I’m having trouble deciding where to begin with space. Unlike numeracy, spacial logic is not so much something that is taught to us as something that is learned though the process of living in our three dimensional, essentially Euclidean world. Flat, round, straight and curved, are all concepts that we grow accustomed to by living with examples.
Historically, geometry is one of the oldest branches of mathematics. The Indus Valley Civilization, the Egyptians, and the Babylonians all had a great working knowledge of geometry by 3000 BCE. Their knowledge was what we would call “applied knowledge.” They had rules of thumb about the side lengths of right angled triangles. They could approximate the circumference of a circle given the diameter. The Egyptians even developed the formula for the volume of a “frustum,” (essentially a pyramid still in the building phase.) However, they did not use logical reasoning to explain why their rules were true. Instead, like we did as children, they observed patterns in the world around them and from those developed their rules.
In 1979 Cathryn Aison commissioned Phillip Glass to compose some music for a Sesame Street segment that she was developing. Watch and listen to the results. You will see patterns which hint at underlying universal rules. Guessing those rules allowed the ancients to build palaces and temples some of which survive to this day.