Re:Leslie Lamport revolutionized computer science with math ...
by raegis on Tuesday May 24, 2022 @11:07PM
(#31500155)
> I still wonder sometimes whether an infinite composition of continuous functions has to be continuous (limit of a sequence) ...
No, as you expected. Take f(x) = x^2 on [0,1]. Then f(f(f(...f(x))) converges to g(x) = { 0, if 0 <= x < 1; 1, if x=1 }
Re:Leslie Lamport revolutionized computer science with math ...
by EGreg on Tuesday May 24, 2022 @11:42PM
(#31500372)
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...
Re:Leslie Lamport revolutionized computer science with math ...
by juhanima on Wednesday May 25, 2022 @06:38AM
(#31502607)
Tossing a coin?
Re:Leslie Lamport revolutionized computer science with math ...
by EGreg on Wednesday May 25, 2022 @07:33AM
(#31503048)
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.)
That's what is being discussed.
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.