Ancient Greeks’ contribution to the foundation of sciences in undeniable. Euclidian Geometry, that accurately describes the space around us,the concept of “mathematical proof”, Aristarchus’ heliocentric theory, the foundation of medicine by Hippocrates, philosophy as expressed by Plato, Socrates and Aristotle are few examples to support this. It’s usual and familiar, whenever tracing back to the foundation of a scientific field, to find references to Ancient Greece. So it might surprise a scholar of the history of Probability Theory that its origins date back to the 16th century. And they might rightfully wonder why did Ancient Greeks not have Probability Theory?

Trying to answer, we’re forced to consider what the operative event is for any invention or discovery.We might approach this the same way a detective attempts to solve a murder

  • Means
  • Motive
  • Opportunity

Opportunity

Probability Theory starts on the 16th century with Gerolamo Cardano trying to calculate the probability of certain outcomes when rolling dice and continues with the correspondence between Blaise Pascal and Pierre de Fermat on a game of chance. So it seems that games of chance provided the opportunity for such a discovery. Mythological Prince Palamedes of Euboea supposedly invented the game of dice. In the palace of Zakros, small tablets were uncovered with figures only on one side and are thought to have been used for a game similar to poker. It seems then, that the opportunity was there for the Ancient Greeks to discover Probability Theory.

Means

Modern Probability Theory includes concepts and branches of Mathematics that were not yet discovered in Ancient Greece. But at its core, the prerequisite to start thinking on it, is nothing more than simple multiplications and divisions. The familiar dice problems used to introduce students to Probability Theory are style-compatible and could be solved with the mathematical tools in Diophantine Arithmetica. So the Ancient Greeks also had the means to discover Probability Theory.

Motive

What about motive then? How did Ancient Greeks feel and think about probability and chance? The closest concept was Carneades’ fantasies, that try to assign (but never quantify) degrees of probability to events for which we have no criterion for truth. But according to Aristotle Every event has a cause. Knowing these causes is Science. The inexistence of a criterion for truth and the uncertainty of the outcome that are core to the concept of probability seem to clash with the deterministic nature of Science as set by Aristotle. After all, the distinctive difference of Ancient Greek Civilization as contrasted to those before it was the replacement of myth with reason.

Why would the Ancient Greeks help the recently and painstakingly cast away Goddess Tyche/Fortuna sneak back into the inner sanctum of Reason, the Science of Mathematics?

In conclusion, then

They simply had no motive.

note: You’d be justified to get whiplash reading this article in a blog about details in mostly tech subjects. While it is detail-oriented and I could argue that it fits the definition, if we’re being honest… I was simply too proud of the thought to leave it out :-)