I love this guy. Best explanations. Got interested from the RSA Video, every time I look something mathematical up, scroll down and there he is. More people need to watch
Excellent video. I had no idea what dimensions were before this although I heard them here and there all the time. A dimension is a way to measure (describe anywhere in) an object or a space based on axis. With 1 axis, what is being measured is called 1 dimensional(you can go left or right in a linear way only). Like when a person is a 1 dimensional and spends his/her whole time in one type of activity so you barely could talk about (measure them) in any other direction. I came here from the "space filling curve" video and this video explains why a shape like the Koch shape is neither one dimensional nor two dimensional. The reason is that (IMO) it is neither on one axis, nor you could ask for two axes on which it's measuring an object. Remember dimension is a way to measure (=move around to ANYWHERE) an object or a space, now for example, if you say the koch is from 0 to 10 on the X axis and 0 to 10 on the Y axis, obviously the koch can not (at least normally) visit any (x,y) point. Just my thoughts, I might be partly or fully wrong, but I hope that helps. P.S: Also for the difference between a direction and a dimension, notice that not all dimensions need to be showable in simple geometrical shapes. So above 3 dimensions, directions are non-existent anymore, and there you have "features". So for example a user database record(a tuple) that has 8 columns(features) is an 8 dimensional thing. Since each of the features let you measure the user(an object), which is exactly what the definition of the dimension suggests.
I love this guy. Best explanations. Got interested from the RSA Video, every time I look something mathematical up, scroll down and there he is. More people need to watch
Excellent video. I had no idea what dimensions were before this although I heard them here and there all the time. A dimension is a way to measure (describe anywhere in) an object or a space based on axis. With 1 axis, what is being measured is called 1 dimensional(you can go left or right in a linear way only). Like when a person is a 1 dimensional and spends his/her whole time in one type of activity so you barely could talk about (measure them) in any other direction.
I came here from the "space filling curve" video and this video explains why a shape like the Koch shape is neither one dimensional nor two dimensional. The reason is that (IMO) it is neither on one axis, nor you could ask for two axes on which it's measuring an object. Remember dimension is a way to measure (=move around to ANYWHERE) an object or a space, now for example, if you say the koch is from 0 to 10 on the X axis and 0 to 10 on the Y axis, obviously the koch can not (at least normally) visit any (x,y) point.
Just my thoughts, I might be partly or fully wrong, but I hope that helps.
P.S: Also for the difference between a direction and a dimension, notice that not all dimensions need to be showable in simple geometrical shapes. So above 3 dimensions, directions are non-existent anymore, and there you have "features". So for example a user database record(a tuple) that has 8 columns(features) is an 8 dimensional thing. Since each of the features let you measure the user(an object), which is exactly what the definition of the dimension suggests.
What if my maths teacher too has a soothing voice like you.All maths classes will be happiest moments of my life
bibliography of dimensions..