Recenty, I watched Talking about his calculation, a colleague particle physicist said that it was a calculated he had advanced to an unprecedented level of precision. What was his tool? A 1980s-era computer program called FORM.
The longest equations used by particle physicists are some of the most complex in science. They use thousands upon thousands of Feynman Diagrams to show possible collision outcomes at Large Hadron Collider. Combining formulas such as these is not possible with pen and paper. Even adding them to computers can be difficult. While the school algebra rules are efficient enough to do homework, their efficiency for particle physics is woefully inadequate.
Computer algebra systems are programs that attempt to solve these problems. For 33 years, FORM has been the best program to help you solve the most difficult equations.
Jos Vermaseren is a Dutch particle physicist who developed FORM. This key component of the infrastructure of particle physics allows for complex calculations. However, as with surprisingly many essential pieces of digital infrastructure, FORM’s maintenance rests largely on one person: Vermaseren himself. He has started to withdraw from the FORM development process at age 73. Because academia rewards publications, and not software tools, there has been no replacement. The situation may not improve, and particle physics could be subject to a dramatic slowdown.
FORM began in the 1980s as computers changed rapidly. Schoonschip by Martinus Vermaseren was the predecessor of FORM. This program, which Martinus Veltman created, is a chip designed to be plugged in to an Atari. Vermaseren wanted to create a program that was more readily available and accessible by all universities. It was written in FORTRAN (for Formula Translation) and he began programming it. FORM is a riff. Vermaseren published his software in 1989. By the early ’90s, over 200 institutions around the world had downloaded it, and the number kept climbing.
Every few days since 2000, a paper in particle physics that cites FORM was published on an average basis. “Most of the [high-precision] results that our group obtained in the past 20 years were heavily based on FORM code,” said Thomas Gehrmann, a professor at the University of Zurich.
Some of FORM’s popularity came from specialized algorithms that were built up over the years, such as a trick for quickly multiplying certain pieces of a Feynman diagram, and a procedure for rearranging equations to have as few multiplications and additions as possible. But FORM’s oldest and most powerful advantage is how it handles memory.
As humans can have short-term memory and long-term memory, so computers also have main and external memories. Main memory—your computer’s RAM—is easy to access on the fly but limited in size. While external memory devices, such as solid-state drives or hard disks hold much more information they are also slower. You need main memory to be able to solve long equations.
In the ’80s, both types of memory were limited. “FORM was built in a time when there was almost no memory, and also no disk space—basically there was nothing,” said Ben Ruijl, a former student of Vermaseren’s and FORM developer who is now a postdoctoral researcher at the Swiss Federal Institute of Technology Zurich. It was a problem because the equations required too much memory. For one to be calculated, the operating system would treat the hard disk like main memory. The operating system, not knowing how big to expect your equation to be, would store the data in a collection of “pages” on the hard disk, frequently switching between them as different pieces were needed—an inefficient process called swapping.
FORM does not use swapping, and instead uses its own approach. The program allocates a specific amount of hard drive space to each term when you use FORM for an equation. The software can keep better track of the parts of the equation by using this technique. This makes it possible to quickly bring the pieces to main memory, without having to access any other data.
Memory has grown since FORM’s early days, from 128 kilobytes of RAM in the Atari 130XE in 1985 to 128 gigabytes of RAM in my souped-up desktop—a millionfold improvement. Vermaseren’s tricks are important. Particle physicists are increasingly dependent on precision as they comb through the Large Hadron Collider’s petabytes to find evidence for new particles. This increases the complexity of their equations.
