I have a debate with my exercise and hiking friends.  Essentially the
debate is whether leaning on exercise machines or hiking with poles
reduces the total caloric burn? Another way of asking this is will I
use the same number of calories if I lean on exercise machines during
the workout compared to not leaning or if I use poles during a hike
compared to not using poles?  Let us assume the time is the same and
let us ignore the weight of the poles that are being carried.

In the case of the exercise machine (assuming we are talking about a
stair stepper type machine) I would say that if it seems less tiring
to lean then it is probably burning less calories.  When hiking, the
total caolries burned should be about the same.  The difference is
that on the mountain the same work is being done with the poles, i.e.
moving your body up it, but divided between yor arms and legs.  On the
exercise machine, only your legs are actaully doing any work and
anything done to makes it easier on them is reducing the overall work
done.