## Dimensional Collapse

Perspective is a most subtle discovery in mathematical studies
Leonardo da Vinci (Attributed)

Collapsing dimensions sound like the premise of a creepy science fiction film.

But art, engineering, and architecture have used them for centuries.

The angles in (A’s) 12th-century painting do not truly represent what the eye sees. Art, up to the 1500s, suffered from this technique.

But with the advent of Brunelleschi’s drawings of Florentine buildings in the early 1400s, artists, engineers, and architects could offer visualizations that more closely mimicked reality. The trick was using a vanishing point where all dimensions necked down to a solitary spot. In (B), it’s in the sky between the central figures of Socrates and Plato.

In my upcoming book with Wiley, Hypernomics: Using Hidden Dimensions to Solve Unseen Problems, I show how simultaneously understanding multiple markets mandates dimensional collapse. Hypernomics has a five-market, 16D drawing representing 3% of world GDP. Hypernomics needs collapsing dimensions to solve hidden problems that artificially constrained approaches cannot see, let alone explain (C).

Modern business analysis mandates dimensional collapse, as does modern art.

## Simplify Results For Management

“Simple can be harder than complex.” – Steve Jobs

Suppose you analyze a market and find four features that help describe a product’s value or sustainable price. Your power form equation reads Price = constant * feature 1^a * feature 2^b…feature 4^d. How can you simplify each expression so that more people can grasp its meaning?

Helicopters (A-C) come in many designs and sizes. You suspect their useful loads, cruise speeds, and the number of engines support their prices. Analysis confirms that, but the resulting equation is complicated. You want to know how noise, or its lack, contributes to prices too. You find data on cabin and sideline decibel levels, but it’s spotty.

You want to be both simpler and more thorough. What to do?

Poring over the data, you find that pound for useful load pound, helicopters with more main blades fetch more money. That’s because rotor systems with more and smaller blades disturb the air less and create less noise. In D, you can take that expression, Blades^d, and depict the projected Value increase as you add blades. Combining D (and like tables for features a-c) with Demand analysis (see the last post) permits fine-tuning against the market’s needs.