Bignose

This was exactly my thought, too. The reference I'd go to would be Synge & Schild Tensor Calculus. It is an "old-fashioned" tensor calculus text, but it develops right up to this exact problem, and if you know calculus and differential equations, you have the necessary prereqs for the book (I've found you need more prereqs for some of the more modern tensor calculus books).

We've actually gotten matter down into the picoKelvin range: http://lib.tkk.fi/Diss/2000/isbn9512252147/ While it wasn't what the authors were looking for in their design of the experiment, I would think that if matter were disappearing, it would probably be the headliner in the abstract of the work in the link above.

Randomness can certainly be defined mathematically, so in that sense, randomness is real. And there are several situations in real life that while maybe not random at the micro level, at a macro level can be described very well by random variables. Turbulence in fluids, the agglomeration/flocculation/breakage of oil droplets, the dispersion of fine particles/droplets, the birth and death of a large population of cells, the precise arrangement of atoms in an alloy or zeolite are just a few that I know of. I guarantee that there are many more I can't think of. And that doesn't include all the "traditional" ones like rolling some dice or shuffling cards. Yes, while the process of shuffling and rolling dice can be deterministic if every variable is accounted for, these can be made random if you intentionally don't account for every variable. Like I said with QM, it may be possible that truly deterministic processes may be found for all of these, but again at a macro level, all can be described very well with random variables. There is a whole branch of mathematics called stochastic calculus that deals with the processes of random variables.

Well, simply force is equal to the time derivative of momentum. [math]\mathbf{F}=\frac{d(m\mathbf{v})}{dt}[/math] F = force m = mass of object v = velocity (force and velocity are bolded because they are vectors) very often, the mass of an object is a constant (only things like rockets which expel mass would have a changing m), so that can be taken out of the derivative [math]\mathbf{F}=m\frac{d\mathbf{v}}{dt}[/math] velocity is the time derivative of position [math]\mathbf{v} = \frac{d\mathbf{x}}{dt}[/math] So, velocity is the change in position with respect to time (that is, motion), and a force is the change of velocity with respect to time, and that force can some from any from your list. That's how a force and motion are related mathematically in physics.

quantum mechanics seems pretty random at its base. There may be deterministic sources underneath that we haven't discovered yet, but QM seems pretty random at the moment.

This is the first step in the crucible of scientific inquiry. If your idea cannot even survive Q&As on an Internet forum, how are you ever going to get serious support for your idea? Besides, scientific rigor is still required in the P&S section. The laws of science still apply, but this section is a little more loose in that people are allowed to propose different speculations, but then must address them and any questions about them scientifically. That's all I've been trying to do is to post questions for you to think about scientifically. I've been trying to help make your theory better, by trying to get you to answer questions about your theory that don't jive with the current understanding. You've been using words that have specific meaning in a scientific sense not according to their specific meaning. Like dimension. Quite simply, by answering the questions I posed, you will help your theory. Because these are exactly the kind of questions any other physicist or mathematician is going to ask, too. They can't just make up formulas, they have to be able to describe something with the formula, and what they describe has to make sense. The length of a second is very well defined: http://en.wikipedia.org/wiki/Second though I think it may be more accurate to say that the duration of a second is very well defined. Length is a metric along a coordinate axis (or dimension!) and again that notion of length is also very well defined. And, again in terms of being very specific, what is the "speed" of a second? It is not up to me to define, this is your idea, why don't you define exactly what you mean by the speed of a second? Time slows down at the speed of light, sure, but there is definitely movement. Again, photons move from one place to another -- a finite distance in a finite time -- so there is definitely movement at the speed of light. Again, I feel like this is a case of using words that have exact meanings in a very inexact way. Poems and novels can get away with this, in science you cannot because when you say things like "movement" it means something very specific. Ultimately, every section on this forum obeys the same rules -- that the posts must be backed up scientifically. As I wrote, this section is a little looser in that initial ideas that aren't as well supported can be proposed, but then they are scrutinized and need to answer questions that are scientifically justified. That's all I've been trying to do, is ask questions in a scientific manner. And ultimately, if those ideas cannot be supported, if those questions cannot be answered, the main idea is rejected.

The medium of communication (this forum) may have made my intention a little unclear, but I wasn't looking for the nuts and bolts (and dollars and cents) of why the experiment couldn't be repeated. I was looking for the big-picture point-of-view as to why there was so much hesitation and reluctance to try to be objective and unbiased about it. You completely ignored my post #35 which I expanded on why the costs are nobody's problem but the believer. You also completely ignored my post #29 which details several of the issues I had when I looked over the published paper. That's why I feel like there hasn't been any discussion of substance, and feel like there isn't much point in continuing to participate. By analogy, I feel like we are discussing opening a nationwide chain of stores and you have spent the last month arguing over whether the stripes painted in the parking lots should be yellow or white instead of any of the truly substantive issues such as distribution, advertising, or manpower. Or, by another analogy, you are trying to straighten the tables and lay out the place settings just perfectly on the sinking Titanic. In other words, don't worry about the smaller details until the larger ones have been addressed! If you can solve some of the large problems, then two things: 1) then you can start to discuss the finer issues like cost and 2) you'll be in a much better place to actually request and improve your chances to receive funding if you can satisfactorily address concerns brought up by the proposal reviewers. So, if you get back to addressing the major issues, maybe this discussion will reignite, otherwise, I see it as pretty pointless.

Let me be perfectly clear, I have stopped replying in this thread, not because "I have been embarrassed into silence" or because I agree with you, but simply because you don't actually address any of the points I bring up. You have a penchant for trying to change the subject (like this whole diversion about Columbus which hss NOTHING to do with ice crystals and this latest one about the cost of the experiments which again has NOTHING to do with actual results or proposed mechanisms) -- stick to the topic at hand rather than trying to divert attention away from the holes in the idea! So, I lost interest because you haven't demonstrated any real interest in discussing the idea in a scientific way. If you do start, I'll come back and participate more fully, but until then, I just don't care anymore.

I dunno. Just a quick browse of a Google search shows that 100 pK (that would be [math]10^{-10}[/math] or 0.000 000 000 1K) is one of the coldest temperatures achieved. See http://lib.tkk.fi/Diss/2000/isbn9512252147/ While it may not have been what the researcher was looking for, I would suspect that if they had found a new state of matter, it would be the main point of the abstract above. If not, you don't have a very big temperature range at all between 100pK and absolute zero for your "superfreezing" oh, and there are already at least more than 5 states of matter (a 5th being a Bose-Einstein condensate, for example). And depending on how precise your definition of "state of matter" is, there could be more than 10 states: http://en.wikipedia.org/wiki/State_of_matter

OK, that's fine, but again no one wrote that it was easy or to treat z as a constant, so it was kind of a weird response to the thread. Also, you still didn't actually define what w was. I'm sure it was a typo (since it doesn't really make any sense), but it is still bad form to just leave any variables undefined -- especially as the OP is an obvious beginner. At least link to a source with more complete information, like linking to: http://mathworld.wolfram.com/Cauchy-RiemannEquations.html Might be nice to say a word or two about them (like, C-R equations come from differentiating a complex function f(z) with respect to z = x + yi i.e. with respect to dz = dx + dyi. Finally, this forum does have a LaTeX capability that will make the math easier to write and read: a la [math]\frac{\partial u}{\partial x} = \frac{\partial v}{\partial y}[/math] and [math]\frac{\partial u}{\partial y} = -\frac{\partial v}{\partial x}[/math] much nicer looking than trying to write out "partial derivatives" where necessary and write the fractions using only ()'s and the / key.

I'm kind of confused by this response because who said complex analysis was simple and who said to treat z as a constant? i is a constant, but obviously not z = x + yi. Furthermore, I agree completely with what Snail wrote... especially in light of your last post where you actually used u as a variable! Though you didn't define what u, v, y, or w was...

There is a whole extension -- Find a good "Complex Analysis" book and you'll see that there is quite a lot in addition to just the calculus of real variables.

This is it right here. This is the whole point of learning limits, because the basic definitions in calculus depend on that definition. If it isn't clear now, it should become clear in the near future.

As much as anything, it is just tradition. It probably started from the fact that they are different quantities, so the units were just given in different ways. Also, the torque, being a moment arm times a force, the units as commonly expressed reflect that. But, that said, they are both still mass*length^2/time^2 as the base units.

The cost is not my problem, the forum member's problem, or science's problem. ONE MORE TIME, Science only tells us how to interpret the results. Science has nothing to say about how the results are obtained, except that the results are impartial, unbiased, and objective. Science also tells us to be skeptical of results and any conclusions drawn from evidence that is biased, partial, and non-objective. Or incomplete. Or not statistically significant. Look, yours is not the only idea that science rejects because of lack of evidence. The first one that comes to mind is the idea of the graviton. While the current model is consistent with the existence of the graviton, and some particle being the force carrier for gravity just like there are particles for the weak, strong, and EM force seems like a very logical continuation -- there still is no conclusive evidence for the existence of the graviton particle. Until such conclusive evidence does exist, skepticism in the belief of the graviton particle is perfectly justified. That hasn't stopped physicist to build different devices to attempt to detect it. And, you know how the vast majority of them get the money to build the devices to attempt to detect the graviton? They write grants and find sponsors. If you think you need a quarter of a million dollars, I guess you better go find someone to sponsor you or you better start writing grant proposals. But, that isn't our problem, and bringing it up is again only a distraction from addressing many of the valid scientific questions that should be addressed. And, it also isn't our problem that you don't have the unbiased, objective, impartial evidence to convince us with. That is your problem, if you want to convince us, because what has been presented to date is scientifically very unconvincing. Here's a farcical and yet similar example. Say I told you that there is an invisible troll that lives in my attic and solves math problems in its head. Are you just going to believe that? Are you going to believe that idea until someone comes along a proves that it isn't true? What if I said that the evidence that causes me to know that he lives there is because I find math books open that I know he is reading at night when I sleep? And then I tell you that I can't prove he exists any better unless someone buys me an infrared camera so that I can catch him on film. Are you just going to accept that his existence is real? I would sincerely hope not, otherwise you are a very gullible person. And this situation is pretty similar. What has been presented so far is unconvincing, and there are many questions need to be answered about the evidence. We aren't just going to believe because you want us to believe. It isn't our fault that your evidence is unconvincing to us. The onus is on you to bring better evidence. It isn't on us to give you money to provide the better evidence.

I looked through this paper this evening, and came away pretty unimpressed. Firstly, the number of tests was pretty small, which means that the difference between the treated and control groups probably isn't statistically significant. (What statistics are presented don't seem right to me, but I didn't actually do the math because I don't have the time tonight.) The variance in the control group was almost twice the mean -- if that isn't a huge red flag that more tests are needed, I don't know what is. That huge of a variance means that the confidence in the mean is very, very low! It is well within the realm of possibility that the treated group's mean is actually around 2 and the control group is around 3 -- completely the opposite of Emoto's idea. Much, much more repetitions are needed to button this up. Secondly, the treated group was found to be a little more "aesthetically pleasing" than the control group -- but what does that even really mean? If the two groups were made of different people, than different people are going to find different things more or less aesthetically pleasing. Thirdly, the journal it was published in has a reputation for being very non-rigorous in that they won't reject papers that aren't supported very well. Fourthly, has anyone ever replicated this work anywhere? The only citations to that paper are from the same group, so no one else has published anything about it. Fifthly, the authors actually present about a dozen different explanations on why the two different batches of crystals may have formed differently (and none of them actually citing any of the crystal growing literature -- the actual science of growing crystals is probably at least an order of magnitude more complex than the authors of that paper even mention). If there are so many other possibilities, why publish such an incomplete work? Sixthly, the citations in the paper seem pretty weak, too. Lots of citations to 1) his own book which is unscientific 2) lots of journals on parapsychology. One of the citations was about how to judge how aesthetically pleasing a web site is -- what exactly does that have to do with crystals? No citations at all about crystal growth, of which there is a very, very rich literature out there. Seventh, scientifically, it would be nice to propose a mechanism by which the crystal growth is affected. I.e. how does the energy level on the faces change so that the growth is different. gain, there is a very rich literature out there on crystal growth. And then, where does that energy come from or go? The laws of thermodynamics are very clear that energy isn't free and has to come from and go somewhere, so the energy to change how the crystals grow must come from somewhere. This may be a little beyond the scope of the current paper, but these are obvious follow up questions that have to be addressed before being convincing. (edited to add: this is exactly what Kyrisch posted about above.) Those are the critiques I saw just from a quick scan. I am sure that I could have more, but I simply don't have the time tonight. Perhaps at a future date.

As stupid as you make it sound, here, there is a little kernel of right in this. And there are debates about what experiments should and should not be funded, especially when the grant-giving organization only has a limited about of money to fund projects with and more people asking for money than the organization has. And, very often, the people deciding what projects are also scientists who use their best judgment as to what experiments will being in the best or most interesting or more useful results. Those people certainly aren't always right. Those people have to use their instinct and try to figure out what is best -- which is imperfect since instinct certainly isn't always right. Judgment calls will always need to be made whether an experiment is worthwhile or not. Just as a for example, it is a fair debate whether or not building bigger and higher energy particle accelerators is worth it or not. There are good arguments on both sides. Nevertheless, this actually has nothing to do with my main point, which you have (deliberately?) misinterpreted again. At its most basic, the scientific method says absolutely nothing about whether experiments are worthwhile to be funded or not. The scientific method only gives us the method by which to interpret the results that we have in hand now, and tells us whether more experimentation in the future is needed or not. That's it. Human politics and money and all the other issues have nothing to do with the method itself. So, again, let's review in the context of Emoto's ideas here. 1) He has an idea about the formation of ice crystals. 2) He posts pictures and post his idea on the Internet 3) Science evaluates those pictures and his idea and comes to the conclusion that the evidence as presented to date is insufficient and that further testing in a more unbiased, more objective, more impartial method needed. Hence, science makes no conclusions about it, except that the ideas of Emoto's are unsupported by good evidence. Without good support, skepticism in the idea is fully justified. 4) What happens next? Again, I ask why no further more rigorous testing? If this idea turns out to be true, the best way to convince people is to re-perform the experiments in an unbiased, objective, impartial way. Then there will be good evidence, and science will accept it. It really and truly is as simple as that. This is what science and the scientific method does for us. It gives us a way to use the evidence we have in hand to either confirm or reject the hypothesis. Or tells us that the evidence we have on hand is insufficient for confirmation or rejection. And, without confirmation, skepticism is still justified. All these strawmen about Columbus and persecution are just distracting from the main thrust of the topic here. Post some better, more objective, less biased, more impartial evidence and everyone will change their mind! Emoto's ice crystals have absolutely nothing to do with Columbus! Post some good scientific evidence that Emoto's idea is right and all this other crud will go away! Every time you post something other than good evidence, you just make your case look weaker and weaker! And makes us more and more convinced that there is no good evidence, which makes our skepticism more and more valid. Show us skeptics why we are wrong! Post the evidence that objectively, unbiasedly, and impartially shows why we are wrong! I make this public promise that I will change my mind and will become one of the strongest supporters -- if and only if strong unbiased, objective, impartial evidence is presented.

No, you are grossly misinterpreting what I wrote. Doing the experiment is exactly what I am advocating for, I wrote nothing about staying put and not doing the experiment. In the terminology of my opinion at the end of my last post, Columbus was a true believer and went out and found the evidence, he wasn't a whiner and didn't sit at home and pout that no one believed him. I am advocating doing the testing to see whether the idea is right or not. That is science. Science is not waiting until all the information is in, science is the process of generating the information, and making sure to generate the info in an unbiased, objective, and impartial way, at least as much as possible. Tests aren't always clearly impartial, and often results can be interpreted many different ways. What science then says is to do different experiments, where more objectivity and impartiality can be achieved. Or design better experiments that are better are discriminating between competing ideas. So.... again, the question is: why the reluctance to further scientific inquiry here? Why can't the experiments be repeated? The evidence presented to date is very biased, very nonobjective, very partial. All science is asking for is more impartiality so that it can be made much clearer whether the idea is right or not. Nothing more, nothing less. Is that really too much to ask?

Reason is not enough for science, though. That's the whole dang point of science! Look, for a long time it was very reasonable and logical to know that the Earth was flat. For a long time, it was very reasonable and logical to know that the earth sat on the back of a giant tortoise. For a long time, it was very reasonable and logical to know that the moon was made of cheese. For a long time, it was very reasonable and logical to know that heat energy took the form of a fluid known as phlogiston. Reason and logic is not enough. Once science started demanding evidence, all the above were utterly demolished. So, that's all that is being asked by science. To not just believe things that sound reasonable and logical, but to bring things that are supported by objective impartial evidence. Is that really too much to ask? If the claimed phenomena were true, why can't it muster up some objective impartial evidence with ease? Why the hesitancy to be put to the test? So long as that hesitancy exists, science is completely 100% justifiably skeptical. That's the way it is so that only ideas supported by evidence are accepted by science. Those are the rules of the game. If you want to be part of the game, you have to play by the rules. If you don't play by the rules, then it isn't science. And the rules demand objective impartial evidence, not just "reason". If you don't follow those rules, then it isn't science. Sure, reason and logic plays its part -- in the forming of an idea or hypothesis. But, the next step that is the science part comes in and tests that idea or hypothesis. The next step searches for the objective and impartial evidence that supports the idea or hypothesis. This is the step that so many get hung up on. They think that just because they have an idea -- an idea that sounds logical and reasonable -- that they are done. But, that isn't science. Science is the next step of testing and looking for supporting evidence, and testing that evidence under fair and impartial and objective conditions, and continually testing until the case for or against the hypothesis is very strong. So, any chance that what is being claimed will subject itself to actual science? It has that first step down -- there is an idea. But, will that idea ever actually be tested scientifically, or will it ever remain just an idea? Or, maybe more the point, will there be objective impartial evidence presented in this thread on a science forum? Or should the thread be closed because there is nothing scientific to discuss? If you want to keep discussing the idea, then many a philosophy or new age forum would be better -- but here on a science forum we are going to demand objective unbiased impartial evidence -- because that's what science does! --------- Finally, persecution claims are an old, old trick and really a diversion from the topic at hand and don't chance the discussion at all. Firstly, it is nothing personal at all -- science demands objective impartial evidence from every single idea, not just the ones it "doesn't like". Secondly, the persecution claims are a strawman at best -- because they don't actually address the questions asked. Namely, can some objective impartial evidence be presented? Thirdly, science rightfully does reject any idea that doesn't have support impartial objective evidence, because then the idea isn't scientific. This isn't persecution -- this is reality. If an idea is unsupported, it is is unscientific. Nothing more, nothing less. It isn't personal, it isn't a "desire to tear his bright and colorful banner down", it is just a statement of fact that an idea unsupported by unbiased objective impartial evidence is unscientific. It didn't survive the crucible of scientific inquiry. This is my own personal opinion, but this is where the true believers and the whiners are separated. The true believers in the idea or hypothesis take their lumps, learn from the experience, and try harder next time to meet the scientific criteria. They learn what constitutes impartial and objective evidence, and hold their next tests to that standard. They try to do the best they can to step up to the standard make their case stronger for the next time. On the other hand, the whiners hand their head in their hands and cry "why is it do unfair?" "You bullies are just trying to ruin my pretty idea" "you guys are just jealous" "you guys just hate anything that isn't in the status quo" etc. etc. The whiners just claim persecution. It's easier. It makes scientist look like "the bad guys". It's easier because there isn't any extra work involved to trying to live up to the objective, unbiased, and impartial standards. And maybe, that's simply because you don't want to do the fair test, because you are afraid your idea will fail. So, you sit in your corner and pout. So, the question I have for you, then, is are you a whiner or a true believer? In that, are you going to sit there are cry about how unfair the standard is, how all we want to do is destroy something beautiful, or are you going to stand up and present some actual scientific evidence and beef up the idea with some science? It's your call. But on a science forum, only choice will gain you any traction at all.

The reason that it won't exist is because of the definition of the norm. There is a symmetry present that will always result in a positive number. I.e. [math]| \mathbf{r} | = (\mathbf{r},\mathbf{r}) = \int_\Omega\omega(\mathbf{x}) \mathbf{r}(\mathbf{x}) \mathbf{r}(\mathbf{x}) d \mathbf{x}[/math] where the (,) notation stands for inner product and [math]\omega(\mathbf{x})[/math] is the weight function of the metric space, which is defined to be positive for all x, too. (Depending on the details, often the square root of the right hand side is taken.) But, all the terms on the RHS are positive, because the weight function is required to be positive and when you take the inner product of a term (a number, vector, function) of itself, it will always be positive. That's just the way all these things are defined to be. Now, you can change the definitions, I guess, but that won't really answer the question. So, really, no -- given the current commonly accepted definition there is no such thing.

Any discussion of your ideas hinges upon your addressing the points I've raised above satisfactory. I've asked many questions, and really have gotten little or no answers. There is no point in discussing any of the deeper ideas until you and address some of the issues with the foundation of your ideas. It's like building a 2nd and 3rd story on a house built on sand -- it has no foundation, and the house will eventually collapse. I'm trying to get you to address some of the basic stuff first so that if you should want to continue to build your house, it will be built on rock and will survive. So: these are the ones I didn't feel were answered satisfactorily at all. (I have many, many more, but these 3 should be enough to get started for now.) In order to discuss your ideas scientifically on a science forum, you need to be able to answer these questions well, using precise and exact terms, and cite examples or experiments that back up your idea. Otherwise, it is all just a story. Science is looking for evidence that what you say is right, not just good story telling to make people believe what you sat is right. So, where is the evidence? Science also won't reject any old theory until a better one comes along. Better in that the new theory is more precise, more accurate, predicts more phenomena, etc. What predictions can your theory make? Can you show some math that shows your theory making predictions? Because the current model is pretty excellent, and while there are undoubtedly better models out there to be discovered someday in the future, a great deal of evidence showing that the new model is better will have to be presented. Are you prepared to present some of that? Because, otherwise, a science forum may not be the place you want to discuss your idea with. All of the stuff in the last paragraph is science. If you aren't willing to do science, then I suggest you take your idea to a philosophy or new age type forum. Because without the stuff above, it isn't science. I'm willing to keep discussing your idea with you scientifically, but the questions I have raised need to be addressed scientifically and satisfactorily. I'll give you all the time you need to address them, but I think that they need to be addressed to continue to discuss your idea on a science-based forum.

...so is spelllling.

A water and ethanol mixture forms a non-ideal mixture. The varied wt% values you have been given may all be correct, it is not going to just be temperature dependent, but also dependent on the concentrations of water and ethanol. What you want is a phase diagram. You should be able to find one in one of many different references at a good university library. One of the CRC handbooks of chemistry and physics should have it, for example. It is almost (almost) unbelievable that an ethanol refinery wouldn't have such information available somewhere to a very high accuracy.

I'm sorry, but this is no clearer to me at all. The definition from wikipedia is pretty good: Shearing in continuum mechanics refers to the occurrence of a shear strain, which is a deformation of a material substance in which parallel internal surfaces slide past one another. It can be written mathematically as: [math]\mathbf{\gamma} = \nabla \mathbf{u} +(\nabla \mathbf{u})^T[/math] where u is the displacement (u = x- x0 where x0 is the initial position if that infinitesimal volume of material and x is its current position) and [math]\mathbf{\gamma}[/math] is the strain tensor. A pure shear would be a case where the displacement is a linear function of one coordinate direction. For example, if u_x = ky, and u_y=u_z=0. That is what I know a shear as. That's what I mean when I ask for equations. Any chance something like this can be presented? Is the formula I presented above any semblance to what you mean? Is your formula anything like what I presented? If it isn't, you probably want to drop the term "shear" because that has a very specific meaning in a scientific sense (as Kyrisch said). and p.s. I don't think anything in Kyrisch's post was aggressive at all. It was a plea for exactness in your words. Science and math aren't like regular English. In science and math, words have a very specific meaning (like shear), so you can just haphazardly throw them around. When you say shear, that is implying a specific mathematical and physical situation. I'm sorry if this isn't what you are used to, but if you should choose to continue to post on a scientific forum, you should expect members to demand exactness in the way you use the scientific language. I hope I am not too out of line in speaking a little for Kyrisch here, but it is nothing personal. This is the same demand that would be made for every member. And, if I or Kyrisch have written something that is unclear, you are also well within your rights to ask us to clarify and use the words as properly as we can.

So... any idea when I can get an answer to my question asking you to explain exactly what "shearing against the time axis" means? Like I wrote above, you are using words I am familiar with in an unfamiliar way. I know what shearing is, I know what a time axis is, but I don't know what "shearing against the time axis" is.