Vertical cross-section of the Sierra Madres, near Oaxaca City. 

You can look at physically “straight” cross-sections of a mountain (or trench), or you can take the vertical cross-section along a path γ in 2-D.

You can think about the landscape as a scalar field in 2-D (puncture the plane if you need to do this to the whole Earth) with the height being a numerical quantity assigned to any point. In that case the image above records the values the scalar field takes along the 1-dimensional γ. (If the scalar field were discontinuous, that would mean you either just biked off a cliff, or biked into a wall.)  Or you can think about it in 3-D — looking around from your bicycle as you ascend the mountain ridge.

Or you can think about it in 4-D — the Earth hurtling and whirling through spacetime, events in a light cone”always there” in the Tralfamadorian past.

Related ideas:

  • projection
  • statistical cross-sections (cohorts, longitudinal data, versus “panel” measurements now)

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