Eureka! – a book review

Eureka!: The Birth of Science by Andrew Gregory

I recently read Eureka!: The Birth of Science by Andrew Gregory. The book deals with a topic that has long fascinated me – the birth of science. In a previous post I argued that this took place in the 12^th century, the age of cathedrals. Gregory takes the view that it happened with the ancient Greeks, and sees Aristotle and Archimedes as among science’s pioneers. He gives a brief defence of this thesis, and provides a quick summary of Greek scientific thought.

Aristotle and Archimedes

I found this book rather short for the subject (177 pages, including bibliography), was disappointed at the lack of endnotes, and found some annoying errors (the Greeks did not consider the universe small, for example – Archimedes took it to be 2 light-years across). But the big unanswered question is: what went wrong? Gregory includes a list of key people at the back of the book, and if you turn that list into a bar chart, you can see that Greek science basically fell off a cliff around 200 BC.

In a brief two-page section towards the end, Gregory suggests that Christianity was somehow responsible for the decline of Greek science, but that simply makes no sense. Was it instead Roman conquest, beginning around 280 BC? Was it the growing separation of aristocratic philosophy from plebeian technology? Was it the replacement of original science by encyclopaedic systematisation (such as that of Pliny)? It would have been nice to have those questions answered.

Goodreads gives this book 3.4 stars; I was rather less enthusiastic.

Eureka!: The Birth of Science by Andrew Gregory: 2 stars

---

The Sand Reckoner

In his short work The Sand Reckoner, Archimedes (c. 287 BC – c. 212 BC) identifies a number larger than what he believed was the number of grains of sand which would fit into the Universe. He was hampered by the fact that the largest number-word he knew was myriad (10,000), so that he had to invent his own notation for large numbers (I will use modern scientific notation instead).

Archimedes’ began with poppyseeds, which he estimated were at least 0.5 mm in diameter (using modern terminology), and which would contain at most 10,000 grains of sand. This makes the volume of a sand-grain at least 6.5×10⁻¹⁵ cubic metres (in fact, even fine sand-grains have a volume at least 10 times that).

Archimedes estimated the diameter of the sphere containing the fixed stars (yellow in the diagram below) as about 2 light-years or 2×10¹⁶ metres (we now know that even the closest star is about 4 light-years away). This makes the volume of the sphere 4×10⁴⁸ cubic metres which means, as Archimedes shows, that less than 10⁶³ grains of sand will fit.

A more modern figure for the diameter of the observable universe is 93 billion light-years, which means that less than 10⁹⁵ grains of sand would fit. For atoms packed closely together (as in ordinary matter), less than 10¹¹⁰ atoms would fit. For neutrons packed closely together (as in a neutron star), less than 10¹²⁶ neutrons would fit. But these are still puny numbers compared to, say, 2^77,232,917 − 1, the largest known prime!

---