Finding Beauty in the Dissonance

You must be adept at thinking about thinking to defeat yourself at procrastination. You must realize there is the you who sits there now reading this, and there is a you sometime in the future who will be influenced by a different set of ideas and desires, a you in a different setting where an alternate palette of brain functions will be available for painting reality.

The now you may see the costs and rewards at stake when it comes time to choose studying for the test instead of going to the club, eating the salad instead of the cupcake, writing the article instead of playing the video game.

The trick is to accept the now you will not be the person facing those choices, it will be the future you – a person who can’t be trusted. Future-you will give in, and then you’ll go back to being now-you and feel weak and ashamed. Now-you must trick future-you into doing what is right for both parties.

We like to think that invention comes as a flash of insight, the equivalent of that sudden Archimedean displacement of bath water that occasioned one of the most famous Greek interjections, εὕρηκα. Then the inventor gets to rapidly translating a stunning discovery into a new product. Its mass appeal soon transforms the world, proving once again the power of a single, simple idea.

But this story is a myth. The popular heroic narrative has almost nothing to do with the way modern invention (conceptual creation of a new product or process, sometimes accompanied by a prototypical design) and innovation (large-scale diffusion of commercially viable inventions) work. A closer examination reveals that many award-winning inventions are re-inventions.

The 20th century Dutch artist Maurits Cornelis Escher was a master printmaker, whose works were heavily infused with ideas from mathematics. This textbook is intended to support a mathematics course at the level of college algebra, with topics taken from the mathematics implied by Escher’s artwork.