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Can Fractals Make Sense of the Quantum World?
Keith found a New Scientist story about fractals and quantum theory. The article says "Take the mathematics of fractals into account, says Palmer, and the long-standing puzzles of quantum theory may be much easier to understand. They might even dissolve away."
So, the problem wasn't that God was playing dice with the universe, rather, it's just a nice Julia set?
Einstein must be rolling in the dimensions of his grave. Fractionally, of course.
I've fallen off your lawn, and I can't get up.
And suddenly LOGO turns out to be the programming language we need to encode the formula for everything.
Go, little turtle, go!
Since I can't tell them apart, I treat all ACs as the same person.
Using fractals as a way of viewing a problem can be useful, but it doesn't fundamentally offer any new ways to solve a problem over conventional methods.
Isn't New Scientist the National Enquirer of the science world?
Fractals are basically the incorporation of decisions into iteratively applied functions of some kind. Physics normally uses mathematics of varying degrees of curves and shapes and spaces to describe things and these functions are continuous to a degree, and so its pretty reasonable to think that such descriptions could be imprecise. Math tends to see "switch and loop and jump" statements as inelegant and those are the essence of fractals.
This is my sig.
An old Canadian friend's brother turned out to be a mathematical physicist working at a Canadian university researching fractal spacetime. Garnet Ord's work supposedly reconciles the notoriously conflicting relativity and quantum mechanical models of spacetime. It seems that the time axis used to be treated as an integer variable, when in fact it's a fractional dimension: a fractal.
I'd say that making relativity and QM interoperate is a good way to "make sense of the quantum world".
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make install -not war
again EVIL people deny that only TIME CUBE can make sense of the world
Well after a brief scan of the actual article I have to admit it is an interesting idea that should be developed further however it isn't science yet. As I keep reminding some the students I work with, in science you create a theory that makes a prediction, test the prediction and if the prediction and experiment agrees go out for a beer otherwise you rethink the theory. If Palmer has developed a prediction, it is not mentioned in the article (or I didn't catch it in my brief glance).
Still an interesting idea that hopefully will eventually lead to some new theories and predictions about how particles behave.
If, as the article suggests, Palmer's theory eventually does away the need for multiple universes, then incalculable damage has been done to the world of science fiction. What fun is it if there isn't a world where the Nazi's won WW2? What's there in that for anyone?
So if I understand this correctly, Palmer is saying that the universe has a finite amount of information variables and at some certain point it will reach that limit? And that every time we try a thought experiment to measure either the position or a velocity of a particle, we risk overstepping that finite limit and thus get results where we can only measure one or the other because to do both sets us beyond the limit? So then can it be inferred that he's saying the universe has a limit then?
Here's to hot beer, cold women, and Glaswegian kisses for all.
Wow, and I thought it was only in computer science that you could talk buzzwords like this.
My first program:
Hell Segmentation fault
Is this something similar to In the Beginning was the Command Line theory of god creating the universe
The demiurge sits at his teletype, pounding out one command line after another, specifying the values of fundamental constants of physics:
universe -G 6.672e-11 -e 1.602e-19 -h 6.626e-34 -protonmass 1.673e-27....
and when he's finished typing out the command line, his right pinky hesitates above the ENTER key for an aeon or two, wondering what's going to happen; then down it comes--and the WHACK you hear is another Big Bang.
Maybe the universe command is a fractal generator and the earth is a insignificant whorl in the universal mandelbrot's set.
Or he could use quantum theory to explain fractals to me, didn't quite get it when John Gleick wrote about chaos in the late 80's
Anyway, want credits for the word 'Quantals' and now I'm off to RTFA.
The problem is that Bell's Thm. tests for hidden variables - essentially "deeper physics".
And Bell's Thm. has been verified repeatedly.
So, either he's arguing that Bell's Theorem is taking us down a blind alley, or he's going to have to figure out someway to make both the fractal understanding and Bell's true. The article in New Scientist doesn't discuss that at all.
In illa quae ultra sunt
Apiologists use buzzwords like this to describe the vascular layout of certain insects.
Knowledge is how to play a game, intelligence is how to win, wisdom is knowing what game to play.
That turtle is working hard holding up the whole Universe.
I only look human.
My mother is a halfling and my dad is an ogre, so that makes me an Ogreling
My friends all made fun of me and said it was just the LSD talking, but I knew I would come to understand the universe if I stared long enough at those posters!
"Wise men talk because they have something to say; fools, because they have to say something" - Plato
FEAR THE TURTLE!
Since I couldn't bother with RTFA, I'm gonna go with a definite maybe.
Quantum fractal chaos unique ergodicity entropy subshift.
After applying fractal math on quantum problems you could notice something dissolving... but is your mind, not the problem.
I did not read the article and I do not know much about Quantum Physics, but I know a thing or two about Hausdorff dimension. While it is an intriguing idea, I really doubt that it is instrumental to "making sense", unless by that they mean an explanation that only graduate students in Topology can understand.
Does Quantum Physics make sense?
No, Next question...
The article was pretty vague handwaving. It didnt actually how any problem was solved with fractal mathematics. It could have tried to explain one example.
No. No, they can't.
Squirrel!
Yes. Yes, they can.
Squirrel!
Comment removed based on user account deletion
Indeed, I do mean that Ord's work (and work like it) will make sense to only advanced mathematicians. But those people have crossed the border from order in the universe to sense in a human mind. Those people can influence scientists and engineers, who in turn inspire artists, which is when most people get a chance to see it make sense. Between art and products (and the very fuzzy boundary between them), eventually our culture encodes that sense. The math is the watershed, and we might already be across it. Discussions like this one on Slashdot are part of the followthrough.
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make install -not war
The article loses me almost immediately when it states that information is lost in a black hole. Anyone who's read Susskind's book knows that this implies all sorts of unpleasantness like the irreversibility of the the S-matrix, and so it is likely incorrect; ie, information is not lost when objects fall into a black hole. This makes sense, because to an outside observer, an object never falls into a black hole, it only approaches the event horizon without ever quite reaching it. Therefore, one would expect that information from objects falling into a black hole is written on the surface of the event horizon. This represents the highest information density possible. This is Susskind's thesis, and it was my understanding that it is becoming the accepted view. Stephen Hawking was a proponent of black-hole information loss, and Palmer was a student of Hawking (20 years ago). Therefore, it is not surprising his theory is based on rejected premises.
| He's not incorporated all of quantum theory into his fractal idea, so this is far from certain,
| but it is a lovely idea.
According to the official Star Trek "bible" given to script writers (it contains facts established
previously that new scripts are required not to contradict), aren't the "Heisenberg Compensators"
fractal dimensional devices?
Only vaguely related to this story but apparently, the mandelbrot shape has been found in cross-sections of magnetic field borders. I only found the reference from one page a while back though, so I can't say how true it is.
Why OpalCalc is the best Windows calc
From TFA:
"the invariant set of the universe"
Ain't that a nifty idea?
Isn't this the same as Stephen Wolfram's "A New Kind of Science"?
http://en.wikipedia.org/wiki/A_New_Kind_of_Science
Nassim Haramein put forth the theory of a fractal universe in 2008: http://theresonanceproject.org/research.html
From the author's abstract at http://arxiv.org/abs/0812.1148
The Invariant Set Hypothesis: A New Geometric Framework for the Foundations of Quantum Theory and the Role Played by Gravity
T.N.Palmer
"Combining these, an entirely analysis is given of the standard "mysteries" of quantum theory: superposition, nonlocality, measurement, emergence of classicality, the ontology of uncertainty and so on."
Palmer and Stephen Wolfram should talk.
who can read the real summary on arxiv? http://arxiv.org/abs/0812.1148
God was playing dice all along, people just failed to realise that dice (in the newtonian limit) are exactly what we consider them not to be, deterministic (under the specific definition adopted here) however the predictions made on the outcome sadly fall in to the regime of chaotic behaviour.
And naturally electrons and other particles, in their manybody couple dependence act just as the dice, deterministicly, but chaotic.
The copenhagen interpretation has been a major mindmelt with regards to making people truely understand quantum mechanics, because it strives for sensation, rather then explanation. The cat isn't both dead and alive, but if you take a 1000 cats, and try to describe the state of all of them with a single value of dead/alive, you end up with a superposition of the states, as anyone of sane mind would expect. What happend to the paradox? There was none.
So that's why you see fractals and patters when you trip on Mushrooms. Reality is a fractal! Man that's deep.
Comment removed based on user account deletion
I feel you're on to something here: Along the lines of the parent post I put on... let's assume that fractals are correct and that Palmer's right. Would that then mean that there is a limit to the universe, in terms of using fractals to make sure we get the calculation just right to avoid 'hitting nothing' when calculating position and velocity? If so, is non-existence quantifiable? Or does the act of measuring it increase existence? My head is starting to hurt here, so I'd like to ask if someone far more knowledgable than I am can answer this. What I'm thinking though, is that if Palmer's correct, then we might have found an edge of the universe (so to speak), and if we have, then wouldn't that put us a whole lot closer towards determining whether or not we are in a simulation (a better way to put it would be : we are the simulation?)
Here's to hot beer, cold women, and Glaswegian kisses for all.
Should be "separate the stack from the heap with his dword"
God is one of these role-play nerds then, with his 20 dimensional dice.
Typical ignorance from a whole number dimensional being. God's fractal dice have 23.5 dimensions.
No, his dice has e^pi dimensions. How could you ever think God's dice would not be transcendental?
God's dice have exactly e^(i*pi) dimensions! Either that or factorial(e^(i*pi)) dimensions. Or maybe both at the same time...
Those who can make you believe absurdities can make you commit atrocities. - Voltaire
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What we are talking about is the basic concepts in Chaos: self-similarity, superposition, and sensitivity to initial conditions.
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The article/author is using fractals, cause they look, well, visually appealing to the typical person (it gets the point across). Heck, I can make triangles fit QM to so point (i.e. Math is Math). But what we're talking about is applying a different set of principles, not of fractals, but actually Chaos Theory.
I agree :) Art is a great way to propagate complex ideas. After reading your reply I looked at a print I have on my wall, and thought that if I wanted to explain to a layperson what we do with foundations of mathematics, I could as well start by showing a picture.
I don't care how many universes there are. In each and every one of them, Fox is canceling SciFi shows I like.
Except for ending slavery, the Nazis, communism, & securing American independence, war has never solved anything.
Strictly speaking, from lower dimensionality of space-time at shorter scale doesn't follow, space-time has a fractal nature at all. The same observation can be made at water surface, where for shorter wavelengths we can observe a distortion of waves due the Brownian motion of water molecules. As the result, even at water surface very tiny 2D surface waves spreads like longitudinal 1D waves and nothing very strange is about it. It's not evidence for fractal or multiple Universe, just for the fact, space-time is composed of particle environment. In this way, such observation is rather evidence of particle Aether model, then the fractal nature of it and every notion of fractals is irrelevant here. BTW every decreasing of dimensionality is manifestation of ISL violation for light and gravity and Lorentz symmetry violation as well (therefore the violation of string theory, which is based on special relativity and it assumes the existence of additional dimensions instead of reduction of their number), etc... http://aetherwavetheory.blogspot.com/2006/07/aether-wave-theory-introduction.html
is very interesting. How can it ever be tested? It feels like a cheap explanation, but if it's indeed the case I wonder how we can ever really know it? I can't find very much credible discussion on this topic.
There is nothing puzzling about quantum theory. It is just unintuitive.
All the bizzare facts can be derived from two simple postulates:
1 - Quantum status are described in a complex vector space with inner product called the Hilbert space.
2 - Evolution of closed quantum systems is unitary. That is, reversible.
There's nothing bizzare about these. I have never seen anyone arguing about them. They can be used to derive quantum mechanics, and, together with the measurement postulate (the really weird one), explain all the experimental data we have.
So, where's the need for a "fractal theory" to "make sense" of quantum mechanics? All I see is a abstract full of buzzwords: "quantum theory of gravity should unify the causal non-euclidean geometry of space time with the atemporal fractal geometry of state space."
We need indeed a reformulation of quantum mechanics capable of accounting for relativity in a mathematically sound way. But that is not done batlantly disregarding experimental data (the Bell inequalities' violations).
entropy happens
Every so often, you get a scientist or mathematician who is
A) extremely smart (i.e., smarter than I am), and
B) just can't *stand* that QED is essentially non-deterministic.
And they posit that Bell was wrong, there's this previously ignored branch of mathematics (Cellular Automata, the stopping problem, and now fractals) that shows that it wasn't *really* random, that it's a deterministic function, and that given absolute knowledge of the universe at point A, you could model it to any point before or after, mathematically.
Of course, upon examination by other people (Also, sadly, smarter than I am), it turns out the underlying logic of Bell's Theorem applies equally to these other forms of mathematics, that they can't reproduce the actual results of QED any better than any other deterministic theory, and the universe is still irritatingly non-deterministic at a fundamental level.
I swear, it's the mathematical equivalent of intelligent design.
Pug
An Invisible Entity of Vast Power whose existence must be taken on faith alone: Liberal Media
Being a mathematician myself, I too find this theory quite refreshing. It seems to tie the scattering of complex ideas that I know as quantum physics into one nice little, intuitive package.
For instance, I've always wondered about the seemingly-coincidental, repetitious nature of the universe. Why is it that an electron is to a nucleus, like a planet is to a star, like a solar system is to a galaxy, like a galaxy is to a super cluster? This cyclic nature is well described and documented in fractals, http://www.ocf.berkeley.edu/~wwu/fractals/mandelbrot.html, and so, the universe having fractal roots makes sense.
Another example: the uncertainty of quantum measurements. Why must everything be measured in statistical values? The continuous nature of the fractal again gives nice intuition into this quandary as well. However, this point leads me to wonder just how reconcilable this mathematical simplification actually is. I'm not a physicist, but I do know that much of quantum physics deals with the concept of discrete: discrete time, energy quanta, etc. Fractals, are, by definition, continuous.
Are these two at all acquiescent?
in 1890s everyone of repute in science said that everything was discovered, science was over and we could go back to religion.
Are we so damn sure that nothing is faster than light which is also possibly tangible in some way, other than those freaking quantum jumps from here and now to then and there with just "instantaneous switching"?
for example a faster light, say light2.0, would "show" both photons and bigger particles.
Measuring would be easy because you could measure this slow thing called "light"(1.0)
Is this angle investigated?
We can get very absorbed with visible light, enough to skip the possibility, altogether, of a faster medium or state of matter.
Because, have we been observing a really large variety of physical phenomena and doing the computations and precise, complex math to exactly get the model fit the observed world.
The computers are good enough, but the models never are. Hence my question.
Are we always looking at an interrelated subset of the more general? Is there an assumption in there that can be disassumed and the whole picture changes even if nothing of that is yet observed?
Is there a whole bunch of calculations about every single application of the theory. The theories are good, because we are using those laws to make superb technology products which we could not, had materials now obeyed the equations we believe. So, I'm not saying that we're groping in our own deluded understanding, I'm asking whether we can be fully sure that NO OTHER material or tangible entity exists which is, for example, faster than light?
Palmer is certainly knowledgable about dynamical systems:
"The Invariant Set Hypothesis proposes that states of physical reality belong to, and are governed by, a non-computable fractal subset I of state space, invariant under the action of some subordinate deterministic causal dynamics D. The Invariant Set Hypothesis is motivated by key results in nonlinear dynamical-systems theory, and black-hole thermodynamics."
(This isn't unsuprising as he works at ECMWF, European Centre for Medium-Range Weather forecasts. Contemporary climate & weather researchers know all about nonlinear dynamical systems.)
In classical physics, the asymptotic distribution of states (where in state space a 'thing' could be) is known as the 'invariant set'.
The "action of a deterministic dynamics" means integrating forward the equations of motion. In some cases, e.g. if you have a chaotic system, you end up with a 'strange attractor', with strange meaning fractal, non integer dimension.
(Simple determinsitic motion, like a stable orbit of a (assumed point mass) planet has an invariant set of a closed ellipse in state space.)
It is also possible to have fractal invariant sets without chaos ('strange non-chaotic attractors').
The paper itself is far from a complete worked out theory, it is at the stage of "here is an interesting suggestion to work on".
It could turn out to be quite wrong---as in predict things that we know are experimentally untrue. It could turn out to be neat idea but useless, or best yet, it could produce new frac
If it turned out to be quite real and useful, it would vindicate Einstein over Bohr on QM.
with his dice :-)
By the way, has anyone thought of the amount of speed reduction of a program that results when you are running the program with a profiler measuring its speeds and performance - we neglect the profiler because it is too small an error in an analog measurement sense, so to speak.
Much like we can tolerate a minor error in the measurement of resistance, current or potential difference using ciruit-theory based instruments - like a high parallel resistance to measure voltage (voltmeter) or a low series resistance to measure current(ammeter).
When you go down to sub-atomic level, there's no smaller instrument to measure an electron's charge, or that of a quark, or the mass of a neutrino and so on.
The maybe you could use differentials to measure these things so that analog-ness could be introduced to create an entity smaller than the electron charge or the neutrino mass for example, not by making such a light particle and putting it on the other side of the weighing machine, but by using things like diffraction or mass differences of smaller particles etc.
That you fundamentally *cannot* think of measuring at the same time as the thing is speeding - that is a bit too difficult to digest.
I'd rather believe that our tools are poor for these measurements and set out to find new tools. By the way, I'd like to remind that the times of great discoveries have always coincided with engineering improvements in unrelated fields of science, which then enable the study of your particular field much easier - like digital computers for studying the otherwise "analog" biological world of the genome or DNA.
Ord's work does not address the "notoriously conflicting relativity and quantum mechanical models of spacetime". The notorious conflict here is between general relativity and quantum mechanics. Ord's work only addresses the relationship between special relativity and quantum mechanics. (Unless he has newer work of which I am unaware.) Specifically, he shows you can use fractal geometry to derive Dirac's equation for a relativistic free electron in Minkowski spacetime. (Or at least, in 2D spacetime; I don't know if he ever generalized it to 4D.)
Well, Dirac wrote down his equation for a relativistic quantum electron back in the 1920s. SR and QM are already known to be compatible. Ord just showed you can reproduce Dirac's equation using a different formalism, with some classical physics coupled to a fractal spacetime. (Presumably; I haven't actually read his papers to evaluate how his theory works.)
The real question is how to reconcile QM with a spacetime that is (a) macroscopically curved and (b) whose curvature depends dynamically on the matter content of the theory. Perhaps fractal geometry may ultimately have insights into that question, but right now it hasn't addressed it.
We had a whole lot of people on here yesterday arguing that it was safe to ignore Freeman Dyson because he was a physicist offering an opinion on climatology. This makes a certain amount of sense, as it is well-known that the climate is not a physical system, so it would be very odd for a physicist to be able to say anything about it.
Today we have a climatologist offering an opinion on quantum theory, and I'm very curious that none of those objective, disinterested people who were so vociferous about the absolute separation of the two fields yesterday have bothered to reiterate their strongly-held opinion today.
What could it be that motivates these entirely honest, not-in-the-least-bit hypcritical individuals to roundly denounce a physicist for commenting on climate, but utter not a peep when a climatologist offers an opinion on physics?
This seems to me to be a mystery at least as big as those that underly quantum theory.
[My only real question right now is whether the troll or flamebait mods will be higher on this. But c'mon people: am I the only one to notice how hypocritical it is for folks to get up in arms about Dyson not being a climatologist, but being absolutely silent about a climatologist making such deep claims about physics?
If you are one of those people: you ought to be ashamed of yourself, and get some better arguments against people like Dyson, because your silence on this thread is going to come up every single time one of you makes the same lame rhetorical move in future. There's stuff to be said for and against AGW, but "he's not a climatologist" is a lame ad hominem that contributes only noise to the debate.]
Blasphemy is a human right. Blasphemophobia kills.
Try smoking some salvia divinorum, you'll see some fractal space-time!
Computers are useless. They can only give you answers.
-- Pablo Picasso
The possible fractal nature of the universe was approached a long while ago from the epistemological, phylosophical by Alan Carter et. al.
http://www.datamodel.co.uk/Reciprocality/www.reciprocality.org/Reciprocality/r3/index.html
I do subscribe to the notion that mathematics can ultimately explain the natural world, but it seems to me that we use whatever the latest math it is we understand to explain the universe. Like back in the day, they thought that the elemental building blocks of the universe were platonic solid. How much math did they have beyond platonic solids? How many different mathematical ideas could they have had, anyway? Now we've had fractals for some 40 or 50 years, and this can explain something.
Is all math going to be found to be expressed somewhere in the universe sooner or later? Is there one kind of math that explains the basis?
Computers are useless. They can only give you answers.
-- Pablo Picasso
I'm not sure if your joking or not but it occurred to me that consciousness is a fractal phenomenon while I was high.
Now that you mention this about the time axis being a fractal... this reminds me very much about Terence McKenna's Timewave Zero/Novelty Theory.
http://www.youtube.com/results?search_type=&search_query=timewave+zero&aq=f
From Wikipedia:
"Novelty theory attempts to calculate the ebb and flow of novelty in the universe as an inherent quality of time. It is an idea conceived of and discussed at length by Terence McKenna from the early 1970s until his death in the year 2000. Novelty theory involves ontology, morphogenesis, and eschatology. Novelty, in this context, can be thought of as newness, density of complexification, and dynamic change as opposed to static habituation. According to McKenna, when "novelty" is graphed over time, a fractal waveform known as timewave zero or simply the timewave results. The graph shows at what times, but never at what locations, novelty is increasing or decreasing. According to the timewave graph, great periods of novelty occurred about 4 billion years ago when Earth was formed, 65 million years ago when dinosaurs were extinct and mammals expanded, about 10,000 years ago after the end of the ice age, around late 18th century when social and scientific revolutions progressed, during the sixties, around the time of 9/11, and with coming novelty periods in November 2008, October 2010, with the novelty progressing towards the infinity on 21st December 2012. --Wikipedia"
And this also connects to the Chinese I-Ching: The Book of Changes. An ancient Chinese divination technique which could connect to modern quantum research?!?
Let me be very clear: I'm not saying that this directly proofs anything, but I for one surely find this very intriguing and inspirational. It opens the mind to new perspectives.
I concur completely... for me it was nn-DMT and mushrooms though.
it sucks that mainstream science shuns the use of such... I guess when dealing with something so hard to wrap symbols around people dismiss it as hallucination and psuedo-science.
on a side note, Terrence Mckenna!!!
http://en.wikipedia.org/wiki/Novelty_theory
his theory is based on these Chinese fractal number patterns called the I Ching that have independently reached the conclusion of 2012 being the end of some sort of era in space-time. I'd expect to be laughed at by most of the slashdot crowd, but nevertheless I'll throw it out there.
http://www.youtube.com/watch?v=P1Xid_zLP4k
i found a point in the set: .02
Utilizing the synergization of benchmark e-solutions to pre-workaround action items!
in this area you already have the theories of Jean-Pierre Luminet ( http://en.wikipedia.org/wiki/Jean-Pierre_Luminet ), he's done a lot of work on the hypothesis what you see in the sky are various windows back to the same universe only younger or older.
I think he even has a criterion to verify it: just find pairs of circles in the sky along which the stars are the same --the only trouble is, to perform this in a meaningful (accurate) way you need an enormous account of computing, since you don't know any centre nor diameter...
Herve S.
I disagree with your characterization of mainstream science. Science uses what works as is evidenced by Kary Mullis being influenced by LSD and discovering PCR. Scientists have run the gamut from kabbalah studying rocket scientists (Jack Parsons), to swinging swiss wife-swapping physicists. The inspiration can come from anywhere, but the key to turning it in to science is reproducibility outside of the transcendental state. A lot of people take acid and talk about the interconnectedness of all things, very very very few take acid and can mathematically relate general relativity and quantum mechanics. Its not so much that science frowns on the use of drugs, its just that for the vast majority of people drugs don't offer the useful states of mind necessary to do science.
With regard to Terrence Mckenna, personally I resonate with some of his ideas. However, there is no rigor to his theories. Terms are ill-defined, his selection of historical points are arbitrary and don't clearly demonstrate an increase in complexity, or even a decrease in complexity. He could have just as easily talked about a flowering east indian culture as the fall of the roman empire because the only selection criteria is whatever supports the Timewave Zero hypothesis. His theory falls apart at the point of "Infinite Novelty" when he claims anything imaginable will happen, but what about mutually exclusive things? Or logically impossible things? And why the I Ching? The african geomancers created a system of binomial mathematics that influenced Leibniz and was a thousand years ahead of its time. What special reasoning led to the selection of the I Ching as a correct divinatory method and further, how did he come to interpret the date of 2012 when chinese I Ching practitioners did not? Terrence McKenna had some wild and great ideas that are worth reading about (I don't like the register of his voice.) but he is not the inspired genius that many people paint him to be. My 2 cents anyway
I like the stuff you're arguing about. I've also wondered about the randomness of his historical points, using what will fit. Oh and it's the exact opposite for me. I like his voice :-) The pace, melody and demeanor is almost hypnotizing. He would make a great evangelical preacher. I guess he is in a sense.
I guess the problem is that what people have experienced goes so far beyond the verbally describable that they can't begin to coin the useful terminology. Mckenna has talked about this before and I wish I could find some written passages about it but I can't. The eastern religions seemed to have found great terminology for these experiences. I guess it's always gonna be regarded as pseudoscience but at this point in the conversation is where I completely lose all will to continue attempting any type of rational, structured argument (what little that was - I was never properly trained in such nor skilled in it)... so I close out with words, words, words, words, words, words.... primate symbol chatter.. meaning? meaning?
They'll say, Okay, there are exactly two, or three or five, or n types of fuzziness, and any fuzzy object HAS to fall neatly into one of these categories. Point out that we're dealing with a continuum, and they'll say, okay, lets assign an exact number to each fuzzy thing depending on where it falls in that continuum. Point out that the number of dimensions of the continum is itself fuzzy, and they'll try another way to impose order.
But the artificial imposition of order sometimes destroys the fragile essence of a concept, like catching a butterfly by hitting it with a hammer.
Fractals do not need a well defined fractal dimension. If they have one, that's nice, but technically, if something had an //ill//-defined fractal dimension, it'd still be a fractal wouldn't it?
There are too many math and physics guys hitting butterflies with hammers. What you end up that way with is conveniently flat, and stationary, but it lacks a lot of the key features of the original butterfly.
Eric Baird
http://erkdemon.blogspot.com/2009/03/hyperbolic-planar-tesselations-by-don.html
(it's the second image)
Four large faces, another four the next size down, twelve more the size below that, and so on.
Eric Baird