|gkr||Z_n = Z/nZ, right?|
|sloof3||gkr: of course|
|action||gkr thought he was all wrong|
|gkr||thought he was all wrong|
|TRWBW||gkr: you mean mod n, yes?|
|Capso||sloof3: No, the point is: no matter WHAT input, you get the SAME output, for the SAME function definition.|
|sloof3||Capso: why would we get the same output|
|Capso||sloof3: That's the whole thing, isn't it?|
sloof3: You know your output, you know what the system is doing, you just don't know what you gave the system.
|sloof3||I was thinking in terms of a system with an observable output and changing input|
|Capso||Your 'observability' defines the probabilities of what you MIGHT have given the system.|
|Capso||So, the OUTPUT needs to stay the same.|
|sloof3||If the output always stayed the same that wouldn't help us would it?|
|Capso||You can only CONSIDER one output.|
All the input values which would get that output.
|sloof3||We don't know the inputs though|
|Capso||The thing is: you're not DETERMINING anything, you're simply getting a rating of a definition FROM an observation.|
Right, we don't know input.
|sloof3||Originally I was only considering a system that had changing inputs.|
We would need at least n outputs for n inputs
|Capso||Sorry, had some disruption here.|
No, your GOAL is to define 'observability' by knowing ONLY the following:
(1) The number of inputs a function might take
(2) The operation (definition) of the function
(3) The output(s?) of the function.
And the 'observability' will simply be you *ability to define the inputs to obtain the output(s?)*.
|sloof3||define the inputs given the outputs|
What I've stated is clearer.
The reason I include the '(s?)' in 'output(s?)' is that I'm still considering whether we should take into account > 1 output.
You need certain inputs to GET those outputs.
f(x,y) = x + y; -- Definition
f(x,y) = 5
f(x,y) = 6