Studying stereology helps give the reader a new perspective on the space around us. We have two eyes that individually see only in two dimensions. We can imagine things in three dimensions, four dimensions and even higher dimensions if we are string theorists. But we really can only see in two dimensions. Even with binocular perspective all we can see are two two-dimensional images. [ The theory of binocular perspective is introduced in Chapter 1 on page 22. As a computational method it is titled "photogrammetry".] Binocular perspective does not really free us from the two-dimensional prison in which we live, but it helps. Stereology is the spatial science that contains computational methods to help us measure quantities in higher dimensionalities from only one or two-dimensional views.
Stereology also explores the meaning of patterns. Patterns may be seem random yet be oriented, have a curvature per area or volume, defining covariances etc. These properties and more can be measured.
Bertrand's paradox (p. 101) questions what does "random" mean in geometry.
Stereology is full of interesting problems that await solution. There are also fun problems in the book. They relate to the statistics of encounter when there is motion.

 
 

    "Martin Gardner-type" QUESTIONS:
  • How much volume of a sausage roll is really sausage? (Seeing in 2-D) p.14.
  • How do you calculate distance from parallax? p.23.
  • How do we estimate chance encounters in hyperspace? p.387.
  • How do we describe the orientation of a random line? (Also random fibers) p.142.
  • What is not random about birds sitting on a wire? p.446.
  • Why does a wobbly drill make a three-cornered hole? (problem #19) p.207.
  • Why did the student who boarded the L-train at random times usually go south? (problem #3) p.386.
  • How many different ways can n integers be added together to equal N? p.360.
  • Why is it that the ratio of the area of a rough surface to its projected area often seems to equal the ratio of the length of a line on that surface to that line's projected length even though it can be proven otherwise? p.305.
  • How do you calculate the surface area of a patient's kidney from a biopsy slice? (problem #7) p.203.
  • How do you estimate the areal fraction of the ground occupied by tree trunks using only a piece of wood as a sight and no other measuring tools? (problem #29) p.210.
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