Re: CDR: Re: Many Worlds Version of Fermi Paradox
hi, --- Jim Choate [EMAIL PROTECTED] wrote: On Fri, 3 Jan 2003, Sarad AV wrote: As you already see-what you say is correct for your definition of proof and axiom. Here is the fundamental error in your thinking, you are trying to argue apples and oranges. how do you know that apples and oranges are not same or are same? Its the way you look at it. Its where what ur definition of an apple and orange is -how you interpret your apples and oranges and how you see your apples and oranges. As my comments alude to, what you are doing is trying to argue geometry using two different 5th's -at the same time-. While it was certainly done historically for a considerable amount of time, that itself is a logical contradiction. There are two choices: There is no contadiction-there is more than one solution to a problem-we just have to accept that. - demonstrate the two are equivalent, and we go forward with our little game ofcourse-i am least interested in games.I am trying to understand things better. - recognize they are not equivalent, and we end the discussion because there is really no discussion to be had Your choice. I did n't say they are equivalent-simply said that there is more than one way at looking at it and there is more than one solution to a problem which are not equivalent since their *domain* is different . Regards Sarath. __ Do you Yahoo!? Yahoo! Mail Plus - Powerful. Affordable. Sign up now. http://mailplus.yahoo.com
Re: CDR: Re: Many Worlds Version of Fermi Paradox
On Sat, 4 Jan 2003, Sarad AV wrote: how do you know that apples and oranges are not same or are same? Its the way you look at it. No, ever see Apple and Oranges cross-breed? -THEY- look at it that way too. So there -is- something there to the cladistic viewpoint. -- We are all interested in the future for that is where you and I are going to spend the rest of our lives. Criswell, Plan 9 from Outer Space [EMAIL PROTECTED][EMAIL PROTECTED] www.ssz.com www.open-forge.org
Re: CDR: Re: Many Worlds Version of Fermi Paradox
hi, --- Jim Choate [EMAIL PROTECTED] wrote: On Sat, 4 Jan 2003, Sarad AV wrote: how do you know that apples and oranges are not same or are same? Its the way you look at it. No, ever see Apple and Oranges cross-breed? well-no in the sense you mean but I can say yes if i define it in a different way :) -THEY- look at it that way too. So there -is- something there to the cladistic viewpoint. Look at this view point. I say that The earth is flat and round. now lets attach a meaning to it that we make a sense out of it. The earth is flat when I observe from the earth. The earth is round when I observe it from space. It depends on the frame of reference. When you are on earth you agree that the earth is flat. when you are in space you agree that the earth is round. how ever you don't agree to me saying that both are right. As you see they are not equivalent either because their *domains*-which is the frame of reference are different. thats my view point. Regards Sarath. -- We are all interested in the future for that is where you and I are going to spend the rest of our lives. Criswell, Plan 9 from Outer Space [EMAIL PROTECTED] [EMAIL PROTECTED] www.ssz.com www.open-forge.org __ Do you Yahoo!? Yahoo! Mail Plus - Powerful. Affordable. Sign up now. http://mailplus.yahoo.com
Re: CDR: Re: Many Worlds Version of Fermi Paradox
On Sat, 4 Jan 2003, Sarad AV wrote: how do you know that apples and oranges are not same or are same? Its the way you look at it. No, ever see Apple and Oranges cross-breed? -THEY- look at it that way too. So there -is- something there to the cladistic viewpoint. -- We are all interested in the future for that is where you and I are going to spend the rest of our lives. Criswell, Plan 9 from Outer Space [EMAIL PROTECTED][EMAIL PROTECTED] www.ssz.com www.open-forge.org
Re: CDR: Re: Many Worlds Version of Fermi Paradox
hi, --- Jim Choate [EMAIL PROTECTED] wrote: On Fri, 3 Jan 2003, Sarad AV wrote: As you already see-what you say is correct for your definition of proof and axiom. Here is the fundamental error in your thinking, you are trying to argue apples and oranges. how do you know that apples and oranges are not same or are same? Its the way you look at it. Its where what ur definition of an apple and orange is -how you interpret your apples and oranges and how you see your apples and oranges. As my comments alude to, what you are doing is trying to argue geometry using two different 5th's -at the same time-. While it was certainly done historically for a considerable amount of time, that itself is a logical contradiction. There are two choices: There is no contadiction-there is more than one solution to a problem-we just have to accept that. - demonstrate the two are equivalent, and we go forward with our little game ofcourse-i am least interested in games.I am trying to understand things better. - recognize they are not equivalent, and we end the discussion because there is really no discussion to be had Your choice. I did n't say they are equivalent-simply said that there is more than one way at looking at it and there is more than one solution to a problem which are not equivalent since their *domain* is different . Regards Sarath. __ Do you Yahoo!? Yahoo! Mail Plus - Powerful. Affordable. Sign up now. http://mailplus.yahoo.com
Re: CDR: Re: Many Worlds Version of Fermi Paradox
On Fri, 3 Jan 2003, Sarad AV wrote: As you already see-what you say is correct for your definition of proof and axiom. Here is the fundamental error in your thinking, you are trying to argue apples and oranges. As my comments alude to, what you are doing is trying to argue geometry using two different 5th's -at the same time-. While it was certainly done historically for a considerable amount of time, that itself is a logical contradiction. There are two choices: - demonstrate the two are equivalent, and we go forward with our little game - recognize they are not equivalent, and we end the discussion because there is really no discussion to be had Your choice. -- We are all interested in the future for that is where you and I are going to spend the rest of our lives. Criswell, Plan 9 from Outer Space [EMAIL PROTECTED][EMAIL PROTECTED] www.ssz.com www.open-forge.org
Re: Many Worlds Version of Fermi Paradox
On Thu, 2 Jan 2003, Sarad AV wrote: An axiom is an improvable statement which is accepted as true. An axiom is a statement which is -assumed to be universaly required-. That is -not- equivalent to 'true' (eg A point has only position is not 'true' but a -definition- which is neither true or false, it just is). If it's unprovable then it's 'truth' is irrelevant, derived statements can be 'true' only if we accept the assumptions. Derived statements can -never- be used to 'prove' the assumptions or else we have circular logic. To talk of an axiom as being 'true' is a logic error (you've actually switched into a meta-mathematics at this stage without recognizing it), it can't be 'false' or everything falls apart (eg Godel's commentary about PM being inconsistent means we can prove -any- statement 'true'). There are examples of such axiomatic statements turning out to be problematic or not required; Euclids 5th and the PM assumption that mathematics is complete (or as Godel says 'consistent'). There are other definitions of 'parallel' that work just as well, but are -demonstrably- (as compared to 'provably') different than Euclids original 5th. Euclids 5th isn't 'false', it's just different. With respect to PM, if we accept the axiom that PM is consistent then we can't prove it, even though we -must- accept it if we want to prove -any- (as compared to 'all') statements 'true'. A Formula is a finite set of algebraic symbols expressing a mathematical rule. Proofs, from the formal standpoint, are a finite series of formulae (with certain specifiable characteristics).Hence any proof has a deterministic and well defined sequence of steps. Godel says differently, what he says -via proof- is that there -are- proofs that can't even be written because individual steps may be true but are unprovably so. Hence, a proof that can't be written down can't be said to have an end since it isn't complete. An algorithm for proving a statement true when fed a unprovable statement -must not halt- or else it is saying the statement is 'true or false', hence it is -not- required to terminate or halt. The primary result of Godel's work here is that 'true' and 'false' are -not sufficient- to describe the behavior of PM. That -any- 'universal algorithm' for proving statements 'true or false' can't exist since some statements -in principle- (never mind practice) are -not provable-. Godel in effect answers the 'Halting Problem' in the negative. This is true by the way I define a proof. You are right in ur context and I am right in my context.So both of us are right?yes,based on the *sense* of what we mean by a proof. No, being 'right' isn't really the issue. I vote for Godel. If we accept his proof then we have the unprovable assumption that PM is consistent (which is ok for an axiom). This means that we have at least -an implication- that it is so. Otherwise we are left with accepting it is false, and hence PM is incomplete and -any statement can be proven false-. How usefull would that be? I don't think very. -- We are all interested in the future for that is where you and I are going to spend the rest of our lives. Criswell, Plan 9 from Outer Space [EMAIL PROTECTED][EMAIL PROTECTED] www.ssz.com www.open-forge.org
Re: Many Worlds Version of Fermi Paradox
hi, --- Jim Choate [EMAIL PROTECTED] wrote: On Thu, 2 Jan 2003, Sarad AV wrote: An axiom is an improvable statement which is accepted as true. An axiom is a statement which is -assumed to be universaly required-. That is -not- equivalent to 'true' (eg A point has only position is not 'true' but a -definition- which is neither true or false, it just is). If it's unprovable then it's 'truth' is irrelevant, derived statements can be 'true' only if we accept the assumptions. Derived statements can -never- be used to 'prove' the assumptions or else we have circular logic. Yes,ok-i understand what you mean. As you already see-what you say is correct for your definition of proof and axiom. I never said you are wrong-I only said that I am right according to my set of defenitions and statements in the context I mean.You are right according to your definitions and statements. you said 2.Gödel asks for the program and the circuit design of the UTM. The program may be complicated, but it can only be finitely long. Wrong, there is -nothing- that says the program must have finite length -or- halt. Acoording to my definition of proof,I am right and according to your definition you are right.But you said 'Wrong', there is nothing... Thats the only thing I disagree with. If we accept that both arguments are right-every thing is clear and there is no more confusion. This discussion never ends other wise because- for a given definition -we interpret it in different ways. Some times we don't agree on the sense of the definition. Its how acccording to the definitions and statements we make,the result we come up with. Thats where-I am not convinced with paradoxes and the fermi paradox either. I agree with the further discussion in this mail-Thats another way of seeing it. To talk of an axiom as being 'true' is a logic error (you've actually switched into a meta-mathematics at this stage without recognizing it), it can't be 'false' or everything falls apart (eg Godel's commentary about PM being inconsistent means we can prove -any- statement 'true'). A Formula is a finite set of algebraic symbols expressing a mathematical rule. Proofs, from the formal standpoint, are a finite series of formulae (with certain specifiable characteristics).Hence any proof has a deterministic and well defined sequence of steps. Godel says differently, yes.he takes it in a different sense. what he says -via proof- is that there -are- proofs that can't even be written because individual steps may be true but are unprovably so. Hence, a proof that can't be written down can't be said to have an end since it isn't complete. An algorithm for proving a statement true when fed a unprovable statement -must not halt- or else it is saying the statement is 'true or false', hence it is -not- required to terminate or halt. The primary result of Godel's work here is that 'true' and 'false' are -not sufficient- to describe the behavior of PM. agreed. That -any- 'universal algorithm' for proving statements 'true or false' can't exist since some statements -in principle- (never mind practice) are -not provable-. Godel in effect answers the 'Halting Problem' in the negative. This is true by the way I define a proof. You are right in ur context and I am right in my context.So both of us are right?yes,based on the *sense* of what we mean by a proof. No, being 'right' isn't really the issue. I vote for Godel. If we accept his proof then we have the unprovable assumption that PM is consistent (which is ok for an axiom). This means that we have at least -an implication- that it is so. Otherwise we are left with accepting it is false, and hence PM is incomplete and -any statement can be proven false-. How usefull would that be? I don't think very. I think-i get your point now-I was comming to the same conclusion.We need a model which works rather than comming up with a model which does not work.If they later disagree with observations we can update our model.Thank you for this discussion-it is very sensible. There is still one thing left-how useful or how close is the fermi paradox to the truth. Regards Sarath. __ Do you Yahoo!? Yahoo! Mail Plus - Powerful. Affordable. Sign up now. http://mailplus.yahoo.com
Re: CDR: Re: Many Worlds Version of Fermi Paradox
On Fri, 3 Jan 2003, Sarad AV wrote: As you already see-what you say is correct for your definition of proof and axiom. Here is the fundamental error in your thinking, you are trying to argue apples and oranges. As my comments alude to, what you are doing is trying to argue geometry using two different 5th's -at the same time-. While it was certainly done historically for a considerable amount of time, that itself is a logical contradiction. There are two choices: - demonstrate the two are equivalent, and we go forward with our little game - recognize they are not equivalent, and we end the discussion because there is really no discussion to be had Your choice. -- We are all interested in the future for that is where you and I are going to spend the rest of our lives. Criswell, Plan 9 from Outer Space [EMAIL PROTECTED][EMAIL PROTECTED] www.ssz.com www.open-forge.org
Re: Many Worlds Version of Fermi Paradox
hi, --- Jim Choate [EMAIL PROTECTED] wrote: On Tue, 31 Dec 2002, Sarad AV wrote: Does a paradox ever help in understanding any thing? Yes, it can demonstrate that you aren't asking the right questions within the correct context. okay. 2.Gödel asks for the program and the circuit design of the UTM. The program may be complicated, but it can only be finitely long. Wrong, there is -nothing- that says the program must have finite length -or- halt. An axiom is an improvable statement which is accepted as true. A Formula is a finite set of algebraic symbols expressing a mathematical rule. Proofs, from the formal standpoint, are a finite series of formulae (with certain specifiable characteristics).Hence any proof has a deterministic and well defined sequence of steps. So since we are 'proving' that the oracle does n't exist-its program has finite. This is true by the way I define a proof. You are right in ur context and I am right in my context.So both of us are right?yes,based on the *sense* of what we mean by a proof. The question is it in a formal system,since we don't have paradoexes in a formal system. Any formal system is consistent, i.e. there is no proposition that can be proved true by one sequence of steps and false by another, equally valid argument-by defenition and property of the system (I call the above defenition a formal system,others might not) we cant have a paradox in a formal system. Godel has demonstrated that this is untrue, that in fact you -can- have -undecidable- statements in a formal system. we cannot as reasoned above.If we have-we don't call it a formal system-it can how ever still be a *consistent* system * note that Godel uses 'consistent' where we use 'complete' * consistent and complete are not the same. Complete means-true for all the possible values of all the domains. Consistent means-true for some values of domains and its consistency is uphelid in the domain but not outside. its the *domain*-which we are concerned about. Proposition XI: If c be a given recursive, consistent class of formulae, then the propositional formula which states that c is consistent is not c-provable; in particular, the consistency of P is unprovable in P, it being assumed that P is consistent (if not, then of course, every statement is provable). propositional formula which states that c is consistent is not c-provable; A Formula is a finite set of algebraic symbols expressing a mathematical rule---its a set of symbols and certainly we cannot prove a set of symbols.Yes thats true. it says proposition formula which states c is consistent is not provable. the consistency of P is unprovable in P, it being assumed that P is consistent (if not, then of course, every statement is provable). Yes-thats what godels second incompleteness theorom says.The following statement is true but not provable. by the way can you point me to a undecidable problem in a formal system? Regards Sarath. ...further clarification (original italics/bold denoted by -*-)... It may be noted is also constructive, ie it permits, if a -proof- from c is produced for w, the effective derivation from c of a contradiction. The whole proof of Proposition XI can also be carried over word for word to the axiom-system of set theory M, and to that of classical mathematics A, and here too it yields the result that there is no consistency proof for M or of A which could be formalized in M or A respectively, it being assumed that M and A are consistent. It must be expressly noted that Proposition XI (and the corresponding results for M and A) represent no contradiction of the formalistic standpoint of Hilbert. For this standpoint presupposes only the existance of a consistency proof effected by finite means, and there might conceivably be finite proofs which -cannot- be stated in P (or in M and A). In other words, There are some proofs that can't be written. -- We are all interested in the future for that is where you and I are going to spend the rest of our lives. Criswell, Plan 9 from Outer Space [EMAIL PROTECTED] [EMAIL PROTECTED] www.ssz.com www.open-forge.org __ Do you Yahoo!? Yahoo! Mail Plus - Powerful. Affordable. Sign up now. http://mailplus.yahoo.com
Re: Many Worlds Version of Fermi Paradox
On Thu, 2 Jan 2003, Sarad AV wrote: An axiom is an improvable statement which is accepted as true. An axiom is a statement which is -assumed to be universaly required-. That is -not- equivalent to 'true' (eg A point has only position is not 'true' but a -definition- which is neither true or false, it just is). If it's unprovable then it's 'truth' is irrelevant, derived statements can be 'true' only if we accept the assumptions. Derived statements can -never- be used to 'prove' the assumptions or else we have circular logic. To talk of an axiom as being 'true' is a logic error (you've actually switched into a meta-mathematics at this stage without recognizing it), it can't be 'false' or everything falls apart (eg Godel's commentary about PM being inconsistent means we can prove -any- statement 'true'). There are examples of such axiomatic statements turning out to be problematic or not required; Euclids 5th and the PM assumption that mathematics is complete (or as Godel says 'consistent'). There are other definitions of 'parallel' that work just as well, but are -demonstrably- (as compared to 'provably') different than Euclids original 5th. Euclids 5th isn't 'false', it's just different. With respect to PM, if we accept the axiom that PM is consistent then we can't prove it, even though we -must- accept it if we want to prove -any- (as compared to 'all') statements 'true'. A Formula is a finite set of algebraic symbols expressing a mathematical rule. Proofs, from the formal standpoint, are a finite series of formulae (with certain specifiable characteristics).Hence any proof has a deterministic and well defined sequence of steps. Godel says differently, what he says -via proof- is that there -are- proofs that can't even be written because individual steps may be true but are unprovably so. Hence, a proof that can't be written down can't be said to have an end since it isn't complete. An algorithm for proving a statement true when fed a unprovable statement -must not halt- or else it is saying the statement is 'true or false', hence it is -not- required to terminate or halt. The primary result of Godel's work here is that 'true' and 'false' are -not sufficient- to describe the behavior of PM. That -any- 'universal algorithm' for proving statements 'true or false' can't exist since some statements -in principle- (never mind practice) are -not provable-. Godel in effect answers the 'Halting Problem' in the negative. This is true by the way I define a proof. You are right in ur context and I am right in my context.So both of us are right?yes,based on the *sense* of what we mean by a proof. No, being 'right' isn't really the issue. I vote for Godel. If we accept his proof then we have the unprovable assumption that PM is consistent (which is ok for an axiom). This means that we have at least -an implication- that it is so. Otherwise we are left with accepting it is false, and hence PM is incomplete and -any statement can be proven false-. How usefull would that be? I don't think very. -- We are all interested in the future for that is where you and I are going to spend the rest of our lives. Criswell, Plan 9 from Outer Space [EMAIL PROTECTED][EMAIL PROTECTED] www.ssz.com www.open-forge.org
Re: Many Worlds Version of Fermi Paradox
hi, --- Jim Choate [EMAIL PROTECTED] wrote: On Tue, 31 Dec 2002, Sarad AV wrote: Does a paradox ever help in understanding any thing? Yes, it can demonstrate that you aren't asking the right questions within the correct context. okay. 2.Gödel asks for the program and the circuit design of the UTM. The program may be complicated, but it can only be finitely long. Wrong, there is -nothing- that says the program must have finite length -or- halt. An axiom is an improvable statement which is accepted as true. A Formula is a finite set of algebraic symbols expressing a mathematical rule. Proofs, from the formal standpoint, are a finite series of formulae (with certain specifiable characteristics).Hence any proof has a deterministic and well defined sequence of steps. So since we are 'proving' that the oracle does n't exist-its program has finite. This is true by the way I define a proof. You are right in ur context and I am right in my context.So both of us are right?yes,based on the *sense* of what we mean by a proof. The question is it in a formal system,since we don't have paradoexes in a formal system. Any formal system is consistent, i.e. there is no proposition that can be proved true by one sequence of steps and false by another, equally valid argument-by defenition and property of the system (I call the above defenition a formal system,others might not) we cant have a paradox in a formal system. Godel has demonstrated that this is untrue, that in fact you -can- have -undecidable- statements in a formal system. we cannot as reasoned above.If we have-we don't call it a formal system-it can how ever still be a *consistent* system * note that Godel uses 'consistent' where we use 'complete' * consistent and complete are not the same. Complete means-true for all the possible values of all the domains. Consistent means-true for some values of domains and its consistency is uphelid in the domain but not outside. its the *domain*-which we are concerned about. Proposition XI: If c be a given recursive, consistent class of formulae, then the propositional formula which states that c is consistent is not c-provable; in particular, the consistency of P is unprovable in P, it being assumed that P is consistent (if not, then of course, every statement is provable). propositional formula which states that c is consistent is not c-provable; A Formula is a finite set of algebraic symbols expressing a mathematical rule---its a set of symbols and certainly we cannot prove a set of symbols.Yes thats true. it says proposition formula which states c is consistent is not provable. the consistency of P is unprovable in P, it being assumed that P is consistent (if not, then of course, every statement is provable). Yes-thats what godels second incompleteness theorom says.The following statement is true but not provable. by the way can you point me to a undecidable problem in a formal system? Regards Sarath. ...further clarification (original italics/bold denoted by -*-)... It may be noted is also constructive, ie it permits, if a -proof- from c is produced for w, the effective derivation from c of a contradiction. The whole proof of Proposition XI can also be carried over word for word to the axiom-system of set theory M, and to that of classical mathematics A, and here too it yields the result that there is no consistency proof for M or of A which could be formalized in M or A respectively, it being assumed that M and A are consistent. It must be expressly noted that Proposition XI (and the corresponding results for M and A) represent no contradiction of the formalistic standpoint of Hilbert. For this standpoint presupposes only the existance of a consistency proof effected by finite means, and there might conceivably be finite proofs which -cannot- be stated in P (or in M and A). In other words, There are some proofs that can't be written. -- We are all interested in the future for that is where you and I are going to spend the rest of our lives. Criswell, Plan 9 from Outer Space [EMAIL PROTECTED] [EMAIL PROTECTED] www.ssz.com www.open-forge.org __ Do you Yahoo!? Yahoo! Mail Plus - Powerful. Affordable. Sign up now. http://mailplus.yahoo.com
Re: Many Worlds Version of Fermi Paradox
On Tue, 31 Dec 2002, Sarad AV wrote: Does a paradox ever help in understanding any thing? Yes, it can demonstrate that you aren't asking the right questions within the correct context. We define a paradox on a base of rules we want to prove. No, a paradox is two things we accept that imply two contradictory answers. 2.Gödel asks for the program and the circuit design of the UTM. The program may be complicated, but it can only be finitely long. Wrong, there is -nothing- that says the program must have finite length -or- halt. We -assume- it is so (which relates to the a priori assumption of PM being complete in order to prove it is undecidable - as opposed to incomplete, which is not the same thing at all). The question is it in a formal system,since we don't have paradoexes in a formal system. Godel has demonstrated that this is untrue, that in fact you -can- have -undecidable- statements in a formal system. The flaw in our assumption is that we can reduce everything to a 'T' or a 'F'. * note that Godel uses 'consistent' where we use 'complete' * Proposition XI: If c be a given recursive, consistent class of formulae, then the propositional formula which states that c is consistent is not c-provable; in particular, the consistency of P is unprovable in P, it being assumed that P is consistent (if not, then of course, every statement is provable). ...further clarification (original italics/bold denoted by -*-)... It may be noted is also constructive, ie it permits, if a -proof- from c is produced for w, the effective derivation from c of a contradiction. The whole proof of Proposition XI can also be carried over word for word to the axiom-system of set theory M, and to that of classical mathematics A, and here too it yields the result that there is no consistency proof for M or of A which could be formalized in M or A respectively, it being assumed that M and A are consistent. It must be expressly noted that Proposition XI (and the corresponding results for M and A) represent no contradiction of the formalistic standpoint of Hilbert. For this standpoint presupposes only the existance of a consistency proof effected by finite means, and there might conceivably be finite proofs which -cannot- be stated in P (or in M and A). In other words, There are some proofs that can't be written. -- We are all interested in the future for that is where you and I are going to spend the rest of our lives. Criswell, Plan 9 from Outer Space [EMAIL PROTECTED][EMAIL PROTECTED] www.ssz.com www.open-forge.org
Re: Many Worlds Version of Fermi Paradox
On Tue, 31 Dec 2002, Sarad AV wrote: Does a paradox ever help in understanding any thing? Yes, it can demonstrate that you aren't asking the right questions within the correct context. We define a paradox on a base of rules we want to prove. No, a paradox is two things we accept that imply two contradictory answers. 2.Gödel asks for the program and the circuit design of the UTM. The program may be complicated, but it can only be finitely long. Wrong, there is -nothing- that says the program must have finite length -or- halt. We -assume- it is so (which relates to the a priori assumption of PM being complete in order to prove it is undecidable - as opposed to incomplete, which is not the same thing at all). The question is it in a formal system,since we don't have paradoexes in a formal system. Godel has demonstrated that this is untrue, that in fact you -can- have -undecidable- statements in a formal system. The flaw in our assumption is that we can reduce everything to a 'T' or a 'F'. * note that Godel uses 'consistent' where we use 'complete' * Proposition XI: If c be a given recursive, consistent class of formulae, then the propositional formula which states that c is consistent is not c-provable; in particular, the consistency of P is unprovable in P, it being assumed that P is consistent (if not, then of course, every statement is provable). ...further clarification (original italics/bold denoted by -*-)... It may be noted is also constructive, ie it permits, if a -proof- from c is produced for w, the effective derivation from c of a contradiction. The whole proof of Proposition XI can also be carried over word for word to the axiom-system of set theory M, and to that of classical mathematics A, and here too it yields the result that there is no consistency proof for M or of A which could be formalized in M or A respectively, it being assumed that M and A are consistent. It must be expressly noted that Proposition XI (and the corresponding results for M and A) represent no contradiction of the formalistic standpoint of Hilbert. For this standpoint presupposes only the existance of a consistency proof effected by finite means, and there might conceivably be finite proofs which -cannot- be stated in P (or in M and A). In other words, There are some proofs that can't be written. -- We are all interested in the future for that is where you and I are going to spend the rest of our lives. Criswell, Plan 9 from Outer Space [EMAIL PROTECTED][EMAIL PROTECTED] www.ssz.com www.open-forge.org
Re: Many Worlds Version of Fermi Paradox
solutions is not the same thing as we have proved that it takes exponential time. For all we know, now, in 2002, there are solutions not requiring exponential time (in # of cities). This is also somewhat relevant to theories of everything since we might want to ask if somewhere in the set of all possible universes there exists one where time travel is possible and computing power increases without bound. If the answer is yes, that might suggest that any TOE based on all possible computations is too small to accomodate a really general notion of all possible universes. And this general line of reasoning leads to a Many Worlds Version of the Fermi Paradox: Why aren't they here? The reason I lean toward the shut up and calculate or for all practical purposes interpretation of quantum mechanics is embodied in the above argument. IF the MWI universe branchings are at all communicatable-with, that is, at least _some_ of those universes would have very, very large amounts of power, computer power, numbers of people, etc. And some of them, if it were possible, would have communicated with us, colonized us, visited us, etc. This is a variant of the Fermi Paradox raised to a very high power. My conclusion is that the worlds of the MWI are not much different from Lewis' worlds with unicorns--possibly extant, but unreachable, and hence, operationally, no different from a single universe model. (I don't believe, necessarily, in certain forms of the Copenhagen Interpretation, especially anything about signals propagating instantaneously, just the quantum mechanics is about measurables ground truth of what we see, what has never failed us, what the mathematics tells us and what is experimentally verified. Whether there really are (in the modal realism sense of Lewis) other worlds is neither here nor there. Naturally, I would be thrilled to see evidence, or to conclude myself from deeper principles, that other worlds have more than linguistic existence.) --Tim May (.sig for Everything list background) Corralitos, CA. Born in 1951. Retired from Intel in 1986. Current main interest: category and topos theory, math, quantum reality, cosmology. Background: physics, Intel, crypto, Cypherpunks __ Do you Yahoo!? Yahoo! Mail Plus - Powerful. Affordable. Sign up now. http://mailplus.yahoo.com
Re: Many Worlds Version of Fermi Paradox
On Mon, 30 Dec 2002, Tim May wrote: And this general line of reasoning leads to a Many Worlds Version of the Fermi Paradox: Why aren't they here? Why aren't they all where? If they were 'here' then they wouldn't be another world now would they? The reason I lean toward the shut up and calculate or for all practical purposes interpretation of quantum mechanics is embodied in the above argument. IF the MWI universe branchings are at all communicatable-with, that is, at least _some_ of those universes would have very, very large amounts of power, computer power, numbers of people, etc. And some of them, if it were possible, would have communicated with us, colonized us, visited us, etc. If they could communicate they wouldn't be different. This is a variant of the Fermi Paradox raised to a very high power. It's muddled thinking raised to a lot of wasted human effort. ps there are -two- different ways to propose the 'many worlds' model. The first being that the worlds occupy the same 'space' but differ in all other characters; in other words they are the same cosmos but with different 'decision trees'. The other is that they exist in a 'meta-space' that seperates -all- metrics; that the many cosmos' are truly each unique and share nothing (note that this model can also contain the first). -- We are all interested in the future for that is where you and I are going to spend the rest of our lives. Criswell, Plan 9 from Outer Space [EMAIL PROTECTED][EMAIL PROTECTED] www.ssz.com www.open-forge.org
Many Worlds Version of Fermi Paradox
On Monday, December 30, 2002, at 01:18 PM, Jesse Mazer wrote: Hal Finney wrote: One correction, there are no known problems which take exponential time but which can be checked in polynomial time. If such a problem could be found it would prove that P != NP, one of the greatest unsolved problems in computability theory. Whoops, I've heard of the P=NP problem but I guess I was confused about what it meant. But there are some problems where candidate solutions can be checked much faster than new solutions can be generated, no? If you want to know whether a number can be factorized it's easy to check candidate factors, for example, although if the answer is that it cannot be factorized because the number is prime I guess there'd be no fast way to check if that answer is correct. Factoring is not known to be in NP (the so-called NP-complete class of problems...solve on in P time and you've solved them all!). The example I favor is the Hamiltonian cycle/circuit problem: find a path through a set of linked nodes (cities) which passes through each node once and only once. All of the known solutions to an arbitrary Hamiltonian cycle problem are exponential in time (in number of nodes). For example, for 5 cities there are at most 120 possible paths, so this is an easy one. But for 50 cities there are as many as 49!/2 possible paths (how many, exactly, depends on the links between the cities, with not every city having all possible links to other cities). For a mere 100 cities, the number of routes to consider is larger than the number of particles we believe to be in the universe. However, saying known solutions is not the same thing as we have proved that it takes exponential time. For all we know, now, in 2002, there are solutions not requiring exponential time (in # of cities). This is also somewhat relevant to theories of everything since we might want to ask if somewhere in the set of all possible universes there exists one where time travel is possible and computing power increases without bound. If the answer is yes, that might suggest that any TOE based on all possible computations is too small to accomodate a really general notion of all possible universes. And this general line of reasoning leads to a Many Worlds Version of the Fermi Paradox: Why aren't they here? The reason I lean toward the shut up and calculate or for all practical purposes interpretation of quantum mechanics is embodied in the above argument. IF the MWI universe branchings are at all communicatable-with, that is, at least _some_ of those universes would have very, very large amounts of power, computer power, numbers of people, etc. And some of them, if it were possible, would have communicated with us, colonized us, visited us, etc. This is a variant of the Fermi Paradox raised to a very high power. My conclusion is that the worlds of the MWI are not much different from Lewis' worlds with unicorns--possibly extant, but unreachable, and hence, operationally, no different from a single universe model. (I don't believe, necessarily, in certain forms of the Copenhagen Interpretation, especially anything about signals propagating instantaneously, just the quantum mechanics is about measurables ground truth of what we see, what has never failed us, what the mathematics tells us and what is experimentally verified. Whether there really are (in the modal realism sense of Lewis) other worlds is neither here nor there. Naturally, I would be thrilled to see evidence, or to conclude myself from deeper principles, that other worlds have more than linguistic existence.) --Tim May (.sig for Everything list background) Corralitos, CA. Born in 1951. Retired from Intel in 1986. Current main interest: category and topos theory, math, quantum reality, cosmology. Background: physics, Intel, crypto, Cypherpunks
Re: Many Worlds Version of Fermi Paradox
On Mon, 30 Dec 2002, Tim May wrote: And this general line of reasoning leads to a Many Worlds Version of the Fermi Paradox: Why aren't they here? Why aren't they all where? If they were 'here' then they wouldn't be another world now would they? The reason I lean toward the shut up and calculate or for all practical purposes interpretation of quantum mechanics is embodied in the above argument. IF the MWI universe branchings are at all communicatable-with, that is, at least _some_ of those universes would have very, very large amounts of power, computer power, numbers of people, etc. And some of them, if it were possible, would have communicated with us, colonized us, visited us, etc. If they could communicate they wouldn't be different. This is a variant of the Fermi Paradox raised to a very high power. It's muddled thinking raised to a lot of wasted human effort. ps there are -two- different ways to propose the 'many worlds' model. The first being that the worlds occupy the same 'space' but differ in all other characters; in other words they are the same cosmos but with different 'decision trees'. The other is that they exist in a 'meta-space' that seperates -all- metrics; that the many cosmos' are truly each unique and share nothing (note that this model can also contain the first). -- We are all interested in the future for that is where you and I are going to spend the rest of our lives. Criswell, Plan 9 from Outer Space [EMAIL PROTECTED][EMAIL PROTECTED] www.ssz.com www.open-forge.org
Many Worlds Version of Fermi Paradox
On Monday, December 30, 2002, at 01:18 PM, Jesse Mazer wrote: Hal Finney wrote: One correction, there are no known problems which take exponential time but which can be checked in polynomial time. If such a problem could be found it would prove that P != NP, one of the greatest unsolved problems in computability theory. Whoops, I've heard of the P=NP problem but I guess I was confused about what it meant. But there are some problems where candidate solutions can be checked much faster than new solutions can be generated, no? If you want to know whether a number can be factorized it's easy to check candidate factors, for example, although if the answer is that it cannot be factorized because the number is prime I guess there'd be no fast way to check if that answer is correct. Factoring is not known to be in NP (the so-called NP-complete class of problems...solve on in P time and you've solved them all!). The example I favor is the Hamiltonian cycle/circuit problem: find a path through a set of linked nodes (cities) which passes through each node once and only once. All of the known solutions to an arbitrary Hamiltonian cycle problem are exponential in time (in number of nodes). For example, for 5 cities there are at most 120 possible paths, so this is an easy one. But for 50 cities there are as many as 49!/2 possible paths (how many, exactly, depends on the links between the cities, with not every city having all possible links to other cities). For a mere 100 cities, the number of routes to consider is larger than the number of particles we believe to be in the universe. However, saying known solutions is not the same thing as we have proved that it takes exponential time. For all we know, now, in 2002, there are solutions not requiring exponential time (in # of cities). This is also somewhat relevant to theories of everything since we might want to ask if somewhere in the set of all possible universes there exists one where time travel is possible and computing power increases without bound. If the answer is yes, that might suggest that any TOE based on all possible computations is too small to accomodate a really general notion of all possible universes. And this general line of reasoning leads to a Many Worlds Version of the Fermi Paradox: Why aren't they here? The reason I lean toward the shut up and calculate or for all practical purposes interpretation of quantum mechanics is embodied in the above argument. IF the MWI universe branchings are at all communicatable-with, that is, at least _some_ of those universes would have very, very large amounts of power, computer power, numbers of people, etc. And some of them, if it were possible, would have communicated with us, colonized us, visited us, etc. This is a variant of the Fermi Paradox raised to a very high power. My conclusion is that the worlds of the MWI are not much different from Lewis' worlds with unicorns--possibly extant, but unreachable, and hence, operationally, no different from a single universe model. (I don't believe, necessarily, in certain forms of the Copenhagen Interpretation, especially anything about signals propagating instantaneously, just the quantum mechanics is about measurables ground truth of what we see, what has never failed us, what the mathematics tells us and what is experimentally verified. Whether there really are (in the modal realism sense of Lewis) other worlds is neither here nor there. Naturally, I would be thrilled to see evidence, or to conclude myself from deeper principles, that other worlds have more than linguistic existence.) --Tim May (.sig for Everything list background) Corralitos, CA. Born in 1951. Retired from Intel in 1986. Current main interest: category and topos theory, math, quantum reality, cosmology. Background: physics, Intel, crypto, Cypherpunks
