of a bounded finite size, so we don’t approach the errors in Buridan’s priciple (I think this is also called unstable problems).
1. Beyond blockchains https://community.intercoin.org/t/intercoin-technology-conse...
2. Experimental improvements https://community.intercoin.org/t/experimental-improvements-...
Anyone who reads the above … I would be very interested in your feedback on our forum.