Bignose

Hats, saddles, etc. are used in a technique known as Finite Element Analysis. The parameters (like magnitude, width, eccentricity, etc.) of this basis functions are solved via the governing differential equations. And, if you do FEA, you know the pathology of the output function is not limited to the pathology of the basis function. So, really, the two cases are pretty much completely incomparable, in no small part because you just presented the final answer, not in any way as to what you solved to get that answer. As swansont points out, there are any number of functions that follow the sparse guidelines you've laid out. Would you care to try again?

yeah, if you're going to allow operators, what's wrong with: [math]9!^{9!^{9!}}[/math] ? that blows [math]9^{9^{9}}[/math]out of the water

We don't have to 'know' what gravity is to be able to make accurate predictions of it. We do know how a certain lump of mass at a certain distance away imparts an attractive force. Just because we haven't discovered the mechanism on how that force is applied, doesn't me we haven't very accurately measured and validated predictions of that force. And, in short, our models are very, very accurate. Using that model of gravity, and another model on how gases behave, we can make a prediction of how much pressure and composition the atmosphere will have as a function of altitude. And those predictions are very, very good. Does this 100% conclusively prove that the atmosphere is due to gravity? No. Nothing is 100% certain. But, the fact that the prediction based on the gravity model is so very, very good means we are just about as certain as can be.

PG, it is written in MATLAB. t is a vector of a lot of different numbers, with its beginning value, end value, and step indicated by their positions in the colons. This will make X1, Y1, and Z1 vectors as well, which are then plotted with the command plot3. Ultimately, however, this is just a subroutine for making a picture. It tells absolutely nothing about why this model is useful, what predictions are made from it. In effect, it belongs in the thread on 'A lingual theory of everything' and the pictures the guys are posting in there. Just because this picture is drawn with a computer and their pictures appear to be drawn by hand is really an insignificant difference. The end is still the same -- pictures without anything rigorous behind it.

citation for this, please

Maha, I literally don't care if a medicine works via 'natural ways, faith, hope,' the wishing of fairies and their pet velociraptors, or the sun god. It just needs to work. I wholeheartedly disagree with 'recovery is not a subject to proof of a medicine'. If recovery isn't the goal, then what is the point? And just to head it off at the pass, if a case is terminal, I do agree with easing the suffering of a patient, helping them come to peace about the situation etc. But in those cases, easing the suffering and coming to peace are the goals. No matter how you slice it, there is a goal set for a course of treatment. If someone is paying for a course of treatment, don't they deserve some amount of assuredness that the treatment does what it promises? That the chances of achieving that goal are greater than just pure luck? If you hired someone to paint your house, and they came every day for a week straight, put up scaffolding, moved equipment around, etc. Then on Friday afternoon asked for money... don't you expect your house to be painted? You wouldn't accept 'covering your house in paint is not subject to proof in this case' would you? Not only covering the house, but if the house was painted, you wouldn't expect it to start peeling 4 weeks later. There is some measure of effectiveness, a goal as it were, implied in paying for having your house painted. I don't see any reason how someone promising medicinal treatment isn't subject to exactly the same. There is some level of effectiveness, some goal, that must be promised. And, to date, every study of homeopathy has shown a level of effectiveness less than or equal to a placebo. Why can't it demonstrate any real effectiveness? If it is so frickin' obviously good, why is it so hard to demonstrate that goodness in a rigorous way? If it is so good, why can't it achieve its goals more often than just dumb luck!?

This statement is almost completely different that what you wrote before. Obviously learning how to misinterpret a mathematical model isn't helpful. But, this isn't exactly profound -- misinterpreting anything isn't really helpful. If I were to learn how to misinterpret Russian (which I don't speak at all) -- that isn't helpful, either. If I misinterpret the meaning of a poem by Robert Frost, I don't see how that can be helpful, too. So, I guess I don't know what your point here really is. Also, I have no idea what 'alphanumeric dogma' is. Maybe the below will help a little... Math doesn't 'prove' anything about these questions. What we do have are mathematical models that make damn good predictions of what is observed. That is, given an airfoil, the ambient air conditions, and how you are using the airfoil -- the math can make a prediction of the amount of lift it will experience. And when that prediction is compared to what actually happens, the prediction turns out to be pretty good. That isn't a 'proof'. But it is an indication that the math model is pretty good. Same thing with gravity -- we have excellent math models that make predictions that agree really well with what is observed. Because these predictions are so good, the mathematical models we have are very well respected. If you don't like what those models are based on, or you think your models are better -- the hurdle to jump is very, very easy: demonstrate that your model makes even better predictions. That really is it. Your models can be based on your baryonic matter, quantum matter, unicorn matter, whatever the heck you want -- if the predictions are better than what we have today, you will get attention. No prediction?... expect to be ignored, especially when you redefine already well established terms. It really is a simple to understand hurdle. I guess the question for you is: do you have it? Do you have any predictions? How do they compare to the predictions made by the current models and how do they compare to the experimental values? Post a graph showing experimental values, the current model predictions, and your predictions and lets see how good your model really is.

PG, placebo effect is the whole point. There has never been a statistically significant study where homeopathy has done better than the placebo. Which means it is isn't effective. All drugs approved by FDA have to demonstrate much greater statistical significance than placebo in order to move through every phase of the drug trials. And studies of homeopathy have been done many times. If it is so good, why can't it ever achieve statistical significance? The worst of it is... because the FDA won't accept anything without statistical significance, that means that the FDA isn't regulating what these people are selling. Which means the ingredients list may say "dandelion pollen" but that doesn't mean that is actually what is in there. The same is true for the vast majority of natural supplements and the like. The danger here is that there could be something in there with a potentially dangerous interaction with something else (known or unknown!) that you are taking. People losing money and pinning false hope on these unsubstantiated claims is bad enough. But the real danger is people being harmed far worse than their original problem. ----------- Now, the topic of placebo is a very interesting one. And I do think that there is a lot more study that can be done on placebo. One of the more interesting ones done just a few years back is that the more expensive someone thinks a drug is, the stronger the placebo effect is. (Just one of many articles on it; http://www.sciencedaily.com/releases/2008/03/080304173339.htm ) I think an awful lot remains to be discovered on how the body does seemingly heal itself. But, that is not what the OP is talking about here.

Lordy no! Not scalar physics! Just wait until they learn about vectors!! And saints help us if they they learn about tensors!!! We're doooooomed.

Counting primes is neither horseshoes nor hand grenades. There really aren't any points for 'close' when doing proofs like this. Look how long it took for the proof of Fermat's Last Theorem. There was many, many that were 'close' but failed in some small way. When doing a proof, it needs to be ironclad, not 'close'.

Kudos. This is quite possibly the most foolish thing I have ever read on this site. You seriously want us to stop learning? Here's a dumb question, then: why are you bothering to try to teach your idea then?

You stood up to use your knowledge of physics to defend the OP. All I did was ask you to follow through with that. No need to take it personally. ... then I see posts like this. And I have my doubts about your self-claimed knowledge. Freshman physics is going to need a major re-write. Again, assuming that you can provide extraordinary evidence to support this extraordinary claim.

Defend the continual use of the word 'superluminal' implying travelling faster than the speed of list. With your 'fairly good Physics', you should know that our theories do not allow anything to travel faster than the speed of light. And furthermore, there has never been a confirmed measured instance of anything moving faster than the speed of light. Extraordinary evidence will be needed to support this extraordinary claim. If you have that evidence, I'd start preparing your Nobel speech now. Otherwise, admit that 'superluminal' claims just aren't supported here.

The authors of Ethics for Dummies (completely subjectively, one of whom is a good friend of mine) and many, many other books on morals and ethics would probably significantly disagree with this.

I don't believe anyone was disagreeing with the notion of existence of the solar wind. What we are disagreeing with is that the solar wind does not have the properties you are assigning to it. Unless you somehow want to claim that dinosaur extinction was because of current induction in transformers or interference of radio waves...

Look at all these particles we know, http://www.pha.jhu.edu/~dfehling/particle.gif, and yet you still can't even name the ones that supposedly fulfill your idea.

But... really?!?! Just because you have a few anecdotes, you automatically assume it true for everyone? You really can't Google and find literally thousands of people posting their story about only children committing suicide?!? (sadly, often the parents.) This is just lazy. And I agree with the above, offensive. If you truly cared, you would have put 7 seconds of research into showing your idea is bunk.

ZOMG, I got a eyewitness account too. "Rudolph was down for the count with a nasty case of Holly Jolly Heebee Jeebees. I mean, I had never seen so much reindeer puke since the Feliz Navidad Flu of Aught Eight. Anyway, without his glowing proboscis, I thought I was dead in the water. Then I remembered the way I navigated before I upgraded to glow-in-the-dark ruminates... the North Star. So, I broke out the sleigh sextant and the candy cane chronometer. Well, at first I thought I might have been rusty with the tools -- there I was giving Rod and Todd Flanders the largest, blackest lump of coal I'd ever seen thinking it was that rotten Dennis the Menace's house. Turns out the damn North Star moved on me! Well that was it, the very next year I started pumping the reindeer feed full of antibiotics and speed right around Halloween. There was no way I wasn't going to have the healthiest, most wide awake reindeer on the 24th of December." -- Kris Kringle in his tell-all autobiography "Ho Ho Ho and I'm Getting Too Old For This Shit" That's it, I'm convinced. Also, just off the cuff here, have I told you guys about how good my satellite TV service is? I mean, they are doing a great job of moving those satellites around despite the Earth doing a celestial tango on its orbit up there. That takes some real skill to keep beaming my Seinfeld reruns. And they know that if I don't get my daily dose of Kramer, I really go koo koo.

OMG! I think we just solved why Apple maps are soooooo bad.

Just because you don't know the evidence, doesn't mean it is nonexistent. Shouldn't you understand the current theory at least reasonably well before you jsut dismiss it out of hand? I'll never understand this all-too-common phenomena: someone decrying the current model as clearly wrong, misinterpreted, and garbage, but then demonstrating zero knowledge of it. You do, though, because you can't even name what kinds of particles they are. The solar radiation the ISS protects itself is known, and the properties are known, and how that radiation interacts is known -- hence they know how to protect themselves. Same thing with the aurora -- the particles that cause that are known, and hence predictions on how good the Northern Lights will be on any given night are possible. I call your particles 'magic' because you still haven't even named them! Why can't you do that? And why support an idea that doesn't even something as simple as the type of particles responsible for the result named? I think it is rather amazing that you don't even see not being able to describe the particles as a giant gaping hole in the idea! Doesn't that seem like a big flaw? It sure does to me.

Ok, so no evidence to back your idea up, then? I mean, I've prompted you 3 times now. Your idea is grossly unsupported by evidence. Come back with evidence, and then you'll get some attention. Otherwise, this isn't science. You're doing nothing more than story telling about magic sun particles.

All I see are perceived problems with the impact extinction model. That's fine and dandy. No scientist worth their salt will be able to tell wou with certainty what happened. They do have clues, though, like the crater, and the fact that the same layer of sediment was found in a very, very disperse locations. http://mygeologypage.ucdavis.edu/cowen/~GEL107/KT.html But, I see no model proposed that does any better. You have mysterious, still unnamed, still undescribed sun particles that by some magic kill things off. And no evidence presented for it, either. If I replaced 'sun particles' with 'despondent alcoholic murderous fairies', your idea is still exactly that same! Science welcomes new ideas. But, for those new ideas to be accepted, evidence has to be provided that supports it. Right now, a great deal of the evidence matches the impact model. Please, please, please cite evidence that matched your sun particle model. And please, please, please actually describe what your sun particle model is. Such as, exactly what particle or particles from the sun are responsible? Your model will never get any traction until you can answer these questions.

And what? Right now, looking objectively, the comet/asteroid impact scenario seems more probable to me. There is at least evidence for it. You have some unnamed magic particle whose properties you have defined as only killing what you personally think would have been killed, and presented no evidence for. The scientific choice is obvious. If I am unclear here or in my previous post, what I am saying is present evidence for your idea. Just because there may be a few open questions about the other idea that doesn't automatically promote your idea to best status. Right now, there is evidence for a large impact causing extinction. Where is the same evidence for your mystery sun particle?

Really? http://news.nationalgeographic.com/news/2003/03/0307_030307_impactcrater.html I'm not going to answer every other question, but I bet there are answers for them if you look for them. And then you can find evidence to support why people think those are the answers. E.g. You can find the research papers where the evidence was dug up, examined, and conclusions drawn. Your unnamed 'sun particles' idea has a lot of holes and will need a lot of evidence to support it. For example, you need to name what kind of particle is responsible. We know quite a good deal about how radiation acts and how it reacts with other matter. Hence, there would be evidence of radiation from the sun based on those interactions. We'd be able to see this evidence in the fossilized bones, plants, eggs, etc.

Just putting 'the' in all-caps isn't a citation. If this is all you're going to provide, then it is not science. You are telling us to take your word on things. This is exactly what a religion does. And has no place on a science forum. Please ask the mods to move your thread to the religion sub-forum.