Bignose

If T=a, then the equation is only true if T=a=1 or x=1. -------------------------- But, I want to second dave's question here: What is the point of the thread? It needs to be at least re-titled from "The Most Important Question Ever" to "please check my cancellation". Because, there is nothing important about this equation at all right now, and the OP hasn't attached any significance to it at all. If x = 1, then there is no point in even leaving x in the equation, and you end up with the very unprofound result a=a. I don't think that a=a is "The Most Important Equation Ever", no matter what a turns out to be.

who?

No, it isn't clearly true. Firstly, to Don, yes anything divided by itself is equal to one. "Making them disappear" is normally called "canceling" but yes, when the exact same factor appears in the numerator and denominator, they can just "disappear". Now, let's look at [math](\frac{T}{T})a^x=T(\frac{a}{T}) ^{ x \frac{\frac{\ln{a}}{\ln{T}} -1 }{ \frac{\ln{a}}{\ln{T}} -1 }}[/math] Taking that as correct (as verified by Don), the numerator and denominator in the exponent on the right hand side at the same. [math]\frac{(\frac{\ln{a}}{\ln{T}} -1) }{ (\frac{\ln{a}}{\ln{T}} -1) } = 1[/math] because both the numerator and denominator are the same. So the big equation becomes: [math](\frac{T}{T})a^x=T(\frac{a}{T}) ^{ x }[/math] The above equation simplifies to [math]a^x = T^{1-x}a^x[/math] Which clearly isn't "true", at least not always. It it true only for three special cases: 1) T=1 2) x=1 or 3) a=0 and x!=0.

mooey, the sum (which you hate) is just so that you include all the roots of g(x) So that if g(x) has 5 roots, you turn the [math]\delta(g(x))[/math] in to [math]\frac{\delta(x-x_1)}{c_1} + \frac{\delta(x-x_2)}{c_2} + \frac{\delta(x-x_3)}{c_3} + \frac{\delta(x-x_4)}{c_4} + \frac{\delta(x-x_5)}{c_5}[/math] If g(x) had 5 roots, the sum would be over i = 1 to 5. It was kind of sloppy notation, but I'd suggest you get used to it. It is fairly common to leave the limits off of sums when (in theory) the limits should be obvious. I should have been more explicit. In this case g(x) = 1-2x The root is x=-1/2 The derivative is -2 So, you can fill in [math]\delta(g(x)) = \delta(1-2x) = \frac{\delta(x+\frac{1}{2})}{-2}[/math] Coincidently, this is the same thing that should happen when you do the change of variables, too. But, change of variables get trickier when g(x) gets trickier. The sum presented above is for any function g(x), polynomial, trigonometric, exponential, etc.

This isn't right. Consider a spherical particle. It can have a location which would be located in a 3 dimensional space. It can then also have a velocity, which would have a "position" in a "velocity" space. Since velocity can be in any of the three spatial dimensions, you have 3 velocity dimensions. So, that's a total of 6 dimensions. You can do the same with accelerations, so that's a total of 9 dimensions. You can also allow the particle to rotate in any of the three dimensions, so now we're up to 15. You can included rotational acceleration, so that 18 dimensions. Now, what if you allow the particle to have different sizes? The volume of the particle is another dimension, so we're up to 19 dimensions. 19 dimensions by considering something as simple as a a spherical particle that rotates and comes in different sizes. That I can say pretty confidently "exists". This doesn't even consider more than one particle. If we consider N particles located in space with a certain velocity (i.e. ignore accelerations, rotations, and size) we can write an equation known as the Liouville equation: [math]\frac{\partial{\rho}}{\partial{t}} + \sum_{i=1}^{N}( \frac{\partial{\rho}}{\partial{x_i}}\dot{x_i} + \frac{\partial{\rho}}{\partial{v_i}}\dot{v_i})=0[/math] This equation determines the probability that particle i (where i goes from 1 to N) will be located in the volume of space [math]dx_i[/math] with a velocity in the range [math]dv_i[/math]. This equation describes a function in 6N dimensions. That is, if there are 100 particles, this is a function of 600 dimensions. I think you can think of many, many situations where there are 600 particles. It is very, very easy to imagine a situation beyond just 3 dimensions. -------------- awww man, I typed all that and now "never mind".... oh well.

The general expression for delta functions is: [math]\delta[g(x)] = \sum_i \frac{\delta(x-x_i)}{|g'(x_i)|}[/math] where the [math]x_i[/math] s are the roots of g(x). I think you can take it from here.

Let's do it in a few separate steps: Let's start with an equation: y = z (call this equation 1) (I'm going to use different letters, so that you see it in a bunch of different ways.) And, given another equation h=r (call this equation 2) Now, let's divide both sides of equation 1 by something, namely h. y/h = z/h. (equation 3) Right? since you divided both side by the exact same thing, this is OK (assuming h doesn't equal 0). Now, since we know from equation 2 that h=r, we can replace any h with an r and still be completely right. So, let's replace one of the h's in (3) with an r. y/h = z/r (equation 4) Final result.. it looks like you divided equation (1) by equation (2), but all the step are valid so long as the denominators aren't zero.

Yeah, you're right. Climate is worthless. Bigfoot probably lives just as easily in the Pacific Northwest as he does in the California desert as he does in the wetlands of Florida. They are all the same. In fact, he probably lives at the bottom of the ocean, on top of Mt. Everest, and on Mars, too. Climate doesn't matter a lick. [/sarcasm] Animals live in a preferred place that best suits them. Climate means everything. Even the most adaptable species on the planet, humans, still are ruled by climate. Go far enough toward the poles and the population becomes awfully sparse. Go far enough toward the heart of a desert, and the population becomes awfully sparse. Bigfoot would be the same -- they are going to live were the climate is the best for them. The best combination of available food, shelter, comfortable temperature. They aren't going to just live wherever. They will follow the food and other resources needed for life. Even people did this -- like the American Indians. They would follow the buffalo herds. They didn't just stay in one place, they went to the place that gave them the best combination of food and shelter and water and comfortable temperatures and basically what they thought was best. Seriously, how can you claim to study any kind of animal and NOT think that climate is important. Climate is darn near everything. If climate isn't important, why aren't all animals everywhere? Seriously, guy, this is ridiculous. OK, where are the Bigfoot bones, then? Should be plenty of them around. Maybe under some boulders, right? -------- I think I am done with this thread. This is like arguing religion or politics. wvbig is obviously set in his beliefs, and won't acknowledge the obvious shortcomings of his so-called evidence. He'd rather believe in long-shots and unlikelihoods. He doesn't seem to want to discuss anything that doesn't support his point of view. Which is fine, he's entitled to it, but doesn't really have much point on a science forum. And, it has become clear he doesn't have much knowledge about science, either, because the claims are becoming more and more ridiculous. So, good luck in your quest, wv. I'd suggest that you do some reading about how real scientist go about discovering new species and learning about known species, but I don't think that you'd bother. You seem pretty set, so like I said, good luck.

Are you even serious?!?!? This is so laughably poor that this has to be a joke, right? So, if the two Dakotas had remained one state, you'd only multiply the answer by 49, right? Or if someday Puerto Rico becomes a state, then you'd have to multiply by 51, then, right? I didn't know Bigfoot could determine the completely arbitrary lines drawn by mankind. I'm sure all 45 or 50 that live in Rhode Island really, really wish that they had all the room the 45 or 50 that live in Montana do. And how did the ones in Hawaii get out there? Fly, swim? However they got out there, it's impressive. And I'm sure Bigfoot does equally well in the desert southwest as he does in the Minnesota north. Give me a break. This really is a poor analysis. A decent analysis would have to involve climate and what percentage of the climate was covered while counting and then extrapolating that the all the other land area with similar climates. You analysis is like saying that since there are Lentipes concolor found in the freshwater streams of Hawaii, Lentipes concolor must be found in all bodies of water, therefore they cover the entire earth. However, Lentipes concolor is native only to Hawaii, so such an extrapolation would be grossly inaccurate. The above two paragraphs also completely ignore all of the other issues about using your "count" as a population estimate. Unless these people are trained spotters -- that is, people who know how to count the population of animals in the wild correctly (by making sure not to count the same animal twice, not to miss too many animals, ensuring that there is sufficient food supply for the estimated numbers, etc. etc) -- the numbers are going to have huge margins of error. Finally, if there are that many -- why hasn't a dead one been found? Surely Bigfoots die once in a while. Why no bones? Why no corpses? Why no definitive trace at all?

You find out what they wrote or told a few confidants later. The point is that not everyone brags about the con job they've pulled on people. Sure, many do, but hardly means that everyone does. One of the best examples I think is L. Ron Hubbard. He was on record saying "The way to make a million dollars is to start a religion." (See proof of this http://www.don-lindsay-archive.org/scientology/start.a.religion.html ) Then he started Scientology. After starting Scientology, he never said he did it just to make money, but in light of his previous comments, it sure is suspicious. If Scientiology was a con job, he never admitted it as such. Obviously, nothing will be 100% conclusive about this. All I can personally cite is myself, and say that I have pulled several practical jokes on friends and coworkers that I will never, ever tell anybody that I did. Is that the same level as putting Bigfoot tracks down? No, but I'm just saying that it is certainly not impossible for someone to pull an elaborate stunt, and never acknowledge their involvement. Which is the harder to believe: That a person can pull a joke/hoax and never tell anybody about it? Or that there is a creature that there has never left any kind of clear evidence of its existence? And, there are rebuttals to the Patterson/Gimlin film: Here's just one I found in about 2 seconds of Googling. http://www.bigfootmustdie.com/patterson-bigfoot-film-fake.html (This critique is actually even written by person who claims to be a Bigfoot believer!) The point isn't so much that the film itself hasn't ever been "completely debunked". The point is that there are many, many valid questions about the film that demand answers that probably cannot ever be answered. The film is hardly conclusive. The film, because of the many issues with it, doesn't really help support a pro-Bigfoot-believer case. You can personally believe whatever you want. But, until some much stronger evidence comes forward, don't count on the scientific community or logically, rationally minded people to fall in behind you.

This is hardly conclusive enough in any way, shape, or form to rationally and logically fall on the side of "Bigfoot exists". Many pranksters have taken their jokes to the grave. The evidence for existence is exceptionally shaky, at its very best. The logical conclusion is nonexistence. Believe whatever you personally choose to believe in, but science demands much, much clearer conclusive evidence.

1) There have also been reports of faeries, leprechauns, dragons, trolls, goblins, griffins, yeti, succubus, elves, etc. etc. Simple "reports" aren't evidence. Mistakes happen. Overactive imaginations happen. Things that are common objects seen under different lighting or unfamiliar circumstances makes us think things that aren't actually there. This kind of "evidence" really isn't evidence at all. 2) No hair sample is perfect. No test is perfect. Hair analysis can make mistakes. And if the sample is corrupted or imperfect in any way, the test method may not come up with results. No database is complete, either. They could be samples from a family of animals that have had a small genetic mutation and their hair grows differently than typical members of their species. There are many possibilities, rather than just assuming Bigfoot exits. 3) I think that scat identification is even harder than hair identification, so everything I said in 2) above holds for scat, too. 4) OK, nothing else has dermal ridges? Or they can't be faked? 5) There are many, many different interpretations of this film. First and foremost is it only a scant few frames and exceptionally grainy. If the costume was any good at all, the resolution of the film is not going to pick up a tiny zipper or snap. And, I guarantee that a person could be trained to mimic the movements of a creature that size. Have you seen the wide variety of unnatural things people can be trained to do? Did you watch any of the Olympics? If someone had the dedication and the knowledge of what a large creature should look like, it can be mimicked. 6) Voice identification may be even harder than scat and hair. There are many, many sounds that known creatures make that aren't perfectly cataloged. And, of course, each animal individual will have its own voice and noises. I mean, just as an example, we are still discovering the exact hows and why cats purr. I guarantee that there are many, many woodland creatures that make noises that have never been recorded yet. 7) Kind of like 5, if someone knew what impressions should or could look like -- what's to stop them from making several fake feet to give the impression of "living flexible toes". The very fact that someone knows what that should look like allows for the possibility that it can be faked. 8) That's awfully specific knowledge about what a supposed Bigfoot was doing. I suspect that there are many other possible interpretations about what this could be. Or faked again. The problem is that there are enough people out there just to make fakes because they think it will be funny. Look how long the people making crop circles kept it up before they came clean. The really big problem is that none of the evidence is very conclusive at all. And in all likelihood nothing is going to be very conclusive until one is actually caught. Science doesn't just go on hunches and what someone really want to believe in. There has to be conclusive evidence. Without conclusive evidence, the most logical choice is that Bigfoot doesn't exist. Is there a chance Bigfoot does exist? Sure, but without conclusive evidence, the most logical conclusion is that there is no such thing as Bigfoot.

Basically, what Atheist said -- the root of the issue is this equation which is written wrong. it should be: [math]\nabla h = \mathbf{0}[/math] A vector ([math]\nabla h[/math]) must, must, must be equal to another vector ([math]\mathbf{0}[/math]) -- in this case the zero vector. You have a vector set equal to a scalar which is essentially meaningless. By setting it equal to the zero vector, you get two equations in two unknowns which should be solvable. p.s. you may want to use \nabla in the LaTeX code instead of \bigtriangledown -- the nabla lines up with the text nicer. It's a little thing, but it is something that I noticed as soon as I read you post.

I know that it probably wouldn't be easily passed or easily enforced, but I'd like to see more free trade with one major restriction. That for every item that is imported, that it has to be manufactured/produced with labor that was paid at the the current U.S. minimum wage. That would eliminate sweatshops and probably significantly reduce the elimination of a lot of the manufacturing jobs here in the U.S. because while not a lot of jobs are minimum wage here, it is probably still a lot cheaper to pay people above minimum wage than it is to pay someone minimum wage and then also pay to transport it. Like I said, I know that this probably won't be passed or easily enforced -- someone would have to interview the workers constantly to ensure they are being paid the U.S. minimum wage -- but I think that it is a fair way to still allow fair trade while still protecting U.S. workers.

Here's some more "abuse": Any math at all? Any way to make a testable, falsifiable, quantitative experiment to prove or disprove your ideas? Words are nice and all, but they only tell a story like a novel. If you have some math to actually back up what you're saying, then present it. You claimed above something "closely related to Maxwell's Equations" so let's see it.

I never said that there would be a difference between how far or fast or anything like that when you put the paperclip on the ball. The point is that the internal forces acting on the ball -- the glue between the paperclip and the ball -- do not change the ability for an outside force to act on the system. Namely a person throwing it. The coupling between a locomotive and an attached car is similar. No matter how weak or strong the force attaching the two cars are, an outside force can still move them. That was my point. It has nothing to do with speed or acceleration. Just the fact that the internal forces really have nothing to do with the external forces.

How the heck do you get this? You've missed some steps/made some errors here... You forgot to multiply the [math]y^2[/math] term by the [math]y^2[/math] term that was in the denominator of [math](\frac{10}{y})^2[/math] to get [math]y^4[/math]. The equation is [math]y^4 - 61y^2 + 100 = 0[/math]. Which can then be solved via the quadratic equation.

The force keeps the locomotive and the wagon moving together. They don't move independently of one another. It has nothing to do with just the locomotive moving. That is just an internal force, the external force, like the force the engine applies on the tracks to make the train move is independent of the internal forces keeping the train together. If you glue a paperclip to a baseball so that the coupling between the baseball and the paperclip is 10,000N, can you not still throw the baseball? The baseball still moves, because its movement is independent of how strong the glue is that is keeping the paperclip attached. Even beyond that... Newton's Third Law doesn't prevent things from moving, either. The train's engine pushes against the track. The track will push back against the train in an equal and opposite direction. This causes the train to move. The tracks are anchored to the ground. So, in reaction to the train pushing against the track, the track pushes against its anchors in the ground. The track pushes against the entire earth. And, the entire earth does move in response to this push -- it is just that the entire earth is so massive the movement caused is very, very tiny. Imperceptibly tiny. Same thing when you jump. You push off from the earth. You move up and the earth moves down. It is just that the earth moves down just a minuscule amount. Minuscule enough that for all practical purposes it is zero. But it does move, and that movement is a direct consequence of Newton's Third Law.

I have to agree with Gilded... you need to expound on this quite a lot. The mathematical notion of a point has served mathematics quite, quite well for a very ling time. And there is no compelling reason at all to change a fundamental definition of mathematics. In fact, though the physical world and the mathematical world don't have to necessarily coincide as has been pointed out in this thread many time, there are many physical situations where using a mathematical point -- a zero dimensional object -- yields exceptionally good results. Treating an ideal gas as a collection of points can be quite accurate for the correct gas (like Helium) and for high temperatures. Modeling the trajectory of a probe on its way to Mars, you can treat the gravitational influence of the distant planets like Uranus and Pluto like there are just point masses. There are others -- the main thesis here being that the physical and mathematical notions of a point can and often do coincide with exceptionally very good results. The biggest thing is that the mathematical notion of a point is still an exceptionally useful learning tool. Sure, a ball flying through the air isn't really a point. But, the full problem taking into account the drag, the lift, the spin of the ball, the turbulence of the air, etc. is a very tough problem. Treating the ball as a point and neglecting the air resistance generates a problem that can be solved. And, in learning to solve the problem, the students get a feel for the skills necessary for problem solving and thinking logically and working it out for themselves. That way they know the basic problem before tackling the more complicated ones with drag, etc. So, you're going to have to present so very, very compelling reasons why the "world view" is no longer compatible with the mathematical notion of a point.

It is simple supply and demand. John Girsham's latest or Stephen King's latest sell more copies in just a few hours than the average science or engineering textbook will sell over the entire run. I think the really amazing thing is that book publishers are even willing to keep publishing these books. Especially with all the electronic media available -- either a professor typing his own notes or available from the research journals -- one can make their own set of permanent and editable notes pretty quickly. The cost is high, but I liked to think of it as part of the investment. I kept all but two of my books, and I know that I've used them all in some way after the classes I used them for. Even if only because I knew where to look something up in one of them faster than in a different book.

Dennis, I think a good analogy would be knowing the definition a word: how to use it properly, how to use it in the right context and all that, but you don't know how to spell it. Does not knowing how to spell it take away from your knowing the word? No. You know what it means and how to use it correctly. To take the analogy further, say you were trying to look up how to spell it, but the dictionary you are using has infinite pages. You know the procedure for looking it up, but you can't ever find the exact word you know because it would take an infinite amount of time. There are algorithms out there than can compute any of the digits of pi you want. You specify "I want the 765,813rd digit" and the algorithm gives it to you. That's completely knowing how to get every single digit. It doesn't matter what digit you ask for, you can get an answer. But, it would take an infinite amount of time to computer an infinite number of digits. Nevertheless, you are missing the bigger point that just because it has an infinite number of digits, doesn't mean we don't know it. It is a number that has many definitions, all equivalent. Again, going to my dictionary/word analogy, if you know someone (say like me and some of my loooong posts) who is unduly prolonged or drawn out, who uses an excess of words, you know exactly what that means. That means, you also know what prolix means. You may have never used/known about the word prolix until just now, but you knew what it meant -- you had a definition for the word prolix, though you didn't know exactly what that word was. In the same way, we have many definitions of pi. We know exactly what it does, what it's properties are, etc. etc., just because we don't know every single digit doesn't mean we don't know it.

foodchain, no one is saying that words and ideas have no value. Quite the contrary, they can have tremendous value. But, the bigger point is that mathematics is the language of the science when you want to be exact. For example, given a ball velocity, a spin rate, and a launch angle, I can predict where a struck golf ball is going to land. The models are good enough that I can predict where it will land within just a few cm, actually. (Testing done indoors with no random variables like wind.) The best words can do is "over there" or "over here" or "behind that sign". For that matter, math lets us launch vehicles to land on Mars. Words cannot do that. The math is necessary to know what the mass of the vehicle, how much the gravity of Saturn is going to influence the probe on it's way, etc. etc. Words can paint a pretty picture, and tell a compelling story -- we've all read novels -- but words alone cannot tell you anything in precise terms. And, depending on the application, preciseness can be very important. For example, I want this message to go precisely to the server this forum is on. And I want the keys to transmit precisely the right value to the computer when they are depressed. Words alone can't make this computer work. So, like I said, words can describe things well. But, to do anything with precision and accuracy, you will need the math.

OK, consider yourself corrected, because you are wrong. The value of pi is known -- just because it is irrational in no way whatsoever means is cannot be known. It just has an infinite decimal representation. (As much as I am loathe to bring this topic back up) Do you consider 0.999999999..... infinitely repeating 9's, unknown? There are an infinite number of digits after the decimal. It just turns out that the infinite number of digits after the decimal fir pi have no nice patten like 0.99999 or 2/7 or any other rational number. Just because there isn't a pattern doesn't mean we can't find out what those numbers are... because we can. We literally know millions of the digits after the decimal point. There are just an infinite number of them, so it is impossible to find every single number. But, we know the methods to find the digits -- that's completely equivalent to knowing the digits anyway. The big thing is that just because there are an infinite number of digits, doesn't mean that the number is "unknowable".

Since math is now irrelevant, I'd suggest to your boss that he can pay you whatever he wants. Your boss can just explain how being paid minimum wage and being paid 10x minimum wage are both very similar, and since they both have common ground, they are really the same. In fact, being paid $0.0001 per hour has common ground with being paid minimum wage, so they are probably the same, too. I like this no math thing. I'm going to pay my bills this way, too. "Dear electric company, paying $5 this month has common ground with paying $50, so they are really the same." And, guess what! I just broke the world record for the 100m sprint. I mean, 1m has common ground (in this case literally!) with 100m so they are really the same, and I just ran 1m in 9.0 seconds flat, so I'm clearly the world's fastest man now. I think I like this brave new world of no math. There are so many opportunities...

If the first semester of physics is taught correctly, there is a large, large amount of calculus in the course. It usually isn't hard calculus, but it is many integrals and derivatives. The calculus was invented largely in order to describe physics correctly, even "classical" mechanics is largely founded on calculus-based mathematics.