Dear CornflowerCicada,
thank you very much for your important thoughts about my essay.
You are right, it may seem that I take mathematics too seriously. My goal was – amongst others – to show that any “necessities” a certain world view may postulate, are – on a logical level – just postulates. The “truths” that follow from these postulates are only as true as the postulates may be.
So when I write how to properly understand my jigsaw puzzle analogy I used this logical fact, together with my belief that there exists a realm where everything is “clear as crystal” (that belief is based on people's experiences during so called “out-of-body experiences” together with the experience of a heavenly realm, so for me it is more than an analogy in this respect).
Two things seem logical to me here: firstly, the human mind operates with opposites, so one can always say that what one considers as “necessary”, is “really” only “possible” (or even “impossible”).
The fact, that you cannot get out of an information processing more than you put in in the first place (be it numbers or postulates) has been shown by Turing and Chaitin. This fact then boils down to realising that ultimately, when we humans or machines use their information processing capacities, they produce – although interesting – tautologies. The interesting part is that these tautologies can be linked together in ways that make sense. Moreover, if we make physics, they seem to tell us something important about the external world. If you look at terms like mass, energy, time, space, these terms define each other mutually in a mathematical as well as in a phyiscal sense. So they have a tautological touch. Nonetheless, they are able to tell us something important about reality.
In the same sense one can make use of this for other areas of reality. For example, in the human mind there exists the idea that laws of physics do “exist”. Similar to mathematics, we can ask where do these laws exist, how has one to imagine them if they exist in a non-local, timeless realm?
Before I come to the second important logical thing I mentioned above, I should also make clear that for presenting to the reader the axiom that God exists and that in my opinion there is presumably another, higher reality, transcendent from pure information processing, I thought it would be necessary to take the reader from the point where most of science is located at present with respect to these questions. I must take that present point of view / understanding serious enough, and then constrast it with my own assumptions in a logical manner, admittedly not without a poetic touch regarding the puzzle piece analogy. Anyways, I thought it would be necessary to lead the reader through a kind of step-by-step procedure of what I myself concluded. Due to page restrictions I had to do this in the most compressed manner, to not deliver something that looks like this comment :-) !
I agree with you, higher mathematics exists only in the human mind. It is a continuation and an abstraction from natural numbers, themselves being an abstraction from the fact of being able to count concrete things in this world. But these higher abstractions enable the formulation of physical laws that are reliable and predictive. In this sense one can assume (not prove or deduce!) that the behaviour of matter is a concrete model of these higher abstractions. But this does not necessarily and automatically mean that these higher abstractions are eternal, platonic in nature.
I do not assume that physical reality is a concrete model of these higher abstractions. I also see no reason for the assumption (except for methodical purposes) to invoke the assumption that math, physical laws, the universe and its functionings are brute facts that may have no further explanations and should be simply taken as given. This in my opinion would counteract logics, the very thing that enables information processing in the human mind and also in the physical world to the extend that we have discovered its existence and sufficiently understand its workings.
Although that's true, I argue that information processing cannot be all there is. The information processing paradigm breaks down at the points where our logics isn't anymore able to unambiguously prove things to be the fact / to be true. This now is the second logical point I want to make:
It especially breaks down at the point at whom we assume that we should take that world view as all there is, as a brute fact, as simply given. Since information processing is an input / output – relation, if we assume the information processing world view as a brute fact, then there exists no input in the first place to propel it to “calculate” something. And if one assumes that in reality it calculates “nothing” - then the information processing paradigm itself is part of that “nothing”, totally ambigous in its assumptions, just a virtual demon in the minds of those who claim it to be the fundamental layer of reality.
Notwithstanding that logical conclusion, it is certainly true that the logically thinking part of the human minds and the external world can be seen as information processing. But if we want to make this picture coherent, in my opinion it would necessitate to think about what information is.
It is lawful, it is reliable, it can structure reality, it can use physical resources, all this qua its power of logic (whatever the latter “really” is)! Thus, there must be something at the core of reality (or at the core of the information processing paradigm, if you will) that is real information, not only statistical noise. For me, that real information, cannot be recovered or facilitated within a universe that is supposed to be merely “information processing”. In my opinion, this real information must be located beyond space and time and must be seen as the original input to make the machine able to at all calculate something meaningfull!
Therefore, I come to the conclusion that there must be a meaningfull realm beyond space and time where our fundamental questions have an answer. This realm then must be somewhat differently perceived than with the human antivalent logics of opposites, since otherwise we gain no truth, no real information because we again run into Gödelian undecidabilities.
But already here on earth, there is no need to doubt everything when thinking deeply about all these issues. One may feel dizzy from time to time when thinking too hard about all of this, and at some point even doubt one's own existence, but this is only due to the fact that we then always do not deal with the real information, but only with an inconsistent model of fundamental reality. Reality, I am convinced, is reliable, has its rules that are independent from the human mind but somewhat also congruent with the information processing outfit of human beings. Therefore one easily can confuse things in the mind and get dizzy. Therefore I tend to not let some model in my mind being more powerful than external reality is!
Best wishes
AquamarineTapir