Any line, really, but let's go with a spiral. The natural coordinate is its arc - there is no rule saying only cartesian coordinates are allowed. Indeed, geographers use latitude and longitude instead, saving a full coordinate.
...which is one less than the three it would take to represent points on a sphere in cartesian coordinates.
If you want me to describe the curve itself, you are essentially asking for an embedding - there are infinitely many of those, and they will depend on the dimension and coordinate system of the superspace.
Of course it's impossible to explicitly describe an embedding without reference to the superspace, but that only goes for one level - you can ignore said superspace when describing the interior of the subspace.
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Any line, really, but let's go with a spiral. The natural coordinate is its arc - there is no rule saying only cartesian coordinates are allowed. Indeed, geographers use latitude and longitude instead, saving a full coordinate.
Lattitude and longitude still make two coordintes… I was not asking about position on a curve, I was asking about the curve itself.
...which is one less than the three it would take to represent points on a sphere in cartesian coordinates.
If you want me to describe the curve itself, you are essentially asking for an embedding - there are infinitely many of those, and they will depend on the dimension and coordinate system of the superspace.
Of course it's impossible to explicitly describe an embedding without reference to the superspace, but that only goes for one level - you can ignore said superspace when describing the interior of the subspace.