Experiments & connections
GIGI, meet ICARUS.
I started with wine records. Of course I ended up thinking about flight.
The wine experiment gave GIGI a few readings from a mathematical fingerprint and asked what another reading could be. It returned a region of possible answers. Add another observation, and that region can shrink.
That sent me straight back to ICARUS. What can an aircraft know before it gets there? A best guess might put it neatly through a narrow passage. But how much room does everything we don’t know need?
ICARUS × GIGI Proposal / browser experiment
The gap stays the same.
What we know changes.
Reveal readings of a hidden disturbance field. The shaded band includes the aircraft and its possible drift over the next 0.8 seconds. Does that whole band fit through the passage?
The mathematical model runs locally in your browser.
Synthetic analytic field · Computed numerical bounds · The aircraft traces the planned approach; it is not a simulated controller response or a live GIGI connection.
A measurement can change the decision.
The passage is 60 centimetres wide. Nothing about its geometry improves when you move the slider. What changes is how much room we have to allow for an unknown disturbance.
The thin line is the planned path. The shaded band adds the aircraft’s size and a bound on how far its centre could drift. Early on, that band reaches the walls. With enough observations, it fits. That does not mean we have learned the whole field; we have narrowed it enough for this particular calculation.
Try the conflicting reading, too. The answer disappears because the observations no longer fit the model. I want that refusal to be as visible as the successful calculation. A flight computer needs to know when its information has stopped making sense.
What is doing the work?
I chose a bounded holomorphic function to create the hidden field. “Holomorphic” means its changes in the two coordinate directions fit together according to a precise compatibility rule. Its real and imaginary components are harmonic: an interior value equals the average around a sufficiently small surrounding circle.
In this toy example, those two components describe two directions of acceleration. The compatibility rule makes one reading constrain what can happen elsewhere. The circle beside the flight map shows the remaining possibilities at one location. We then allow for variation around that location before calculating the drift band.
The exact model, units, and calculation
The synthetic oracle is f(z) = 0.15 + 0.25z + 0.10z². Its magnitude is at most 0.5 on the unit disk. Inference receives only the revealed observations and the looser bound |f| ≤ 1, not the oracle’s coefficients. The real and imaginary outputs become acceleration components with scale 1 m/s².
The seven observation locations are the origin, then six equally spaced points on radius 0.65. The withheld query is z = 0.5 + 0.2i. A physical distance of 5 m corresponds to one unit of z. The browser computes marginal value disks through Schur interpolation, following the same mathematical construction as GIGI’s bounded-function module.
The field region has radius 0.75 m, within the working disk |z| ≤ 0.8. Schwarz–Pick bounds spatial variation by (0.75 / 5) / (1 − 0.8²) = 0.4167. Add this to the query disk’s radius r to bound acceleration uncertainty throughout the region. Over 0.8 s, the position allowance is ½ × 0.8² × (r + 0.4167) metres.
The planned centre travels 0.5 m, centred on the query point. The calculation checks that the whole centre-error tube stays inside the field region. The aircraft has a 0.08 m footprint radius; its required half-width is that radius plus the position allowance. It fits only below the passage’s 0.30 m half-width.
This assumes exact initial position and velocity, additive acceleration, and nominal cancellation of the disk-centre acceleration. It does not model actuator limits, vehicle attitude, turbulence, or feedback dynamics. The enclosing band uses the full-horizon allowance at every displayed position, conservatively. The numerical disks are not interval-certified safety bounds.
In a measured flight model, coordinate meaning, model mismatch and the dynamics would need their own validation. Putting two arbitrary wind readings into a complex number does not make them holomorphic.
And where GIGI becomes interesting.
Building the model is one job. Keeping it available, current and accountable is another.
I want GIGI to store a prepared analytic object and answer new questions without rereading the entire original dataset. The answer should carry its data revision, its operating regime, and the assumptions that make it meaningful.
If the aircraft changes configuration, or the observations change, the old answer belongs to an old situation. If we replay yesterday’s flight, we should be able to recover what the system actually knew yesterday. That combination—mathematical inference with durable memory—is the proposal.
The first application I would test is telemetry: whether incoming fingerprint readings agree, and whether a distribution changes between operating windows. The flight experiment here explores the next question: how could a planner use the uncertainty that remains?
Did the aircraft change, or did its description?
ICARUS already uses a concrete double cover. Two opposite unit quaternions, q and −q, describe the same physical orientation. A jump in stored components does not necessarily mean the aircraft moved abruptly.
That is a very practical version of the question I keep coming back to. A monitoring system needs to distinguish a physical change from a change in representation. The quaternion double cover and the two harmonic components here are different mathematical structures, but both make the meaning of a coordinate matter.
The bounded-function calculations already work in GIGI. Persistent analytic objects and their use by ICARUS are proposed engineering work. This browser experiment gives that proposal something concrete to examine.
I want to see how far we can take it.
Bee