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.

Hypernomics, Missing Dimensions, & Price Determination: 2nd in a Series

“Everything must be made as simple as possible. But not simpler.” ― Albert Einstein

In the last post, Paul Samuelson said equilibrium prices exist where supply meets demand.

While prices for simple products work that way, Value analyst Sheila (A) suspects markets for more complicated products behave differently.  She knows she can account for mountaintops using latitude, longitude, and altitude referencing the equator, prime meridian, and sea level, respectively (B).

With each of the 44 dots representing a unique flat screen tv’s features and price, she finds she can plot the model’s size (C) or cycles per second (D) against prices and get significant but mediocre R2s.  She works to improve her prediction.

In E, she discovers she can plot Price (Dim 3) against the tv’s refresh rate (Hz, Dim 1) and its size (Diag. “, Dim 2) as ordered triples, using an origin of (0,0,0) as a starting point.  With Hz and Diag. “ as Valued Features 1 and 2, respectively, she predicts flat-screen Value (as sustainable prices) with an R2 of 97.0% and a P-Value of 4.85E-32.  She accounts for other features as needed.

All multi-attribute markets have similar “lost dimensions.”

#markets #innovation #hypernomics #prices #dimensions #wsu