THERE IS NO NEED FOR THE CONCEPT OF VOLUME IN HEAVEN
On July 13, 2017 my wife and I were driving up to the SE Denver area for our sons/soon-to-be daughter-in-laws wedding. We pulled over to a rest stop in the pan handle of Texas where I read a historic sign inside that said something like this:
You know those circles you see on the ground when you look out an airplane window...well, those are NOT UFO's...they are farmers fields being irrigated from a well in the center of the circle with a radius arm of a quarter mile long irrigation pipe....you can place four of these circular irrigation fields inside a square mile but there is over 20% wasted space.
As soon as I read that I had to figure out if they were right as I continued driving. I am very good at mathematics in my head so I figured out the correct answer to be about 21.5% waste.
As a mathematician I could not stop myself from expanding upon the problem so then I went to 3 dimensions and ask the question, "How much wasted space would be outside four spheres (with a quarter mile radius) placed in a cubic mile and estimated it to be over 70%!
When my wife took over driving I used my cell phone calculator to check my work finding the spheres wasted space to be 74%. Now my curiosity was getting the best of me so I had to continue into 4, 5, 6, & 7 dimensional spheres in equal dimensional cubes. To my surprise as the dimensions of the spheres went up the volume quickly approached zero so the waste quickly climbed to 100%! Then I tried a pi dimensional sphere and the results proved that the volume falls exponential with rise in dimension, as a pi dimensional sphere was closer to the 4-D spheres in wasted space than the 3-D spheres.
This is when I had the revelation that in heaven there is no need for our concept of volume!
Possible Bible Verses to reflect on:
1). Jesus has the ability to appear easily in the 3-D world where ever He wishes. Here are two in which the doors were locked.
John 20:19 On the evening of that firstday of the week, when the disciples were together, with the doors locked for fear of the Jewish leaders. Jesus came and stood among them and said, "Peace be with you!"
John 20:26 A week later his disciples were in the house again, and Thomas was with them. Though the doors were locked, Jesus came and stood among them and said, "Peace be with you" 27 Then he said to Thomas, "Put your finger here' see my hands. Reach out your hand and put it into my side. Stop doubting and believe."
2). And how about the walking on water and the boat and its occupants immediately reaching the shore where they were heading?
John 6: 19-21 When they had rowed about three or four miles, they saw Jesus approaching the boat, walking on the water, and they were frightened. But he said to them,It is I; don't be afraid." Then they were willing to take him into the boat, and immediately the boat reached the shore where they were heading.
3). And when Jesus had His conversation with Nicodemus
John 3:12 I have spoken to you of earthly things and you do not believe; how then will you believe if I speak of heavenly things?
Here is math"
Summary of the Volume Relationships by Dimension
Dimension Volume Formula Volume of N-Dimensional Sphere Wasted Space in N-Dimensional Cube
four N-Dim Spheres with radius 0.25 miles with four N-DIM Spheres placed in
all sides of Cube equal 1 mile
2 π R ^2 78.5398% full 21.4602% empty space
3 (4/3)πR^3 26.1799% full 73.8201% empty space
4 (1/2){π^2}R^4 7.7106% full 92.2894% empty space
5 (8/15){π^2}R^5 2.0562% full 97.9438% empty space
6 (1/6{)π^3)R^6 0.5047% full 99.4953% empty space
7 (16/105)(π^3)R^7 0.1154% full 99.8846% empty space
To continue onto up to 10-dimensional spheres goto the website https://en.wikipedia.org/wiki/Volume_of_an_n-ball
or just click here and scroll down to the table. If you scroll a little beyond the 10-dimensional table, you'll see the high dimensional formula below which I used to calculate the PI dimensional sphere.
And what about the pi dimensional spheres? Use the formula
Dimension Volume Formula Volume of N-Dimensional Sphere Wasted Space in N-Dimensional Cube
four N-Dim Spheres with radius 0.25 miles with four N-DIM Spheres placed in
all sides of Cube equal 1 mile
PI (1/square root of (N*PI))*(2*PI*e/N)^ TRUNCATE(N/2)*R^N
so in this case (1/PI)*(2e)*(.25)^PI 8.8881% full 91.1119% empty space
So Volume has an exponential inverse relation: As the dimensions increase the volume decreases exponentially!
Thus no need for Volume in Heaven.
You know those circles you see on the ground when you look out an airplane window...well, those are NOT UFO's...they are farmers fields being irrigated from a well in the center of the circle with a radius arm of a quarter mile long irrigation pipe....you can place four of these circular irrigation fields inside a square mile but there is over 20% wasted space.
As soon as I read that I had to figure out if they were right as I continued driving. I am very good at mathematics in my head so I figured out the correct answer to be about 21.5% waste.
As a mathematician I could not stop myself from expanding upon the problem so then I went to 3 dimensions and ask the question, "How much wasted space would be outside four spheres (with a quarter mile radius) placed in a cubic mile and estimated it to be over 70%!
When my wife took over driving I used my cell phone calculator to check my work finding the spheres wasted space to be 74%. Now my curiosity was getting the best of me so I had to continue into 4, 5, 6, & 7 dimensional spheres in equal dimensional cubes. To my surprise as the dimensions of the spheres went up the volume quickly approached zero so the waste quickly climbed to 100%! Then I tried a pi dimensional sphere and the results proved that the volume falls exponential with rise in dimension, as a pi dimensional sphere was closer to the 4-D spheres in wasted space than the 3-D spheres.
This is when I had the revelation that in heaven there is no need for our concept of volume!
Possible Bible Verses to reflect on:
1). Jesus has the ability to appear easily in the 3-D world where ever He wishes. Here are two in which the doors were locked.
John 20:19 On the evening of that firstday of the week, when the disciples were together, with the doors locked for fear of the Jewish leaders. Jesus came and stood among them and said, "Peace be with you!"
John 20:26 A week later his disciples were in the house again, and Thomas was with them. Though the doors were locked, Jesus came and stood among them and said, "Peace be with you" 27 Then he said to Thomas, "Put your finger here' see my hands. Reach out your hand and put it into my side. Stop doubting and believe."
2). And how about the walking on water and the boat and its occupants immediately reaching the shore where they were heading?
John 6: 19-21 When they had rowed about three or four miles, they saw Jesus approaching the boat, walking on the water, and they were frightened. But he said to them,It is I; don't be afraid." Then they were willing to take him into the boat, and immediately the boat reached the shore where they were heading.
3). And when Jesus had His conversation with Nicodemus
John 3:12 I have spoken to you of earthly things and you do not believe; how then will you believe if I speak of heavenly things?
Here is math"
Summary of the Volume Relationships by Dimension
Dimension Volume Formula Volume of N-Dimensional Sphere Wasted Space in N-Dimensional Cube
four N-Dim Spheres with radius 0.25 miles with four N-DIM Spheres placed in
all sides of Cube equal 1 mile
2 π R ^2 78.5398% full 21.4602% empty space
3 (4/3)πR^3 26.1799% full 73.8201% empty space
4 (1/2){π^2}R^4 7.7106% full 92.2894% empty space
5 (8/15){π^2}R^5 2.0562% full 97.9438% empty space
6 (1/6{)π^3)R^6 0.5047% full 99.4953% empty space
7 (16/105)(π^3)R^7 0.1154% full 99.8846% empty space
To continue onto up to 10-dimensional spheres goto the website https://en.wikipedia.org/wiki/Volume_of_an_n-ball
or just click here and scroll down to the table. If you scroll a little beyond the 10-dimensional table, you'll see the high dimensional formula below which I used to calculate the PI dimensional sphere.
And what about the pi dimensional spheres? Use the formula
Dimension Volume Formula Volume of N-Dimensional Sphere Wasted Space in N-Dimensional Cube
four N-Dim Spheres with radius 0.25 miles with four N-DIM Spheres placed in
all sides of Cube equal 1 mile
PI (1/square root of (N*PI))*(2*PI*e/N)^ TRUNCATE(N/2)*R^N
so in this case (1/PI)*(2e)*(.25)^PI 8.8881% full 91.1119% empty space
So Volume has an exponential inverse relation: As the dimensions increase the volume decreases exponentially!
Thus no need for Volume in Heaven.