by 'vector' they just mean a list of numbers (ex. [32,5,8,11]). By dimension they mean the number of items in the list. In the above example it's a 4 dimensio

by 'vector' they just mean a list of numbers (ex. [32,5,8,11]). By dimension they mean the number of items in the list. In the above example it's a 4 dimensional vector. Make the numbers binary digits and voila. By hyperdimensional they mean the list has 500 or more items.