The k2p blog

The underlying compulsion

Is thrift, parsimony, a sort of minimalism, part of the fabric of the universe?

Occam’s razor (known also as the principle of parsimony) is the principle that when presented with alternative explanations for the same phenomenon, the explanation that requires the fewest assumptions should be selected. While Occam’s razor is about how to think and describe phenomena, I am suggesting that parsimony of action, the path of least resistance is deeply embedded in causality and in all of existence.

Why is there something rather than nothing? Why does the universe exist? The answer is all around us. Because it is easier to be than not to be. Because at some level, in some dimension, in some domain of action and for some determining parameter, there is a greater resistance or opposition to not being than to being. Why does an apple fall from a tree? Because there is, in the prevailing circumstances, more resistance to it not falling than in falling. At one level this seems – and is – trivial. It is self-evident. It is what our common-sense tells us. It is what our reason tells us. And it is true.

It also tells us something else. If we are to investigate the root causes of any event, any happening, we must investigate the path by which it happened and what was the resistance or cost that was minimised. I am, in fact, suggesting that causality requires that the path of sequential actions is – in some domain and in some dimension – a thrifty path.

A plant grows in my garden. It buds in the spring and by winter it is dead. It has no progeny to appear next year. Why, in this vast universe, did it appear only to vanish, without having any noticeable impact on any other creature, god, or atheist? Some might say it was chance, others that it was the silent hand of a larger purpose. But I suspect the answer is simpler but more fundamental. The plant grew because it was “easier”, by some definition for the universe, that it grow than that it not grow. If it had any other option, then that must have been, by some measure, more expensive, more difficult.

In our search for final explanations – why the stars shine, why matter clumps, why life breathes – we often overlook a red thread running through them all. Wherever we look, things tend to happen by the easiest possible route available to them. Rivers meander following easier paths and they always flow downhill, not uphill. Heat flows from warm to cold because flowing the other way needs effort and work (refrigerator). When complexity happens it must be that in some measure, in some domain, staying simple faces more resistance than becoming complex. How else would physics become chemistry and form atoms and molecules? Why else would chemistry become biochemistry with long complex molecules? Something must have been easier for biology and life to be created than to not come into being. The bottom line is that if it was easier for us not to be, then we would not be here. Even quantum particles, we are told, “explore” every possible path but interfere in such a way that the most probable path is the one of least “action”. This underlying parsimony – this preference for least resistance – might well deserve to be raised to a status older than any law of thermodynamics or relativity. It might be our first clue as to how “being” itself unfurls. But is this parsimony really a universal doctrine or just a mirage of our imperfect perception? And if so, how far does it reach?

We can only elucidate with examples. And, of course, our examples are limited to just that slice of the universe that we can imperfectly perceive with all our limitations. Water finds the lowest point (where lowest means closest to the dominant gravitational object in the vicinity). Light bends when it moves from air into glass or water, following the path that takes the least time. Time itself flows because it is easier that it does than it does not. A cat, given the choice between a patch of bare floor and a soft cushion, unfailingly selects the softer path. It may seem far-fetched, but it could be that the behaviour of the cat and the ray of light are not just related, they are constrained to be what they are. Both are obeying the same hidden directive to do what costs the least effort, to follow a path of actions presenting the least resistance; where the minimisation of effort could be time, or energy, or discomfort, or hunger, or something else.

In physics, this underlying compulsion has been proposed from time to time. The Principle of Least Action, in physics, states that a system’s trajectory between two points in spacetime is the one that minimizes a quantity called the “action”. Action, in this context, is a quantity that combines energy, momentum, distance, and time. Essentially, the universe tends towards the path of least resistance and least change. Newton hinted at it; Lagrange and Hamilton built it into the bones of mechanics. Feynman has a lecture on it. The principle suggests that nature tends to favor paths that are somehow “efficient” or require minimal effort, given the constraints of the system. A falling apple, a planet orbiting the Sun, a thrown stone: each follows the path which, when summed over time, minimizes an abstract quantity called “action”. In a sense, nature does not just roll downhill; it picks its way to roll “most economically”, even if the actual route curves and loops under competing forces. Why should such a principle apply? Perhaps the universe has no effort to waste – however it may define “effort” – and perhaps it is required to be thrifty.

The path to life can be no exception

Generally the path of least resistance fits with our sense of what is reasonable (heat flow, fluid flow, electric current, …) but one glaring example is counter-intuitive. The chain from simple atoms to molecules to complex molecules to living cells to consciousness seems to be one of increasing complexity and increasing difficulty of being. One might think that while water and light behave so obligingly, living things defy the common-sensical notion that simple is cheap and complex is expensive. Does a rainforest  – with its exuberant tangle of vines, insects, poisons, and parasites  – look like a low-cost arrangement? Isn’t life an extremely expensive way just to define and find a path to death and decay?

Living systems, after all, locally do reduce entropy, they do build up order. A cell constructs a complicated molecule, seemingly climbing uphill against the universal tendency for things to spread out and decay. But it does so at the expense of free energy in its environment. The total “cost”, when you add up the cell plus its surroundings, still moves towards a cheaper arrangement overall and is manifested as a more uniform distribution of energy, more heat deposited at its lowest temperature possible. Life is the achieving of local order paid for by a cost reckoned as global dissipation. Fine, but one might still question as to why atoms should clump into molecules and molecules into a cell. Could it ever be “cheaper” than leaving them separate and loose? Shouldn’t complex order be a more costly state than simple disorder? In a purely static sense, yes. But real molecules collide, bounce, and react. Some combinations, under certain conditions, lock together because once formed they are stable, meaning it costs “more” to break them apart than to keep them together. Add some external driver – say a source of energy, or a catalyst mineral surface, or a ray of sunlight – and what might have stayed separate instead finds an easier path to forming chains, membranes, and eventually a primitive cell. Over time, any accessible path that is easier than another will inevitably be traversed.

Chemistry drifts into biochemistry not by defying ease, but by riding the easiest local, available pathway. It is compulsion rather than choice. Action is triggered by the availability of the pathway and that is always local. Evolution then – by trial and error – makes the rough first arrangement into a working organism. Not a perfectly efficient or excellent organism in some cosmic sense, but always that which is good enough and the easiest achievable in that existential niche, at that time. One must not expect “least resistance” to provide a  perfection which is not being sought. A panda’s thumb is famously clumsy – but given the panda’s available ancestral parts, it was easier to improvise a thumb out of a wrist bone than to grow an entirely new digit. Nature cuts corners when it is cheaper than starting over.

Perhaps the reason why the spark of life and the twitch of consciousness evade explanation is that we have not yet found – if at all we are cognitively capable of finding – the effort that is being minimised and in which domain it exists. We don’t know what currency the universe uses and how this effort is measured. Perhaps this is a clue as to how we should do science or philosophy at the very edges of knowledge. Look for what the surroundings would see as parsimony, look for the path that was followed and what was minimised. Look for the questions to which the subject being investigated is the answer. To understand what life is, or time or space, or any of the great mysteries we need to look for the questions which they are the answers to.

Quantum Strangeness: The Many Paths at Once

Even where physics seems most counter-intuitive, the pattern peeks through. In quantum mechanics, Richard Feynman’s path integral picture shows a particle “trying out” every possible trajectory. In the end, the most likely path is not a single shortest route but the one where constructive interference reinforces paths close to the classical least-action line. It also seems to me – and I am no quantum physicist – that a particle may similarly tunnel through a barrier, apparently ignoring the classical impossibility. Yet this too follows from the same probability wave. The path of “least resistance” here is not some forbidden motion but an amplitude that does not drop entirely to zero. What is classically impossible becomes possible at a cost which is a low but finite probability. Quantum theory does not invalidate or deny the principle. It generalizes it to allow for multiple pathways, weighting each by its cost in whatever language of probability amplitudes that the universe deals with.

It is tempting to try and stretch the principle to explain everything, including why there is something rather than nothing. Some cosmologists claim the universe arose from “quantum nothingness”, with positive energy in matter perfectly balanced by negative energy in gravity. On paper, the sum is zero and therefore, so it is claimed, no law was broken by conjuring a universe from an empty hat. But this is cheating. The arithmetic works only within an existing framework. After all quantum fields, spacetime, and conservation laws are all “something”. To define negative gravitational energy, you need a gravitational field and a geometry on which to write your equations. Subtracting something from itself leaves a defined absence, not true nothingness.

In considering true nothingness – the ultimate, absolute void (uav) – we must begin by asserting that removing something from itself cannot create this void. Subtracting a thing from itself creates an absence of that thing alone. Subtracting everything from itself may work but our finite minds can never encompass everything. In any case the least resistance principle means that from a void the mathematical trick of creating something here and a negative something there and claiming that zero has not been violated is false (as some have suggested with positive energy and negative gravity energy). That is very close to chicanery. To create something from nothing demands a path of least resistance be available compared to continuing as nothing. To conjure something from nothing needs not only a path to the something, but also a path to the not-something. Thrift must apply to the summation of these paths otherwise the net initial zero would prevail and continue.

The absolute void, the utter absence of anything, no space, no time, no law, is incomprehensible. From here we cannot observe any path, let alone one of lower resistance, to existence. Perhaps the principle of least resistance reaches even into the absolute zero of the non-being of everything. But that is beyond human cognition to grasp.

Bottom up not top down

Does nature always find the easiest, global path? Perhaps no, if excellence is being sought. But yes, if good enough is good enough. And thrift demands that nature go no further than good enough. Perfect fits come about by elimination of the bad fits not by a search for excellence. Local constraints can trap a system in a “good enough” state. Diamonds are a textbook example. They are not the lowest-energy form of carbon at the Earth’s surface, graphite is. Graphite has a higher entropy than diamond. But turning diamond into graphite needs an improbable, expensive chain of atomic rearrangements. So diamonds persist for eons because staying diamond is the path of least immediate, local resistance. But diamonds will have found a pathway to graphite before the death of the universe. The universe – and humans – act locally. What is global follows as a consequence of the aggregation, the integral, of the local good enough paths.

Similarly, evolution does not look for, and does not find, the perfect creature but only the one that survives well enough. A bird might have a crooked beak or inefficient wings, but if the cost of evolving a perfect version is too high or requires impossible mutations, the imperfect design holds. A local stability and a local expense to disturb that stability removes a more distant economy from sight.

Thus, the principle is best to be stated humbly. Nature slides to the lowest, stable, accessible valley in the landscape it can actually access, not necessarily the deepest valley available.

A Zeroth Law or just a cognitive mirage

What I have tried to articulate here is an intuition. I intuit that nature, when presented with alternatives is required to be thrifty, to not waste what it cannot spare. This applies for whatever the universe takes to be the appropriate currency – whether energy, time, entropy, or information. In every domain where humans have been able to peek behind the curtain, the same shadow of a bias shimmers. The possible happens, the costliest is avoided, and the impossible stays impossible because the resistance is infinite. In fact the shadow even looks back at us if we pretend to observe from outside and try and lift the curtain of why the universe is. It must apply to every creation story. Because it was cheaper to create the universe than to continue with nothingness.

It may not qualify as a law. It is not a single equation but a principle of principles. It does not guarantee simplicity or beauty or excellence. Nature is perfectly happy with messy compromises provided they are good enough and the process the cheapest available. It cannot take us meaningfully to where human cognition cannot go, but within the realm of what we perceive as being, it might well be the ground from which more specific laws sprout. Newtons Laws of motion, Einstein’s relativity, Maxwell’s equations and even the Schrödinger equation, I postulate, are all expressions of the universe being parsimonious.

We can, at least, try to define it: Any natural process in our universe proceeds along an accessible path that, given its constraints, offers the least resistance compared to other possible paths that are accessible.

Is it a law governing existence? Maybe. Just as the little plant in my garden sprouted because the circumstances made it the easiest, quietest, cheapest path for the peculiar combination of seeds, soil, sunlight, and moisture that came together by chance. And in that small answer, perhaps, lies a hint for all the rest. That chance was without apparent cause. But, that particular chance occurred because it was easier for the universe – not for me or the plant – that it did so than that it did not. But it it is one of those things human cognition can never know.