Summations Only

Density is the amount of mass within a volume divided by that volume. It is a property of a system and is not located at a point. Insofar as the "location" of density might be meaningful, its location is the entire extent of the system.The fulcrum (or barycenter of a group of masses) is a point with no volume. So you can't just calculate the density at that point by dividing the total mass by zero volume. In this case L'Hopital's rule doesn't help. You can't divide by zero and therefore, by definition there's no such thing as "density at the barycenter". There's no such thing as density at any point. Your claims of such a thing are meaningless.If you want to calculate density in a small volume near the fulcrum or barycenter, then divide the mass contained within that volume by the volume.Of course, of you divide the mass of both people and the teeter-totter and divide by their total volume, that is almost certain to be the highest density of any set of the parts of the system (unless the board is aerogel and big). But that density is not located at a point, it's a property of the system.

You'll have to convince me that L'Hopital's rule is applicable. Assume any reasonable function you want for the mass within a volume.Edited by JonF, : No reason given.

OK, I'll give that one to you, you are correct.However, the density at a point is not a function of things which are far away from that point (unless you can think up some pathological case in which it is). Especially, the density at the barycenter of the Sun-Jupiter-Saturn system when the barycenter is outside the sun is damn close to zero. I'm not sure what PL is trying to say, but he obviously does not know what density is.

You can talk about the average density within a volume or over several points. Not at a point. An average by definition requires more than one density and more than one point or volume.You probably can't talk about average density in whatever way you mean it. The average density of the Sun-Jupiter-Saturn system can be calculated, but it has no location. It's just a property of the system.Note that the barycenter of that system is a point. When the barycenter is outside the Sun, the density at the barycenter is near zero; it's the vacuum of space. You need to define precisely and mathematically what you mean by "average density". I think you don't know what you mean, but you certainly don't mean it in any conventional manner.Give us your formula for calculating average density. Until then your claims about it are meaningless.Edited by JonF, : No reason given.

Well, if you define a region, and then sub-regions, and calculate the average density of each sub-region, then "highest average density" does have some meaning.BUt I have no idea what PL means by "highest average density" or even "density". It's his own idiosyncratic and so far secret meaining

Commonly held but incorrect.Clearer than the rest of your incoherent ramblings, though. That's an improvement.

What keeps an airplane up is way off topic. Briefly, you are assuming that the same pairs of molecules that separate at the leading edge must rejoin at the trailing edge. Tain't so, there's no such restriction. The full answer is complex, look it up if you're interested.I see you've relapsed into incoherent gibbering.

OK, what you call "accelerating expansion" happens in our everyday world. You've made no connection between those and our Universe. You need some evidence that is observations of the characteristics of the Universe, not allegedly analogous processes. Arguing by analogy is a fallacy. Analogies are useful for explaining certain characteristics of established phenomena but they are not evidence for the existence of phenomena other than themselves. You are asking us to rely on your intuition for scientific conclusions. Sorry, it just doesn't work that way. Especially since there are such severe problems with your hypothesis that you obviously can't address (e.g the expected blue shift of some galaxies). Plus we know (and obviously you don't) that extending "common sense" conclusions drawn from our everyday experience to the very small and the very large, both of which are far from our everyday experience, is often wrong.It doesn't matter whether or not you can think of an accelerating expansion that does not slow down. It doesn't even matter whether or not there exists an accelerating expansion that does not slow down other than the Universe's. The Universe's expansion could well be unique in the Universe, since the Universe is nothing like what we experience on Earth.

Your extrapolation from small scale phenomena on Earth to the entire universe is not justified.Rather than repeating your claim, you should concentrate on why others don't find it convincing.Personally, I don't find it convincing because you are basing your entire "theory" on a massive extrapolation with no observations of the universe to establish a basis for that extrapolation.

See, this is one reason why nobody can take you seriously. You are wrong and apparently incapable of thinking about your own model.The air molecules that move towards the nozzle of a vacuum cleaner start out widely separated and move towards the nozzle from different directions. No matter what the pressure or acceleration, those molecules have a component of motion towards each other. If that were happening in the Universe, we would see very distant galaxies moving towards us, i.e. blue shifted.You also should learn some fluid mechanics, especially the difference between static and dynamic pressure.

Still no evidence supporting your "theory". Analogies aren't evidence. Now you're saying that the evidence is hidden beyond the edges of the observable universe.So no evidence, no calculations, nothing but unfounded assertions. Not even interesting assertions.

The universe is not a gas. Boyle's law does not apply.

They're evidence of something. They aren't evidence in support of your thesis until you make an evidence-based connection between then, not just a wild extrapolation.Edited by JonF, : No reason given.

I don't care if you've got a billion of them. Your unjustified extrapolation to the Universe is the problem. I can't, since for the Universe we don't know. The Universe is wildly different form the "experiments" you've listed, and there's no reason to believe it acts like any of those "experiments".

Assuming your conclusion. Nobody cares about your personal incredulity. It's irrelevant. Assuming your conclusion again. For example, the expansion of space has no effect on Earth because Earth's matter is gravitationally bound. So things happen in space that don't happen here. Well of the top of my head:

• {ABE} As far as any of us can tell, it's refuted by observations. All your "experiments" involve components approaching each other, which in the Universe would give rise to blue shifts of distant galaxies*.
• Any extrapolation in science is dangerous, and should be viewed with suspicion unless there are good arguments for such extrapolation.
• The Universe is not a gas
• All your examples cover a volume of a few cubic meters or less. The OU is about 82,300,000,000,000,000,000,000,000,000,000,000,000,000,000 cubic meters. The vast difference in size almost certainly does matter (cf expansion of space, above).
• The expansion of the OU is omnidirectional. None of your examples are.

I could probably come up with more, but you can start with that. During your teaching stint did you ever look up the meaning of "extrapolate"? It's not a synonym for explanation. All your "experiments' are analogies which (as I've pointed out before) are useful for explanation but are not evidence for the thing itself. Definition of extrapolate:

quote:

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[To] extend the application of (a method or conclusion, especially one based on statistics) to an unknown situation by assuming that existing trends will continue or similar methods will be applicable

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{emphasis added}You need to justif your assumption that your gigantic extrapolation is valid.-----------*A few nearby galaxies have a small blue shift. That's because the local group is gravitationally bound. Note that I said "distant" galaxies.Edited by JonF, : Forgot the most important one!