If you have no idea what I'm talking about, please go get it for free:
http://fruwillsetyoufree.batcave.net/
Now on to bussiness.
Have any other Discordians here read Los Frupanishads? What are your thoughts? Are you now a "FRUtestent?"
Interesting, in part. I confess I only skimmed it (just now). In part, it seems to be a line-by-line ripoff of the original PD. Instead of the Chao, there's a snake biting its tail. Instead of a telegram to Jehovah there's a telegram to Jesus. Instead of a parable about Grayface there's a slightly different parable about Grayface. Instead of a pope card there's a guru card. Is this an iteration of the PD or a cheap knockoff?
This FRU person. God of Laughter. I dig the idea that laughter itself is divine. Personally, I'm more attracted to a hot blonde Greek Goddess than someone with a snake thing for a head.
A lot of the longer prose was amusing, but very difficult to read due to size and resolution. Is there a full-page PDF available?
ah that nutty mal3
no pdf so far. What I liked most about it was the sense of "balance:"
-Eris: Creative Disorder
-Der Golden Goat WOT called Entropy: Destructive Disorder
-Fru: Man's relation to disorder.
At least thats how I understood it. It pleases me to see the "creative illusion," the idea that has made "creative/destructive" as the two "sparring" forces in the universe. The Principia claims we will find "the foolishness of all ORDER/DISORDER. They are the same!" I believe we must extend this to creation and destruction as well.
But I digress.
I also found the "5 esoteric gates of the pineal glad" to be interesting, along with the Hypocratic oath and The Bullshit Affirmation.
Wait... isn't this that thing Mal the Tertiary was pushing?
Idem: yes.
The site needs a forum.
:lol:
Except that entropy doesn't destroy things, it just makes things stagnant. And it probably doesn't apply to the universe anyway, since the 2nd law of thermodynamics only applies to certain types of systems and the universe may not be one of those types.
ha, so BF means BrainFuck
i shoulda guessed
also, i'm not quite sure i agree with what you just said about entropy.
Quote from: PeregrineBF on August 19, 2007, 08:52:51 PM
Except that entropy doesn't destroy things, it just makes things stagnant. And it probably doesn't apply to the universe anyway, since the 2nd law of thermodynamics only applies to certain types of systems and the universe may not be one of those types.
For someone who's so into chaos, you're applying order in quite a few places.
The second law of Thermodynamics: The entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium.
This says that the total energy available to do work in an isolated system approaches zero. Nothing can move when entropy has taken its course. However, the "isolated system" bit is key. The universe may not be an isolated system. If it isn't (and it probably isn't), the second law of thermodynamics does not apply to it as a whole (Though it does apply to some parts of the universe, and those parts may be very big.)
Of course, since entropy merely represents the probability of certain states being much higher than others in phase space then a system may come out equilibrium eventually. Total entropy need not be the end of everything, even in an isolated system. It's just so unlikely that it will take many trillions of years for anything to happen, if it ever does.
One also has to assume that the universe is a chaotic system to apply the second law of thermodynamics to it. If it isn't, then the second law does not apply. But it probably does. It's the isolated system bit that is in doubt, really.
And order does not eliminate chaos. Chaos can come from seemingly ordered systems.
For example: The quadratic map of X-> X^2+c where c is a real parameter. It's even more fun if you do it on the complex plane (z -> z^2+c). Highly chaotic, but a very simple, ordered beginning. And yet the chaos seems to contain ordered parts as well...
Quote from: PeregrineBF on September 04, 2007, 08:21:37 PMAnd order does not eliminate chaos. Chaos can come from seemingly ordered systems.
For example: The quadratic map of X-> X^2+c where c is a real parameter. It's even more fun if you do it on the complex plane (z -> z^2+c). Highly chaotic, but a very simple, ordered beginning. And yet the chaos seems to contain ordered parts as well...
Hold on a second. How are you defining chaos here?
American heritage dictionary says, "A condition or place of great disorder or confusion. " Which seems to imply the inability to predict what will happen next. But you seem to have a formula there which, if you do the math, will tell you
exactly what will happen next.
What am I missing here?
Agreed. Chaos cannot be contained within an orderly mathematical formula. It seems to defeat the purpose.
Of course order lies hidden in Chaos... just as Chaos lies hidden in Order. Didn't you get the memo?
Actually, some of the more Theological around here have decided that when talking metaphysics, Chaos* was the combination of Order and Disorder.
That is, disorder is the opposite of order, and only one half of the Chaos that is Universe.
*Chaos as Eris, as primordial, as Universe.
Quote from: LMNO on September 04, 2007, 08:36:34 PM
Actually, some of the more Theological around here have decided that when talking metaphysics, Chaos* was the combination of Order and Disorder.
That is, disorder is the opposite of order, and only one half of the Chaos that is Universe.
*Chaos as Eris, as primordial, as Universe.
I've often considered that model and it seems quite useful. Of course, I like the metaphor too as a reminder of how much the interpretation of the data imapcts what we see (is it order, is it chaos? It depends on how you're programmed....)
Quote from: LMNO on September 04, 2007, 08:26:29 PM
Quote from: PeregrineBF on September 04, 2007, 08:21:37 PMAnd order does not eliminate chaos. Chaos can come from seemingly ordered systems.
For example: The quadratic map of X-> X^2+c where c is a real parameter. It's even more fun if you do it on the complex plane (z -> z^2+c). Highly chaotic, but a very simple, ordered beginning. And yet the chaos seems to contain ordered parts as well...
Hold on a second. How are you defining chaos here?
American heritage dictionary says, "A condition or place of great disorder or confusion. " Which seems to imply the inability to predict what will happen next. But you seem to have a formula there which, if you do the math, will tell you exactly what will happen next.
What am I missing here?
this is mathematical chaos. sort of.
the formula given is the one of the mandelbrot fractal.
given different values of C (Z is always initialized to 0+0i), the "orbit" of the value of Z when iteratively applied this formula is either stable, periodic, goes off to infinity or chaotic. which makes up (respectively) the inside, inside, outside and edge of the mandelbrot set.
the thing is, a lot of iterative systems are often highly chaotic. even when they're governed by very simple rules. but because the output of the system gets fed back into it, it becomes very hard to predict the output of the system after a high number of iterations.
the mathematical definition of chaos is, something like, a system that changes over time, for which a certain pertubation in initial condition yields an exponential (relating to time) difference in output.
this means, if you have a chaotic system, say a point which moves in a way governed by very simple rules. say you have two points, but they're only 0.01 units apart, if you iterate this system, with 10 timesteps they may be 0.1 units apart, but with 100 timesteps they may be 10000 units apart, and with even more they'll be completely uncorrelated with eachother.
i could give some simple examples another time if you like. (not that i'm the expert on chaos theory, but i know a bit about it)
No need.
Mathemetical Chaos Theory is, to me, much different than what most people call "Chaos". Much like the word "particle" means a much different thing when you're talking about electrons.
And yes, after a high number of iterations it can be unpredictable, but if your calculate each one, it certainly isn't.
So, it sounds to me like Pere is conflating two separate definitions here.
no.
because it is only predictable in theory
if you even try to do it in practice, in a sufficiently chaotic system there will be precision errors, and they will, after only a few iterations explode exponentially to make the entire system unpredictable.
and even if you are going to try and calculate it all completely symbolic (= no loss of precision), after a number of iterations you will need a piece of paper larger than the known universe to write down all the symbols.
these are very real limits to the predictability of chaotic systems, even when they're based on very simple deterministic rules. often, the best you can do is to try and describe the large-scale behaviour of the system on a higher level, but (as we can see so clearly in the social sciences) you're going to have to accept a large margin of error with such descriptions.
the problem with chaotic systems is, that because of its exponential error-propagating properties, the old saying "but one day surely we'll have the technology to calculate this" simply has turned out to be wrong. some things cannot be solved with moar computing power, no matter how simple they seem.
If such things cannot be calculated, how is the Mandelbrot pattern achieved?
the mandelbrot set is the set of points (represented as a complex number: x+iy) for which the iterative formula does not go off to infinity. this is the black "inside" of the mandelbrot set. the pretty colours on the outside are generated depending on which iteration the "orbit" of the point goes outside a certain treshold circle (usually the circles of radius 2 units), after which it is guaranteed to go to infinity, so the calculation can stop there. (and going off to infinity is not considered chaotic)
the points on the inside of the set will eventually converge to a point or a number of fixed points, so that's also not chaotic either.
only the points exactly on the edge between the inside and the outside of the set may display chaotic behaviour .. but then i would think not even all of them .. now you're making me wonder as well, which parts of the mandelbrot set are really chaotic in the "tiny pertubation of initial conditions causes exponential difference after some time" meaning.
possibly there are different kinds of chaotic behaviour. i know at least that you can calculate the "Lyapunov exponent" for a chaotic system, which is a measure of the speed of the exponential increase in error. maybe it's rather low for the mandelbrot fractal?
i know i've run into precision problems with the mandelbrot set, but nothing that couldn't be solved by just slapping a few extra bits of precision on.
on the other hand, if you look at the weather-prediction as a traditional chaotic system, i'm very sure about the computational limitations, because you need an exponential increase in computing power in order to gain a linear increase in prediction power (or possibly even less, because we actually *have had* an exponential increase in computing power since the 60s and is predicted to continue for at least some 10-15 more years).
I guess the boundary points of the Mandelbrot set are chaotic in the sense that exactly at the edge of the set, an "infinitesimal" movement on the complex plane results in a large change in long term behaviour. There's your sensitivity to initial conditions.
yeah, but that would be the case for every "treshold" function. and not all of them are chaotic. i think. i guess i'll have to read more about chaos theory.
Quote from: Professor Cramulus on August 07, 2007, 09:53:51 PM
A lot of the longer prose was amusing, but very difficult to read due to size and resolution. Is there a full-page PDF available?
Out of boredom one day I started to "clean up" Los Fru and make it somewhat legible. I think I only got the first page done and I got bored again decided to masturbate instead.
I'm definitely no expert either, but this is what I'm thinking right now:
The Mandelbrot set is a "map" of complex polynomials. The polynomials themselves aren't chaotic; each one just either diverges, converges or it's periodic. The map, however, can behave "chaotically". On the edge of the set, a tiny movement in essentially any direction will bring "unpredictable" changes in behaviour of the polynomial. Or something.
It's easier to make sense out of the logistic map for example... it has one dimension less to worry about.
I just want to throw in that this is really interesting.
I don't have a whole lot to add because I'm very slow with math (not bad, per se, just take a while), but I'll be damned if it's not one of the coolest freaking things out there.
So, you know, keep up the good work. That's all I really have to contribute to this. It's god damned fascinating, though.
Well we sure jacked this thread good. And what happened to my avatar?
avatars got lost with the servermove.
but you're right (about what you said in your previous post), so what were we talking about again? it's late, i'll try to figure it out maybe tomorrow :)
I couldn't even upload a new one, apparently the attachment thingy is write-protected or somesuch. How do you people do it, host your own?
And I actually think the incessant threadjacking is one of the things that make this forum great! Let's discuss that!
1) yes host it at imageshack, photobucket, etc
2) threadjacking is nice though i kinda like where this thread is at now, although the trend so far is that treadjacks only made it better
3) i also realize it is "tomorrow" right now you i owe you some complicated reply about chaos and the mandelbrot set (i thought i was going to pull Julia in there as well, you realize, poor Gaston never could have seen what beautiful things they look like?) , but to be honest it's not nearly "tomorrow" enough, i woke up halfway the night and didn't really get any proper sleep since. bweargh.
I'm going to add something on Mandlebrot tonight. As you may be aware, I am not overly thrilled or enamoured with Chaos Theory in general, at least when compared to what most people call Chaos.
Stay tuned.
Yes, i should reiterate that what mathemeticians (and many physicists) call "chaos" is much different than what most other people call "chaos", which is different than many Discordians at this site (and elsewhere) call "chaos".
To conflate all three to make some sort of point seems to be pointless.
well yes, partly.
they are not the same.
but they all share unpredictability.
that was part of your point, and your problem with peregrineBF's statement. that mathematical chaos is not unpredictable. but it often is.
although the meanderings of the threadjack about mandelbrot showed that the mandelbrot set is a bad example of this (there is probably unpredictability in that set, but it's not very obvious or illustrative)
nurbldorff mentioned the logistic map (http://en.wikipedia.org/wiki/Logistic_map), a much simpler fractal (doesn't use complex math) and demonstrating the prediction problems of mathematical chaos much clearer.
Well, yeah.
I feel I could simplify it even more and say that as you begin to add more variables, it becomes harder to predict what the outcome will be beforehand, and eventually becomes nearly impossible until you actually perform the calculations 9substitute numbers fro variables.
For example, the best you can say about a trail of cigarette smoke before hand is that it will most likely travel upwards. To know how it will actually behave would take an insane amount of computing power, plus a mountain of data about the environment, and the combustible material.
Gosh, I really hope i didn't just contradict myself there.
If you're in a pub, the smoke will automatically gravitate to the nearest off duty policeman, who will then issue you a £50 on the spot fine.
True story.
The Man™: the Overriding Variable.
Quote from: LMNO on September 11, 2007, 02:33:54 PMWell, yeah.
I feel I could simplify it even more and say that as you begin to add more variables, it becomes harder to predict what the outcome will be beforehand, and eventually becomes nearly impossible
yes. chaos and complexity are closely related.
Quoteuntil you actually perform the calculations 9substitute numbers fro variables.
until how what? sorry maybe i get confused by the typo but what are you trying to say here?
QuoteFor example, the best you can say about a trail of cigarette smoke before hand is that it will most likely travel upwards. To know how it will actually behave would take an insane amount of computing power, plus a mountain of data about the environment, and the combustible material.
Gosh, I really hope i didn't just contradict myself there.
i dunno if you did
but the point i've been trying to make for some time now, is it wouldn't only take an *insane* amount of computing power, but in order to predict it beyond a very finite and tangible timespan, it would require an *impossibly insane* amount of computing power. not "today impossible but maybe in 10 years" but more "impossible to get the initial state of up to enough precision due to the uncertainty principle" or "impossible to calculate in any reasonable timespan as compared to the current estimated age of the universe" or even "impossible to store the state of with enough precision, comparing the amount of memory chips needed to the size of our solar system".
i think i could probably say with certainty that -for example- we'll never be able to predict a reasonable weather forecast past the three weeks range. no matter what kind of computing power we'll throw at it.
(and as far as i understand quantum computing (which is hardly at all), it isn't going to help very much. maybe just to keep Moore's law going for another decennium or two -- which would be quite impressive nonetheless)
also, Cain :lol:
gah. fucking server.
LOL post ruint.
that means i win?
so anyway, it's obvious that Benoit Mandelbrot invented the first breakbeats.
chaos = unpredictable = syncopated
QED
Basically, i was saying instead of variable, plug in actual numbers.
The math equivalent of "doing the experiment".
Also, syncopated beats are predictable, but not uniform.
The problem doesn't only lie in lack of computing power. The thing is, no matter how much computing power you've got, you still have the problem of accuracy of your initial conditions. A calculation that is iterating a formula over time will accumulate error. Usually this is OK, you can still make accurate predictions because your model is stable (the error may grow linearly or something like that), but in a "chaotic" or ("dynamical") system, this error will blow up very quickly and overtake the scale of the measurement itself. At which point the calculation becomes useless. This puts a cap on the predictions you can make in a real system, even with unlimited computing power.
In order to know where the cigarette smoke went, you'd have to get position and speed measurements of each particle of smoke when it leaves the cigarette, plus every molecule of air surrounding it, which in turn will be influenced by the movements of everyone in the room. Even if you could measure all of that simultaneously, you'd still only have finite accuracy - if nothing else, ultimately limited by Heisenberg's uncertainty principle.
I'm not sure about the actual numbers, but I saw some calculations that said something like, even if you had a set of really accurate sensors reading temperature, humidity, wind speed, etc every cubic meter in the entire atmosphere giving readings every second, you still couldn't even theoretically predict weather reliably (whatever that means) for longer than something like a week. The model is just too sentitive to errors. Within days you get to a point where the system can go either way, depending on differences in initial conditions smaller than the accuracy of your instruments - essentially the old "hurricane butterfly" thing.
Btw, I'm not even sure what the "everyday" definition of chaos is, if there is even such a thing... what do most people mean by "chaos", exactly?
Quote from: nurbldoff on September 11, 2007, 06:18:41 PM
The problem doesn't only lie in lack of computing power. The thing is, no matter how much computing power you've got, you still have the problem of accuracy of your initial conditions. A calculation that is iterating a formula over time will accumulate error. Usually this is OK, you can still make accurate predictions because your model is stable (the error may grow linearly or something like that), but in a "chaotic" or ("dynamical") system, this error will blow up very quickly and overtake the scale of the measurement itself. At which point the calculation becomes useless. This puts a cap on the predictions you can make in a real system, even with unlimited computing power.
In order to know where the cigarette smoke went, you'd have to get position and speed measurements of each particle of smoke when it leaves the cigarette, plus every molecule of air surrounding it, which in turn will be influenced by the movements of everyone in the room. Even if you could measure all of that simultaneously, you'd still only have finite accuracy - if nothing else, ultimately limited by Heisenberg's uncertainty principle.
I'm not sure about the actual numbers, but I saw some calculations that said something like, even if you had a set of really accurate sensors reading temperature, humidity, wind speed, etc every cubic meter in the entire atmosphere giving readings every second, you still couldn't even theoretically predict weather reliably (whatever that means) for longer than something like a week. The model is just too sentitive to errors. Within days you get to a point where the system can go either way, depending on differences in initial conditions smaller than the accuracy of your instruments - essentially the old "hurricane butterfly" thing.
Btw, I'm not even sure what the "everyday" definition of chaos is, if there is even such a thing... what do most people mean by "chaos", exactly?
*ding!*
I think one interpretation of Chaos that I like fits well with what nurbldoff said.
Here we are with models and math (which is just a complex model). However, (let's all say it together ;-) ) the model is not the thing being modeled. Thus, the model doesn't have all of the data, thus there are unknowns. These unknowns, are denizens of the Void, children of Eris and that damned undefinable X.
OK, I get what you're saying, but for correctness I have to clarify that the actual model can be chaotic. So, even if you had such a model that perfectly described a real system (OK, OK, a pure mind concept but bear with me) it would still behave chaotically. The fact that models are never perfect descriptions of reality is a separate problem, of course adding to the trouble with predictions.
But I guess "unpredictability" is a large part of what people generally mean when they talk of chaos.
Doesn't the "unpredicatbility" stem from imperfect knowledge of the conditions?
If we had complete knowledge of the conditions, why wouldn't we be able to predict the motion?
Quote from: nurbldoff on September 11, 2007, 06:38:18 PM
OK, I get what you're saying, but for correctness I have to clarify that the actual model can be chaotic. So, even if you had such a model that perfectly described a real system (OK, OK, a pure mind concept but bear with me) it would still behave chaotically. The fact that models are never perfect descriptions of reality is a separate problem, of course adding to the trouble with predictions.
But I guess "unpredictability" is a large part of what people generally mean when they talk of chaos.
Oh don't get me wrong, I agree with what you're saying. If we could create a Simulacrum of this Universe somewhere else in the Multiverse complete with monitors and measuring tools... we still wouldn't be able to predict the weather, and in that lies Chaos in one sense.
Chaos in another sense is that none of our models can actually get to the point where we could model all the data.
Further Chaos in that we can't even agree on which data should be there because of perception and interpretation. Yet more Chaos in the sense (as Old Uncle Al said) that in all of our models we swap X, Y and Z around in the values slots but we still don't actually get anywhere (There is no God, we came out of Primordial Soup is swapping X for Y and Panspermia is X for Z and the whole concept of abiogenesis was thought to be rubbish of the Middle Ages... until we wanted to stick it back in a model ;-) )
Quote from: LMNO on September 11, 2007, 06:40:29 PM
Doesn't the "unpredicatbility" stem from imperfect knowledge of the conditions?
If we had complete knowledge of the conditions, why wouldn't we be able to predict the motion?
Because Heisenberg was an ass and keeps sticking his fingers in from beyond the grave.
QuoteIf we had complete knowledge of the conditions, why wouldn't we be able to predict the motion?
I guess we would, if we had a perfect model and unlimited computing power. But this knowledge seems to be fundamentally unattainable.
Quote from: nurbldoff on September 11, 2007, 06:54:03 PM
QuoteIf we had complete knowledge of the conditions, why wouldn't we be able to predict the motion?
I guess we would, if we had a perfect model and unlimited computing power. But this knowledge seems to be fundamentally unattainable.
Nope, Heisenberg's Principal would show up and give all the models afterschool detention.
I have a rant about that, by the way.
Hiesenberg used incredibly crappy metaphors in describing what's going on.
I really should just save these things and repost where needed.
QuoteThe "uncertainty principle"
The Schrödinger field pattern in position space determines where a detection event is likely to be found, and its pattern in wavelength space determines the momentum we associate with the object causing the event. If the events are localized in a small region, the wave pattern will be localized but consequently it will contain many elementary waves – its momentum will not be well-defined.
Conversely, if the momentum detector clicks only for a narrow range of momentum values, the wavelength is well-defined, and the wave pattern must extend over many cycles – its location in space is not well-defined. You can have waves with well-defined position or well-defined momentum, but not both at once. This is the true meaning of the uncertainty relation first enunciated in 1927 by Heisenberg.
To be precise, the relation states that among many measurements on a large set of systems each described by the same wave function the range of momentum values times the range of position values is greater than or equal to Planck's constant times a certain number.
The number depends on how you define the ranges or spreads, commonly written Δq and Δp, where q and p stand for position and momentum. For the most common statistical definition (the standard deviation of the measurements) the constant is 1/4π. Thus the algebraic formula: ΔqΔp ≥ h/4π. A similar relation exists between the range of measured energy values ΔE and the interval of time Δt during which the system is allowed to evolve undisturbed.
The "Heisenberg uncertainty relation" emerged in an atmosphere of confusion from which it has never quite escaped. Much of the fault lies with Heisenberg himself who was not content with setting forth the bare theory, more or less along the lines I have described above (but in mathematical language), he also tried to make the result more comprehensible with suggestive physical arguments.
For example, he implied that the uncertainty has its origin in the inevitable disturbance caused by the measurement process (which is not inherently a quantum concept). Bohr objected to these explanatory efforts, convinced that the matter was deeper than Heisenberg made it out to be.
As I see it, most problems of interpretation are resolved by the simple fact that the microscopic theory does not refer to any physical waves or particles. It refers to well-defined detectors and unambiguous events of detection. Accounts that ascribe position to particles and momentum to waves apply macroscopic language inappropriately to microscopic nature.
You can set a detector to register an event with well-defined momentum, or you can set it to record an event with well-defined position. That does not entitle you to say that the event is caused by a "wave" or by a "particle."
Douglas Hofstadter has an essay about how the Uncertainty Principle is really widely misunderstood.
Basically he underscores that quantum mechanical reality does not correspond to macroscopic reality. That Heisenberg was talking about quanta, not systems on the level which we can personally observe. The metaphor usually carries, but should not be seen as a law or nothin'.
LMNO: Right. But in most actual cases, the limits of measurement are much larger than Heisenberg's. Instruments have limited resolution, there are disturbances, interference, etc. And no system (OK, maybe the universe as a whole) is completely isolated from everything else.
Cramulus: certainly. Looking at the uncertaity relation, it just tells us that the uncertainty in position times the uncertainty in momentum (=velocity*mass) is larger than or on the order of Plancks contant. Planck's constant is
Quotereally small
. That means that these uncertainties are generally of no consequence in a macroscopic system (see above).
But really, Heisenberg has nothing to do directly with chaos theory. Chaotic behaviour is in the
Quotemodel
.