I’m not sorry for all of the geometry writing… have you ever read Euclid’s Elements? People interested in classical math will read the definitions, axioms, and learn to write formal proofs using postulates. I’m not that person.
I’m interested in reasoning and learning how these ideas can be translated into other things. For example, a surface.
Surfaces are things which contain breadth and length, and the edges of surfaces are lines. Remember that lines are breadthless lengths. A plane surface is a surface that sits evenly within straight lines — straight lines have points, making them finite.
People who do creative acts often look for the blank canvas to create on. The blank canvas represents infinite possibilities without limits — much like a surface. Corporate types call it “blue sky” thought. Euclid might call this — thinking on surfaces.
I prefer plane surface thought. Thought that involves thinking within finite lines — constraints. Constraints are like force multipliers on creativity — it’s no longer about all the possibilities it’s now about all the possibilities within bounds. It’s that type of environment where out of the box ideas are best generated! Watch Apollo 13 and you’ll see tons of examples of plane surface thinking.
Next time you’re confronted with a problem that requires you to make a solution think about your space. Is your ability to create a surface without limits? Or, are their straight lines — constraints — bounding you? Likely, you have constraints, and that means your next act is to understand those constraints, embrace them, and begin thinking what’s possible?