If we see the imaginary number as the fault line in science, then the whole construct can be deconstructed, and becomes metaphysics again. Is Science = Metaphysics? And is there a synthesis?
Just some quick thoughts jotted down this morning.
One of the most important philosophers, arguably, of the 20th century was Jacques Derrida. I have to admit, it’s been some 16 years since I read him, so what follows is a bit sketchy, and will have some mistakes in it, but the main points are in line.
Derrida developed a technique called deconstruction. The main idea is that in a text, or system of thought, there is a central idea, call it a center around which that system is built. This central idea is held up, but only at the expense of what is called ‘the supplement”. Call it, and this will be wrong, thesis and antithesis, and just to make that point. So this center will push “the supplement” down, and “put it in the margins of the text.” Yet, the supplement is always there.
If we can now analyze the text, carefully, we can find that supplement. It is woven into the text like a trace. And if we then see that supplement from a different viewpoint, it is like pulling the trace, a thread out of a textured garment, and the whole thing will unravel. Free play is once more possible where before only suppression was the case. This process is called Deconstruction.
In a way, and philosophers may now chastise me for that(or not?), it is not unlike Hegel’s dialectic, where the two opposites contain a kernel of the respective other. In Hegel’s dialectic, a synthesis, or elevation of the two terms, into something new could be reached.
If done carefully, maybe the supplement and center can also be synthesized into something new.
Science and metaphysics: center vs supplement
So I want to try to apply this technique of deconstruction, or Hegel’s dialectic and elevation, to science and metaphysics (at its extreme, religion). As stated before, one of my highest goals is a synthesis of science with spirituality, so this is a topic dear to my heart.
Historically, science was suppressed by religion, at least Christianity. For example, when Copernicus, Kepler and Galileo declared that the bible was wrong, and the earth is not the center of all, the church, all powerful at the time, condemned them.
So religion, especially Christianity, saw science as a threat to its existence, and by upholding itself as the center, it made science the supplement, and “pushed it to the margins.”
And then science usurped.
And the roles flipped. Now science puts religion and metaphysics into the role of the supplement. Because it also sees metaphysics as a thread. Why? Because religion and metaphysics explain something to humans that science can never to: they question of why? And I don’t mean just the simple causal relationship between, say, the billiard ball being struck “like that” will result in a motion “like this.” But “the great Why?”, that of creation, of why there is something instead of nothing? That “why” is in the domain of metaphysics. And science tries to keep itself clean of all metaphysics.
But, as Hegel might argue, both contain a kernel of the other. That is human wonderment, it is at the root of both.
Now, Derrida would look for the, let’s call it, the “fault line” in a text. And since arguably everything, including our lives, has a textual quality, this can be applied to things other than a strict text. As stated above, if we can then see that fault-line differently, the whole “story changes.” It’s like a paradigm shift, instantaneously. At that point, the supplement can assert itself again, or ultimately, there is free play again and we can reach a new synthesis or elevation.
The fault line of science: the imaginary number?
Is there a fault line in science?
I have scant evidence for now. But my gut feeling is the fault line is the “imaginary number.” Or better, it is what makes the whole fault-line palatable. Because the imaginary number is simply taking the whole construct of numbers to its logical conclusion (for example, negative numbers are really not that obvious either), it’s final end, which shows the supplement until it stares us in the face.
Analytically, the imaginary number is the square root of negative one, defined as i = √-1 . And we don’t know what that can possibly be. It has no solution “in the real world.” So when mathematicians first came across it, they said for centuries that it does not make sense. But over time, some other interpretations were developed that gave us a better sense for it, like the geometric interpretation, in which the imaginary number is “simply” tied to rotation by -90 degrees. OK, but to make that work, a new space had to be invented, the “imaginary plane.”
And so on.
I don’t want to go into the details.
And I have not concluded my research on this yet. But in the back of my mind, I still have this nagging sensation that we simply explained something away that cannot be explained by “simply” introducing new layers of abstractions, new concepts, and so on. So my “final verdict,” if there will ever be one, is not fully formed yet.
My gut feeling, however, is that at the heart of it, we simply don’t know what the imaginary number is.
So, allow me to make this assumption, a thesis so to say: we really do not know. Let me assume here that the imaginary number can really never be explored, or be understood, with normal concepts. We can see its usefulness, we can use it (like negative numbers already), but ontologically, it’s meaning is unclear.
Yet, it strings itself through all science.
(As a side, all science CAN be expressed mathematically without the imaginary number, it is just not as convenient, but each such concept is then just a mapping to the concept of the imaginary number, and thus it is still there implicitly, in the margins).
In that case, the imaginary number is the fault line of science. That’s my thesis.
And we are back to metaphysics. In that case, if the imaginary number can really not be explained or understood, all science is but another metaphysics. No, it IS metaphysics.
(And it may already have turned back into all that, because modern string theory cannot be proven empirically, so string theory basically asks us to do the same as religions do: to believe. But that is another story.)
So, if the above is true, then science, taken to its extreme, becomes metaphysics. With a more “scientific flavor,” of course. Yet at the heart of it is something that cannot be explained, that is my feeling. Something that makes sense, and should be there, the imaginary number, but something we cannot know what it is.
That’s the thesis, my thesis. And I am sure, real mathematicians will shoot holes in it, but it is the role of thesis to put forward and challenge an existing belief system. So I’ll work myself through it.
But, if we can come to see all this, and that is a big if in my mind at the moment, can we create a synthesis of both sides? An elevation? What then is the common thing in both science and metaphysics? What new would emerge?
I don’t have an answer, but maybe I already gave one above. Right now, it seems to be as good an answer as any. So I’ll say it again: “wonderment.” The attempt to understand. And before all that, or rather in all that, before we attempt to have an explanation, either through science or metaphysics or religion or what, there has to be wonderment. Human wonderment.
None of this was meant to be strictly fully thought out. I just jotted it down quickly. As stated, I have my own doubts. So I will leave it open as a question, an inquiry: is science, taken to its extreme, not just metaphysics?
So I’ll leave my musings at that.
But it lays out a direction, a possible way to reconcile science and metaphysics, and through this, I believe spirituality.
Namaste — I and the Divine in me bow to You and the Divine in You.
Copyright © Hanns-Oskar Porr