5. The logs of the data values from each experiment should fall approximately on a straight line. For the paper balls, the slope of the line, and therefore the dimension, should be between 2 and 3. If we ignore its thickness, a flat sheet of paper has dimension 2; consequently, a crumpled paper ball must have dimension at least 2. On the other hand, a solid ball has dimension 3; consequently, a crumpled paper ball must have simension at most 3.
Think of gradually deforming the flat sheet into a solid ball. As the crumpled paper becomes more like a ball, the dimension gets closer to 3. Why does its dimension not increase to 3? The crumpling process generates spaces of a range of sizes, preventing hte dimension from reaching 3. Stiff paper has a wider range of space sizes, including some that are relatively large, giving a dimension closer to 2. For light weight paper (or reprocessed paper), the range of space sizes is smaller, giving a dimension closer to 3.
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