Gravity

[Usagi]

If the line is longer, there are more points. Where does my reasoning go wrong?

Reasoning about infinity is hard. You really do have to look into some of the branches of math the previous poster mentioned in order to start to grasp it.

For example, you asked about the set of all even numbers and the set of all (even + odd) numbers. It turns out that, contrary to intuition, it can be mathematically demonstrated that those two sets are of exactly the same size. Not merely both infinite, but of the same magnitude of infinity.

There are, however, larger magnitudes of infinity. The set of all real numbers is provably larger than those other two I just mentioned, even though they are all infinite.

(The method of proof in these cases is actually not that hard to grasp, but it’s unintuitive. If you can line up the two sets in a one-to-one correspondence, then they are the same size. If you can’t, they aren’t. The set of positive integers can be lined up against the set of positive even integers by doubling each one – 1 lines up with 2, 2 with 4, 3 with 6, and that can be continued forever – so they are the same size. On the other hand, it is impossible to do that with the set of positive integers and the set of positive reals.)

Since you just said that the points on the two line segments you’re comparing can be placed into one-to-one correspondence, you have demonstrated that the infinity of points in each line is of the same magnitude even though the lines are of different lengths.

Usagi

 

[Usagi]

I thought gravity means that the acceleration of objects is always the same? BTW, the object of this thread was whether gravity can be proven to be a real thing…

Some of us are very confused as to what the object of this thread actually is.

When you say “gravity,” what do you mean there? Obviously, you are not asking us to prove that things are attracted to the earth, since that is demonstrably true. What are you trying to prove or disprove?

The acceleration due to gravity on Earth is fairly constant and is usually given as a little over 9.8 meters per second per second (called one gravity or one g). Even that varies slightly given that the Earth is not a perfect sphere. But that number is just what you get when you do the calculation for Earth. The acceleration due to gravity on the Moon is about a sixth of that, around 1.6 meters per second per second.

So, um, what are you asking?

Usagi

 

[thinkandmull]

We got sidetracked by the infinite stuff. To my mind, I’ve always naturally what the ancients probably held, that weight/heaviness is a natural inherent attribute of almost all natural things. Then the modern doctrine of gravity came about. I just want to know if the evidence for gravity is most definitely proven. Thanks

 

[Tomdstone]

If the line is longer, there are more points. Where does my reasoning go wrong?

Consider the function y = 5x/3 which is a bijective (1-1 onto) map that takes the closed interval [0,3] onto the closed interval [0.5]. The interval [0,3] has length 3. The interval [0,5] has length 5. The function given 5x/3 pairs each point on [0,3] to a corresponding point on [0,5]. Similarly the inverse function 3x/5 does the reverse. There are exactly as many points on [0,3] as there are on [0,5]. This is covered in many high school math courses.

 

[thinkandmull]

Consider the function y = 5x/3 which is a bijective (1-1 onto) map that takes the closed interval [0,3] onto the closed interval [0.5]. The interval [0,3] has length 3. The interval [0,5] has length 5. The function given 5x/3 pairs each point on [0,3] to a corresponding point on [0,5]. Similarly the inverse function 3x/5 does the reverse. There are exactly as many points on [0,3] as there are on [0,5]. This is covered in many high school math courses.

I know, but by another reasoning, there must be more points if you add a segment to another segment. Are there not points on the second segment? Infinities don’t make sense to our reason

 

[Tomdstone]

I know, but by another reasoning, there must be more points if you add a segment to another segment. Are there not points on the second segment? Infinities don’t make sense to our reason

Special care must be taken with the infinitely large and with the infinitely small. This is spelled out in various math courses.

 

[thinkandmull]

In math courses they try to make sense of it, but from another side they don’t make sense, as with the other infinity paradoxes I spelled out earlier

 

[Usagi]

We got sidetracked by the infinite stuff. To my mind, I’ve always naturally what the ancients probably held, that weight/heaviness is a natural inherent attribute of almost all natural things. Then the modern doctrine of gravity came about. I just want to know if the evidence for gravity is most definitely proven. Thanks

Can you give more detail on what would be the difference between your/the ancient belief and what you consider the “modern doctrine of gravity”? I’m afraid I am still not completely understanding.

Usagi

 

[ThinkingSapien]

I thought gravity means that the acceleration of objects is always the same?

If by “same” you mean “constant” than no. It decreases with the square of the distance between two bodies and increases with the product of the masses of two bodies.

BTW, the object of this thread was whether gravity can be proven to be a real thing…

It’s been consistent. The transport of probes and satellites from our earth to the other bodies in the solar system are all dependent on calculations for transferring bodies from being under the primary gravitational influence of one body to another.

Portions of Newtons experiments on gravity can be repeated here on earth if your are deeply interested.

 

[Cone]

I thought gravity means that the acceleration of objects is always the same? BTW, the object of this thread was whether gravity can be proven to be a real thing…

It’s always the same on earth. It’s much less on the moon, because the moon is smaller. If you doubt gravity is real, trying jumping off your roof. You’ll be reminded.

 

[thinkandmull]

If by “same” you mean “constant” than no. It decreases with the square of the distance between two bodies and increases with the product of the masses of two bodies.

It’s been consistent. The transport of probes and satellites from our earth to the other bodies in the solar system are all dependent on calculations for transferring bodies from being under the primary gravitational influence of one body to another.

Portions of Newtons experiments on gravity can be repeated here on earth if your are deeply interested.

I am deeply interested in learning about the experimental proofs for gravity. I believe at least in the Garden of Eden heaviness was an essential quality of things, not a force added to it. Maybe the universe went haywire after the fall

As for the infinity stuff, if there is a one to one correspondence between odd and even plus odd, the same reasoning would say that there is a one to one correspondence between 3 to infinity and all even plus odd numbers. And yet if you add the number one, the odd would be the greater infinity, for how else could you have a greater infinity than if you added something to it? So I have to modify my position. There is a one to one correspondence between all the odd and odd numbers, not odd to even plus odd. I think I have finally seen a light on the infinity paradox’s I listed. Maybe that which our mind can’t grasp is the less than one space dimensions, two of which equal one area of space.

 

[Tomdstone]

As for the infinity stuff, if there is a one to one correspondence between odd and even plus odd, the same reasoning would say that there is a one to one correspondence between 3 to infinity and all even plus odd numbers. And yet if you add the number one, the odd would be the greater infinity, for how else could you have a greater infinity than if you added something to it? So I have to modify my position. There is a one to one correspondence between all the odd and odd numbers, not odd to even plus odd. I think I have finally seen a light on the infinity paradox’s I listed. Maybe that which our mind can’t grasp is the less than one space dimensions, two of which equal one area of space.

The infinity of the natural numbers: {1,2,3,4,…} is less than the infinity of a real line interval [0.1]. This is what is meant when someone says that the cardinality of the natural numbers is less than the cardinality of the real numbers. There is a question as to whether or not there exists a set whose cardinality is is strictly between that of the integers and the real numbers.
However, there is a mathematician who claims that this problem can be solved in the multiverse.

 

[ThinkingSapien]

I am deeply interested in learning about the experimental proofs for gravity.

You might want to check out a publication by Newton titled “Philosophiæ Naturalis Principia Mathematica” ( Mathematical Principles of Natural Philosophy ).

I believe at least in the Garden of Eden heaviness was an essential quality of things, not a force added to it. Maybe the universe went haywire after the fall

Are you using “heaviness” to mean something other than “weight”?

 

[thinkandmull]

The infinity of the natural numbers: {1,2,3,4,…} is less than the infinity of a real line interval [0.1]. This is what is meant when someone says that the cardinality of the natural numbers is less than the cardinality of the real numbers. There is a question as to whether or not there exists a set whose cardinality is is strictly between that of the integers and the real numbers.
However, there is a mathematician who claims that this problem can be solved in the multiverse.

What do you mean in the last sentence??

As for the topic of this thread, drop a book… I remember being a kid and thinking it was so weird to say something pulled or pushed it, instead of believing it fell because weight was naturally inside it due to mass. Can’t things fall merely because nothing holds them up? If the doctrine of gravity is true, there is something weirdly unnatural about this world, maybe caused by sin

 

[Tomdstone]

If the doctrine of gravity is true, there is something weirdly unnatural about this world, maybe caused by sin

I doubt that gravity was caused by the sin of Adam and Eve.

 

[magnet]

I am glad that gravity kept everything in the Garden of Eden firmly held to the ground. Otherwise the creation of Eve from Adam’s rib would have resulted in the two creatures just floating off into space. If there was no gravity, even they would not have the ability to create Abel and Cain.

 

[thinkandmull]

You guys can’t use your imaginations to think of a world in which things fall because they are naturally heavy??

I believe that the entire universe completely changed after the fall, that the world was probably even flat before it

 

[magnet]

You guys can’t use your imaginations to think of a world in which things fall because they are naturally heavy??

I believe that the entire universe completely changed after the fall, that the world was probably even flat before it

Is anything unnaturally heavy?

 

[thinkandmull]

You don’t even believe in heavy! You think its an external force, not a quality like extension is a quality of mass

 

[Tomdstone]

I believe that the entire universe completely changed after the fall, that the world was probably even flat before it

Interesting. So the earth was flat before Adam and Eve committed sin, but after they sinned, the earth became spherical shaped?