Mathematics and music have a pristine, otherworldly beauty that is very unlike that found in other human endeavors. Both of them seem to exhibit an internal structure, a unique concatenation of qualities that lives in a world of their own, independent of their creators. But mathematics might be so completely unique in this regard that its practitioners have seriously questioned whether mathematical facts, axioms and theorems may not simply exist on their own, simply waiting to be discovered rather than invented. Arthur Rubinstein and Andre Previn’s performance of Chopin’s second piano concerto sends unadulterated jolts of pleasure through my mind every time I listen to it, but I don’t for a moment doubt that those notes would not exist were it not for the existence of Chopin, Rubinstein and Previn. I am not sure I could say the same about Euler’s beautiful identity connecting three of the most fundamental constants in math and nature – e, pi and i. That succinct arrangement of symbols seems to simply be, waiting for Euler to chance upon it, the way a constellation of stars has waited for billions of years for an astronomer to find it.
The beauty of music and mathematics is that anyone can catch a glimpse of this timelessness of ideas, and even someone untrained in these fields can appreciate the basics. The most shattering intellectual moment of my life was when, in my last year of high school, I read in George Gamow’s “One, Two, Three, Infinity” about the fact that different infinities can actually be compared. Until then the whole concept of infinity had been a single concept to me, like the color red. The question of whether one infinity could be “larger” than another sounded as preposterous to me as whether one kind of red was better than another. But here was the story of an entire superstructure of infinities which could be compared, studied and taken apart, and whose very existence raised one of the most famous, and still unsolved, problems in math – the Continuum Hypothesis. The day I read about this fact in Gamow’s book, something changed in my mind; I got the feeling that some small combination of neuronal gears permanently shifted, altering forever a part of my perspective on the world. Read more »
On a whim I decided to visit the gently sloping hill where the universe announced itself in 1964, not with a bang but with ambient, annoying noise. It’s the static you saw when you turned on your TV, or at least used to back when analog TVs were a thing. But today there was no noise except for the occasional chirping of birds, the lone car driving off in the distance and a gentle breeze flowing through the trees. A recent trace of rain had brought verdant green colors to the grass. An antelope darted into the undergrowth in the distance.
The town of Holmdel, New Jersey is about thirty miles east of Princeton. In 1964, the venerable Bell Telephone Laboratories had an installation there, on top of this gently sloping hill called Crawford Hill. It was a horn antenna, about as big as a small house, designed to bounce off signals from a communications satellite called Echo which the lab had built a few years ago. Tending to the care and feeding of this piece of electronics and machinery were Arno Penzias – a working-class refuge from Nazism who had grown up in the Garment District of New York – and Robert Wilson; one was a big picture thinker who enjoyed grand puzzles and the other an electronics whiz who could get into the weeds of circuits, mirrors and cables. The duo had been hired to work on ultra-sensitive microwave receivers for radio astronomy.
In a now famous comedy of errors, instead of simply contributing to incremental advances in radio astronomy, Penzias and Wilson ended up observing ripples from the universe’s birth – the cosmic microwave background radiation – by accident. It was a comedy of errors because others had either theorized that such a signal would exist without having the experimental know-how or, like Penzias and Wilson, were unknowingly building equipment to detect it without knowing the theoretical background. Penzias and Wilson puzzled over the ambient noise they were observing in the antenna that seemed to come from all directions, and it was only after clearing away every possible earthly source of noise including pigeon droppings, and after a conversation with a fellow Bell Labs scientist who in turn had had a chance conversation with a Princeton theoretical physicist named Robert Dicke, that Penzias and Wilson realized that they might have hit on something bigger. Dicke himself had already theorized the existence of such whispers from the past and had started building his own antenna with his student Jim Peebles; after Penzias and Wilson contacted him, he realized he and Peebles had been scooped by a few weeks or months. In 1978 Penzias and Wilson won the Nobel Prize; Dicke was among a string of theorists and experimentalists who got left out. As it turned out, Penzias and Wilson’s Nobel Prize marked the high point of what was one of the greatest, quintessentially American research institutions in history.Read more »