are objects in the 2nd dimension allowed to bend?or must they always be perfectly flat?could imagine a 2D object being able to bend here in the 3rd dimension but what would the same be like for a person being "bent" in the 4th dimension?
>>16970583A 2D object can bend only when it is in an ambient 3D (or higher) space, e.g. a sphere.Any 3D object in ambient 3D space is flat. A 3D object can only bend when it is in an ambient 4D (or higher) space.There is the obvious generalization.
>>16970583yeah? look up curved spaces
>>16970584so we're in the 4th dimension right now?
>>16970590No. Are you retarded?
>>169705832D object is by definition always flat it it's 2D reference frame
>>16970605No it isn't.
>>16970583A dimension could be a variable and the addition of another variable is the addition of another dimension A pattern that was primarily manifesting on the second variable of the ceno-pythagorean categories or something like that could have variables added from negative or positive dimensions while still primarily manifesting on the second variable or something like that
>>16970583ever heard of curved lines?
>>16970583Pure dimensions are just convenient abstractions.In reality it's all about the degrees of freedom of interactions leading to apparent dimensions.Something "2D" being bent into higher dimensions is just a relaxation of the constraints that defined 2D-ness to begin with.Or in real life examples we can observe particles in materials exhibiting higher than 3D degrees of freedom.We're only in 3D universe to the extent that we focus on the way that light or gravity or other effects appear to propagate in that way.
>>16971344what decides the number of degrees of freedom in a given context?
>>16971421aipac
>>16971421Intuitively the minimum number of variables you need to specify to define the state of the whole system. For just a point you can fully define it's position relative to some arbitrary origin using 2 values if it's on a 2d surface, regardless of the shape of the 2d surface. Some faggot is probably going to come in here and be like "But muh fractals!!!" You're very smart and we are all very proud of you
>>16971344>>16971553So by your logic, a system with N continuous degrees of freedom is actually N-dimensional, because it takes an N-dimensional state space to match the variables that govern its behavior. Which means a rigid body is "actually" 6D, even though all six of those Ds depend on it actually existing in 3D space. Seems like the one conflating reality with convenient abstractions is (You), anon.
