3 ms·

So can someone help me with my understanding I read the paper and feel I have a grasp of it but there is still one thing I don't understand he says >Buridan’s

by hpoe 7y ago

So can someone help me with my understanding I read the paper and feel I have a grasp of it but there is still one thing I don't understand he says >Buridan’s Principle. A discrete decision based upon an input having a continuous range of values cannot be made within a bounded length of time. Shouldn't it instead read > Buridan’s Principle. For a discrete decision based upon an input having a continuous range of values, there exists some values such that a discrete decision cannot be made within a bounded length of time. Because clearly there are many instances that a discrete decision is made in a bounded length of time, as shown by the car does stop or goes for many values of x even though there is a bounded length of time; however there is certain values of x that result in the train running over the car, but not all. Ergo, only some values of x will result in a decision being made impossible in a bounded period of time. Can someone help me understand the flaws in my thinking or understanding?

teraflop 7y ago
The only difference between your phrasing and the paper's is terminology. By definition, a "bound" is a limit, i.e. a range that the outcome falls into. Saying that the time to make a decision is bounded simply means that you can always rely on it to happen within that limit.
- hpoe 7y ago
  Okay so what I am to understand by the phrase > cannot be made within a bounded length of time. Is not that it will not happen within a certain time period but rather I cannot with certainty fix an upper or lower bound on the amount of time it will take to reach a decision for all possible values of the input X. Thank you for your reply I had to noodle on it a bit but think I get it now.
  - mikorym 7y ago
    Not bounded means that if you give me a number x then there is some y that is bigger than x. So, in the context of the paper, if you thought that your computer always made a decision after a week, then there is some situation whereby the computer takes longer than a week. For the record, I think the mathematics is sounder than the computer science which in turn is sounder than the social science. As the author admits when he mentions Kepler, we can't really prove Buridan's Principle. But I think it goes further than this in the social aspect: We don't know whether indecision at traffic lights is even accurately modeled by Buridan's Principle. Then the question becomes not whether it's true, but whether it is a good model. And these kind of models are always dangerous ground in the social sciences. Edit: The reason why I say the mathematics is sound is because he rephrases the usual notion of compactness: https://en.wikipedia.org/wiki/Compact_space https://en.wikipedia.org/wiki/Compact_space.

by hpoe 7y ago

teraflop 7y ago

The only difference between your phrasing and the paper's is terminology. By definition, a "bound" is a limit, i.e. a range that the outcome falls into. Saying that the time to make a decision is bounded simply means that you can always rely on it to happen within that limit.

hpoe 7y ago
Okay so what I am to understand by the phrase > cannot be made within a bounded length of time. Is not that it will not happen within a certain time period but rather I cannot with certainty fix an upper or lower bound on the amount of time it will take to reach a decision for all possible values of the input X. Thank you for your reply I had to noodle on it a bit but think I get it now.
- mikorym 7y ago
  Not bounded means that if you give me a number x then there is some y that is bigger than x. So, in the context of the paper, if you thought that your computer always made a decision after a week, then there is some situation whereby the computer takes longer than a week. For the record, I think the mathematics is sounder than the computer science which in turn is sounder than the social science. As the author admits when he mentions Kepler, we can't really prove Buridan's Principle. But I think it goes further than this in the social aspect: We don't know whether indecision at traffic lights is even accurately modeled by Buridan's Principle. Then the question becomes not whether it's true, but whether it is a good model. And these kind of models are always dangerous ground in the social sciences. Edit: The reason why I say the mathematics is sound is because he rephrases the usual notion of compactness: https://en.wikipedia.org/wiki/Compact_space https://en.wikipedia.org/wiki/Compact_space.