Recently I watched a fellow particle physicist talks about a calculation he has taken to a new level of precision. His tool? A computer program from the 1980s called FORM.
Particle physicists use some of the longest equations in all of science. To look for signs of new elementary particles in collisions at the Large Hadron Collider, for example, they draw thousands of pictures called Feynman diagrams that describe the possible outcomes of collisions, each encoding a complicated formula that can contain millions of terms. It is impossible to summarize formulas like these with pen and paper; even adding them with computers is a challenge. The algebra rules we learn in school are fast enough for homework, but for particle physics they are woefully inefficient.
Programs called computer algebra systems attempt to handle these tasks. And if you want to solve the biggest equations in the world, for 33 years one program has stood out: FORM.
Developed by Dutch particle physicist Jos Vermaseren, FORM is a key part of the particle physics infrastructure needed for the most difficult calculations. However, as with many essential elements of digital infrastructure, the maintenance of FORM largely relies on one person: Vermaseren himself. And at 73, he began to take a step back from the development of FORM. Due to the incentive structure of academia, which rewards published papers, not software tools, no successor has emerged. If the situation does not change, particle physics could be forced to slow down considerably.
FORM got its start in the mid-1980s, when the role of computers was changing rapidly. Its predecessor, a program called Schoonschip, created by Martinus Veltman, was released as a specialized chip that you plugged into the side of an Atari computer. Vermaseren wanted to create a more accessible program that could be downloaded by universities around the world. He started programming it in the computer language FORTRAN, which stands for Formula Translation. The name FORM was a riff on it. (He later switched to a programming language called C.) Vermaseren released his software in 1989. By the early 1990s, more than 200 institutions around the world had downloaded it, and the number kept growing.
Since 2000, a particle physics paper that cites FORM has been published every few days, on average. “Most of them [high-precision] the results that our group achieved over the past 20 years were heavily based on the FORM code,” said Thomas Gehrmann, professor at the University of Zurich.
Part of FORM’s popularity has come from specialized algorithms that have been built over the years, such as a trick for quickly multiplying certain elements of a Feynman diagram and a procedure for rearranging equations to have the fewest multiplications. and possible additions. But the oldest and most powerful advantage of FORM is the way it manages memory.
Just as humans have two types of memory, short-term and long-term, computers have two types: primary and external. Main memory (your computer’s RAM) is easy to access on the fly, but its size is limited. External memory devices such as hard drives and solid-state drives hold much more information but are slower. To solve a long equation, you need to store it in main memory so you can easily work with it.
In the 80s, both types of memory were limited. “FORM was designed at a time when there was almost no memory and no disk space. Basically, there was nothing,” said Ben Ruijl, former Vermaseren student and FORM developer, who is now a postdoctoral researcher at the Swiss Federal Institute of Technology Zürich. This posed a challenge: the equations were too long to be handled by main memory. To calculate one, your operating system had to treat your hard drive as if it were also main memory. The operating system, not knowing what size to expect from your equation, stored the data in a collection of “pages” on the hard drive, switching back and forth frequently as different pieces were needed – an inefficient process called swapping.
FORM bypasses the exchange and uses its own technique. When you work with an equation in FORM, the program allocates each term a fixed amount of hard disk space. This technique makes it easier for software to track the location of elements in an equation. It also makes it easy to bring those parts back to main memory when needed without accessing the rest.
Memory has increased since FORM’s debut, from 128 kilobytes of RAM in the Atari 130XE in 1985 to 128 gigabytes of RAM in my bloated desktop, a million-fold improvement. But the tricks developed by Vermaseren remain crucial. As particle physicists sift through petabytes of Large Hadron Collider data to search for evidence of new particles, their need for precision, and thus the length of their equations, grows longer.
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