Bignose

This is a classical logical fallacy -- an argument from incredulity. Just because you can't see how something is possible, does not in any way whatsoever mean that something is impossible. http://en.wikipedia.org/wiki/Argument_from_ignorance Basically, you have to show some evidence that what you believe is impossible; your beliefs on the matter are essentially meaningless without evidence. You can have your strong opinions/feelings/intuitions about something, but that's all they are -- opinions. In the 1890's I very much doubt that many people would have believed it was possible to transmit moving pictures and sounds into every single person's home, but obviously today that is common and done in multiple ways. Unless something can be proven to impossible (like by breaking a fundamental law of physics), the arguments from incredulity don't carry any meaning.

I dunno, pioneer. What "tool" hasn't ever been manipulated by those with a motive? Math/statistics/science is only one entry in a long list of things that people use to sound authoritative with, but is really just another way to try to grab power. State-run media (like in Russia, Zimbabwe, Myanmar) is another. Religion is probably the real biggie. How many things have been done in the name of a god? It is just another thing that needs to be viewed with skepticism. It is easy to just look at a statistic like "red headed people get 8% of the tickets, but are only 4% of the population, so they are being profiled unfairly" and agree with the conclusion that is made. (** Just to be perfectly clear, I completely made that up**) But, the real question is rarely so simply clear cut. A fair number of red headed people have some Irish lineage, and there are a fair number in New England maybe the New England police just write more tickets than the rest of the country and it appears that the red haired people are being targeted. What is the sample size? which leads to the question what is the chance that it is just coincidence? There was a significant apple scare in the 1970's -- a medical study linked cancer and apples. As you can image, for a time the sales of apples completely plummeted. But, it was all a coincidence. The subjects of the study just happened to get caner at a higher rate completely naturally. And, this was only one study, out of many others that showed the benefits of apples -- but the media ran with it -- and like I said, the sales of apples plummeted. It didn't take too long to realize what happened -- but it is important to note that it wasn't a mistake in the traditional sense -- there was a strong correlation between the subjects of that study who all ate apples and cancer. But, correlation does not mean causation. Anyway, like I said, I think that statistics is just one more thing to manipulate today. There was a time -- late 90's -- where you could predict the outcome of a global warming study with pretty good accuracy just by looking at the funding source. You can still accomplish that today with gun studies. It really doesn't matter who is telling you anything -- the important thing is to use your own brain and don't just take someone's word for it. Ask for some evidence to back things up. Ask the tough questions. Don't let someone get away with using any of the common logical fallacies like appeal to authority. Don't let someone turn it around on you just for asking questions "How do you know what I say isn't true" -- it doesn't work that way, the claimer has to show the evidence for his statements, you don't have to entertain any and all whimsical notions until they have been disproven. Skepticism today seems to have become almost a dirty notion. I've seen people become almost angry at me for asking for evidence of the statements they made. As in political correctness taken to some extreme says that we have to accept all different ideas until proven wrong. But, that just isn't right -- if someone makes a statement, it isn't an unreasonable or unfair or wrong point of view to ask them for some evidence to back up their statements. I'm not talking about opinions, but when they make factual-like statements. Skepticism is something there is precious little of today, so just always look at these things through a skeptical eye. Stats are just another thing used to skew points of view, and I think that they need to be viewed as such.

No, No, a thousand times No. This is NOT the way it always is in physics. Physics is about prediction pure and simple. Physics predicts how much energy is needed to get satellites into orbit. Physics predicts the corrections due to relativity that is needed so that those satellites give us accurate GPS data here on the ground. Physics predicts the internal workings of the sun, the internal working of quasars, etc. Physics tells us how a golf ball flies through the air, how airplanes fly through the air, how blood flows through out capillaries, how to manufacture swimsuits so that Olympic swimmers eek out extra milliseconds in competition. Etc. Etc. Etc. Physics is all about the experiment and prediction. Sure, some experiments cannot be performed yet -- we admittedly aren't 100% sure what is going on in the sun, but we can use the best data we have to data to make predictions and in the future if we do have the ability to gather data from the sun itself, then the models may have to be refined. But, if you don't make predictions, you are NOT doing physics. I'm sorry, without predictions, you are doing metaphysics or -- as where this thread got moved to -- pseudoscience.

OK, I'll bite. Please use your theory and mathematics to make one testable prediction. Describe one test that can be made completely objectively and will be completely Boolean -- that is, will be clearly confirming or falsifying your theory -- nothing wishy-washy where the experiment "sort of" matches your idea. Because, unless there is something that your extra mathematics can predict that the old theories cannot, all you have here is word and symbol salad. So, let's see something besides just words and equations (some of which are just wrong, BTW -- the 2-norm of a vector is [math]||\mathbf{v}||_2 = \sqrt{v_1^2 + v_2^2 + v_3^2}[/math] you forgot the squared on each of the terms on your second equation and your notation is a little confusing because usually there are components in the x, y, z directions, not actually x,y,z themselves which is why you usually see the components as [math]v_1, v_2, v_3[/math] or [math]v_x, v_y, v_z[/math] and not as [math]x, y, z[/math]. But the big problem is that your vector norms are just wrong. The general form of vector norms are [math]||\mathbf{v}||_n = (v_1^n + v_2^n + v_3^n)^\frac{1}{n} [/math] where n is usually limited to some integer. You have n equal to 2 and 1 in the same equation which just isn't right. ) Let's see your theory demonstrated in some clear cut fashion. p.s. if you learn to use this forum's LaTeX math typing system, your equations will be much, much, much easier to read. LaTeX is pretty easy really and well worth a few minutes to learn

"The are lies, damn lies, and statistics" -- Mark Twain Basically, what you are looking for is some actual practical science to be taught in the classroom. Unfortunately, this just isn't the status today. The kids are taught science as just another collection of facts to memorize. The colors in the spectrum are ROY G. BIV. The eras of the earth are Cenozoic, Mesozoic, Paleozoic, etc. The distance from the earth to the moon is 384000 km. Etc. Etc. Etc. It is even to the point where the steps in the "scientific method" are just a list of things to memorize. There is no practical discussion/use made of them. There is no skepticism/burden of proof taught in schools. That's why Head On as a product can exist for more than 5 mins. If everyone learned some basic skepticism, everyone would see right through the claims. Same thing with the magnetic bracelets. The statistics come into play too, because sure these products claim some improvement/healing... which is true. But, the improvement isn't statistically significant above placebo. I'd like to see them spend an entire year of science classes just on placebo & statistical significant if that is what it took to teach people about this. Part of it also is that large numbers are essentially meaningless. A guy last week got two holes-in-one in one round. Golf Digest said that the odds were 1 in 161 million. What does that really mean? Why even quote it (other than it makes a catchy sound-bite-like phrase)? Why the accuracy to 3 figures -- 1 in 100 million or 200 million is practically equivalent. The numbers are especially troublesome when health reports come out. Especially when they report the relative statistics. "Eating bacon increases your chance of toe cancer 35%" (Please note I completely made that up.) Well, if you chances of toe cancer were 1 in 100,000, they are now 1.35 in 100,000 if you eat bacon. Not a large increase, especially if you like to eat bacon. But, saying 35% makes it look like a huge dramatic increase in risk. Same thing about the health benefits -- "drinking coffee lowers the risk 10%" Again, if it was 1 in 100,000, if you drink coffee, now it's 0.9 in 100,000, again pretty tiny. And, if you don't like coffee, then it almost certainly isn't worth forcing it down. Dr. Dean Adell has a very good book that expounds on this: Eat, Drink, and be Merry. He talks about how the media likes the relative statistics because it makes it seem more significant. But, the basic tenets of good health have been known for a long time -- eat a wide variety of things and exercise more often than never and your chances of a long healthy life are pretty good.

There are many ways, but always liked the conversion from Cartesian to cylindrical coordinates: [math]dxdy = rdrd\theta[/math] To find the area of a space, you integrate over the limits of the space. In Cartesian coordinates, the limit is described by [math]x^2 + y^2 = R[/math], but in cylindrical coordinates, the equation of the circle is much simpler: [math] r = R[/math] So, in cylindrical coordinates: [math] A = \int^{2\pi}_0\int^R_0 rdrd\theta = \pi r^2[/math] You get a completely analogous result in spherical coordinates in 3-D: [math]V = \int^{\pi}_0\int^{2\pi}_0\int^R_0 r^2 \sin\theta drd\theta d\phi = \frac{4}{3}\pi r^3[/math] The conversions from coordinate systems completely take care of themselves.

The thing is, hobz, is that just fitting your data to a curve is fairly easy. You define some fitness measure -- sun of squares is usually popular -- and then adjust the parameters of the distribution to minimize the fitness measure and then find which curve with its best best set of parameter fits overall the best. But, I want to return again to the nature of the phenomena being measured. This should give you the best insight as to what distribution is the most meaningful. I won't repeat the examples from my first post, but just give you another. The Weibull distribution is used when analyzing failures (of anything, mechanical, electrical, etc.) because it is based on the idea of the weakest link in the chain breaks first. A good statistics and probability book should have some good discussions on the origins of the distributions. A curve fit is also kind of a trivial exercise without further data gathering -- what curve best fits not only the current data but the future data as well. As more data comes in, it may become more apparent which shape of curve is better. Finally without any resolution of whether the maximum is peaked or rounded, the exponential and Laplace distributions are both going to fit that data pretty well.

The ideal, though not always possible, best place to start would be from the physical phenomena that generated the sample. Is the physical phenomena going to have a certain distribution? If it is, then the data should as well, or be of a "similar" function. Secondly, examining the measuring device of the data can also sometimes yield insight. I remember a buddy taking a psychology course where the teacher confidently proclaimed that every human train is distributed normally. That is utter nonsense, because I don't think that hetero-homo sexuality is normal with a large number "sort of straight and sort of gay" in the middle -- it's probably pretty bimodal with large lumps straight and large lumps gay and only a few in the middle who are unsure. But, the teacher can make that proclaimation because every trait in psychology is measured by filling out the "strongly agree, agree, neutral, disagree, strongly disagree" questionnaire (or something similar) and then the trait the test is supposed to measure is gotten from the average of how the person answers those questions. It is the Central Limit Theorem completely at practice there. It isn't that every trait is normal, but the sum of a large number of independent observations from any distribution will approach normality. The test measured the trait over and over and over again, enough that the CLT took over and make it appear like every trait is distributed normally. But, the psychology teacher didn't have the math knowledge to understand that. That aside is just to show that the measuring device can influence the expected statistics as well. If it was a temperature probe that averages the temperature over a period of time, for instance, you may run into CLT issues again, especially if the averaging period is much longer than the fluctuation period. However, all that said, if you don't have any clues, there is a branch of statistics that deal with goodness of fit. You should be able to find topics on goodness of fit in more advanced statistics books.

Chapman and Cowling's The Mathematical Theory of Non-Uniform Gases has a derivation based on kinetic theory of gases Batchelor's An Introduction to Fluid Dynamics has a good derivation, as does Bird, Stewart and Lightfoot's Transport Phenomena. In fact, any fluid mechanics book that covers the more mathematical side of the subject -- as opposed to the "rules of thumb" side of the subject like pump sizing and estimating pressure drop in a pipe based on a chart of friction factors, etc -- all of which is very important, don't get me wrong, it just isn't related to the mathematical/differential equation side of fluid mechanics -- will have a decent derivation. The wikipedia derivation isn't all the great, unless you already know it. Definitely try the Bird, Stewart, and Lightfoot reference.

As this sure looks like homework, and the forum rules prohibit giving answers directly to homework questions, I will only provide generals hints. Do feel free to post what work you have done and members can help check your work, but do not expect your work to be done for you. a) You have to make an assumption that the acceleration will be constant. Based on the the relationship between acceleration and velocity, you should be able to answer this. b) This one uses the relationships between acceleration, velocity, and distance. c) see b) d) in addition to comments about b) this one also uses the relationship between force and acceleration.

What are you career goals? More application -- in particular computer based -- discrete math. More theory and pure mathematical based -- number theory. Or just take both. But, talking with your adviser and the probable lecturers involved is probably the best idea.

But, just how are you going to make things colder? Heat flows from warm to cool, and the many(, many, many, ...) times validated laws of thermodynamics show how no matter how efficiently you tap into that warm going to cool, there you'll never be able to get all the energy back. Some is always lost. Whenever you cool something down artificially, like your refrigerator for example, that takes more energy to so do than we'd get back from tapping the heat flowing back into the fridge.

Spherical coordinates seems like a more natural choice to me. The mirror's particular angle necessary to ensure the target is illuminated would be a function of the spherical coordinates.

I know that this may be completely futile, because it is very hard to argue with ardent faith. However, I'm still going to ask... were there any controls in this experiment at all? For example, surely the words in the Bible would retain their power no matter what language they are spoken in, right? So, you set up an experiment where someone reads both verses from the Bible and versus from War and Peace in a language completely unfamiliar to the test subject. If the Bible verses really retained their "power" there should be clear statistically significant effect over placebo when the translated Bible verses are spoken versus the translated pieces from War and Peace. The foreign language is critical, because if the person understands or recognizes the words, that can have a very significant physiological response.

Well, there are many reasons the varieties that have been cultured are the ones that were picked. Some of them have been mentioned -- the variety that grows best in the given conditions is probably the biggest one. The variety was picked because it was the one that gave the largest or best fruits consistently. Consistently can mean a lot of things, too -- most resistant to disease, most resistant to pests, etc. Lots of variables there, but don't think that taste was discounted either. Obviously if the fruit tastes better, then more will be sold or sold for a higher price, and that's a considerable factor, too. On a similar note, in terms of corn and soybean farming these variables can be exceptionally detailed. With the GPS systems in use today, the farmers can get a pretty good map of the soil conditions over the span of their land. And with the different soil conditions, different varieties of corn may be best on different parts of the acreage. Or, different fertilizers or pesticides may be better or needed on different parts of the land. The days of just buying one type of seed are gone, the farmers trying to maximize profits today keep records and plant many different varieties of seed. Then, during harvest, again the GPS systems are used to accurately measure how each area did. Telling the farmer what varieties worked and what didn't and suggesting improvements for next year. Living in Iowa, I know that this is the state of modern corn and soybean farming, but there is no reason to think that any other type of farming is any different.

Because the Earth is all one piece, the Northern hemisphere and the Southern hemisphere don't "rotate in opposite directions". They rotate in the same direction. It's not like if you jump over the Equator, you have to suddenly change directions. The sun rises in the East and sets in the West in both hemispheres -- if they were rotating in opposite directions, that couldn't be. Now, if you look at the Earth rotating from atop the North Pole and compared that with looking from the South Pole, then, yes, it will look like it is rotating in opposite directions. But, that is all a matter of perspective. Just like if I threw a ball at you, the perspective is that the ball is coming towards you, but my perspective is that the ball is leaving me. Which is correct? They both are, from our perspectives. On top of that, ecoli's point about reference frames being arbitrary is still valid too. In one reference frame, the Earth would appear to have a certain rotation. In a second reference frame, one that is rotating more, the Earth may have a slower rotation speed. In a third we could choose a reference frame where the Earth had no rotation or a reference frame where the Earth actually spun the opposite way. All of these are equally valid points of view. The exact same thing can be done with lateral movement, too. In one frame, the Earth sits still, in another the Earth is zooming through space. It's just like that example if the ball I threw to you. In one frame, yours, the ball has a negative velocity in my frame the ball has a positive velocity. It's all a matter of perspective.

If you look on Amazon.com or any good university library for books under the subject of "process control" you'll find a lot of good information. I'd suggest one with something like "Introduction to ..." or "Practical" or something like that in the title. Something geared toward an undergraduate level. (I learned from Ogunnaike and Ray's Process Dynamics, Modeling, and Control which is geared a little more towards chemical process controls but the idea about control is the same whether it is the temperature, or a robotic arm.) This of course assumes that you have the necessary math to start the book -- differential equations, matrix algebra, etc. If you don't have that, you'll probably need to fill that void first.

As much as anything, Slinky, it was my hope that my post wasn't so much trying to confound you with math, but a plea to be very careful with how you use words. Saying something like "gravity = time" is meaningless because -- like I wrote out above -- the force of gravity is proportional to the acceleration is has on an object and acceleration requires a concept of time to define acceleration. So, setting these two very different and related concepts equal to each other doesn't mean anything. In order to make sure everyone knows what everyone else is talking about, you have to be very precise in the way you use words. When I talk about a "force" in physics terms, everyone well versed in physics knows what I mean -- they also know I am not talking about momentum or energy or velocity or acceleration or etc. Physics isn't completely perfect about this, but it tries very hard to make sure not to use ambiguous words or words with multiple meanings or interpretations. So, again, calling gravity = time has no meaning. I don't have any treatises in me, and I don't know the mechanism by which the passage of time changes during acceleration. I do know that the effects aren't just relegated to gravity, however, the physics is completely independent of what is causing the acceleration, be it gravity or magnetism or some futuristic warp-drive system. Any acceleration changes the passage of time. But the big thing is to be very careful with your word choice and be very careful with not intertwining concepts that are already well defined. You second post in this thread seems better about not just re-using words in a casual manner. But, the first is gobbledygook.

To really complicate things, not all votes are/were created equal in Texas. Each district was weighted based on the turnout in the last national election. The districts with the larger percentages of it's voters that voted Democratic last time got more weight. Democratic primary votes in Austin counted almost twice as much as a primary vote from the rural panhandle. It really seems like a needlessly complex system. Vote, caucus, whatever -- pick one and stick with it. And, I really think that it is unfair to have your vote count less just because more people voted for Bush in your district. It's almost like they are punishing you for not going out an campaigning. I heard a radio interview where lots of people didn't realize that this was how the weighting system worked, and they chose not to go out and vote last time around because Bush was going to win Texas without a fight. So, they are being punished for living in a district with poor voter turnout. It really is unfair if you had gone out and voted last time. Maybe your vote should count less if you didn't vote last time -- that at least seems fair to me.

If he only knows algebra, that's going to be an exceptionally hard book to get very far into. Chapter 2 covers calculus and then expands from there. This looks like a very good book for someone who already knows the subject matter, not a good one to learn from. What the OP needs is a book with lots of practice problems, with answers so he can check his answers to the text. I'd recommend going to the library and finding a precalculus book. It should pick up where algebra left off (probably a decent amount of review, too) and work on it. Do lots of practice problems. Then do a calculus book, again, lots and lots of practice problems. Don't just read it and think you know how to do it -- you have to practice it over and over to own the knowledge. A precalc and calc book should keep you busy for quite some time.

There are some interesting applications. Non-Fickian diffusion can be described using fractional calculus. Normal Fickian diffusion can be described by [math]\frac{dc}{dt} = \frac{d^2 c}{dx^2}[/math] where c is a concentration, t time, and x position. Non-Fickian diffusion obeys [math]\frac{dc}{dt} = \frac{d^n c}{dx^n}[/math] where if 2>n>1 the diffusion is called "accelerated" or "fast" if n>2 the diffusion is called "retarded" if n<=1 the diffusion is sometimes called "bombastic" The viscoelasticity of polymers can sometimes be described by fractional calculus as well. In a fluid, the stress tensor is a function of the gradient of velocity, velocity of course being the derivative of position with respect to time. In a solid, the stress tensor is a function of the gradient of the displacement or position -- in a way the zeroth derivative of position is position. In a viscoelastic material, there are both "fluid-like" and "solid-like" components to it. Sometimes, an appropriate stress tensor can be made by a weighted sum of the fluid stress tensor and the solid stress tensor. But, there are other models out there that make the stress tensor a function of the gradient of a fractional derivative of position. [math]\mathbf{T} = f(\nabla \frac{d^n \mathbf{x}}{d t^n} ) [/math] where 0<n<1. While there are a few applications out there, I suspect that it will remain a curiosity more than anything. They are very hard to work with -- almost always requiring the use of Fourier or Laplace transforms. And usually a more simple model (made of derivatives of integral order) can be generated that can mimic the results of the fractional derivatives. Lastly, in today's world of computational models, I'm not very sure how to model a fractional derivative via discrete methods. It is pretty straightforward to model first and second derivatives on a grid, but I don't really know how I'd go about modeling the 1.5th derivative. This really hampers it's usefulness as a model. However, I would bet good money that someone has figured out how to discretize fractional derivatives.

So now gravity has been calculated wrong, too, eh? You're going to have to prove this as well. The calculations are fairly easy, actually, so I'm very interested to see where those went wrong.

I don't see how you can say that 7 miles is "relatively deep within the Earth's crust" when the diameter of the earth is almost 8000 miles. Please answer this also: one of the main reasons we know the mass of the earth is because we know how it moves around in it's orbit. If it had significantly less mass, it's orbit would be significantly different. The density of liquid iron is around 7200 kg/m^3 (Taken from http://homepage.ntlworld.com/oxfordtours/workitoutnet/castaid/spruecalculator/densci.htm and converted units). The density of liquid hydrogen is around 67.8 kg/m^3. (Taken from http://www-safety.deas.harvard.edu/services/hydrogen.html and converted the units) Even taking some of the less dense blends of iron on that table linked above, the density difference between liquid hydrogen and liquid iron is one hundred fold. How to you explain this missing mass?

Within you theory, then, please remedy this conundrum. Given that gravity = time. Gravity is a force. [math]F = G\frac{m_1 m_2 }{r^2}[/math] where F is the gravitational force between two objects, with masses m_1 and m_2. The distance between the two objects is r, G is a constant. A force is mass * acceleration. [math] F = ma[/math] The acceleration felt by object 1 in this case is [math]a_1 = \frac{F}{m_1}[/math] acceleration is the second derivative of position with respect to time. [math] a = \frac{d^2 x}{dt^2}[/math] But, if time = gravity, how do I put this into this equation? Force is proportional to acceleration which is the second derivative of position with respect to time. If gravity isn't a force, what else could it be? And, if gravity is a force, how does it get remedied with the definitions of force and acceleration which has time in it?

Just to back swansont up here -- consider a micron size particle of gold (not all that uncommon in the making of catalyst particles). Gold has a density of 19,320 kg/m^3 (almost 20 times that of water) but if it was only a droplet with a micron diameter, it would only weigh 8.1*10^-8 milligrams. Pretty light object with a very high density. It is important to note the difference between intensive and extensive properties of objects. An intensive property (also known as a bulk property) does not depend on the size of the system being investigated. For example, the density of gold is 19,320 kg/m^3 no matter if we look at a drop a micron across, a millimeter across, a meter across, or a kilometer across. Other intensive properties are temperature, viscosity, chemical potential. An extensive property does depend on the size of the system being looked at. Some examples of extensive properties are mass, length, volume, mass, total energy. The gravitational pull is based on extensive properties -- the gravitational pull between two masses depends on the masses of those two objects and the distance between them. Assuming they are far enough away, then they can probably be treated as point sources of mass in the center of mass of each object. If they are not far enough away, the local density of objects could have a small effect. I.e., compare standing next to a mountain versus standing next to a plain. There will be a small gravitational pull towards the mountain as well as toward the center of the earth versus standing on the plain you will only be pulled toward the center of the earth. Now, the effect is small, and in almost every single case negligible. As a third example, if you were standing on a plain and on your left side under the ground was a very large deposit of gold and on your right side was a very large deposit of aluminum (density 2700 kg/m^3, much less dense than the gold) then there would be a slight pull toward your left side, like with the mountain. Again, in this case, the local density has a gravitational effect. To be completely accurate, the way you figure the gravitation pull in this case would involve the integral of all the mass. But, get far enough away, and these local density changes get smeared together, and again you can treat it all as one point source of mass. It is very rare that the level of detail involving local density changes is needed.