the importance of visualization

For a long time I have been a fan of the SAT question of the day site.

The Official SAT Question of the Day™

I always get these right at which point my wife chimes in - "Great. You're as smart as the average high school senior."

The other day the question was:

A 25-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on concrete 7 feet from the base of the building. If the top of the ladder slips down 4 feet, then the bottom of the ladder will slide out how many feet?

This immediately screamed out Pythagorean theorem - the old a² + b² = c². I just needed to plug in the numbers. Despite this I felt compelled to draw this picture:

I then solved for n which was 24, plugged that in to get 20, and then solved again to get 15. So the correct answer was that the ladder moves out an additional 8 feet.

So even when the answer is obvious to the average high school student, a picture is worth a thousand words. Now imagine the average building, mechanical part, or bridge. It seems so obvious that visualization is the first step to experiencing something before it is real.