Galileo’s Pulse
Some episodes in the history of telling time
Thinking in many frequencies
My family and friends have been asking me why I have been thinking so much about time in the last few years.
This may seem odd, but it has to do with how our models of public dialog are broken. Everywhere I turn, I experience a culture that thrives on a toxic combination of oversimplification and doubling down on it.
From sports talk to polarized social media to 24-hour news, we are being trained to take positions that reduce complexity to simplicity and, when challenged, more stridently entrench ourselves in our certainties, especially during election seasons, which seems to be all the time.
Anything less than this is deemed weakness.
This is unhealthy, and there is nothing inherently natural about it.
It is also very difficult to escape. We are nodes in deeply nested feedback loops too numerable to list. While we may not control the content and the channels, we certainly control our desires, our experiences, and our thoughts because each of us occupies multiple nodes in the feedback loops that make us who we are.
One way to resist this has been to train my mind to operate on different frequencies. My thoughts may appear odd and out of joint, which is my intention. This essay will be no exception.
Time, for me, has proven to be an excellent subject for finding a different frequency. I make no claims that it must be everyone’s.
As an example of accessing another frequency, I want to make another descent — this time into Galileo’s pulse to trace its motions.
Pendulums, Pulses, Time
This story is probably apocryphal, but fact or fiction doesn’t matter here. Galileo is said to have discovered the uniformity of pendular motion by watching the swinging of a lamp in a cathedral. He hypothesized that even though each swing of the lamp was getting shorter in distance, each swing took the same amount of time [1].
To prove this, he needed a clock, but he is in a cathedral where, unlike the rigors of a monastery, there is no need for measuring time precisely and accurately.
He used his pulse.
As we descend into this story, we will find nothing but entangled motions. ‘Telling time’ emerges as Galileo compares two motions: the swinging lamp and the beating pulse. He uses his pulse (which is itself a complex mashup of neurophysiological motions) to count the number of beats it takes for a single oscillation to occur.
A few things to notice.
First, time is not an autonomous thing. Galileo is not directly observing time in the natural world. His act of observation creates time by measuring one motion against another.
Second, time is a complex dance of motions that, in this case, Galileo improvises on the spot. (The pulse and the swinging lamp are not the only motions in play, as we’ll see.)
Third, this complex dance lasts only so long as these motions collaborate in some reproducible and predictable fashion — i.e., they form collaborative patterns of mutual interactions. These patterns can be temporary. If someone were to stop the swinging lamp, the system would cease having time for all intents and purposes. (Of course, other times would continue on: Galileo’s pulse would continue to beat and his body will continue to age.)
With these three points, we have described the very basics of how time emerges from motion.
That brings us to ‘telling time.’
There is no inherent and natural connection between pulse rates and oscillating lamps. This has to be created, and Galileo’s attention is another set of motions that selects a motion to be measured and the other to be the measuring device.
There is no end to this descent. All we will find is motions dancing together with more or less regularity. If we were to stare into Galileo’s attention, we would only find millions of neurological and physiological motions working together to hold his eyes in position and for his brain to count pulse beats [2].
Let’s keep going with Galileo’s pulse because everything gets more complex, but also more clear, the deeper we descend into his heart beat.
The Pulsilogium
While Galileo uses his pulse to measure the oscillations of the pendulum, his real goal is to make the pendulum into the ultimate measure of time — i.e., he intends to flip the relationship on its head.
In other words, he temporarily uses his pulse as the improvised clock in order to verify that a pendulum can become an accurate clock. By 1637, he had come up with plans for a pendulum clock, though he never built one.
We see the flipping of the relationship throughout Galileo’s life. He will use a pulsilogium to measure pulse rates of medical patients. Often considered among the first precise medical devices, it used a pendulum with an adjustable string length to time between diastolic and systolic motions.
In the pulsilogium, what is the measuring rod and what is the thing measured has been reversed [3].
Time as Abstraction
In the 1650’s, Christiaan Huygens will turn Galileo’s findings into a working pendulum clock.
Model for a pendulum clock by Christiaan Huygens
This is an important moment in my journey through thinking about time.
Here is what I see:
When Galileo uses his pulse to measure the time of the swinging lamp, we see that time is not a self-contained thing, nor is it entirely abstracted from the situation itself. It is visceral and local. There is no object in this scene that can be said to be ‘True Time’ (I’m using Newton’s phrase here).
Time emerges from a coordination and regularity of motions working together. In this instance, it is an improvised human construct.
To be sure, it is on its way to becoming the purely abstract and universal time that Newton would envision — and that forms our common understanding today.
As soon as Huygens starts building clocks that are completely self-contained, time starts to look and feel like a real thing separate from all of the other things in the cosmos.
Telling time changes significantly: comparing motions is no longer necessary because the clock contains all the motions required for us to witness the movement of time on the clock’s face. This face hides the highly coordinated motions of its inner workings in the same way that the digital numbers on an oven provide a drastically simplified understanding of otherwise remarkably complicated motions of incalculable atoms, which we know simply as heat.
Time starts to take on its modern life as primarily a clock’s face. It starts to appear as pure abstraction independent of motion. While clock makers are at work, Newton will canonize this purely abstract True Time in his Principia.
In fact, Newton explicitly creates, in the preface to the first edition (1686), the branching that sends science and mechanics in different directions:
But since we are concerned with natural philosophy rather than manual arts, and are writing about natural rather than manual powers, we concentrate on aspects of gravity, levity, elastic forces, resistance of fluids, and forces of this sort, whether attractive or impulsive. (Cohen and Whitman trans., page 382)
From here on out, science will hide its relationship to the dirty business of ‘manual powers’ by pursuing the purely abstract. Motion will become untethered from time as both become pure abstractions measurable by natural laws (motion) and clocks (time).
It will take Einstein to reconnect time and motion a little more than 200 years later [4].
Time Travels
Let’s follow briefly the history of pendulum clocks into the history of navigation, which entangles us in a very dark place indeed. We all know what cargo was being carried in many of those ships [5].
These histories were never separate. Accurate timekeeping at sea was, for some, the crucial solution to ‘The Longitude Problem’ [6]. Without accurate timekeeping, you could never know with certainty how far east or west your ship had traveled. This was a very real, dangerous, and expensive problem for the naval and commercial powers of the colonial age.
Huygens thought his pendulum clocks were already good enough, but that proved false, especially when the seas were anything other than smooth [7].
Galileo’s pulse was caught up in the Longitude Problem as well.
He thought he could solve the longitude problem with a helmet fitted with a telescope for accurately observing and measuring the amount of time each of Jupiter’s moons disappeared behind the giant planet. In his lifelong attempts to prove Copernicus right, he had shown the movements of Jupiter’s moons to be both uniform and frequent enough (1000 or more times per year) for measurements at sea.
His pulse got in the way of his solution: “Galileo himself conceded that, even on land, the pounding of one’s heart could cause the whole of Jupiter to jump out of the telescope’s field of view.” Here the pulse appears from within the complex dance to be the disrupter of time [8].
John Harrison, the 18th century clock maker who eventually was acknowledged to have solved the Longitude Problem, will spend most of his life (1693-1776) creating accurate clocks completely impervious to the motions of the seas. It is a tale of highly coordinated motions, temperature corrections, material selection, various lubricants and many other engineering accomplishments designed to allow time to travel undisturbed by what is happening outside the clock.
Peter Galison has called this ‘the search for movable time’ [9].
We have now arrived at a crucial point in the history of time:
The clock must travel through nature without nature disturbing its highly coordinated motions. Time, therefore, need no longer be only local and visceral. The clock, closed in on itself, must move through a hostile environment that is hell-bent on disturbing its uniform motions [10].
BTW: You can still see Harrison’s clocks running at the Royal Observatory in Greenwich. The video below is H-2. It’s all just coordinated motions hidden behind the clock face.
John Harrison's H-2 at the Royal Observatory
Religion and Science
Let’s return to Galileo’s pulse and further broaden our perception of the scene in the Pisa cathedral. We’re going to find science and religion entangled within each other’s compositions of time and their orchestrated motions.
Galileo’s pulse and the swinging lamp are probably surrounded by the Catholic mass, which has its own liturgical tempos and rhythms, including the swinging of the lamp, quite possibly spreading incense [11].
Galileo carves out his experience of time (using his pulse to measure the swinging lamp) within the liturgical motions surrounding him. As Carlo Rovelli writes in his recounting of this story, ‘The scientist was observing the oscillations during a religious service in which he was evidently not particularly absorbed…’ [12].
Let’s imagine that there is a mass going on at this moment. We’ll see how two different regimes of time can operate in and around each other without harmonizing.
Perhaps the priest presiding over the liturgy notices Galileo’s attention elsewhere. For him, Galileo’s lack of attention is only so because of the composition of motions over which the priest presides. From that perspective, Galileo’s soul is at stake, as well as the priest’s own power to command the attention of his flock. But Galileo is not distracted. He is onto something else more important for him.
Both are necessarily blind to each other’s experience of time and how they are living within the complex dance of motions surrounding them. Both might say that they are attending to Truths that are more True than the other’s Truths.
By 1633, the church will have its revenge — assigning Galileo to house arrest for the remainder of his life — only to be corrected in 1992.
Relativism?
Where does science begin and religion end? What is fixed and what is in motion? What is time if its history can only be understood as myriad entanglements in navigation, clocks, liturgies, and swinging lamps measured by human heart beats?
At the end of this exercise, I have to ask myself: Have I just created a grand vision of moral relativism? Yes and yes.
To the first yes: if you believe that one of these perspectives that I have traced by staring into in Galileo’s pulse should be nailed down as the True Perspective, then I will appear to be a relativist. On what basis would I or anyone else make the selection? What blindness do I willing accept in order to call one of these perspectives True and the others False?
In this case, ‘relativism’ is an absolutist’s accusation.
To the second yes: I proudly call this relativism insofar as relativity itself seems to go ‘all the way down’ and thus escapes the relativist/absolutist impasse.
I know that I am blurring a distinction between relativism and relativity. But if relativity, especially as it becomes quantum, is telling us that it’s motion all the way down — motions that are not necessarily governed by timeless laws — where is the ground on which absolute morality can rest?
A morality built on different frequencies of time and experience should acknowledge that perception is highly malleable — expandable when it needs to be and concentrated when it needs to be. We should always be aware that any one of these perspectives will require what William James called, ‘A Certain Blindness in Human Beings.’
Footnotes
I’m using Carlo Rovelli’s characterization of what Galileo ‘discovers’ as he tells it in Reality Is Not What It Seems, Riverhead Books, 2017, page 180. There are other accounts that describe a different discovery. See, for instance, Lee Smollen’s account in Time Reborn, Penguin, 2014, page 15; and Dava Sobel’s account in Longitude, 2007 edition by Bloomsbury, pages 36-7. Rovelli’s, however, seems a bit more realistic in terms of what could have been understood in this episode.
Dean Buonomano’s Your Brain Is a Time Machine (Norton 2017) is an excellent source for understanding the relation between neurophysiological processes and the brain’s ability to tell time. In his interview with Sean Carroll, he captures this understanding of telling time in a single sentence that I find helpful: “Rather, any dynamical system, any system that changes in some reproducible fashion can be used to tell time in principle. And the brain, of course, is the most complex dynamical system we know of.” From Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas: Dean Buonomano on Time, Reality, and the Brain, Mar 29, 2021
As Dava Sobel tells us, ‘Galileo, who, as a young medical student, successfully applied a pendulum to the problem of taking pulses, late in life hatched plans for the first pendulum clock.’ (Longitude, Bloomsbury 2007, page 36.) Longitude was originally published in 1995. Dean Buonomano discusses the pulsilogium in Your Brain Is a Time Machine, pages 135-6.
In Einstein’s special relativity article from 1905, he theorized the difficulty of coordinating time across space using linked clocks as examples. We may think of this as the scientific work of an isolated genius, but his work in the Swiss Patent Office was directly related to the practical problem of coordinating clocks in a network of accurate time keeping for an economy highly dependent on coordinating various transportation modes into a reliable system.
This darkness is conspicuously absent in Sobel’s telling of the tale of the Longitude Problem. It is equally absent from the Royal Observatory’s exhibit on this history — at least it was when I visited in September of 2023.
Dava Sobel’s 1995 Longitude remains the most popular version of this story. This video from Cambridge University, featuring Simon Schaffer (Leviathan and the Air-Pump, 1985), is a good introduction to the topic: ‘The Longitude Problem.’
Longitude, page 37-9.
Longitude, page 26. See pages 24-8 for Sobel’s narrative on how Galileo participated in The Longitude Problem. Sobel doesn’t cite a source for this, but Galileo does refer to the difficulties of holding still while trying to make accurate observations in Sidereus Nuncius (The Starry Messenger, 1610). The experience of biathletes or archers shooting between heart beats corroborates the problem of the pulse Sobel points to here.
On the problems of accurately assessing longitude at sea, Galison writes, ‘… getting a precision clock to guard proper time in the unsteady motion of a ship’s cabin or on a mule’s back was never easy. Add the vagaries of temperature, moisture, and mechanical failings, and the provision of a stable, precise chronometer became one of the most difficult machine problems ever attacked. For John Harrison, the extraordinary eighteenth-century clockmaker, efforts to build an accurate seagoing clock consumed the whole of his life.’ Einstein’s Clocks and Poincaré’s Maps, Norton 2003, page 102.
There is another history to unpack here — that of the history of ‘nature’ becoming something to be overcome and dominated by human culture and technologies. In Contrat Naturel, Michel Serres will make precisely this point with respect to Galileo: ‘Galileo is the first to put a fence around the terrain of nature, take it into his head to say, “this belongs to science,” and find people simple enough to believe that this is of no consequence for man-made laws and civil societies, closed in on human relations as they are.’ We now have science emerging from the creation of ‘nature’ as a category separate from and prior to ‘society.’ (The Natural Contract, Elizabeth MacArthur and William Paulson, trans., University of Michigan Press, 1995, pages 81-86.)
The typical Catholic liturgy used portable censers swung from chains, thus making them pendulums. It was not out of the ordinary for a censer to be hung from the ceiling.
Carlo Rovelli, Reality Is Not What It Seems, page 180. Lee Smollen starts his account of this story with boredom: ‘Bored during a service in the Pisa cathedral, Galileo noticed the time it took a hanging lamp to sway from side to side was independent of how wide its swing was.’ (Time Reborn, page 15.)