Re: The infinite list of random numbers
Norman Samish wrote: Suppose an ideal random number generator produces, every microsecond, either a zero or a one and records it on a tape. After a long time interval one would expect the tape to contain a random mix of zeroes and ones with the number of zeroes equal to the number of ones. Is this necessarily true? Is it possible that, even after an infinite time had passed, that the tape could contain all zeroes or all ones? Or MUST the tape contain an equal number of zeroes and ones? Why? If you have a reference dealing with this topic, please let me know. Thanks, Norm Samish I don't think we can view time in terms of time passed and infinite. I think we can look at the problem in terms of a set of numbers over all time, or we can look at a set of numbers issued as a stream sampled over finite time. I think a set of numbers can only be defined as infinite over all time, not tested as such. To be able to say that a process will be random at infinite time would seem to imply a deterministic process that can generate non determinism. :) As for the ideal random number generator, if it's truly ideal, you could easily never see it produce anything buts all ones or all zeros for your lifetime, then promptly after you're dead, it starts producing something that appears random to a temporally constrained observer. An ideal random number generator could only be proved to be ideal over all time since any finite sampling of the stream would necessarily introduce order into the evaluation, lowering entropy and reducing randomness. IMO Robert W. _ Do You Yahoo!? Get your free @yahoo.com address at http://mail.yahoo.com
Re: The infinite list of random numbers
All arrangemets are equally likely, but the probability is, of course, zero. So with probability one you don't get only zeros. There is a theorem that says that any finite arbitrary configuration will appear an infinite number of times in an infinite random sequence with probability one. Saibal Neil Lion wrote: It's undefinable. You're just as likely to get all zeros, or all ones, as you are to get any arrangement of numbers you care to mention (or can mention); the probability being 0 for each, I suppose. The difference is, there are some infinite binary strings of numbers you cannot define without an infinite description (semantic paradoxs aside).. which one assumes, are 'truly' random. From: Norman Samish [EMAIL PROTECTED] To: [EMAIL PROTECTED] Subject: The infinite list of random numbers Date: Thu, 08 Nov 2001 20:41:30 -0800 Suppose an ideal random number generator produces, every microsecond, either a zero or a one and records it on a tape. After a long time interval one would expect the tape to contain a random mix of zeroes and ones with the number of zeroes equal to the number of ones. Is this necessarily true? Is it possible that, even after an infinite time had passed, that the tape could contain all zeroes or all ones? Or MUST the tape contain an equal number of zeroes and ones? Why? If you have a reference dealing with this topic, please let me know. Thanks, Norm Samish _ Get your FREE download of MSN Explorer at http://explorer.msn.com/intl.asp
Re: The infinite list of random numbers
It's undefinable. You're just as likely to get all zeros, or all ones, as you are to get any arrangement of numbers you care to mention (or can mention); the probability being 0 for each, I suppose. The difference is, there are some infinite binary strings of numbers you cannot define without an infinite description (semantic paradoxs aside).. which one assumes, are 'truly' random. From: Norman Samish [EMAIL PROTECTED] To: [EMAIL PROTECTED] Subject: The infinite list of random numbers Date: Thu, 08 Nov 2001 20:41:30 -0800 Suppose an ideal random number generator produces, every microsecond, either a zero or a one and records it on a tape. After a long time interval one would expect the tape to contain a random mix of zeroes and ones with the number of zeroes equal to the number of ones. Is this necessarily true? Is it possible that, even after an infinite time had passed, that the tape could contain all zeroes or all ones? Or MUST the tape contain an equal number of zeroes and ones? Why? If you have a reference dealing with this topic, please let me know. Thanks, Norm Samish _ Get your FREE download of MSN Explorer at http://explorer.msn.com/intl.asp
Re: The infinite list of random numbers
Yes I suppose so, there are an infinite number of ways to arrange an infinite number of zeros (or ones), but it's little odds, because they are essentially the same string as far as we are concerned. Each infinite arrangement with zeros and ones together is distinct however. More generally, all the definable arrangements of zeros and ones, would have prob. 0. From: Saibal Mitra [EMAIL PROTECTED] To: everything [EMAIL PROTECTED] Subject: Re: The infinite list of random numbers Date: Fri, 9 Nov 2001 18:45:15 +0100 All arrangemets are equally likely, but the probability is, of course, zero. So with probability one you don't get only zeros. There is a theorem that says that any finite arbitrary configuration will appear an infinite number of times in an infinite random sequence with probability one. Saibal Neil Lion wrote: It's undefinable. You're just as likely to get all zeros, or all ones, as you are to get any arrangement of numbers you care to mention (or can mention); the probability being 0 for each, I suppose. The difference is, there are some infinite binary strings of numbers you cannot define without an infinite description (semantic paradoxs aside).. which one assumes, are 'truly' random. From: Norman Samish [EMAIL PROTECTED] To: [EMAIL PROTECTED] Subject: The infinite list of random numbers Date: Thu, 08 Nov 2001 20:41:30 -0800 Suppose an ideal random number generator produces, every microsecond, either a zero or a one and records it on a tape. After a long time interval one would expect the tape to contain a random mix of zeroes and ones with the number of zeroes equal to the number of ones. Is this necessarily true? Is it possible that, even after an infinite time had passed, that the tape could contain all zeroes or all ones? Or MUST the tape contain an equal number of zeroes and ones? Why? If you have a reference dealing with this topic, please let me know. Thanks, Norm Samish _ Get your FREE download of MSN Explorer at http://explorer.msn.com/intl.asp _ Get your FREE download of MSN Explorer at http://explorer.msn.com/intl.asp
Re: Article: The Parallel Universes of David Deutsch
Brett Hall wrote: There is a difference between saying The existence of the physical world is certain (i.e: we can prove it) and I believe that the physical world exists. This is analagous to our trust in the laws of physics we can hold the belief that Quantum Theory is a true description of reality - without being absolutely certain that it is infallible. It's for this reason we don't 'stay in bed' as you say. A fallibalist does not say I can prove Physical Reality doesn't exist - the fallibalist has the belief that we can be skeptical about everything. I think a pretty good starting point is to assume that physical reality exists and obeys physical laws (I think this is different to the philosophy of Bruno) - but I'm not about to say that my opinion in this matter is a demonstrable certainty. - Original Message - From: [EMAIL PROTECTED] [Gordon]Just to add it still does not get away from the Non-physical at least the Physical has something to start with,where in the past when Philosophy and old QT talk of the non-physical it got us know where and if we took it totally nothing would have got done instead we believe in the Fantasy and things got done and later discovered Comp through this Physical theory so I thing right or wrong it has a lot more to tell us then just saying it not there and staying in bed. The problem is the ambiguity of the expression physical reality exists and obeys physical laws. I for sure bet physical reality exists and obeys physical laws. At least in *some* sense for I wouldn't try to extract that physical reality (including the laws) from number's psychology if I was not believing in those physical reality-laws first. I just ask where those physical laws (and sensations) come from, and I give an argument (UDA) showing that: IF it exist a level such that *I* remain invariant through a digitalisable functional substitution (+ Church Thesis, + a minimal amount of arithmetical platonism = comp), THEN, in short, the physical laws are *necessarily* given by a sort of modal summation on arithmetical self consistent extensions. In a second step thanks to recursion theory and provability logic (two children of Post Godel Turing ...), which are really the modern science of I, I extract the logical structure of the UM possible physical propositions. Sometimes I just say that I interview some Sound Universal Machine (SUM) asking her about those consistent extensions. It is a purely Arithmetical version of UDA. My thesis = UDA + AUDA. UDA and AUDA can be understood separately, but both are more persuasive taken together. AUDA needs familiarity with logic. The future should show if we get the Quantum or Something Else, and the future should confirm the quantum or something else. I mean in the long run comp could be falsifiate, giving the wrong mass for some bosons. Well, for now I got just a promising (imo) arithmetical orthologic. It is still an open question if a Universal Quantum Machines lives there. What is nice is that such question can be at least precisely formulate. (Gordon, I'm not staying in bed! :) Bruno UDA links: http://www.escribe.com/science/theory/m3044.html
