Most things you do with numbers have nothing to do with spatial relations.
Imagine you have a dataset for multiple people: Length of thumb, length of index finger, length of middle finger. Each person (point) in this dataset has 3 attributes (dimensions) and can be represented within a 3-axis coordinate system.
Want to add the attribute “Length of ring finger” to the dataset? Boom, gained another dimension. Each point representing a person suddenly got 4-dimensional.
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