D&G analyze the degrees of defining space as being smooth or striated. Striated space is ridged, like the scratches on a rock, or the grooves of a record. The striations are fractal and infinite, lines within lines all the way down. Striated space is defined and mapped space. Smooth space is that which has no differences between it. D&G note that “smooth space is always being transversed”, that we move through it without stop, since we don’t notice any points.

Both smooth and striations are abstractions, and actual space is both. D&G use felt as an example of a space that feels smoooth, but is infact numerous intertwined patches.

As a fractal space, it is possible to measure an infinite amount into the space. I’m reminded of the map maker who makes a 1:1 map that covers the country.

In music the striation is the variance of interval and frequency. D&G rely on Riemann’s notions of local geometry and space to explain. We can map what we can experience and know around us, but can not determine the linkages between that space and any other. This theorem shares with the post modern notions of relativity, where we can only define by our own perspective from our own vantage point. Returning to music, it is the variance of interval and frequency that we are experiencing at that moment, which we can then encapsulate into a defined space.

D&G then study the line as a point of distinction, analyzing the use of the line in art, particularly nomadic art. To D&G nomads drew at close range, and dealt only within the local geometry. There was no distinction of space. Their wall drawings take on the haptics of their surface. The ideas of space then become conferred into the use of line in later art. Greek and Egyptian art use the line to reduce the sky or sea into a horizon. We now have the abstract line, which is the beginning of artistic expression over what we percieve. The abstract line condenses and changes space as a means of expression.