Considering the elastic interval's strictly limited domain of influence, purely and only mediating between its two ends, it is interesting to speculate about how such a thing may be visualized. In space, we can see the spring as only its two ends, two dots, since its remainder has no influence upon anything else. On the other hand, it's important to see the spring as a whole. An elastic interval is paradoxically both a twoness and a unity. Combining these two aspects, it would seem most appropriate to see a spring as a circle which intersects space at two locations, though this may seem strange at first.
Extra dimensionality is required in order to have both apparent twoness and actual unity.