Of Blurry Maps and Gaps: Why Visualize Uncertainty (2)

We keep talking of this uncertainty in the display as if it were just a blurry surface of a clearer, firmer data object underneath (if we could only scratch the grime away) What about other qualities of data (consistency, validity, integrity) — we don’t represent those in our charts. Is uncertainty really an attribute, a property, like a color, shading, gradient, color?

Uncertainty is slippery: it doesn’t want to be contained, it leaks everywhere. When we show on the graph that reaching this threshold has that uncertainty, we can hear, like an echo, the implicit: “… assuming those conditions, with this uncertainty”, and so forth, a snake eating its tail. Probability distributions don’t help — we end up with the ill-posed question of a “distribution of distributions”; information entropy doesn’t help — we have to ask over what partition of the probability space? So we say axiomatically: the uncertainty we show is all the uncertainty there is.

And it resists being held in place. To exhibit it we need a solid background of determinism to pin it to, a uniform and conditional something underneath that won’t move while we operate. Meanwhile business keeps hurling discontinuity and chaos at us, high variance is rocking hard, uncertainty against a background of uncertainty, enough to make one nauseous. Articulate it, nail it down, at least we’ll know on which side the uncertainty lives, what is foreground and what, background.

So we imagine that the lens is faulty, we see smudgy double and triple contours, and if we only sharpened the lens we’d see crystal clear. (Or we can hire an expert, for example I can sell you a license at a friend’s price) That our display of data is a move in a larger negotiation, here is where we stand on what business is and will be, now Business Reality across the gap, your move, we’ll take turns: we’ll look at the actuals, re-assess, correct course, take action before the turn is called; then let the business reality play out as it will.

Or the hubris mentioned in the introduction: that the display of data is an agreement, with a plan of execution for Business Reality (we did our part of course, everything’s aligned: organizational merit, the right kind of vision, the right kind of people, right place, right time, circularity be damned).

There is a delusion (from business school to business jail) that it’s a game about laws, patterns, supply to be consumed, demand to be met or created, equilibria to be reached, performance to be optimized. A quest for patterns, predictive theory, algorithms following the tracks of unknown beasts straight to their den. In reality why even imagine patterns and equilibria?

To keep with the admittedly strained image, but bear with me within this safe space: why even imagine firm objects behind the blur? What if the fog keeps thickening, and between us and the business reality we’re trying to map, we have an immense conceptual gap, an abyss? Moreover we also make it so, we move the lens, we pick the feature and metric to observe, we send a signal to this shared business reality, creating chunks of it on the fly ours to own. For the rest, for what our strategy actually does when enacted, we might as well imagine an AI process that keeps hurling events in our path following its own free-like, as-good-as-free, will. A worthy partner, finally, capable of uncertainties wilier than our lack of knowledge or error of measurement, but original, improvisational, deadly moves.

So it’s not just future outcomes. Everything we chart or map is already drenched in uncertainty: the historical data, the tech tools, our products, today’s business environment. It is also an uncertainty of not-knowing (among other kinds): we don’t know how long the game has been playing, or even which games we’re in, or the other players, or even who’s on our team and who or what or when, against us (they don’t either, there’s no privileged position though some teams do sit on more solid ground). We don’t even know what constitutes a “move” — whatever we interpreted or misinterpreted, business reality always enacts itself before and in front of data. We do stare hypnotized at the multi-view live data streaming, and squeeze that last microsecond out of the fiberoptic and parallelized GPU farms. It comforts us and terrorizes us, all for naught. Across the gap, we get no compromise, no agreement, no points, no averaging, no merit, no negotiation.

Uncertainty is our best tool for relevance, it’s where the rubber meets the road, where things matter, in creating value in the common business reality we all share and struggle with. And a dangerous fetish: visualizations gel into a scenography populated by our own myths, our own laws for Reality to follow. (A shoutout here to every business improvement book and consultancy out there, including your favorites, yes the ones where AI saves us from ourselves, and mine, where it doesn’t.)

Yet these visualizations, and especially the mathematical ones around probability distributions — probability density functions, cumulative functions, survival functions, stochastic processes — are also a rare exact toolset for grounding and making data displays relevant, a solid toolset handy for poking and ferreting in the dark. There’s a risk in attaching a distribution theory to the data, a bluster in claiming that concession and digging.

We’re at such a handicap, the blur is so pervasive, that every ratty map helps, every little bit of direction we get from that mathematics on the chalkboard, every simulation that crashed our farm. Even with those sharpest and most solid of tools in hand, actually extending our mathematical display clear across the gap seems impossible.

Indeed how do we say something we don’t know, about a business object we sort of do? More precisely (and confusingly), how do we describe (and with metrics!) how we don’t know that something; because that’s exactly what we try with our probability distribution display: like trying to see the back of your head, or trying to catch yourself unawares in a reflection.

We’ve all done this when faced with an audience, caught by a question — we keep elaborating on what we do know, empirical data, sensor data, historical data, transactional data, survey data, organizational data, institutional data… we keep spraying data until it draws out the contour of the answer. We list all the ways in which we don’t know; we list what our teams have tried. Most of all, we keep relying on theory, even while talking about business measures: these here are mathematical facts, here are the distributions and limit theorems, convergence, semi-random processes, here’s what the back propagation reveals about the loss function.

Maps of this world on this side of the gap — the probability density function, the survival function — allow us to speak of places in that world over yonder: the tails of the probability density function, the inflection point on the survival function, the rate of convergence, the direction of convergence, are as many toponyms. And to orient ourselves standing on the edge, looking over the gap at an epic battle where our business destiny is being decided, and trying to make sense of these blurry pics.

In my mental garage of data tinkering with shiny tools, I imagine rendering uncertainty as first-order: I am unaware (and I’d like to be fact-checked in the comments) of such visualizations or conceptualizations, ones that treat uncertainty as on par with data. I envision them used in a business model exploratory context, or as a tool for that last millioompf of delta in business performance, in the vein of interactive and looping simulations, VR style. We’d interface by changing the angle of the gaze, taking virtual steps. Or even better, act in that virtual world, supplying a carrier signal or acting in continuous mode, and as we repeat our actions the visual (audified, hapticized) effect of the looping action is modulated by the parametrized probability distribution. The looping simulation samples data on the fly, maybe with different modes, cumulatively vs. an evolving snapshot. In this representation we’re looking at (hearing and touching) the uncertainty itself. With repeated action participants would presumably develop a neurally based sense for uncertainty, training an ability or craft of “diving through uncertainty”, climbing, digging, mining. It would be interesting to play with detaching sampling time from in-world time here, with reversibility and asymmetry.

Audification you say? mapping to pitch is so last year… It would be interesting to map to timbre, say, map moments in the probability distribution to Fourier coefficients and modulate the immersive sound, operating the stops and drawbars for the exact nuance of the bourdon pipes.

A VR like that might work well: display uncertainty not as a marginal property leading the eye to some more important object, but dead center, first-order, structural, equal (we can even understand it as orthogonal or dual to data). In this view, what we call uncertainty would be the lens we’re looking with, and the various data — the invented history, the imagined future — are how we move the lens, on this side, the mathematized, theory-laden side of the gap. Where we see uncertainty projected onto the lens, but we don’t extend past the tool, into the gap, we stop right there, eye on the lens, forehead locked tightly into the VR glasses, so that blurry and smudgy impression is the best we get, and a technical and mathematical marvel: when we know where that edge is, when we’ve mapped the contour of uncertainty, we can stake out that domain right along the edge.

Let me push the image a little: that data edge does have a contour, the data horizon has a curve. The world across the gap is where our businesses live and die along the irreversible river of time, with these towering thresholds like ancient sequoias looming over our fate, and it is where everything that matters, matters. We’re on this side though with our panoply of data and tools, a growing treasure trove of data and a mixed bag of tools of various power and range. We seem to be facing something akin to a hard law that ties data tools and the maps they produce to Normality

The power of data tools to map across the gap is inverse to their Normality

with normality understood again in the loosest of senses — where randomness is a variation from error that decreases with data volume, linear approximations do approximate, moments are finite, processes converge fast, estimators are robust. In that light, our processing of data is all a type of mining (even the microsecond of this very moment’s transactional data), all our reading of data is a prediction (even of old warehouse data). It means that with the fantastic tools we have for normality, we can mine very well and deep that narrow strip along the edge, as long as we drop tall tales of prospecting far and wide; it’s that gold and those tools that are the daily sustenance. And it holds the immense promise that working on tools away from normality (non-linear, extremal, diverging, with estimators that are very slow) will help us navigate the uncharted provinces far beyond that gap.