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In a dataset with k numeric attributes, you can visualize the data as a cloud of points in k-dimensional space - the stars in the sky, a swarm of flies frozen in time, a two-dimensional scatter plot on paper…creatures such as flies don’t know about north, south, east and west - although, being subject to gravity, they may perceive up-down as being something special. As for the stars in the sky, who’s to say what the “right” coordinate system is? Over the centuries, our ancestors moved from a geocentric perspective to a heliocentric one to a purely relativistic one, each shift of perspective being accompanied by turbulent religious-scientific upheavals and painful reexamination of humankind’s role in God’s universe.
— Ian Witten & Eibe Frank, introducing the concept of principal components analysis in Data Mining: Practical Machine Learning Tools and Techniques. Data mining, as evidenced by this passage, is for wizards from the deep age.