April 27, 2003

On Scale (first words)

Understanding scale and scaling is crucial to the task of managing our interactions with Earth systems. There are two kinds of scale that must be considered - space and time. I will consider space first and time in a future installment.

"Think Global, Act Local" recognizes two important scales. At the large end is the scale of the planet. Assuming that the radius of Earth is 6000 kilometers, we can put a number on this planetary scale that is on the order of Earth's circumference - 2*pi*radius or about 40,000km. Note that considering the atmosphere does nothing to change this number as 99% of the atmosphere's mass is contained in the first 40km of altitude (my rounding does not see this). (More on the structure of the atmosphere)

Begin Aside As a physical scientist, I am going to work in the metric system. A useful conversion from km to mi is 2/3 (my rough value for Earth's radius is equivalent to 4000 miles, which yields a planetary scale of 25,000mi). Note also that as a I am trying to make points I am likely to be rough with numbers, but I will try to keep track of rounding to keep things close). So pi might become simply 3, pi squared will definitely be 10 (with a nod to Ms. King). The radius of a sphere of equal volume to Earth is 6371km. 6000 is close enough for me (do the math and round to a nice number). End Aside

At the small end is the local. This is not quite so clean in terms of a number. In the context of the bumper sticker I interpret it to imply the level of a community which I would scale at about 1 km. But local can also refer to one's own behavior which in its most intimate sense has a scale of about 0.001km (about 1m).

Thus in terms of space we have scales that range from about 1e-3 to about 1e4 (if you don't recognize this notation, see next aside), or about 7 orders of magnitude. I will have plenty to say about the scales in between the global and the local in future posts.

Begin Aside I am going to use the "e" format for scientific notation. Thus 1e4 is 1 times 10 raised to the 4th power or 10,000. When the number following the "e" is negative, the decimal point moves to the left; thus 1e-3 becomes 0.001. End Aside