> On 25 Feb 2020, at 09:23, Alan Grayson <[email protected]> wrote:
>
>
>
> On Monday, February 24, 2020 at 9:06:45 PM UTC-7, Alan Grayson wrote:
>
>
> On Monday, February 24, 2020 at 6:55:59 AM UTC-7, Bruno Marchal wrote:
>
>> On 24 Feb 2020, at 05:44, Alan Grayson <[email protected] <>> wrote:
>>
>>
>>
>> On Sunday, February 23, 2020 at 5:08:16 AM UTC-7, Bruno Marchal wrote:
>>
>>> On 21 Feb 2020, at 14:25, Alan Grayson <[email protected] <>> wrote:
>>>
>>>
>>>
>>> On Friday, February 21, 2020 at 3:40:51 AM UTC-7, Bruno Marchal wrote:
>>>
>>>> On 20 Feb 2020, at 21:59, Alan Grayson <[email protected] <>> wrote:
>>>>
>>>> I think Bruce's position is that quantum processes are inherently random
>>>> and thus NOT computable. Doesn't this conclusion, if true, totally
>>>> disconfirm Bruno's theory that the apparent physical universe comes into
>>>> being by computations of arithmetic pre-existing principles or postulates?
>>>> AG
>>> On the contrary, Mechanism reduces the apparent indeterminacy to the
>>> computable. With mechanism, things might be too much non computable, when
>>> you take the first person indeterminacy into account. Then the math shows
>>> that this refutation of mechanism does not work, as the computations are
>>> done with the exact redundancy making the physical reality enough
>>> computable to get stable histories.
>>>
>>> Mechanism entails that the physical reality cannot be entirely computed,
>>> like it predicted that no piece of matter can be cloned. Indeed, it emerges
>>> from a non computable statistics on infinitely many computation, which are
>>> not algorithmically recognisable in arithmetic. We can test mechanism by
>>> measuring its degree of non computability. Too much computable would be
>>> more problematic than too much non-computable.
>>>
>>> Bruno
>>>
>>> I really can't follow the above. What I understand by mechanism (as you
>>> define it), is that the human nervous system, and presumably a human being,
>>> can be duplicated by computers.
>> Yes. If you want, we could define a mechanist practitioners as someone
>> accepting an artificial prosthesis, like an artificial heart (a pump), or an
>> artificial kidney ( filter machine), etc. A mechanist is then someone
>> accepting this whatever organ is concerned, and in particular an artificial
>> and digital brain.
>>> If that's what you mean, can you explain each sentence above. For example,
>>> how does mechanism reduce the apparent indeterminacy to the computable? And
>>> so forth. AG
>> Self-duplication is made possible by the Digital Mechanism. If you agree
>> that with self-duplication,
>>
>> I don't. Although it has some plausibility, there's no way that arithmetic
>> alone can CREATE space and time. A computer can create "points" in a
>> hypothetical grid, and various types of distance formulas, but it cannot
>> create space or time.
> Arithmetic cannot create space and time. I agree with you. That would be
> rather magical indeed.
>
> Then arithmetic cannot create other worlds! End of story. Case closed. AG
>
> But once you assume digital mechanism,
>
> If arithmetic can't create other worlds, it throws grave doubt that digital
> mechanism is true. AG
>
> and once you understand that the simple arithmetical truth emulates all
> computations, you can understand that arithmetic create the experience of
> space-time, and indeed, with, apparently until now, the right redundancy
> which explain the “many-world” aspect of the physical reality, and that is
> confirmed mathematically, in the sense that we recover quantum logic for the
> logic of experimental s-certainty, relatively to the computational states
> accessible from arithmetic, by universal numbers/machines “living” in there.
> The quantum is explained by the digital “seen from inside”. We get the qubits
> for the bits when seen from the bits, roughly speaking.
>> BTW, what's your definition of physicalism? AG
> The idea that physics is the fundamental science.
>
> With mechanism, this does not work, (I can show this), and we have to explain
> the “illusion of a physical world” by a statistic on all machine “dreams",
> where a dream is just a computation rich enough to support a “self-aware
> observer”
>
> So, with a false theory of mechanism, or digital mechanism, and arithmetic
> which you admit can't create space (and probably time as well), you claim to
> derive a self-aware observer? AG
>
> (which can be defined in arithmetic by a consistent machine having enough
> rich cognitive abilities (precisely: believing in enough induction axioms, if
> you have heard about theories like Peano arithmetic, or Zermelo-Fraenkel set
> theory, those are typical examples of such digital (immaterial) machine.
>
> Yes, I am aware of those axioms, and, as I have written, Peano's axioms imply
> arithmetic, but not IMO, of other worlds. AG
>
> Test of memory; is Zermelo-Fraenkel set theory just Peano's Axioms (PA) plus
> the Axiom of Choice? TIA, AG
ZF is set theory. It contains a faithful realisation of arithmetic. Actually it
contains many such representations. The usual one use von Neuman representation
where 0 is represented by the empty set {}, and n is represented by n united to
{n}.
That gives 3 = {0, 1, 2} = { {}, {{}}, {{}{{}}} } for example. Each number
becomes the set of its predecessors.
This makes ZF-minus, or ZFC-minus (that is ZF, or ZF + the axiom of choice,
minus the axiom of infinity) equivalent to Peano arithmetic.
Now ZF, or ZFC is just ZF-minus, or ZFC-minus to which you add the axiom of
infinity; which says that there is a set omega such that
1) it contains 0 (the empty set), and
2) it is such that if it contains x, it contains x union {x}.
That makes it close for the set theoretical successor relation s(x) = x union
{x}. It contains (intuitively) all natural numbers.
And then you can prove in ZF that there are an infinity of higher and higher
infinite cardinals, etc.
So, by abusing language, up to the faithful representation, it is correct to
say that ZF is mainly PA + an axiom of infinity.
Now, interestingly, the axiom of choice is not needed by ZF to prove anything
in arithmetic. So ZF and ZFC proves the same theorems of arithmetic. You can
use the axiom of choice freely, as it can be proved that we can eliminate its
use after. This requires a bit more mathematics to be shown. So, with respect
to the arithmetical reality, ZF and ZFC are the same.
Bruno
>
> With mechanism, physics is reduced to computer science or to arithmetic, in
> the same sense that for most educated people today think that biology can be
> reduced to physics, in principle of course.
>
> My first older result is simply that mechanism (the idea that we could
> survive with a digital brain/body) is incompatible with weak-materialism or
> with physicalism (the idea that there is a physical universe having a
> fundamental ontology, not reducible to any other science).
>
> Bruno
>
>
>
>
>
>
>
>
>
>
>> like in the Washington-Moscoow thought experiment, the person is unable to
>> predict his immediate particular personal future feeling, despite being
>> certain (assuming Mechanism and all default hyoptheses) that it will be
>> either like feeling to be in Moscow or like feeling to be in Washington,
>> then you understand that mechanism entails the existence of a personal,
>> subjective (first person) indeterminacy.
>>
>> Then you will need to understand that the elementary arithmetical truth
>> implement all computations (including all quantum computations, notably), in
>> the original sense of Turing, Church, Kleene (cf the 1930s papers), which
>> makes us, in any “here and now” indexical state, indeterminate on which
>> computations continue us, making eventually the physical science as a
>> statistics on all (relative) computations, among an infinity (which are
>> indeed realised in that elementary part of arithmetic).
>>
>>
>>
>>>
>>> On of the things I seriously dislike about MW, which makes it utterly
>>> REPELLENT (Steven Weinberg's word), is that there are too many damned
>>> worlds! For example, when one considers the worlds created when putting on
>>> left or right shoe first, this just scratches the surface of how many
>>> worlds are created -- not just two worlds, but uncountably many (if space
>>> is continuous) when one considers how many distinct worlds are created just
>>> for the case of the left shoe first. I am referring to the uncountably many
>>> ways to put on one's left shoe first. For me, this is hardly an ELEGANT
>>> Cosmos, but rather a downright SILLY one! AG
>>
>> When you decide to put the left shoes, in bot “quantum Mechanism” à-la
>> Everett, or in arithmetic, only the consistent extensions must be taken into
>> account, and if you decide to put the left shoe, you will put in all
>> continuation that left shoe. Both the quantum and the purely Mechanist frame
>> does not make everything happening, only the consistent (with you local
>> belief) extension will occur, in the vast majority of extensions.
>>
>> Bruno
>>
>>
>>
>>
>>>
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