Where we learn that you can be the source of vibrating invisible friction. I’m not kidding.
In the living room of the house I grew up in, there was a big ol’ grandfather clock that my mom picked up at a garage sale and, with the help of one of my brothers, restored back to working condition. When it was oh-so-quiet in the room and I’d be curled up in my chair
reading, at some point I’d become tuned into the steady beat of the clock’s pendulum. A metronomic soothing sound.
The clock had to be manually wound regularly – which was a sort of performance art in and of itself, what with the pulling of the chains of the cylindrical-shaped weights so that they’d be brought to the top of the clock’s cavity that they hung in. We usually didn’t notice that it needed to be wound until someone would be staring at it inquisitively, then peeking around the corner to look at the time on the clock in the other room, and then there’d be a sort of dance back and forth comparing clocks till they’d finally exclaim that someone needed to re-set and wind the grandfather clock.
I was told long ago that I wasn’t allowed to touch the grandfather clock never mind actually wind it since those weights were heavy and the case they were in was entirely glass. So, if I was curled up in that reading chair when there was a clock-winding proclamation, I’d just shrug and mumble something about how I was not allowed to touch it, and then I’d go back to my book. I had also come to realize that the slower the time ran on the clock, the longer the time in between its rather jarring on-the-hour chimes, which startled everyone in the house no matter what room you were in. And if you were in the same room at the top of the hour, perhaps deep into a book, 😳😩😱
I never really thought much about the mechanics of how the clock’s weights and its pendulum interacted with the hands moving on the clock face and keeping time. And then a few months ago, I was again in the presence of this very same grandfather clock, and figured I’d look up the mechanics of it.

The pendulum is attached to a gear, and each time the pendulum does a complete swing, the second hand moves. The minute and hour hands are also attached to gears that are attached to the pendulum, but they each move after the appropriate amount of complete swings of the pendulum.
When the chains are pulled to bring the weights up, the weight provides potential energy for that pendulum swing. Hence, when the weight has almost sunk to the bottom and has unwound its attached chain, that potential energy has now dissipated.

I’m quite pleased to confirm that pendulums are absolutely a math thing.
Like, D E E P L Y so.
Author James Gleick even refers to it as “the laboratory mouse of the new science.” Way back in ye olden math dude times, back to those fellows who have those names that we are all familiar with, like Galileo and Newton, it seems everyone was messing about with pendulums; Galileo and his inclination to measure the space & elapsed time of a pendulum’s swing – it’s oscillations –
and his conclusions of the constant consistency of it all was…comforting and couldn’t be contained thereby concluding that there was a regularity to their motion, hence him conceiving – though never actually physically creating – the first pendulum clock, and then Newton as well with that gosh darn cradle of his and his Laws of Motion (of which there are three).
The pendulum was actually first (notably) studied by Aristotle, all the way back in Ancient Greece times, in the period known as B.C., tho Aristotle wasn’t so much focused on the pendulum’s motion but rather the eventual state of where that pendulum would end up, at rest. A tad more philosophical when going about some of his studies and experiments, this totally related to that whole Golden Mean thing of his, right? Where the desirable middle is between two extremes – one of excess and the other of deficiency, though, c’mon, I’d think that a little flux of movement dipping this way and that must be a healthy contributor to preventing stagnation.
Smack dab in the time period overlapping the end of Galileo’s life and the beginning of Newton’s was the Dutch physicist, Christiaan Huygens, who I just refer to as The Clock Guy.
Huygens is credited (and got the patent for) creating the first working pendulum clock ~70(!) years after Galileo first conceived the possibility of it. Huygens was able to hurdle the primary issue that others hadn’t solved – which was that a pendulum clock, thus far, tended to lose on average 15mins per day. Huygen’s invention lost just 15sec per day.

via Wikimedia Commons
Of course, a key factor affecting a pendulum’s swing and the steady regularity of its oscillations is friction.
Friction can come from a variety of sources, like a physical object touching what is swinging. Or there could be what’s called a ‘damping force,’ where the interaction that is causing the pendulum’s swing to slow down or stop isn’t applied directly to the bob (that thingee at the bottom of the string of the pendulum) itself, rather it’s something that is restricting the air and space, and therefore the movement, of the pendulum. A damping force is actually changing the vibrations in the air which upsets the oscillations of that pendulum swing.
Another significant factor is inertia, that inherent resistance to friction applied to a motion. My fave visual representation of inertia is: Picture yourself riding in a car. The car slows down suddenly. Your body, on the other hand, – especially the upper part of your body – does not slow down at the same moment that the car does. That’s an inertia of motion. If I swing a pendulum and I’m too close to a wall and that bob hits that wall, the upper part of the string that’s tied to the bob will bend out and wiggle-waggle (<<< scientific term) till it can resume an equilibrium as the bob comes to rest.
When I explored equilibrium in a previous essay, I stated what I consider to be a mantra: “Equilibrium. That’s all that we want. That’s all any of us want, really.” I always snap to attention when I hear or read anything about equilibrium; I really do look at the attainment of it as the ultimate pot of gold at the end of a rainbow. When I’d rather innocently (re)researched the mechanics of a grandfather clock, I hadn’t considered that a state of equilibrium would play a part in an object that exists to keep time. Now, it’s so obvious to me.
I had actually had my own personal exploration with pendulums years ago, though the focus here was on spiritual mechanics as opposed to physical mechanics. In the divinatory arts, at its most basic, a pendulum can be used as a tool to get clarification on answers to any and every sort of questions, and just like all pendulums, it is ‘powered’ by energy. And also just like all pendulums, it’s reactive to the vibrations around it. The general belief is that the source of this energy emits from what is commonly described as the spiritual world, and in turn you could also deem that there’s a fair amount of the user’s own intuition that drives their own energy to emit forces upon the directions of how the pendulum might swing.
My oh-yaaaah moment of bridging the spiritual and mechanical pendulum worlds was in understanding the universal effect of vibrations to a pendulum’s movement. Coming upon the use of the word damping in my math-related pendulum research to explain the non-physical alteration of the vibrations in the air seems to be a linguistic cousin to what in the divinatory arts of using a pendulum as a tool is which is that it’s just another form of dowsing – like using a wishbone-shaped stick to detect water underneath the ground’s surface. Damping. Dowsing. Energy vibrations.
My search for personal equilibrium is what compelled me to learn about the spirit world side of using a pendulum in the first place. More oh-of-course-that-makes-sense connections have arisen for me, actually, as I wrote this essay; I can now clearly associate the soothing cadent sound of the grandfather clock’s pendulum as it spoke its rhythm, to the varying intensities of the energy of the swing of my pendulum as the telling yes or no answer was determined.
In Leidy Klotz’ book, “Subtract: The Untapped Science of Less,” when talking about using less (energy, resources, money) to change a system, the author references how we learn in high school about the predictive behavior of a swinging pendulum because we “know the height from which it was released.” He also notes that Kurt Lewin, a German-American psychologist in the early 20th century, known as a pioneer in social, organizational, and applied psychology ,and who, along with his colleagues (who would subsequently label their work as Gestalt, the German word for ‘perception’) “recognized …that our understanding of human behavior could use a Galilean revolution of its own.”
Klotz goes on to say:
Just as object-independent concepts of inertia and friction helped Galileo connect experimental observations with causal influences, the Gestalt scholars sought the invisible forces that might help explain human behavior …[and] just as inertia and friction made Galileo’s models more accurate, Lewin’s approach better explained human behavior. Of course, when you consider all these forces together, you leave the comfort of predictability.
“Subtract: The Untapped Science of Less” by Leidy Klotz (pg. 176-177)
This pendulum research not only connected two very present parts of my life – the math world and, I suppose, the spirit world to each other – I’m now weighing what more I can consider and think deeper on. Knowing that a pendulum has historically represented regularity and predictability – yet what is the role of inertia, and who – and how?!? – does that play into my trust of what I do when I’m using my pendulum for clarification – that is all something I’d be very open to having further discussion about.
Your mathematical and life path is more complex than the path of a pendulum or a child on a swing. .. your path is unique and highly sensitive to initial conditions.
“How to Free Your Inner Mathematician” by Susan D’Agostino (pg. 56)
Thanks math, you’re the best.