Bignose

Again, I may be getting the notation used in the pseudocode wrong, but how I interpret the subroutine is that any object that is inputted is then set to the value of 5. So with that in hand, go through the steps of the main program. I don't think that there is anyway you should be getting 8, because there are no addition operators in this program as given.

If I am reading everything correctly, I would say that you have not interpreted it correctly. Take more time to think about what the subroutine is inputting and outputting.

Here, here. I too like having what is a relatively common name. You can Google to your heart's content, but I've got plausible deniability for all of them. "Sure, you found a picture of Paul Smith, but not the right Paul Smith" To the OP: I prefer my relative anonymity to formality. I don't think that there is much to be gained from using a 'real' picture versus the risks incumbent with willingly giving up anonymity. So, while I appreciate the sentiment behind the idea, I'm going to choose not to participate.

So, this statement has mathematical implications. We know how much gravity force the Sun exerts, and how much gravity the Earth exerts. Demonstrate that the amount of radiation from each is exactly in the proportion of the known gravities. You need to support these statements rather than just tossing them out. Here's another data point to consider. The planet Uranus has considerable gravitational force, but its core is known to be relatively cold. If your supposition is correct, how does it jive with the known data about Uranus?

You may want to re-read this thread. Because I think you've literally given us no evidence at all. Just told us what you think. If you ever want to seriously present this idea in a scientifically rigorous way, expect questions and expect people to ask you for the evidence that supports your idea. I really don't know why you're rage-quitting on us. I'm at least a tiny bit interested -- I did stop and bother to post after all. You may have some really good ideas, but they have to be scientifically supported.

Well, they have been holding Artificial Intelligence in Education conferences for 30 years in a row now: http://iaied.org/conf/event/12/ I don't want to sound like a jerk, but I Googled "artificial intelligence in education" and the above was the first link, but the next several hundred also look promising. I don't see why we should do your web searching for you: http://bit.ly/1iE29sH

And I still say that it matters not at all what you say. Science doesn't take just the word of anyone, Einstein, Newton, you, me, my imaginary green pegasus named Ned, no one. Science needs evidence. If you are going to claim "Negative energy can not be hypothetical because it is responsible for the expansion of the universe", then you need to back it up. Please do so.

I didn't read any fine print. I'm asking you to support your assertion. This is a science site, what you merely think doesn't mean a whole lot. Science is interested in the evidence. So provide some evidence of this assertion.

jaiii, I know you are relatively new to this site. But, this is a science site. Please provide substantial extraordinary evidence to support this extraordinary statement. Please demonstrate, in some detail and citations, how a prediction with negative energy fits the observations better than any other model.

It seems like you've made up your mind about this question already. Maybe you ought to tell us why you think that this arrangement will have 'negative energy'? Because by the currently best known physics, as far as we know, this doesn't have much meaning.

There are good references for the compressibility of water on its wikipedia page: http://en.wikipedia.org/wiki/Properties_of_water As above, real actual physical water is compressible, at least some small amount. The real art of answering scientific questions is to know when it is appropriate to use certain assumptions or not. In general, the assumption of treating water as incompressible will introduce such a small percentage of error, that it is completely acceptable. But, in certain very high pressure and high temperature applications, it may needed to be accounted for. I don't have much other advice other than you need experience to know when it is and isn't ok to use those assumptions.

There is no guarantee to find global minimums when using local searches, like Powell's. As far as other options, there is a rich, rich literature on this subject, something I'm not going to re-type all here. This can span everything from starting local searches (like Powell's or other similar ones) from a bunch of different points and taking the best, to more directed randomizations like genetic or evolutionary algorithms. Really, I'd suggest you do some more reading, because given the sparse information you provided, there really isn't much more to suggest.

It's not often the exact same joke can be used in the same thread twice: The question at hand is: What % of our brain do we need to necromance an almost 8 year old thread?

John's answer is pretty good. Another way to think about it is that, sure the final destination of both limits is the the volume going to zero, but the Jacobian helps make sure that both trajectories on their way to the voluem going to zero are the same. For a very simplified example, lim of x as x goes to 0 = 0 as well as lim of x^2 as x goes to 0 = 0. But, the trajectory each makes on its way to zero are obviously different. The Jacobian in effect modifies the trajectory so that it isn't just the final limit that is the same, but the trajectory into that limit.

I disagree. If you don't think so, then propose a better one. I'm going to stick with the tried-and-true scientific method. I disagree. My claim is not an appeal to authority because I did not tell you that statistics is right because Einstein, Newton, Hawking, or the Tooth Fairy says it is right. I am saying that you are demonstrating a great deal of ignorance on the subject by continuing to claim that statistics doesn't have rigorous proofs. If anything, the logical fallacy here is your appeal to ignorance, because you are trying to tell us that because YOU don't understand the proofs in probability theory, those proofs must clear be wrong (or not 'pure' or 'rigorous' or whatever other adjective you try to put here). It is no longer an appeal to authority if an entire community has demonstrated the usefulness of the work. I have already addressed this supposed "lack of proofs" above. And it IS your extraordinary claim that statistics isn't valid. When it has been demonstrated valid many, many, many times over. It is on you to show this. Statistician live up to their word every single day. It is you that is not living up to your word of invalidity. Fortunately, whether statistics is useful or not doesn't rely on your concession. If you chose not to seek greater understanding that is your problem. But this claim of invalidity needs to be dropped without extraordinary evidence. I also want to ask: what proofs in math don't require 'context'? You mentioned the calculation of the area of a circle earlier. That requires context, too, you know. I.e. the context of plane geometry. This claim that statistics is lessor because it requires context demonstrates an ignorance of all mathematics in my mind. You're on a science forum. Application to reality is THE primary metric of the success of science. Furthermore, if you think it doesn't validate it, then propose some metric that would. It is easy to lob hand grenades at something to tear it down. But unless you are willing to replace it with something, all it is is spiteful destruction. You want to know the best thing? If you can actually propose something even better, science will gladly embrace it. BECAUSE SCIENCE ALWAYS GOES TOWARD THE IDEA WITH THE BEST APPLICATION TO REALITY. So, if you hate statistics so much, what should we replace it with? You need to demonstrate that your replacement will be just as successful or more than statistics, though. And that will be a hard climb. Because whether you like it or not, statistics has proven supremely valuable and accurate. Even if you think the definitions aren't 'real' or 'representative of reality', the fact that it works still means a great, great deal. A good example is entropy. Entropy isn't 'real' in that you can't measure it directly with an entropy-meter like you can measure temperature with a thermometer. And it has was initially appears to be a very goofy definition. But, it has proven its usefulness over and over. Just like the values calculated in statistics. You may not like entropy or variance, but their usefulness has been demonstrated time and time and time again. Again, this is an interpretation issue. Statistics itself will actually even tell you this. It can even tell you how likely its predictions are to be wrong. Pretty amazing, isn't it? I have not read the paper. It would be nice if you cited it completely (i.e. who the authors are, what journal it came in, what year, etc.) so that others can look it up. Nonetheless, I think some questions about this are: was the statistics wrong, or the interpretation wrong? Was there a wrong assumption? Are you sure it was statistics that was wrong, or was the economic model wrong? Does the community agree that it was 'statistics' that was wrong or some misinterpretation thereof? Or is it just you? I have invited you several times now to discuss specific issues. If you want to present more of the background of this paper and discuss it, I am willing to do that. But just throwing out a single paper, with no greater framework around it, doesn't demonstrate anything. Nor does the market crash demonstrate that statistics was wrong. Again, if anything, statistics in the broad sense would have demonstrated that market crashes will always happen. If this is the best evidence you can dig up of statistics being invalid, I'm not sure you're going to get much traction. Again, I object strongly to the use of the word 'unproven' here. Just because you don't understand the proofs, doesn't mean they are unproven. Then why did you come to a discussion forum?!? It's actually a bigger question about this whole thread. Namely, what was the point? If you are here to fill some of your gaps about statistics, then why the hostility to what I and many other have been saying? If you are here to demonstrate to us that statistics aren't 'valid', then as I wrote above, it's put up or shut up time. Start bringing evidence. If you are here just to preach from your own gospel of your personal views against statistics, then you are in violation of the rules of this science forum, and the mods ought to close the thread. If something else, please enlighten us. Because the discussion part of this thread has been very lacking on your side. You keep just saying things are 'invalid' or 'not pure' or 'ambiguous' but refuse to take any time to understand when someone tries to give you a different point of view. Or define the terms or give examples when asked. Are you being deliberately obtuse? Or are you actually here to try to understand why I and many, many other people have no problem with accepting its validity? Statistics isn't just something I accept because I was taught it in school, or read it in a book. I accept it because I use statistics every single day, and by golly it works! That's the highest praise for a scientific idea. And, again, when models don't work perfectly, that doesn't mean you just completely toss them out. You refine those models, and see if you can't improve their predictions. I, for one, am glad that all of statics wasn't abandoned the first time a bridge collapsed. I, for one, am glad that all of pharmacology wasn't abandoned the first time a drug didn't work. I am not saying that statistics and its interpretation is perfect -- I think I've been very clear on this all thread. But, I am also not willing to just nuke the entire thing just because it hasn't worked perfectly every single time. Again, name a single science anywhere at any time that has lived up to that standard. So, in conclusion, if you have an improvement to statistics to make it better in your mind, let's see it. Otherwise, I don't see what the point in continuing this thread is just so you can continue to baselessly claim that statistics doesn't have proofs and rigor or any other of your wishy-washy ill-defined adjectives. This forum doesn't exist so you can spout your personal gripes. You can start your own webpage for that. This forum exists for us to all learn from one another. I have tried to learn why you have a problem with statistics, though you haven't been very forthcoming and clear, so I don't think I've helped much if any. But it becoming rather clear that you aren't here to learn from us, either. ---------------------------------- Added: In response to the paper above, here is a good quote: Chris Rogers from the University of Cambridge, sums up the view of many academics working in financial maths: “the problem is not that mathematics was used by the banking industry, the problem was that it was abused by the banking industry” from here: http://www.actuaries.org/ASTIN/Colloquia/Helsinki/Presentations/Embrechts.pdf Which is what I've been saying from the very beginning. Everything you've brought up is a problem with the use of the statistics, not statistics itself. Yet, you are trying to throw the mathematics under the bus. I don't see why.

I think you'll find that every science has this same thing. That models in all branches of science have failed on occasion. Statistics is no different in that science learns from its mistakes and adapts. For examples, a lot of times what people took as valid assumptions when calculating statistics weren't really valid. Again, it is not just statistics where this is a concern. Bridges collapse. Cars catch on fire. People die from drug interactions. Do these invalidate statics, automotive engineering, and pharmacology? Because I feel you're doing the exact same thing to statistics. Sure, there are times when the predictions is makes don't come to bear. But that is every single field of science. Hell, one could make a decent argument that statistics is the most upfront science about this, because by its very nature it fully admits that its predictions will not be 100%. I do think you owe it to yourself to study probability theory more in depth. There are many, many proofs in this branch of mathematics, and to claim otherwise just shows an ignorance of the field. Similarly with your comment about how it is non-rigorous. You are claiming something about the field that just isn't true. It may be ambiguous to you, but that is reflective of your level of knowledge on the subject, not the subject itself. And really, that's some of why this forum is here -- to help people exchange knowledge. I do hope you'll take some time to review what I an the many others have posted in this thread to demonstrate that before you just declare it non-valid, that you ought to learn more about it. Better yet, if you have questions, ask. We'll do our best to answer them for you. But ultimately, I'm sorry, but before I'm going to take your or anyone else's word that statistics isn't valid, you're going to have to provide extraordinary evidence to support this extraordinary claim. Because I've seen a great deal of evidence that statistics is valid. Your word alone isn't enough. This is a science forum. Statistics has proven itself very valid, very non-ambiguous, and very, very useful to a great deal of people. If you wish to change that, start providing evidence. As I wrote above, you're simply declaring it so doesn't make it so. My declaring that the sky is polka dotted and my car runs on unicorn wishes doesn't make that so, either. This thread is nearly 100 posts long now. It's put up or shut up time. If you wish to continue to declare statistics 'invalid', you had best start providing evidence of it.

In the real world, I really dislike the idea of redefining dividing by zero in any situation because 'undefined' has worked really, really well for us to date. Redefining division by zero to any value in any situation opens up the door to 'prove' that most any number can literally be equal to any other number. And on a practical note, I like when the calculator or computer throws up an error because it tells us we did something wrong. If it didn't, and set division by zero to some value -- too many people rely too much on the computer and these possibly significant error would be missed. I mean, too many errors are missed as it is because the computer is implicitly trusted too much, so taking away at least some of possibilities of catching those errors seems like a really poor idea to me. So, I'm going to stick with undefined. Besides, the gamma function (the extension of factorial to the reals) has poles at each of the negative integers: http://en.wikipedia.org/wiki/Gamma_function The graph of which makes that obvious. It needs to remain undefined at those points, just like the tangent function is undefined at points, so that all its properties remain in tact.

My suggestion is, then, to work on your message. Because just describing one case as "pure" and another as "ambiguous" doesn't really help. This is a science forum, and you need to provide evidence to back it up. That is part of what I kept asking you for examples of what was a "pure" calculation and what was an "ambiguous" one. Examples will make it concrete of exactly what you're talking about and put us all on the same footing. I invite you to come back and try again any time you want. I do want to help clear up this confusion for you, because I do think that to summarily dismiss all statistics is doing yourself a disservice. It is my opinion, that we generally don't do enough statistical work, because correctly calculated and interpreted statistics can be extremely meaningful and powerful descriptors. See, for example, the list of 6 questions I brought up quite some time ago. All of those are very important questions to answer correctly, and with judicious use of statistics, answers to those questions are very possible. But, I think a main point of yours -- that all too often statistics use is not very judicious -- does serve as a good reminder to us all.

Sure. It ought to. Because you are right that the details do matter. That what what I was driving at with "do you try to find every single person and ask them? Or do you ask 500 people? Or do you pull 1 state's DMV records? Or do you make a poll on Facebook?" Each of those different ways of trying to answer the question have different assumptions build in, different biases, etc. That doesn't mean that the answers each gets is wrong. It just means that each answer has its own context and meaning. That meaning does have to be understood by anyone who tried to use that number. And I agree that far too often it is not. But that doesn't mean that the math itself it wrong. It means that the way the math was used it wrong. Do you see what I am driving at? Or are you still stuck on the math itself being wrong somehow?

Think of it in terms of the new health care act. Gov't needs to put a certain amount of money in the system to pay for all that health care. Older people require more health care. So, as a first try, I want to know the average age of all the people so that I can put a certain amount of money aside for all people.

You can keep calling it artificial if you like, but the mathematics is well developed for it, and well verified over and over and over again. For example, if you wanted to know the average age of every citizen of the United States... do you try to find every single person and ask them? Or do you ask 500 people? Or do you pull 1 state's DMV records? Or do you make a poll on Facebook? Each of these are valid in their own way, and each will get different errors. But statistics can actually quantify those errors. No, I've read them, and am spending significant time trying to understand your issues, and trying to help fix what I think are misconceptions. I wanted to start with the mean since it is a simple beginning point. As I wrote earlier, let's start with the problems about mean before we tackle something more complex like variance. And now I can be a smart-ass too and write "it is as if my posts weren't read at all." ----------------------------- So, are you willing to do that, or should I just pack it in because you've made your mind up and you don't really want to discuss this, but are here to try to preach your personal gospel about what you think are the failings of statistics? I think I've shown I'm willing to have a discussion if you are. But you need to do your part of it, friend. You need to quit just calling things names, like 'pure' or 'artificial' and actually tell me what you mean by that. Or give examples of what you think is wrong, etc.

Adv, here's a good example of what I am thinking you are saying. Set1: [1, 2, 3, 4, 5, 6, 7, 8, 9] Set2: [1, 1, 1, 1, 5, 9, 9, 9, 9] Two very different distributions, but both have a mean of exactly 5.0. And you are correct that is someone said both sets are the same because each set's mean is 5.0, they would be in very significant error. But, that is also why other statistics about the sets were invented, like the variance (and skewness, and kurtosis, etc.). Math isn't going to fix people poorly attributing meaning to the calculations. But that doesn't make the math 'un-pure'.

How is that any different than coordinate points in geometry? The average coordinate is also the one that minimizes the distance between all the points. I.e. it is the exact same calculation. How is one more 'pure' than the other? Ah, see, now you're on to a different subject. Data measuring and gathering. And a little bit of model fitting. Statistics has mathematics to deal with each of these, actually. But, I agree, that if the samples from the population are not done with care, then just blindly using the mean of those samples as the mean of the entire population can lead to large errors. Look, if you are saying that an average doesn't capture all the details of the data, you're exactly right. But, it's not intended to. It is intended to mush everything together and get one single value. You're right in that if people take that mean out of context, as sacrosanct, or attribute more value to it than there really is, bad things happen and poor interpretations follow. It especially gets bad since in most cases, you can't measure every element of the population, so you take samples from it, and the mean of that sample also has to be interpreted. But, here's the great thing -- the math of statistics handles that. If you sample in a certain way, you can calculate how likely the mean of the samples you took is actually the mean of the entire population. Will you know 100%, of course not. But this goes back to issues brought up 70 posts ago, like destructive testing. I completely, 100%, totally, and without any hesitation agree that interpretation of these numbers is all too often done poorly. But this doesn't affect the 'purity' of the mathematics. Just because one is geometry and the other is samples doesn't make one more right or wrong than the other.

Please back this up instead of just stating it. You're right, I don't understand, because you aren't explaining it very well. I don't understand why it is 'pure' in geometry, but 'artificial' in statistics.

Really? Now you're going to claim that sums and division is not math at all? You are free to find whatever relationship you want. But to simply the language, statisticians and mathematics have set a specific definition of a mean. It doesn't do any good to try to discuss what you think a 'mean' is, if you are going to use your own definition. It doesn't do us any good to argue about a Tesla Roadster when what I call a Tesla Roadster, the rest of you call a 'banana'. So, let's just stick with the accepted definitions, shall we. Please write out in formulas what the difference between these two calculations are. Because I don't see how an average coordinate is "pure, for geometry purposes" and somehow the average in statistics is hence not-pure? So, please write out exactly the pure calculation, and the not-pure one, please.