*Fixed Point Devolution* -- 12 Oct 1999 * Dreams are near the end. On 01 Sep 1999 23:42:52 GMT, ekans64@aol.com (Ekans64), to alt.dreams.lucid (subject: Evolution) wrote: >You know something just came to me when I was watching the news and >they wer debating on whether or not the theaory of evolution should >be taught in schools. Well one man said that what we’re hearing >about evolution being wrong from Christians is that they are >interpreting it all wrong and that jewish people thought that the >theory of evolution confirms what the bible says. I am not sure if >what the man said was all correct but if you think about it you can >kind of see how it could confirm it. The animals are created in the >same order as the animals were supposed to have evolved and last is >humans, just like in the theory of evolution. The Bible says that >they were created in just a few ‘days’ but perhaps a day to God is >much different than a day to people? Who knows. Well and also >evolution doesn’t say really how life started so maybe that guy was >write. But I would really like to know if jewish people really think >that the theory of evolution confirms what the bible says. If anyone >has answers, please reply. J.D. On Thu, 2 Sep 1999 20:17:50 +0300, “DreamWave” , to the original post, responded: >I’m not jewish but, >If they are leaving evolution out, >I demand that they leave teaching “round world” geography and >start teaching that world is flat (as in the Bible). >Well, the evolution theory might not be right but it’s got more >creditability than the Bible. > > . . . It matters not what you demand. It matters not what truth is. It only matters who has power, and what they do with it. Logic check (T or F): A religious power tells people the infallible interpretation and inference of the word of the prophets and the writings of the apostles, . . and they arrest, imprison and burn people for disagreeing or acting in discordance with the party line. a) Therefore, bible scripture truly *does* mean what the organization says it means, the said power-organization herewith acting in some sort of agency role for the god of the bible. b) If the power-organization operational word-of-god is discredited, then the bible scripture is necessarily proven invalid. Discourse: In our system, the power -- civic-wise -- is by assent of the people, by way of the form of democratic republic. The assent is obtained in whatever manner -- charismatic appeal, craft, trickery, whatever, -- and for whatever the purpose of the obtainer of the power, be that virtuous or evil. The appeal for the power is made to the coalition set of minds that will effect gain of the power. This said, a winning coalition set is comprised of quite simple minds that, generally, aren’t encumbered with talent to know an invalid argument (or even need an argument); if the right button is pushed, blatant invalid arguments are totally persuasive, and may be considered to be quite clever. A popular invalid argument form is to take the stupidest “argument” offered for the contrary conclusion, ridicule it, and since there are two conclusions, yours and theirs -- and you’ve just shown “their argument” to be totally stupid, then “necessarily” your conclusion is correct -- without having to present a logically valid argument to your conclusion. A variation on the above might be: see how stupid people are who accept that conclusion, therefore that conclusion is invalid; leaving (only) my conclusion, which is what you all wanted to hear, anyway. I was raised an evolutionist in my home and in public school. At the age of 18, I thought the fossil record was evidence of the fact of the theory of evolution -- like, the theory of gravity is shown to be true. I did not know then that I was indoctrinated in *A Lie* -- and not honestly informed -- in both domains. (The developmental environment is exampled by the TV nature shows -- PBS, Discovery, The Lying Channel.) (Incidentally, I don’t discuss the subject with my father who is abundantly kind to me, and whom I love. To this day, he affectionately recalls the episode with his high school teacher who was favoring creation over evolution, and when my father demanded “proof,” “an argument,” or whatever, the teacher could only say, like, that’s just the way it is. And my exercises in logic truly fly speedily over his head. You see, if, by definition, it is lacking in intelligent reason to suppose a creation process god, then any talk that in some way involves any idea other than thermodynamically insulated mechanistic process is foolishness. This, notwithstanding refinement of propositions to the fundamental presuppositions and premises.) The Creation Theory presupposes the fantasy that the different kinds of life came into being by way of a creation process that is supernatural, a process interposed on -- invasive upon -- the mechanistic nature processes. The creation process cannot be demonstrated scientifically -- i.e., shown by way of experiment -- and it must be presupposed by faith. Creation necessitates a god, or something, that purposed to do this creation, and tangentially might purpose to do something supernatural any time the god wanted. The fossil record is totally consistent with this generalized creation mechanism, i.e. it is totally consistent with the hypothetical system. The Evolution Theory presupposes the fantasy that the different kinds of life came into being by way of a mutation process that is natural, a process consistent with the mechanistic nature processes. The theory supposes that by way of genetic mutation and natural selection, new kinds came into being generationally linked to prior kinds. And this isn’t supposing just taller or more robust of the same kind, its supposing generational linkage to a different kind -- a biological thing, like in the case of sexed life forms, the two of which could not breed. The evolution process cannot be demonstrated scientifically -- i.e., shown by way of experiment -- and it must be presupposed by faith. The evolution system necessarily excludes a creation god, although it may allow a god so long as the god is irrelevant (or is, in a non-creation way, running the natural processes, which is saying the same thing, -- this form of god presupposable by faith). The fossil record is not consistent with this generalized evolution mechanism. Thru geological time, there are bunches of one kind, and then comes the appearance of bunches of an evolved kind -- with nothing evidentiary of the mutative development from the one to the other. Any explanatory theory for this, also, cannot be demonstrated scientifically and must be presupposed by faith. So why does the U.S. Government support one fantasy to the exclusion of the other? Because the disjoint fantasies engender disjoint political societies; and the powers that be believe in the evolution fantasy, by faith. The trick is preventing full disclosure to the simple minds -- along with all the persuasion schemes I mentioned at the outset. The foundational simple-mind lie is the redefinition of what a religion is. And it makes perfect sense to the believers in the religion of evolution (-- the usage of that term for which the evolutionist would quite likely consider totally in error, *because* of its redefinition). A religion *now* is presupposition by faith in a system of universe operation that incorporates a (relevant) god (or perhaps presupposes by faith a position on god and supernatural effects?). Evolution, presupposition by faith in a system of universe operation that does not incorporate a god or supernatural effects, is thus not religion -- it’s science. My thinking is that public financed education would better purpose to train people for life talent-wise, like, to prepare for social functions, to develop research and analytical skills, as opposed to shaping their minds to think “properly.” But that cannot be, for educating and indoctrinating the people is primary in political warfare. And, as a finance professor of mine once said, what good is power unless you use it. On Sun, 5 Sep 1999 09:45:56 +1000, “.Nisaba Merrieweather” in reference to the original post, wondered: > . . . > >How does this relate, in your opinion, to lucid dreaming - why is it >relevant? On Thu, 02 Sep 1999 10:20:53 GMT, lgardner@otter.mbay.net (Lisa Gardner) replied to the original post: >Well... there is an occult theory that evolution only happened >after *involution*, ie, a... “going inwards”, kinda... that >physical evolution only happened *after* the earth had made the >journey in successive steps from non-physicality into full >physicality, which is where it (and we) are now, according >to this theory. According to this theory, we are to move >upwards in successive steps into a less physical state. > >Following this theory, it could be the case that god’s creation >of man, the world, etc. describes the initial perios of creation, >that that occured before even *involution* took place, and >that the theory of evolution that we all know and love or hate, >may describe the evolutionary process which started to take >place only *after* we reached full physicality. > >Almost as if the whole involution/evolution were an equation >that could only be worked out recursively... god would devise >the equation, but the value of the equation could not actually >be worked out until the... equation had recursed “all of the >way” to the point where actual values (and not *just* variables) >were hit, and so values could be plugged into the equation >recursively now, and the value worked out in successive upward >recursive steps “on the way back up” to the point at which there >*were* no more variables. > >I can’t remember right now the correct mathematical lingo >for talking about the process of recursion more precisely, >hopfully there’s someone reading who does, who understands >what I’m saying here, and who can elaborate in a way which >makes more sense. > >anyway, physical evolution as we understand it these days >could correspond the working out of the value of the >equation based upon the set of basic elements of the >equation, those basic elements having been found by the >“downward working” or “solving” of the recursive equation >worked out by god. > >Involution would be “the solving of the equation”, physical >reality would be “the set of solutions to the equation”, >physical evolution as we like to think of it would be a small >part of the “plugging back into the now recursively defined >set of values of creation”. > >make sense to anyone out there? The bible would be talking >about involution, not evolution. > >Lisa You’re thinking back to the discrete math concept of the “recurrence relation” and perhaps “solving the recurrence relation.” Notation -- ‘n sub #’ means “n subscript #” .ge. means “greater than or equal to” and .le. means “less than or equal to” Definition -- A function f: N into R (the function f mapping N into R) is said to be *recursively defined* provided, for some positive integer ‘n sub 0’, the following hold: 1. The values of f(1), f(2), . . . , f(‘n sub 0’) are known. 2. For n > ‘n sub 0’, f(n) is defined in terms of f(1), f(2), ..., f(n-1). We call f(1), f(2), ..., f(‘n sub 0’) the *initial values* of f and refer to the equation describing f(n) in terms of f(1), f(2), ..., f(n-1) as a *recurrence relation* for f. Example: The Fibonacci recurrence relation -- f(n) = f(n-1) + f(n-2) for n .ge. 3 (1) and f(1) = f(2) = 1 The undergrad problem of “solving the (linear) recurrence relation” is to find an explicit formula for f(n). That is, to find a formula for getting f(n) just using *n* (as opposed to figuring f(n) by recursively progressing from the initial values, to the value of function for the nth term). Example from (1), above -- Initial valures: f(1) = f(2) = 1 f(3) = f(2) + f(1) = 1 + 1 = 2 f(4) = f(3) + f(2) = 2 + 1 = 3 f(5) = f(4) + f(3) = 3 + 2 = 5 . . . So the sequence is: 1, 1, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... . . . and you can get to f(whatever n) by figuring forward starting with f(3) and the initial values for f(1) and f(2). But find a formula for f(whatever n) explicitly in terms of *n*. There’s a recipe you have to follow (and along the way, you’ll have to factor an expression to get a general solution; then to get the specific solution that goes with the initial conditions -- you’ll have to solve *m* equations for *m* unknows, *m* being the number of initial values that were pre-defined). For the example (1), f(n) = {(1/sqrt5)[(1+sqrt5)/2]**n} - {(1/sqrt5)[(1-sqrt5)/2]**n} for n element of N, n .ge. 1 where, [sqrt5] means “the square root of 5” [**n] means “to the exponent n” So, that’s the value of the recursively defined function for any term *n*, obtainable without figuring forward all the way from f(1). But to where does this lead, in terms of your devolution - evolution scheme? You define a sequence from an explicit beginning (that does not converge, for the linear recurrence relation). A model with an explicite -- yet unknowable -- beginning doesn’t lend itself well to a continuous, infinite time-space system. To take your approach into a more useful model for “truth understanding,” which is to where this whole mind study leads -- What is Truth? -- you need to re-adventure the mind-realm of mathematics, where it begins in Analysis. Consider -- The Fixed Point Principle Definition. Let {X; rho} be a metric space and let f: X into X. The function f is said to be a contraction mapping if there exists a real number c such that 0 < c < 1 and rho(f(x), f(y)) .le. c rho(x,y) for all x, y elements of X. [The function rho is called the metric on X. rho(x,y) can be considered as the distance function of the metric space -- the distance from a point x to a point y. For example, Let X be the set of real numbers R, and let the function rho on RxR be defined as rho(x,y) = |x-y| (5.1.4) for all x,y elements of R, where |x| denotes the absolute value of x. We call rho(x,y) defined by Eq. (5.1.4) the usual metric on R, and we call the metric space {R; rho} the real line.] The following result is known as the fixed point principle or the principle of contraction mappings. Theorem. Let {X; rho} be a complete metric space, and let f be a contraction mapping of X into X. Then (i) there exist a unique point x* element of X such that f(x*) = x* (5.8.6) and (ii) for any ‘x sub 1’ element of X, the sequence {‘x sub n’} in X defined by ‘x sub n+1’ = f(‘x sub n’), n = 1, 2, . . . converges to the unique element x* given in (5.8.6). The unique point x* satisfying Eq. (5.8.6) is called a fixed point of f. In this case we say that x* is obtained by the method of successive approximations. What’s happening here is that when you operate the function on any value in X, and recursively operate the function on the prior “value of the function,” it doesn’t matter what value in X you started with, you approach the same value in the limit of the sequence, where f(x*) = x*. Note that it can be that X is an open and unbounded set -- like, the real line in R, space in R3, or time-space in R4. Yet, you can start with *any* point x in X, recursively operating the contraction mapping, and you necessarily end up at x*. To prove you get to x* it isn’t required that you define *what* x you started with, but just that you started with *some* x in the infinite set, and that f is a contraction mapping. The Fixed Point Theorem and proof is scanned in: FixedPointThm_bw300.bmp File size = 756 Kb (131 Kb zipped). Its a b&w bitmap scanned at 300 dpi. To view it, open Start -- Programs -- Accessories -- Imaging. From a simple link page . . . http://roswell.fortunecity.com/milkyway/416/summer/summer.html . . . select FixedPointThm.zip to download. An example of the Fixed Point Principle (that I made up) -- Let X = {x elements of R: (1 +1/n*) .le. x .le. n*, for any n* element of N .ge. 2} (Whatever n* you want, X is therewith defined.) So, for any n* you choose (an integer, 2 or greater), X is the set of real numbers from (1 + 1/n*) to n*. Let f:X into X be defined by f(x) = 1 + 1/x f(x) is a contraction mapping. (proof omitted) Demonstrating the fixed point principle: Choosing n* = 100, for example, X is the set of all real numbers from 1.01 to 100 Choose any ‘x sub 1’ from X, like, choose ‘x sub 1’ = 50 ‘x sub 2’ = f(‘x sub 1’) = 1 + 1/50 = 1.02 ‘x sub 3’ = f(‘x sub 2’) = 1 + 1/1.02 = 1.98039... ‘x sub 4’ = f(‘x sub 3’) = 1 + 1/1.98039... = 1.50495... ‘x sub 5’ = f(‘x sub 4’) = 1 + 1/1.50495... = 1.66447... . . . (You can quite simply program Excel to demonstrate these successive approximations.) The fixed point that successive approximations approach is the irrational number phi = 1.6180339... Its the number for which 1 subracted from it, is equal to its reciprocal (-- or, 1 added to it is equal to its square -- which is saying the same thing). phi - 1 = 1 / phi or phi = 1 + (1/phi) (You can solve for it by the quadratic formula, too.) It happens that if you take the Fibonacci series (1, 1, 2, 3, 5, 8, ...) defined above, and successively calculate f(n) / f(n-1), like, 2 / 1 = 2 3 / 2 = 1.5 5 / 3 = 1.666... 8 / 5 = 1.6 . . . in the limit, you approach the same number, phi. (This is a non-linear recurrence relation.) There is evidence in the design of the Pyramid in support of the conjecture that the designer, in 3500 B.C.E or whenever, knew about phi and the Fibonacci series, and purposed to bring attention to it. (And this is apart from the fact that phi is necessarily closely approximated given a pi-designed pyramid. The knowledge of pi and the purposeful pi-design is, except to one presupposing by faith the contrary, absolutely demonstrated). * Sunday, 19 Sep 1999, Drm: a) The scene: like a typical large room in a university center, like where there could be events or displays for people to pass by and see. People are lightly distributed around the room in small groups of association. Some portable tables are set up beside where I was standing. Right at the beginning, I pick up a small table -- knowing a few persons nearby are watching this, particularly noticing a middle-aged man and a college-type girl right by me who sort of know me. I proceed to a stairway carrying the table on top of my head, continuing down the stairs that go down to the ground floor level. b) I was on the sidewalk of a dark street, on a warm night -- but near me, the scene is moderately lighted. I’m pulling a wagon (radio flyer type) containing a set of my dad’s books that are in a cardboard sleeve for the set. Two out of the set of six were not in the cardboard sleeve -- a space for the two, and four were there. I was just moving them from where they had been in the house, to . . . wherever, another location nearby down the street -- but this was in like a downtown locale, late at night. c) I’m like in a mall, at where the main aisle opens to the side for one of the large stores. But where the large store would be is all covered over in gray, as if like gypsum board. For that matter, all the walls in view are like that -- the side walls along the passage to where the large store would be. No one is in the scene, as it begins like this, all quiet for a moment, and I’m seeing into this empty cul-de-sac. Then, . . . Crash! A battering ram machine come out of nowhere from the right, ramming into the wall along the left side of the passage. Now the action is frenzied. I see a guy, and he is, like, with me. Then, a robot character comes android-running out of the hole where the wall was crashed in (the battering machine is not around at this point). The robot was made to be a replica of the guy I had seen just before. The understanding of what’s going on is perceived by me densely as the action is fast but brief. The domain inside where the wall was rammed in, had been sealed off for a very long time. The robot was made in the likeness of a “founder” and the robot knew about this founder from its programming input of the historical records. And now, what was going on was -- when the robot came out -- he sees him, the founder, here for real, the one in whose likeness he was built. The domain was a sealed and protected enclave, as for an underground political civilization. It was like from a movie in which the government was established on good principle, but then evil corrupted the government power, and some holdouts to the original good principle had sealed off themselves, there maintaining the good principle for a very long time, holding the founders of the principle in a sort of reverence. The whole while, on the outside, the corrupt government prospered -- all the people of the land not caring, resigned to, whatever to, the corrupt government. The government held in high priority to eradicate the holdouts to the original, the prior government, -- they were the only ones who knew what the old government was -- the meaning of the constitution under which it was founded. (Like, so long as the documented historical fact was in existence, it was a threat to the Government Lie. If the memory of what truly *had been* could be erased, the Lie could not be necessarily found untrue.) The corrupt government was not a different government in law, but different in fact. It was not a “new” government -- like, not a new constitution with a new beginning, but it was a different government in “meaning” -- the same words, but with the meaning of the words changed. So the common people were able to be duped and herded in the grand tradition of the great heritage of the land. But the government power full well new it was a different government, that it had taken control exacting government upon the different principle, -- not by full disclosure to the people and the people’s assent to the change, but by subtle manipulation and calculation, they were able to change the meaning of the words of the constitution. So it was in *fact* a different government as much as if a new constitution had been devised with different words. But it was by *definition* the same government as the original one, because there was continuity to the original and the original was still in place -- just that the meaning of the words were changed. (Now, to the common person intellectual, extending his or her thoughtfulness toward a historical consideration of the nation’s constitutional law development -- this was good, because that was what was intended in the original meaning -- supposedly.) But this, really, was all above the common people’s minds to care about. The government was “good”, and any threat to it was “bad”. Right away, I run into the room inside of the big hole of rubble, stepping quickly over rubble pieces. Its like an office area, well lighted, -- what’s left after the battering ram machine bashed into the complex. I reach down to grab some of my important stuff -- time is of the essence. I grab a stack of a few plastic 1-inch notebooks -- all gray, except the one on top was purple with a yellow file folder tucked inside. (Its actually my notebook from the class on Discrete Stochastic Processes. Inside are the chalkboard notes, including a version of the fixed point theorem. Its from the chapter on “Expected Total Discounted Reward” -- i.e., determining the optimal decision policy for maximizing the present value of an infinite-horizon reward model (infinite series of of future rewards), each reward being obtained in a probability process operated according to the decision policy; and calculating the value of that maximized reward.) I take a moment arranging the notebooks in my hands. (If they are stacked with binder sides all aligned together, it gets uneven and they slip around.) Then, I’m seeing out onto like a vast enclosed monument. Nearest me is an enclosure of dark water -- like a reflecting pond. Rising above the water a couple feet is the perpendicular edge of what is like a pale beige plateau. What I’m seeing is a monument of like smooth marble. Cut out along the front edge that meets the dark reflecting pond is the center of the southern boundary of Texas. I see etched lines in the smooth, absolutely flat surface, noticing the boundary of Texas along adjoining state lines. The pond-monument interface is the Mexican boarder. I perceive the notion that, of the portion of the USA that is in the monument, the state lines are etched in the surface. But all of the USA is not in the monument. Along both the left and the right sides are very tall chain-link fences that run in straight lines off into the distance. Just estimating, they begin like where western New Mexico is and where Alabama is. What’s obvious to me is that the monument is physically here in the manner of a perspective drawing -- the fences, on the left and right, that are going off into the distance, are angling inward dramatically. When you do a perspective drawing, you can choose the imaginary point at which parallel lines going off into the distance would meet (if you drew them that far). So, you can make the perspective effect more or less pronounced. These fences in the dream-scape, which I knew went straight away in a single direction, angled inward (and upward) in a pronounce manner as if to a perspective point. I knew that the new-corrupt government had control outside the fences. The fence on the right was a ways away, and I wasn’t looking over there, but I knew things over there were the same as on the left where I was looking -- a hot sunny day, traffic on a multi-lane freeway, trucks, cars, dusty air -- everybody working -- and that’s what they wanted, just to keep working and everything was fine, . . and the government could do whatever it wanted. This scope of the conflict between the government and the “foundationists” I will call them, was beyond the awareness (or concern) of the satisfied, working people. The people were not apprised by the government of its concern over, attention to, the “foundationists.” (Remember, the common people aren’t supposed to know there *was* a change of government.) The “underground conflict” was between the government and the “foundationists.” The people were content working, and they worked for the economy of the government, they supported the government in whatever it wanted to do. Then (quite peaceful in this different scene), Seeing like a topographical map scene above an area of the Great Planes (an expanse a few hundred miles across, disappearing peripherally), in the center -- the river that flows east, that was originally named *Rio Jesus Maria* (-- recall, written on the inside of the ring worn by Jeanne d’Arc was, “JHESUS MARIA”). A moment in this scene, and a male narrator says, “There were two crop failures.” [end] It reminds me of what Will Durant wrote -- A nation is born stoic, and dies epicurean. At its cradle (to repeat a thoughtful adage) religion stands, and philosophy accompanies it to the grave. In the beginning of all cultures a strong religious faith conceals and softens the nature of things, and gives men courage to bear pain and hardship patiently; at every step the gods are with them, and will not let them perish, until they do. Even then a firm faith will explain that it was the sins of the people that turned their gods to an avenging wrath; evil does not destroy faith, but strengthens it. If victory comes, if war is forgotten in security and peace, then wealth grows; the life of the body gives way, in the dominant classes, to the life of the senses and the mind; toil and suffering are replaced by pleasure and ease; science weakens faith even while thought and comfort weaken virility and fortitude. At last men begin to doubt the gods; they mourn the tragedy of knowledge, and seek refuge in every passing delight. Achilles is at the beginning, Epicurus at the end. . . (and on Babylon --) . . . The army fell into disorder; business men forgot love of country in the sublime internationalism of finance; the people, busy with trade and pleasure, unlearned the arts of war. . . * * * * * * Reply to: angel_marvelzombie@yahoo.com