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? 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 *
>
> * 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
>>
>>
>>
>>
>>
>>> > --
>>> > You received this message because you are subscribed to the Google
>>> Groups
>>> > "Everything List" group.
>>> > To unsubscribe from this group and stop receiving emails from it, send
>>> an
>>> > email to everything-li...@googlegroups.com.
>>> > To post to this group, send email to everyth...@googlegroups.com.
>>> > Visit this group at https://groups.google.com/group/everything-list.
>>> > For more options, visit https://groups.google.com/d/optout.
>>>
>>
>> --
>> You received this message because you are subscribed to the Google Groups
>> "Everything List" group.
>> To unsubscribe from this group and stop receiving emails from it, send an
>> email to everything-li...@googlegroups.com.
>> To post to this group, send email to everyth...@googlegroups.com.
>> Visit this group at https://groups.google.com/group/everything-list.
>> For more options, visit https://groups.google.com/d/optout.
>>
>>
>>
> --
> You received this message because you are subscribed to the Google Groups
> "Everything List" group.
> To unsubscribe from this group and stop receiving emails from it, send an
> email to everything-li...@googlegroups.com <javascript:>.
> To post to this group, send email to everyth...@googlegroups.com
> <javascript:>.
> Visit this group at https://groups.google.com/group/everything-list.
> For more options, visit https://groups.google.com/d/optout.
>
>
>
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
