Parmenides and Time Crystals

1000 words, 5 minute read

On Nature is the oldest work of European philosophy still extant. The verse epic was composed in the 5th century BCE by Parmenides of Elea, a pre-Socratic Greek philosopher, widely regarded as ‘the father of Western philosophy’ and ‘the father of Western science’. 

Parmenides divides Being into two modes: the “Way of Truth” (Aletheia) and the “Way of Seeming” (Doxa). Most scholars hold that the realm of Aletheia is preeminently real…and Doxa? Not so much! 

But Parmenides anticipated such a misinterpretation and took pains to refute it at the outset: “But nevertheless you shall learn…how the things that seem had to have genuine existence, permeating all things completely.” In other words, there is no ‘thing’ without Doxa. Doxa is real, genuine, and universal…as is Aletheia!

Which words did you not understand, Herr Plato (4^th century BCE)? Doctor Popper (20^th century CE)? Nothing spreads quicker or endures longer than interpretive error. For example, we’ve completely misunderstood the 5^th century Book of Job as well.

 “…What-is (in the mode of Aletheia) is ungenerated and imperishable…whole, single-limbed, steadfast, and complete; nor was it once, nor will it be, since it is, now, all together, one, continuous…Thus coming-to-be is extinguished and perishing not to be heard of…it is not right for what-is to be incomplete; for it is not lacking, but if it were, it would lack everything…Therefore, it must either be completely, or not at all.”

Every actual event needs a little Aletheia in its life. It is not enough to say with Heraclitus, “Everything flows!” Whatever ‘flows’ flows relative to what is static. Nor can we define stasis solely in terms of variations in the rate of change. Change is necessarily ‘change from’ and/or ‘change to’. Aletheia is the immobile point from which every actual event must be evaluated; it is the universal measure, ergo the Truth.

On the other hand, by applying Bateson’s criterion, ‘a difference that makes a difference’, we see that participation in Aletheia alone cannot constitute an actual event. Aletheia is undifferentiated and inert: imperishable, whole, steadfast, complete, one, continuous. It cannot pass Bateson’s test.

Nor can an actual event exist exclusively in the realm of Doxa. As card waving Heraclitians, we like to say that change is the only constant; what we used to call ‘stability’ is just a measure of variations in the rate of change. 

However attractive to our modern sensibilities, this view makes no sense, empirically or logically. In the realm of Doxa, everything is perpetually coming to be and/or perishing. Therefore, nothing ever really is. There is Past and there is Future but there is no Present; without Aletheia, eternal presence, there is no now.

“To come to be and to perish, to be and not to be, and to shift place and to exchange bright color,” – Parmenides describes what it is to exist in the realm of Doxa. An actual event needs Doxa, ‘genuine existence permeating all things completely’, as much as Aletheia – ‘ungenerated and imperishable’. Like sex and marriage before the Summer of Love (1967), Aletheia and Doxa are inseparable. 

Actual events occupy a space between Aletheia and Doxa and resonate with both. Since Plato, the pre-Socratic philosophers, Parmenides included, have been ignored by the academy. However, their ideas and models, often without attribution, pop-up, most recently in Kant, Heidegger, Sartre, and Whitehead.  

In 2025 a team of physicists led by Leo Joon Il Moon discovered a configuration of matter that is reminiscent of the ideas found in On Nature. In a ‘Rondeau Time Crystal’ (RTC), aka ‘Time Rondeau Crystal’, a pattern repeats indefinitely across time. Immediately, you can see that these new entities combine permanence (Aletheia) with proliferation (Doxa). 

An RTC consists of three phases which I’ve labeled: Alpha, Delta, and Omega. I propose that we equate RTC’s Alpha phase with Parmenides’ Aletheia and Omega with Doxa. 

Drawing heavily on the work of Alfred North Whitehead, I understand Alpha to be the set of permanent, objective values that motivate, guide, and judge every actual event. Doxa, then, is the set of eventualities, possible outcomes, all potential matters-of-fact to the extent that they embody, reflect, and are not inconsistent with, Alpha values.

The relationship between Alpha and Omega is determined. The realm of Delta, on the other hand, is the home of indetermination: free will, intentionality, agency…plus chaos. Nothing that happens in Delta is caused or even influenced by anything else. Whatever happens is causa sui and sui generis. But there’s more!

The topology (shape) of Delta is a function of its position between Alpha and Omega – like a hammock strung between two trees. As a result, conditions in Delta are conducive to the emergence of ‘local’ islands of low entropy, i.e. increased order. That order takes the form of patterned relationships among elements and patterns resonate. Specifically, patterns, actual but transient in Delta, resonate with potential but eternal patterns in Omega. 

Patterns in Alpha resonate with patterns in Omega, uniting the two. Patterns that emerge indeterminately in Delta may (or may not) resonate with patterns in Alpha and Omega, but whenever patterns resonate, they fuse: one pattern, many manifestations.

The Parmenidean-Moon model channels Hugh Everett’s Many Worlds Interpretation of Quantum Mechanics. Actual events in Delta resonate with potential events in Omega and eternal values in Alpha, resulting in a World that is both concrete and atemporal. 

Again, Parmenides was out in front:  “…She (the goddess) devised Love (Erota), first of all the gods…” Erota ↔ Resonance. Our earliest model of Being reappears as the latest in a string of recent cosmological breakthroughs that began with Relativity. What a gift it is to be alive today, curious and conscious!

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Hilma af Klint — The Ten Largest (1907) presents human life as a continuous process of growth, transformation, and renewal, from childhood through old age. Using vibrant color, spirals, and organic forms on monumental canvases, the series visualizes invisible forces—spiritual, emotional, and biological—that shape becoming rather than fixed identity. The paintings suggest endless possibility by treating change not as disruption, but as the fundamental rhythm of existence itself.