User blog comment:Boboris02/MBOT/@comment-1605058-20161218195724

Let me note that my comments are based off only the body of the blog post, as I haven't read all of the comments.

"MBOT is based of ZF or ZFC." To be honest, I have looked through all of the post and I don't see anything which would remind me of ZF or ZFC in any way, apart from using logical connectives and union symbol in a confusing, nonstandard way.

I won't comment on "MBOT can recreate EVERY possible function", since you seem to already have addressed that in another comment.

A major problem which comes up is, when you define \(\Delta_x\), you say "the strongest possible system describable in \(x\) symbols or less". I have two questions: first, "strongest" in what sense? How do you compare "strength" of two systems? Second, describable how? In English? (probably not, because paradoxes) In some formal language? (you never describe any such language; you mention the connectives but you don't mention e.g. what stuff can appear on both sides of \(\Rightarrow\)). Same about \(\Delta_x[n]\) - describable in what language?

"...that leaves them open for any definition that you can set". This is the vaguest description I have encountered in a while. How can we "set" a definition of these? Do we again use paradox-prone natural language, or a formal system which you have yet to describe? In the examples section, you seem to be using a weird mixture of symbols you have given and a phrase "system inside a [another system]".

Let me attack a particular example. Take a look at your "definition" of BEAF. The first three lines - let's say for now I'm fine with them. But they all deal with expressions involving three \(\Rightarrow\)s, while the last one has only one \(\Rightarrow\). How does it connect to the others? Also, let me note that I will not be satisfied with an answer how it is related in this example, I want to know how such things would be related in a general system. I won't even mention that you don't have exponentiation, or subtraction in your system description, nor you have constants \(0,1\). You need that to have a well-defined notation.

Let's look what comes later. You describe \(\Phi(a)\cup b\) in terms of a system involving arbitrary number of arrows. But above you have only described the system which uses three arrows. In order to make that definition at all sound, you need to describe systems with any number of arrows, which would probably require infinitely many symbols (don't you even think of using ellipses in a formal system).

What the hell does "repeating the system n,m times" mean? Even worse, what is "repeating the system \(n\Rightarrow m\), k times" supposed to mean? Is \(n\Rightarrow m\) a number all of a sudden?

Below I can see you are trying to define \(\Phi(a)\cup 2\) recursively, but you are completely missing any sort of base case.

Can you describe (in English) what you are trying to achieve with the \(\Phi(a) \Rightarrow b = \Phi^b(a) \Rightarrow (\Phi(a) \Rightarrow (b-1)) \cup a \Rightarrow a\) system? First of all, what does \(\Phi^b(a)\) mean? \(\Phi\) is not a function, so how can it be iterated (assuming this is what the superscript is supposed to mean)? Second, it seems like when replacing \(\Phi(a)\Rightarrow b\) with the right hand side, the numbers involved are just getting larger and larger.

Now we are getting to the uncomputables... What does "overgrowing" mean? What does "overgrowing another function/system F(n) by @ at a time" mean? By the way, \(^{>}+(@) F(n)\) looks more like a cat sat on a keyboard than something that is supposed to relate two functions.

"Phi systems are like word descriptions,but with symbols and thus any function that can be described on paper can be described in a Phi system." I don't know how you jump to that conclusion; apart from the issue that you can't define NOOP itself and related, you can't even describe all functions with words, so it doesn't make sense.

I am a bit stumped on how you've reached the count of around 20 symbols on that formula which you claim describes \(\Sigma(n)\). Unless you take the whole \(\ldots 00\underbrace{111\ldots 111}_m00\ldots\) as one symbol, in which case you get 18 symbols, this is a lot more, and if you did that, then let me just ask a simple question of what a "symbol" is... Also, this part of a formula is the second vaguest thing I have seen in a while. Apart from the fact that the ones considered when dealing with \(\Sigma(n)\) needn't be consecutive, you are using ellipses (NEVER DO THAT), and these can be interpreted in infinitely many ways - maybe the leftmost \(\ldots\) means "any string whatsoever", and the middle one represents "an elephant is hiding there, I don't know how to typeset it into LaTeX". Do I have to comment on \(\infty\) appearing in the formula?

Finally, how in the world does that even represent anything even remotely related to Turing machines?! Do you talk about the tape containing only zeroes and ones anywhere in the formula? Anything about the machine head moving only one cell at a time? Heck, where does it mention the notion of state transition? read-write head? Oh wait... I think I know. All of that is hidden in this single, little, innocuous looking \(\neg\) symbol, isn't it? But let me just mention how utterly ridiculous that is. If you stuff into what you call one character a description which would take a paragraph or two even to describe in an intuitive, nonformal way, then I think it's not risky to say, even ignoring everything else in this blog post, that what you describe is not formal.

"This is exactly K-systems,exept this time it's well-defined!" sorry, nope.

"...it did not use any fixed languige for it's definition.Mine has" sorry, nope.

I think I've said enough detrimental things so as a consolation, let me mention that I like the name BIG NOOB :)