10/2/15 – It has been two weeks since my last Musing, but in that time, there seems to have been a remarkable confluence of "synchronicity", if I understand that term correctly.
I have mentioned several times that my ideas have been, and are still being, influenced by the ideas of other thinkers. Of course that is an understatement that is true for everyone, and on reflection, it couldn't be otherwise. But in order to explain my musings to any readers who might happen across these words, and to give credit where credit is due, those influences should be explained and acknowledged.
At this moment, my mind is fairly bursting with some new ideas, and some ideas confirming my own previously held ideas, that have been brought to my attention over the past two weeks. I'll try to sort them out here by covering them in the context of my interactions with the individuals who have presented the ideas.
Those individuals include Greylorn, Armahedi Mahzar, Gregg Rosenberg, Sam Harris, and Max Tegmark. I'll take them in that order.
My interaction with Greylorn has been the subject of many of these musings and there has not been much change in that relationship during the past two weeks. I mention Greylorn simply for completeness.
Next is Armahedi Mahzar. I'll refer to him as "Arma", as he does in his Internet postings. I discovered Arma by subscribing to an email exchange dealing with George Spencer-Brown's "Laws of Form". I have been interested in Arma's work and his claims but I have never taken the time to understand or master his work. I could, however, understand his overall objective. He was trying to discover the ultimate foundational axioms of logic.
As his work progressed, the results he reported were surprising and exciting to me. Just in the past two weeks, he published a fairly understandable summary and conclusion to his work. He claimed that all of logic, thus all of mathematics, could be reduced to just one axiom.
Arma summarized the development of logic over history by relating the major advances in logic to major advances in human technology. Thus, Aristotle's verbal-based logic followed the Agricultural Revolution; Boole's numerical (zeros and ones) logic followed the Mechanical Industrial Revolution: Peirce, Frege, Spencer-Brown, and Kaufman's various forms of diagrammatic expressions of logic followed the Electrical Industrial Revolution; Venn, Jevons, Marquand, and Peirce's various electro-mechanical logical machines followed the electronic age; and now computers are the logical machines at work in the Internet age.
In itself, this is an interesting if unimportant series of relationships, but Arma's claim is that he has shown that all of these logical systems of expressions are equivalent. (I just realized that the list above leaves out Whitehead and Russell's Propositional Calculus which should have been included somewhere.)
This discovery (my discovery of Arma and his work) relates to the subject of my musings by suggesting the mechanism for the very original bootstrap operation that kicked off the development of reality from its most fundamental, primitive, and original beginning. From what I know of George Spencer-Brown, that was the goal he set for himself as well.
In my previous musing, I speculated on the nature of the primordial equivalent of space-time. I suggested a starting point of two, one, or even zero dimensions of "something". Whether that "something" was some kind of thing or stuff or whatever is a question we will put off until later on.
Prior to answering that question, we might be able to make sense of the question of how it, whatever "it" turns out to be, behaved. And we might be able to deduce how that behavior could have resulted in the complex reality we experience today.
That leads into the next influence: Gregg Rosenberg. I am currently re-reading his book, A Place for Consciousness, in an effort to introduce his concepts to Greylorn. I think Rosenberg has developed a logical and believable framework for the existence of the phenomenon of consciousness. With some minor name changes, his hierarchy of "Natural Individuals" matches very closely with Beon Theory, or so I think.
But the hierarchy of Natural Individuals also suggests a structure for whatever existed at the crucial primordial event of the beginning of reality. It provides a sort of stage for the very original bootstrap operation I mentioned earlier.
Rosenberg's Natural Individuals have two fundamental properties: an effective principle and a receptive principle. These are in a sort of Yin-Yang relationship in that each defines the other and one can't exist without the other. These two principles form the basis of causality and they bear a striking resemblance to Greylorn's Aeon/Dark Energy relationship. It seems to me that Arma's basic logical axiom could be a formal description of that relationship and from it the behavioral consequences for all of reality could be deduced.
As I muse over this, it reminds me of my Dentist Chair experience in which I was encouraged to work on discovering the mathematical basis of reality.
The next individual on my list of influencers is Sam Harris. I have been following some of Sam's blogs which I find interesting but not compelling. As I think I previously mentioned, at one time I intended to read Sam's Free Will but later realized it would be a waste of time. Spending a little time on his blogs has been fun and interesting and has contributed to my interest in Max Tegmark. I watched a conversation between Sam and Max that made me realize that I need to read Max's book, Our Mathematical Universe: My Quest for the Ultimate Nature of Reality. Just this morning I started reading it.
But before I proceed, I should mention a little history that led to my interest in Tegmark. Long ago, while studying math in college, I formed the opinion that Cantor had erred in introducing his theory of infinity into mathematics: it was inconsistent. I later learned that a huge controversy had erupted at its introduction, with Leopold Kronecker and L E J Brouwer opposing it and David Hilbert and later Bertrand Russell supporting it. Hilbert won the day and mathematics has included the nonsense-ridden notion of infinity ever since.
I wrote an essay expressing my displeasure with the notion of infinity and my proposed solution to the problem back in 2001. Later I made a series of videos explaining the problem and my proposed solution, hoping to get the attention of some young mathematician who might pick up the gauntlet and pursue the project of expunging mathematics of all notions of infinity. It was a faint hope.
Several weeks ago, during one of my breakfasts with Dave, he mentioned that a friend of his had watched the videos and/or had read the essay. Later, that same friend sent me an email linking to an interview with Max Tegmark in which Max explained that it would make sense to do away with the notion of infinity in mathematics. Here was my guy. I decided to learn more about Max and possibly make my suggestion to him. After listening to his conversation with Sam Harris, I went directly to Amazon to order the book.
But, of course, before I did, I read the one-star reviews. Those almost convinced me not to bother, just as similar reviews had discouraged me from buying Harris' book. But after reading just one five-star review, I was convinced that I should buy the book. Now, this morning, after having read only the covers and the first half-dozen pages, I am convinced that it will be extremely rewarding to read the entire book. In fact, I may feel relieved of the pressure to figure out the basis of reality myself and relax knowing that Max will do it for me.
That probably won't happen though. I just looked up the references to "infinity" in Max's index and it doesn't look like he champions the cause of getting rid of infinity in his book with the vigor I think it deserves. Worse, he freely uses the terms "infinite" and "infinity" as if he accepts the notions right along with everyone else. I may still have work to do.
I am also eager to discover whether or not he incorporates any of Rosenberg's or Arma's ideas in his speculations. If not, then I may be able to make some suggestions to him along those lines. I still feel motivated to continue these musings but it seems as if some new paths have opened up in front of me.
Right now I am sort of running out of gas and all I have done is tell you a little background of some recent influences on my thinking. Before I close this out, I'll remind you of where we are in the development of an explanation of reality starting at the very beginning.
In the big picture, we have described reality as an elaborate structure of several levels of dimensionality, each with some sort of relationship with other levels both above and below. Without having read Tegmark's book yet, I suspect that this structure might align with his ideas of multiple universes.
Focusing in on the small picture of the origin of reality, it seems that we might not get an easy answer to the question of the ultimate constituent, whether of some kind of thing, or some kind of stuff. But we might make some progress anyway. If we have a concept of some sort of what I called a spatio-temporal environment, and can posit some kind of occupant in that environment that is ultimately simple, whether it is a Spencer-Brown type of distinction like Yin/Yang, figure/ground, on/off, true/false, something/nothing, zero/one, or Rosenberg's effective/receptive principles, Arma's logic may explain how they proceed to develop into something much more rich and complex. That sort of summarizes the task that lies ahead.
Thanks again for reading this far.
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