> On 29 Aug 2018, at 02:30, [email protected] 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] <javascript:> 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. > 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 >>> > <https://groups.google.com/group/everything-list>. >>> > For more options, visit https://groups.google.com/d/optout >>> > <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 >>> <https://groups.google.com/group/everything-list>. >>> For more options, visit https://groups.google.com/d/optout >>> <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 >> <https://groups.google.com/group/everything-list>. >> For more options, visit https://groups.google.com/d/optout >> <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] > <mailto:[email protected]>. > To post to this group, send email to [email protected] > <mailto:[email protected]>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <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.
