How our species tamed one of the trickiest concepts in the universe without realizing it.
Back in the 1780s — or back when I read a bit about the 1780s in Grade 10 — Immanuel Kant weighed in on a debate between Newton and Leibniz. Although the physical grounds involved in the debate are refuted once and for all by Einstein, to me, this argument’s philosophical significance remains.
Newton, articulating this view in his Principia, saw that locations in space as absolute coordinates, independent of where an object might be situated in space. However, Leibniz held an opinion that positions in space were mere relations between objects.
In Newton’s terms, we can pick all objects in the universe and transform their locations (shift everything to the left by 1m, rotate everything with a point by 5 degrees, etc.), and the result is a substantial a real change. However, Leibniz holds that since such changes preserve all spacial differences between all pairs of objects, this does not change anything.
Kant assumed a position against Leibniz, by showing that mere conceptual relations cannot capture all there is to spatial relations. Consider a universe with nothing but a glove. Be it right-handed or left-handed, if there is absolutely nothing else we can invoke to provide a point reference, then all Leibniz can say, using spatial relations in terms like, “is 1cm from”, “is above”, etc., is that all the relations between the various parts of the 2 gloves are exactly identical.
This to Kant led to a logical paradox: Leibniz’s theory says that two obviously non-identical objects give rise to the same set of point-wise relations. There exists, Kant probably feels, something essential to the space we inhabit that is beyond its contents.
That is much a dive into the thoughts of subjectivity and morality as I consider necessary.
Practically, there is indeed something that we might miss out by using a dictionary of pairwise distances. Chemists call this chirality, and in some other fields we call it mirror symmetry.
Relativity had told us that space-time depends on observers and every world line experiences are equally meaningful and unique.
Fifty years after that, someone cleaned up some bird droppings and learned about the first light after the big bang — the Cosmic Background Radiation (CMB).
While it may or may not tell us the universe’s preferred choice, on the large scale, for up, down, left, right (The Axis of Evil Problem), its unique angular variations do provide us with a practically static background, upon which cosmological features, as well as our self-image, can be located.
While I attended driving school in 2016, I once laughed at the sticker in the middle of the car dashboard.
There might not be as much to deride, really.
Before the techniques to efficiently cut open our peers became widely available, for the better or otherwise, on the exterior, we saw ourselves as another left-right symmetric group of animals on a land that offers little discerning of global directions.
For us, gravity may be the only Old Faithful in our environments. It always points towards the natural “down”, where we leap away from, and fall back to; it affects us so much that weightlessness messes up with many fundamental bodily functions of the fittest individuals of our little space faring civilization.
For split-second decisions in an emergency, at least, there might just not be enough cues for all of us to be born as proficient in the differences of “left” and “right”, as “up” and “down”.
Of course, the genetic preference of handedness is another matter, but I’d argue that without a wide-spread cultural left-right idea, people’s handedness part of nature that we interact with, rather than knowledge of ourselves. House cats are more commonly left-handed and they don’t seem bothered.
Generations before mechanics and philosophy (and aforementioned industrial cutting-things-open), one day, our ancestors first verbally communicated the passage of time.
In many ancient languages that a version of the word “clockwise” arose, this direction was almost uniformly picked to follow the direction by which shadows rotate under the sun.
(In the northern hemisphere, that’s clockwise indeed. )
When artisans caught up, this naturally became the direction by which time (figuratively) passes in many of our societies. We then projected the same principle onto other stuff that spin, formulating prehistoric intuitions of vector calculus without equations, for shells, for whirlpools, etc.
The main idea I wanted to get across is just that.
A fundamental divide, and yet our solution its pretty much the result of randomness, just like our other stuff.
Were it not for the initial clump of matter that formed the milky way where we are, were it not for the solar nebula that coalesced in this particular way; were it not for the particular geological aeon among many that we arose to a world that’s more interesting on one side of the equator … — we might not be here — our clockwise might as well be the other direction.
Several of my students have asked me why we have right hand rule for electromagnetism, and similarly often, why electrons carry a negative charge.
Not-surprisingly, the sign of electronic charge is another coincidence. The ancient Greeks discovered that rubbing amber (ēlektron) causes electrostatic phenomena. It was the first, and it happen to be negatively charged.
Right-hand rule, then, to me is just a framework to consistently bridge those two serendipitous human definitions.
You’ve got to pick a side, after all, as Kant might have agreed on.
Afterthought: angular momentum
Newton’s first law is so simple that the fact it can get terrifying, is a terrifying observation in itself. I have come back to finish this essay after spending some quality time on the departmental merry-go-round during The University’s Open Day.
In the audio that’s now silenced. I half-jokingly remarked that the smoothness of all those joints have stopped me from ever asking again where the department’s budgets went to.
And yet, the truth is that when I am set into rapid motion, and dropped the only thing that might slow me down, hopelessness comes in, fast.
Were there not the slight friction of the axle, and not a carpet just centimeters below, there’s nothing, ever to stop my rotation. No torque I can easily produce, and, as is almost always the case in the cosmos, little external torque to aid us either.
That pretty much sums up the condition of our earth, our sun, our galaxy, and maybe our local galactic group — with the suitable choice of time scale… In a universe that possibly all things are relative, rotation, the conserved angular momentum, the act of spinning, is a beautiful quantity that’s quite absolute.
They say it’s a life-long journey to orient yourself. I guess for all of us as a species it might be quite similar.
Glove 3D Model:
Axis of evil (cosmology):
Bilateral (left/right) symmetry – Berkeley Evolution Library
Leibniz’s Influence on Kant (Chp. 5: Space and Time) – Stanford Encyclopedia of Philosophy
Why animals have evolved to favor one side of the brain – ScienceDaily