<p>Your mindless mumbling is far more coherent than MY mindless mumbling...</p>
<p>I know basically nothing about Chaos Theory, but what you said seems to make sense to my simple mind. =)</p>
<p>well, I was not saying it from a mathematical viewpoint! I'm not saying that u r correct w/ your reasonings though! (I mean, I got lost in the middle, and won't comment on ur mathematical reasonings for this reason! but for the time being, I can only comment that ur last portion of reasoning is questionable) I was just saying it, say for example from the physical viewpoint, afterall, chaotic dynamics strongly pertains to the physical behavior of the nature (well, completely to be accurate) The theory can't exist in the black hole, where the pattern of 'intial condition' is 'predictable' (as far as scientists know), and such initial condition can actually dismantle the 'unpredictable characteristic' of chaos theory.........well, I'm referring to the Linear Autonomous System where a linear vector field is such that x'=Ax AeR (n,n,)....................never mind, I guess I've started to do some mindless mumblings too!
And it's wiser to return to the original discussion of the thread!</p>
<p>Interesting. Actually, I believe that we should hijack this thread. :D </p>
<p>= = =</p>
<p>It analyzed it from a mathematical standpoint, but what I can be generalized to describe physical events. What you said is true - having complete knowledge of the initial conditions of an event [the Big Bang is often used as an example] theoretically would dismantle determinism and would allow us to predict the "future" of the event. However, does this apply to black holes? It is merely theoretical or is it possible to have full knowledge of the "initial conditions" within a black hole? Well, you haven't exactly specified what the "initial conditions" would be for a black hole. Are you referring to the initial conditions of the formation of a black hole, in which case we would be able to accurately predict the development of the black hole? Or, are you referring to the "initial conditions" of an object as it enters the black hole, in which case we would be able to determine the position and velocity of the object as it "progresses" through the black hole? Anyway, I feel that this discussion pertains more to the Schrodinger Equation than Chaos Theory.</p>
<p>By the way, what grade are you in? Are you experienced in the field of quantum mechanics [you list it as one of your interests; it is one of my interests as well].</p>
<p>That's the entire point of chaos theory. Lorenz, my friends. NOTHING CAN BE PREDICTED SINCE WE WILL NEVER KNOW THE ICs that well.</p>
<p>How 'bout the word "nice"?</p>
<p>Mathwiz - As I said, that pertains more to the Schrodinger</a> Equation than Chaos Theory.</p>
<p>
[quote]
The Schrodinger equation plays the role of Newton's laws and conservation of energy in classical mechanics - i.e., it predicts the future behavior of a dynamic system. It is a wave equation in terms of the wavefunction which predicts analytically and precisely the probability of events or outcome. The detailed outcome is not strictly determined, but given a large number of events, the Schrodinger equation will predict the distribution of results.
[/quote]
</p>
<p>ChaosTheory, guess what, I actually went right to the last para 'by the way, what grade are u in.....' since I actually wanted not to proceed w/ the discussion! Well, yeah, I've deep passion for Astrophysics (DEEP! :D). Again, I hate to deal w/ mathematical equations which seems to be intimidating at times, but see I'm also acutely interested in quantum mechanics (i.e. physics too) and Black Hole! So, my interest is kinda wierd!
Well, I'm a 10th grader and I'm NOT at all experienced in the field of quantum mechanics! (surprised right?!) In fact, I've minimal knowledge on astronomy, black hole, quantum physics (everything, but I'm determined to expand my knowledge on all these subjects voluminously when I get time, see, my HS doesn't even offer AP Physics, or simple Astronomy courses! That's why I'm going to a better place, hopefully I can make it in NCSSM, the decision comes out next day! OMG!!!)
I'm sure you know tons more than me. Well, except the mathematical equations, I wrote evrything else from my preliminary knowlege, if u read that again, it's very evident. And for the mathematical equations (I just wikipedied it! sorry for fooling u and making it look like I've some inner knowledge on quantums, which I probably will very soon though!) Do u still want me to reply to ur questions that u throwed at? (I won't be real good at answering them w/ such restricted knowledge though :( But I will just tell my 'simple' based on 'reasons' sorta explanations if u want to carry on w/ the discussion....by the way the Schrodinger equation--I've no idea on this equation though!)</p>
<p>Here are some books that I think you would definitely enjoy:</p>
<p>Quantum by Jim Al-Khalili <- Devoted entirely to quantum mechanics.
The Road To Reality by Roger Penrose
The Universe in a Nutshell by Stephen Hawking
A Brief History of Time by Stephen Hawking
A Briefer History of Time by Stephen Hawking
Simply Einstein by Richard Wolf
Six Easy Pieces by Richard P. Feynman
Surely You're Joking, Mr. Feynman! by Richard P. Feynman
The Fabric of the Cosmo*s by Brian Greene
*The Elegant Universe by Brian Greene
A Passion For Mathematics by Clifford A. Pickover
The Solar System by Giovanni Caprara</p>
<p>I am in 9th grade. We both have very similar interests. :) But, I do enjoy the mathematics involved in astrophysics as well. My high school doesn't offer any AP classes, but I think much of the AP curriculum doesn't focus on this type of physics. One of my close friends applied to NCSSM this year [She's on this board, actually - Didnotfaillife. We attend the same school.]. I will be applying next year. I am assuming you attend a school in NC. Which school do you attend? Your high school sounds like mine. :D</p>
<p>I would love to hear your reasons. Admittedly, I am not much of an expert, either, but it is interesting [I need to find a new word] to see another perspective.</p>
<p>OMG!!! Didnotfaillife, I PMed her the most during my stay in CC, mostly dealing w/ NCSSM sorta discussion! I always thought u r a senior or sth like that! So, u r from RTP area too! NOw, I feel for u and Didnotfaillife, like u people have one of the toughest competitions!!! Why haven't I ever seen u posting at the SVSM thread in Summer Program place?! Your assumption is correct, Richmond Senior HIgh School--the school which supposedly play good football but can never go any further than the next rounds :(. (I don't know much of football, so don't ask!) Yeah, I agree too that the APs never focus on it, but NCSSM certainly does! In fact, I've seen their astrophysics website, and was really amazed at seeing all the things they do! That's a BIG reason why I'm applying! HOw can ur HS be like mine? Okay, I'm going to write my reasonings in the next post, but I'm just saying that it won't be intellectual though, just basic and completely my basic reasonings :D</p>
<p>By the way, I'm too lazy to read books (of any kind! even, I didn't finish the Stephen Hawking's book on BlackHole! I just can't get started w/ the books!) Have u read all those books!? I will keep the list, hopefully, I may be able to get in touch w/ one of those boosk!
U have any questions w/ NCSSM particularly, ask me! I've probably asked almost all kinds of questions that can be asked thru e-mail to them! Try for NCSSM next yr real hard, it's worth trying! (I only hope I can make it! :( IF I can't I don't know what will happen! I simply can't take the rural atmosphere of NC anymore!)</p>
<p>ok, two more words to retire:</p>
<p>HELLA</p>
<p>HYPHY</p>
<p>omfg norcal sux!</p>
<p>Chaos Theory : care to explain to me (PM or on this thread) what an attractor is? I've been trying to study Chaos theory via Wikipedia, and their definition of Attractor is something I'm not really grasping. And while we're on the topic, any good online resources/books for learning Chaos?</p>
<p>why studying via wiki?</p>
<p>it's the most immediate/convenient source for me to look through, and I don't know any good "beginners" books to start with.</p>
<p>Oh, ok, so u r another dude interested in chaotic theory!</p>
<p>yup lol but so far I only have a grasp of the fundamentals. but it really is a very attractive field, esp w/ it's application across so many fields</p>
<p>Well, I've decided to go ahead and just do some more discussion on this (to show my reasonings at first) </p>
<p>Now, this is what I believe in----Chaos Theory is REALLY predictable----i.e. its patterns r really unpredictable! (how's that! lol!) (as of now)</p>
<p>Initial Condition---well, big bang can possibly be the initial condition, but I've focused on the initial condition of when a particle enters the black hole--something like that! Since the mass of black hole is SO HEAVILY concentrated, it's certainly possible (or is it impossible) to predict? well, this is the part I'm really confused. TO solve this dilemma, I rather look at the bigger image, in the larger perspective of physical action where the magnetic radiations r also absorbed rather than trying to analyze the molecular activities of black hole which I don't think the scientists yet have still any clue. So, I decidedly conclude that the pattern of bLaCkHoLe is predictable---the pull that it generates obstruct the predictable pattern of chaos theory (i.e. it gets PREDICTABLE, in the way that it will not be existing as an 'unpredictable manner' rather the rays will be following a uniformed pattern (I am just guessing wildly, I guess it won't!) since it's being pulled in the same way!) So, where am I getting wrong? I'm sure there gotta be major flaws in my reasonings, where is it?</p>
<p>hmm, well chaos theory applies only to nonlinear dynamical systems (to the best of my knowledge), so woudln't you be saying that a black hole is such a system? I just don't know if that'd be the case, because black holes by their very nature seem to defy any bounds like that</p>
<p>so this thread went from discussing words to the Chaos Theory?</p>
<p>anyway,
get rid of:
-anyway
-absenteeism
-totally
-like
-dude
-awsome
-rad (hardly anyone uses it anymore anyway)
-conflagration
-A
-amalgam
-malignancy</p>
<p>It will stop until Chaos replies, and I had no reason to start the discussion!</p>
<p>Imran Nazir (!), I don't think I said chaos theory is a linear dynamical system though!</p>
<p>Maybe it's just that I'm tired and have a headache, but I didn't understand a word fo that.</p>