The choice about what is a peak should be the climber’s, not the list maker’s.
– Gerry Roach 
Peak Power 
For some time in Colorado, a single, simple criterion has been used to determine
if a summit is a peak or a false summit: For a summit to be a peak, it must
rise at least 300 vertical feet above the saddle connecting it to its parent.
If just one criterion is going to be used, this is a good one. There is nothing
sacred about 300 feet – it’s just a round number that makes sense
in Colorado. This criterion serves most people most of the time, and the Colorado
peak lists on this site use it. However, some people’s aesthetic sense will
be better served with lists based on 500 feet of rise, or perhaps, 150 feet. 
It seems then, that any definition for what is a peak should provide a framework
that yields a progression of answers. The choice about what is a peak should be the climber’s,
not the list maker’s. Any peak defining system should provide a series of lists based on different
values of the constants that underlie the system. For example, with the simple
verticalriseabovetheconnectingsaddle system, lists could be published for 150, 300, 500 and 1,000 feet.
The climber would then be free to choose a peak bagging constant and its attendant list.
The 1,000foot list would only include the real monarchs of each range.
The 150foot list would be much longer and would include summits that the higher numbered lists
discarded as falsies. 
With this approach, peak bagging becomes a continuum, and the climber is never done.
There is always more, and this is the way it should be. As an initial prize, you might climb all of
Colorado’s Fourteeners on the 1,000foot list. Later, you could expand your achievement to 150 feet.
By the time you get to 40 feet, you will need more accurate maps, and probably will move on to other
challenges. 
It seems clear that the answers about what is a peak lie in each major range’s topography.
The best peak definition system would feed 3D topography data and a whatisapeak algorithm into a computer,
then the lists would come pouring out. Of course, we will always argue about the details of the
whatisapeak algorithm, but the climber is free to choose its application to the data.
Such a grand treatment is beyond the scope of this discussion. 
By adding a second criterion, I have gone beyond the simple, verticalriseabovetheconnectingsaddle system.
The second criterion is the separation between the two summits.
This is not a new idea, but I have given it a fresh look. I summarize my twocriterion system as follows.
I multiply the rise by the separation to get what I call a summit’s power.
If a summit has sufficient power, then it is a peak, otherwise it is a falsie.
The climber determines what sufficient power is. A semiformal series of definitions follows.
It may seem a bit much at first, but bear with me as it all works out in the end,
and this system is the basis for some fun, interesting peak lists. 
Assumption: Everest is a peak 
Discussion: This whole process could be rearranged to eliminate this assumption,
but it’s more fun this way. If Everest is not a peak, then I don’t know what is. 
Definitions: 
 A point is any location on the Earth’s surface.
 A summit is a point from which it is down in all directions
along the Earth’s surface.
 A summit’s altitude is its height above sea level.
 A traverse is a route on the Earth’s surface
between a point and a summit.
 The connecting ridge between a point and a summit is the
highest possible traverse between the point and the summit.
 The connecting saddle between a point and a summit is the lowest point
on the connecting ridge between the point and the summit.
 The rise between a point and a summit is the difference
between the altitude of the connecting saddle between the point and the summit,
and the summit’s altitude.
 The separation between a point and a summit is the shortest,
straightline map distance between the point and the summit.
 The connecting power of a point and a summit is the rise
between the point and the summit multiplied by the separation
between the point and the summit.
Discussion: If we measure the rise in feet and the separation in miles,
then the units of connecting power are footmiles.
 A summit is a peak relative to a peak constant C
if its connecting power to the higher peak with the highest connecting saddle
is greater than or equal to C.
Discussion: Note that we are looking for a higher connecting peak.
This is why we need the assumption that Everest is a peak.
The climber gets to choose the peak constant C.
In a practical application, the peak constant’s units will be the same as
the connecting power’s units.
This is not absolutely required in a general solution.
 A peak’s radix R is a function such that R is greater than or equal to 1.
Discussion: The radix can be any function of the climbers choosing.
The radix is best chosen empirically after examining a range’s topography.
The assumption that R be greater than or equal to 1 is a convenience.
A more general solution can relax this requirement.
 A peak has an extent equal to the peak’s radix
multiplied by the peak’s altitude.
Discussion: With a radix of 1, a peak’s extent is equal to its altitude.
We need the concept of extent to contain singular mountains like Orizaba in Mexico.
The system breaks down if we have to look too far for a neighbor.
 Two peaks are neighbors if there are no other peaks
on the connecting ridge between the two peaks.
Discussion: Note that a neighbor must be a peak relative to the same peak constant C.
 A peak is a monarch if it has one or more neighbors inside its extent, and they are all lower.
Discussion: A monarch is usually the highest peak in a group or range.
 A peak is a sovereign if it has no neighbor inside its extent.
Discussion: These peaks are very lonely. Orizaba is a good example.
 A peak’s power is the minimum connecting power between the peak
and a neighbor inside the peak’s extent, or between the peak and any point on the extent.
Discussion: Now that we have contained the sovereigns, we can calculate the real peak power.
Note that we can calculate a peak’s power even if it has no neighbors.
 A ranked peak is a peak that has a power greater than or equal to
its peak constant C.
Discussion: Note that we are using the minimum connecting power to calculate peak power
and not just the connecting power to the higher peak with the highest connecting saddle.
This is the difference between a ranked peak and a peak.
It is possible for a summit to be a peak but not a ranked peak.
 A peak’s parent is the closest, higher ranked peak.
Discussion: It is interesting to be on a summit and know where the nearest higher peak is.
A fine point is that the parent may be a different peak than the higher ranked peak above
the highest connecting saddle. In the rare case where there are two or more connecting saddles
of the same elevation leading to different, higher, ranked peaks,
the closest peak is the parent.
 If a summit is not a peak, it is a falsie.

List Creation 
I have applied my PeakPower system to Colorado’s Fourteeners.
I have chosen four peak constants, each with units of footmiles: 1,000, 500, 300, and 150.
For convenience, I refer to one footmile as a power point or point, and I have used a radix of 1.
As the constant C decreases, the number of ranked Fourteeners increases from 43 at 1,000 points,
to 45 at 500 points, to 49 at 300 points, to 56 at 150 points.
If a summit is named and over 14,000 feet, it is on the lists regardless of its power.
It may not be ranked. Note that a peak’s neighbor can change depending on C,
since the neighbor must also be a peak relative to C. 
On the 150 or 300 point lists, Uncompahgre is Colorado’s most powerful peak, and this matches an aesthetic sense.
With the critical, mountaineering look that smaller peak constants offer, the peakpower system finds the
singular, highly visible Uncompahgre. With 500 or 1,000 points, Pikes Peak emerges as Colorado’s most
powerful peak, and this matches a broader aesthetic sense of the way things should be, since
Pikes stands alone and is visible for vast distances. It is not a coincidence that Pikes holds Colorado’s
largest elevation gain. In a simple, twocriterion way, my PeakPower system understands this. 
Many of Colorado’s named and favorite Fourteeners are not ranked on either the 150 or 300point lists.
The topography speaks without emotion. In compensation, three new ranked Fourteeners appear on the 150point list.
They are Point 14,340 alias “North Massive,” Point 14,134 alias “South Elbert,”
and Point 14,132 alias “South Massive.” I have also added several other
lowpower, unnamed 14,000foot summits to the 150point list.
If you are a real Fourteener aficionado, you will climb every summit on this extended list. 
As on other lists, I have extrapolated the elevations of unmarked summits and interpolated the elevations of
connecting saddles. I add half the contour interval (20 feet for most quadrangles) to the highest closed contour
of an unmarked summit, and I add half the contour interval (20 feet) to the highest contour line
that does not go through a saddle. I round separations to the nearest 0.1 mile. 
To view my PeakPower Fourteener lists, get the
1st edition of my Fourteener Guide. 
Always looking for peak constants that lead us to unknown, majestic peaks,
– Gerry Roach 