FRACTRAN has a goto instruction so it is not a total model of computation but my claim is that Ar is a total model of computation. maybe unrolled FRACTRAN is a total model of computation too, I have to think about that
in my model it's the platform job to handle the user input and your program output you just write your function and the platform calls your program for example f(time,input_data,key_a,key_b,key_c,...) . if you are very very patient and don't care about the program length you can just compute every output of your program for every possible input. according to [this](https://web.archive.org/web/20230505022436/http://page.mi.fu...) paper a single loop and four basic arithmetic operation is enough to simulate a turing machine so my idea was that to unroll the loop and my conjecture is that we don't need the loop and only four operations is enough to compute all total computable functions
it takes a lot of time and patient to come up with a function that works for all n and also have a short length, let me try if I can solve this problem it may takes a few hours or days or maybe months I'll post the solution here so stay tuned. but if you want to make your life easier you can generate the function in a meta language so you can always be sure that your software does not have a halting problem
(now I can reply here, let me repeat it again)
it depend how you want to display the result to the user, you can just compute a number that represent an html page showing the numbers from 1 to n
(it seems like I can't reply to your last comment so I do it here)
it depend how you want to display the result to the user, you can just compute a number that represent an html page showing the numbers from 1 to n
the language is obviously (at least to me) turing-complete in the limit of the program length. even if you don't buy my argument that it is also turing-complete without the limit notice that in ordinary programming you never need a function that is valid on all input because actual computers have time and memory limitation
if you don't want to melt your brain :D you just precompute the value of any functions f(x) for x<n otherwise you need to be very clever I explained my idea in the link
consciousness is like a joke, if you think it needs an explanation you already miss it.
I struggled with myself to convince Dennett that his conscious so much that I ended up losing it myself I hope you don't make the same mistake that I did
consciousness is equivalent to the halting function h(p,n) where p is a physical process and n is time, we know how to turn a physical process into a virtual process but we don't know how to turn consciousness itself into a virtual process
I can see that you can symbolically talk about the power set of (0,1) and say it's cardinality is bigger than the set itself (although I haven't studied sets and cardinalities deeply enough) but I can't see what Real numbers offers against the computable Universe hypothesis
the proofs that I've read shows that the list of infinite binary strings between [0,1] are uncountable because the invert of the diagonal of the list is not on the list, do you know any proof that does not refer to the invert of the diagonal?
you can't prove something just by assuming it that would be trivial, if we can build or convince ourselves how to build a wormhole or a time machine then we can believe in Real numbers
if you put 1 out then there is no reason to believe it is uncountable because you can sort the list such that the diagonal is all 0s (if you know an argument that shows [0,1) is uncountable I'd be happy to know)
didn't read the whole article but I have to say that having a non-mechanical process in the ontology of the Universe does not mean nonsense, it's not obvious that AI is not possible but also it's not obvious that we are just a body so why should we believe in a meaningless and boring universe rather than a meaningful and wonderful one and also if it turns out that there is no room for a non-mechanical process in the Universe then we can believe that consciousness is equivalent to existence meaning if the Universe seems meaningful and wonderful then it is really meaningful and wonderful no matter how much you try to explain the meaning and wonder away.