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Would you drown in a bottomless ball pit?
The 2019 Stack Overflow Developer Survey Results Are InHow would you interpret this question focusing on problem solving?Finding an circle inside distribution of elemetsHow do you find what angle you would have to turn to be facing an object at a certain pointHow would you prove this question?Is the heat ball really a ball?If circle made out of a completely flexible material were draped over a sphere, what would happen?What will the volume of the ball bearing be?Why do volume and surface area of unit ball in $mathbbR^d$ behave the way they do for $d uparrow$?Shortest path that avoids a ballexisting name for name for a “castable” 3d object?
$begingroup$
Imagine a bottomless ball pit, just to clarify, it means a bottomless pit filled with uniform hollow balls. From "experimentation" I know that there is still airflow at the bottom of a 0.5 meter tall ball pit. I assume that this is because air can still flow in the gaps between the balls.
But in a bottomless pit, can there be a situation where there will be no available pass for air to reach a certain depth.
Also, related, can there be a case of not total lack of air, but reduced air flow to the point of not allowing human life at a certain depth (not enough new oxygen will come to replace the CO2 released by the human).
So in other words, in a bottomless pit filled with uniform spheres, is there a depth where all routes for the air to reach will be cut off?
If not, assuming that at a certain depth $h$ there is $f$ air-flow, is there a depth where the available airflow will be $f_0 << f$?
(Not sure how to mathematically properly define "airflow").
The standard ball size is (according to Wikipedia) is
no larger than 3 inches (7.6 cm) in diameter
geometry spheres
asked Mar 30 at 17:55
SIMELSIMEL
372317
$endgroup$
add a comment |
$begingroup$
Imagine a bottomless ball pit, just to clarify, it means a bottomless pit filled with uniform hollow balls. From "experimentation" I know that there is still airflow at the bottom of a 0.5 meter tall ball pit. I assume that this is because air can still flow in the gaps between the balls.
But in a bottomless pit, can there be a situation where there will be no available pass for air to reach a certain depth.
Also, related, can there be a case of not total lack of air, but reduced air flow to the point of not allowing human life at a certain depth (not enough new oxygen will come to replace the CO2 released by the human).
So in other words, in a bottomless pit filled with uniform spheres, is there a depth where all routes for the air to reach will be cut off?
If not, assuming that at a certain depth $h$ there is $f$ air-flow, is there a depth where the available airflow will be $f_0 << f$?
(Not sure how to mathematically properly define "airflow").
The standard ball size is (according to Wikipedia) is
no larger than 3 inches (7.6 cm) in diameter
geometry spheres
asked Mar 30 at 17:55
SIMELSIMEL
372317
$endgroup$
$begingroup$
I would say that this is a physics problem and not a math problem. I would guess that even though air could flow, circulation would be low, and you would be re-breathing the same air, and yes you would eventually suffocate.
$endgroup$
– Doug M
Mar 30 at 18:11
$begingroup$
@DougM, I also wasn't sure about where to post the question. But I want to disregard the issue of circulation, by "airflow" I mean that if there is $a$ "empty" area at a certain level, and that it's connected to at least $a$ empty area above it, that it's $a$ "airflow", or that $a$ surface area of air reaches this depth from the top. I really have trouble with formulation this notion.
$endgroup$
– SIMEL
Mar 30 at 18:16
$begingroup$
This is not a mathematics problem.
$endgroup$
– copper.hat
Mar 30 at 18:53
add a comment |
$begingroup$
Imagine a bottomless ball pit, just to clarify, it means a bottomless pit filled with uniform hollow balls. From "experimentation" I know that there is still airflow at the bottom of a 0.5 meter tall ball pit. I assume that this is because air can still flow in the gaps between the balls.
But in a bottomless pit, can there be a situation where there will be no available pass for air to reach a certain depth.
Also, related, can there be a case of not total lack of air, but reduced air flow to the point of not allowing human life at a certain depth (not enough new oxygen will come to replace the CO2 released by the human).
So in other words, in a bottomless pit filled with uniform spheres, is there a depth where all routes for the air to reach will be cut off?
If not, assuming that at a certain depth $h$ there is $f$ air-flow, is there a depth where the available airflow will be $f_0 << f$?
(Not sure how to mathematically properly define "airflow").
The standard ball size is (according to Wikipedia) is
no larger than 3 inches (7.6 cm) in diameter
geometry spheres
asked Mar 30 at 17:55
SIMELSIMEL
372317
$endgroup$
Imagine a bottomless ball pit, just to clarify, it means a bottomless pit filled with uniform hollow balls. From "experimentation" I know that there is still airflow at the bottom of a 0.5 meter tall ball pit. I assume that this is because air can still flow in the gaps between the balls.
But in a bottomless pit, can there be a situation where there will be no available pass for air to reach a certain depth.
Also, related, can there be a case of not total lack of air, but reduced air flow to the point of not allowing human life at a certain depth (not enough new oxygen will come to replace the CO2 released by the human).
So in other words, in a bottomless pit filled with uniform spheres, is there a depth where all routes for the air to reach will be cut off?
If not, assuming that at a certain depth $h$ there is $f$ air-flow, is there a depth where the available airflow will be $f_0 << f$?
(Not sure how to mathematically properly define "airflow").
The standard ball size is (according to Wikipedia) is
no larger than 3 inches (7.6 cm) in diameter
geometry spheres
geometry spheres
asked Mar 30 at 17:55
SIMELSIMEL
372317
asked Mar 30 at 17:55
SIMELSIMEL
372317
asked Mar 30 at 17:55
SIMELSIMEL
372317
asked Mar 30 at 17:55
SIMELSIMEL
372317
asked Mar 30 at 17:55
SIMELSIMEL
372317
372317
$begingroup$
I would say that this is a physics problem and not a math problem. I would guess that even though air could flow, circulation would be low, and you would be re-breathing the same air, and yes you would eventually suffocate.
$endgroup$
– Doug M
Mar 30 at 18:11
$begingroup$
@DougM, I also wasn't sure about where to post the question. But I want to disregard the issue of circulation, by "airflow" I mean that if there is $a$ "empty" area at a certain level, and that it's connected to at least $a$ empty area above it, that it's $a$ "airflow", or that $a$ surface area of air reaches this depth from the top. I really have trouble with formulation this notion.
$endgroup$
– SIMEL
Mar 30 at 18:16
$begingroup$
This is not a mathematics problem.
$endgroup$
– copper.hat
Mar 30 at 18:53
add a comment |
$begingroup$
I would say that this is a physics problem and not a math problem. I would guess that even though air could flow, circulation would be low, and you would be re-breathing the same air, and yes you would eventually suffocate.
$endgroup$
– Doug M
Mar 30 at 18:11
$begingroup$
@DougM, I also wasn't sure about where to post the question. But I want to disregard the issue of circulation, by "airflow" I mean that if there is $a$ "empty" area at a certain level, and that it's connected to at least $a$ empty area above it, that it's $a$ "airflow", or that $a$ surface area of air reaches this depth from the top. I really have trouble with formulation this notion.
$endgroup$
– SIMEL
Mar 30 at 18:16
$begingroup$
This is not a mathematics problem.
$endgroup$
– copper.hat
Mar 30 at 18:53
$begingroup$
I would say that this is a physics problem and not a math problem. I would guess that even though air could flow, circulation would be low, and you would be re-breathing the same air, and yes you would eventually suffocate.
$endgroup$
– Doug M
Mar 30 at 18:11
$begingroup$
I would say that this is a physics problem and not a math problem. I would guess that even though air could flow, circulation would be low, and you would be re-breathing the same air, and yes you would eventually suffocate.
$endgroup$
– Doug M
Mar 30 at 18:11
$begingroup$
@DougM, I also wasn't sure about where to post the question. But I want to disregard the issue of circulation, by "airflow" I mean that if there is $a$ "empty" area at a certain level, and that it's connected to at least $a$ empty area above it, that it's $a$ "airflow", or that $a$ surface area of air reaches this depth from the top. I really have trouble with formulation this notion.
$endgroup$
– SIMEL
Mar 30 at 18:16
$begingroup$
@DougM, I also wasn't sure about where to post the question. But I want to disregard the issue of circulation, by "airflow" I mean that if there is $a$ "empty" area at a certain level, and that it's connected to at least $a$ empty area above it, that it's $a$ "airflow", or that $a$ surface area of air reaches this depth from the top. I really have trouble with formulation this notion.
$endgroup$
– SIMEL
Mar 30 at 18:16
$begingroup$
This is not a mathematics problem.
$endgroup$
– copper.hat
Mar 30 at 18:53
$begingroup$
This is not a mathematics problem.
$endgroup$
– copper.hat
Mar 30 at 18:53
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Since the kissing number of spheres is 12, and spheres can only touch at a point, I'd say that there always exists a path for the air to take, no matter the depth, i.e. a packing of sphere's won't be airtight.
In terms of airflow, I guess that depends on how it's defined, but I think I'd be worried about the weight in balls crushing me before I worried about running out of air.
answered Mar 30 at 18:06
Michael BiroMichael Biro
11.7k21831
$endgroup$
$begingroup$
Assume that the balls are massless and very strong, they don't apply pressure on the body and will not crush me, nor do they deform or change shape. Also, disregard hunger or other problems, only the amount of empty "caverns" reaching the top.
$endgroup$
– SIMEL
Mar 30 at 18:24
$begingroup$
@SIMEL Then yes, you can always trace out a path for air to take from the surface to you.
$endgroup$
– Michael Biro
Mar 30 at 18:27
add a comment |
$begingroup$
If you assume that there even can be air within the pit this means it is contained in an atmosphere with oxygen. Any such atmosphere, it seems reasonable, has finite volume (I guess I'm assuming it doesn't cross between atmospheres...). Then if the balls are constant size you have an immediate contradiction to the supposition. Else you're assuming you can change the size of the balls and now I think you can design a fractal to block any flow.
answered Mar 30 at 18:13
MariahMariah
2,1471718
$endgroup$
$begingroup$
I have an endless amount of oxygen for this experiment and an infinite atmosphere. This is a question about the empty spaces between the balls and less about what fills them. You can't change the size of the balls, they are all uniform in size. But if you have a solution with a smaller size of ball, it is ok, as long as there is "safe" depth where you can breath under a finite depth of the balls, meaning, the answer "if you make the balls the size of water molecule you'll drown is not good, because there is safe depth with water".
$endgroup$
– SIMEL
Mar 30 at 18:19
$begingroup$
@SIMEL ok.. just take a size small enough so that the space between four touching spheres is smaller than an oxygen molecule - then grid this.
$endgroup$
– Mariah
Mar 30 at 18:38
$begingroup$
yeah, this is taking the size of a water molecule, but the problem with this is that there is no safe depth with it, I want there to be a safe depth where I can still breath, which doesn't happen with water, and see if with depth the area of empty passages leading to the surface reduces.
$endgroup$
– SIMEL
Mar 30 at 19:07
$begingroup$
@SIMEL why don't you just add balls in each "layer" until we reach this critical size?
$endgroup$
– Mariah
Mar 30 at 19:40
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Since the kissing number of spheres is 12, and spheres can only touch at a point, I'd say that there always exists a path for the air to take, no matter the depth, i.e. a packing of sphere's won't be airtight.
In terms of airflow, I guess that depends on how it's defined, but I think I'd be worried about the weight in balls crushing me before I worried about running out of air.
answered Mar 30 at 18:06
Michael BiroMichael Biro
11.7k21831
$endgroup$
$begingroup$
Assume that the balls are massless and very strong, they don't apply pressure on the body and will not crush me, nor do they deform or change shape. Also, disregard hunger or other problems, only the amount of empty "caverns" reaching the top.
$endgroup$
– SIMEL
Mar 30 at 18:24
$begingroup$
@SIMEL Then yes, you can always trace out a path for air to take from the surface to you.
$endgroup$
– Michael Biro
Mar 30 at 18:27
add a comment |
$begingroup$
Since the kissing number of spheres is 12, and spheres can only touch at a point, I'd say that there always exists a path for the air to take, no matter the depth, i.e. a packing of sphere's won't be airtight.
In terms of airflow, I guess that depends on how it's defined, but I think I'd be worried about the weight in balls crushing me before I worried about running out of air.
answered Mar 30 at 18:06
Michael BiroMichael Biro
11.7k21831
$endgroup$
$begingroup$
Assume that the balls are massless and very strong, they don't apply pressure on the body and will not crush me, nor do they deform or change shape. Also, disregard hunger or other problems, only the amount of empty "caverns" reaching the top.
$endgroup$
– SIMEL
Mar 30 at 18:24
$begingroup$
@SIMEL Then yes, you can always trace out a path for air to take from the surface to you.
$endgroup$
– Michael Biro
Mar 30 at 18:27
add a comment |
$begingroup$
Since the kissing number of spheres is 12, and spheres can only touch at a point, I'd say that there always exists a path for the air to take, no matter the depth, i.e. a packing of sphere's won't be airtight.
In terms of airflow, I guess that depends on how it's defined, but I think I'd be worried about the weight in balls crushing me before I worried about running out of air.
answered Mar 30 at 18:06
Michael BiroMichael Biro
11.7k21831
$endgroup$
Since the kissing number of spheres is 12, and spheres can only touch at a point, I'd say that there always exists a path for the air to take, no matter the depth, i.e. a packing of sphere's won't be airtight.
In terms of airflow, I guess that depends on how it's defined, but I think I'd be worried about the weight in balls crushing me before I worried about running out of air.
answered Mar 30 at 18:06
Michael BiroMichael Biro
11.7k21831
answered Mar 30 at 18:06
Michael BiroMichael Biro
11.7k21831
answered Mar 30 at 18:06
Michael BiroMichael Biro
11.7k21831
answered Mar 30 at 18:06
Michael BiroMichael Biro
11.7k21831
11.7k21831
$begingroup$
Assume that the balls are massless and very strong, they don't apply pressure on the body and will not crush me, nor do they deform or change shape. Also, disregard hunger or other problems, only the amount of empty "caverns" reaching the top.
$endgroup$
– SIMEL
Mar 30 at 18:24
$begingroup$
@SIMEL Then yes, you can always trace out a path for air to take from the surface to you.
$endgroup$
– Michael Biro
Mar 30 at 18:27
add a comment |
$begingroup$
Assume that the balls are massless and very strong, they don't apply pressure on the body and will not crush me, nor do they deform or change shape. Also, disregard hunger or other problems, only the amount of empty "caverns" reaching the top.
$endgroup$
– SIMEL
Mar 30 at 18:24
$begingroup$
@SIMEL Then yes, you can always trace out a path for air to take from the surface to you.
$endgroup$
– Michael Biro
Mar 30 at 18:27
$begingroup$
Assume that the balls are massless and very strong, they don't apply pressure on the body and will not crush me, nor do they deform or change shape. Also, disregard hunger or other problems, only the amount of empty "caverns" reaching the top.
$endgroup$
– SIMEL
Mar 30 at 18:24
$begingroup$
Assume that the balls are massless and very strong, they don't apply pressure on the body and will not crush me, nor do they deform or change shape. Also, disregard hunger or other problems, only the amount of empty "caverns" reaching the top.
$endgroup$
– SIMEL
Mar 30 at 18:24
$begingroup$
@SIMEL Then yes, you can always trace out a path for air to take from the surface to you.
$endgroup$
– Michael Biro
Mar 30 at 18:27
$begingroup$
@SIMEL Then yes, you can always trace out a path for air to take from the surface to you.
$endgroup$
– Michael Biro
Mar 30 at 18:27
add a comment |
$begingroup$
If you assume that there even can be air within the pit this means it is contained in an atmosphere with oxygen. Any such atmosphere, it seems reasonable, has finite volume (I guess I'm assuming it doesn't cross between atmospheres...). Then if the balls are constant size you have an immediate contradiction to the supposition. Else you're assuming you can change the size of the balls and now I think you can design a fractal to block any flow.
answered Mar 30 at 18:13
MariahMariah
2,1471718
$endgroup$
$begingroup$
I have an endless amount of oxygen for this experiment and an infinite atmosphere. This is a question about the empty spaces between the balls and less about what fills them. You can't change the size of the balls, they are all uniform in size. But if you have a solution with a smaller size of ball, it is ok, as long as there is "safe" depth where you can breath under a finite depth of the balls, meaning, the answer "if you make the balls the size of water molecule you'll drown is not good, because there is safe depth with water".
$endgroup$
– SIMEL
Mar 30 at 18:19
$begingroup$
@SIMEL ok.. just take a size small enough so that the space between four touching spheres is smaller than an oxygen molecule - then grid this.
$endgroup$
– Mariah
Mar 30 at 18:38
$begingroup$
yeah, this is taking the size of a water molecule, but the problem with this is that there is no safe depth with it, I want there to be a safe depth where I can still breath, which doesn't happen with water, and see if with depth the area of empty passages leading to the surface reduces.
$endgroup$
– SIMEL
Mar 30 at 19:07
$begingroup$
@SIMEL why don't you just add balls in each "layer" until we reach this critical size?
$endgroup$
– Mariah
Mar 30 at 19:40
add a comment |
$begingroup$
If you assume that there even can be air within the pit this means it is contained in an atmosphere with oxygen. Any such atmosphere, it seems reasonable, has finite volume (I guess I'm assuming it doesn't cross between atmospheres...). Then if the balls are constant size you have an immediate contradiction to the supposition. Else you're assuming you can change the size of the balls and now I think you can design a fractal to block any flow.
answered Mar 30 at 18:13
MariahMariah
2,1471718
$endgroup$
$begingroup$
I have an endless amount of oxygen for this experiment and an infinite atmosphere. This is a question about the empty spaces between the balls and less about what fills them. You can't change the size of the balls, they are all uniform in size. But if you have a solution with a smaller size of ball, it is ok, as long as there is "safe" depth where you can breath under a finite depth of the balls, meaning, the answer "if you make the balls the size of water molecule you'll drown is not good, because there is safe depth with water".
$endgroup$
– SIMEL
Mar 30 at 18:19
$begingroup$
@SIMEL ok.. just take a size small enough so that the space between four touching spheres is smaller than an oxygen molecule - then grid this.
$endgroup$
– Mariah
Mar 30 at 18:38
$begingroup$
yeah, this is taking the size of a water molecule, but the problem with this is that there is no safe depth with it, I want there to be a safe depth where I can still breath, which doesn't happen with water, and see if with depth the area of empty passages leading to the surface reduces.
$endgroup$
– SIMEL
Mar 30 at 19:07
$begingroup$
@SIMEL why don't you just add balls in each "layer" until we reach this critical size?
$endgroup$
– Mariah
Mar 30 at 19:40
add a comment |
$begingroup$
If you assume that there even can be air within the pit this means it is contained in an atmosphere with oxygen. Any such atmosphere, it seems reasonable, has finite volume (I guess I'm assuming it doesn't cross between atmospheres...). Then if the balls are constant size you have an immediate contradiction to the supposition. Else you're assuming you can change the size of the balls and now I think you can design a fractal to block any flow.
answered Mar 30 at 18:13
MariahMariah
2,1471718
$endgroup$
If you assume that there even can be air within the pit this means it is contained in an atmosphere with oxygen. Any such atmosphere, it seems reasonable, has finite volume (I guess I'm assuming it doesn't cross between atmospheres...). Then if the balls are constant size you have an immediate contradiction to the supposition. Else you're assuming you can change the size of the balls and now I think you can design a fractal to block any flow.
answered Mar 30 at 18:13
MariahMariah
2,1471718
answered Mar 30 at 18:13
MariahMariah
2,1471718
answered Mar 30 at 18:13
MariahMariah
2,1471718
answered Mar 30 at 18:13
MariahMariah
2,1471718
2,1471718
$begingroup$
I have an endless amount of oxygen for this experiment and an infinite atmosphere. This is a question about the empty spaces between the balls and less about what fills them. You can't change the size of the balls, they are all uniform in size. But if you have a solution with a smaller size of ball, it is ok, as long as there is "safe" depth where you can breath under a finite depth of the balls, meaning, the answer "if you make the balls the size of water molecule you'll drown is not good, because there is safe depth with water".
$endgroup$
– SIMEL
Mar 30 at 18:19
$begingroup$
@SIMEL ok.. just take a size small enough so that the space between four touching spheres is smaller than an oxygen molecule - then grid this.
$endgroup$
– Mariah
Mar 30 at 18:38
$begingroup$
yeah, this is taking the size of a water molecule, but the problem with this is that there is no safe depth with it, I want there to be a safe depth where I can still breath, which doesn't happen with water, and see if with depth the area of empty passages leading to the surface reduces.
$endgroup$
– SIMEL
Mar 30 at 19:07
$begingroup$
@SIMEL why don't you just add balls in each "layer" until we reach this critical size?
$endgroup$
– Mariah
Mar 30 at 19:40
add a comment |
$begingroup$
I have an endless amount of oxygen for this experiment and an infinite atmosphere. This is a question about the empty spaces between the balls and less about what fills them. You can't change the size of the balls, they are all uniform in size. But if you have a solution with a smaller size of ball, it is ok, as long as there is "safe" depth where you can breath under a finite depth of the balls, meaning, the answer "if you make the balls the size of water molecule you'll drown is not good, because there is safe depth with water".
$endgroup$
– SIMEL
Mar 30 at 18:19
$begingroup$
@SIMEL ok.. just take a size small enough so that the space between four touching spheres is smaller than an oxygen molecule - then grid this.
$endgroup$
– Mariah
Mar 30 at 18:38
$begingroup$
yeah, this is taking the size of a water molecule, but the problem with this is that there is no safe depth with it, I want there to be a safe depth where I can still breath, which doesn't happen with water, and see if with depth the area of empty passages leading to the surface reduces.
$endgroup$
– SIMEL
Mar 30 at 19:07
$begingroup$
@SIMEL why don't you just add balls in each "layer" until we reach this critical size?
$endgroup$
– Mariah
Mar 30 at 19:40
$begingroup$
I have an endless amount of oxygen for this experiment and an infinite atmosphere. This is a question about the empty spaces between the balls and less about what fills them. You can't change the size of the balls, they are all uniform in size. But if you have a solution with a smaller size of ball, it is ok, as long as there is "safe" depth where you can breath under a finite depth of the balls, meaning, the answer "if you make the balls the size of water molecule you'll drown is not good, because there is safe depth with water".
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– SIMEL
Mar 30 at 18:19
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I have an endless amount of oxygen for this experiment and an infinite atmosphere. This is a question about the empty spaces between the balls and less about what fills them. You can't change the size of the balls, they are all uniform in size. But if you have a solution with a smaller size of ball, it is ok, as long as there is "safe" depth where you can breath under a finite depth of the balls, meaning, the answer "if you make the balls the size of water molecule you'll drown is not good, because there is safe depth with water".
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– SIMEL
Mar 30 at 18:19
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@SIMEL ok.. just take a size small enough so that the space between four touching spheres is smaller than an oxygen molecule - then grid this.
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– Mariah
Mar 30 at 18:38
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@SIMEL ok.. just take a size small enough so that the space between four touching spheres is smaller than an oxygen molecule - then grid this.
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– Mariah
Mar 30 at 18:38
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yeah, this is taking the size of a water molecule, but the problem with this is that there is no safe depth with it, I want there to be a safe depth where I can still breath, which doesn't happen with water, and see if with depth the area of empty passages leading to the surface reduces.
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– SIMEL
Mar 30 at 19:07
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yeah, this is taking the size of a water molecule, but the problem with this is that there is no safe depth with it, I want there to be a safe depth where I can still breath, which doesn't happen with water, and see if with depth the area of empty passages leading to the surface reduces.
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– SIMEL
Mar 30 at 19:07
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@SIMEL why don't you just add balls in each "layer" until we reach this critical size?
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– Mariah
Mar 30 at 19:40
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@SIMEL why don't you just add balls in each "layer" until we reach this critical size?
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– Mariah
Mar 30 at 19:40
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I would say that this is a physics problem and not a math problem. I would guess that even though air could flow, circulation would be low, and you would be re-breathing the same air, and yes you would eventually suffocate.
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– Doug M
Mar 30 at 18:11
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@DougM, I also wasn't sure about where to post the question. But I want to disregard the issue of circulation, by "airflow" I mean that if there is $a$ "empty" area at a certain level, and that it's connected to at least $a$ empty area above it, that it's $a$ "airflow", or that $a$ surface area of air reaches this depth from the top. I really have trouble with formulation this notion.
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– SIMEL
Mar 30 at 18:16
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This is not a mathematics problem.
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– copper.hat
Mar 30 at 18:53