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I appreciate these intelligent attempts to engage with the CTMU. Thank you.
However, there may be a bit of confusion regarding what the CTMU is. While it is not without important physical ramifications, they are not its raison d'etre. It is not about the prediction of specific physical effects; that's empirical induction, which proves nothing about anything. It's about finding a consistent overall description of reality, mankind, and the relationship between them...something on which mankind can rely for purposes of understanding, survival, and evolution. It explains how a universe can generate itself in order to experience itself through its sensor-controllers (us), and rather than relying on murky or nebulous pseudo-concepts, it does so in the clearest possible way. (One needs a feel for philosophical reasoning and a capacity for abstraction.)
Although its sufficiency for this purpose may not be immediately evident in the introductory 2002 paper reviewed here, it is hands-down the best theory for this purpose. It answers important questions that other theories haven't even asked. To say "I see nothing here worth my time or attention!" amounts to saying "I don’t care about the overall structure of reality, what I am, or what my proper place in reality might be. I like solving my own little problems and getting a paycheck! Now show me something I can use!" To which I can only respond, that's not the wavelength I'm on, because it's not the wavelength of greatest utility to mankind. Mankind doesn't need another techie billionaire - they're a dime a dozen, and I see nothing impressive coming out of them. I have no doubt whatsoever that I could vastly outperform any of them.
I see a few derisive comments to the effect that the CTMU fails to pass the "grammar test" for formal programming languages. (1) The CTMU is not a formal system, but a Metaformal System. That it's not a standard formal system should have been obvious from reading the 2002 paper. (2) The CTMU is not (primarily) a computational system. It's a "protocomputational system". Protocomputation is a pre-mechanical analogue of computation - this is absolutely necessary for a generative system in the CTMU sense - and so much for "well-ordering". (3) A generative grammar is simply a nonterminal substitution system that produces terminal expressions by an adaptively ordered sequence of substitutions; everything else is open. I've explained how this works in several papers. When you get around to those, maybe I'll comment some more.
I also see comments to the effect that given competent and significant work, all I have to do is publish it in some "reputable academic journal". This, of course, is nonsense. Academic journals tend to be run by the same libelous acadummy nincompoops who have been falsely labeling me an "Intelligent Design Creationist" all these years while sneaking around like rats in the woodwork and running me down behind my back (which I have on good authority). Pardon my language, but I wouldn't publish last week’s grocery list in one of their circle-jerk outhouse rags if they paid me. I simply wouldn't feel right about giving them yet another opportunity to lie, call me names, and plagiarize me at their convenience. Most of them are vermin, and they can piss off.
The CTMU is not conjectural, but a lock. So as much as I'd like to humbly efface myself in an outpouring of false modesty, I'll merely point out that arguing with the CTMU amounts to undermining one's own argumentation, whatever it may be. People have been trying to get over on the CTMU for the last 35 or so years, and not one has ever gotten to first base. This was not an accident. If you think you see a mistake or critical inadequacy, the mistake and the inadequacy are almost certainly yours.
As far as "formal mathematics" is concerned, the entire CTMU is mathematical to the core. If it isn't so in the "formal" sense, then your "formal rules" (i.e., your axiomatization and/or rules of substitution) are inadequate to characterize the theory. (Here's a hint: the CTMU evolves by generating new axioms called "telons". The system is innately Godelian. I began publishing on this theory in the same year that Roger Penrose published "The Emperor's New Mind", at which time he hadn't said anything about undecidability that I'd missed. Since then, the gap has only grown wider.)
Thanks for your attention…and again, for your intelligent comments.