1. Probability and Chance, Fritz Mauthner's Studies of Improbability

To begin with, I must take a very simple concept to show you at hand of a very special example from Mauthner's work how hard the search for truth is. You all know that there has long been what is called in mathematics the calculus of probability. It's quite easy to grasp the principle involved. Let's assume, for example, that you have some dice. I don't want to lead you astray into gambling with them, but let us say you have some dice. You know that they are so arranged that there is a single dot on one side, two on another, and so on, up to six dots on one of the six sides. If you roll these dice, they can turn up any one of the six sides; there are six possibilities. Now we can ask what the chances are of turning up a \(6\). You might really want to know what the chances are of getting a \(6\) when you shake the dice cup and throw the dice. The mathematician makes his calculation and says there are six possibilities; there is thus one-sixth of a chance of turning up a \(6\) on a single throw. You see how unlikely this possibility is. You would have to run through all six possibilities to be certain of a particular outcome. The numerator and the denominator would have to be identical, since certainty would equal \(1\) (\(\frac{6}{6} = 1\)). Probability is therefore six times smaller than certainty in throwing dice.