Different types of chance

Jacques Monod

When we don’t know why something happens, we usually say that it is due to chance. But this statement is ambiguous, because there are two different types of chance:

• Epistemological chance, where the cause of what’s happening is well-known, but so complex that it remains outside the scope of our knowledge. Almost all games of chance (dice, roulette, lottery jackpot) are examples of this type of chance. Rolling dice conforms to the laws of mechanics, but the conditions are so complex that we cannot predict the result of each roll. This type of chance is what Jacques Monod called operational uncertainty in his book Chance and Necessity (1970):

This term is used... in relation to the game of dice, or roulette, and the calculation of probabilities is used to predict the result of a play. But these purely mechanical and macroscopic games are not "the result of chance" except because of the practical impossibility of controlling the throwing of the dice or the ball with sufficient precision. It is evident that a very high precision launching mechanism is conceivable, and would make it possible to largely eliminate the uncertainty of the result... The same thing happens, as will be easily seen, in... many phenomena where the notion of chance and the calculation of probabilities are applied for purely methodological reasons. (My translation into English).

Sin, Redemption and Extraterrestrial Intelligence

Ray Bradbury

Ray Bradbury wrote a story titled The Man that can be summarized thus:

In its expansion through the galaxy, the human species encounters many extraterrestrial intelligences. The captain of an interstellar Earth ship arrives on a distant planet and hears about something recently happened there. Little by little he discovers that God has become man on that planet and has granted them Redemption, although not in a bloody way. The captain wants to meet him, get in touch with him, but it’s too late: he has left (at least, he thinks so). Then the captain decides to dedicate his life to traveling to other planets in the hope of finding Christ on one of them.

Narciso Ibáñez Serrador adapted this story for the radio, and in doing so he changed a few things: the title, which became The Triangle, and the form of Redemption: they kill the Redeemer by nailing him to a triangle, rather than a cross.

Extraterrestrial intelligence and original sin

C.S. Lewis

These speculations may seem irrelevant, since we do not know if extraterrestrial intelligence exists. In fact, the probability of its existence is 50%, as I explained in a previous post, by which I mean that we know nothing, that we might as well flip a coin to decide. However, some serious theologians and science fiction authors have raised this question, so it may not be absurd to discuss it here.

Jean Jacques Rousseau asserted that man is good by nature, but society makes him evil. All the evidence we have refutes him. In every attempt made to correct this situation by modifying social structures, for example, in the French Revolution (which introduced the guillotine); in the Russian Revolution (which introduced the Gulag); and in German National Socialism (which introduced gas chambers); things have gotten worse. It is clear that we are prone to evil by nature, although we may also be capable of great heroism. That inclination to evil is a consequence of what we call original sin.

Are cities and companies biological structures?

Geoffrey West

The book Scale: The universal laws of life and death in organisms, cities and companies, by Geoffrey West, from the Santa Fe Institute, which I discussed in the previous post, asserts that cities and companies are subject to laws very similar to those that apply to living beings. They are general laws, applicable to all entities of these types, regardless of their origin. West explains it this way:

Remarkably, analyses of such data show that, as a function of population size, city infrastructure—such as the length of roads, electrical cables, water pipes, and the number of gas stations—scales in the same way whether in the United States, China, Japan, Europe, or Latin America. As in biology, these quantities scale sublinearly with size, indicating a systematic economy of scale but with an exponent of about 0.85 rather than 0.75...[F]ewer roads and electrical cables are needed per capita the bigger the city. Like organisms, cities are indeed approximately scaled versions of one another, despite their different histories, geographies, and cultures, at least as far as their physical infrastructure is concerned.

Strange curves and biological structures

Von Koch's Snowflake Curve

In general, geometric objects are usually classified according to the number of their dimensions, like this:

• Points have zero dimensions.
• Lines (straight lines or curves) have one dimension.
• Surfaces have two dimensions.
• Volumes have three dimensions.

Furthermore, mathematicians often work with objects that have more than three dimensions, which are very difficult for us to imagine.

At the beginning of the 20th century, the Swedish mathematician Helge von Koch discovered a strange curve (the von Koch snowflake), which has the following properties: