mooeypoo

Oh, I know that, timo, it looked like the stuff we had done in Quantum. But most of the processes to solve these type of question that I've seen so far go something like "Let us assume a wave-like solution" and go on from there. I wanted to see if I can understand how the solution was done so I can see *why* the assumption is made. Awesome, thanks! This looks awesomely familiar... I think I've seen it in E/M when we tried to consider boundary problems, like a charged box. I might be mistaken, but I think so. We had that with three variables (X'', Y'' and Z'') and did this to separate them. I don't quite remember what this method is called, which is slightly annoying 'cause I'd like to read more about it. Any ideas? I'm working it out now and will post what I did so I can see if I got it right. Thanks!! ~mooey K, here's my process. Is this right? [math]\frac{d^{2}y}{dx^2}=\frac{xk}{c}[/math] [math]dy=\frac{k}{c}\int x dx^2 =\frac{k}{c} \int \frac{x^2}{2}+C dx[/math] [math]y(x)=\frac{k}{2c} \left( \frac{x^3}{3}+Cx+D \right)[/math] AND [math]\frac{d^{2}y}{dt^2}=tk[/math] [math]y(t)=k\frac{t^2}{2}+E dt=\frac{k}{2} \left( \frac{t^3}{3}+Et+F \right)[/math] and the final equation is: [math]y(x,t)=\frac{k^2}{4c} \left( \frac{x^3}{3}+Cx+D \right)\left( \frac{t^3}{3}+Et+F \right)[/math] So now, I should open this up and use the initial conditions to solve for C, D, E and F, right? I should have 4 initial conditions in this case, y0(t), y0(x) and those two as primes. Am I doing this right? Meh, this makes no sense, I'm supposed to be getting something "sin/cos" or exponential at least. What am I doing wrong?

Guys, I don't mean to be annoying here, but can we try NOT to confuse the poster? This is a derivative question. The poster seems to have the basics semi-clear, so let's concentrate on that and stop posting subjects that make this entire thing overly complicated. bimbo36, your replies to the derivatives are correct: Yes. [math]\frac{d}{dx} sin(x) = cos(x) [/math] [math]\frac{d}{dx} \sqrt{x} = \frac{1}{2}x^{-\frac{1}{2}} = \frac{1}{2\sqrt{x}}[/math] Only in your exercise, it's not the square of x, but rather the square of another function, "sinx". What do you do when you have a derivative of a function of x? Chain rule. Take the general derivative and multiply by the derivative of the function itself. So, if I had only this: [math]\sqrt{sin(x)}[/math] I will start by considering the square root as its own general function, and multiply by the derivative inside: [math]\frac{d}{dx} \sqrt{sin(x)}=\frac{1}{2\sqrt{sinx}} * (\text{(derivative inside:)} cosx)[/math] So you have the two MAIN derivatives to use. Go read Cap'n's tutorial about the chain rule again, now it's all about organization and multiplying the right chain rules. ~mooey

It depends how you define contraction, science, ontology, and the word "and".

Okay, I took an ODE class and we barely touched PDEs. I am trying to figure it out now, but I am having troubles understanding how to solve this seemingly very simple equation. I could use a bit of a guidance, even to sites or texts that explain the concept. [math]a\frac{d^{2}y}{dx^2}-b\frac{d^{2}y}{dt^2}=0[/math] Where a and b are constants. If this was on the first order, I'd be doing separation of variables, and integrating both sides (I think) but this is second order.. I'm a bit lost. Thanks! ~mooey

Isn't that what we do as critical thinkers? Assign probability of success values to variables? We don't guess those, we do that according to a certain rational methodology, namely experimentation and evidence, but that is what we try to do. I still fail to see how a concept of a deity is relevant as a solution in any step. I understand that religious people think that, I just don't see how it follows logic. If the claim is that it doesn't have to follow logic, okay then. But... I thought that it was supposed to be "logical", and I don't see how it is at any stage of the process.

I think you're getting confused for nothing. Do you know what the derivative of sinx is? Do you know what the derivative of sqrt(X) is? The first couple of posts were about trying to understand what he question asks. I doubt that they're asking for an infinite series or sum according to what I see from the poster. Do correct me if I'm wrong. Now, to the point. You don't need a graph. You don't need to explain this formula in words. Derivate with chain rule. Just so we know your level (and hence how to helpyou) can you tell us what grade this is for, and if you've done any sort of derivatives and chain rule exercises?

Moved to homework help.

The link worked for me, but here it is again: http://goo.gl/eRgVf

I fixed the link (got broken in copy/paste). Check it out. Arguing against something you don't understand results in misrepresenting the ACTUAL theory while you're at it. Without noticing it, lemur, that's what you're doing. Not only is that frustrating to fix (and results in the "where the heck do I start" reaction by most people) but is also a logical fallacy: Strawman. It's not just unfair to the theory, it's unfair to the person trying to explain things. ~mooey

What I am asking you is to consider that this might be so because you don't have all the information. These are not concepts that can be summed up in a single forum thread. If you really are interested in what things *really* are, you should open yourself and do a bit of research. No one is against personal interpretation, but you can't insist on a personal interpretation without understanding what the accepted interpretation is. I recommend you read the concept of relativity, lorentz transform, doppler effect and special relativity a bit. It will help you understand why things are the way they are, and from THERE, you can try and reach your own conclusions. My definitions are physical. Yours are lingual. You are asking a question about the physics, you should at least try to use the proper language. Physics is empirical and language is not. The whole reason that physics uses rigid mathematical definitions is to prevent misunderstanding and make the terms clear cut and without a shred of doubt as to what they mean. Because physics is empirical. Yes. It's because each frame is relative to each of the other frame. Sure. You can be quite sure E/M waves have peaks and troughs in more than just theory. If you have doubt, you can go do your own little research about it. You can even measure the peaks and troughs at home in your own microwave. I have an experiment to show this in my site: http://www.smarterth...speed-of-light/ Yes, you can't look at light as non-dual and expect to understand what goes on physically. Many of the effects are *due* to its behavior as a light/wave duality. ... I'm sorry, but that doesn't cut it. You are trying to do your own physics without knowing what the actual physics says. That's not rigorous. It's insistent. If you think you have better theories (which is just fine) you should at the very least first do the research as to what the current theory *says*. You can't expect to ask a question, get a relatively simplified answer (since I can't paste the entire of relativity, why it is the way it is, why we know it, where it came from and how we derive it in a single thread) and then use the simplified version to decide that your version of things is better. It's not fair to the theories that are actually said by physics, don't you agree? This is another reason you have to treat light as dual. The energy is related to the photons (matter). Frequency is about its wave behavior. Not accelerated, moved. Special relativity is not about acceleration it's about velocity. Other than that, yes. ~mooey

Not just lurking, he's part of the new management. Surely, you mean "Oh Xenu"

Where did the square root go? You start out with the big square root, take a derivative of it, and then multiply by the derivative of whatever is inside it (chain rule). But as you do that, you have another square root. Don't let that scare you, all it means is that you need to multiply the derivative again (chain rule). But as you do THAT derivative, you encounter yet another square root. Again don't fear, just continue the chain rule. It is a chain rule problem. It's just a longer one that requires three chains. Start it out, and I can guide you better once I see how you do the first few steps.

That's because the only AVAILABLE options are all unlikely. So you pick out of "the best". You do the same in relation to the God issue, which would go back to what I was saying in my previous post.

For years I've been complaining about the google ads that feature the church of Scientology in science forums. I thought it was inappropriate, honestly. But then they approached us, offering their remedies, and after going through their dienetics book and experiencing the exhilaration of their personality test, I am sold. My thetan has never felt more right(-angled). I want to welcome our new bosses to the forum and encourage everyone to denounce science, get rid of psychology, dump electricity and magnetism and connect two conducting rods to a measuring device and hold them tightly in both hands, and let Tom out of the closet. Cheers and good luck to us all!

I apologize if my response made it seem like I am condescending. I didn't mean it that way. I was slightly frustrated for not understanding you, so my questions were actually meant to guide you towards helping me understand what you meant, not to rub it in your face. The fact you kept repeating the same incorrect definition made me think you didn't understand me in the first place, so I kept repeating it in different ways. I didn't mean to be rude. And by the way, the links I supplied are really for your benefit; the wiki page has a lot of really good info on how relativity works and how the transformation from frame to frame is done. It's basic math, so it's not as intimidating if you don't have "high level" math. Also, one more thing: You need to realize that you're asking for answers about high level physics. High level physics is often not intuitive, and involves high level concepts. They're *hard* to simplify, and sometimes, quite honestly, almost impossible to simplify without losing context or accuracy. I'm trying - and many other physicists on the forum often say the same and encounter the same problem -- but you have to give us a bit of leeway here. You can't expect a subject to be overly simplified but also accurate when the concept is high level and sometimes requires also high level math to TRULY understand the source of. I felt like you're not cooperating with me; if I tell you that a term makes no physical sense and you keep repeating it in your question, it doesn't really help me help you understand what physics actually says rather than what you think it says. This isn't against you personally, but you need to try and understand things from that perspective. It's difficult to explain something without cooperation. They are. You just defined them in a language-manner rather than in a physical manner. I gave you the physical definition. In a physical context, that's what we use otherwise nothing makes sense. That is an okay way to imagine it, but when you encounter a conceptual problem like you had initially, it's NOT an accurate description and it's what increases your confusion. Wavelength and Frequency depend on one another and are related, but they're not the same. Also, the word "Frequency" might mean what you just said when it is spoken in conversations, but in PHYSICS, it is not that. There are quite a number of terms that are used differently in common language than they are used in physics. As you've seen with Janus' replies to me, the word "Halo" is used in common language differently than it is used in physics, which is resulting in misunderstanding (like the one I had with regards to Dark Matter). For me to avoid misunderstanding, I need to understand the context used in PHYSICS. So I accept Janus' remark, forgo the definition I thought I knew and accept the physical one. If I don't trust him (which I don't have to) I can look up the physical definition online, examine it, and use the actual accepted definition. Sticking to the definition I think makes sense to me on the expense of the actual definition used in physics will not help me understand the physical concept. On the contrary, it will just make me more confused. That's what happened with your definition of frequency. I am attempting to explain that frequency is NOT number of waves not because I don't like the way you imagine things, I attempt to correct this definition because when you look at it from the perspective of relativity (which is a physics concept) it makes no sense and confuses you. On top of that, I personally don't know what you mean when you say that, so that also doesn't help with *my* attempts to figure out where your confusion lies. It actually doesn't complicate the math, but it may complicate the intuitive nature of the concept. Here's the reason why I posted the Lorentz Transform link: I wanted you to see what details we need to make this transformation. This would show you that if I know the velocity of one frame relative to another I can make a transformation. The red- or blue-shift and length contraction and time dilation is a *RESULT* of this calculation. If I understand your confusion correctly, you seem to think it's a detail you plug in (as in you need to know the blue/red shift in advance) -- it's actually a result of the movement. Of course, if you have the red/blue shift you can calculate the velocity, but the red/blue shift is a *result* of the relative movement. For that matter, there will be a DIFFERENT length contraction from one reference to another than there is relative to any other frame. When I took my first special relativity class we had a problem to solve with two spaceships and the moon. A man stands on the moon and two spaceships move one towards and one away from the man in two different speeds. The problem asked to solve for length contraction, time dilation and relative velocity of everyone from all three frames. You ended up having 6 different relative velocities, 6 different relative length contraction, etc. It's relative. They're all relative. They are a RESULT of the calculation.... Here's where I think your problem lies: You are not intercepting the waves more frequently. You're intercepting the "peaks" more frequently. I think you might want to go over the (more basic, but very very similar) concept of the Doppler Effect. The wave itself moves at the same velocity, but it is more "compact" (the peaks are closer together), so you get the frequency higher. Or, alternatively, it's more "elongated" so the peaks are further apart, and you get lower frequency. You need to understand, when you use a definition that makes no sense in physics but ask about a physics explanation it is confusing and, quite honestly, frustrating. You want an explanation in the context of physics, there's no reason why you can't use the definitions in that context. I'm all for helping you imagine or conceptualize ideas, but we have to speak a common language or we really won't understand each other at all. Yes, that's a good way of looking at it. Spacetime and the speed of light are related. In fact, the speed of light (measured in meters per second, usually), is actually not a "basic unit of space" but rather a conversion of spacetime. The relationship to time is right, you can think of it as a result of the higher/lower frequency. If you want to look at the equations, that's also how we calculate the red and blue shifts. You are confusing me again. No one would measure your movement as quantity of waves. If you are close enough, they will measure your velocity in the regular matter of how much time it takes you to go from point A to point B relative to me. That works if I know how far point A is from point B. If I don't know the distance, then I can measure the frequency shift to see your velocity. So if I understand your definitions right, it would be "number of peaks" per second (which is not exactly frequency, but close enough) which is fine. Just for the sake of proper definitions (and whoever may be reading this), frequency is not really "number of peaks" per second, but rather number of periods per second. In circular motion, it's number of revolutions per second. In waves, strictly speaking there are 2 "peaks" per period, one upwards and one downwards. I just want to make sure we're clear.. If I understand you correctly, then saying "number of peaks" is not physical and I would very much rather we DON'T use it, but it is at least better than "number of waves" which can be easily confused with intensity or interference. I know I may be a bitch on occasion (many.. occasions..) but this time, my insistence that we use proper definition is not just my lovely and loving character. It really does confuse the matter. A lot. Again with number of waves, I shall replace it with "number of peaks" and then with "higher/lower frequency". Please tell me if this replacement is *not* what you mean. It is true that you can measure an object's speed by calculating the frequency shift. The only thing you must have in order to do that is the *original* frequency. So for example in faraway stars we know what type of radiation is emitted by them, and hence what frequency they *SHOULD* have vs the frequency we see. We use the shift to calculate their velocity either towards or away from us. Does this make it clearer? Is that what you meant? That's why you don't "count waves", lemur. What you count is how many revolutions / periods there are in a second, and for that it doesn't MATTER when you start or finish counting. All I need to do is start counting revolutions and then stop after EXACTLY one second. I then have the frequency. 10 Hz is translated directly into 10 1/second where 1/second is "per second". Hence, 10Hz is in fact 10 revolutions per second. You don't have to count ALL the peaks that exist, just how many fit in one second.... hence, it doesn't matter how many peaks there are in general but only what is the frequency of that particular wave. Lastly, we often simplify things for the sake of understanding the basics. But when you're in space there actually ARE MORE than just "one wave" coming at you. "Number of waves" is confusing because it may imply that there are a number of waves - each with a different frequency or phase - that intersect. That creates interference and all sorts of fun things we can calculate, and create a whole NEW wave that is the interference of 2 or more waves. So.. please... I'm not being just annoying for the sake of being annoying. Please stop saying "number of waves". It's not right and it's confusing. ~mooey

Just out of personal experience, this looks like a screenshot from a list of questions with instructions. I am guessing it's the simpler version. I await bimbo36 to clarify. ~mooey

I am not sure I understand what's not understood? If you have 2 options, and one option is not likely to exist (10% is "unlikely", I think, but most definitions, no?) or even "less likely to exist", doesn't it mean that automatically it is less good as an option than the other, regardless of *any* other property?

I didn't mean to be condescending, I apologize if that's how it came through. I was truly confused, and since the term kept repeating itself, I was getting a bit frustrated. We should try and stick to existing terms so we know what we are all talking about. ~mooey

Because in order to support the fact it is infallible, you need it to exist. 10% chance of existence is lower than anything else with higher chances, obviously, which automatically will make ANYTHING with higher chance of existence better at being able to support the possibility of either fallibility or infallibility or percentages of accuracy. We can argue about that (I only partially agree). I am not exactly sure how this line of argument is relevant to the topic, though? Actually, quite honestly, I don't quite know what any of this is relevant to the topic anymore.

Ha! Nice... Thanks

Are the ellipses (...) inside or outside of the root? They look to be outside of it... The original poster should answer that, though....

They would still be higher probability of success of a deity that is *unknown* and its methods completely unknown and unmeasurable. And they would still be lower probability of success than more empirical/scientific methods. Hence, while they are probably less good than a more empirical way of making a choice, they are still better than an unknowable and unknown deity... Why not? The mere fact that an expert or even an amateur work INSIDE reality is better than anything that works outside it, logically speaking. Anything that is absolutely known to exist is better than something that is not as absolute in its existence. No? That, yes, I accept. I don't *personally* go by it, but I do see the point of that. My own point, though, was that logically you can't really equate consulting a deity (or having "divine" suggestion) with consulting any other human or yourself. ~moo P.S Regarding the claim that God doesn't give you higher odds, rather just a reassurence -- could you not replace that by ANYTHING else that you trust? replace it with "Mom" or "Me" or "My lover" or "Best Friend" or "The pink unicorn" and it's equally true; all you need is to have trust in this thing you ask the question of. My point is that I don't quite see how God is unique in this, and hence why would we claim logically that it has any room in a list of potential places to ask a question in. If we do, then we should add "The Pink Unicorn" and "Aliens from Ursa Minor" to the list, as well as about a billion other possibilities that result in the same thing.

This is a chain rule problem. Go from "outwards" and then "inwards" in sequence. [math]y=\sqrt{sinx+\sqrt{sinx+\sqrt{sinx}}}[/math] Start with the differentiation of the big square root, then multiply by the derivative inside it, which includes a square root, etc. If you post how you started it, we can help you continue. We don't give final answers here, just help you get there. ~mooey

I think this is the source of our disagreement: lemur (if I understand you correctly) claims that it's just about picking different authority. I claim that while it might be about that, the different authorities are not equal logically. Anything that exists and has a defined methodology is, in my view, preferable on something that is unknown, unknowable and whose existence is outside the realm of reality.

Go to the source - the scientific method - medicine. Take the opinion of 5 more doctors. There are more options.... my point is that I am not going to refer to a deity on this. I don't quite see a reason to refer to one ever, specially if it is comparable to making one's own judgment, in which case I don't see a situation where doing that is not superior to asking a deity. I have a logical problem with this paragraph. I haven't tried talking with UFOs, either. Or digging a hole through the earth to China. I also haven't tried taking LSD and having my own version of divine revelation (and this isn't disrespect - the Greeks did it much the same with drugs). There are a whole bunch of things I -- and you -- didn't try. So if this is our current "set", God doesn't fit there either. Even if God does, it seems there are about a billion other things that I didn't try that seem better and with higher odds of success (like I said above). So the question remains - why appeal to the divine at all? (I will answer the rest later, I must run to class) ~moo