Science makes progress in the same way as a bunch of kids collectively building a Dr Seuss castle in Minecraft. Pieces are added, removed, moved, swapped, new towers sprout in unexpected directions. But knowledge emerges from the squabble, and some contributions become foundations from which whole edifices rise.

For example: a pair of black holes in orbit around one another will eventually merge. To paraphrase Hemingway’s description of bankruptcy, this happens gradually, then all at once. The details of the gradual phase were worked out in 1964 by Philip Peters, then a Caltech PhD student.

Peters’ paper initially sat quietly in the literature. Its citation count – in our Minecraft analogy, the number of blocks other kids stacked on top of it – was almost dormant for 20 years. In 2025, however, it is clocking up mentions every couple of days, as shown below.

The paper started to get attention at the tail end of the 1980s. This was due to the results of long-term observations of a pair of orbiting neutron stars – objects almost as compact as black holes – which showed that they were, indeed, slowly approaching each other. The change is tiny, and exactly matches Peters’ calculations.

The paper truly takes off in 2015, half a century after it was written, thanks to the detection of the “all at once” part of the picture: gravitational waves generated directly by black holes merging with one another.

Peters’ paper is a quiet masterpiece. There would have been no shame in limiting a first analysis to black holes orbiting each other in perfectly circular fashion. But the paper tackles generic, elliptical orbits right out of the gate. This makes for some extra-spiky math, because to understand real-world systems, you need to solve the full problem. Reading the paper, I knew I was encountering the work of a “physicist’s physicist”.

Naturally, I was curious to know who Peters was and what else he had done. A quick search reveals he was hired as an assistant professor at the University of Washington straight out of his PhD, and continued to work on relativity. But the 1964 result published as a grad student and a related effort with his advisor are his only major hits. His other papers quietly fill gaps in our collective understanding, squaring up crooked stones in the structure of physics, rather than establishing major new foundations.

That said, a search on Philip Peters name turns up a panegyric from the American Journal of Physics, a publication aimed at university educators. It specialises in the sort of detailed exposition Peters was good at, and he was apparently one of their most dedicated referees. To quote:

… at the University of Washington, Phil is a mainstay in the physics major program serving as advisor to the Student Physics Society and as chair of numerous committees on undergraduate affairs. […] Phil has given long, frequent, and valued service as a referee for the American Journal of Physics. He has been cited as conscientious, thorough, fair, and knowledable, laboring hard and anonymously for the benefit of us all.

Sounds like a lovely guy. Sadly, the next reference to him in Am. J. Phys. mourns his “untimely death” in the spring of 1994.

When I initially went looking for Peters, I accidentally turned up an entirely different person, with a near double palindrome in name and institution: Peter Phillips (not Philip Peters) based at Washington University (not the University of Washington).

Phillips’ career is also remarkable, but for entirely different reasons. Like Philip Peters, Peter Phillips was by all accounts an excellent teacher. Likewise, he worked in theoretical physics and gained his PhD on the West Coast in the early 1960s, but at Stanford rather than Caltech. But an encounter with parapsychologist JB Rhine convinced him to veer away from theoretical physics and devote his energies to studying the paranormal.

Phillips was quickly up and running, with James McDonnell of the aerospace company McDonnell-Douglas donating half a million dollars (a great deal of 1970s money) to set up a lab. Phillips made a splash with claims that two young men were able to bend spoons with their minds, Uri Geller style. Unfortunately for him, the men in question had been trained by magician and skeptic James Randi and infiltrated into the lab to demonstrate the over-credulous nature of exponents of parapsychology.

To his credit, Phillips fronted up and retracted his claims, but years later parapsychologists are still angry about what they see as Randi’s deception. Even the CIA (spooks having long had a sideline in ESP research) was upset.

In his later years, Phillips became a 9/11 “truther”, which he apparently never recanted.

The upshot of this near-namesake situation is that I spent a couple of weeks feeling confused, and a little sad, until I went back and read more closely. For all that a mathematical result does not depend on the person who found it, I was relieved to see I had conflated two very different individuals.

But it still strikes me as ironic that Peters, whose work has stood the test of time, has a smaller online profile than Phillips.

That said, it is good to know that Peters would have felt the satisfaction of seeing 1993 Nobel Prize awarded to the discoverers of the binary neutron star system, knowing that he had laid a foundation stone for that whole tower of science. They say a person is not truly dead until their name is no longer spoken, in which case the paper we cite as “Peters (1964)” has earned a thoughtful man a place among the immortals.

CODA: The black hole mergers are driven by the emission of gravitational waves, and these are a key prediction of Einstein’s theory of general relativity. Physicists debated for close to forty years as to whether these were a mathematical illusion. That argument was settled in the 1950s by Feynman. Peters’ contribution is a technical one – he quantified the rate at which two orbiting bodies will approach one another – but is vital when analysing specific astrophysical systems.

Header image from Mojang Dr Seuss Minecraft package.