silber@sbphy.ucsb.edu (05/26/89)
Let 'random sequence' (:== a sequence whose observable characteristics correspond to the observable characteristics of a sequence of physical events which we identify as 'random'. If we KNOW that the sequence was generated by an 'algorithm', then it is PSEUDO-random. However, the sequence corresponding to the motivating physical phenomenon (whose pattern cannot be generated by any algorithm known to us) is of a different epistemological order, viz. 'RANDOM'. We can never transcend the realm of partial knowledge, and even if we believe that on some ultimate scale everything is pseudo-random, we can't prove it. so 'free-will' vs. 'determinism' is just a matter of aesthetics!
gpmenos@phoenix.Princeton.EDU (G. Philippe Menos) (05/27/89)
In article <1862@hub.ucsb.edu> silber@sbphy.ucsb.edu writes: >...If we know that the sequence >was generated by an 'algorithm', then it is PSEUDO-random. However, Is this a cop-out? Why say pseudo-random, we know it's not even close to random -- that randomness cannot even be achieved. >the sequence corresponding to the motivating physical phenomenon (whose >pattern cannot be generated by any algorithm known to us) is >of a different epistemological order, viz. 'RANDOM'. First, this seems like a bit of a leap. The fact of a different level of analysis does not in itself justify the assumption of randomness, especially if you're correct in your later statement about the realm of partial knowledge. Second, I'm not sure what you mean by "motivating physical phen." Are you alluding to some physical basis for consciousness, which has roots in random behaviour? Oris this an allusion to Neo-Darwinism? I'm in a fog; but that's no doubt my fault. Still, how could we think consequtively, if the mind and its evolution were not guided by some algorithm that we have yet to discern; an algorithm that might even allow for randomness and non-rational forms of knowledge... But an algorithm nevertheless. That is, order and law, at the foundation. > We can never >transcend the realm of partial knowledge, and even if we believe that >on some ultimate scale everything is pseudo-random, we can't prove it. If we are doomed to partial knowledge, why take any position at all, as is implied in the continued usage of the term "pseudo-random". Actually, even our partial knowledge seems to point always to the underlying order and law that is the basis of any functioning system, whether a machine, a human, or a universe. Here's an interesting story... (I think)... In 1967, a few mathematicians and biologists were chatting over a picnic lunch organised by Victor Weisskopf, prof. of physics at MIT. A "weird" discussion took place as the conversation turned to the subject of evolution by natural selection. The mathematicians were stunned by the optimism of the evolutionists about what could be achieved by chance. The wide rift between the participants led them to organise a conference on "Mathematical Challenges to the Neo-Darwinian Theory of Evolution"...(skip to the conference)... which opened with a paper by Murray Eden, Prof. of Electrical Engineering at MIT, entitled "The Inadequacy of Neo-Darwinian Evolution as a Scientific Theory". Eden showed that if it required a mere six mutations to bring about an adaptive change, this would occur by chance only once in a billion years --while, if two dozen genes were involved, it would require 10,000,000,000 years, which is much longer than the age of the earth. (See Gordon R. Taylor's "The Great Evolution Mystery"). "Since evolution does occur and has occured, something more than chance mutation must be involved." With all best wishes, -Phil
cs_bob@gsbacd.uchicago.edu (05/27/89)
>Here's an interesting story... (I think)... In 1967, a few >mathematicians and biologists were chatting over a picnic lunch >organised by Victor Weisskopf, prof. of physics at MIT. A "weird" >discussion took place as the conversation turned to the subject of >evolution by natural selection. The mathematicians were stunned by >the optimism of the evolutionists about what could be achieved by >chance. The wide rift between the participants led them to organise a >conference on "Mathematical Challenges to the Neo-Darwinian Theory of >Evolution"...(skip to the conference)... which opened with a paper by >Murray Eden, Prof. of Electrical Engineering at MIT, entitled "The >Inadequacy of Neo-Darwinian Evolution as a Scientific Theory". Eden >showed that if it required a mere six mutations to bring about an >adaptive change, this would occur by chance only once in a billion >years --while, if two dozen genes were involved, it would require >10,000,000,000 years, which is much longer than the age of the earth. >(See Gordon R. Taylor's "The Great Evolution Mystery"). "Since >evolution does occur and has occured, something more than chance >mutation must be involved." > This IS an interesting story, and it shouldn't surprise anyone who's ever been exposed to evolutionary biology, but you don't know what you're up against. You see, the counter to this argument is, "Yes, but if there are 10,000,000,000 possible worlds (that is, planets) where life could have evolved, then the chance it would have evolved somewhere is very great." This from people who call themselves scientists. Essentially the argument is "yes, the chances are slim, but they are non-zero, so in a very large universe over a very large space of time, life was bound to emerge sometime, purely by accident." The adherents to this version of Darwinism are often as reluctant to give up their world view as any creationist. I don't know why, but any suggestion that evolution is active, as opposed to passive, (known as Lemarckianism, or some such, after the person credited with first proposing the possibility) is treated as utter heresy. Certainly Lemarck's (sp?) hypothesis, in which he used giraffes as a primary example, is naive, but why are we expected to seriously accept this " very, very slim possibility" argument? What is the advantage to a "passive" view of evolution over the "active" alternative? R.Kohout
cik@l.cc.purdue.edu (Herman Rubin) (05/27/89)
In article <1862@hub.ucsb.edu>, silber@sbphy.ucsb.edu writes: > Let 'random sequence' (:== a sequence whose observable characteristics > correspond to the observable characteristics of a sequence of physical > events which we identify as 'random'. If we KNOW that the sequence > was generated by an 'algorithm', then it is PSEUDO-random. However, > the sequence corresponding to the motivating physical phenomenon (whose > pattern cannot be generated by any algorithm known to us) is > of a different epistemological order, viz. 'RANDOM'. If there is a computable algorithm producing the sequence, it is NOT random. This algorithm could even have inputs of preceding physical variables. The test that the sequence is produced by the algorithm is the proof that the sequence is NOT random. A random sequence has the property that there is no non-prescient test which the sequence will fail with positive probqbility. -- Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907 Phone: (317)494-6054 hrubin@l.cc.purdue.edu (Internet, bitnet, UUCP)
mkamer@cs.columbia.edu (Matthew Kamerman) (06/01/89)
I have been following the discussion of free will vs. determinism, randomness vs. hidden order, etc., with some interest and I have a question for those involved. Might these distinctions be a matter of degree rather than kind? For instance, might free will be those actions for which the simplest predictive model CAPABLE OF BEING RUN TO COMPLETION IN A TIME PROPORTIONATE TO THE SCALE OF ACTIVITY (busy beavers aren't acceptable models for real phenomena!), requires an amount of information of near the same magnitude as that contained in the system itself? Might a pseudo-random sequence effectively achieve true randomality if in addition to meeting all standard distribution criteria, its period of repetition is beyond the capacity of the fastest available computing device running for a period comparable to the age of the universe? We exist in a finite domain which constrains both the rate at which information propagates (relativity) and the accuracy with which any object can be modeled (quantum mechanics). In such a domain, there are practical limits on computability far more severe than those usually stipulated by Complexity Theorists. The practical limitations of physical systems may be sufficient to transform distinctions of degree into usefully symbolizeable distinctions of kind.
cik@l.cc.purdue.edu (Herman Rubin) (06/01/89)
In article <228@cs.columbia.edu>, mkamer@cs.columbia.edu (Matthew Kamerman) writes: ......................... > Might a pseudo-random sequence effectively achieve true randomality > if in addition to meeting all standard distribution criteria, its > period of repetition is beyond the capacity of the fastest available > computing device running for a period comparable to the age of the > universe? As far as the period of repetition goes, this is no problem at all. It is easy to construct pseudo-random sequences with arbitrary periods at reasonable computational cost, and XORing one of these to your favorite candidate should take care of that problem. But your use of standard is improper. There are so many reasonable randomness criteria that I would not believe that enough were used. I have done a simulation with approximately 25,000 bits per trial, and I can easily envision 1,000,000 bits per trial. What assurance can you give me that the standard tests will prevent erroneous results? One test the sequence will fail is the test that it was produced in the way it was. -- Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907 Phone: (317)494-6054 hrubin@l.cc.purdue.edu (Internet, bitnet, UUCP)