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.

Proper Production Possibility Curves

There are no solutions; there are only trade-offs
Thomas Sowell

Forget the “classic” choice model between guns and butter with its single imaginary frontier. Such notions offer no basis for action. Never settle for heuristics when you can have analytics. To reveal true alternatives, we’ll need to do some heavy lifting.

In 4D.

No, really.

In A, we find an aircraft Demand Frontier in yellow. If we want to make 100 units (Quantity – Dimension (Dim) 1), we find our price limited to $393M (Price – Dim 2). For 55 copies, our price could rise to $610M (purple lines). In A’s Value Space, the sustainable price goes up with range (Dim 3) and velocity (Dim 4) but down with added units; thus, the angled Value Response Surface for 55 units is higher than that for 100 units. They form straight lines in log space where they intersect their respective price ceilings (the horizontal yellow and purple planes in Value Space). In B’s linear space, those intersections form multiple curves revealing the proper trade-offs. The yellow line shows us we could build a plane with 10K in range, with a max V of just over 1400 KPH.

It takes work to find Demand and Value, but in the end, we get insight available nowhere else.

Don’t Leave Money On The Table

“The more you learn, the more you earn” – Warren Buffett

In this true story, we hide the names to protect the players and don’t tell you the venue, either.

In 2014 (A), we ran three market Y value equations (not shown).  All showed that Project X was under-priced.  We find validation of these projections in 2021, as used X versions sell for more than their original $1M price (also not shown).  X sold amply, with 300 units in the market by 2021, and if C’s assumptions were correct, it made a profit, too (D).  Joy in Mudville!  But wait a minute.

Had X’s producers studied Y’s Demand Frontier (B), they might have noticed its negative slope of -1.24.  That means that at the limiting slope, had X’s price been raised to $1.34M, it would have made more revenue, despite the sales drop.  Also, with fewer units, recurring costs fall (C).

The overall effect in D is that selling Project X too cheaply costs Y both revenue and profit.

Hypernomics notes it’s easy to think that if a project makes a profit, it is doing well. But if we learn about all the market forces at work, often we’ll find well isn’t well enough.  Don’t leave money on the table because you didn’t study your market thoroughly.

#hypernomics #innovation #markets #marketanalysis #pricing #analytics