|Normal statistical distribution.|
The text makes reference to a uniform statistical distribution.
Probability is a well-known mathematical concept that was initially defined to quantify random data in mathematically known environments and has been extended to other situations.
For instance, the probability that the next car passing near me has a license plate with four identical figures is computed by dividing the number of favorable cases between the number of possible cases. The first number is ten: 0000, 1111, 2222, ... , 9999. The second is ten thousand: 0000, 0001, 0002, ... , 9998, 9999, in a uniform distribution. Therefore the indicated probability can be computed as one thousandth. Here we haven’t considered that vehicles can be removed from circulation, an independent random process that would not change significantly the result of the computation.
The problem is, sometimes we are interested in computing data in mathematically unknown environments. This can happen, for instance, when we ignore the number of favorable cases, or the number of possible cases, or both. In such situations, we can estimate the unknown data with more or less uncertainty. We speak then of a priori probability.
|Allen Telescope Array in the SETI project|
Let us consider, for example, the probability of existence of extra-terrestrial intelligence. In this case we don’t know the number of favorable cases, as we have never detected any.
The a priori probability depends, in fact, on the context. For instance, we can try to find the probability that there is intelligent life around a solar system different from ours in the galaxy of the Milky Way. The number of possible cases would then be the number of stars in the Milky Way. The number of favorable cases can be estimated in different ways, giving completely different probabilities, which range from a situation where we are currently alone in the galaxy (a zero probability, for we don’t count as an extra-terrestrial intelligence) to the possible existence of one thousand million intelligences similar to us (which gives a probability approximately equal to one hundredth).
But if we consider the probability that there is intelligent life around a solar system different from ours anywhere in the universe, the number of possible cases becomes the number of stars in the universe. In this case this number is also unknown and could even be infinite, when we would have two different situations:
- Either the number of favorable cases is finite, in which case the a priori probability would be zero.
- Or the number of favorable cases would also be infinite, and then we would have to apply other mathematical tools to estimate the probability, for we cannot divide two infinities.
|Message sent in 1974 from the Arecibo Observatory|
The same post in Spanish