Bignose

Ya. Your point was that 'seemingly random constructs have some pattern behind them'. And I really object to stating that when there is no evidence of it. I keep asking you guys to back these statements up. If there is a pattern, present it. I'm not going to support any assertions about patterns until they can be supported. Mathematicians have good reason to believe NP v. P, even though it isn't proven. But I have not seen any real mathematician say they believe in a pattern in the primes without evidence. Once again, this does not mean that there is no value in looking for one. But, apart from a few of you guys, I don't see anyone else insisting on there being a pattern, especially when you guys can't back these statements up. That's what I'm saying. That's pretty much all that I've said in this thread. That you guys can believe whatever you want, but unless you're prepared to back patterns up with something definitive, the current state of our knowledge is that primes are distributed randomly. Saying anything else good against the very best of our current knowledge.

Look, I don't care what assumptions, realizations, conceptualizations, or constructions you want to make. The simple truth is that no definitive pattern has been found. That is the state off our best knowledge today. To say otherwise is a falsehood. Once again, if you disagree, just show us the pattern. All this other stuff is immaterial to this point. All your personal opinions on how likely that there is a pattern is immaterial. All my personal opinions are immaterial. The current state of our knowledge is known. Why do you continue to argue it?

From the limited information here, I don't see why this couldn't be remedied fairly easily. Surely there is a community college or junior college near yout hat offers an introductory physics course for a minimal cost?

So, I think that the confusion stems from the fact that implicit in the model is that [math]\mu[/math] is a constant. If [math]\mu[/math] is taken to be a constant, than indeed, you can define it to be Friction Force/Normal Force. In the same way you can define [math]\pi[/math] to be Circumference of a Circle/Diameter of a Circle. But, just like [math]\pi[/math], once you've set your model to be a fixed [math]\mu[/math] you get to use it in all difference situations. So, in the example above, if we measure [math]\mu[/math] on earth, under earth's gravitational field, the model assumes that indeed [math]\mu[/math] is the same on the moon, on Jupiter, on the sun, etc. Just like you can use the same [math]\pi[/math] for calculation of a circle's area, or a sphere's volume. Now, all that said, unlike [math]\pi[/math], [math]\mu[/math] is very rarely constant under every situation. There is usually at least some amount of weak normal force dependence on it. There is usually a weak environmental component to it (i.e. vacuum vs. earth's atmosphere vs. pure nitrogen are probably different) and a weak temperature dependence. As mentioned above, it is important to use the term Normal force and not just weight. They are the same in a lot of situations, but not always. I.e. consider the simple situation of 2 blocks stacked on top of each other... In short, I think it is best understood that the use of [math]\mu[/math] above is just a model. A model that is very successful under a good range of circumstances, but not always. And it is important to understand when this model is appropriate and it isn't.

Yeah, oops. 17* above the horizon. My bad. For reference, the loft on a typical driver is between 8* and 12*, and modern instruction asks players to try to hit up ever so slightly... between the inelasticity of the impact and this slight hit up, that's where the launch in the high teens comes from.

TaylorMade (a golf equipment manufacturer) was using the slogan "17 degrees, 1700 rpm" in its ad copy this past year. Specifically, this is means that a launch angle of 17 degrees from vertical, with a backspin of 1700 rpm yields maximum distance. It made for good ad copy, but wasn't exactly true. If someone hits with a lower speed, then they need higher than 17* launch angle and more spin for lift. If someone hits with a very high swing speed, then need a lower launch angle and lower backspin otherwise there will be too much lift. However, we're talking launch angles of 12 or 14* for the very high swing speed players, and launches of 20 or 22* for the very low swing speed players. In short, 45* is no where near the maximum distance launch angle for a golf ball, for the various fluid dynamic effect swansont mentioned above. 45* launch angle is like hitting a golf ball with a 9 iron or pitching wedge. Guys hit driver off the tee when they want maximum distance. There actually is software out there, TrajectoWare http://www.trajectoware.com/wrap.php?content=description.htmlthat takes into consideration how an actual golf ball interacts with the air. The equations it is based on are in the physics literature (I wrote one of these myself for a project and it agrees pretty closely with the other models out there). The real ones used in industry are proprietary -- i.e. TaylorMade is not sharing code with Titleist who isn't sharing with Calloway, etc. Each of them are trying to eek out as much distance as they can from their own club designs and ball designs. But, this software will quickly show that 45* launch angle for a golf ball is far from maximum distance.

http://www.livescience.com/48922-theory-of-relativity-in-real-life.html?google_editors_picks=true I thought this was really interesting. This forum cites GPS frequently as "tangible evidence of Relativity working", but it might be good to have 7 more in the holster here...

there is no argument with this. The argument is with your statement here: because 'things' was never defined and seemed to mean 'everything' based on your following statements. and you used 'real' here: to again support the idea that all things (as in all things that are measurable) must be quantizable. Again, why I think you are mixing up quantizable and quantifiable is because if you put 'quantifiable' in the above statements, they are perfectly true. But insisting on the word 'quantized' and similar is in error here.

I still think you are using it as a synonym for quantified, however. quantification: to determine, express, or measure the quantity of.

davidavid, quantized does not mean the same thing as quantifiable, or quantified. quantized means that every number is a multiple of some unit, or quanta. For example -- and I am going to make up a completely farcical example -- if a quanta of coolness was one Fonz, then every measurement of coolness would be a multiple of one Fonz. 10 Fonzies or 17 Fonzies would be valid, but there would be no such thing as 17.5 Fonzies. However, if there were no such thing as a quanta of coolness, but we still had a coolness meter, then 17.5 Fonzies would be meaningful, and quantified. So, if you are truly claiming that everything is quantized (and not just quantifiable), then you need to tell us what the 'Fonzie' of time, velocity, voltage, etc. all are. Not the unit that quantifies these measurements, but the quanta itself that all valid measurements must be a multiple thereof. MigL gave a good example of an number that cannot be quantized, [math]\pi[/math], because it is irrational. Another good one is [math]\sqrt{2}[/math], which is the length of the hypotenuse of a right triangle with two legs of length 1.

As I wrote above, the LHS is from the definition of variance and the RHS is to represent the average of the sample variances. In short, I go all the way back to the very first statement I wrote in reply to your calculations: The average of sample variances, in general, will not be equal to the population variance. You showed this yourself with your calculations. To correctly combine sample variances, you need to follow the methodology provided in the link. In effect, you have to combine all the samples together into one, so the formula weights each sample variance by how may instances were in that sample + by how far the sample mean was from the combined sample mean. The link shows how to do it for 2 samples, there exists generalizations for any number of samples.

You dropped the subscript c in on the X term. That is important. See the definition of X_c

Sure, sure. Where is the list of crackpots who were wrong? Long forgotten as is appropriate. Furthermore, it is a simple truth that science is a human activity and ergo has all the same positives and negatives as any other human activity. For most of history, there were really only a very select few who even had the possibilities of conducting science. Typically, only the very wealthy or powerful, simply because most people literally had to spend the great deal of their time surviving. Only the very wealthy or otherwise supported had time to sit around and think and try to do scientific type work. This is a main reason the church seemed so active in science -- because priests were supported by the people and had at least some time to do other stuff. Sure, sometimes The Church as an organization took a stance, but fairly often it was priests where were some of the best scientists at the time and they would have good arguments with people not necessarily representing what was doctrine. It also wasn't all that long ago that science was very nationalistic. If you lived in Germany in the 1930s and 1940s, if your science did not agree with the current political agenda, in the best case, you lost your job. Or were shot. Stalin ran a very similar regime. To the point that Lamarkism was favored over something like Darwinism and decisions made on crop planting were based on it and directly led to the Russian famines. There are lessons from history here that we try not to repeat. This is at least some of the reason there is such passion about anthropogenic global warming. It is not much a stretch to see which political parties are pro- and con-AGW. Science would like to think the we are above this today. That said, there are still political issues that cloud sciences. This was years ago, and I apologize because I can't find the source today, but there was a meta-study of the studies about gun violence and in the end a very high correlation between the funding source for the study and the results of the study. As in, when the NRA funded a study, lo and behold guns weren't all that bad, and etc. And, really, the gun issue is a complicated one. The exact same data can be shown to support or refute many different statements. So, yeah, all the way back to the top, science is a human activity. Humans aren't perfect. Heck, even simpler than what I wrote above is the simple truth that resources are limited, and many someones out there have to make decisions on what to put those resources into. Even with all the available info, those someones aren't doing it perfectly. Humans aren't perfect. But, to conclude this, what cannot be denied, and the reason that the list of 'crackpots who turned out the be right' even exists is EVIDENCE. Evidence was brought forth to support those ideas. And in the end, ideas that match evidence always eventually win the most favor. That is what is missing from nigh on almost every single 'speculative' or 'crackpot' idea that gets presented. It seems that so many of them get caught up in all the stuff I wrote above plus all the other people have written about above, that evidence doesn't seem to be important. But evidence is literally the most important. I don't care about anyone's history, education, background, experiences, or anything else like that. Show me some level of prediction based on your idea, and how closely that idea matches what is known. That's it. That is the ultimate objective metric of science. The delta between prediction and measurement.

Neither. Just square brackets used so that they look different than regular parentheses.

MonDie, the problem is that you can't just average sample variances like this and expect the result to be meaningful. Take a look at http://www.emathzone.com/tutorials/basic-statistics/combined-variance.html You are expecting [math]\int_{POP} (x-\mu_{POP})^2 f(x) dx = \int_{SAMP} y \int_{\Omega_y} (x-\mu_{y})^2 f(x) dx dy [/math] where the LHS is the population variance and the RHS is the average of sample variances (the inner integral represents that variance calculation over a single sample). And there is no real reason why the two should be equal in the general case.

Your life may be substantially longer, but right now with security as lax as it is in far too many places on the internet, identity theft is a real concern and your longer life may be filled with a great deal more troubles. Without a doubt, in the year 2014, there are incredibly significant reasons to protect your information on line.

I've always intuited it thusly: since you are only taking a sample, you need to be more conservative in the possible variance in the whole population. Whereas if you know the entire population, you don't need to be conservative because you know the variance by definition. To me, it is simply a way of being a little more sure that your sample variance range has captured the true population variance.

It is at least an interesting idea. The questions above from the other posters do immediately come to mind, as in what is information and why must it be stored somewhere... Also, to be considered a viable alternative, it needs to be able to recreate the dark matter maps we have right now. See, e.g., http://www.space.com/14176-dark-matter-biggest-map-unveiled.html In short, you have a story, but it isn't very scientific yet. To make it scientific, you need to expand on it and see what predictions it creates and how closely those predictions agree with what we've observed (like that map linked above).

Science is primarily about making accurate predictions. Those predictions are compared with measurements. The idea whose predictions that are closest to measurement is considered the best. If something is immeasurable or unobservable, then you can't make.a prediction that agrees or disagrees with it. So, no, science is not very interested in the immeasurable. Because if you can't measure it, it might as well not be there. Because if it is immeasurable, it is exactly the same as not being there. And why believe something is there when there is no way of determining if something is there or not? I hope this answers your questions a drives you to think how to turn your idea into predictions. Because, again, the current understanding of gravity makes predictions that agree very well with measurements. Unless your idea can do better, interest in your idea scientifically will be low.

Still no answer on how observing or not observing changes the mass of my ball. Let me cut to the chase. You have a lot of scientific sort-of buzzwords thrown together there. Does it actually lead to any useful predictions? Something testable? Something I can measure at home? Using the current theory of gravity, I can calculate how much force my foot will feel when I drop my bowling ball on it from waist high. Can your information, fractal, language actually quantitatively describe this? More than "it will hurt, a lot" can? I mean, this is a science forum. I'm looking for actual useful predictions. Right now, the current understanding of gravity does this, very well. I wouldn't trust us to land a probe on Mars with fractal past, present, and future sentences. But I would with the current understanding of gravity; and we successfully do this fairly often really. If your idea can't be turned into testable predictions, it isn't science, and it isn't very interesting for those of us who actually want to do something useful like use it to make predictions.

I don't see how this answers my question about how my bowling ball's mass changes if I observe the event of it hitting the pins or not...

This really doesn't make a lot of sense to me. My bowling ball has the same mass whether I observe it striking (or splitting!) through the pins or not. I don't see how my watching (observing) the event of impact changes its mass.

Yes. There are forces like drag and lift. Considering the very brief way the question was asked, I consider this brief answer sufficient, unless there is more specifics you want to ask...?

You know what would demonstrate this? Actually showing it making predictions that agree with measurements. As I wrote above, how much more prelude is there? When, when, when are we going to see some actual predictions? I'm going to reserve my 'not perfect' comment until you can, you know, actually demonstrate what you've claimed you can do about 5 times now. It's time to put up. Let's see it already. If we don't understand something, we'll ask, don't worry. If the reply to this will be more copies of definitions from a dictionary or another 1000 words of 'introduction' or just promises of what you can do, I'm just about done here. As Strange wrote, we're on the second page now, 30+ posts in. Let's see something already. Please?

It does have a real sense of beauty about it, sure. But it certainly isn't perfect. And experimental evidence to support it very weak at this time. About the best that can be said is that is still falls within known experimental constraints. So, how much prelude is left? When are we actually going to get an actual testable and falsifiable prediction? As above, I am willing to listen if you can demonstrate actual predictions. But my appetite for prelude and flourished promises of what to come is waning.