Source: Open University - GB062 Creative Thinking Course.
Question:
Imagine you have a rope long enough to go around the circumference of the Earth. If you extended that rope by two metres, how big would the gap be between the earth and the rope?
Answer:
Most people assume the space would be infinitesimal, but actually it’s more than thirty centimetres.
You may recall the circumference (c) of a circle is 2
r, i.e. 6.28 times the radius of the circle. So 2r, where r is the radius of the Earth, is the circumference of the Earth, and the circumference of the rope is 2
r + 200 cm. The radius of the Earth plus the gap between the rope and Earth is therefore 2 (r+g) where g is the gap between the Earth and rope.
2
r = c
2
(r+ g) = 2r + 200 cm
2
g = 200 cm
g = 200/6.28 = approximately 32 cm
Remarkably, adding two metres to the circumference will result in an increased radius of about 32 cm.
In contrast, adding two litres of water to the ocean would raise the water level infinitesimally, as we correctly surmise intuitively. We are misled by applying an inappropriate heuristic: that larger size leads to a smaller change, which we use because it works well in apparently analogous situations.