> On 29 Aug 2018, at 02:30, agrayson2...@gmail.com wrote:
>
>
>
> On Tuesday, August 28, 2018 at 2:19:40 AM UTC-6, Bruno Marchal wrote:
>
>> On 27 Aug 2018, at 19:54, agrays...@gmail.com <javascript:> wrote:
>>
>>
>>
>> On Saturday, August 25, 2018 at 1:11:47 AM UTC-6, Bruno Marchal wrote:
>>
>>> On 25 Aug 2018, at 01:15, agrays...@gmail.com <> wrote:
>>>
>>>
>>>
>>> On Friday, August 24, 2018 at 12:25:03 PM UTC, telmo_menezes wrote:
>>> On 23 August 2018 at 06:31, <agrays...@gmail.com <>> wrote:
>>> >
>>> >
>>> > On Thursday, August 23, 2018 at 2:01:24 AM UTC, Jason wrote:
>>> >>
>>> >>
>>> >>
>>> >> On Wed, Aug 22, 2018 at 4:43 PM <agrays...@gmail.com <>> wrote:
>>> >>>
>>> >>>
>>> >>>
>>> >>> On Tuesday, August 21, 2018 at 3:22:04 PM UTC, Jason wrote:
>>> >>>>
>>> >>>>
>>> >>>>
>>> >>>> On Tue, Aug 21, 2018 at 1:16 AM <agrays...@gmail.com <>> wrote:
>>> >>>>>
>>> >>>>> I've been looking at the Wiki article on this topic. I find that I
>>> >>>>> really don't understand what it is, or why it's important. Maybe a
>>> >>>>> few
>>> >>>>> succinct words from the usual suspects can be of help. TIA.
>>> >>>>>
>>> >>>>>
>>> >>>>
>>> >>>>
>>> >>>> Bruno provided a great definition and background of the Church-Turing
>>> >>>> Thesis. I will try to answer why it is important and comes up often in
>>> >>>> our
>>> >>>> discussion.
>>> >>>>
>>> >>>>
>>> >>>> The Church-Turing thesis says that anything that is computable is
>>> >>>> computable by any computer. In other words, there is nothing that the
>>> >>>> computer in your cell phone can't compute, that your laptop or that a
>>> >>>> super
>>> >>>> computer (or even a quantum computer) can. It just comes down to
>>> >>>> having
>>> >>>> enough time and memory.
>>> >>>>
>>> >>>> This is why you don't need to buy a new phone with new hardware every
>>> >>>> time you want to install a new app. Regardless of the type of CPU in
>>> >>>> your
>>> >>>> phone, it can be extended in its power of what it might compute only
>>> >>>> given
>>> >>>> some new software. It is in this sense that computers are
>>> >>>> "Universal", they
>>> >>>> are universal in the same sense that of a universal remote, or in the
>>> >>>> sense
>>> >>>> that a record player is a universal sound imitating device. A record
>>> >>>> player
>>> >>>> might emulate the sounds of an orchestra, Britney Spears, whale songs,
>>> >>>> etc.,
>>> >>>> all it needs is the appropriate record and it can produce the sound.
>>> >>>>
>>> >>>> In the same sense, all a Turing Machine (computer) needs to imitate
>>> >>>> (or
>>> >>>> emulate) the right program or function is the right software. Because
>>> >>>> of
>>> >>>> this, anything that can be described in software, be it a brain
>>> >>>> emulation,
>>> >>>> an AI, a virtual environment, a virtual machine or operating system,
>>> >>>> can
>>> >>>> never know what hardware is running it, because the Church-Turing
>>> >>>> thesis
>>> >>>> says that any computer is capable of running it.
>>> >>>>
>>> >>>> This is why if consciousness is computable (the computational theory
>>> >>>> of
>>> >>>> mind) we cannot know what is computing us (e.g. we could be in a
>>> >>>> matrix type
>>> >>>> simulation for all we know). The other implication is that if
>>> >>>> computations
>>> >>>> exist in mathematics (and they do), then we exist within mathematics.
>>> >>>> Mathematics (or at least the part necessary to describe computations)
>>> >>>> becomes the fundamental science of what we experience and what is
>>> >>>> possible
>>> >>>> to experience or what we may predict about our future experiences
>>> >>>> (physics).
>>> >>>>
>>> >>>>
>>> >>>> Jason
>>> >>>
>>> >>>
>>> >>> If someone digitizes (emulates) the Mona Lisa, is this equivalent to
>>> >>> the
>>> >>> Mona Lisa?
>>> >>
>>> >>
>>> >> If you digitize a person and put the digitized Mona Lisa before them, it
>>> >> is equivalent to the real Mona Lisa to that person, at least as far as
>>> >> they
>>> >> can tell.
>>> >>
>>> >>
>>> >>>
>>> >>> Can you write a function which is not computable? AG
>>> >>>
>>> >>>
>>> >>
>>> >> If by not computable you mean it never returns, then this is easy:
>>> >>
>>> >> function foo():
>>> >> while (true)
>>> >> {
>>> >> // loop forever
>>> >> }
>>> >>
>>> >> There are also programs for which no one knows if they are computable or
>>> >> not. If you can prove whether or not this function ever completes, you
>>> >> will
>>> >> be world famous, and may even earn a million dollars (though I think the
>>> >> prize has been retracted, it might be oferred again):
>>> >>
>>> >> Step 1: Set X = 4
>>> >> Step 2: Set R = 0
>>> >> Step 3: For each Y from 1 to X, if both Y and (X – Y) are prime, set R =
>>> >> 1
>>> >> Step 4: If R = 1, Set X = X + 2 and go to Step 2
>>> >> Step 5: If R = 0, print X and halt
>>> >>
>>> >> All you have to prove is the computer either never gets to step 5 or
>>> >> that
>>> >> it does get to step 5. Mathematicians have been working on a related
>>> >> problem for 300 years, no one has solved it yet.
>>> >>
>>> >>
>>> >> Jason
>>> >
>>> >
>>> > I was asking about a well-defined mathematical function that can be
>>> > written
>>> > in closed form, or possibly as an infinite series. I believe that all
>>> > such
>>> > functions are computable. I was not discussing subroutines that might
>>> > never
>>> > terminate. If all well defined mathematical functions are computable, why
>>> > did computability become a big deal? AG
>>>
>>> It is not true that all well-defined functions are computable. You
>>> have already been given examples by Jason and John of well-defined
>>> mathematical functions that are non-computable.
>>>
>>> You seem to confuse "well-defined" with "written in closed form". The
>>> latter is not even well-defined (heheh) because it hangs on the idea
>>> of a set of "well-known" functions, and people already have different
>>> ideas on what that set includes. Having well-known representations
>>> such as sin(x) or e^x, or even x + y does not magically make the
>>> related computations non-algorithmic. How do you think you learned how
>>> to add, subtract, multiply and divide in basic school? Those were
>>> algorithms.
>>>
>>> Well-defined just means that there is a non-ambiguous way to know if a
>>> given value corresponds to a given input of the function. If I tell
>>> you to consider the function f, such that its value is zero no matter
>>> the input, then I gave you a well-defined function in plain English.
>>> There is nothing magical about notation.
>>>
>>> Telmo.
>>>
>>> So a "function" must have a well defined domain set, finite or infinite,
>>> and is not limited to closed forms but includes infinite series and
>>> algorithms. In such case, an infinite loop, even if it has an initial
>>> value, is not a function and not computable, whereas all closed forms are
>>> computable. Agreed? AG
>>
>> Infinite loop can be extended into the computable. The problem are infinite
>> computations getting more and more complex, and with no loop.
>>
>> I don't see why an infinite loop can be computable. I see there are
>> subtleties in this concept. AG
>
>
> We will come back on this. If there is a loop, it might be dented and the non
> computable function is not computable only in a superficial manner: it can be
> extended into something computable, but that will not be the case for most
> machine’s attribute. But you need to have a some understanding of the
> diagonal of Cantor.
>
>
>
>>
>> I am not sure what you mean by close form.
>>
>> Initially, I meant something that can be written down explicitly or
>> expressly, like a polynomial, and can be calculated for every value in its
>> domain. I then extended it to infinite series or sums, which converge. I
>> then accepted that functions could include software algorithms. AG
>
> OK. (That is a combinator, actually, but we will come back on this).
>
>
>
>
>>
>> No worry, we will see soon, example of well defined functions which are not
>> computable. Basically all attributes of universal machine are not computable.
>>
>> This seems very UN-intuitive. Incidentally, my computer broke down again due
>> to a faulty repair two months ago. I am using a library computer which
>> limits my time and is unavailable on Sunday. It will slow my plan to study
>> some of your material, including Cantor's proof. AG
>
> OK. Actually I will be slowed down too, as the exam period has begun today.
>
>
>>
>> Finally, a general critical comment on your theory, CMIIAW, that
>> consciousness causes the illusion of matter and the apparent reality of
>> events and processes. As I previously noted on this or a related thread,
>> consciousness seems to be a late comer to the universe.
>
>
> I can understand, but here mechanism will change this, in an admittedly quite
> counter-intuitive way.
> We will have:
>
> Number ==> consciousness ==> matter/universes ==> human consciousness.
>
> How can consciousness be (logically) prior to matter when we have hugely
> strong evidence of the opposite?
Because human consciousness requires matter. But matter requires a more general
form of consciousness.
> Can you give a plausibility argument? Mine would be this, acquired on some
> LSD trips on a galaxy long long time ago and far far away; whatever we see as
> we view the world appears to partake in consciousness; Yes, "inanimate"
> matter as well. AG
The plausibility will be arise from computationalisme. If the brain is
“digitalisable”, then it is faithfully emulated in infinitely many computations
in arithmetic.
That is why I explain a bit of the combinators and Turing machine: to explain
that the notion of computation is a mathematical notion. It does not involve
any physical, nor metaphysical hypothesis, except for the thesis of Church,
Turing, Post, Kleene. I will come back on this when I have more time.
Bruno
>
>> It's easy to identify events and processes that occurred way before any
>> identifiable consciousness existed, such as the formation of the Sun, Earth,
>> and Moon. I'd be interested in your comment on this issue. I commend you for
>> your guts to attempt solve the problem of consciousness, but because of what
>> I just wrote, I don't believe your theory can explain what I believe you
>> represent it doing. AG
>
> "My theory” is Digital Mechanism. It helps to formulate the mind-body
> problem, and to suggest a solution which is closer to Plato’s idealism than
> to Aristotle’s materialism (current paradigm in science and religion today).
>
> Bruno
>
>
>
>>
>> Bruno
>>
>>
>>
>>
>>>
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