Bignose

ok, sure, that doesn't mean that isn't still rare. There are an infinite number of rational numbers, too, but there are more irrational numbers. Just because something is infinite, does not mean it isn't rare.

Polynomials are only one class of many, many different functions. You got all those trigonometric, exponential, logarithmic functions, most of which won't have a closed form integral. Then all those special functions, like the error function, gamma function, Bessel functions, hypergeometric functions, etc. There are an infinite number of functions. So again, it is really only rare special cases where closed form integrals will be found, necessitating numerical integration techniques the vast majority of the time, meaning that "infinite precision" will not be achieved in any finite amount of time for the vast, vast majority of integrals.

I really only know the tip of the iceberg about quantum mechanics. I know, for example, that there is a ton of stuff I don't know. I think to make the requisite knowledge "wallet sized" one would end up needing a microscope in order to read the font. Point is -- there is no such thing as a wallet sized cheat sheet for quantum mechanics. It is a complicated subject. That is why there are many science popularizations done; in order to try to create analogies or pictures for people to understand. But, it must be remembered that those are merely analogies or cartoons, not the actual events happening. And not what the actual theories say. The closest thing to 'wallet sized'? Roger Penrose's 2004 book The Road to Reality: A Complete Guide to the Laws of the Universe. It is 1100+ pages, but it does its best to start from basic arithmetic and develop all the necessary tools. And that takes 1100+ pages. And there is no doubt that a book of that nature can really only survey the info, not go into much depth at all. This is why college degrees take years and years. There is no such thing as wallet-sized when it comes to this subject. Maybe what I am really saying is that it would be nice if the people who show up here trying to destroy QM would have all worked their way through a book or two in order to actually understand what the theory does and doesn't say before they try to tear it down. The really embarrassing part of that is that there are tons of open questions about QM. I can say with certainty (even with how little I know) that it is a certainly incomplete theory, and may even be flat out wrong. But, so many people try to tear down already known and repeatedly confirmed results -- you can't just wave those away. And you can't wave away the successes QM has had. Any new theory will have to incorporate these known results as special cases or similar... the known accuracy between prediction and experiment will always be true.

Apology accepted. And I don't think my questions are unanswerable, they are just questions that need some answers should this idea be pursued in a scientific manner. They may not be immediately answerable, but they are questions that could be answered if someone should try to actually develop this idea.

And I am telling you that this will only happen in special circumstances. Most often, when there is a nice closed form for the limit when delta x goes to zero. In the great wide variety of integrals, ones where this happens is exceptionally rare. Most cases, you have to use numerical integration, where there will be no such thing as infinitely accurate. In the general case, infinite accuracy cannot happen. (I am going to ignore the rest, if you have more problems with me, please take it out of the public viewing, and use the PM system.)

Do you think that maybe I am asking you these questions because maybe I am trying to help you answer the question? I'm not just asking them so I can hear the words rattle about in my head. I am trying to lead you to clarify exactly what you mean. If you are looking for truly infinite accuracy for all but the special case, then you might as well give up. Because it won't happen. It cannot happen in a finite amount of time. This is a perfectly valid answer to your question, whether you like the answer or not. Now, if you took the time to think about the questions I asked you, about just how accurate you really need to be in your application, I can suggest numerous numerical integration methods. The techniques for them depend on things like -- how accurate you need to be, how quickly you need to compute answer, and how complex the integrand is. For example, a great deal of computational fluid dynamics simulaitons use very crude integral estimations at the beginning of a run so that the computations process quickly and return answers on the order of magnitude of what's correct. This allows the large scale flows to be resolved quickly. Then they transition to more accurate and costly computations in order to resolve the finer details of the flow. How fine details need to be resolved? Well, gee, there's that question about how accurate one really needs to be again!. What I am not going to do is just write a treatise on numerical integration for you addressing all the issues, because quite frankly, there are many excellent texts written on the subject that apparently you didn't want to be bothered to read. Lastly, if you have a problem with what people post in your thread, report it to a moderator. I was trying to help answer an ambiguous unclear question as best as I knew how -- by probing you for more details so I could best answer it. If you don't want this help, then feel free to go to another site. If you just want rote, unthinking, boiler-plate answers, then just stick to search engines.

Sheesh, was this meant to be really rude? It sure comes off that way. You missed my and ACUV's bigger point that infinitely accurate just isn't going to happen except in some very special cases. That in the definition of your problem, you determine how accurate you need your calculations to be. There are some integrals that are only needed to be +- 5% accurate. There are others where 1 part per million is significant. The problem at hand determines how accurate one needs the solution to be.

sorry, thought I was helping you develop your idea. Sheesh, if you are this rude to people trying to make your idea stronger, then what are you ever going to do to someone trying to argue against your idea? (Oh wait, I read that other thread...) Good luck ever trying to actually show your work to other real scientists -- if you take this much offense to anonymous Internet peer review, how are you ever going to handle people asking you pointed questions face-to-face like at a conference, or getting a rejection letter from a journal?

A well designed experiment could find even 'marginal' differences. If going to Mars would be 'dramatic' per your own word, then again, I would think that differences could be measured here on Earth. But, really, this demonstrates the incompleteness of the idea as posed. I didn't participate in your other thread, but this one is similar in that to truly be useful, you need numerical predictions. For example. What do you consider dramatic? What do you consider marginal? How many neutrinos does it take to equal one IQ point? With numerical predictions, you can actually see what kind of experiment it would actually take on Earth? I.e. would it take 1,000 people doing tests once a month? or 100,000 people doing tests every day? Without numerics, its really all just guesses. Edited to add: http://owl.phy.queensu.ca/talks/desert03.ppt even shows a significant measurement difference between day and night, for example -- see slide #21

There may be (plenty of) logical fallacies, and while I disagree with the idea (our body creates plenty of its own energy, i.e. from food), at least there is a testable prediction in there. Namely, that mankind's IQ will significantly drop if they were to live to Mars. What would really help, however, is would be some sort of prediction by how much. And, frankly, with a well timed and conducted experiment, you don't even have to send somebody to Mars to prove this. This difference between aphelion and perihelion is about 5 million kilometers. Enough that there should be a significant difference in the sun's neutrino flux from aphelion to perihelion. Again, with some well designed experiments, there should be a demonstrable difference in mankind's IQ from 3 January to 3 July in any given year, including demonstrable trends increasing or decreasing depending on which side of 3 January the date the test is conducted.

I think this is a good point. Because unless it is a special case where an exact integral is known, truly infinite accuracy would require infinite calculations, clearly impossible to do in the lifetime of the universe. This is true of any iterative or limit calculation. I mean, any of those series approximations for pi can be done forever, but you'll never have 'infinite accuracy' for pi, since it is a never terminating, never repeating decimal representation, you'll never have the accuracy you seek. For most needs, approximation of an integral can be done to sufficient accuracy within a finite amount of time. A lot of times properly choosing what constitutes sufficient accuracy is part of the art of solving the problem; and it usually involves balancing the uses of the available computing power & speed, and possibly the accuracy of any measuring equipment used.

Not sure this is really needed. There seem to be many textbooks under the general category of "introduction to quantum mechanics". David Griffiths 2004 book under that exact title seems like a good place to start. If that one is found lacking, seems to be many more listed on Amazon.com. Someone who is more familiar with the texts may also come along and suggest their favorite texts. What I am saying is that what is going to be posted here that isn't in those texts?

Laugh Out Loud.... there isn't even an arrow in the picture. Nor does it even attempt to answer any of the questions in the thread above.

This kind of stuff has been tried before. Microsoft for years has asked you to enter a product key to validate your copy of Windows or Office. The very first ones were laughably simple to beat -- it just had to be a number with the correct number of digits and was mod 7. They have improved since then. However, the unique numbers and letters are still created by an algorithm, and once that algorithm is cracked, then fakes can be printed easily. I don't see how this idea wouldn't be different. The numbering system will be created by an algorithm of some sort, all it takes is a cracking or reverse engineering to that algorithm and fakes can be made. Yes, even the pseudo-random number generators by a computer are crackable. In fact, your 9 digits required for a unique container number is fairly small compared to the 20 or so characters most software asks you to enter to validate them. If one is a counterfeiter, purchasing many samples of the real in order to help crack the valid number generating algorithm could be well worth it, if it lets you produce your own valid numbers. Ultimately, the solution is that stores should only be buying from reputable resellers/distributors, and the producers should maintain a list of resellers/distributors that they guarantee will have the real product. The producers should be auditing those distributors regularly to ensure that they aren't acquiring or creating their own fakes. No amount of 18, 20, or even 200 digit codes will beat managing by actually walking around; and by that I mean the drug producers actually auditing books, records, and talking with the employees of the distributors. Look, I understand the need, and if done right, it could be a help. But it isn't perfect -- the overselling by using phrases like "complete stoppage" should probably be dropped. There will always be people who don't bother to check before taking their medication; I bet that segment of the population will be larger than you think. There will always be people who will make counterfeits so long as it is profitable to do so; solving this side of the issue requires a potent enough law enforcement system to actually protect intellectual property. Most of the world doesn't have that yet. There will always be distributors and other resellers who will purchase from another reseller without complete provenance because the price is right; again, this needs to be checked with random and thorough auditing by the producing company. In short, no system will even be 100%.

So, then, why aren't you trying to explain it better so that we will understand?

What disrespect have I shown you? This really irritates me, since I have spent time replying to your posts, trying to show you where you have done something unscientific and pointing it out. I could have just simply dismissed the idea -- because there were and are lots of grounds to dismiss it with. You may hold whatever beliefs and realities you want, but you can't post them on a science forum and not expect it to be critiqued. ALL work in science is critiqued. ALL work in science is judged on how well its predictions matches with experiment. As I wrote before, this is not personal. I respect your personal beliefs, but I only respect scientific beliefs when they are supported by objective evidence. This isn't an equation. There is no equals sign.

So, we finally got one that I agree with, and is dimensionally sound. There are a few assumptions in the above equation -- specifically that speed is a constant during the entire time duration. But, I sure hope you aren't claiming to have invented the above, since it is pretty much a definition. And then we have all of this:.... So, which of these are your formula? Why can't you post exactly how it is used? (in words, not in a video, not in a spreadsheet). Do to the example I've been asking about for many, many days now. Going from (x, y, z) = (0 meters, 0 meters, 0 meters) to (1 meters, 1 meters, 1 meters) in 1 second. Use your equation, whichever one is correct, and show us how you plug the (0, 0, 0) and (1, 1, 1) into it and get an answer. Please use the correct units the whole way through, as well.

Not to be too rude about it, but it makes as much sense as claiming the ability to add units of time with units of length.

Sure, and most of the 'products of combining' that 3 & 4 are nonsense. Such as 7. How exactly did you add 3 units of time to 4 units of distance? What is the sum of 3 hours and 4 kilometers? 7 choo choo trains? 7 strands of spaghetti? 7 volumes of the Encyclopedia Britannica? Also, suppose that was 3 hours, you do realize that is 180 minutes, right? Which makes '7' then a wrong answer.... 180 minutes + 4 kilometers is clearly 184 choo choo trains. So which is the 'right' answer? 7 choo choo trains, or 184 choo choo trains? Pancakes Or Sushi Tastes Imbittered Now Guy Looking Into Krystal Elephants Thoughts, However Integrate Songs Igloos Sit Nocturnally Turbid Everyone Voices Indignation, Damnation, Exclamation Northward Causing Explosions Seriously, unless there is a lot more to this idea than what you've presented here, expect your letter to be ignored. Note this is not me trying to be mean at all (tone doesn't convey in this medium), just trying to give you fair warning to not expect much.

I cannot disagree more. Please cite a single ANY other equation in use by anyone professionally (that is, not another amateur such as the above postings) where units of measurement aren't included. You won't. There is not a single example of a successful equation where "units are a thing of the past." In fact, the fashion for many years was to change the constants in an equation to accommodate the unit system chosen -- you'd find in old text books and handbooks an "English" equation and a "metric" equation. The fact that every single equation that has ever been published requires the correct units, leads me to strongly consider your equation in is flat out wrong if it doesn't return the right units. It is possible it is correct? It is possible -- it could be the very first one ever. But you're going to have to provide a ton of extraordinary evidence to support this very extraordinary claim. Much, much more than just "I am sure about this I can not say why". At this point, you're not doing anything even close to science. You are asking us to believe you on faith. That is basically the opposite of science. At this time, I'd recommend you step back, regather yourself, and try to collect evidence to support your claims. Because without evidence to support your claims, you are just story telling and expecting us to believe you on faith. Definitely not science.

How can you be so sure you are right without a prediction and a comparison of that prediction to experimental results? 'Rightness' in a scientific sense is not a measure of how strongly one believes in an idea, or how well spoken about an idea one is -- this isn't the dark ages any more where the people in power got to dictate what people should believe in. This is the modern era of science, and you need to make a prediction, then compare how well that prediction agrees with a measured result. THIS is why I keep asking you for an error estimate compared to a known result -- i.e. the Cartesian distance metric. So, now you've changed the formula yet again, and now it is a length cubed over a time. So, you have a volume per unit time? How can this be an answer to a question where a length is needed? Me: "How far is it to the market from here?" You: "Oh, about 700 cubic feet per second." Me: "Quit talking nonsense" Do you understand that units are really important? That your equation has to provide units that actually answer the question? This is an exceptionally easy first check on how valid an equation is. It is not the only check -- all the compare prediction with measurement stuff I've been harping on and all -- but it is a first check. Since your equation returns a volume per unit time, and not a distance as you claim, why should anyone bother to continue to look? Units are critically important, whether you choose to ignore them or not -- and just declare yourself right. Frankly, the hubris you've shown in your willingness to ignore the problems with the units -- and specifically I am talking about statements like "I am still correct in my statement a 3 is a 3 and a 4 is a 4 different combined variations does not make their product a 3 or a 4 but a sum of or a factor of..." -- where you just declare you are correct, really is annoying. Dimensional correctness is paramount to the usefulness of an equation. Without the right units, whatever answer an equation gives, is wrong. Whether or not the base number is right or not. The units cannot be ignored. In fact, the base number will radically change depending on the unit. The question "how far is it to the market from here?" can have answers like 1 mile, 1.6 km, 1.6 million mm, 1760 yards, 0.87 nautical miles, 3520 cubits, or 8 furlongs. AND THOSE ARE ALL THE SAME ANSWER! Because the number gets changed depending on what unit is used. This is why it doesn't matter if the equation spits out the right number without the right units -- because the fact that it gave a right answer (whatever that really means without the right units) it just purely coincidence. If your equation spits out 3520 cubic meters per day, are you really going to claim that is correct because it got "3520", but not the cubits? If so, then we might as well say that every equation is correct for predicting anything, because we can always create a system of units where we will get the correct number less the units. And that just doesn't sound very useful to me.

lol, this thread has taken a rather humorous turn.

+1, I have nothing more to add here, just wanted to indicate that it is exactly what I would have written...

balderdash Here are you equations per the latest post as near as I can tell Follow along, I am going to put the typical units behind the word in square brackets like so: speed [distance/time] So, the first equation is: (speed [distance/time] + altitude [length])*altitude[length] HOW CAN YOU DO THE ADDITION IN THE SET OF ()'s ?!? The units aren't compatible. You cannot add a speed and a length. You cannot add ANY incompatible units. 1 mile + 15 lumens = nonsense 4 bananas + 7 sheep = nonsense any m/s + any other m = nonsense.... The second equation is (distance [length] + altitude[length])*altitude[length] At least here, the two terms in the ()'s are the same unit. So they can be added together. But them you multiply them by another length, so you get a length squared or an area. An area is a nonsensical answer to the question: "what is the distance between too points". That is, no one asks "How far it is to the market from here?" and expects an answer like "15 hectares." Because that is a meaningless answer. Look, you have to get the right units -- if you agreed to accept a job for 50,000 dollars a year, you don't expect your boss to come around on pay day and drop grains of sand on your desk and declare that in his world, a grain of sand IS a dollar. The units are of critical importance. This has been shown to be true in EVERY SINGLE SUCCESSFUL PREDICTION MADE WITH EQUATIONS TO DATE. This really is non-negotiable if you want you idea to be taken seriously. A video is a terrible place to post how a math problem is done. Could you please post all the steps on the forum? Because 35.207 feet is very, very different than [math]\sqrt(3)[/math] which is the tried and true answer. I am not doing a personal attack. I am pointing out what I see as flaws in the presentation. I am not trying to 'disprove' anything. And really, all you got to do is post compelling evidence as to why your idea is right. Really, if anything, YOU are doing the 'disproving' by not answering questions straightforwardly and with compelling evidence how your idea matches experiment. The more compelling evidence you can provide showing your idea working, the more support you will receive. The more shifty, indirect, incoherent answers provided... the more likely people are going to just reject it as nonsense. And, in the bigger picture, this is the scientific process -- namely reviewing of others work. If you can't handle an anonymous Internet critique of your work, how are you ever going to actually ever present it at a conference or submit a paper for publication? They will be far harsher with their critiques than we have been. Frankly, right now, what you have would in all likelihood be ignored. If you can start answering my and others' questions straightforwardly (there are a bunch on the first page we haven't ever gone back to), you significantly improve your chances of not being ignored. On the other hand, if you want to continue to consider this a personal attack, then I will quit trying to prod you in a direction to make your idea stronger and stop participating in this thread. It's your call.