Bignose

So can any other series. See https://oeis.org/wiki/Welcome for a pretty large list. Are all of these 'sacred', too? Define time vector. The time variable is involved in a lot of vectors, but time itself isn't typically taken to be a vector. What?!? This statement seems totally unjustified to me.

I guess I should be glad that you willingly admit this. It is easier to tear down than build up. ... Kind of useless, though, no? I guess I am ultimately a practicalist. If you don't have something to improve the situation, just pointing you what you perceive to be problems isn't all that interesting, because it actually isn't doing anything.

Beauty is in the eye of the beholder, I guess then, eh? Ok. Argue it all you want. Can you actually demonstrate it in any way? If no, then I guess I don't see what the point in 'arguing' it is... More opinions. Here on the science forums, we like to deal with science. Any evidence you can provide to support anything here?

Yes, this is not surprising, since a matrix of all 1s clearly does not have linearly independent rows or columns. That's where all the 0s come from, the non independence. The last single value represents the one row or column vector that is independent.

So, what's your point? You don't want water to be known casually or colloquially as 'a universal solvent' anymore? I think anyone who seriously needs to know about solvents looks up solubilities as needed. I don't think anyone seriously thinks that water has to dissolve everything...

But, take to heart what I wrote above. There are reasons people are saying they think what you are claiming about your simulation and what you've actually written are different. You need to dive deeper and do your best to understand their point of view. I never wrote a simulation that was 100% correct. I never wrote a simulation that someone didn't completely justly point out errors and limitation in them, or even things I got just plain wrong. I never wrote a simulation that didn't take many months of in-depth research and understanding of the problem. So, it isn't that I think you should drop this conversation. I think you should do a lot more reading and learning about why everyone is saying what they are saying. My knowledge in QM is very limited, but from what I've read, I think they raise very good points. They have good reasons for writing what they wrote. To make your model and your understanding better, you should take the time to understand why they are saying what they are saying.

Theoretical, Let me start with saying that it is awesome that you took your coding skills and turned them into a simulation. There are a very large number of people who don't have the skills to do that, and even if they had or could learn the skills, they don't have the will or motivation to do it. You are way ahead of most people, certainly most of the people who join this forum to talk about an idea they had. You may have heard the scientific process described as "confrontational". Like many things, this has a common use definition, and scientific use definition. In common use, confrontational typically means fighting, strong disagreements, etc. Typically, this means a conflict of some sort. However, in the scientific use, conflict is rarely there. The confrontational part is that scientists are always challenging each other's models to find cases where they don't work, or cases where they predict something wrong. As much as anything, they are exploring the capabilities of the model and seeing just how useful. Remember that in science, the usefulness of a model is almost wholly based on how many accurate predictions that model can make. So, I think what you are seeing in this thread is people being scientifically confrontational about your model. They are trying to point out where it does and doesn't many accurate predictions. They are finding out its range of validity. I think you are taking this a little like the common definition of being confrontational, when that really isn't intended to be that way. I have given many presentations at conferences about simulations I have written, and there are always many, many questions that are confrontational in the scientific sense. Other scientists are going to suggest possible problems, possible improvements, and generally do their best to test the model that is presented. What I always did was take their comments to heart and do my best to learn why they said what they did. No matter what, I always learned something more. I suggest you take some time and look deeper into what the people are saying here. Because by doing so, you are only going to make your level of understanding deeper and stronger, and that will lead to a better model. I think that is all any of us want, most of all you, right?

The difference is that we had evidence for a long time that Newtonian physics was violated (e.g. the precession of Mercury was known for a long time), but we've never found a violation of a conservation law yet. Not saying that they are 100% iron clad, but so far given the millions of tests they have passed, you need to present incredibly extraordinary evidence for this incredibly extraordinary claim. Not to beat a dead horse here, but if you didn't want constructive criticism of your idea, then why post it to a discussion forum? People are just trying to help shape your idea to conform to knowledge we already have. If you really didn't care, why bother posting it? Ergo, I conclude that you do care at least a little, and if you take a few moments to engage with people here, they can help you in making your idea better, stronger, and more rigorous. But if you really don't care about a stronger, better, more accurate idea, then I guess "adieu".

I am confused by your use of matter, energy, and even continuum here... I guess this if probably futile, but still any chance of presenting a model directly? Because this unconventional use of terminology is making things really confusing. With a model presented, we can see exactly what it is you are saying.

Sooooooo, it's not one continuum that fills all space, then? I thought that was your main point above. Either its one continuum that fills all space (and thusly has one set of properties) or you're telling me it is magic and changes its properties to match exactly what we observe and remain undetectable. Your question above it exactly what I am asking you, and needs a good answer. You are the one telling me that there is one single continuum that fills all space. That light (that everything) travels through it as a wave. Well, give that that is so, the equation I gave above for how waves travel through a continuum was given above. And requires the continuum to have some kind of density, a mass per unit volume. But if that continuum was out there, then everything else that moves through that space should experience some drag. Because unless mass is zero, the drag can't be zero. It's not that 'the continuum has changed', it's that I am taking your idea to the very next step and noticing a contradiction between your idea and what is observed. I guess the choice is yours here: you can either chose to understand the issue I've brought up or you can continue to throw more words at it and hope it satisfies me. It probably won't, but I will probably stop replying because the second choice there isn't science, and I participate on this forum to discuss science. If you don't want to discuss science, then I'm going to choose not to participate. And, as a word of friendly advice, see swansont's note above. If you continue to refuse to engage scientifically, you will get this thread closed. How does an 'energy fluctuation' change a continuum's properties? What are the fluctuations that the Earth has or a photon has to that as each moves through this continuum, it changes from massless to apparently extremely rigid? Any chance you can present a model from which testable predictions can be made? Or are you just going to keep telling me that this wondrous stuff that you can't even define has all these amazing properties?

Any idea just how much scientific literature is published in any year? Any month? Heck, any day? I am reasonably confident that there is a lifetime of reading just based on a single month's published scientific literature. Expecting us all to know exactly every article you are talking about is ridiculous. This is why at the end of every even slightly reputable article, there is a whole list of the other works cited. No human being knows even one tenth of 1 percent of all the scientific literature. This is certainly not my area of expertise -- so I probably would never see this article -- but I do enjoy reading about different things. I would have liked to have read about this, direct from the authors, and not based on your interpretation of what you remember.

I don't think that that is quite it. Because I've posted repeatedly that attempting to find a pattern or fast algorithm fro the primes is useful. We've learned a lot of number theory in these attempts. And even if no pattern is found, the attempts and the knowledge gained is still useful. But I keep reading from Unity and Peter that there is a pattern that can speed up calculations and predict primes. But despite many months of repeated claims, neither can actually demonstrate it. So I just don't get why they insist on posting to this thread that there are patterns when that does not represent our current knowledge. I go back to that powerpoint presentation that was linked some time ago. Note how that author presents it. He shows how algorithms are somewhat close to achieving the goal. That a pseudorandom algorithm has some success. But then he acknowledges that it isn't 100% successful. That our current knowledge does not have a 100% accurate algorithm. This is all that I am asking for in this thread -- correct word usage. I don't want a student to come by and read this thread and be confused by these strongly worded statements about patterns in the distribution of the prime numbers and not have them backed up. I want people reading this thread to understand that until those statements can be backed up, they do not represent our current knowledge. That our current knowledge is that the primes are random.

Wow, this is some amazing stuff. How does it have no mass when planets move through it, but mass to allow wave propagation like light through it? Magic? Or, maybe you need to think deeper about what I am asking here. There is a blatant contradiction here. Just telling me that "it has every property" is hand waving gibberish. It is certainly not scientific. If that is going to be your answer to all our questions about your proposed continuum, then there is nothing scientific and nothing all that interesting here. Science is about making models that make predictions that agree with reality. If your model can't even get mass vs. no mass right, then its predictive power is very low, and hence scientifically uninteresting. The current models make very good predictions. You need to be able to do likewise to have something scientifically interesting. This story telling you have here doesn't cut it. Sorry. If you are interested in exploring this idea scientifically, then this forum has people who can help you. I am offering to help you. But I'm not going to pay much attention if you aren't going to pay attention to criticisms and just declare that your continuum has "every property" and hand wave it away. A non-Newtonian fluid can exhibit different apparent viscosities under different conditions and even at different times, but I've never seen one that exhibits positive density behavior in one condition and zero density behavior in another. If you know of one, I'd appreciate it if you cite it. I know the fluid mechanics literature pretty well, but I certainly don't know it all. Besides, this maybe fixes one slight issue. I had a total of 7 that need to be addressed. Just saying 'non-Newtonian' doesn't fix them all.

How does the 'energy level' affect the speed of waves through it? I posted the known equation for speed of waves through a medium. Please show how it works for your medium. Also, the energy level of an object does not affect the drag. See the drag equation posted above. None of those variables are 'energy level'. Please show me the drag equation for your medium. Show me these equations so that I understand how the jumble of words you've said make sense. Because, I am sorry, but I do not really know what you mean by those words. This is why having a model and showing us what predictions it makes is supremely valuable.

No I am not. I am using your own words. I never mentioned empty space. I am using your assumption about it being full. I want to know how this continuum can propagate waves fast enough that the speed of light it what it is, yet behaves in such a massless and viscosityless way that the planets motion seems to not be affected by any drag whatsoever. No assumptions about empty space in this question. Just using your idea here, and expecting you to be able to answer a question about your completely and totally non-empty space.

Yes, right, we have the relationship for the speed of a wave in a continuum: [math]a = \sqrt{\left(\frac{\partial p}{\partial \rho}\right)_s}[/math] for a = c, then this derivative has to have a very high value. The change in pressure in the medium has go up a very, very large amount with just a small change in density. In other words, it must be very rigid. But, then we also have the equations for drag in a continuum: [math]F_D = \frac{1}{2}\rho v^2 C_D A[/math] But, the planets don't seem to experience any drag in their motion -- though this continuum that you say is everywhere -- so one of the terms on this right hand side has to be 0 since the force of drag is 0. 1/2 and C_D are constants, so they can't be 0. v^2 is the velocity squared. We know the planets are moving, so v isn't 0. A is the cross sectional area, that isn't 0. That only leaves the density, [math]\rho[/math]. But, based on what you're saying, the density can't be zero, because it is were zero, the wave speed formula would be broken. There has to be some density for waves to propagate through it. This one of many problems that needs to be explained by your idea. How can this continuum have both of these properties? Rigid enough for light to travel through it, but massless so that planets don't experience any drag at all?

How? I am using your word. Continuum. If there is no empty space -- your continuum -- it has to be rigid enough that the wave motion of light moves at a very high speed. Yet, your continuum has to be massless and viscosityless that the motion of planets through it remains unaffected. This has to be explained. Quit telling me that it is different. You are the one proposing a continuum that fills all space. I am just pointing out what this continuum has to do to fit with the observations that we have -- namely the speed of light and the motion of the planets. Now, quit dodging these questions, and answer how your continuum has these properties?

Everything you're used to describe as your continuum are the properties that were attributed to the luminiferous aether. Just saying "they aren't the same" doesn't fix anything. I could call it "banana pudding", but all it is doing is renaming something that has already been proposed and not detected. Again, I don't care what you call it, if there is a continuum out there, why haven't any of the experiments designed to detect a continuum found anything? How does this continuum have some properties that are unlike anything close to what we've observed to date? What experiment will detect it?

No, you aren't answering my questions. Per my question #1, this continuum must be a fluid, otherwise you need to explain why a solid continuum spread itself everywhere (just like a fluid does). And you need to answer all my other questions -- how is this continuum so rigid that the speed of light is so very, very high? Yet this continuum is massless and viscosityless that planets move through it with no retardation? Etc. Feel free to replace the word 'fluid' with continuum in every question. The questions remain the same and need to be answered. Thoroughly and rigorously please, not just hand-waved away.

Right, this continuum (you're the one who used 'jelly'. I frankly don't care what you call it) has to have all the properties of my points 1-7). Please fully and rigorously explain how your continuum does this and why none of the experiments designed specifically to find such a continuum have all come up with null results to highly precise values?

I think we know that both theories are 'wrong' in that they are obviously incomplete. We know that we can't marry the very large with the very small yet. However, it must be acknowledged that both theories are also very 'right' in that, in their domains of validity, they have been supremely successful as making very accurate predictions. Any new idea that comes along will subsume all the successes of both GR and QM. As a meta comment, this is exactly what GR did with Newtonian mechanics. Physics knew Newtonian mechanics wasn't completely right. They had some known cases, like the precession of Mercury, that couldn't be explained with Newtonian mechanics. Then relativity came along, and was able to make predictions that agreed with what was observed. But the really great thing was that in relativity, if you take the equations and apply them to things that aren't very large, or things moving nowhere near the speed of light, they reduce back to the tried-and-true Newtonian mechanics. This is what the idea that unifies GR and QM together will have to do. This super-idea will have to make the same predictions GR does in the domain of near light speed and very high accelerations, and it will also have to make the same predictions QM does in the domain of the very small. Because we know that GR and QM are both very, very good in their specific domains.

The problem is that your jelly has to start taking on some very magical like properties in order to fit the obervations we have today. 1) It has to be fluid in order to fill all of space (if it was solid, it wouldn't fill all of space) 2) Despite it being a fluid, it has to be very rigid to support the waves of light that travel at the speed of light (far, far faster than the speed of sound in all known substances) 3) In addition, it has to be massless and viscosityless, because the planets, comets, stars, galaxies etc. move through space without any retardation of movement. 4) it also is obviously transparent, incompressible, and continuous to very small scales 5) The Michelson-Morley experiment pretty conclusively proves that the earth is not moving through such a fluid, as the design of the experiment was to find the differences in the behavior of light as light traveled perpendicular to the earth's motion through the fluid or with the earth's motion through the fluid. This experiment has been repeated over and over with increasingly sophisticated and sensitive instruments and today the is no measured effect larger than 1 in [math]10^{-17}[/math]. 6) If the fluid is moving with the earth, the first obvious question is why the earth is so lucky and the fluid follows our truly somewhat bumpy path as we orbit the sun, as the solar system orbits the Milky Way galactic center, etc... And secondly there have been numerous experiments to detect the effects of this fluid if it were necessarily following us with null results. even if you can explain all of the above 7) The theories of special relativity and general relativity are supremely successful and don't require any such fluid. Can any 'fluid'-based ideas match the predictive successes of SR & GR? Please post them if they can. The above questions are how science works. If you can adequately and rigorously explain every single point above, especially #7 and show that your fluid based predictions are as good or better than our current models, you will receive a great deal of attention from scientists. But, because of the above questions, the 'majority of scientists' have rejected this fluid based idea because the necessarily properties of this fluid are incredibly unlikely to occur and have never been detected. It isn't a question about thinking for yourself. Science really isn't this combative. Science is about making prediction that agree with what is observed. To date, predictions based on such a fluid as you've described here make predictions that don't agree with what is seen. Science has properly rejected it as it is worse model than what we have now. If you can fix it, then I'd definitely be interested. But right now, you have a lot of unanswered questions.

Well, I guess this is progress as your quote before was there was no evidence. Now it is apparently circumstantial. Not sure exactly what that means in a mathematical sense. But, at least your admission that there is more than 'no' evidence, is a step in the right direction. The Sieve just uses the tautology that the sequence of prime numbers are each prime. Again, what this thread has been wholly about is finding a quicker algorithm or pattern or function to predict all the primes without directly implementing the definition of primes. This thread is not about finding the superficial patterns like "prime numbers will not occur at divisions at 2, 3, 5, or 7." We all know that, and understand that. The question at hand is without doing this directly, can you build a sequence that contains every prime number?

I don't think it is fair to say that there is 'no evidence'. We have all the evidence of the set of the currently known primes. And to date, no pattern or algorithm has been found to be able to predict this full set of primes. This is why I harp so strongly on the state of our current knowledge. We have a lot of knowledge. And, to date, that knowledge is a great deal of evidence that the primes are random. Again, this could be shown wrong some day, but you can't describe our current knowledge as 'no evidence', because there has been a great deal of work and knowledge created to date. No amount of wordsmithing or trying to subtlety trying to twist our current knowledge is going to get me to agree with you on this. What would get to agree is demonstration of a pattern. Something I've asked for for the 6+ months this thread has been open.

Kramer, why didn't you cite or link back to the article you read so that the rest of us can take as look and see? Trying to answer questions based on your remembrances of a random article doesn't seem like it had a good chance of being productive, especially considering how most of your threads go... edited to fix grammar mistake.