The inverse square law

[jj]

I'm not sure what you mean. There's no problem with gravity following an inverse square law. But neither would there be any problem if it didn't.

Really, there wouldn't?

That would rather serious indicate other than 3 full-sized spatial dimensions.

Again, if you have an object with 3 spatial dimensions, and you expand and contract it by a factor of "r", what does its area do?

 

[BillyJoe]

.....and it's no coincidence that the Moon always shows the same face towards the Earth.

Careful.

 

[CurtC]

OK, so the server with the link in the OP is up again, and I read that page. It was a plain old explanation of the inverse square law.

Once you've accepted the principle of conservation of energy, the inverse square law falls right into your lap. Can you explain what's so amazing that it seems to prove the existence of god?

 

[Andonyx]

Really, there wouldn't?

That would rather serious indicate other than 3 full-sized spatial dimensions.

Again, if you have an object with 3 spatial dimensions, and you expand and contract it by a factor of "r", what does its area do?

jj, I think people are really missing the point of what happens when you spread ANYTHING out evenly in all directions.

The inverse square law applies to light, sound, and ANYTHING that travels outward equally in all directions.

If you took a finite quantity of Jello-brand Jello gelatin snacks and tried to make a hollow sphere out of it, then tried to stretch that sphere evenly to twice its original radius, the gelatin comprising the sphere would then be 1/4 the thickness of its original size.

 

[Iconoclast]

If you took a finite quantity of Jello-brand Jello gelatin snacks and tried to make a hollow sphere out of it, then tried to stretch that sphere evenly to twice its original radius, the gelatin comprising the sphere would then be 1/4 the thickness of its original size.

I haven't bothered to do the math, and I'm sure this'll come back to haunt me, but surely your jello analogy works with a disc and not a sphere.

 

[CurtC]

No, he means a sphere. Or rather, a spherical shell. Imagine covering a basketball with Jello, then taking an equal amount of Jello, and covering a beach ball with exactly twice the diameter of the basketball. The Jello on the beach ball will be 1/4 the thickness. This is the inverse square law.

Another application is why larger mammals stay warm more easily than smaller ones. If you have two identical animals, except that one is twice as tall, wide, and deep, the bigger one will have eight times the volume, but only four times the surface area. Eight times the volume generate 8x the heat, but you have only 4x more surface area to get rid of the heat.

 

[BillHoyt]

Right, but why an inverse, and why inverse square?

"Viaduct? Vy not a horse, a chicken or a rabbit?"
-Marx brothers

"Why don't you buy a toupee with some brains in it?"
-Three Stooges

Gee, I don't know, Tr'olldini, let's think about this. Distance increases, and the intensity decreases. Astounding that this would give us an inverse, no? Let's scratch this great mystery deeper. Oh, an area measurement? That might explain the square, no?

 

[Andonyx]

I haven't bothered to do the math, and I'm sure this'll come back to haunt me, but surely your jello analogy works with a disc and not a sphere.

Well, no. It's a sphere, that's kind of how you get to the inverse square law. We're talking about three dimensions, not two.

What I did state wrongly was that it's thickness would be 1/4 which is misleading.

It's Surface area quadruples. Which for a constant amount of jello would mean it's thickness would have to reduce by 3/4.

So my statement is in fact correct, it just doesn't spell out the phenomena correctly. But here, is the math:

A sphere of Radius 3 meters has a surface area of 113.094 square meters.

4 Pi (3^2) = 113.094

A sphere of radius 6 meters has a surface area of 452.376

4 Pi (6^2) = 452.376

So the total surface area has increased by 4 times.

Thus if you take a point source of light at the center of the sphere of constant intensity...As the light spread over 360 degrees extends twice is far, the same amount of energy is spread over 4 times the area.

This works for ANY angle, which is how we get the inverse square law. The amount of energy sread over a 90 degree angle of that same phere at three feet would be 1/4 the emount spread over a 90 angle at 6 feet.

 

[Andonyx]

I should add that the reason it works between one and two dimensions is the same reaosn it works between thee and four dimensions as been stated above.

When you move from a linear measurement like radius, to a two dimensional measurement like surface area, you have literally an exponential difference. That is the linear measurement increases by a power of 1, the surface area measurement increses by a power of 2. So if linearity increases 2 times, surface area must increase four times. (Likewise volume would increase 8 times, or 2^3).

Similarly if you were measuring surface area first, a two dimensional measure, and doubled your surface area, the difference between surface area and volume is only 1 exponential value. And so as you doubled surface area, Volume would increase 4 times. Thats 2^2 versus 2^3.

Does that make sense to anybody, or should I refrain from trying to explain these things because I'm not good at communicating math concepts....

 

[69dodge]

Originally posted by Andonyx
When you move from a linear measurement like radius, to a two dimensional measurement like surface area, you have literally an exponential difference. That is the linear measurement increases by a power of 1, the surface area measurement increses by a power of 2. So if linearity increases 2 times, surface area must increase four times. (Likewise volume would increase 8 times, or 2^3).

Your numbers are right, though "exponential" is the wrong word. The area and volume of a sphere, which are proportional to r² and r³, respectively, are polynomial functions of its radius r, not exponential functions. Examples of exponential functions are 2^r and 3^r.

Similarly if you were measuring surface area first, a two dimensional measure, and doubled your surface area, the difference between surface area and volume is only 1 exponential value. And so as you doubled surface area, Volume would increase 4 times.

This is wrong. If you doubled the surface area, the radius would be multiplied by the square root of 2, and the volume would be multiplied by the cube of that, namely, twice the square root of 2.

 

[T'ai Chi]

Gee, I don't know, Tr'olldini, let's think about this. Distance increases, and the intensity decreases. Astounding that this would give us an inverse, no? Let's scratch this great mystery deeper. Oh, an area measurement? That might explain the square, no?

Do you agree with jj's ideas of character assasination through making fun of nicknames? You might want to reconsider your approach Bill.

Yeah, I understand area. The mystery is why the 2 exponent specifically. What conditions arose to lead to that? Why aren't we measuring area in something other than stuff squared?

One doesn't fully explain the inverse square law by saying that it comes from area; they just present a 'just-so' circular story about it.

Moreover, is the formula exactly something like 1/r^2, or is there some other stuff in the formula? Did the formula come from theory, or from a more experimental approach, like regression?

 

[jj]

I should add that the reason it works between one and two dimensions is the same reaosn it works between thee and four dimensions as been stated above.

When you move from a linear measurement like radius, to a two dimensional measurement like surface area, you have literally an exponential difference. That is the linear measurement increases by a power of 1, the surface area measurement increses by a power of 2. So if linearity increases 2 times, surface area must increase four times. (Likewise volume would increase 8 times, or 2^3).

Similarly if you were measuring surface area first, a two dimensional measure, and doubled your surface area, the difference between surface area and volume is only 1 exponential value. And so as you doubled surface area, Volume would increase 4 times. Thats 2^2 versus 2^3.

Does that make sense to anybody, or should I refrain from trying to explain these things because I'm not good at communicating math concepts....

Well, you mean polynomial instead of exponential, but other than that...

Exponential is something else, it's f(x) = a * e^(bx)+c;

 

[Andonyx]

Your numbers are right, though "exponential" is the wrong word. The area and volume of a sphere, which are proportional to r² and r³, respectively, are polynomial functions of its radius r, not exponential functions. Examples of exponential functions are 2^r and 3^r.This is wrong. If you doubled the surface area, the radius would be multiplied by the square root of 2, and the volume would be multiplied by the cube of that, namely, twice the square root of 2.

Thank you, good catch.

 

[jj]

Do you agree with jj's ideas of character assasination through making fun of nicknames? You might want to reconsider your approach Bill.


Do you agree that you often troll this group, that you put yourself to total ridicule once, and that you continue with a new "identity" and continue to do so?

Do you deny that you were Whodini?

Do you deny that you use the same tactics, and the same evasions and mystical approach?

Do you insist that it's "character assasination" to point out your continued misbehavior?


Yeah, I understand area.


Good, good.


The mystery is why the 2 exponent specifically. What conditions arose to lead to that? Why aren't we measuring area in something other than stuff squared?


I thought you understood area. Primary among that would be understanding the meaning and definition of area, from which we wind up with units squared.


One doesn't fully explain the inverse square law by saying that it comes from area; they just present a 'just-so' circular story about it.


One explains the inverse square law exactly like that. The fact that you do not understand one's explaination does not make that explaination circular.


Moreover, is the formula exactly something like 1/r^2, or is there some other stuff in the formula? Did the formula come from theory, or from a more experimental approach, like regression?

"regression"??? Why would "regression" be involved here?

The fact it APPLIES TO ANYTHING comes from observation. The calculation of "lines of flux" or whatever you choose comes from basic mathematics.

Now, let us assume that gravity is not quite inverse-square law. What would that imply for orbits? Try it, use an exponent of other than 2, and see what you get for an orbit. Just try.

 

[Andonyx]

Do you agree with jj's ideas of character assasination through making fun of nicknames? You might want to reconsider your approach Bill.

Yeah, I understand area. The mystery is why the 2 exponent specifically. What conditions arose to lead to that? Why aren't we measuring area in something other than stuff squared?

It's not like we have a coice. When you have something you only measure in a straight line, you don't need to call it anything else but inches or feet because you're only using ONE dimension.

When you measure in area you are measuring height by width...since we keep our units uniform (that is once square inch is one inch wide by once inch tall) We have an inch squared!

That's not like we chose that arbitrarily, it the nature of using TWO dimensions to express something.

One inch Cubed, on the other hand is one inch by one inch by one inch.

That's how we measure volume in THREE dimensions.

Where do you get this idea that we just CHOSE 2 out of nowhere. It's the way to measure in two dimensions?

And it's not as thouth the inverse sqaure law is anything other than a transformation of the various formulas for finding surface are.


We didn't make up what a sphere is, and we didn't make up how you finde it's surface area, that's is a physical property of a sphere, the rest is simply math.

 

[phildonnia]

So it isn't perfect, and God hasn't managed to put any bodies in "perfect" circular orbits either. He do that and I'll believe.

I wonder if there are natural processes that could gradually massage any orbit into an elliptical one. Consider the following apparent manifestations of perfection:

The orbital period of Pluto is exatly 1.5 times the orbital period of Neptune.

The so-called "Trojan asteroids" are found exactly 60 degrees ahead and behind Jupiter.

Oh, and I can't resist:
The Earth is exactly 40000 km in circumference, from pole to pole. Not approximately, but exactly. This is irrefutable proof that God uses the metric system.

 

[scribble]

I must be lucky then. We recently had a lunar eclipse. iI was darn near perfect here.

Well, the shadow of the Earth at the distance of the moon is actually much larger than the moon, not at all a 'perfect' match.

I remember years ago, seeing my first solar eclipse through the little hole you make in paper. It was also perfect. All you could see was the ring of fire, barely, and equally, around the rim of the sun.

That's lucky. I've seen one eclipse like that in my life. Where I'm at, all the rest have been partial eclipses, or not visible at all. The shadow of the moon on the Earth is smaller and from different locations will give a different show. You got lucky. Many people travel across the world to take photos of an eclipse. Ask yourself why that would be necessary if they're so perfect.

Think about this once: If you have 3 objects that sooner or later come into an alignment with each other...and one gives off light, so that a shadow is cast; what is the odds that that shadow cast will be the same size as the object it is cast upon?

Depends on the objects. Three random planetary bodies, I'd say the chances are pretty slim. It's irrelevant - as you can see, that's not the case here.

Now I suppose a skeptic could simply say, "So what? This doesn't prove that this happened by design. It could simply be a matter of..that it is. It is, because it is. If it wasn't this way...would we think any less of our universe? (Sort of like asking ourselves if we think any less of our forests because the trees are not in perfect rows)."

Well, that's not this skeptic's response.

But...because it *IS* perfect, geometrically, to have this occur, just as there is order out of chaos to have it just so happen that there is inverse square properties....it causes someone like myself to contemplate if this is just all random chance, or stems from some sort of order caused by a designer.

You're working off of false "facts" and false reasoning. People here have tried to explain to you why the inverse-square law is an obvious geometrical necessity. It's as though you're using the fact that triangles have three sides to prove God. It only demonstrates you have an incomplete understanding of the things which you are discussing.

We haven't touched on crystral formations yet, have we? [/B]

No, but I'd love to hear your thoughts on them. As wrong as your statements are, I find them fascinating. I don't mean that in any sort of a condescending way; I'm quite enjoying this conversation.

 

[69dodge]

Forget about light bulbs emitting light. I agree that the law of conservation of energy implies that irradiance follows an inverse square law. Also forget about Jello. I agree that the law of conservation of Jello implies that Jello thickness follow an inverse square law. I'm not talking about any of that.

I'm just talking about gravity. Suppose, for example, that gravity were proportional to distance, like a spring, instead of being inversely proportional to the square of distance. So what? Can anyone describe why this violates energy conservation? (Springs don't violate it.) How would you go about extracting arbitrary amounts of energy from a system that obeyed this type of gravity?

 

[Andonyx]

Well, I'm not sure how it would violate conservation either.

I mean I don't think the inverse square law really has much if anything to do with conservation of energy.

I mean a Laser does not follow inverse square law at all. It doesn't have to because it doesn't spread equally in directions because it only uses coherent waves of photons.

But one is still not getting any MORE enegry out of a laser than is put into it.

Likewise, if gravity extended in only one direction from a source, it would not follow the inverse square law.

But that still doesn't violate conservation of any kind. That I'm aware of at least.

Maybe I'm not understanding your question.

 

[69dodge]

Originally posted by Andonyx
Likewise, if gravity extended in only one direction from a source, it would not follow the inverse square law.

No, suppose it extended uniformly in all directions, but it still were proportional to d instead of 1/d².