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I was wondering if you could possibly look over my (@koitiluv1842) X posts from 5/ to 12/ replying to Dr. Christopher D. Long (@octonion) on BCA (= block cellular automata) and tensors-decompositions/-factorizations, which I posted on 6 August 2024, please. Excuse me the inconvenience, though; X ...

Thanks in advance for your kind reply.
https://medium.com/cantors-paradise/ext ... f1f9b48760

God has given me the answer to the above question:
The UTM-ness of all CAs can be proven as follows:
Let "P = PCA-ness." and "C = colorized-CA-ness." .
Then the requirements for computation-principles denies the "dialectical/dialetheist" logical contradiction of both P-UTM-ness negating C-UTM-ness ...

In connection with this topic, I was wondering if anyone could possibly reply to the below questions of mine, please:
https://www.conwaylife.com/forums/viewtopic.php?f=11&t=4807
I would like to know especially by all means whether colorized CA also act as UTM.
Cf.:
https://www.conwaylife.com ...

In connection with this topic, I was wondering if anyone could possibly reply to the below questions of mine, please:
https://www.conwaylife.com/forums/viewtopic.php?f=11&t=4807
I would like to know especially by all means whether colorized CA also act as UTM.
Cf.:
https://www.conwaylife.com/forums ...

Also, I ask you everyone to add what the mech would be in the cases that
1. the different (shades of) colors represent the reals/fractions between 0 and 1 including both of them;
2. the different (shades of) colors show the integer values from - n to n
or from - (minus/negative) potential-infinity ...

I was wondering if you would possibly tell me:
1. how a CA works, if it consists of cells with from two to potentially-infinite states/colors, rather than only 0 and 1 (or black and white);
and
2. whether also a PCA like that can works as a UTM.
(Please see below:
https://www.conwaylife.com/forums ...

Simplest example but a beat cheating - take a rule where some states are deterministic and some probabilistic. Say you have probabilistic signal that can die out with small probability but a deterministic logical operations on that signal. Now you want to create an output of A and B in form of A ...

Excuse me: I'm quite a lay-person about this ( = CA) field; I was wondering if you could possibly clarify in plain, every-day English the significance (for the PCAs' UTM-ness problem) of your comment by those technical terms, please.
Or perhaps: do you mean by "arbitrarily small" -- a perfect ZERO ...

Here is a surrogate/substitute URL for the above broken link:
https://hutschi.wordpress.com/2020/07/12/dm-d-argument/
The Liar Paradox criticism belongs there as a part of it (as part of "Kommentare/commentaries" in English).

You are absolutely right! The PCA that can tell that it is telling a lie is The Liar in The Liar Paradox, both of which are unreal/non-existent:

https://forum.wordreference.com/conversations/february-2022.1616506/page-3

But the "randomized algorithms"-producing "randomizing algorithms" only need ...

Then, could you work any "chaotic" CA as a TM?
The main idea about the above problem is like this:
You meet a total stranger (who may be a villager from The Truths-Tellers Village but who may be a villager from The Liars Village) at a point where the roads to your destination A and to another place ...

Could you possibly give a probalbilistically-computing computer like a PCA ( = probabilistic cellular automaton) a function of self-assessments or self-reports to be able to say self-referentially, but, of course, also probabilistically: "I'm making a correct judgment/computation. ( = I'm telling a ...