Billions and Billions

The first chapter opens with the story of the phrase that stuck to Sagan's name. Sagan writes that he never said «billions and billions» in «Cosmos». Johnny Carson put the words in his mouth by parodying him on his show. Even now, people on the street or on a plane ask Sagan to say it. Sagan smiles and compares it to Sherlock Holmes never saying «elementary, my dear Watson» and Humphrey Bogart never saying «play it again, Sam».

Then Sagan turns to big numbers themselves. A million is a thousand thousands, a billion a thousand millions, a trillion a thousand billions, and Sagan recalls the British and American habits of writing them. A postage stamp marked «50 milliarden» from the German inflation of 1923 comes from Sagan's own collection. Exponent notation is shown by example: to multiply ten to the third by ten to the ninth, it is enough to add the exponents. A table in a box says that counting one number a second, you need more than a week to reach a million and half a lifetime to reach a billion.

The second chapter is the legend of the invention of chess. The vizier of a Persian king asks, as a reward for the new game, for one grain of wheat on the first square, two on the second and four on the third. By the 64th square the number reaches about 18.5 quintillion grains, weighing 75 billion tons, equal to 150 years of the world's present grain harvest. Sagan says he does not know how the story ended and that it may only be a fairy tale. On a board of 100 squares the wheat would weigh as much as the Earth.

Next, Sagan shows exponential growth in everyday life. Ten dollars invested 200 years ago at 5% a year would be worth $172,925.81 today. Inflation eats pensions by the same law. A bacterium that doubles every 15 minutes would reach the weight of the Sun in two days, but food runs out and the curve flattens. Sagan applies this to the AIDS epidemic and to world population: then six billion, doubling in about 40 years. The way out, Sagan argues, is to reduce poverty, spread contraception and give women real political power.

The chapter goes on with Leo Szilard, who in September 1933, waiting at a traffic light in London, hit on the idea of a nuclear chain reaction. Sagan presents it as the frightening face of exponential growth and writes that Szilard spent the rest of his life warning about the dangers of this weapon. Radioactive half-life is explained by the same logic: by this method the Turin Shroud was found to date from the 14th century and the Earth to be 4.6 billion years old. At the end, Sagan says that knowing something quantitatively, not only qualitatively, deepens understanding.

The part of chapter three that was read turns abruptly to another subject: why are people so drawn to watching others run and hit each other? Sagan cites the Cherokee phrase calling competitive sport «the little brother of war», the 1969 «Football War» between El Salvador and Honduras and fan violence. This part shows that the book is more a social essay collection than a science book.

• Clear language that explains complex numbers with everyday examples (interest, inflation, bacteria)
• A style that softens dry mathematics with legends, anecdotes and personal memories (the stamp collection, the Carson episode)
• Boxes and tables: names of big numbers, time needed to count, the full solution of the wheat problem
• An epigraph at the head of each chapter (Archimedes, Fourier, William James)
• A broad view that ties scientific thinking to social questions (population, poverty, nuclear weapons)