Amir R. Alexander

Pre-Birth of The Calculus... does metaphysics matter? The outer brackets of this book might be from Luther's pinned-up Theses to the Glorious Revolution in the UK in 1688. The medieval world was stable, even stagnant. The modern world is fertile and chaotic. Alexander understands that metaphysics - the foundations of mathematics - is not the sole determiner of social transformation. But the philosophy of mathematics is right there in the fray. It has a seat at the table. Just like today, show more Turing's Halting Theorem went from a curiosity of mathematical logic to the seed of our ongoing transformation into some kind of cybernetic society. What kind, it's not easy to predict with any confidence!

I especially liked the descriptions of some of Wallis's reasoning here. I'm a math-physics-engineering geek, so this stuff is deep in my bones. But to be able to peek over Newton's shoulder to see where his ideas came from - just a delight!

There's not too much math here. Alexander works hard to help the reader stay on track. This is really a history book, with just enough math to be able to follow the action. It'd be fun to do a parallel math book, to explore much more fully why experimental mathematics is not so reliable, and e.g. how did Cauchy convergence develop out of Wallis's experiments with infinite series.

But now, in the midst of this coronovirus pandemic, that puts a spear point on the climate change cudgel - people are looking for certainties, when scientists can only offer possibilities and probabilities. We are edging closer to yet another religion versus science war, and the stakes could hardly be higher. This book is a nice refresher course on how ideas matter. show less

The Great American Grid was not designed to be practical. Instead, the straight lines and right angles were to represent something much more important: freedom. The grid’s instigator was Thomas Jefferson, who regarded the western United States as a tabula rasa for the revolution’s ideas of liberty. He proposed dividing the land into boxes oriented to the points of the compass, to be sold for a standard price. The son of a land surveyor, Jefferson applied to the western territories the show more ideas of his intellectual hero: Isaac Newton. As a young man, Jefferson had wanted to be a mathematician and he was greatly influenced by Newton’s idea that space exists independently of whether it is occupied by a physical object. Newton held that the area between the vertical and horizontal lines in a grid was empty space, a vacuum of potential. Jefferson believed that this empty space left room for humans to be free.

In Liberty’s Grid Amir Alexander explains how Jefferson used Newton’s ideas to install this now-archetypal feature of the US landscape. However, as the book’s subtitle suggests, Jefferson’s ‘mathematical dreamland’ was always more idealistic than practical. The settlement of the West, and its division into a grid, was predicated on the assumption that the territory was vacant. In fact, much of it was not. Native American ancestral lands west of the Appalachians had been protected by British law, but with the Crown expelled, these rights were annulled. Jefferson brought his proposal before Congress in 1796. Despite opposition from George Washington, who maintained that Jefferson’s lattice design would be impractical, the bill passed. Over the ensuing century and a half, 1.4 billion acres of land were imprinted with the grid.

Several factors made the project intrinsically flawed. Most ironically for Jefferson the mathematician, as well as for Jefferson the philosopher, the equality of the plots was superficial. As Alexander explains: ‘One settler might acquire a plot of rich and level farmland, with a stream flowing near the edge, providing a reliable source of water and a suitable site for a mill. A less-fortunate neighbor might end up in possession of a plot of exactly the same shape and size but made up of bone-dry rocky hills. And all for the same price.’ Furthermore, the plots were set along the lines of the compass. Because of the curvature of the earth, lines of longitude converge as they head north. The further north the plot, the smaller it was.

Read the rest of the review at HistoryToday.com.

Daniel Rey is a writer based in New York. show less

I truly enjoyed this book and definitely recommend it.

Admittedly I had expected more on the evolution and rationale of the method of infinitesimals. Instead I encountered a vivid story about the power struggles, the religious fervors, and the contests of ideas and ideals during 16th and 17th century Europe that were intertwined with this “dangerous” mathematical tool. I felt Amir Alexander pulled together these diverse currents into a cohesive, rich tale. The method of infinitesimals show more held a latent and un-tapped power. And those who dared say they played with it to solve as yet unsolved problems invited tragedy and triumph upon themselves.

Why would the Society of Jesus and the Roman Catholic Church regard a mathematical theory as heresy? Moreover, why were the Jesuits driven to orchestrate smear campaigns to discredit the brightest and most creative scientific minds in Italy in the first half of the 17th century? Why did they feel like they had to ruin their lives? The Jesuits did this so completely that Italy’s brilliant candles of scientific innovation were effectively blotted out? Why would the nobles and royalist-sympathizers of post-medieval Europe fear an infinitely small quantity, believing it could unleash chaos and more civil war in England in the second half of the 17th century? Why indeed.

Amir builds the backstory of these fears and weaves them into the many skirmishes and outright public battles the method of infinitesimals had endured. Italy lost. England won. Had it not, the modern world might still be in the Dark Ages. show less

I can think of a number of counterexamples to the author's claim that natural scientists can't be Byronic heroes. Victor Frankenstein, anyone? (I never said they had to be real people.) He's right about engineers, though.