Bignose

The above doesn't address the dimensional inconsistency. You can't add 4 bananas to 7 sheep and call it 11 Volkswagons. You have to add like units to like units. You can add a foot to a mile, because both a lengths. You can't add a velocity to a distance, because one is a length per unit time and the other is just a length. If you want to account for motion of the Earth, there are mathematics for rotating and translating coordinate systems. The math is a little trickier than non-moving coordinates, but again, this is a problem mathematics has addressed already. Lastly, I don't know how you can claim this equation allows 'time travel'. Unless you mean the trivial case in that we all move forward in time. Because if you are invoking the extraordinary claim of 'time travel' in the 'Back to the Future', H.G. Wells, 'Star Trek' sense, then this claim is going to require some awfully extraordinary evidence. Since it has been a struggle to even get you to calculate the distance from (x,y,z) = (0,0,0) to (1,1,1), I suspect that the evidence for time travel in the Star Trek sense doesn't exist. I would be pleasantly surprsied to be proven wrong, but without evidence, this claim really should be flat out rejected.

Well, there is a new word you haven't used in this thread before. What exactly do you mean by 'arbitration'? What exactly is wrong with what I posted? What are you objecting to here? Edited to add -- I do apologize. I thought this was a reaction to the methodology. It is in fact a reaction to my assertion that 'the starting place' is rather arbitrary. I wanted to leave the above note in there since I had it posted for several hours. And then I am going to go ahead and defer to the next post in this thread by Phi For All, and his defense of the arbitrary starting point. Again, sorry I misinterpreted your post here.

More or less. Again, to me the starting point is rather arbitrary. Also, I do think it is important not to gloss over some things in the chain "prediction B, observation B, prediction C". I would have written this is: prediction B, observation B, calculate error between prediction B and observation B, evaluate the feasibility or likelihood of the model that lead to prediction B based on that calculated error, reject the model or refine it as needed (maybe no refinement at all), THEN made prediction C and repeat.

3 thoughts: 1) still no error estimate using actual numbers, and still no calculation I gave you using tour method 2) "(Speed(Time) + Altitude(Time))*Altitude(Speed)" is dimensionally unsound. How does one add a speed and an altitude (in the first set of parentheses)? What is 5 m/s plus 1000 feet of altitude? 3) "This is the same with distance traveled during time at altitude one will be different than altitude two" really? if I travel 1000 feet at an altitude of 1000 feet, this will be different than travelling 1000 feet at an altitude of 10,000 feet? How is that possible? They are both 1000 feet! 1000 feet is 1000 feet! Do you mean in relation to degrees of latitude & longitude? That is, at an altitude of 1000 feet, travelling 1 degree latitude is a different distance than when at an altitude of 10,000 feet? If so, there is a known answer to this too -- it simply involves calculating the great circle between the two points at that altitude. And the arc length along that great circle is dependent on radius (altitude). Again, this is a consequence of the definition of the distance metric in spherical coordinates. I really, really think you need to be very clear about what you are trying to do here.

Do you want a case in point where your observation --> theory pattern fails? Take a look at your thread on matter. In post #12 (http://www.scienceforums.net/topic/68992-what-is-matter-anyway/page__view__findpost__p__702544) you wrote: And as I pointed out in that thread, this is just wrong. The atoms themselves don't change with the phases. Just the energy level by which the atoms and molecules interact -- that's why we have the gas, liquid, and solid phases, as well as several other phases of matter you didn't even bother to name. You observed gases, liquids, and solids and you tried to extrapolate that back to the atoms (dare I say, predicted that those would also be properties of the atoms?). It is a good try, but it fails in the face of experimental evidence. That's why the prediction & comparison step is the real meat of science today. It is no longer good enough to make statements that sound "good enough" or "logical enough" or "plausible enough". Lastly, I think it is fine to have concepts that are wild and imaginative. Science needs that. Craves it even. New thoughts and concepts are always desired. But, they are never in isolation. Just having a new thought or idea is not enough to be worth anything to science. To be worth something, you have to use that new idea to make predictions and then compare how good those predictions are to experiment. That's the worth. New ideas are needed, because otherwise there would never be new predictions. But then those new predictions are judged based on how well they agree with reality. And then once we have valid predictions, we can do all sorts of things previously un-thought of. Like, land a rover on Mars using a parachute and reverse thrusters. If we didn't have exceptionally well validated models (predictions) of celestial mechanics, gravity, booster rockets, atmospheric drag, and chemical reactions (just to name a few), we wouldn't have been able to make that landing on Mars successfully. Would you have been comfortable paying millions of dollars to land a probe on Mars with just "well, we watched a lot of things land here on Earth"?

If the next piece of information is an actual calculation of the error of the tried-and-true distance metrics, then yes. Don't forget your claim above is that "distance ... becomes flawed at a 3-dimensional level". If you can actually demonstrate that flaw, and how much error that flaw causes, then I will move on. I don't plan to move on without it.

No, you didn't. You summarily declared that you didn't have to answer the question because "I am not a scientist". That's all fine and dandy for your personal beliefs, but on a science forum, it doesn't fly. The fact that (0,0,0) doesn't work with your equations should be a huge flag that something is wrong. Because the positioning of (0,0,0) is completely arbitrary. Nature doesn't know if I have labelled a point (0,0,0), (6,12,954), or [math](\pi, e, \pi^e)[/math]. This is a related issue to what I pointed out above that you get the exact same answer no matter what coordinate system you use as well. Nature doesn't know whether I am applying a Cartesian, cylindrical, spherical or any other coordinate system. Nature's laws are coordinate-system independent. When I compute the distance between (x, y, z) = (0,0,0) and (1,1,1) using the Cartesian metric.... I don't need a speed or a time. All I need is [math]\Delta x = 1-0[/math], [math]\Delta y = 1-0[/math], and [math]\Delta z = 1-0[/math], no speed, no time in there, just the differences between the coordinates. Again, I think you are seeking a solution to a problem that doesn't exist. AND, you certainly haven't provided any example where the distance metric fails.

I have to agree with ACG in comment to this. If you are really going to stick to this, then you need to not post on a science forum. Because on a science forum, we expect some semblance of science.

Quite simply, observation alone will only tell you about the things you have observed. The power of prediction is that you attempt to create knowledge about things you haven't directly observed. For example, by making a prediction about how tall a tree is based on how many years its been alive, and then confirming that prediction using a suitable sample of experiments, you don't have to cut down every tree in the forest and count its rings to make a good guess about the distribution of ages of trees in that forest. Or, to take a recent example, making predictions allowed us to land a probe on Mars without having had to go to Mars and experiment how to land probes on Mars.

I frankly don't care what the starting point is: hypothesis, questions and answers, 'logic', tea leaves, or a blow to the head. The bigger point is that science to a large extent doesn't care about that first step. It cares about making predictions and then comparing that prediction to measurements. Whatever that 1st step is, what is really important is to get past just that 1st step, and actually make predictions and check their accuracy. Too, too many people think that 1st step is sufficient, that their creativity, logic, or tea leaves is enough to create something meaningful. And while there is a lot of good to be said for being creative and coming up with new ideas -- the crucible of science is almost completely: what predictions can be made using the idea, and how good are those predictions. We have moved past the dark ages where ideas are judged based upon how much one likes the idea. In science, ideas are judged by accuracy of predictions.

Considering I do think that you haven't really understood my objections to date, I hope that you don't just run crazy with the following information and misuse and misinterpret and otherwise not understand it. BUT, have you even looked at the spherical coordinate system? http://en.wikipedia.org/wiki/Spherical_coordinate_system Mathematicians have already solved the problem of describing velocities in a spherical system. That is, the r in the coordinate can interpreted as the altitude, and the two angles are related to latitude and longitude. But MOST importantly -- When done properly, the answer one gets when using Cartesian coordinates is exactly the same as the answer one gets when using spherical coordinates. (and any other set of properly defined coordinates when the conversions are done correctly.) That is, is you have two points in space, the distance between them are exactly the same no matter if you measure the distance with a Cartesian metric, a spherical metric, or any other properly defined ones. All you have posted are results of your calculation -- you have not compared them to anything. So you don't have any idea if something is "positive", "negative", "pink", or "watermelon". Without comparing the results of your calculation with something, you have zero context about what you are calculating. Anyone can just throw symbols together and calculate something. That doesn't make what they calculated meaningful. And to this point, this is why I've been trying to get you to compare your calculating against the tried-and-true Cartesian distance metric. You claimed that all 3-D distance measurements had errors -- why can't you demonstrate exactly how much error there is? Why can't you repeat the same calculation I did in your model?

So, the water that falls from the sky has different atoms depending on whether it is raining, snowing, or just humid out? I think that it is pretty well known that the phase change is well described without invoking changing the constituent atoms.

Nope. I certainly don't agree. You haven't shown a single piece of supporting evidence for ANY of the claims you've made here, despite my asking you to specifically do so. So, there is no real reason to believe you. Just like I would hope that you wouldn't agree to believe that I keep a pet unicorn in my garage without providing ample evidence. Right now, all your claims are about as believable as a family of unicorns that speak fluent Armenian living in my garage (yes, it's huuuuuge).

I'm not watching any more videos. If there is an answer to my question, it doesn't require a video; all that is needed is a post. The answer to my question is a number. Something like "5% error". Why? If there is no error in the tried and true formulas, why does it need to be replaced? Mathematics doesn't expire, it doesn't get old. We aren't declaring Euclid's Elements wrong just because they are some 2500 years old. Because they are still right. And the distance metrics set up in mathematics don't need to be replaced, because they are still right, too.

Any of various mathematics software (Mathematica, MathCAD, etc.) or even most programming languages (C, Fortran, Python, R) can compute this using the exact definition of the binomial distribution. In fact, I suspect that this is the point of the problem -- not to check the student's 'look something up in a table' skills, but the check the student's ability to used some slightly more advanced computation tools.

This really isn't anything too profound. The extension of the natural logarithm to the negative numbers is commonly expressed as [math]Log(z) = \ln® + i\theta[/math] where [math]z=r\exp(i\theta)[/math]. For a real negative number, [math]\theta = -\pi[/math]. So, all you did was shove a fairly weird negative number in there. To be exceptionally pedantic, the natural logarithm isn't defined on anything but the positive reals. Usually, this extension is called the complex logarithm function, and hence the slightly different symbol 'Log' used above. more here: http://en.wikipedia.org/wiki/Complex_logarithm

proximity1, I apologize if I've offended you in any way. But I don't quite understand the response above. My point is that while it is easy to point out problems and cry "woe is us", it is much harder to actually think of solutions to fix problems. That is, it is easy to point out things that are wrong, but much more meaningful to point out good solutions. I am sorry to say, but in the work force, we call those people "howler monkeys" because they like to sit there an hoot and howl and make a lot of noise, but don't actually help solve anything. So, let's start over, start clean: I agree that there are some possibilities for some very negative consequences in the future. While I don't quite agree with how negative some of the posts have been, again, I do agree that there are distinct possibilities of negative consequences. I, of course, would prefer to minimize these possibilities as much as possible. What concrete suggestions do you have for minimizing these possibilities?

Suggest some concrete, well-reasoned ideas and my bet is that attitudes will be swayed by those good ideas. So, do you have any?

This doesn't seem like all that good idea to me. 2 through 9 all look like the same on the left hand sides, but all have different evaluations on the right hand sides. I don't see how this is an improvement over the tried and true. Furthermore, via an extension of the the tried and true using 2-D vectors, all of the above can be recreated. Without redefining an operator that really doesn't need redefining.

So, you assume I have no wider perspective? Isn't this ALSO the exact same error you are accusing me of, just the reverse? That is, you don't what I base my statement on, so you just assume that I don't have a wider perspective? First and foremost, I backed up my statement with 3 wider-perspective statements. E.g. the information sharing age is finally bearing fruit, the amazing yields that crops have today relative to their yields of not that long ago, and the future of green energy. Secondly, (and this is stuff you wouldn't know unless you asked) I try my best to be knowledgeable about a wider world, and try my best to keep a broad perspective. I am not going to say I am perfect at it -- I do have a full time job and other responsibilities -- but I do try. And to that point, I will counter your citations with Gregg Easterbrook's book The Progress Paradox. In it, he makes an awfully compelling case as to how much better off people on the whole are. In particular, he focuses on America and why as a people we report being more unhappy than ever yet we have much, much more of the things that supposedly make us happy. He points out that we have more cars, larger homes, more college education, and overall (ooops, that's that word again) a much better life than any generation before us. Yet, we are more unhappy than ever. Easterbrook's main thesis of the book is that we as a people need to realize that there is much more than material goods needed to be happy and content with life -- i.e. you can't ignore the spiritual side of happiness. But, I can also use the book as a citation for evidence that in terms of living-well, the population as a whole is moving in the right direction. And then every other financial report coming out of China seems like is mentions their "growing middle class". Those people aren't leaving the upper class to become middle class -- they are moving from the poor to the middle class. And while I guess I don't know the exact details of how many homes and cars their new middle class own, I'm guessing it more than it was. And the same thing is happening in the other BRIC countries, too. That's Brazil, Russia, and India. They are also creating new middle classes based upon the rapid development in their countries. So, I don't know. Maybe I don't have enough perspective -- I will 100% agree that I could always use more. But I also don't think I just threw my comments out there without any perspective of a drowning man. If anything, I think that the pessimism shown demonstrates a lack of perspective of the average member of the 7 billion. Because while here in America I would agree that on average our middle and lower classes are stalled or maybe even slipping backward a little -- on a global perspective things are getting much better for the average member. Ok, I'll bite. So far, there have only been cries about things going wrong. What specific actions should we take? What should be rally around? All I see is a listing of his perceived problems, not actual solutions.

And darn near every single generation has written very similar things. The foil to all the above are the large number of really good things that are happening, too. The Internet is bringing information exchange to unprecedented levels -- and helping over turn dictatorships and pseudo-dictatorships all around the globe. I honestly believe that in about a generation, there won't be a single one left on the planet. Genetics allows us to grow plants with a drought and pest resistance that is almost unbelievable from a perspective of just a decade ago. Even with the drought in the Midwest, it actually won't be all that bad of a harvest; not as good as the farmers would have liked considering the early spring planting they got in, but all in all, it isn't going to be a disaster. Green alternative energy is still at just the beginning of its possibilities, and while it isn't a certainty that it will pan out, there are a great number of amazing things being done at this moment. While there certainly are troubling things going on, losing perspective of all the good things going on as well doesn't really accomplish much. This certainly doesn't mean that I am saying we should ignore the troubling things. But, I am saying that in a wider perspective, mankind on the whole is progressing at a fairly incredible rate.

Maybe I didn't communicate it well. What I meant was that a student can sit there and come up with clever ways to calculate the area of a trapezoid, for example, but if they can't add correctly, it doesn't do any good to identify a trapezoid as a rectangle and two triangles. More to my point: while I wholeheartedly agree that the teaching of mathematics is largely motivated poorly, I don't think that is any excuse to remove exercises and work from the students. In fact, in general, I think that most students do not do enough repetition of the exercises. When one is studying algebra, completing the square should be second nature. And the only way that happens is by practicing it over and over -- like most anything, people only get better by practicing. No matter how much artfulness a student may have, if they don't have mastery of machinations (e.g. the grammar) of the subject, they aren't going to get far. As an example, I think that a fair number of the threads in the Speculations forum are very creative, very artful, and very imaginative. But the vast, vast majority of them have authors who are misunderstanding or misinterpreting some of the very basics of the sciences they are trying their hand at -- and yes, there are even a few threads in there about mathematics. Practice makes perfect, and to do a fair amount of mathematics, you do need well honed skills to do them efficiently and correctly. Again, I am certainly going to agree that that practice needs to be much better motivated, explained, and taught. But, I am also saying that unless the student is an absolute savant, there is no replacement for practice.

What percent inaccurate is: I am really only going to ask one more time for a concrete specific example where the Cartesian distance metric calculates a distance in error. If you can't provide one, I just don't understand the motivation for 'fixing' something that isn't broken.

You video did not show a specific example where the tried and true Cartesian metric -- when correctly used and not some averaging thing -- fails. And you mispronounced Cartesian.

Why would you use an average here? The distance metric for Cartesian spaces is very well defined, and doesn't introduce the errors of averaging. This seems to be you trying to fix a problem of your own introducing. Any examples where the tried and true distance metric fails?