On Wednesday, August 29, 2018 at 12:14:50 AM UTC-6, Bruno Marchal wrote: > > > On 29 Aug 2018, at 02:30, [email protected] <javascript:> wrote: > > > > On Tuesday, August 28, 2018 at 2:19:40 AM UTC-6, Bruno Marchal wrote: >> >> >> On 27 Aug 2018, at 19:54, [email protected] wrote: >> >> >> >> On Saturday, August 25, 2018 at 1:11:47 AM UTC-6, Bruno Marchal wrote: >>> >>> >>> On 25 Aug 2018, at 01:15, [email protected] wrote: >>> >>> >>> >>> On Friday, August 24, 2018 at 12:25:03 PM UTC, telmo_menezes wrote: >>>> >>>> On 23 August 2018 at 06:31, <[email protected]> wrote: >>>> > >>>> > >>>> > On Thursday, August 23, 2018 at 2:01:24 AM UTC, Jason wrote: >>>> >> >>>> >> >>>> >> >>>> >> On Wed, Aug 22, 2018 at 4:43 PM <[email protected]> wrote: >>>> >>> >>>> >>> >>>> >>> >>>> >>> On Tuesday, August 21, 2018 at 3:22:04 PM UTC, Jason wrote: >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> On Tue, Aug 21, 2018 at 1:16 AM <[email protected]> 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. >
*If human consciousness requires matter, it can't be logical prior to matter as you earlier asserted. But maybe you're referring to a more general, presumably more primitive form of consciousness, to which I alluded to below (earlier). But this more primitive form of consciousness has nothing to do with human brains. For this reason, I find your system, to the extent I understand it. self contradictory. AG* > > * 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 >>> >>> >>> >>> >>> >>>> > -- >>>> > 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 [email protected]. >>>> > To post to this group, send email to [email protected]. >>>> > 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 [email protected]. >>> To post to this group, send email to [email protected]. >>> 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 [email protected]. >> To post to this group, send email to [email protected]. >> 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 [email protected] <javascript:>. > To post to this group, send email to [email protected] > <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 [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
