Right, I get the basic math behind it, mostly, though I'll admit it's been 10 years since I've done physics equations in school.

*Waits for someone to get mean and use that against him later. But, figures everyone already knows he's not a physics prof.* Heh.

Okay, I get the velocity bit. That's simple. Acceleration is fine too, change in speed over time, rather than static speed. Now it's been a while since adding the rest into the equation (IE, throwing in mass). Now I'm trying to recall exactly what it means to multiply mass by velocity or multiply mass by acceleration. I guess it's been a while. What exactly are we saying when we multiply a measure of distance by a measure of weight? I mean what does that actually tell us about what we're describing? Maybe that's where I'm getting a bit hung up... I kind of get mass as an analogy to energy "pressure" (IE, the more energy that's packed into the same space, the more "mass" something has). I'm just wondering, I guess what it means to multiply mass by a distance. Say three kilograms multipled by 5 feet.

I mean what is that saying to us? I feel dumb asking that... But what is the product of these. For some reason I'm wantingto say 15 kilogram-feet, which for some reason just isn't making sense to me for some reason... Maybe it's just late.

So, just for weird argument's sake, let's say we've got a mass of 3 Kg with a velocity of 5 meters per second, what exactly does the momentum formula MEAN? 3Kg*5m/s

Having been slightly confounded, I consulted wikipedia.

"The velocity of an object is given by its speed and its direction. Because momentum depends on velocity, it too has a magnitude and a direction and is a vector quantity. For example the momentum of a 5-kg bowling ball would have to be described by the statement that it was moving westward at 2 m/s. It is insufficient to say that the ball has 10 kg m/s of momentum because momentum is not fully described unless its direction is given."

Seems your definition left a little something off. Velocity isn't just distance and seconds. It's direction and speed. It's a vector, among other things. I think that makes a little more sense than strictly speed. IE, momentum is mass * velocity. But velocity is direction PLUS speed where speed is the distance over time. Of course that complicates things a bit... But makes a little more sense, I think?

But, basically you then know how fast something is moving, how "mass"ive it is, and which direction it's moving. Though I'm not quite sure how multiplying it helps?

So then in the example above, one could say it's a 3 kg mass, moving at 5 meters per second in a particular direction. Or if one want to be slightly more ambiguous, one could simply call it a ray in a known direction and disregard direction, though that's technically cheating, it sounds like.

It's been a while since I've done this. Hopefully it'll come back, kind of like riding a bike as the math neurons come back on... ;o]

Again Force seems to have been oversimplified as well. It's a change in momentum over time.

Wikipedia doesn't seem to have a really cogent thought on the definition of Energy, unfortunately. However, in their "Intensity" article they say bluntly:

"Anything that can carry energy can have an intensity associated with it."

So, I guess I'm still asking: If mass an energy are interchangeable, or mass carries or otherwise converts from energy, can it have an intensity associated with it. If so, what does that mean? Since energy semi-directly (through e=M(C^2) ) correlates to "mass" it seems like mass can have an "intensity" relationship with Energy.

And the Force article on wikipedia says:

"Instead of a force, the mathematically equivalent concept of a potential energy field can be used for convenience. For instance, the gravitational force acting upon a body can be seen as the action of the gravitational field that is present at the body's location. Restating mathematically the definition of energy (via definition of work), a potential field U(r) is defined as that field whose gradient is equal and opposite to the force produced at every point."

Which seems to get at the same analogy I was trying to make with my analogy to a beach ball. That mass seems to me to maybe just be a manifestation of the intensity of energy across a gradient sphere from the center of mass/energy. Or maybe thought of a different way, the tighter you pack energy, the more "mass"ive it gets per area. Essentially like pressure. The tighter you pack the same amount into a smaller area, the more force it exerts per square or cubic area. Perhaps that's the geometric relationship you spoke of earlier in the thread?

I guess I might ask the question, if you have the same amount of energy packed into a smaller area, are the masses equivalent, just more tightly packed, or is the smaller object with the same amount of energy more massive 'cause it also factors in the energy used to compress it, thus it's actually got more mass because it has more energies involved in keeping it tightly packed?

If the latter is true, that the smaller object compacted from an object the same as the larger object has more mass because of being compacted... Could we say that if we ignored the energies used packing the same starting energy into a smaller space that the energies would still be the same, thus the masses are equal? And it's strictly due to the conservation of energy factoring in the energy used in packing that the smaller object is considered to have more mass? IE, 1 kg of material in a 1 cubic meter sphere versus 1 kg of material in a 1 cubic centimeter sphere (ignoring packing energies) would be equivalent; whereas the same starting mass and final volumes accounting for packing energies to get the original 1 kg into 1 cm would favor the 1 cm object as having more energy, thus more mass?

Just trying to get it all straight in my head, sort of. ;o] I think I'm kinda' getting it now. Despite taking the long way about it.

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As regards your statements:

"I can't follow your logic, because you are somehow under the impression that language can communicate reality. But it can't, reality can only be understood by experience, not by logic. And it cannot be communicated by language, but only by mathematics.

Just for starters, "intensity" is just a word. It is DEFINED as the flux of power through a unit surface area at some distance from an isotropic emitter. Intensity has nothing to do with being intense, it's just the number of Watts of energy going through a square of a certain size at a certain distance. All that "equation" really tells you is that the farther you are from a light the dimmer it appears. There is no great mystery there."

I might point out a few things...

I think you contradicted yourself in the first paragraph...

"it cannot be communicated by language, but only by mathematics."

If ya' really want to get technical, mathematics is a language. So, by that reasoning, mathematics, being a language ALSO cannot communicate reality... Math is just symbols on a page, and like anything else it can be written as poorly as someone wants and be just as undescriptive as natural language. In some cases, the assertion that math is the purest form of physics is utter bull, to be frank. I think it was Alfven who once said something to the effect "the mathematicians wrote beautiful, elegant equations. Sadly it was only the plasma that didn't see the elegance, and refused to obey them..." Math is a modeling tool, and math can be a logical language. So, if we can't understand the universe by logic or communicate about it with language, as you've suggested, we seem to have set back the study of physics and possibly philosophy by a hundred to a thousand years 'cause we'll have to throw out whatever's a language and whatever's logic and go with something else. *wink*

Okay, maybe now I'm just being, I dunno. I'm tired, and it's late...

Intensity has "nothing" to do with being intense? Ohh, that's cute. It's a measure of X over area Y at distance Z. Dimness, is intensity, is "how intense" the light is at distance. Let's not get into semantics, m'kay? So, what is the "flux of power" that's being measured at a distance. Power factors in, what, velocity, mass, distance, etc. Basically it's measuring the push, or the work being done at a distance (to boil it down). And that's pretty much exactly what I'm saying, or trying to say. Mass is just the "push" or intensity of energy at a certain distance along a spherical gradient (or something to that effect). As you said previously intensity's a geometric function, yeah? So why can't mass be a geometric function of "energy" (with conversion rates according to E=M(C^2), M=E/(C^2), and/or M/4Pi=E/4Pi(C^2) ).

Alrighty, I'm done. I'll probably look at this tomorrow and say "I should write that late at night anymore..." *wink* Have a good one.