Engineers are passionate about making things. We want to make new objects and we want to make new understandings. Most of all, we want to make new realities. Taking a look at some of the ways engineers use pictures to build can point us to how we can all create diagrams to understand, explain, and make better worlds.

Mechanical designers have to think in ranges of numbers Not just 100, but 100 plus or minus two. They have to because the real world is not perfect. Have you ever measured the length of a wall? You likely found a value that suited your purpose, but how precise was it? Perhaps you measured the wall to the nearest quarter-inch. Yet, many of the objects that enrich our lives, including computer chips and Lego bricks, are manufactured with delicate precision too fine for us to fathom. The creation of any physical object from raw materials is subject to all kinds of variation. The cross-section here shows two parts that a designer wishes to fit together. It is not enough to merely specify the desired dimensions, a one-inch metal peg to fit a one-inch hole. If the hole is drilled a little too narrow, and the peg left a little too thick, then these manufacturing errors may compound to make the fit impossible. In addition to the one-inch dimensions, the designer must also specify a tolerable amount of variation. This variation is indicated here as the darkly lined region of each part's cross-section. As long as both parts are created within their ranges, ...

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