Good Vibrations?

Over a year ago, I wrote an article “Wrong but Interesting?” wherein I noted that an idea can be wrong but still valuable for generating new ideas. In that article, I noted an example of an idea that I found wrong, and also not interesting: That “everything is vibrations.”

I love the Beach Boys song “Good Vibrations” for its beautiful metaphors and how the music itself represents these good vibrations. But it is a metaphor and not a literal reality. I might say that I am “on the same wavelength” as my wife, or that I am “in tune” with a friend I am talking to. These are analogies that date back to the early days of radio.

Early radios were finicky, and you were very aware of tweaking the knobs to get your radio exactly in tune with the transmitter.

It might help to understand why it seems that vibrations are everywhere.

More than 2,500 years ago, Pythagoras discovered that the musical pitch of a plucked string is inverse to its length. He imagined the movement of the Sun, Moon, and planets played a “Music of the Spheres” beyond our awareness.

At the other end of the scale, string theory proposes that all matter is ultimately formed out of tiny strings vibrating in different ways.

In my physics and math studies, one of the earliest systems we learned is the “harmonic oscillator.” A common example is a pendulum. Another common example is a weight hanging from a spring.

It is within any system that if you push the thing away from its resting position, something tries to push it back toward its resting position. In everyday life, we don’t see many actual pendulums or weights hanging from springs. But one of the wonders of mathematics that I love is the idea of approximation. It turns out that almost everything in the world “to first order approximation” is a harmonic oscillator!

Doesn’t this mean that the “New Age” people are correct that everything is about vibrations? And being in or out of tune, synchrony or harmony? Not really. If “everything” is a harmonic oscillator, then this actually makes it less interesting as an explanation.

Back to the radio analogy. If radio was all about just getting in tune with the transmitter, then you would hear nothing at all. It is the breakdown of the perfect tuning that carries all of the interesting information. This is called “modulation.” You are familiar with Amplitude Modulation (AM) and Frequency Modulation (FM).

But digital devices use what is called Pulse-code Modulation (PCM). If you look inside a computer, do you think you will see lots of things vibrating? Again, in a trivial sense the answer is yes. Because almost everything looks like a harmonic oscillator to the
first approximation.

More than 200 years ago, the mathematician Fourier showed that any arbitrary waveform or signal could be represented as a sum of different pure sine wave vibrations. You simply have to adjust the amplitude, frequency, and phase of each vibration and add them up – and, voilà, you have your chosen signal. We call this collection of summed sine waves a “Fourier Series.”

But is this a useful way to understand what is going on inside a computer? No. Computer scientists think in terms of on/off bits. And in terms of gates that take a set of inputs and create a logical output based on those inputs. 

Yes, in principle, you could do a Fourier analysis of the signals in a computer and be hypnotized by the ever-changing vibrations. But when you awaken from your trance, you will realize you have learned nothing useful about what is happening.

Likewise for our brains. In the 1800s, scientists discovered brain waves. It is a fact that there are characteristic frequencies of these brain waves, and each is associated with a certain activity. From slow Delta waves in deep, dreamless sleep on up through Theta, Alpha, Beta, and Gamma. The latter at frequencies up to 100 Hz, associated with higher mental and motor functions.

But this clearly covers only very coarse behavior of our 86 billion brain neurons. Imagine what your TV picture would look like if everything was just simple vibrations! Nothing but mesmerizing moiré patterns. Your TV picture is created by complex interactions of actors, cameras, and coordinated illumination of pixels.

Yes, it is trivially true that “everything is vibrating.” But the wonders of the world are far more rich, interesting and complex!