Oscillating Infinity (Revised)

[Strange]

Also, the reason light cannot escape a black hole has nothing to do with its velocity. It is about the curvature of space-time. 

[AbnormallyHonest]

11 hours ago, Mordred said:

The light escaping a BH isn't a recessive velocity. A recessive velocity maps a commoving volume ie changes in radius (expansion) The FLRW is a commoving coordinate metric. 

A BH the radius is static and the coordinate Scwartzchild metric is also static. In this case we are dealing with gravitational redshift as per the event horizon escape velocity. Where as commoving coordinates involve cosmological redshift.

Observers do affect both but in a different manner one is a change in volume while the a variation in density distribution.

 

the stretching of space away from the observation, as viewed through only one dimension is always going to be recessive. It doesn't make sense to account for that recession to be calculated by volume unless the light traversed the space to the viewer in an indirect path through it. (This is pertaining to light emitted from the source if the singularity, not light fallin at an angle) In both cases the light originates from a point that is infinitely recessing away from the viewer with greater velocity with respect to the distance away from the perception. Any lateral differences from being stretched inward or outward would be irrelevant in a one dimensional view.

Also, as a singularity, is it not theorized that space "curves" infinitely? Wouldn't that also be a change in volume? Also, in a finite amount of anything (such as space) wouldn't a change in volume also be directly related to density? As our view of local space seems to have have a different rate and amount of this expanded volume... does that not also effect the distribution of the density as well?

[Mordred]

spacetime curvature is a relationship involving time dependancy and mass density. It doesn't alter the radius of the volume, you need to be careful between differences in coirdinate length via ct and proper length. Remember tge light path can change without a change in volume.

Edited July 27, 2017 by Mordred

[Strange]

On 02/07/2017 at 9:49 AM, AbnormallyHonest said:

The problem with the hotel anology is the same thing as saying in 2 dimensional space area is infinite, but adding a 3rd dimension creates infinite volume. Neither is less infinite but volume represents exponentially more points in space.

1. The hotel analogy (actually, I'm not sure this is an analogy; it is more a thought experiment in mathematics) has nothing to do with two versus three dimensions.

2. The order of infinity of a 2D surface or a correspond 3D volume is the same; it entirely depends on whether you use real numbers or integers to define the points within that area or volume. (There being infinitely more real points than integral points.)

3. A volume does not contain "exponentially" more points than an area.

It is almost as if you don't know what you are talking about.

On 02/07/2017 at 9:49 AM, AbnormallyHonest said:

The hotel paradox is like reducing infinite volume to only infinite area and then adding a finite z value to increase that infinity incrementally, but that is not observant of the potentially infinite volume you must dismiss in order to accommodate a reduced dimensional reasoning (or reduced potential by assuming infinite is contained on one end in a linear expression of it... to say it has a finite begininning, or can only have differing values in one direction).

That is pretty incomprehensible but I am certain that it has nothing to do with the Hilbert Hotel. 

A better analogy is the natural number line.

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In a hotel with an infinite number of rooms, there is no "first" room, because the first room is exactly as far away from infinity as the very last room is, meaning there is no start and no end... it is infinite.

This is obviously nonsense. If we take the obvious mapping from the hotel rooms to the set of natural numbers, we can see that there is a first number (that is: 1) and there are an infinite number of integers following that. So an infinite series can have a beginning and no end.

Similarly, there is a Room 1 (next to the reception desk) and an infinite number of rooms after that.

It is almost as if you don't know what infinity means.

[AbnormallyHonest]

On 7/27/2017 at 5:21 PM, Strange said:

1. The hotel analogy (actually, I'm not sure this is an analogy; it is more a thought experiment in mathematics) has nothing to do with two versus three dimensions.

2. The order of infinity of a 2D surface or a correspond 3D volume is the same; it entirely depends on whether you use real numbers or integers to define the points within that area or volume. (There being infinitely more real points than integral points.)

3. A volume does not contain "exponentially" more points than an area.

It is almost as if you don't know what you are talking about.

Exponential: Relating to a mathematical expression containing one or more exponents. ◇ Something is said to increase or decrease exponentially if its rate of change must be expressed using exponents. A graph of such a rate would appear not as a straight line, but as a curve that continually becomes steeper or shallower.

Well apparently your command of the English language may not be as well versed as your mathematics... or perhaps its the other way around?

On 7/27/2017 at 5:21 PM, Strange said:

That is pretty incomprehensible but I am certain that it has nothing to do with the Hilbert Hotel. 

A better analogy is the natural number line.

Well, honestly it would be similar to saying there are an infinite number of rooms on the 1st floor, but there are an infinite number of floors with an infinite number of rooms. So instead placing people on the next floor, you move an infinite number of people down one room and just continue to fill in the first floor. You have to disregard not only the infinite number of floors, but also the infinite number of rooms on each floor in order to justify that diminished dimensional understanding of infinity.

On 7/27/2017 at 5:21 PM, Strange said:

A better analogy is the natural number line.

This is obviously nonsense. If we take the obvious mapping from the hotel rooms to the set of natural numbers, we can see that there is a first number (that is: 1) and there are an infinite number of integers following that. So an infinite series can have a beginning and no end.

Similarly, there is a Room 1 (next to the reception desk) and an infinite number of rooms after that.

It is almost as if you don't know what infinity means.

To say there is a first room? Infinity is every possible value. To limit yourself to one "set" of numbers is really just a metric expansion because those values will inherently adopt the smallest possible increment that can be achieved, because infinite is infinite. The separation of the values in any "set" of infinity is just as infinitely narrow as any other "set" of infinity. Your're just applying a transformation to the value system in order to create the idea that it is a "set". It's almost as if you don't understand infinity.

[Strange]

16 minutes ago, AbnormallyHonest said:

Well apparently your command of the English language may not be as well versed as your mathematics... or perhaps its the other way around?

So the volume would be exponentially related to area if it went something like 3^r rather than r³. (Which is what the sentence you quoted said.)

17 minutes ago, AbnormallyHonest said:

Well, honestly it would be similar to saying there are an infinite number of rooms on the 1st floor, but there are an infinite number of floors with an infinite number of rooms. So instead placing people on the next floor, you move an infinite number of people down one room and just continue to fill in the first floor. You have to disregard not only the infinite number of floors, but also the infinite number of rooms on each floor in order to justify that diminished dimensional understanding of infinity.

Still doesn't make any sense.

If there are an infinite number of rooms on each floor, then you can accommodate a new guest by asking everyone on the first floor to move along one.

You could accommodate an infinite number of guests by asking everyone on each floor to move up to the next floor.

But I have no idea what point you are trying to make.

19 minutes ago, AbnormallyHonest said:

 Infinity is every possible value.

No it isn't. And I have no idea what the rest of that paragraph means.

[AbnormallyHonest]

1 hour ago, Strange said:

So the volume would be exponentially related to area if it went something like 3^r rather than r³. (Which is what the sentence you quoted said.)

The caret (^) symbolizes that the following number is superscript.

1 hour ago, Strange said:

If there are an infinite number of rooms on each floor, then you can accommodate a new guest by asking everyone on the first floor to move along one.

You could accommodate an infinite number of guests by asking everyone on each floor to move up to the next floor.

But I have no idea what point you are trying to make.

Yes, you do. Thank you.

1 hour ago, Strange said:

No it isn't. And I have no idea what the rest of that paragraph means.

Which has more, if I count to infinity in evens, or in 5's? What has more value, 2/infinity or 5/infinity? It doesn't matter which numbers you use, if you're rationalizing it's value to infinity, the separation of the values is always the same, you're just changing the labels.

[Strange]

1 hour ago, AbnormallyHonest said:

Which has more, if I count to infinity in evens, or in 5's?

You can't count to infinity.

But the ordinality of both sets is the same.

Quote

What has more value, 2/infinity or 5/infinity? 

Neither has any value.

Quote

It doesn't matter which numbers you use, if you're rationalizing it's value to infinity, the separation of the values is always the same, you're just changing the labels.

That doesn't seem to mean anything. Do I need to make allowances for your first language not being English?

1 hour ago, AbnormallyHonest said:

The caret (^) symbolizes that the following number is superscript

So what? It is clear you don't know the difference between a polynomial and an exponential function.