Leibniz’s Insight? Looking forward and back

Leibniz disassociated ‘substance’ from ‘material’ and reasoned that the world was not fundamentally built from material.  His is not simple or familiar reasoning but it was clear to Leibniz that for a substance to be real, it had to be indivisible and since matter was infinitely divisible, the true nature of reality could not be material.  This bit of philosophical history startled the students in one of my calculus classes who were fully embedded in the materialist perspective of the sciences, and whose only experience with the name Leibniz came from his role in the development of calculus.  But even today, there is disagreement about whether the universe is made from matter or from concepts. As Frank Wilczek says in The Lightness of Being,

Philosophical realists claim that matter is primary, brains (minds) are made from matter, and concepts emerge from brains.  Idealists claim that concepts are primary, minds are conceptual machines and conceptual machines create matter.

Wilczek was making the point that Wheelers “its from bits” idea (that the universe is composed of information) provides a way for both to be true. There’s not much value in wondering what the word ‘machine’ actually means in this context.  But the idealist’s claim is consistent with Leibniz’s and, often, computational ideas are traced back to Leibniz.  What’s important, in my opinion, is that the debate persists. In a post earlier this year, I reported on the view being explored by physicist Max Tegmark who proposes that perhaps reality is so well described by mathematics because our physical world is a mathematical structure.  He once said this:

So I think we’re all living in a gigantic mathematical object – not one of the simple ones that we learn about in high school math. We’re not living inside of a cube or a dodecahedron or in the set of integers, but there’s some more complicated mathematical object, maybe M-theory, maybe some – more likely something we haven’t discovered yet which somehow is our reality.

In April, I collected some references to quantum information theory and Vlatko Vedral, whose idea that information (defined to a large extent by probability) builds the fabric of the universe is discussed in his book Decoding Reality. And just recently, I was introduced to Gregory Chaitin’s most recent work where mathematics and biology are nicely woven as he explores the idea that life is evolving software (his most recent book is: Proving Darwin: Making Biology Mathematical) As I see it, we are finding mathematics in the way we perceive, and in everything around us.  Cognitive neuroscientists see it emerging from the hard-wiring that the human organism shares with other creatures (namely its talent for discerning and encoding magnitudes), and some cosmologists imagine it is the very fabric of the universe.  Chaitin’s work finds it provocatively equivalent to how we understand a living thing. In an essay on Leibniz, Complexity and Incompleteness, Chaitin makes the following observation:

You see, the Discours was written in 1686, the year before Leibniz’s nemesis Newton published his Principia, when medieval theology and modern science, then called mechanical philosophy, still coexisted. At that time the question of why science is possible was still a serious one. Modern science was still young and had not yet obliterated all opposition.    (emphasis my own)

All of this new rumbling about mathematics and reality encourages a hunch that I have had for a long time – that the next revolution in the sciences will come from a newly perceived correspondence between matter and thought, between what we are in the habit of distinguishing as internal and external experience, and it will enlighten us about ourselves as well as the cosmos. New insights will likely remind us of old ideas, and the advantage that modern science has over medieval theology will wane.  I expect mathematics will be at the center of it all. Leibniz had a philosophical dream where he found himself in a cavern with “little holes and almost imperceptible cracks” through which “a trace of daylight entered.”  But the light was so weak, it “required careful attention to notice it.”  His account of the action in the cavern (translated by Donald Rutherfore) describes this:

One frequently heard voices which said, “Stop you mortals, or run like the miserable beings you are.” Others said, “Raise your eyes to the sky.” But no one stopped and no one raised their eyes… I was one of those who was greatly struck by these voices. I began often to look above me and finally recognized the small light which demanded so much attention. It seemed to me to grow stronger the more I gazed steadily at it. My eyes were saturated with its rays, and when, immediately after, I relied on it to see where I was going, I could discern what was around me and what would suffice to secure me from dangers. A venerable old man who had wandered for a long time in the cave and who had had thoughts very similar to mine told me that this light was what is called “intelligence” or “reason” in us. I often changed position in order to test the different holes in the vault that furnished this small light, and when I was located in a spot where several beams could be seen at once from their true point of view, I found a collection of rays which greatly enlightened me. This technique was of great help to me and left me more capable of acting in the darkness.