Mrnobody

Super late to the party, but if you are still interested, there's a nice video that explains a very similar thing but on an inclined treadmill. The concept is the same except that you are climbing stairs instead of a flat surface. Think that staying still doesn't cost energy, and that makes you go down. Therefore staying "still" (as opposed to going down with the stairs) cannot also cost no energy, and must cost something. Turns out that something is exactly the energy required for an equivalent ascent.