Penrose, Plato, and the Trinity.
While New Atheist views (espoused by Dawkins, Daniel Dennett, Sam Harris, et al.) tend to focus on the field of evolutionary biology, the sphere of physicists and mathematicians seems to have a much more nuanced view of the relationship between science and metaphysics. In particular, mathematics stands distinct from science per se in that it does not make specific verifiable claims of empirical fact (much of mathematics does not directly relate to the physical world at all); rather, it provides a formal structure, a framework, by which we can communicate and generalize abstract notions. In some sense, these decontextualized abstract notions themselves can be said to have an existence independent of physical manifestation and our ability to perceive them. These three ideas - abstract (Platonic/mathematical) ideal, imperfect manifestation in physical reality, and the human mind’s perception of pattern in the physical world and transference of physical phenomena into abstract ideals - lie at the foundation not only of mathematics, but true religion as well.
In the first chapter of his excellent The Road to Reality, Sir Roger Penrose introduces a diagram illustrating this threefold relationship:
Plato made it clear that the mathematical propositions — the things that could be regarded as unassailably true — referred not to actual physical objects (like the approximate squares, triangles, circles, spheres, and cubes that might be constructed from markers in the sand, or from wood or stone) but to certain idealized entities. He envisaged that these ideal entities inhabited a different world, distinct from the physical world. Today, we might refer to this world as the Platonic world of mathematical forms….
This was an extraordinary idea for its time, and it has turned out to be a very powerful one…. It tells us to be careful to distinguish the precise mathematical entities from the approximations that we see around us in the world of physical things. Moreover, it provides us with the blueprint according to which modern science has proceeded ever since. Scientists will put forward models of the world — or, rather, of certain aspects of the world — and these models may be tested against previous observation and against the results of carefully designed experiment….
If the model itself is to be assigned any kind of “existence”, then this existence is located within the Platonic world of mathematical forms. Of course, one might take a contrary viewpoint: namely that the model is itself to have existence only within our various minds, rather than to take Plato’s world to be in any sense absolute and “real”. Yet, there is something important to be gained in regarding mathematical structures as having a reality of their own. For our individual minds are notoriously imprecise, unreliable, and inconsistent in their judgments….
Thus, mathematical existence is different not only from physical existence but also from an existence that is assigned by our mental perceptions. Yet there is a deep and mysterious connection with each of those other two forms of existence: the physical and the mental. [In the figure above] I have schematically indicated all of these three forms of existence — the physical, the mental, and the Platonic mathematical — as entities belonging to three separate “worlds”, drawn schematically as spheres. The mysterious connections between the worlds are also indicated, where in drawing the diagram I have imposed upon the reader some of my beliefs, or prejudices, concerning these mysteries.
It may be noted, with regard to the first of these mysteries — relating the Platonic mathematical world to the physical world — that I am allowing that only a small part of the world of mathematics need have relevance to the workings of the physical world…. Likewise, in relation to the second mystery, whereby mentality comes about in association with certain physical structures (most specifically, healthy, wakeful human brains), I am not insisting that the majority of physical structures need induce mentality…. Finally, for the third mystery, I regard it as self-evident that only a small fraction of our mental activity need be concerned with absolute mathematical truth! … These three facts are represented in the smallness of the base of the connection of each world with the next, the world being taken in a clockwise sense in the diagram. However, it is in the encompassing of each entire world within the scope of its connection with the world preceding it that I am revealing my prejudices….
On this view, everything in the physical universe is indeed governed in completely precise detail by mathematical principles….
In William Blake’s Newton, we see this very same threefold mystery: Here, the man emerges from the earth and produces a representation of the geometry (γεωμετρία; geo = earth, metria = measure) of which the earth is made.
Newton (1795) by William Blake
Likewise, we can easily see the Platonic significance of the Christian trinity as well.
Handcolored woodcut, ca. 1500, origin unknown
Here, the Holy Trinity of Christianity is presented as a triangle: Father (Pater, which might stand for “earth”), Son (Filius, “man”), and Holy Spirit (Spiritus Sanctus, “platonic ideal”) in an triangular relationship, three equal and essential parts of God. The connections between them (”non est”) assert the independence of the parts, while their connections to the center (”est”) assert their importance in the integral whole. We might say also that the human conception of mathematical truth is not the truth itself; that manifestation in the physical world is not the Platonic form; and that the physical world consists of much more than human minds. But the relationship remains the same: timeless, illustrated through myriad imperfect forms, this knowledge has been transmitted from ancient (pre-scientific) times to us today, and we continue to find new manifestations of the Trinity. There’s a lot more to be said here; this touches upon the significance of mythology, sacred geometry, and mysticism: these have always been vehicles by which humans could codify and transmit eternal truths. We may use science to perceive the details, but we use religious/mythological and mathematical abstraction to incorporate, generalize, and interpret this knowledge.
In this way, true religious/spiritual knowledge does not properly occupy the space of empirical scientific knowledge, but rather serves as a counterpart to abstract mathematical knowledge, existing the the Platonic (meta) realm, rather than making specific claims of empirical truth in the physical realm.
May 27th, 2009 at 8:29 am
Thank you for this interesting insight into the relationship between the separate and yet united fragments of nature.
In Eastern Orthodoxy, I have heard of the trinity as expressed by the terms, Father (consciousness), Logos (son / physical force), and Spirit (the energy that unites every particle, physical and metaphysical).
God is ultimately is the combined force of all three of these universal energies. Thus the word “God’ has be historically interchanged with the word “Nature”, so long as it is understood that the Nature of the universe also encompasses the trinity of forces.