gkr | Z_n = Z/nZ, right? |

TRWBW | gkr: yes |

sloof3 | gkr: of course |

action | gkr thought he was all wrong |

gkr | thought he was all wrong |

TRWBW | gkr: you mean mod n, yes? |

gkr | Thanks. Yep TRWBW. |

sloof3 | wow... |

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. |

sloof3 | Capso: yes |

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 |

Capso | That's vague. 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. Okay, suppose: f(x,y) = x + y; -- Definition f(x,y) = 5 f(x,y) = 6 Etc. |