Probability “0” Is Not Impossibility

Comments

3 responses to “Probability “0” Is Not Impossibility”

1. 

   August 2, 2020

   AshGreen

   Awesome! No words. You always go one step beyond.

   There is so much great, useful information here. Thank you! Thank you! Thank you!
   Read our guide if you wish.
   Thebestpickers

   Thanks again 🙂

   Loading…

   Reply
2. 

   February 29, 2016

   Gjalt-Jorn Peters

   Excellent post, thank you for sharing! Some thoughts:

   1) actually, as Evi explained to me, dart boards consist of fibre bound together. The darts stick in between the fibres, so actually with this metaphor, there exist a finite number of potential points where the darts can end up 🙂
   2) The paragraph starting with “what we can do” isn’t entirely clear – why would we “do” that? You just countered a critical comment, but it’s not entirely clear to me where the narrative is going from here.
   3) I personally find the generalisation from this specific example, where you show how resolving this issue requires subjective consensus, to ‘all probability’, dubious. I think it’s quite possible that probability is objective, yet the example you provided happens to have some properties rendering probability /in that example/ subjective. So I’m not entirely convinced yet that all of probability is subjective 🙂

   Loading…

   Reply
   1. 

      February 29, 2016

      fbenedictus

      Thanks for your comments!

      Let me begin by (meta-)commenting on your point 2) (“why ‘do’ the dividing?”). Hopefully my answer will also address your point 3) and then we will be in a good position to address point 1) (perhaps you meant this in a tongue-in-cheek fashion, but it is a very good point).

      You’re right, I could have been clearer in the 2nd paragraph. The reason for ‘doing’ it (making the division in the first place) is that the possibility of probabilistic reasoning depends on it. Traditionally the degree of probability is defined as the number of favourable cases divided by the number of possible cases. For example, the probability of throwing an even number of eyes with a fair die is ½ Because there are six possible outcomes of which three are even numbers.

      In every other situation in which we want to reason about probabilities we must also determine how many possibilities there are and how many of those are favourable. That is why we must divide the area of the dartboard. Firstly we must determine how many points there are which can potentially be hit by a dart: this gives us the number of possible cases. The number of favourable cases of course depends on the question: if we are interested in the result of only one throw this number equals one.

      I hope that the above shows why it is justified to generalise our results to all situations in which traditional probability is applied: in all these situations we need the two conventions on which probabilistic reasoning is founded. We need to determine the number of cases (and this often involves subdividing infinite sets) and we must assume that the different cases are equally probable.

      And now for point 3), which is perhaps the most important of all. Your friend states that the dartboard consists of a finite number of smaller areas because it is made out of discrete fibres. Let us assume that one of the dartplayers is a physicist and let us ask her whether she can be sure that the fibres are separate. Where does one fibre stop and where does the area in between the fibres begin? The problem is that we can never be sure because of the finite resolution of our measurements (we can’t even be sure that discreteness exists at all; perhaps what we conceive of as material particles are actually excitations in some universal matter-field). And although these botherations may sound like nitpicking in the case of the dartboard, for a physicist working with nuclear particles it is not so obvious where the transition lies between matter and space (just think of electron-clouds; where is an electron at any given point in time?). So whereas it may be reasonable to approach the dartboard with the help of traditional probability, the scientist cannot do so.

      One last remark: you suggest that I am trying to convince you that probability is a subjective affair, but that is not the case. What I’ve been trying to show is that the application of probability theory depends on certain conventions and that these conventions are subjective because they can be differently chosen by different individuals. However, that does not mean that probability in toto is a subjective affair: given certain conventions a certain degree of probability is an objective fact.

      Loading…

      Reply