Re: Applied vs. Theoretical
From Osher Doctorow [EMAIL PROTECTED], Tues. Dec. 3, 2002 1326 Tim May gives a very detailed account of his ideas on category and topos theories, and I will only comment on a few of his ideas and some of Ben Goertzel because of space and time limitations. I think that Tim and I, and hopefully Ben, do not differ on the extreme usefulness of being able to generalize concepts across many different fields and subfields. MacLane and Lawvere's category theory TRIED to do that, and the effort is certainly commendable. Perhaps it is more than commendable. As one who seldom receives commendations, I may tend to give them less often to others than I did when I started out in mathematics/science. Nevertheless, I perceive or understand what Ben refers to as a certain lack of deep results in category theory as compared with my Rare Event Theory for example - although Ben understands it relative to his own experiences. The theorems that Tim has cited are one counterexample class to this, but where are the great predictions, where is there anything like the Einstein Field Equation, the Schrodinger Equation, Newton's Laws, Fermat's numerous results, Maxwell's Equations, the Gauss-Bonnet Theorem and its associated equation that ties together geometry and topology, Non-Euclidean/Riemannian Geometry, Euclidean Geometry, the Jacobsen radical, Gauss-Null and related sets in geometric nonlinear functional analysis, Godel's theorems, or even Hoyle's Law or the Central Limit Theorems or the almost incredible theorems of Nonsmooth Analysis and Kalman filters/predictors and Dynamic Programming and the Calculus of Variations and Cantor's cardinals and ordinals and Robinson's infinitesimals and Dirac's equations and Dirac's delta functions and Feynmann's path history integrals and diagrams and the whole new generation of continuum force laws and on and on. Sure, category theory can go in to many fields and find a category and then take credit for the field being essentially a category, and I can go into many fields and find plus and minus and division and multiplication analogs and declare the field as an example of Rare Event Theory [RET] or Fairly Frequent Event Theory [FFT or FET] or Very Frequent Event Theory [VFT or VET] or a plus field or a minus field or a division field or a multiplication field. And both Category and RET-FET-VET theories can show that many of their concepts cross many fields. This is very commendable, although to me it is old hat to notice that something like a generalization of a group crosses many branches of mathematics, whereas RET-FET-VET classes such as GROWTH, CONTROL, EXPANSION-CONTRACTION, KNOWLEDGE-INFORMATION-ENTROPY tend to cross not only branches of mathematics but branches of physics and biology and psychology and astrophysics and on and on. But string and brane theory are suffering from precisely what category theory is suffering from - a paucity of predictions of the Einstein and Schrodinger kind mentioned in the second paragraph back, and a paucity of depth. Now, Tim, you certainly know very very much, but how are you at depth [question-mark - my question mark and several other keys like parentheses are out]. I will give an example. Socrates would rank in my estimation as a Creative Geniuses of Maximum Depth.The world of Athens was very superficial, facially and bodily and publicly oriented but with relatively little depth, and when push came to shove, rather than ask what words meant, it preferred to kill the person making the inquiries. What it was afraid of was going deep, asking what the gods really were, why so-called democracy ended at the boundaries of Athens and even was inapplicable to all people in Athens, what democracy really was, why the individual and the group/humanity were not equally important, when the Golden Mean and the Golden Extreme as I would call it [for example, valuing Knowledge rather than compromising between Knowledge and Ignorance] applied. You mentioned, Tim, that the Holographic Model is still very hypothetical. Are we to understand that G. 't Hooft obtained the Nobel Prize for a very hypothetical idea [question-mark] among others. I have actually generalized the Holographic Principle and it follows from RET-FET-VET Theory. But it happens to be an example of DEPTH of a type that Category Theory does not know how to handle. It says that LOWER DIMENSIONS CONTAIN MORE KNOWLEDGE-INFORMATION THAN HIGHER DIMENSIONS - IN FACT, ALL OF IT, with appropriate qualifications. I will conclude this rather long posting with an explanation of why I think Lawvere and MacLane and incidentally Smolin and Rovelli went in the wrong direction regarding depth. It was because they were ALGEBRAISTS - their specialty and life's work in mathematics was ALGEBRA - very, very advanced ALGEBRA. Now, algebra has a problem with depth because IT HAS TOO MANY ABSTRACT POSSIBILITIES WITH NO [MORE CONCRETE OR NOT] SELECTION CRITERIA AMONG THEM. It is somewhat
Re: Mathematics and the Structure of Reality
From Osher Doctorow [EMAIL PROTECTED], Tues. Dec. 3, 2002 1601 Tim, I quote first your comment early in your posting on my RET theory. [TIM] I don't think the world's nonacceptance of RET means it is on par with category theory, just because some here don't think much of it. [OSHER] Next, I quote your own apparent sensitivity to your belief that somebody might be attacking you, from later in the same posting. [TIM] On your second point, about how are you at depth?, I hope this wasn't a cheap shot. Assuming it wasn't, I dig in to the areas that interest me [OSHER] What in the world are you talking about - what does depth have to do with a cheap shot [question mark - my question-mark key is out]. And what kind of a pun is that some here not thinking much of RET thereby not putting it on a park with category theory. This last sentence, if it is not a cheap shot, is definitely worthy of all the scientific research that can be brought to bear on the typist of the sentence. First of all, there has been no discussion with me participating in which somebody previously told me that they don't think much of RET theory. Second, in the same posting, you claim in effect to not understand RET theory. Those two sentences approximately are all you say in this posting on RET theory. Then you go on to generalize to quote some here not thinking much of RET unquote, which gives the impression that there may be more than you, and you have not even stated that you do not think much of it since you claim to not understand it - which, incidentally, is far easier to explain than category theory [and all my explanations of it are easier - that is the advantage of knowing fuzzy multivalued logics, which apparently you do not], and so you have the distinction of understanding what is harder to explain and not understanding what is easier to explain - a phenomenon definitely worthy of the fullest research to which science can be put. Still, your replies are worthy of commenting upon because they pioneer new directions in errors but also give some interesting references as a redeeming feature.Your picture of Socrates is perhaps the funniest of all your pictures, and that is especially interesting because you are already in the non-fuzzy-multivalued-logic camp, so now you move into the non-philosopher camp - which, believe it or not, is also where Smolin, Rovelli, MacLane also are. So you think that in essence Socrates was an idiot, the citizens of Athens were heroes, and Plato was a hero, and Sir Roger Penrose was a hero. If you had the slightest background in philosophy beyond philosophy 1 and 2, you would know that Plato wrote the biography of Socrates - that nothing is known of Socrates beyond what his STUDENT Plato wrote, and that Plato literally worshipped Socrates, and that Plato described in detail how the horrible citizens of Athens destroyed Socrates and forced him to take poison.Then, toward the end of your posting, you claim that this Athens was nothing like the Athens you studied - even though you cite Plato as one of the great philosophers in effect. One would have to believe that you were there before Plato, somehow interposed between Plato and his teacher Socrates, studying all this wisdom [from where, if I may ask] and going around polling Athenians [certainly not examining the psychology or culture or history of Athens - a poll would more likely reflect the beliefs of conformists whether in science or politics]. Your master step, however, was your discovery that G. 't Hooft obtained the Nobel Prize not from the Holographic Principle but from his work on the electroweak force, contrary to my claim that he obtained it for the Holographic Principle among other things. Most Nobel Laureates in physics obtain their prizes for the so-called sum total of their work, although specific highlights are often mentioned and apparently may be the only ones mentioned. I assumed that 't Hooft's Holographic Principle was included. In any case, if you think as you claim that the Holographic model is still very hypothetical, you are out of line of what is one of the core concepts of string, brane, supersymmetry, TQFT, loop theory, and on and on at the present time. Since you keep referring me to your references, glance through the arXivs in physics and mathematics from the 1997s through 2002. Or read one of my explanations on one of the sites that I have cited in previous postings. I will conclude this posting with a summary of what I think your orientation is. You, and your apparently closest hero John Baez, are COMPUTER PEOPLE. Computer people, in my 64 years of experience in life, have almost always near 0 verbal ability and about 50 percent quantitative ability on a scale of 0 to 100. They have NO philosophical ability, which computers also don't have, and their use of logic is confined to reading proofs of theorems that have already been invented by somebody else and making stupid machines
Re: Applied vs. Theoretical
From Osher Doctorow [EMAIL PROTECTED], Sunday Dec. 1, 2002 1243 Sorry for keeping prior messages in their entirety in my replies. Let us consider the decision of category theory to use functors and morphisms under composition and objects and commuting diagrams as their fundamentals. Because of the functor-operator-linear transformation and similar properties, composition and its matrix analog multiplication automatically take precedence over anything else, and of course so-called matrix division when inverses are defined - that is to say, matrix inversion and multiplication. It was an airtight argument, it was foolproof by all that preceded it from the time of the so-called Founding Fathers in mathematics and physics, and it was wrong - well, wrong in a competitive sense with addition-subtraction rather than multiplication-division. There is, of course, nothing really wrong with different models, and at some future time maybe the multiplication-division model will yield more fruit than the addition-subtracton models. And, of course, each model uses the other model secondarily to some extent - nobody excludes subtraction from the usual categories or multiplication from the subtractive models. What do I mean when I say it was relatively wrong, then, in the above sense [question-mark]. Consider the following subtraction-addition results - in fact, subtraction period. 1. Discriminates the most important Lukaciewicz and Rational Pavelka fuzzy multivalued logics from the other types which are divisive or identity in their implications. 2. Discriminates the most important Rare Event Type [RET] or Logic-Based Probability [LBP] which describes the expansion-contraction of the universe as a whole, expansion of radiation from a source, biological growth, contraction of galaxies, etc., from Bayesian and Independent Probability-Statistics which are divisive/identity function/multiplicative. 3. Discriminates the proximity function across geometry-topology from the distance-function/metric, noting that the proximity function is enormously easier to use and results in simple expressions. It sounds or reads nice, but the so-called topper or punch line to the story is that ALL THREE subtractive items above have the form f[x, y] = 1 plus y - x. ALL THREE alternative division-multiplication forms have the form f[x, y] = y/x or y or xy. Category theory has ABSOLUTELY NOTHING to say about all this. So where are division and multiplication mainly used [question mark]. It turns out that they are used in medium to zero [probable] influence situations, while subtraction is used in high to very high influence situations. Come to your own conclusions, so to speak. Osher Doctorow - Original Message - From: Tim May [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Sunday, December 01, 2002 10:44 AM Subject: Applied vs. Theoretical
Re: Alien science
From Osher Doctorow [EMAIL PROTECTED], Sat. Nov. 30, 2002 1005 I agree generally with Tim May on mathematics and physics vs computers and AI. My most amusing example is something of a Jonathon Swift parody of all four of these fields. Gulliver lands on an island inhabited by mathematicians, physicists, computer scientists/computer engineers, and AI people, all competing. He notices that they all rushing ahead to greater and greater complication and complexity and so on, and it occurs to him that this might be their weak point. Could they all have overlooked something simple [question-mark]. He discovers, as it so happens that I discovered some 20 or so years ago, that they are all using division and multiplication to formulate relationships involving influence and causation [I omit calculus limits for those unfamiliar with them], and minimally using subtraction and addition. Gulliver then reformulates all of their theories using subtraction and/or addition, and it turns out that all of the resulting theories are completely different from the old ones. Not one person among all the island's so-called geniuses had come up with the very tiny idea of changing from division/multiplication to subtraction/addition in all of their work. Upon presenting this fact to the gathered people of the island, the people debate for a long time, and then decide that Gulliver knows more, so they decide to drop their entire four fields and start all over again much more slowly, this time not racing to greater complication before analyzing the simple concepts that they are using. The name Socrates is mentioned as an example. The predictions of several popular science writers on the island such as Professor Kaku to the effect that computers are going to almost literally swamp everything else are accordingly considerably modified to say the least. Osher Doctorow - Original Message - From: Tim May [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Saturday, November 30, 2002 2:37 PM Subject: Alien science On Saturday, November 30, 2002, at 01:32 PM, Ben Goertzel wrote: ... I think this is certainly a plausible prediction of the future, but I see it as an unlikely one. I think that intelligent software programs will be brought into existence within the next 10-50 years, and that among other effects, this will cause a physics revolution. Furthermore, it will be a revolution in a direction now wholly unanticipated. It will be interesting and exciting if you are right, but I think the kind of AI you describe above and below is further off than 10-30 years, though perhaps not 50 years. Right now we analyze data about the microworld in a very crude way. For example, we scan Fermilab data for events -- but what about all the other data that isn't events but contains meaningful patterns? Create an AI mind whose sensors and actuators are quantum level, and allow it to form its own hypotheses, ideas, concepts, ontologies Do you really think it's going to come up with anything as awkward and overcomplex as our current physics theories? I have no idea. True, it may come up with all sorts of weird theories. But, absent new experimental evidence, will these new theories actually tell us anything new? Your point about AIs exploring physics is an interesting one. And you are right that Egan has his AIs, his uploaded Orlandos and even his computer-produced Yatima, looking very much like humans. Not at all like the Entities of Vinge's Deepness, Zindell's Neverness, or Stephenson's Hyperion series. But let us imagine that an advanced AI were to be turned loose on a Newtonian world. I can well imagine that such an entity, left to its own devices, might come up with weird names for inertia, mass, friction, etc. Perhaps even synthetic combinations of what we take to be the basic vectors of classical mechanics. Instead of 3-space being so primal, phase spaces of 6, 18, and even many more dimensions would perhaps be more natural to such a mind. (Needless to say, given that today's best AI programs and computers are having a very hard time even doing naive physics, a la ThingLab and its descendants, I'm not expecting progress very quickly. And ThingLab is more than 20 years old now, so expecting massive breakthroughs in the next 10-20 years seems overly optimistic.) More importantly, would an AI version of classical physics, complete with incomprehensible (to us) phase spaces and n-categories and so on, including constructs with no known analogs in our current universe of discourse, would this version give any predictions which differ from our own? In short, would the AI's version of physics give us any new physics? My hunch is no. It might be better at solving some problems, just as the mental architecture of birds may give them much better abilities to solve certain kinds of 3D problems than we have had to evolve, and so
Re: Good summary of Bogdanov controversy
From: Osher Doctorow [EMAIL PROTECTED], Sunday Nov. 10, 2002 5PM Thanks to Tim May for the site reference. I read the story, and it's quite interesting. It's the first time I've looked at this in detail, although I heard a rumor about it. I have a few comments that I'd like to make now. 1. The acceptance of nonsense for publishing or Ph.D.s or M.A.s or M.S.s is obviously wrong. 2. The cause of the acceptance needs to be investigated by scientists and philosophers and others. 3. History tells us a few things about nonsense if we study it carefully, especially the history of Creative Geniuses like Beethoven, Shakespeare, Paul Dirac, Einstein, Schrodinger, Socrates, Plato, Mozart, etc. I will itemize these below beginning with 4, but I'll just mention that they fall under Mediocrity, Ingenious Imitation, and Creative Genius. 4. Mediocre scientific people in my definition don't even have the ability to imitate (see below). 5. Ingenious Imitators in science (and similarly for music, literature, etc.) imitate other scientists but only go 0 or 1 step ahead of whomever they are imitating. 6. Creative Geniuses go more than 1 step ahead of anybody else working on the same or similar problem or anybody else in the field or subfield. 7. Having spent most of my 63 years of life in Academia, both as a student and as a teacher/researcher in mathematics including statistics and mathematical physics, it is my opinion that more than 99% of mathematicians and physicists are Ingenious Imitators, and I have a stong suspicion that this is the case in most other academic fields. 8. Peer review is the usual way of determining which papers are published in scientific journals, and it follows from 7 if I am correct that most peer reviewers are Ingenious Imitators, and therefore that what gets published in most journals is at most one step ahead of the previous person (and possibly 0 steps ahead). 9. The solution to the problem of 8 and similar difficulties with Ph.D. and Masters Degrees is in my opinion a positive one rather than a negative one, namely, to foster more Creative Geniuses in Mathematics and Physics (and other fields). 10. In my opinion, Ingenious Imitators can become Creative Geniuses with sufficient education, tolerance, practice in accepting and thinking up new ideas, learning tranquility rather than anger or fear, and guidance from other Creative Geniuses or Creative Problem Solvers (a sort of borderline type between Creative Genius and Igenious Imitators, which I'll explain another time hopefully). Giving up Materialism, including Money-Related Materialism, Power Materialism, and Sensation Materialism, which includes giving up bureaucracy or the interest in becoming part of it, is key in this. Osher Doctorow, Ph.D. One or more of California State Universities and Community Colleges (Mathematics, Statistics) - Original Message - From: Tim May [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Sunday, November 10, 2002 12:44 PM Subject: Good summary of Bogdanov controversy A good summary of the Bogdanov controversy is in the New York Times today. URL is http://www.nytimes.com/2002/11/09/arts/09PHYS.html Some of the folks we like to quote here are quoted in the article, including Lee Smolin, John Baez, Carlo Rovelli, etc. Also, the latest Wired print issue has a fairly good survey article by Kevin Kelly about theories of the universe as a cellular automaton. Konrad Zuse gets prominent mention, along with Ed Fredkin. I didn't read the article closely, so I didn't notice if either Tegmark or Schmidhuber were mentioned. The usual stuff about CA rules, Wolfram's book, etc. Things have been quiet here on the Everything list. I haven't been commenting on my own reading, which is from books such Physics Meets Philosophy at the Planck Scale and Entanglement. Isham's collection of essays on QM should arrive momentarily at my house. My interest continues to be in topos theory, modal logic, and quantum logic. --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: Good summary of Bogdanov controversy
From: Osher Doctorow [EMAIL PROTECTED], Sunday Nov. 10, 2002 5:45PM Duraid, Well said! I am very happy that some Australians have a sense of humor, which I hadn't realized until now. I know that British and Irish humor are excellent. USA humor varies between the mediocre and the sublime. This reminds me of the last time that I wrote similarly about Creative Genius on the internet to a forum of rather incompetent (mostly) teachers, after which one teacher replied with a hysterical email accusing me of implying that I am a Creative Genius and everybody else is ___ (expletive deleted). Her argument was that teachers are so dedicated and loving and kind and generous and...etc., that to criticize them was tantamount to blasphemy. I hesitated to tell her (and I did not) that expletives deleted as a way of life are more common among the Mediocre than other categories in my opinion. My wife, Marleen J. Doctorow, Ph.D., a licensed clinical psychologist for over 30 years, would be very proud of me if she had any time left after her patients. Oops! Did I imply anything about her? If so, I withdraw my last sentence. : ) Osher - Original Message - From: Duraid Madina [EMAIL PROTECTED] To: [EMAIL PROTECTED] Cc: [EMAIL PROTECTED] Sent: Sunday, November 10, 2002 5:39 PM Subject: Re: Good summary of Bogdanov controversy 1. The acceptance of nonsense for publishing or Ph.D.s or M.A.s or M.S.s is obviously wrong. 4. Mediocre scientific people in my definition don't even have the ability to imitate (see below). Why are you being so hard on yourself?? Tongue firmly pressed against cheek, Duraid
Enormous Body of *Evidence* For Analysis-Based TOES
From: Osher Doctorow [EMAIL PROTECTED], Mon. Sept. 23, 2002 12:32PM I refer readers to http://www.superstringtheory.com/forum, especially to the String - M Theory - Duality subforum of their Forum section (membership is free, and archives are open to members, and many of my postings are in the archives), during the last few days, in which I have provided literature references and sites from very recent research mostly that puts Analysis via determinants and/or negative exponentials at the forefront of science - not merely the interesting Fredholm type determinants and the Slater determinants, but determinant maximization in general (with constraints). Fields crossed by these include quantum theory, general relativity, information theory, communications theory, experimental design, system identification, statistics as a whole, geometry, computer programming, entropy, experimental design, algorithms including path-finding algorithms for convex optimization, etc. Let me very briefly recapitulate why determinants are Analysis-based rather than Algebra-based. The expression 1 + y - x, which can be generalized to c + y - x for arbitrary real constant c (or even to non-real expressions, but that is another story) or simply written y - x with incorporation of c into y or x, is continuous and CRITICAL to outgrowths of Analysis including probability-statistics (for Rare Event scenarios), fuzzy multivalued logics (see below for those who believe that logic is algebraic), proximity functions, geometry-topology based on proximity functions. Determinants generalize y - x to a finite alternating series. Alternating series in general generalize determinants. The same site (earlier postings) explains why fuzzy multivalued logics and logics in general are Analysis-based rather than Algebra-based, although many mathematical and non-mathematical logicians unfamiliar with Analysis have believed otherwise. Osher Doctorow
Re: Tegmark's TOE Cantor's Absolute Infinity
From: Osher Doctorow [EMAIL PROTECTED], Sat. Sept. 21, 2002 11:38PM Hal, Well said. I really have to have more patience for questioners, but mathematics and logic are such wonderful fields in my opinion that we need to treasure them rather than throw them out like some of the Gung-Ho computer people do who only recognize the finite and discrete and mechanical (although they're rather embarrassed by quantum entanglement - but not enough not to try to deal with it in their old plodding finite-discrete way). Mathematics and Physics are Allies, more or less equal. I prefer not to call the concepts of one inferior directly or to indirectly indicate something of the sort, unless they really are contradictory or something very, very, very close to that more or less. As for a computer, maybe someday it will be *all it can be*, but right now I have to quote a retired Assistant Professor of Computers Emeritus at UCLA (believe it or not, bureaucracy can create such a position - probably the same bureaucratic mentality that created witchhunts and putting accused thieves' heads into wooden blocks so that they could be flogged by passers-by in olden times), who said: *Computers are basically stupid machines.*We knew what he meant. They're very vast stupid machines, and sometimes we need speed, like me getting away from the internet or I'll never get to sleep. Osher Le Doctorow (*Old*) - Original Message - From: Hal Finney [EMAIL PROTECTED] To: [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Saturday, September 21, 2002 7:18 PM Subject: Re: Tegmark's TOE Cantor's Absolute Infinity Dave Raub asks: For those of you who are familiar with Max Tegmark's TOE, could someone tell me whether Georg Cantor's Absolute Infinity, Absolute Maximum or Absolute Infinite Collections represent mathematical structures and, therefore have physical existence. I don't know the answer to this, but let me try to answer an easier question which might shed some light. That question is, is a Tegmarkian mathematical structure *defined* by an axiomatic formal system? I got the ideas for this explanation from a recent discussion with Wei Dai. Russell Standish on this list has said that he does interpret Tegmark in this way. A mathematical structure has an associated axiomatic system which essentially defines it. For example, the Euclidean plane is defined by Euclid's axioms. The integers are defined by the Peano axioms, and so on. If we use this interpretation, that suggests that the Tegmark TOE is about the same as that of Schmidhuber, who uses an ensemble of all possible computer programs. For each Tegmark mathematical structure there is an axiom system, and for each axiom system there is a computer program which finds its theorems. And there is a similar mapping in the opposite direction, from Schmidhuber to Tegmark. So this perspective gives us a unification of these two models. However we know that, by Godel's theorem, any axiomatization of a mathematical structure of at least moderate complexity is in some sense incomplete. There are true theorems of that mathematical structure which cannot be proven by those axioms. This is true of the integers, although not of plane geometry as that is too simple. This suggests that the axiom system is not a true definition of the mathematical structure. There is more to the mathematical object than is captured by the axiom system. So if we stick to an interpretation of Tegmark's TOE as being based on mathematical objects, we have to say that formal axiom systems are not the same. Mathematical objects are more than their axioms. That doesn't mean that mathematical structures don't exist; axioms are just a tool to try to explore (part of) the mathematical object. The objects exist in their full complexity even though any given axiom system is incomplete. So I disagree with Russell on this point; I'd say that Tegmark's mathematical structures are more than axiom systems and therefore Tegmark's TOE is different from Schmidhuber's. I also think that this discussion suggests that the infinite sets and classes you are talking about do deserve to be considered mathematical structures in the Tegmark TOE. But I don't know whether he would agree. Hal Finney
Re: Tegmark's TOE Cantor's Absolute Infinity
From: Osher Doctorow [EMAIL PROTECTED], Sat. Sept. 21, 2002 10:39PM I've glanced over one of Tegmark's papers and it didn't impress me much, but maybe you've seen something that I didn't. As for your question (have you ever been accused of being over-specific?), the best thing for a person not familiar with Georg Cantor's work in my opinion would be to read Garrett Birkhoff and Saunders MacLane's A Survey of Modern Algebra or any comparable modern textbook in what's called Abstract Algebra, Modern Algebra, Advanced Algebra, etc., or look under transfinite numbers, Georg Cantor, the cardinality/ordinality of the continuum, etc., etc. on the internet or in your mathematics-engineering-physics research library catalog or internet catalog. To answer even more directly, here it is. *Absolute infinity* if translated into mathematics means the *size* of the real line or a finite segment or half-infinite segment of the real line and things like that, and it is UNCOUNTABLE, whereas the number of discrete integers, e.g., -1, 0, 1, 2, 3, ..., is called COUNTABLE. If you accept a real line or a finite line segment or a finite planar geometric figure like a circle or a 3-dimensional geometric figure like a sphere as being *physical*, then *absolute infinity* would be physical. If you don't accept these as being physical, then you can't throw them out either - if you did, you'd throw physics out. So there are *things* in mathematics that are related to physical things by *approximation*, in the sense that a mathematical straight line approximates the motion of a Euclidean particle in an uncurved universe or a region far enough from other objects as to make little difference to the problem. There are also many things in mathematics, including the words PATH and CURVE and SURFACE, that also approximate physical dynamics. Do you see what the difficulty is with over-simplifying or slightly misstating the question? Osher Doctorow - Original Message - From: [EMAIL PROTECTED] To: [EMAIL PROTECTED] Cc: [EMAIL PROTECTED] Sent: Saturday, September 21, 2002 6:59 PM Subject: Tegmark's TOE Cantor's Absolute Infinity For those of you who are familiar with Max Tegmark's TOE, could someone tell me whether Georg Cantor's Absolute Infinity, Absolute Maximum or Absolute Infinite Collections represent mathematical structures and, therefore have physical existence. Thanks again for the help!! Dave Raub
A New Start
From: Osher Doctorow [EMAIL PROTECTED], Fri. Sept. 6, 2002 8:36AM After my discouragement of yesterday, I have decided to give myself one more chance to try to be compatible with everything-list. I have just downloaded J. Schmidthuber's *A computer scientist's view of life, the universe, and everything,* (1997), and it is well enough written that I apparently will be able to understand it. I also have one of the other two papers that were available on the everything-list site, which I understood fairly well several weeks ago. I will take this opportunity to write/type a few words about Knowledge (K for short) rather than information (I), distinguishing between them as the semantic (meaning) part of that whose syntactic part is information vs information itself. There are several directions in which I have developed K, but the simplest way is to consider that K contains primitive pointlike or stringlike elements which may have fuzzy truth values (on a scale between 0 and 1 for the non-trivial cases) or probabilities or both assigned to them. Let us call these K-points for brevity. Each K-point has MEANING, and I will regard this as a primitive undefined concept in this presentation, although one can develop things from several other viewpoints.The word *MEANING*, however, is to be used in practice rather similarly to its dictionary definition(s) and intuitively is like ideas, thoughts, cognitions, provided that they are accompanied by *understanding* rather than merely regarded as sounds or sights or perceptions with nothing that can be specified behind them. I do relate it here at all to the computational linguistics idea of *meaning*. Knowledge (K) is regarded as continuous or piecewise continuous and connected or piecewise connected, and could theoretically either increase or decrease or remain constant, although in fact I postulate somewhat analogously although apparently not structurally related to entropy in thermodynamics that K increases in time in the universe. In fact, letting E symbolize entropy, I postulate that the rate of increase of K in time exceeds the rate of increase of E in time, symbolically: 1) Dt(K - E) 0 where Dt is the partial derivative with respect to time, although I am open to generalizing it to covariant or gauge derivatives and so on. Equation (1) has an interesting interpretation, namely, that instead of disorder increasing overall in the universe with time, the ordered part of Knowledge increases with time - possibly by matter converting to radiation in whole or in part, or possibly by some other scenario. Even the notion of a radiation form of life is not excluded in these considerations - in fact, it may be indicated. It might be in some places combined with material form of life, as in the human brain, where the global aspects may relate more to radiation and the local aspects more to matter. There is a well accepted physical theory of the initial radiation-dominated era of the universe succeeded by a matter-dominated era in which radiation still plays an important part, and several theorists consider that a radiation type of era will eventually constitute a third era. Does this mean that digital computes do not do anything?No. They calculate very fast. They store discrete steps and discrete Knowledge representations (or attempted representations via syntax) and discrete syntax. When they calculate very fast, they sometimes produce numerical approximations to solutions of differential or integral equations which we do not know how to produce otherwise, and this helps increase Knowledge, although I think that is it qualitatively somewhat inferior to CAUSAL KNOWLEDGE. There is factual knowledge (details) about the real world, there is causal knowledge about what causes or influences what in the real world, and there is speculative or even fictional or fantasy *knowledge* about things or events or processes that are not considered to be real or to have real analogs in the real physical or even psychological worlds. Digital computers can help factual knowledge, but so far they have not helped causal knowledge much. Does K (Knowledge) relate to multiple universes, multiple histories, etc.? This is a more advanced question than I can deal with here. I think that multiple universes and multiple histories are interesting ideas, but that at the present time their logical and physical and philosophical structures have not been well established. If they exist, then I have no doubt intuitively that K applies to them as well. Finally, the mathematical formulation of Causal Knowledge in my Rare Event Theory (RET) resides in fuzzy multivalued logical x--y or its probability-statistics analogs or proximity function - geometry-topology analogs.There are 3 types of x--y, which correspond respectively to Rare Events (Lukaciewicz and Rational Pavelka fuzzy multivalued logics (FML) in the non-trivial case), Fairly Frequent Events (Product
Serious *Mistake* by Schmidthuber
From: Osher Doctorow [EMAIL PROTECTED], Fri. Sept. 6, 2002 11:45AM I have read about half of J. Schmidthuber's *A computer scientist's view of life, the universe, and everything,* (1997), and he has interesting ideas and clarity of presentation, but I have to disagree with him on a number of places where he uses conditional probability including his section Generalization and Learning. I hasten to add that I do not view alternative theories as *wrong* but as competing and that they should almost all survive for competition, motivation, and also because many of them turn out to have useful contributions long after they have been regarded as *discredited*. Schmidthuber (S for short) concludes that generalization is impossible in general by using a proof based on conditional probability, and similarly he concludes that the learner's life in general is limited by also a conditional probability proof. Most readers will undoubtedly stare at this statement in bewilderment, since as far as they know nothing is wrong with conditional probability. They are partly correct and partly wrong. Nothing is wrong with conditional probability, which is the main tool of the Bayesian school (or as I abbreviate it, the BCP or Bayesian Conditional Probability-Statistics school), for Fairly Frequent Events.For Rare Events, something very strange happens. This was how my wife Marleen and I began our exploration of Rare Events in 1980. Conditional probability divides two probabilities and regards that as an indication of the probability of one event *given* another event, where *given* is used in the sense of *freezing the other event in place*. Some real analysis experts will argue that this is all justified by the Radon Derivative of the Lebesgue-Radon-Nikodym theorem(s), not quite realizing that the proof of those theorems only hold up to equivalence classes outside sets of measure ZERO. But events of probability zero are the Rarest Events. Moreover, division of probabilities blows up even in small (one-sided) neighborhoods of probability 0 since division by 0 is impossible. Thus, not only can conditional probability not model events of probability 0, but it cannot even model events of probability close to 0 (Rare Events). Is there a simple solution? Yes!Product/Goguen fuzzy multivalued logical implication x--y is defined as y/x for x not 0. So it corresponds to conditional probability where x and y are carefully chosen probabilities in the probability-statistics analog. Lukaciewicz and Rational Pavelka fuzzy multivalued logical implications (Rational Pavelka is the predicate logic generalization of Lukaciewicz propositional logic) are x--y = 1 + y - x for y = x for the non-trivial case. The latter does not involve division by 0 and does not blow up in any (one-sided) neighborhood of zero. Logic-Based Probability (LBP) uses precisely the same definition of 1 + y - x in place of y/x for exactly the same probabilities x, y which BCP uses. My wife and I introduced LBP in 1980. It may be remarked here the Godel fuzzy multivalued logic, which we showed applies to Very Frequent (Very Common) Events, uses x--y = y and refers in the probability-statistics analog to INDEPENDENT events, and since in general events are not independent unless that can be established in special cases, LBP is the correct result to use. So when S claims that generalization is impossible in general and that the learner's life is limited in general, he has to be referring to Fairly Frequent Events, not Rare Events or even Very Frequent Events (which use the Godel analog). But surely that leaves much room for S to maneuver in?In a way, yes, and in a way, no. S is very interested in the Great Programmer or even a decreasing sequence of Great Programmers each delegating authority to the other in different universes and so on. The Great Programmer thinks on the level of the Universe or All Universes or the particular Universe in the sequence. So we have to ask: which type of fuzzy multivalued logic or its probability-statistics analog (or proximity function - geometry - topology analog, which we developed as exact analogs of the above) most influences the Universe(s)? The answer turns out to be very simple, namely Lukaciewicz/Rational Pavelka (Rare Event) or its probability-statistics analog LBP.This is because in our universe it is generally agreed that a Rare Event called a Big Bang occurred (I have proven that even if it did not, as in Steinhardt-Turok and Gott-Li cyclic or backward time loop cosmological theories, LBP is the key influence probability), and that very rare events such as inflation and the transition from radiation-dominated to matter-dominated eras and transition from non-accelerating to accelerating universe which fairly recently occurred - that all of these Rare Events played critical roles in the development of the Universe. I should also mention that Shannon Information-Entropy and its
Re: Serious *Mistake* by Schmidthuber
From: Osher Doctorow [EMAIL PROTECTED], Fri. Sept. 6, 2002 6:17PM Bill Jefferys says: Nonsense. It's done all the time for events of low probability. If *doing something all the time* is your reply to nonsense, then can I assume that not doing something is your reply to *sense*?Ah well, the subtleties of logic! Do you really want to argue about division by 0 and near 0 denominator? Why don't you think about if for a few days or weeks. I would hate to see you lose so easily. Osher Doctorow - Original Message - From: Bill Jefferys [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Friday, September 06, 2002 2:19 PM Subject: Re: Serious *Mistake* by Schmidthuber At 12:20 PM -0700 on 9/6/02, Osher Doctorow wrote: Thus, not only can conditional probability not model events of probability 0, but it cannot even model events of probability close to 0 (Rare Events). Nonsense. It's done all the time for events of low probability. Bill
Re: Schmidhuber II implies FTL communications
From: Osher Doctorow [EMAIL PROTECTED], Thurs. Sept. 5, 2002 5:07PM Wei Dai, Good! I will try to access the paper almost immediately. I have long been partial to FTL as a conjecture. When Professor Nimtz of U. Koln/Cologne came up with his results, or shortly thereafter, and interpreted them favorably toward FTL, I emailed him, and he was kind enough to send me copies of some of his papers by regular (*snail*) mail/post. Some of the non-Analysis school have indicated here and on other forums that the pendulum has swung too far away from algebra/arithmetic/number theory, but the loop theorists like Smolin and Ashtekar and a number of people in string/brane/duality theories who follow their leads, not to neglect the MacLane/Lawvere Category theorists in mathematics and physics, actually constitute an extremely large Mainstream today rather than a downtrodden minority (although the Gauge Field Theorists still claim the *largest Mainstream* title). My tendency is to follow the least popular path in science and in several other fields. That was the way of life of Socrates, and also of many of the greatest Creative Geniuses in history - including Kurt Godel, who is still being berated by conformists shuddering at the thought that there might be limitations as to what assumptions can lead to. Osher Doctorow - Original Message - From: Wei Dai [EMAIL PROTECTED] To: Russell Standish [EMAIL PROTECTED] Cc: Hal Finney [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Thursday, September 05, 2002 4:50 PM Subject: Schmidhuber II implies FTL communications On Mon, Sep 02, 2002 at 12:51:09PM +1000, Russell Standish wrote: This set of all descriptions is the Schmidhuber approach, although he later muddies the water a bit by postulating that this set is generated by a machine with resource constraints (we could call this Schmidhuber II :). This latter postulate has implications for the prior measure over descriptions, that are potentially measurable, however I'm not sure how one can separate these effects from the observer selection efects due to resource constraints of the observer. I just found a paper which shows that if apparent quantum randomness has low algorithmic complexity (as Schmidhuber II predicts), then FTL communications is possible. http://arxiv.org/abs/quant-ph/9806059 Quantum Mechanics and Algorithmic Randomness Authors: Ulvi Yurtsever Comments: plain LaTeX, 11 pages Report-no: MSTR-9801 A long sequence of tosses of a classical coin produces an apparently random bit string, but classical randomness is an illusion: the algorithmic information content of a classically-generated bit string lies almost entirely in the description of initial conditions. This letter presents a simple argument that, by contrast, a sequence of bits produced by tossing a quantum coin is, almost certainly, genuinely (algorithmically) random. This result can be interpreted as a strengthening of Bell's no-hidden-variables theorem, and relies on causality and quantum entanglement in a manner similar to Bell's original argument.
Re: Schmidhuber II implies FTL communications
From: Osher Doctorow [EMAIL PROTECTED], Thurs. Sept. 5, 2002 5:43PM I have accessed the paper by Yurstever, and I want to mention that I have been pursuing the algorithmic incompressibility thread on [EMAIL PROTECTED] in connection with supersymmetric theories of memory. The reception there was partly one of interest from a member of the Royal Statistical Society, but lately two members have complained about (a) off-topic, and (b) too lengthy emails of mine. This is definitely progress toward the Socratic position, and I am encouraged. : ) I am very impressed by the algorithmic incompressibility viewpoint of randomness, although I should point out that it is only one (but a very good) viewpoint. Now I will continue reading the Yurtsever paper. Osher Doctorow
Page 2 of Yurtsever (relates to Schmidhubert II implies FTL communications)
From: Osher Doctorow [EMAIL PROTECTED], Thurs. Sept. 5, 2002 6:17PM I have now read page 2 of Yurtsever, having previous read page 1, and I must confess that his style does not quite have the clarity of my style - his is more like the clarity of Sigmund Freud's style : ) However, I am happy to see that he recognized the role of Godel's incompleteness theorem on his page 1. On page 2, Yurtsever put the cart before the horse in a sense by telling us what would happen if his theory turns out to be correct, but since he plans to prove it in pages 3ff, he can be forgiven for that. I notice in connection with his last 2 paragraphs of page 2, which run over into the first 2 paragraphs of page 3, that he seems to agree with Sir Roger Penrose and me (independently - I have never met Sir Roger) that brain activity cannot be faithfully simulated on a digital computer. Sir Roger, by the way, like me (I have been told) rather dislikes computers and does not (or at least when last I heard about it) even answer email on computers. I am slightly different in that I both write and answer email, but I rather dislike digital computers although I will defend to the death their right to have their own opinions. : ). I have not yet decided about quantum computers, analog computers, molecular computers, laser/light computers, etc. My argument about brain activity is far simpler than Sir Roger's - I derive it from mathematical fuzzy multivalued logics and their probability-statistics and proximity function-geometry-topology analogs, which does not make use of randomness as incompressibility or even computer randomness at all. Speaking of randomness, I pointed out that incompressibility randomness is only one interpretation of randomness. To those of us who grew up and spent at least half of our lives in the non-computer world (or at least, the not heavily computerized world), probability and statistics vs computer viewpoints are not quite the same thing. When somebody in one of my statistics classes tells me that something is random, I tend to be slightly put off. You see, everything is random in a sense in probability-statistics. Even the non-random world so-called is random, only the probability of the random part is near or at zero - which, strangely enough, does not mean impossible or the null set. Let me clarify the latter. The probability of an impossible event, like the probability of the null set, is zero. But an uncountably number of things have probability zero. In n-dimensional Euclidean space or even spaces that are rather similar to it, any n-k dimensional subset (k = 1, 2, 3, ..., n - 1) has probability zero provided that a continuous random variable has a distribution on that space or on a volume of space containing the events in question. The proof is the same as the corresponding proof for Lebesgue measure. Moreover, the same is true for time, not such space, since an event that occurs at only one point in time has dimension 0 in time, and so has dimension one less than the time dimension of 1, and so the above result holds. So in 3-dimensional Euclidean-like space or 3+1 Euclidean-like spacetime, points, strings, planes, plane figures or their approximations laminae, curves, lines, line segments, curve segments, 2-dimensional surfaces of 3-dimensional objects (e.g., the surface of the human brain, the surface of a human being which is usually skin, the surface of an organ, the surface of the earth, etc.), they all have probability 0 under the rather general assumption that a continuous random variable has a distribution on space(-time), e.g., the Gaussian/normal distribution. The events at or near probability zero, and likewise processes of those characteristics, are RARE EVENTS/PROCESSES (RARE EVENTS for short). Now that I have started elaborating, I will conclude with one other note of caution. In what might look like an Old Testament prohibition, I should say that *ALL IS NOT IN CONCATENATED STRINGS OF SYMBOLS.* In fact, it might be more accurate to say that almost nothing is in strings, but that might be misunderstood, so I restrain myself. In my theory, which I refer to as Rare Event Theory (RET), I distinguish between SYNTAX and SEMANTICS. Of course, computer people do that too, and computational linguists. But when push comes to shove, they mostly regard information as SYNTAX. In order not to confuse myself with computer people or computational linguists, I distinguish between information, which is syntactic, and KNOWLEDGE, which is semantic in the usual dictionary sense of MEANING - what symbols and words and propositions and sentences MEAN.I am not at all sure that incompressibility captures KNOWLEDGE so much as SYNTAX. However, we will let that pass for now, except for the slight detail that Knowledge, Memory, and Rare Events appear to coincide - although part of it is a well-motivated and well-indicated conjecture. In any case, I will continue
Re: Schmidhuber II implies FTL communications
From: Osher Doctorow [EMAIL PROTECTED], Thurs. Sept. 5, 2002 10:25PM I don't know whether Hal Finney is right or wrong after reading pages 5-8 of Yurtsever, since Yurtsever writes like David Deutsch and Julian Brown and so many other members of the quantum entanglement school - no matter how many words they put in, they always leave out interconnecting logic and physics. Most mathematical psychology models have in the past been of this type, believe it or not, which is probably why mathematical psychology is today one of the most backward fields. I think that, despite NASA's alleged use of chaos avoidance in some satellite or missile, chaos theory is more or less in the same boat. I spent some time on an internet forum discussing David Deutsch's work some time ago, and neither Deutsch nor his friends had the faintest idea what I was talking about, and the feeling is mutual. I used to think that misunderstandings between scientists (including mathematicians) are not usually deliberate, but I am beginning to even question that in reference to quantum entanglement because such dogmatism and intolerance and lack of spelling out steps characterizes the field. And it's OK with some people, because they've been doing that as a way of life with less complicated stuff and getting away with it! If nothing else, entanglement as a continuous or connected process/event can't be as easily faked or double-talked as entanglement as a bunch of discrete steps. Unless somebody has some comments to make about my work, much of which is at http://www.superstringtheory.com/forum, I'll go back to the forum where I can continue my continuous are piecewise continuous approach. Actually, they can reach me at [EMAIL PROTECTED],. if they have any useful comments. Osher Doctorow Osher Doctorow - Original Message - From: Hal Finney [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Thursday, September 05, 2002 7:32 PM Subject: Re: Schmidhuber II implies FTL communications Wei writes: I just found a paper which shows that if apparent quantum randomness has low algorithmic complexity (as Schmidhuber II predicts), then FTL communications is possible. http://arxiv.org/abs/quant-ph/9806059 This was an interesting paper but unfortunately the key point seemed to pass by without proof. On page 5, the proposal is to use entangled particles to try to send a signal by measuring at one end in a sequence of different bases which are chosen by an algorithmically incompressible mechanism. The assumption is that this will result in an algorithmically incompressible set of results at both ends, in contrast to the state where stable measurements are done, which we assume for the purpose of the paper produces algorithmically compressible results. The author writes: This process of scrambling with the random template T guarantees that Bob's modified N-bit long string of quantum measurements is almost surely p-incompressible..., and that Alice's corresponding string (which is now different from Bob's) is also (almost surely) p-incompressible It's not clear to me that this follows. Why couldn't Bob's measurement results, when using a randomly chosen set of bases, still have a compressible structure? And why couldn't Alice's? Also, does this result depend on the choice of an unbalanced system with alpha and beta different from 1/2? This short description of the signalling process doesn't seem to refer explicitly to special alpha/beta values. If not, could the procedure be as simple as choosing to measure in the X vs + bases, as is often done in quantum crypto protocols? If we choose between X and + using an algorithmically incompressible method, will that guarantee that the measured values are also incompressible? Hal Finney
Re: Time as a Lattice of Partially-Ordered Causal Events or Moments
From: Osher Doctorow [EMAIL PROTECTED], Tues. Sept. 3, 2002 8:26AM It also depends on the logic that one chooses (e.g., Lukaciewicz/Rational Pavelka and Product/Goguen and Godel fuzzy multivalued logics - see P. Hajek Metamathematics of Fuzzy Logics, Kluwer: Dordrecht 1998 for an excellent exposition except for his mediocre probability section).. See my contributions to http://www.superstringtheory.com/forum, especially to the String - M Theory - Duality subforum of their forum section (most of which is archived, but membership is free, and archives are accessible to members). Or my paper in B. N. Kursunuglu et al (Eds.) Quantum Gravity, Generalized Theory of Gravitation, and Superstring Theory-Based Unification, Kluwer Academic: N.Y. 2000, 89-97, which has some further references to my earlier work. Analysis including nonsmooth analysis does combine the discrete and the connected/continuous, but in my opinion it generally regards the discrete as an approximation to the continuous/connected or piecewise continuous/piecewise connected (pathwise, etc.). One confusing point, I think, is the tendency of many mathematical logicians to identify with algebra and in fact to claim that their field is a branch or outgrowth of algebra. This was originally claimed by *Clifford Algebra,* but Clifford himself and many of his wisest descendants/followers such as Hestenes of Arizona State U. realized than the opposite true - *Clifford Analysis,* *Spacetime Algebra,* and so on are typical terminology used by the latter and others to indicate that they are really dealing with analysis and geometry and related things. Why do so many mathematical logicians identify with algebra?Largely, in my opinion, because algebra is much more mainstream-accepted than mathematical logic (and popular, and respected, etc.), but also because algebra is abstract and mathematical logic seems to many of its practitioners to be more abstract than concrete. I have cautioned in various places that even in pure mathematics there needs to be a balance between abstractness/abstraction and concreteness/physical application. Analysis historically has had much more of this balance (rough equality of abstraction and concreteness). There are also many built-in biases in mathematical and theoretical physics, and one of them in my opinion is the bias toward dissolution of geometry at the sub-Planck level.Part of this is the pre-quantum computer bias toward the discrete and finite or at most countably infinite and the digital vs analog computer bias (in favor of digital computers). The real line and real line segments of course are uncountably infinite and connected, and thee would essentially be no applied mathematics or mathematical physics for example without it - and not much pure mathematics either.It helps to occasionally look back in mathematical history, especially to Georg Cantor's Contribution to the Theory of Transfinite Numbers, which even Birkhoff and MacLane in their algebra textbooks made sure to include. Of course, Birkhoff ended up in applied differential equations and hydrodynamics largely, but MacLane has never been accused of being Analysis-inclined to my knowledge, and Birkhoff started out at least algebraic. I hope that we can resist the temptation to go into absolutes. I am glad to see that you started your reply with a tolerant and compromising tone, and I will end this posting with a similar tone. The discrete and the connected are in my opinion different theories or parts of different theories overall, and they are also parts of different interpretations. My view is that science progresses by tolerating different theories and different interpretations for competition and because many supposedly wrong theories or interpretations end up much later having something useful to contribute. The majority of scientists (the *Mainstream* as I refer to them) do not subscribe to this view, but consider that science advances in a spiral by *killing off* the wrong theories or by only generalizing (including generalizing in the limit) the partly correct theories - the Law of the Jungle viewpoint of competition by (intellectual) warfare or *cannibalistic* absorbtion as opposed to the Competing Teams idea of competition in which one keeps other teams alive in order to keep competing and for motivation and ultimately because one respects them and regards them as like oneself trying to achieve the *Impossible Dream*. You may find my contributions to math-history (see the Math Forum and epigone sites) to be interesting in this regard. Osher Doctorow - Original Message - From: Tim May [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Monday, September 02, 2002 11:07 PM Subject: Re: Time as a Lattice of Partially-Ordered Causal Events or Moments On Monday, September 2, 2002, at 09:22 PM, Osher Doctorow wrote: From: Osher Doctorow [EMAIL PROTECTED], Mon. Sept. 2, 2002 9:29PM It is good to hear
Re: Time
From: Osher Doctorow [EMAIL PROTECTED], Sat. Aug. 31, 2002 9:52PM Hal Finney, John Mikes, and the others on the parts of this thread that I have read have contributed some interesting ideas and questions. I have not read the *time* articles in Scientific American, but I would like to put in a good word for at least the principle of inter-translating between quantitative and verbal languages, including the question of what to do about *rough* translations. Many quantitative people are very hesitant to publish in or contribute to the *popular* journals and literature including books and public-directed internet because they seem to feel that they would lose something important (*rigor*) in the translation and that their audience won't amount to *research material* anyway.I've taught mathematics/statistics and done research in mathematical physics and mathematical modeling at the college level (and occasionally Secondary levels) since the 1970s (I'm 63 years old), and I'm of the opinion that Creative Geniuses of the Leonardo Da Vinci and Pierre De Fermat level were verbal-quantitative geniuses (they happened to also be several hundred years ahead of their times, which is not quite true of many Nobel Prize winners). I would also say that Kurt Godel, Paul Dirac, Steven Weinberg (well, until recently anyway), Lord Francis Bacon, Shakespeare, Bach, Beethoven, Mozart, Vivaldi, Cervantes, Erwin Schrodinger, Einstein, G. 't Hooft, and Socrates especially reveal strong verbal-quantitative Creative Genius abilities and skills. In the process of translating back and forth between verbal and quantitative modalities, one stimulates associations and memories and ideas in both types of memory storage, and they seem to influence each other into further combinations and ideas. Largely because of this, I consider that it is better to translate *roughly* than not at all, and that if the main idea is conveyed, the details can wait to some extent for later if ever - the main ideas may well contribute to someone's Creativity. Scientific American and also various internet forums and discussion groups have done that mostly, and I like to point out that good side to them. I also think that the tendency to label *time* schools by individuals' names would better be changed to describing time schools by brief labels as to what they do. For example, *computer-time* versus *no special time-orientation* hardly seems a basis for categorizing time, although they could well contribute to some other categorization of time or something else. For myself, I think discrete versus continuous time and spacelike vs non-spacelike (in the sense of the 3+1 labellings vs the 4-dimensional ideas which just regard time as another spacelike axis or dimension) are more useful. Of course, it is interesting to ask how computers relate to time - and I think that we will eventually have to tackle the question of how quantum computers and analog computers for example differ from digital computers on this question. Osher Doctorow Ph.D. One or More of California State Universities and Community Colleges - Original Message - From: Hal Finney [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Saturday, August 31, 2002 2:25 PM Subject: Re: Time John Mikes writes: would it be too strenuous to briefly (and understandably???) summarize a position on time which is in the 'spirit' of the 'spirited' members of this list? It seems to me that there are two views of time which we have considered, which I would classify as the Schmidhuber and the Tegmark approaches. In the Schmidhuber view time is of fundamental importance, and in the Tegmark view it is basically unimportant. Schmidhuber models the multiverse as the output of a computational process operating on all possible programs. Since computation is inherently sequential, it imposes a time ordering on the output. It is natural to identify the time ordering of a computation with the time ordering of events in our universe. So the simplest interpretation of the Schmidhuber model as an explanation of our universe is to picture the computer as generating successive instants of time as it operates. An obvious problem with this is that time appears to have a more complex structure in our universe than in the classical Newtonian block model. Special relativity teaches us that simultaneity is not well defined. And general relativity even introduces the theoretical possibility of time loops and other complex temporal topologies. It is hard to see how a simple interpretation of Schmidhuber computation could incoporate these details. Stephen Wolfram considers some related issues in his book, A New Kind of Science. He is trying to come up with a simple computational model of our universe (not of the multiverse, but the same issues arise). In order to deal with special relativity he shows how a certain kind of computational network can have consistent causality even
