They’re an unlikely pair of sleuths—a robust statistician from Denmark and a soft-spoken historian from Alberta, Canada. But together, they are tracking some of Galileo’s most important discoveries, by following his ink.

About four years ago, Steen Andersson, professor of mathematics at Indiana University Bloomington, got a visit from Wallace Hooper, a computer programmer and historian of science at IUB. Hooper had what Andersson calls “an extremely interesting problem” concerning Galileo Galilei, the 17th-century Italian natural philosopher and mathematician who made many fundamental contributions to physics and astronomy.

Hooper’s problem had to do with organizing Galileo’s scientific papers. A prolific, ambitious thinker, Galileo covered scores of pages, or folios, with proofs, diagrams, drawings, and calculations. Historians are fortunate, notes Hooper, that so much of Galileo’s scientific writing (as well as his letters and financial records) survived. Unfortunately, Galileo didn’t date his scientific works, leaving historians to centuries of mystery, confusion, and at times, rancorous confrontation as they have tried to determine the correct order of his writings.

Scholars have grouped Galileo’s scientific papers by several methods, including sorting them by the pages’ watermarks and matching them to references in his letters, which do bear dates. Hooper decided to look closely at Galileo’s ink.

In Galileo’s time, ink was a perishable commodity, lasting only two to three months. No matter how good an ink vendor was, Hooper says, he couldn’t recreate precisely the same ink twice. So Hooper figured if he could determine which of Galileo’s manuscript pages carried ink of the same composition, he could argue that those pages were written during the same brief time period.

Using data collected from Galileo's original ink by proton-induced x-ray emissions technology, statistican Steen Andersson is helping to date some of Galileo's most important scientific writings. photo Courtesy Wallace Hooper |

Hooper traveled to
Italy to collaborate with physicists in Florence. They used proton-induced x-ray
emissions (PIXE) technology
to collect measurements from tiny spots of ink on original pages in *Ms. Gal.
72*, *Galileo’s Notes on Motion*.

“We found out that the inks are mainly composed of iron, but with the iron also comes copper, zinc, and lead,” Hooper says. “Iron is the common denominator in all cases, so the raw data were in terms of ratios—the amount of lead to iron, copper to iron, zinc to iron.

“The question was, how do we take this data and make some sort of case out of it?” he continues. “If we were going to make substantive comparisons from one document to another, we had to develop some kind of mathematical technique.”

Hooper called on Andersson, who had recently finished four years as director of IUB’s statistical consulting office in the Department of Mathematics. His questions raised just the kind of mathematical problem Andersson delights in.

“I have a high interest in applied statistics, which is intellectually very challenging,” says Andersson, who is an expert in the area of multivariate statistics. “You have a bunch of data, and you know there is information there, but how should you extract the information about the certain thing you want to know, and what are your assumptions when you extract it?”After several meetings with Hooper, Andersson developed a statistical model based on Dirichlet distributions to compare the inks. Starting with the assumption that the inks were the same, Andersson and Hooper wanted to know whether differences in two sets of ink samples were large enough to call the inks different or too small to support a distinction between them.

Statistically speaking, Andersson explains, the model enabled them to say that “two inks are identical because there is nothing in the data that says they could not be the same. Maybe there is a difference, but you cannot see it in the data.”

The model also showed the opposite, when two inks were different. Hooper cites an example of two pages whose ink data looked very similar when analyzed with simple regression analysis. “It took Steen’s method to demonstrate that they are separate,” he says.

By correlating the ink data from the undated papers with dated letters, Andersson notes, “We can actually say, for example, that in October 1603 Galileo goes to a new ink, he uses the same ink until January of the next year, then he changes ink, then he travels and gets new ink from the place he has gone to. We can follow the ink all his life.”

Based on ink similarities,
Hooper hypothesizes that three discrete pages in *Ms. Gal. 72*—folios
179, 152 recto, and 91 verso—actually belong together. Hooper says that
in close sequence, these three pages show how Galileo worked out problems in
an incorrect definition of accelerated motion he first proposed in 1604.

“The inks demonstrate a very strong relationship between 91 verso and 152 recto,” Hooper says. “Without the ink evidence, it’s harder to make the case, but with Steen’s analysis, it’s kind of undeniable.”

The same analysis also makes clear that 179 is written in a different ink. “You have to accept that, too,” Hooper says. Still, Andersson and Hooper believe it may be possible to make the case for the sequence of all three folios by matching their inks with dated correspondence and financial records. Further studies in Florence are planned.

According to Hooper,
determining such sequences in the page order of *Ms. Gal. 72* allows scholars
to better follow the intellectual path Galileo took to discover his revolutionary
theories of motion and mechanics. “If we get a description of what it’s
like for these brilliant guys to figure these things out,” he says, “we
can understand more about how scientific theories work.”

Something of Galileo’s intellectual pursuits echoes in Andersson’s own passion for mathematics. “Thinking about mathematics, you are quite alone, but that world is kind of perfect,” he says. “Whenever you discover a new result in mathematics, several new questions come up that you want to answer, and you know the answers are out there somewhere, waiting for your own discovery.”