Re:Oil-Canning
by doubloon on Sunday October 08, 2023 @11:31AM
(#37811348)
whats interesting is how bending a 2d object into the third dimension makes it stronger.
now if you bend a 1d object into the second dimension, is it stronger? i am not sure, it is hard for me being roughly 3 dimensional to analyze 1 d objects. but i would for example consider a zig-zag spring-like shape to perhaps be stronger than a single line.
what about a 3d object? if you bend it into the fourth dimension... does it get stronger? and how would you go about doing that? well the first challenge is that there is no fourth spacial dimension that we are aware of. or is there? what we do instead is to mix materials, for example rebar iron into concrete objects.
but this makes you wonder what exactly is strength? it is the behavior of an object under external force. and what is force? Well it has its own dimensionality. a 2d object such as a flat metal in a 3d space can experience forces in the 3rd dimensional direction, but also forces in its 2d plane. the freedom of the 3rd dimension is what gives it the weakness in fact, as in a 2d world the 2d sheet of metal would not bend into the 3rd dimension, it may squish in the 2nd dimension only, but it wont buckle because it cant because theres no 3rd dimension to buckle into.
the funny thing is that unless you have a third dimension, there is no reason for a 2d object to be bent to increase strength.
in other words with the freedom a dimension brings, it also brings weakness to objects in dimensions less than the space involved. for example given a space of dimension n, any shape conforming to a dimension less than n has an inherent weakness. to be strong in dimension n, you must have a shape that varies into dimension n.
in dimension 3, the string (1d) and sheet (2d) are both strengthened by bending into dimension 3. a string can be formed into a spring shape and is stronger. same with 2d sheets, bending = strength. the interesting bit is that a purely 3d shape such as a solid cube is strong but extremely heavy. so by using objects of lower dimension to fill the 3d space you get lighter and stronger objects.
in other words if there were a fourth spatial dimension, which 3d objects had freedom to protude into, then 3d objects would be greatly weakened vs their situation in purely 3d space. however you could use 3d objects bent into certain 4d shapes to be stronger against 4d forces, but also lighter than a 4dimensional solid shape.
do we have four dimensional forces? i am wondering if somehow the curvature of space-time itself has aspects of a fourth spatial dimension, since it can in a sense present a force on the 3d shape.
so imagine like this, a 1d shape, a line segment, living in a linear space, a space that locally appears flat, but in an enormous scale it is a circle, which is actually 2d. this line segment goes most of its life imagining there is no such thing as 2d, or 2d forces, until one day perhaps the grand circle undergoes an anomaly in the 2nd dimension, and the line segment is subject to 2d forces. even though it remains in 1d space. that 1d space itself is being pushed into a 2d direction. and now lets say there is a small gradient across this 1d space, so that some of it is pushed more into a 2d direction by these 2d forces than the other, and the line segment happens to be on this gradient, will the line segment be able to detect that it has been in part of 1d space that has undergone 2d forces and motion? would this be equivalent of a 1d line segment figuring out how to build a gravity wave meter in 1d space?
in other words, are Gravity Waves a form of Oil Canning?
now if you bend a 1d object into the second dimension, is it stronger? i am not sure, it is hard for me being roughly 3 dimensional to analyze 1 d objects. but i would for example consider a zig-zag spring-like shape to perhaps be stronger than a single line.
what about a 3d object? if you bend it into the fourth dimension... does it get stronger? and how would you go about doing that? well the first challenge is that there is no fourth spacial dimension that we are aware of. or is there? what we do instead is to mix materials, for example rebar iron into concrete objects.
but this makes you wonder what exactly is strength? it is the behavior of an object under external force. and what is force? Well it has its own dimensionality. a 2d object such as a flat metal in a 3d space can experience forces in the 3rd dimensional direction, but also forces in its 2d plane. the freedom of the 3rd dimension is what gives it the weakness in fact, as in a 2d world the 2d sheet of metal would not bend into the 3rd dimension, it may squish in the 2nd dimension only, but it wont buckle because it cant because theres no 3rd dimension to buckle into.
the funny thing is that unless you have a third dimension, there is no reason for a 2d object to be bent to increase strength.
in other words with the freedom a dimension brings, it also brings weakness to objects in dimensions less than the space involved. for example given a space of dimension n, any shape conforming to a dimension less than n has an inherent weakness. to be strong in dimension n, you must have a shape that varies into dimension n.
in dimension 3, the string (1d) and sheet (2d) are both strengthened by bending into dimension 3. a string can be formed into a spring shape and is stronger. same with 2d sheets, bending = strength. the interesting bit is that a purely 3d shape such as a solid cube is strong but extremely heavy. so by using objects of lower dimension to fill the 3d space you get lighter and stronger objects.
in other words if there were a fourth spatial dimension, which 3d objects had freedom to protude into, then 3d objects would be greatly weakened vs their situation in purely 3d space. however you could use 3d objects bent into certain 4d shapes to be stronger against 4d forces, but also lighter than a 4dimensional solid shape.
do we have four dimensional forces? i am wondering if somehow the curvature of space-time itself has aspects of a fourth spatial dimension, since it can in a sense present a force on the 3d shape.
so imagine like this, a 1d shape, a line segment, living in a linear space, a space that locally appears flat, but in an enormous scale it is a circle, which is actually 2d. this line segment goes most of its life imagining there is no such thing as 2d, or 2d forces, until one day perhaps the grand circle undergoes an anomaly in the 2nd dimension, and the line segment is subject to 2d forces. even though it remains in 1d space. that 1d space itself is being pushed into a 2d direction. and now lets say there is a small gradient across this 1d space, so that some of it is pushed more into a 2d direction by these 2d forces than the other, and the line segment happens to be on this gradient, will the line segment be able to detect that it has been in part of 1d space that has undergone 2d forces and motion? would this be equivalent of a 1d line segment figuring out how to build a gravity wave meter in 1d space?
in other words, are Gravity Waves a form of Oil Canning?