Mixing
Can a realistic rubber mannequin be turned inside-out.
A realistic human-shaped mannequin is made of topological-grade rubber.
All the body cavities that are accessible from outside without piercing any tissue, are faithfully reproduced, for example the digestive tract and the nostrils. Ear drums are assumed to be intact.
The interior of the dummy is coloured pink and the outside is sprayed blue.
Is it possible for the dummy to be turned inside-out to form a sphere with a few holes in such a way that only pink shows and only blue is hidden?
general-topology
asked Nov 20 '18 at 13:00
chasly from UK
1426
|
show 3 more comments
A realistic human-shaped mannequin is made of topological-grade rubber.
All the body cavities that are accessible from outside without piercing any tissue, are faithfully reproduced, for example the digestive tract and the nostrils. Ear drums are assumed to be intact.
The interior of the dummy is coloured pink and the outside is sprayed blue.
Is it possible for the dummy to be turned inside-out to form a sphere with a few holes in such a way that only pink shows and only blue is hidden?
general-topology
asked Nov 20 '18 at 13:00
chasly from UK
1426
2
New advertisement phrase: "topological-grade materials". To be understood only by mathematicians.
– Zvi
Nov 20 '18 at 13:11
What's not clear to me is whether "turned inside out" means "is there an embedding of this surface with this property?" or "is there a regular homotopy of this initial embedding to the inside-out embedding? " or "is there an isotopy of ...?"
– John Hughes
Nov 20 '18 at 13:20
It's not even clear to me what "exterior" means here. Do the pink and blue regions share a boundary? If so, what shape is it? A disjoint union of circles maybe?
– MJD
Nov 20 '18 at 13:26
Does the "interior" include "All the body cavities that are accessible from outside without piercing any tissue," and is the "outside" every other part of the surface?
– David K
Nov 20 '18 at 13:36
1
@MJD - 'Exterior' means what most people would think of. You can imagine someone being spray-tanned. There would be an arbitrary but clear boundary just inside each nostril. Similarly at the lips and the anus. Also the urethra - even though a cul-de-sac - would be pink inside. Someone has mentioned the Eustachian tubes as well.
– chasly from UK
Nov 20 '18 at 13:37
|
show 3 more comments
A realistic human-shaped mannequin is made of topological-grade rubber.
All the body cavities that are accessible from outside without piercing any tissue, are faithfully reproduced, for example the digestive tract and the nostrils. Ear drums are assumed to be intact.
The interior of the dummy is coloured pink and the outside is sprayed blue.
Is it possible for the dummy to be turned inside-out to form a sphere with a few holes in such a way that only pink shows and only blue is hidden?
general-topology
asked Nov 20 '18 at 13:00
chasly from UK
1426
A realistic human-shaped mannequin is made of topological-grade rubber.
All the body cavities that are accessible from outside without piercing any tissue, are faithfully reproduced, for example the digestive tract and the nostrils. Ear drums are assumed to be intact.
The interior of the dummy is coloured pink and the outside is sprayed blue.
Is it possible for the dummy to be turned inside-out to form a sphere with a few holes in such a way that only pink shows and only blue is hidden?
general-topology
general-topology
asked Nov 20 '18 at 13:00
chasly from UK
1426
asked Nov 20 '18 at 13:00
chasly from UK
1426
edited Nov 20 '18 at 13:06
asked Nov 20 '18 at 13:00
chasly from UK
1426
asked Nov 20 '18 at 13:00
chasly from UK
1426
asked Nov 20 '18 at 13:00
chasly from UK
1426
1426
2
New advertisement phrase: "topological-grade materials". To be understood only by mathematicians.
– Zvi
Nov 20 '18 at 13:11
What's not clear to me is whether "turned inside out" means "is there an embedding of this surface with this property?" or "is there a regular homotopy of this initial embedding to the inside-out embedding? " or "is there an isotopy of ...?"
– John Hughes
Nov 20 '18 at 13:20
It's not even clear to me what "exterior" means here. Do the pink and blue regions share a boundary? If so, what shape is it? A disjoint union of circles maybe?
– MJD
Nov 20 '18 at 13:26
Does the "interior" include "All the body cavities that are accessible from outside without piercing any tissue," and is the "outside" every other part of the surface?
– David K
Nov 20 '18 at 13:36
1
@MJD - 'Exterior' means what most people would think of. You can imagine someone being spray-tanned. There would be an arbitrary but clear boundary just inside each nostril. Similarly at the lips and the anus. Also the urethra - even though a cul-de-sac - would be pink inside. Someone has mentioned the Eustachian tubes as well.
– chasly from UK
Nov 20 '18 at 13:37
|
show 3 more comments
2
New advertisement phrase: "topological-grade materials". To be understood only by mathematicians.
– Zvi
Nov 20 '18 at 13:11
What's not clear to me is whether "turned inside out" means "is there an embedding of this surface with this property?" or "is there a regular homotopy of this initial embedding to the inside-out embedding? " or "is there an isotopy of ...?"
– John Hughes
Nov 20 '18 at 13:20
It's not even clear to me what "exterior" means here. Do the pink and blue regions share a boundary? If so, what shape is it? A disjoint union of circles maybe?
– MJD
Nov 20 '18 at 13:26
Does the "interior" include "All the body cavities that are accessible from outside without piercing any tissue," and is the "outside" every other part of the surface?
– David K
Nov 20 '18 at 13:36
1
@MJD - 'Exterior' means what most people would think of. You can imagine someone being spray-tanned. There would be an arbitrary but clear boundary just inside each nostril. Similarly at the lips and the anus. Also the urethra - even though a cul-de-sac - would be pink inside. Someone has mentioned the Eustachian tubes as well.
– chasly from UK
Nov 20 '18 at 13:37
2
2
New advertisement phrase: "topological-grade materials". To be understood only by mathematicians.
– Zvi
Nov 20 '18 at 13:11
New advertisement phrase: "topological-grade materials". To be understood only by mathematicians.
– Zvi
Nov 20 '18 at 13:11
What's not clear to me is whether "turned inside out" means "is there an embedding of this surface with this property?" or "is there a regular homotopy of this initial embedding to the inside-out embedding? " or "is there an isotopy of ...?"
– John Hughes
Nov 20 '18 at 13:20
What's not clear to me is whether "turned inside out" means "is there an embedding of this surface with this property?" or "is there a regular homotopy of this initial embedding to the inside-out embedding? " or "is there an isotopy of ...?"
– John Hughes
Nov 20 '18 at 13:20
It's not even clear to me what "exterior" means here. Do the pink and blue regions share a boundary? If so, what shape is it? A disjoint union of circles maybe?
– MJD
Nov 20 '18 at 13:26
It's not even clear to me what "exterior" means here. Do the pink and blue regions share a boundary? If so, what shape is it? A disjoint union of circles maybe?
– MJD
Nov 20 '18 at 13:26
Does the "interior" include "All the body cavities that are accessible from outside without piercing any tissue," and is the "outside" every other part of the surface?
– David K
Nov 20 '18 at 13:36
Does the "interior" include "All the body cavities that are accessible from outside without piercing any tissue," and is the "outside" every other part of the surface?
– David K
Nov 20 '18 at 13:36
1
1
@MJD - 'Exterior' means what most people would think of. You can imagine someone being spray-tanned. There would be an arbitrary but clear boundary just inside each nostril. Similarly at the lips and the anus. Also the urethra - even though a cul-de-sac - would be pink inside. Someone has mentioned the Eustachian tubes as well.
– chasly from UK
Nov 20 '18 at 13:37
@MJD - 'Exterior' means what most people would think of. You can imagine someone being spray-tanned. There would be an arbitrary but clear boundary just inside each nostril. Similarly at the lips and the anus. Also the urethra - even though a cul-de-sac - would be pink inside. Someone has mentioned the Eustachian tubes as well.
– chasly from UK
Nov 20 '18 at 13:37
|
show 3 more comments
2 Answers
2
active
oldest
votes
As far as I know, humans are homologous to a torus because of the digestive track. A torus cannot be bent into a sphere.
answered Nov 20 '18 at 13:15
Rchn
49015
1
There is a nose.
– Charlie Frohman
Nov 20 '18 at 13:16
1
Good point, ears are also connected to the nose.
– Rchn
Nov 20 '18 at 13:20
This is not a true sphere because surface holes are allowed - just not big enough to see through.
– chasly from UK
Nov 20 '18 at 13:21
add a comment |
It seems pretty clear that the blue region is connected and the pink region is not. On the other hand I can imagine painting a blue band around a pink sphere and then deforming the sphere in such a way that the blue band is folded upon itself and "hidden" while the pink regions remain visible, but what you have then is not a "sphere with a few holes," you have something that looks (from the outside) like a sphere separated into two parts by a crack.
answered Nov 20 '18 at 14:04
David K
52.6k340115
add a comment |
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2 Answers
2
active
oldest
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2 Answers
2
active
oldest
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As far as I know, humans are homologous to a torus because of the digestive track. A torus cannot be bent into a sphere.
answered Nov 20 '18 at 13:15
Rchn
49015
1
There is a nose.
– Charlie Frohman
Nov 20 '18 at 13:16
1
Good point, ears are also connected to the nose.
– Rchn
Nov 20 '18 at 13:20
This is not a true sphere because surface holes are allowed - just not big enough to see through.
– chasly from UK
Nov 20 '18 at 13:21
add a comment |
As far as I know, humans are homologous to a torus because of the digestive track. A torus cannot be bent into a sphere.
answered Nov 20 '18 at 13:15
Rchn
49015
1
There is a nose.
– Charlie Frohman
Nov 20 '18 at 13:16
1
Good point, ears are also connected to the nose.
– Rchn
Nov 20 '18 at 13:20
This is not a true sphere because surface holes are allowed - just not big enough to see through.
– chasly from UK
Nov 20 '18 at 13:21
add a comment |
As far as I know, humans are homologous to a torus because of the digestive track. A torus cannot be bent into a sphere.
answered Nov 20 '18 at 13:15
Rchn
49015
As far as I know, humans are homologous to a torus because of the digestive track. A torus cannot be bent into a sphere.
answered Nov 20 '18 at 13:15
Rchn
49015
answered Nov 20 '18 at 13:15
Rchn
49015
answered Nov 20 '18 at 13:15
Rchn
49015
answered Nov 20 '18 at 13:15
Rchn
49015
49015
1
There is a nose.
– Charlie Frohman
Nov 20 '18 at 13:16
1
Good point, ears are also connected to the nose.
– Rchn
Nov 20 '18 at 13:20
This is not a true sphere because surface holes are allowed - just not big enough to see through.
– chasly from UK
Nov 20 '18 at 13:21
add a comment |
1
There is a nose.
– Charlie Frohman
Nov 20 '18 at 13:16
1
Good point, ears are also connected to the nose.
– Rchn
Nov 20 '18 at 13:20
This is not a true sphere because surface holes are allowed - just not big enough to see through.
– chasly from UK
Nov 20 '18 at 13:21
1
1
There is a nose.
– Charlie Frohman
Nov 20 '18 at 13:16
There is a nose.
– Charlie Frohman
Nov 20 '18 at 13:16
1
1
Good point, ears are also connected to the nose.
– Rchn
Nov 20 '18 at 13:20
Good point, ears are also connected to the nose.
– Rchn
Nov 20 '18 at 13:20
This is not a true sphere because surface holes are allowed - just not big enough to see through.
– chasly from UK
Nov 20 '18 at 13:21
This is not a true sphere because surface holes are allowed - just not big enough to see through.
– chasly from UK
Nov 20 '18 at 13:21
add a comment |
It seems pretty clear that the blue region is connected and the pink region is not. On the other hand I can imagine painting a blue band around a pink sphere and then deforming the sphere in such a way that the blue band is folded upon itself and "hidden" while the pink regions remain visible, but what you have then is not a "sphere with a few holes," you have something that looks (from the outside) like a sphere separated into two parts by a crack.
answered Nov 20 '18 at 14:04
David K
52.6k340115
add a comment |
It seems pretty clear that the blue region is connected and the pink region is not. On the other hand I can imagine painting a blue band around a pink sphere and then deforming the sphere in such a way that the blue band is folded upon itself and "hidden" while the pink regions remain visible, but what you have then is not a "sphere with a few holes," you have something that looks (from the outside) like a sphere separated into two parts by a crack.
answered Nov 20 '18 at 14:04
David K
52.6k340115
add a comment |
It seems pretty clear that the blue region is connected and the pink region is not. On the other hand I can imagine painting a blue band around a pink sphere and then deforming the sphere in such a way that the blue band is folded upon itself and "hidden" while the pink regions remain visible, but what you have then is not a "sphere with a few holes," you have something that looks (from the outside) like a sphere separated into two parts by a crack.
answered Nov 20 '18 at 14:04
David K
52.6k340115
It seems pretty clear that the blue region is connected and the pink region is not. On the other hand I can imagine painting a blue band around a pink sphere and then deforming the sphere in such a way that the blue band is folded upon itself and "hidden" while the pink regions remain visible, but what you have then is not a "sphere with a few holes," you have something that looks (from the outside) like a sphere separated into two parts by a crack.
answered Nov 20 '18 at 14:04
David K
52.6k340115
answered Nov 20 '18 at 14:04
David K
52.6k340115
answered Nov 20 '18 at 14:04
David K
52.6k340115
answered Nov 20 '18 at 14:04
David K
52.6k340115
52.6k340115
add a comment |
add a comment |
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2
New advertisement phrase: "topological-grade materials". To be understood only by mathematicians.
– Zvi
Nov 20 '18 at 13:11
What's not clear to me is whether "turned inside out" means "is there an embedding of this surface with this property?" or "is there a regular homotopy of this initial embedding to the inside-out embedding? " or "is there an isotopy of ...?"
– John Hughes
Nov 20 '18 at 13:20
It's not even clear to me what "exterior" means here. Do the pink and blue regions share a boundary? If so, what shape is it? A disjoint union of circles maybe?
– MJD
Nov 20 '18 at 13:26
Does the "interior" include "All the body cavities that are accessible from outside without piercing any tissue," and is the "outside" every other part of the surface?
– David K
Nov 20 '18 at 13:36
1
@MJD - 'Exterior' means what most people would think of. You can imagine someone being spray-tanned. There would be an arbitrary but clear boundary just inside each nostril. Similarly at the lips and the anus. Also the urethra - even though a cul-de-sac - would be pink inside. Someone has mentioned the Eustachian tubes as well.
– chasly from UK
Nov 20 '18 at 13:37