Bignose

No, you're misunderstanding what I am saying. You are free to speculate, but expect people to ask lots of pointed questions. And furthermore, should you refuse or ignore questions, then your speculations look weaker and weaker. You don't have to answer everything immediately. Common courtesy, however, would be to acknowledge that a question has been asked and the estimate when you would be able to give that question a full answer. No one expects you to be able to answer every single question immediately. Just let people know when you will have the time to answer their questions as fully as possible. And it isn't just things you are personally speculating... you are assuming some things to be facts and givens and then basing ideas on those assumptions. But, if those assumptions are flawed -- the things you think are facts really aren't -- you can't build anything up. If you just start with something, you have to cite where that starting point is accepted by the scientific community. Or if your starting point is just speculation as well, then all it is is word salad. That is to say, lots and lots of words, but with no substance behind them. One more time, I'd invite you to answer this direct question: what is your definition of consciousness? In asking you to answer direct questions and solidify your base assumptions, we are in fact trying to help you build a strong theory that is rooted in accepted science. We aren't trying to make this personal, and I really hope that you'll understand that it has never meant to be personal even if you did/are taking it that way. We are trying to show you how to argue your points successfully based on the principles of good science. We are trying to help you make your words more substantive.

We are all free to speculate as much as you want. But, look. You came to an Internet forum based on science. If you didn't want your speculations to be poked and prodded and questioned and debated, you shouldn't have posted it on an open forum. You should have posted on a personal website, or a personal blog. But, you came to this forum, and people here aren't just going to be convinced by a bunch of pretty words or phrases like "it begs to reason" or "it's been said". We are going to probe deeper and see if the science behind the idea is sound and ask questions and point out logical errors. This forum wouldn't be able to call itself a science forum if its members didn't do these things. So, I'm not sure what exactly you were expecting, but this is a taste of how real science acts. Science is going to ask hard questions and be very unaccepting without good referencing and a solid foundation from which to build theories and ideas. I'm sorry that the reaction wasn't exactly what you wanted. I had hoped that you'd have taken the opportunity to use the "reboot" of the thread to try and evaluate some of your claims. To answer some of the most pressing questions -- like defining what exactly is consciousness. But, unfortunately you either got distracted or just didn't want to do it. And when you don't answer questions that have been asked directly at you, you are going to find it awfully hard to convince people. Refusal to answer direct questions shows where the weaknesses of the idea are. If you go to any scientific conference anywhere, after every single presentation there is time for the audience members to ask questions and the presenter is expected to answer them. Fairly often, the impact of the information the presenter presents isn't judged just by how good the presentation itself is, but how well the presenter answers the questions asked of him after the talk itself is done. Answering questions posed to you well is a reality of the scientific method. So, again, I'm sorry you didn't get the reaction you wanted. But, the forum has nothing to apologize for because the members have given you a lot of leeway, and have only done what good scientists would do. Even speculations need to have some basis in fact to root them down. And, if speculations cannot stand up to repeated questioning, then what kind of speculation do you have? If it withers under the scientific process, then you have no speculation at all -- you have a failed speculation. Speculations are great and highly encouraged, but they also have to welcome a review process. If your speculation isn't mature enough to be able to handle a review process, then you need to go back and work on it some more. Or it needs to be abandoned. It really is that simple.

The basics are the same no matter what the year. If you want the latest stuff, you're going to go look in the journals anyway. This is true on an awful lot of classical physics and math. The basics of fluid mechanics are a true 50 years ago as they are today -- and a 50 year old textbook still does a good job teaching it now if it did then. Obviously, if it was poor then, then it will probably be poor now. But, classical Newtonian physics, calculus, probability, etc. etc.: the fundamentals of these have been known for a long time. And, since your first post said "I would really like to get a good introduction" anything that is written well is going to perform that duty. Frankly, I'd personally be looking for older books I could buy out a used book store, because they are going be something like 1/10th the price of a new one, and pretty much all the information is going to be the same. But, to each their own.

I'm going to suggest a sort of reboot here: Graviphoton, please list in one post in this thread every speculation that your think someone else is putting forth and needs evidence to support it. That person can either then provide the evidence and/or show you where what they have written is not a speculation. In the exact same way, graviphoton, I think everyone should list what they think you are speculating on and what you need to provide evidence for. In this way, everyone can clear the air, and start on that solid foundation that was talked about. To begin, graviphoton, you probably should address this direct questions aimed at you from mooeypoo "You are speaking of consciousness in about 3 different threads, and in none of them have you spoke, explained or proven what consciousness IS." So, graviphoton, to clear the air, please provide a definition of consciousness, backed up the requisite sources. If you need/want extra time to answer this question, please just state that, and estimate about how long you think it will take until you have an answer. Now, lastly, I just want to say that this clearing the air is a double-edged sword. If you continue you to ignore these direct questions, you are going to lose a lot of credibility. If you really "take science very seriously" then these are direct questions that deserve answers. And that is how science works, gravi, you get asked direct questions, and to earn any kind of credibility, you have to answer every direct question.

Klaynos, I think the second one does. Check the table of contents on Amazon.com

A classic in the field is Statistical Physics by Lifshitz and Landau. Part 1 is book 5 in their Course of Theoretical Physics. Part 2 is book 9 in their Course. It isn't easy, but if you get through the entire book, you will have an excellent working knowledge of statistical physics. And if you like other topics in physics, the entire Course by L&L is highly recommended.

To be able to function in everyday life? Addition, subtraction, multiplication, division, and maybe just a little basic probability. And of course all the things that go with it, fractions, decimals, percents, etc. So... from that perspective, I guess there isn't much need to take math much past the 5th grade or so unless you are going to be one of the few people who really actually use higher level math in their work -- engineers, physicists, surveyor, basically any of the sciences. Obviously that was a very rhetorical statement. Here's the real and true value of mathematics education: it is not very much the methods and techniques that are important to learn, as it is very important to learn how to logically approach problems and learn problem solving skills. And mathematics is a perfect environment for practicing problem solving skills. The tools are well-defined: addition only adds two things together, nothing else. The problems (until you get to some very high level math) are usually well defined, and they have a definitively right or wrong answer: no wishy-washy "yes, but no" kind of answers. Compare that to real life, where the tools are imperfect and the problems can either have several answers or no answer at all. Learning how to solve math problems is a very test lab for teaching and learning problem solving skills. And if this aspect of math was emphasized rather than the "everyone's got to do it" or creating farcical situations trying to show how the students can apply trigonometry or calculus or geometry. That's not to say that teaching examples is bad, but I think that more emphasis needs to be placed on the fact that the math class is there to teach problem solving skills, not necessarily trig.

If you don't learn how to research for yourself, university is going to be a world of hurt. You do understand that a lot of classes are NOT going to talk about everything you have to know to pass the exams in class, don't you? In fact, a well designed university class should have somewhere around 20 to 40% of the material is not discussed in class at all -- the students are expected to read and learn the material on their own. You're also going to have to write lengthy research papers, where regurgitating the material in the text book is going to get you a D. You are going to be required to look things up from different sources and critically evaluate them yourself. You might as well start learning these skills by learning how to lookup a few questions yourself.

Sure. Fix the mistakes and we'll be much, much closer to being able to have a discussion. You still haven't answered my questions about any kind of testable prediction with your math, but that question is kind of moot with bad math. Fix the math, and then we can discuss further later.

I think I can answer these bast in reverse order: your answer the #3 is correct in most typical situations, that is, being dealt 3 cards in a row and looking at all three in your hand and the chances of them all being red. But, the answer obviously implies that it was sampling with replacement, because the chance of a red card out of a normal 52 card deck is one half and the answer given is (1/2)^3. So, there is probably a mistake in the question statement of #3 #2 can probably be easiest seen if you break the question statement down into its component parts: Turn "what is the probability of drawing the same color three times in a row" into "what is the prob. of drawing black 3 times in a row + what is the prob. of drawing red 3 times in a row + what is the prob. of drawing yellow 3 times in a row" Calculate each of the three in the right hand side, and then add them up and see if that doesn't get your answer. #1 is actually going to be just like your answer (not the book's answer) to #3. Do the same thing -- find what the chances are of not opening corn the first time, then what the chances are of not opening corn the second time (which changes because it is sampling without replacement). I hope this helps.

One more here, and then I'm giving up. How can that last line be? [math]a^{2}=b^{2}=a^{2}+b^{2}i^{2}[/math] Where do you get this last [math]i^{2}[/math] ?? and if each of these are equal to each other, then the 1st and 3rd are equal: [math]a^{2}=a^{2}+b^{2}i^{2}[/math] Now, subtract [math]a^{2}[/math] from each side: [math]0=0+b^{2}i^{2}[/math] which means that [math]b=0[/math] Or, if the second and third equations are equal to each other: [math]b^{2}=a^{2}+b^{2}i^{2}[/math] Now, [math]i^{2}=-1[/math], so [math]b^{2}=a^{2}-b^{2}[/math] Now, move that [math]-b^{2}[/math] to the left hand side: [math]2b^{2}=a^{2}[/math] But, since you start with [math]b=a[/math], [math]2a^{2}=a^{2}[/math] so the only way [math]2a^{2}=a^{2}[/math] is true is if [math]a=0[/math]. The only way [math]a^{2}=b^{2}=a^{2}+b^{2}i^{2}[/math] is true is when both [math]a[/math] and [math]b[/math] are zero. You can't just play games with the rules of mathematics. There are rules that have to be followed. Otherwise, you end up with nonsense results like a=b=0 as the only possible solution/conclusion. Like I said, I'd seriously suggest you sit down with a good math book and work these things out. Maybe with a tutor. I know the title sounds bad, but books like Algebra for Dummies are actually probably pretty good. I've been very pleased with the half a dozen other .. For Dummies books I've seen, so if the Algebra one is worthy of being published with the rest of the line, I'm willing to bet it is pretty good. But, I cannot stress enough, that when you make simple mistakes like this, every single conclusion you make based on your derivations is completely suspect and hence meaningless. If you want your work to mean something, you have to quit making these simple mistakes. RE: " Again, the equations i use everyday, are much different to standard algebra, which i haven't sat down to do it like this in years." I'm not sure what this means -- if you are using equations, aren't you adding, subtracting, multiplying and dividing things? That's all we've really done here so far... The mistakes you are making are just like filling out your tax return and saying "I paid 100 dollars in the first half of the year, 200 dollars in the second half... so that means I paid 400 dollars total. I am supposed to pay 350 in taxes this year, so 400-350 means I get a 50 dollar refund." The math is wrong, and the government isn't going to just accept it. You will get a letter telling you your math is wrong, and that you aren't getting 50 dollars back, that you owe the government 50 (and probably some penalties to boot!). The government checks you math and doesn't accept your final conclusions, and it is the same way with your "derivations". Making these simple mistakes means that any conclusions you draw at the end are completely suspect. Correct these mistakes, and then maybe there can be a discussion about this. But, with all these mistakes, I go right back to the phrase I used above: word salad.

This one isn't right, either. Somehow, somewhere in there you got the first term squared correctly, but now you aren't squaring the second! Somehow you actually do end up with the final right answer, but the line on the right side of the equation there is dead wrong. I don't know how you can even get that. (It may be a typo and if it is, just acknowledge it as such.)

You claim to know how to do polynomials, yet you keep getting this wrong. Look. Distribute the first multiplication: (5 + i√16)(5 − i√16) = 5*(5 − i√16) + i√16*(5 − i√16) now, distribute each of the remaining multiplications: 5*(5 − i√16) = 5*5 - 5*i√16 and i√16*(5 − i√16) = i√16*5 - i√16*i√16 So 5*(5 − i√16) + i√16*(5 − i√16) = 5*5 - 5*i√16 + i√16*5 - i√16*i√16 And lo and bold, look what happens! 5*5 = 25 !!!! You can't avoid it!!!! This is basic multiplication!!!!! The final answer is 25+16 = 41!!! it is NOT, NOT, NOT, NOT 21!!!! You obviously do NOT know how to multiply these things if you keep making this mistake over and over and over. Please go learn the basic rules of math and come back, because until you can learn how to multiply these things, none of your other analysis can mean anything. Every equation you "derive" is suspect. I'm sorry, I usually don't get quite so bent out of shape like this, but it's been like talking with a brick wall... you just simply refuse to see the errors you make over and over and over. These errors aren't difficult to see and I don't know how much clearer to make it! Sit down and learn these things properly before you post more wrong things, please.

Look at this equation you've written. How can the first term in the first brackets, [math]a[/math], be multiplied by the first term in the second brackets, [math]a[/math], and NOT result in [math]a^2[/math] ?!? Unless you are redefining mathematics, why do you keep defending this mistake? What's really weird that you get the second term right.... you get [math]\sqrt{b}[/math] times [math]\sqrt{b}[/math] as [math]b[/math]. Why don't you see the mistake in the first part?!?

If you are looking at this page: http://en.wikipedia.org/wiki/Complex_conjugate You are missing a huge part of the equation. The overline that denotes the complex conjugate. It is NOT [math] 4 + 8i = 4 - 8i[/math] it is [math]\overline{4 + 8i} = 4 - 8i[/math] You cannot, cannot, cannot just remove the overline. The overline denotes performing a specific operation -- the operation of taking the complex conjugate. Without the overline, your equations are just plain wrong. Note the overline in the following equations: [math] \overline{7} = 7[/math] [math] \overline{i}= -i[/math] The overline is an absolutely critical part of the equation that renders the equations meaningless when left off. I cannot stress that enough. Neverthemind the larger issue that wiki isn't a definitive source anyway. Any fool can edit wikipedia to make it say what they want it to say. But, the definition of complex conjugate is in many mathematics texts, and you have to denote it somehow. The overbar is common, a superscript asterisk is another. But, you cannot just not put anything on it, because it is wrong. Finally: regarding [math](a - \sqrt{b})(a + \sqrt{b}) = a(a+\sqrt{b}) - \sqrt{b}(a+\sqrt{b}) = a^2 + a\sqrt{b} - \sqrt{b}a -\sqrt{b}\sqrt{b} = a^2 \mp b [/math] you are just wrong unless you are redefining mathematics.

I agree with Klaynos' equation, not yours Graviphoton. If your basic mathematics aren't even right, how can the conclusions you draw based on that math be right? Look, I'm not trying to put down your creativity and thinking about these ideas. More than anything, I am trying to look at it from a practicality standpoint. That is, what can this math be used for? I know what Newton's laws can be used for... calculating the flight of a golf ball for example. I know what Kepler's laws can be used for, predicting where Mars will be when we want to land a probe on it. I know what the Navier-Stokes equations can be used for, predicting the pressure drop when flowing through a pipe. Etc. etc. Those mathematics weren't performed just for the sake of performing them. They were performed with a specific application in mind (as I listed above). So, unless you can show what your math can be directly applied to, it becomes meaningless. There is no discussion possible either. What's to stop me from telling you that you are wrong, that there are really 4 times that are important, Tdi, tdi, tDi, and TDi? Nothing at all, because your math doesn't describe something and my math won't describe something either. It isn't a question of doing experimentation and whether you want to do them or not. How about this: can you simply describe an experiment that would either confirm or destroy your ideas? I'm not even asking you to perform it, I am just asking you to think of some test could possibly one day be performs that would test your ideas. If you can't, then, I'm going to stick with calling it word salad. Look, you are 1 step ahead of most people who claim to have brand new ideas, you've at least attempted to provide some mathematics to describe what you are trying to say. The math has some fundamental errors in it, but, at least you've tried. I'm trying to get you to take a few more steps in the right direction, but thinking about how you can test your math and ideas. Just having math itself is not enough. Like I said above, the math is performed in order to describe something -- or, to put it another way, to make predictions with. So, describe a situation where your ideas can be tested to see if your math matches what actually happens or whether your theories are wrong. That's what I'm asking.

I'm going to assume that you mean that they start out as stationary and then gravity is "turned on". (A situation that cannot exist in the real world.) Otherwise the questions yourdad is asking need answers. But, you seem to be confusing the concept of force and acceleration. Both objects experience the exact same force. The same force pulls both objects to the center of gravity of the two objects. That force is given by [math] F = G\frac{m_1 m_2}{r^2} [/math]. But, if the two object have different masses, then the acceleration on the two objects is different. [math]F = ma[/math] The force, F, is the same, but since the m is different, [math]F = m_1 a_1[/math] & [math]F = m_2 a_2[/math] So, there is no difference between the situations as you present them, they are the same (after a little algebra).

[start sarcasm] Vishal's right... just look at history. Don't you guys remember the violent gangs of Newtonites that repeatedly kidnapped Einstein and beat him with sacks of oranges to try to shut him and his general relativity up? I mean, the Newtonites tried and tried to keep the secret that Newtonian physics don't have all the answers quiet. And, let's not forget the celestial orbists that tried to spread rumors about Kepler in the newspapers to discredit him and his idea that the planets move in ellipses. Remember how they tried to convince people that Kepler was boinking Emperor Rudolf's wife? And they told everybody that the comets Kepler saw weren't harmless, that they were the end of the world? Finally, don't forget all the people who were jealous of Gauss. "No one can calculate logarithms in their head" they said -- they just knew he had them written on his arm up his sleeves. And, of course, those jealous of him had some success, that's why it's not just Gauss' Divergence Theorem. It's the Gauss-Ostrogradsky Divergence Theorem. [/end sarcasm] Ok, In all seriousness, Vishal, I think you seriously underestimate how much science would welcome discoveries of the kind you are talking about. Science is not about protecting the status quo, science is about expansion of the knowledge as fully as possible. If such over-unity devices could be shown to exist and work as promised, sure lots of science would have to be re-written, but almost every scientist I know wouldn't be angry about it -- they'd relish the opportunity to be part of the re-writing! That's what drives scientists as it is today! The ability to discover something that no one has ever discovered before! If the new theories predicted phenomena better than the old one, they are replaced. Sure, a few individuals may be angry/upset/jealous of a new paradigm, but as a whole science is exceptionally open to new ideas and theories. All that is needed is evidence that backs up what people are saying. Period. Evidence that passes tests and demonstrates without question that what the claimant is claiming is true. To date, no devices have passed rigorous testing. (And, you do realize that several actual working scientists -- the "people in white lab coats" you wrote of -- do participate on this forum, don't you? You aren't just talking to a bunch of people unskilled in the practical workings of science and experimentation. You are speaking with a bunch of experts on the subject.) You bring the claims here, all we want is some evidence of what you say. The members of this forum and the scientific community don't have to entertain every far-fetched notion until proven wrong. You don't have to entertain the notion that I have an invisible troll that lives in my attic and solves differential equations in his head until YOU prove it wrong. I have to prove that such a troll does exist before it has to be believed. And it is the same thing here. We don't have to believe that over unity or zero point energy devices exist and work until proven wrong -- you are claiming that they work, so you have to bring the evidence. It is as simple as that. Bring the evidence and I personally guarantee I will publicly change my mind. I suspect most of the other regular members of this forum will make the same promise to change their mind if you bring us the evidence. But, without evidence, our skepticism is completely justified.

The second to last statement, [math]a-bi=a+bi[/math], is just wrong except for one special case, [math]b=0[/math]. The last statement is completely meaningless, especially the last equation: [math]i=-i[/math]. Again, unless [math]i=0[/math], but [math]i[/math] is the imaginary unit. You can't have the negative of something be equal to itself unless it is a zero. I didn't read the middle stuff, but if these are the final conclusions/results, you've done something quite, quite wrong. Unless you plan on completely re-writing the laws of mathematics, what you've written here is 100% meaningless. Like I said above, this is all word/equation salad until you can show some practical demonstrable test and application.

there are several books that I am familiar with: Modeling and Computational Methods for Kinetic Equations by Degond, Pareschi, and Russo. and The Fokker-Planck Equation by Risken and Frank Any good CFD (computational fluid dynamics) book will show techniques on how to solve the Euler equations because they are a good test case to build up to solving the Navier-Stokes equations.

Don't worry, tree. With that kind of attitude, she surely won't be his girlfriend for long...

PauloChem, The deal is that it sure looks like a homework problem. And, given the decent chance that it is a homework problem, it is the forum's policy NOT to directly do homework (and homework-like) problems. Besides, you can learn how to do this yourself. The tree has already given you a start. Do the steps he suggests, add row 1 and row 3 and post the results. If you want us to confirm that what you're doing is correct, the forum will do that. But, we won't spoon-feed you. You'll get much, much more out of it by doing it yourself rather than one of us doing it for you anyway. Give it a try, and we'll help you correct any mistakes along the way.

That's very true. To borrow a statistic from baseball the difference between a 0.300 hitter (not awesome, but good enough that in the major leagues you're going to keep your job) and 0.250 hitter (perceived as below average, needing improvement) is one hit a week. One extra hit in an average of 6 games a week. But, a player with a .250 average is viewed as "poor" on a major league level. That the guy needs some help. It may just be that he's had some hard luck -- his mechanics are solid, and he's hitting the ball well, he's just hitting them at the fielders. The major league hitters can hit it to different fields, but no one is skilled enough to hit major league pitching to very specific spots -- and a guy hitting .250 for a time, may be in fact be an actual .300 hitter, but just had some bad luck. Even top of the game players like Alex Rodriguez or Albert Pujols will have stretches where they hit 0.250 for a month and nothing is wrong. It is human nature to want to look for causations for things -- it is fundamental to mankind's thirst for knowledge. But, in that quest, we have learned that some things aren't always going to have direct causations. Some things are going to behave statistically/probabilistically. Quantum mechanics is probably the biggest one, but things like statistical mechanics of gases, turbulence in fluid flows, the stock market, the agglomeration/flocculation of particles or oil droplets in fluids, Brownian motion, birth-death processes in bacteria/cells, etc. etc., all have very high dependence on random variables as near as we can tell today. Like I said above, I would not have a problem with science classes taking an entire year -- maybe about 8th grade or even 10th grade -- and driving home some of these issues. Teach skepticism and learn how to interpret the magnitude of the numbers that are reported. Teach how correlation does not imply causation (I really like the example of how ice cream sales and shark attacks are very highly correlated in the U.S. and that only implies causation if you want to say that the sharks like to attack people who eat a lot of ice cream). Teach just how often coincidence really and truly does occur. (A good example is my fiance had a period of time when she was in 6 car wrecks in 6 years, none of which were her fault -- I said "well, that just shows that it had to happen to someone. The entire curve gets filled out with several hundred million drivers in the U.S., and there are enough accidents that it just happened to happen to you. Someone out there has had 10 wrecks in 10 years, so be happy that isn't you" Like I said, every time, the police determined it wasn't her fault, so it is nothing but pure coincidence. She isn't driving poorly to get into all those wrecks, she just was in the wrong spot at the wrong time fairly often.) I don't know if a class like that would help, but there are some very fundamental misunderstandings out there today that I think could be remedied reasonably easily if an effort was made to remedy them.

Look at the matrix algebra involved with the definition of the trace: [math] tr(\mathbf{A}) = A_{ii} [/math] where the repeated index indicates summation (i.e. Einstein notation) So [math] tr(\mathbf{AB}) = (AB)_{ii} = A_{ij}B_{ji}[/math] now rearrange the order of multiplication [math] = B_{ji}A_{ij} [/math] then, contract on the repeated index i [math] = (BA)_{jj} [/math] finally, note that the j is just a dummy variable (any letter can be used, i, j, k, p, etc.) and that this step looks just like the first step applying the definition of the trace. So [math] (BA)_{jj} = tr(\mathbf{BA}) [/math] Therefore [math] tr(\mathbf{AB}) = tr(\mathbf{BA}) [/math]

... and here is your problem, at least on this forum. We aren't going to do your work for you. If you tell us where you are confused, where you are making mistakes, show us all the work you have done up to the point you are stuck, then we'll help. But, we aren't just going to answer your questions for you. Post the work you have done to this and your other questions first, and then the members of the forum will help you.