On 09 Nov 2012, at 13:50, Roger Clough wrote:
Hi Bruno Marchal Arithmetic is just numbers.
Not at all. you need laws so that numbers can enter in relation with each other.
The relation x < y, for example is Ez(x + z = y) The relation x divides y, for another example is Ez(x* z = y) So you need + and *, and you need axioms to relate the laws, like x + 0 = x x + (y + 1) = (x + y) + 1 x *0 = 0 x*(y + 1) = x*y + xAnd by Gödel this will capture a tiny part of the arithmetical truth, but by Putnam-Davis-Robinson-Matiyasevich (70 years of work by quite talentuopus logician) that theory can (at least now) easily be shown Turing universal.
They have no meaning and are (3p) unless observed from a fixed identity (1p).
Yes. But their relations can be such that some 1p emerge. That follows either by comp, or by the usual definition of knowledge + the incompleteness theorem (see my papers, but of course this needs some math and computer science to study)
As proof of that consider these three arithmetic characters from mandarin:十五 二十二 四 The meanings of these are 15 22 4 But you have to makes sense of the characters before you use them.
Absolutely. Chinese baby will learn that 五 is the number of digits handing the human arm.
In other words, you need a fixed, conscious observer.
Here you made a jump. I agree with you though, but "technically" this might need elaboration.
Bruno
Roger Clough, [email protected] 11/9/2012 "Forever is a long time, especially near the end." -Woody Allen ----- Receiving the following content ----- From: Bruno Marchal Receiver: everything-list Time: 2012-11-08, 11:00:12 Subject: Re: Leibniz: Reality as Dust On 08 Nov 2012, at 16:35, Richard Ruquist wrote:On Thu, Nov 8, 2012 at 10:25 AM, Bruno Marchal <[email protected]> wrote:On 08 Nov 2012, at 14:51, Richard Ruquist wrote:Stephan, If the compact manifolds of string theory are all different anddistinct (as I claim in my paper from observations of a variable finestructure constant across the universe), then the manifolds shouldform a Stone space if each manifold instantly maps all the others intoitself, my (BEC physics) conjecture, but also a Buddhist belief- Indra's Pearls. If so, youall may be working on implications of string theory- like consciousness.However, in my paper I claim that a 'leap of faith' is necessary to go from incompleteness to consciousness (C). Would you agree? Bruno saysC emerges naturally from comp.More precisely, I say that consciousness and matter emerges from elementary arithmetic, *once* you bet on comp, that is the idea that the brain or the body can be Turing emulated at some right level so that you would remainconscious. BrunoAnd of course what I am hoping as a physicist rather than a mathematician or logician is that the compact manifolds may be the basis of the elementary arithmetic from which spacetime, matter (ie., strings) and consciousness emerge.Is it not more elegant if we can derived the strings (which are rather sophisticated mathematical object) from arithmetic (through computationalism)?It seems to me that string theory assumes or presumes arithmetic. Indeed it even assumes that the "sum" (in some sense, 'course) of all natural numbers gives -1/12. In fact all theories assume the arithmetical "platonia", except some part of non Turing universal algebraic structures.However, I do not understand what it means "to bet on comp".You bet on comp when you bet that that you can survive with a digital brain (a computer) replacing the brain. Comp is just Descartes Mechanism, after the discovery of the universal machine. The biggest discovery that nature do and redo all the times.Does the whole shebang collapse if brains do not exist?No.But brains cannot not exist, as they exist, in some sense, already in arithmetic. The whole shebang is a sharable dream. I call the computer universal number to help people to keep their arithmetical existence in mind. I will say more in FOAR asap. You can find my papers on that subject from my URL, but don't hesitate to ask any question, even on references. The simplest, concise, yet complete (with the references!) paper is this one:http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.htmlSimply state, what I say is that consciousness *and* matter (physics) is in your head, a bit like the mystics. But then I show a constructive version of that statement allowing any Universal machine to derived physics by looking inward, and then we can compare the comp-physics (the physics in the head of the universal Turing machine) with empirical physics, so that we can test comp.Bruno---------- Forwarded message ---------- From: Stephen P. King <[email protected]> Date: Thu, Nov 8, 2012 at 7:54 AM Subject: Re: Leibniz: Reality as Dust To: [email protected] On 11/8/2012 6:19 AM, Roger Clough wrote: Hi Stephen P. King Time and space don't exist as substances so they don't influence the monads, which as you say are eternal. Further, there is no "substance space". So the monads are not organized in any way. The monads can be thought of as a collection of an infinite number of mathematical points.From dust we come and to dust we shall return.Hi Roger, The absolute disconnection of the monads is what makes them a'dust'. This is exactly what is a Stone space - the dual to a Boolean algebra. ;-) The idea is that any one monad has as its image of other monads the vision of a mathematical point. This fits the idea of that the classical universe is "atoms in a void" as taught by Democritus.http://www.scottaaronson.com/democritus/lec1.html What Craig and I are proposing is to add time to this idea. Theevolution of the dust from one configuration to another is the arrowof time. Switching to the dual, we see teh evolution of Booleanalgebras, whose arrow is the entailment of one state by all previousstates. These two arrows face in opposite directions ... A => A' Stone space | | ....A*<=A*' Boolean algebra The duals aspects of each monad evolve in opposite directions. Roger Clough, [email protected] 11/8/2012 "Forever is a long time, especially near the end." -Woody Allen ----- Receiving the following content ----- From: Stephen P. King Receiver: everything-list Time: 2012-11-07, 19:01:19 Subject: Re: Communicability On 11/7/2012 11:48 AM, Roger Clough wrote: Hi Stephen P. King That sounds like Leibniz. Each monad contains the views of all of the other monads in order to see the whole, not from just one perspective. Hi Roger,Yes, and that is why I like the idea of a Monad. I just don't agree with Leibniz' theory of how they are organized. Leibniz demanded thattheir organization is imposed ab initio, he assumed that there is aspecial beginning of time. I see the monads as eternal, never creatednor destroyed, and their mutual relationships are merely theco-occurence of their perspectives. This makes God's creativity to be aneternal action and not a special one time action. Roger Clough, [email protected] 11/7/2012 "Forever is a long time, especially near the end." -Woody Allen ----- Receiving the following content ----- From: Stephen P. King Receiver: everything-list Time: 2012-11-06, 18:17:30 Subject: Re: Communicability On 11/6/2012 11:11 AM, Roger Clough wrote: What happens if I mistake a statue of a beautiful woman for the real thing, thus turning, eg, a statue of pygmalion into an actual woman ? Or mistake fool's gold or gold foiled chocolates for actual gold coins ? Does the world actually become cloudy if I have cataracts ?It is not just about you. It is about the huge number of observers. Whatmatters is that they can communicate with each other and mutually confirm what is "real". Why do you imagine that only humans can be observers? -- Onward! 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