Section 9:    Isolation

Isolation is a fun conceptual tool, somewhat independent of prominence theory.  Isolation is the measure, proposed by Greg Slayden, of the distance in miles from a summit to anything higher.

Say that you were standing on a summit as the sea level rises around you.  At the point that the rising ocean reaches the summit on which you stand, how far would you have to swim to reach the first speck of dry land?

That dry land may be on the slope of your summit's next-higher neighbor, or it may in an entirely different direction.  Isolation need not equate to the distance across a key saddle, as shown in the following figure, where I(x) equals the isolation value for Summit X.  Isolation corresponds to the radius of the largest circle for which a summit is the highest point.  All summits, except Mt. Everest, have an isolation value.

Greg Slayden and Aaron Maizlish researched the isolation of summits in contiguous United States and found 41 peaks with an isolation value of 100 miles or more.  Worldwide, Greg has found 42 peaks with 1,000+ miles of isolation; a list that correlates somewhat to the list of high prominence mountains, but with the inclusion of several low summits on remote islands or in low-relief parts of the world.  Extensive isolation tables can be found at www.peakbagger.com.  This would be a good completion list for the truly cluastrophobic.

TABLE:  WORLD SUMMITS WITH AT LEAST 1,000 MILES ISOLATION
provisional list by Greg Slayden

Isolation, of course, correlates pretty well to prominence and to lists of high points of political entities, as they measure different aspects of the same phenomenon, a vertical protuberance on the earth's surface.  Prominence is purely a height function, and isolation is purely a distance function.

Low mid-oceanic islands can have high isolation values and low prominence, as evidenced by the appearance of Tristan da Cunha and Easter Island on the worldwide list.  The U.S. list has some isolated low rises too:  Sugarloaf Mtn., the high point of the central Florida peninsula (E=311, P=275) is the twelfth most isolated "summit" in the U.S. at 211 miles. 

Of the 40 most isolated summits in the U.S., 20 are also among the 57 most prominent (P>5,000'), and 29 have P>2,000'.  19 of the 41 are also state highpoints.

(End of essay, for now)