On Saturday, February 29, 2020 at 3:45:48 AM UTC-7, Bruno Marchal wrote:
>
>
> On 29 Feb 2020, at 06:45, Alan Grayson <agrays...@gmail.com <javascript:>>
> wrote:
>
>
>
> On Tuesday, February 25, 2020 at 7:17:13 AM UTC-7, Bruno Marchal wrote:
>>
>>
>> On 25 Feb 2020, at 09:23, Alan Grayson <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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.
>>
>
> *What are the elements in the large brackets on the right? AG *
>
>
> I write again the whole set representing 3
>
> 0 is represented by the empty set { }.
>
> 1 is the set which has a unique element which is the empty set: { { } }
>
> 2 is represented by the set { 0, 1} which is equal to { { } { { } } }
>
> 3 is represented by the set {0, 1, 2 }, which is { { }, { { } }, { { } {
> { } } }. }.
>
>
>
>
>
>> 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}.
>>
>
> *How do you distinguish x from {x}? AG*
>
>
> x is some object, usually some set in “pure set theory”, but it could be
> anything.
> {x} is the set with a unique object which is x.
>
> OK?
>
> Bruno
>
*It's extraordinarily subtle. Not sure it's OK. After all, the concept of
"set" is primitive and more or less undefined, as is the empty set. You
name the empty set, zero, or 0. Then we have an element or some object
called x, and the set containing only x, as well as the union of the two.
Is the union also a set if x isn't? AG*
>
>
>
>
>
>
>> 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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