Again, another two months has slipped by since my last musing. My excuses are the same as before so I won’t elaborate or apologize. My musing time is rather short at the moment because I spent the better part of the day composing and sending an initial letter to Max Tegmark. In it, I explained that I like his book but was disappointed that he didn’t make the case to jettison the notion of infinity from mathematics and that he had evidently succumbed to the same psychological trap so many others have fallen into: that of assuming that if extra spatial dimensions exist then we should be able to see them.
With that letter sent, I will try to turn my thoughts to uninterrupted musing.
In my last conversation with Greylorn, we confirmed that we agree on a lot of issues on which we are in serious disagreement with philosophers, scientists, and theologians alike. In a nutshell, we both think that there exists a non-physical intelligent designer of chemistry, galaxies, and living organisms, that this designer is far from being perfect, omniscient, omnipotent, or infinite, and that the ultimate origination of reality was extremely simple without a trace of consciousness in existence.
We then tried to isolate our fundamental disagreements. We identified one and I was left with the assignment to do some thinking in the attempt to resolve this disagreement. That is what I am doing now.
The disagreement was on what I called, in a previous musing, the spatio-temporal environment of the earliest inception of reality. In Beon Theory, Greylorn has posited that this earliest state of reality consisted of two things: Raw Energy (or as it is known today, Dark Energy) and Aeon and that these two occupy three-dimensional space, either together or separately. Following Occam, I prefer to consider that the original state of reality consisted of only a single spatial dimension, if that.
Greylorn’s challenge to me was to explain how that kind of existence even makes sense. He said he cannot visualize anything real that consists of, or resides in, a single spatial dimension. He asked me to work on some kind of explanation of that possibility.
Here’s what I think about it after having mulled it over in spurious episodes of sleeplessness and while doing mindless work.
His specific question to me was, “How can anything exist in one dimension?”. So I asked myself, “Indeed, how can anything exist in three dimensions, or in any other space?”
The pre-Socratic philosophers asked this question framing it in the simple question, “Does reality consist of things or stuff?” Democritus favored “things” and coined the term ‘atoms’ to name them, while most of the other pre-Socratic philosophers favored “stuff”. There were several candidates for this “stuff” which were favored singly or in combination by various philosophers. Earth, air, fire, and water were among the favorite candidates.
The difference between “things” and “stuff” was in the extent to which you could in principle divide it. For “things” there was a limit (e.g. atoms) but for “stuff” the division could proceed indefinitely. That is, there was no limit to how fine you could grind up the “stuff”.
As I am sure I have pointed out before, I am adamantly opposed to accepting the notion of infinity for any purpose. So for me infinitely divisible “stuff” is an impossibility. So that leaves “things” as the ultimate constituent of reality. So what could “things” possibly be?
I believe it was Bertrand Russell (or was it Albert Einstein?) who defined a ‘thing’ to be that which obeys the laws of physics. That might be useful, or not; we’ll see.
According to Tegmark, Richard Feynman said: “I believe it is that […] all things are made of atoms—little particles that move around in perpetual motion, attracting each other when they are a little distance apart but repelling upon being squeezed into one another.”
That image gives us a model to work with. It works just as well in one, two, or three dimensions as long as we don’t insist on a description of what the “things” actually are. We could imagine that they are hard spheres, or maybe as I think Plato suggested, small hard platonic solids. Or we could adopt the more modern notion that they are packets of vibrations of some medium or other.
OK, then the immediate questions would be, What are those spheres or cubes made of? And what exactly is the medium that vibrates? It’s as if we’re dealing with a 5-year-old kid asking endless questions.
The way out is provided by Euclid. He realized that he couldn’t define all the terms he used and instead took a selected set of them and declared that they were “primitive” and didn’t need definitions or explanations. Primitives were considered to be self-evident.
Among Euclid’s primitives were points, lines, and planes. With these, and some well-chosen axioms, Euclid developed what was arguably the most successful mathematical system of all time. His mathematical structure was accepted by philosophical giants like Kant to serve as a model of reality. It seems like we can adopt this same strategy.
So, to answer Greylorn’s question to me, I would say that a one-dimensional primordial reality could consist of a finite set of “points” moving about on a “line” according to some rule like the one suggested by Feynman above. That rule would constitute the “law(s) of physics” which would then, according to Russell (or Einstein), qualify our “points” to be called “things”.
This leaves a few questions open: What was the shape of that line? How many things are (or were) there at the very beginning? What exactly is that rule of attraction/repulsion? I have run out of time, so the rest will have to wait for the next musing.
©2015 Paul R. Martin, All rights reserved.