From here to Astragalo

Now that I’m back to the relatively autumnal setting of Brighton, I can’t help reflecting on last week’s meeting. On Monday evening I attended a cocktail party in a very pleasant bar in Castiglioncello overlooking the sea. Sunset views are something of a speciality from this location:


Anyway, the name of the place we were in was Astragalo. I checked and, as I suspected, this the Italian word for astragalus, which has an approximately tetrahedral shape. Astragalus is also a kind of plant, which is perhaps more likely to be associated with the name of a seaside bar, but that spoils the connection I wish to make with probability theory, a topic that came up regularly during the conference I was attending, so I’ll ignore it.

Nowadays gambling is generally looked down on as something shady and disreputable, not to be discussed in polite company, or even to be banned altogether. However, the formulation of the basic laws of probability was almost exclusively inspired by their potential application to games of chance. Once established, these laws found a much wide range of applications in scientific contexts, including my own field of astronomy. The astragalus provides a very early example.

Gambling in various forms has been around for millennia. Sumerian and Assyrian archaeological sites are littered with examples the astragalus (or talus bone). This is found just above the heel and its roughly tetrahedral shape (in sheep and deer at any rate) is such that when it is tossed in the air it can land in any one of four possible orientations; it’s fairly similar in fact to the four-sided dice used in some role-playing games. The astragalus can be used to generate “random” outcomes and is in many ways the forerunner of modern six-sided dice. The astragalus is known to have been used for gambling games as early as 3600 BC.


Unlike modern dice, which began to appear around 2000BC, the astragalus is not quite symmetrical, giving a different probability of it landing in each orientation. It is not thought that there was a mathematical understanding of how to calculate odds in games involving this object or its more symmetrical successors (right).

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