Recently, I’ve been watching a fellow particle physicist talks about a calculation he’s pushed to new heights of precision. His tools? A computer program from the 1980s called FORM.
Particle physicists use some of the longest equations in all of the sciences. For example, to look for signs of new elementary particles in collisions at the Large Hadron Collider, they drew thousands of pictures called Feynman diagrams that depict possible collision outcomes, each The picture encodes a complex formula that can be millions of terms long. Compiling formulas like this with pen and paper is impossible; even adding them by computer is a challenge. The algebra rules we learn in school are fast enough to do our homework, but for particle physics they are unfortunately less efficient.
Programs known as computer algebra systems attempt to handle these tasks. And if you want to solve the biggest equations in the world, over the past 33 years one program has stood out: FORM.
Developed by Dutch particle physicist Jos Vermaseren, FORM is an important part of the infrastructure of particle physics, necessary for the most difficult calculations. However, as with many essential parts of digital infrastructure, the maintenance of FORM largely depends on one person: Vermaseren himself. And at the age of 73, he started to stop developing the FORM. Due to the incentive structure of academia, which awards published papers, not software tools, no successors emerged. If the situation doesn’t change, particle physics could be forced to slow down dramatically.
FORM began 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 make the program more accessible for universities around the world to download. He started programming it in the FORTRAN computer language, which stands for Formula Translation. The SAMPLE name is a riff on that. (He later switched to a programming language called C.) Vermaseren released his software in 1989. By the early 90s, more than 200 organizations around the world had downloaded the software. and this number continues to grow.
Since 2000, an average of one particle physics paper citing FORM has been published every few days. “Almost [high-precision] the results obtained by our team over the last 20 years are mainly based on the SAMPLE code,” says Thomas Gehrmanna professor at the University of Zurich.
Some of the FORM’s popularity comes from specialized algorithms that have been built up over the years, such as the trick to quickly multiplying certain parts of a Feynman chart and the procedure for rearranging the equations to get as few as possible. Multiplication and addition are better. But the oldest and most powerful advantage of FORM is the way it handles memory.
Just as humans have two types of short-term and long-term memory, computers also have two types: primary and external. Main memory—the computer’s RAM—is easy to access quickly, but is limited in size. External memory devices such as hard disks and solid-state drives hold more information but are slower. To solve a long equation, you need to save it in main memory so that you can easily work with it.
In the 80s, both types of memory were limited. “FORM was built at a time when there was virtually no memory and no disk space—essentially nothing,” says Ben Ruijl, an alumnus of Vermaseren and developer of FORM, now a postdoctoral researcher at the Swiss Federal Institute of Technology Zurich. This poses a challenge: The equations are too long for main memory to handle. To compute one, your operating system needs to treat the hard disk as if it were main memory as well. The operating system, no matter how large your equation is, will store data in a set of “pages” on the hard disk, frequently switching between them as different parts are needed—an inefficient process. The result is called a swap.
The SAMPLE ignores the swap and uses its own technique. When you work with an equation in FORMAT, the program assigns each term a fixed amount of space on the hard disk. This technique allows the software to easily track the positions of the parts of the equation. It also makes it easy to put those parts back into main memory when needed, without accessing the rest.
Memory has grown since the early days of FORM, from 128 kilobytes of RAM in the 1985 Atari 130XE to 128 gigabytes of RAM in my improved desktop—a million-fold improvement. But the tricks that Vermaseren developed are still important. As particle physicists rummage through petabytes of data from the Large Hadron Collider in search of evidence of new particles, their need for precision and thus the length of their equations grows longer. than.
