This essay is about a writer who goes by the name Science of Illumination. He argues (or hints) that because mathematics is used to describe just about everything in quantum mechanics, then what it describes must be “mental” or “spiritual”. Yet a field equation, for example, certainly isn’t “divine breath”. This is yet another example of the many spiritual idealists and anti-materialists who quote the big names and ideas of quantum physics exclusively to advance their spiritual idealism. If you read Science of Illumination’s essays, for example, never once does he quote a physicist or a scientific idea outside the context of “spirituality” and religion. Never once.

Science of Illumination wrote the following in response to an essay I wrote called ‘There Are No Materialists’:
“According to modern science, all matter ultimately reduces to a set of mathematical equations which defy all materialistic interpretation. In the words of Nobel laureate Werner Heisenberg, ‘the electron is not a thing’. Renowned physicist Sir James Jeans explains that ‘All the pictures which science now draws of nature are mathematical pictures [ ].’ Thus any ontology that could reasonably called ‘materialist’ or ‘physicalist’ would appear to an idealist to be based on an error of misplaced concreteness.”
All this was written by a someone who holds a strong self-described “spiritual” position against both materialism and physicalism. In Science of Illumination’s Medium biography, he describes himself as a
“[p]hysicist (Ph.D.), Roman Catholic Eucharistic Minister, initiate of the Inayati, Jerrahi, and Rafai Sufi Orders, disciple of Mata Amritanandamayi”.
Science of Illumination says that as far as idealists are concerned, the distinction between materialism and physicalism doesn’t matter… He’s absolutely right! After all, neither physicalism nor materialism are idealism. Yet I fail to see how a basically Pythagorean position (see later) helps him.
When Science of Illumination hints that it’s all equations, how does that help prove the existence of God, or help show Sufi “Oneness”? Contemporary neo-Pythagoreanism in physics is, after all, perfectly compatible with a “soulless” or purely structural physicalism.
Like Science of Illumination, many anti-materialists and conscious-first spiritualists stress the non-physicality of fields, etc. Yet a materialist can go back to Michael Faraday and accept that physicality doesn’t always mean that something can be touched in the everyday sense, or that particles are tiny “hard balls”. Yet a field is still a physical state of space.
Science of Illumination, again like many idealists and anti-materialists, is very keen to quote well-known physicists to advance his own spiritual position. He quotes Werner Heisenberg, Sir James Jeans above, and, elsewhere, Max Planck, Albert Einstein, Arthur Eddington, Bohm, etc… So Erwin Schrödinger may well have loved the Upanishads, yet he explicitly warned against “silly” attempts to find God in the wave function.
I can even help Science of Illumination by going back to Isaac Newton. He was literally an alchemist and occultist. However, Newton’s Principia contains precisely zero alchemy. And Newton didn’t call gravity “The Science of Divine Attraction” or anything like that.
To move to Faraday again. He was a devout Christian Sandemanian who never claimed that magnetic induction was “oneness” in action.
Science of Illumination expresses his spiritual, idealist and, basically, political case against physicalism and materialism in the following way:
“This superficial focus on fragmentation, while overlooking the underlying oneness, has produced great technological advances, but as a worldview it is ignorance, avidiya, toxic to the individual and to humanity.”
The “oneness” obviously refers to Science of Illumination’s reading of eastern religious texts (as with avidiya). The political angle is shown by his reference to “ignorance”, as well as by his view that materialism is toxic to the individual and to humanity. However, I’m not going to spend any time on the rhetoric and politics here: I’ll stick to the science and philosophy.
Neo-Pythagoreanism
Stating the vital-importance of mathematics doesn’t work for those with “spiritual”, religious and/or idealist leanings. (Historically, the original Pythagoreans were religious in many ways.) What is it about “all is number” that’s spiritual or idealist? Sure, the all-is-maths idea can be cited as a cudgel against physicalism and materialism. Yet it still doesn’t advance consciousness-first philosophy or any “spiritual” stuff.
Even if we move against the old Pythagorean position in which “things are numbers” and move to modern structural Pythagoreanism, this position still offers nothing to the philosophical spiritualist.
To the neo-Pythagorean, the universe is “made of” mathematical relationships, something stressed by Ontic Structural Realists. Those relationships can indeed be described as a “particle” or a “probability wave”. (That said, Ontic Structural Realists argue that “every thing must go”.) Yet you can’t squeeze the juice of spirituality or idealism out of any of this.
Science of Illumination rams his point home even more in the following:
“The quote from Heisenberg is a reference to certain fundamental aspects of quantum physics, which I assumed materialists and physicalists would be quite familiar with, since they both claim their understanding of the nature of matter is based on science, and quantum physics is the science of the nature of matter.”
This was a reply to my own response to Science of Illumination.
The irony in the words “I assumed materialists and physicalists would be quite familiar with” is clear. Does he really believe that any professional physicalist philosophers aren’t familiar with all this? Even many laypersons are familiar with it!
Against Neo-Pythagoreanism
In physics, it’s indeed the case that everything “said” about particles, forces, fields, spacetime, etc. is said with mathematics…
What else could be used to describe these micro-entities and extremely intangible phenomena? Apart from metaphors such as “fields”, “particles”, etc., there’s simply nothing else that can be used. Yet that doesn’t mean that there’s no territory to map or that we must become Pythagoreans.
There’s nothing fundamentally wrong with words like “fields”, “particles”, etc. Or, more accurately, they do fail in some respects, yet work very well in other respects. No one believes that a scientific field has grass or flowers growing within it. Yet the word “field” still works. No one believes that a particle is a ultra-small ball or even a “hard thing”. Yet the word “particle” has proven to be very useful.
Even the “unreasonable effectiveness of mathematics” doesn’t mean — or have the consequence — that the world itself is mathematical. More strongly, the effectiveness of mathematics in physics doesn’t have the (logical) consequence that the world itself must be mathematical… That’s unless being mathematical simply means that the world is describable by mathematics. It may even mean that most aspects of the world described by physicists can only be described by mathematics.
To neo-Pythagoreans, the world and its parts are actually mathematical — not instantiations of universal consciousness, and not the contents of mind. This means that it isn’t that maths is simply helpful for describing the world — the world itself is mathematical. Again, this has nothing to do with consciousness or anything spiritual. Here’s John Barrow on the Pythagorean position:
“[The Pythagoreans] maintained ‘that things themselves are numbers’ and these numbers were the most basic constituents of reality.”
The physicist and cosmologist Max Tegmark puts the contemporary case for neo-Pythagorean being in the following very concrete example:
“[If] [t]his electricity-field strength here in physical space corresponds to this number in the mathematical structure for example, then our external physical reality meets the definition of being a mathematical structure — indeed, that same mathematical structure.”
To spell out the above.
Tegmark isn’t saying that maths is perfect for describing the “electricity-field strength” in a particular “physical space”. He’s saying that the electricity-field strength is a mathematical structure. In other words, the maths we use to describe the electricity field is one and the same thing as the electricity field. Thus, if that’s the case, the “miracle of mathematics” is hardly a surprise! That’s because this miracle is essentially a situation in which maths is describing maths. (If maths is describing maths, then the word “describing” is surely not an apt word to use in the first place.)
Tegmark gives us more detail on his position when he tells us that
“there’s a bunch of numbers at each point in spacetime is quite deep, and I think it’s telling us something not merely about our description of reality, but about reality itself”.
So perhaps there’s a difference between saying that “things themselves are numbers” (as the ancient Pythagoreans did), and saying that the world is mathematical. (I may be drowning in a sea of grammar here.) The latter may simply state that the world exhibits features which are best expressed (or described) by mathematics. The former, on the other hand, says that the world literally is mathematics.
Again, none of this can be used to advance spiritual idealism.
Note:
(1) The following paragraph is taken from the essay above:
“In physics, it’s indeed the case that everything ‘said’ about particles, forces, fields, spacetime, etc. is said with mathematics… What else could be used to describe these micro-entities and extremely intangible phenomena? Apart from metaphors such as “fields”, “particles”, etc., there’s simply nothing else that can be used. Yet that doesn’t mean that there’s no territory to map or that we must become Pythagoreans.”
This idea will be extended in a future essay.
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