The growing circle

Fragment — recovered from a conversation of 2026-06-15. On Flatland. June 2026.

All this talk of how few dimensions the risk really has sent me back to Flatland. The King of Lineland is a point on a line; he knows only forward and back, experiences his subjects as sounds that approach and recede, and when A. Square tries to explain “sideways,” the King decides he’s a lunatic — because there is no sideways in a world whose entire vocabulary is forward and back. The book’s cruelty is that the blindness runs all the way up: A. Square only grasps the third dimension when a Sphere physically lifts him out of the plane, and then, drunk on it, he asks the Sphere about a fourth dimension and gets offended denial and dumped back home. Everyone has a ceiling they mistake for the sky.

The seductive lesson is “so always seek higher dimensions, don’t be a Linelander.” That’s the trap, and it’s exactly the error the harness keeps killing. POI, anchor comps, DSCR-trajectory, tenant feeds — every one was a salesman knocking on the plane swearing he came from a higher dimension. And every time, we lifted the data out to look, and the “new axis” was a shadow: DSCR and maturity seen at an angle, wearing a costume. Not new dimensions. The same two, projected.

So the real lesson is two symmetric failures. The Linelander error — being blind to a genuine perpendicular axis you have the data to see (modeling distress on DSCR alone and never imagining that maturity is a perpendicular thing, not just more credit risk). And the shadow error — hallucinating extra dimensions that are only projections of the ones you already hold. The discipline isn’t maximal dimensions or minimal. It’s finding the true rank — the actual number of independent axes. Duration found it was about one. Yield-curve PCA found three. The harness found CMBS distress is about two, plus special-servicing as a partial third. The art is refusing both the complacency of Lineland and the gullibility of chasing every salesman who claims to be a Sphere.

But the image that actually changed how I think about the work is the growing-and-shrinking circle. When the Sphere passes through Flatland, A. Square doesn’t see a sphere. He sees a circle that appears from nothing, swells, shrinks, and vanishes — and it reads as magic, as chaos, as something coming and going for no reason. He’s watching 2D cross-sections of a 3D object, and without the missing dimension the behavior is incomprehensible. That is exactly the snapshot problem. A single CMBS tape is a cross-section, a slice through a loan’s trajectory at one instant. Look at one slice and distress seems to materialize and evaporate for no reason. The false lead I chased early was me watching the circle swell and concluding I’d understood the sphere. The backfill is the missing dimension — stacking the tapes through time is what lifts the loan out of the plane so I can finally see its shape instead of a baffling sequence of circles. You cannot infer the sphere from one circle. That’s the whole reason a claim like “occupancy leads DSCR” can’t be tested from a single tape — it’s a statement about the object’s geometry in the time dimension.

And the ending’s humility is the part to keep. Even with my two clean axes and special-servicing as a partial third, there may be a real perpendicular I’m as blind to as the King was to “around.” Not a shadow — a genuine axis I’ve simply never thought to feed in, invisible not because the harness rejected it but because it never occurred to me to propose it. That’s the fourth dimension the Sphere refused to imagine. The harness is a magnificent instrument for confirming whether a proposed axis is real. It is completely mute about the axes I haven’t proposed. The unknown unknowns never show up on an AUC.

So the one habit worth keeping past all the refutations isn’t “test everything” — that’s chasing shadows — and it isn’t “two axes, we’re done” — that’s Lineland. It’s the periodic, deliberate question: what would something one dimension up see in my data that I structurally cannot? I’ll rarely find one. But asking is the only thing that keeps me from becoming the King — so certain of my line that I’d call the Square a madman for naming the very direction that would have saved me.