Take three snapshots of a share’s price chart around a results announcement. The first is the moment a report far ahead of expectations lands, before the market has processed it. The news exists, but the price still reflects the old information. The second spans the weeks that follow. The price jumps at the open without finishing the job. The shares keep travelling with the surprise as estimates and slower investors catch up. The third is a year later: the surprise is ancient, its implications priced, and the chart wanders on no news.
Ask in which snapshot the price itself holds a pattern an active investor can trade. Not the first: the opportunity there is in reading the report, before any pattern has reached the price. Not the third: whatever was knowable has been incorporated. Only the middle holds a pattern, and only in passing. The pattern is the price absorbing the news, and absorption ends.
What kind of problem is this?
It looks like a fact about one anomaly. The shape underneath is more general. There are two instincts about where opportunity lives. One prizes the finished end: the fully efficient market, where randomness is the sign of a job well done. The other prizes the untouched end: the report that has landed and not yet been read. The three snapshots show that both miss the same thing. The pattern peaks in the middle. Saying anything precise about that needs a way to measure structure. The disciplines that have thought hardest about that measurement are algorithmic information theory and the physics of complexity.
So let’s borrow.
This is the multi-model move: recognise the shape of a problem, find the discipline that has thought rigorously about that shape, and import its frameworks deliberately rather than reinventing them from scratch.
The lens we are borrowing is called apparent complexity. The physicist Sean Carroll built it with Scott Aaronson and Lauren Ouellette. It puts a number on how interesting a system looks: the structure it shows at the scale an observer sees. The recipe has two steps: blur the picture, then measure how hard the remainder is to describe.
The Static And The Swirl
Carroll’s demonstration is a thought experiment that repeats the three snapshots. Photograph a cup of coffee at three moments. First, the cream sits in an untouched layer on the black coffee. Half a minute after the spoon, the cup is a tangle of pale tendrils and dark channels. A few minutes later, it is a uniform light brown. Suppose the three photographs are idealised: same resolution, same format, no camera noise. Compare their file sizes. The first and third compress readily. Compression exploits repetition, and those photographs are mostly uniform regions with short descriptions. The middle file resists. Every tendril differs from its neighbours, so every part of the picture needs its own description.
The measuring stick comes from the Russian mathematician Andrey Kolmogorov, who had already given probability its modern axioms. In 1965 his paper gave the definition: an object’s complexity is the length of the shortest program that produces it. A string of a billion zeros is enormous but simple: “print zero a billion times” generates it in a line. A string of a billion random digits admits no such shortcut. The shortest program is no shorter than the string itself. File size is a working stand-in, because compression hunts for exactly those shortcuts.
The blur is there because of what happens without it. By Kolmogorov’s count, the random string is the most complex thing there is. To any observer it is just noise. Zoom in far enough and every cup is that string: at molecular grain, all three photographs are static. So blur the image first, averaging away the molecular detail. Then compress what remains and read the file size. Random static now blurs to uniform grey and compresses away. The layered cup and the blended cup stay short, as before. Only the half-mixed cup resists, because its tendrils survive the blur. The measure now agrees with the eye: structure scores high, while order and noise score low.
Three photographs are only three points. Build a simulation of the cup and let it mix, and you will see the whole curve. Entropy, the physicist’s measure of disorder, rises from start to finish. Apparent complexity climbs as the tendrils form, peaks around the middle, and falls back as the cup blends. Disorder only accumulates; structure rises and dies.
Before leaving the cup, take two properties of the measure with you. First, the measure reads the present, not the peak. Nothing in that moment says it is the top of the arc. Settling that takes a model of what remains, or the rest of the run. Second, the answer depends on the blur. A different coarse-graining gives a different complexity, and there is no blur-free view.
The Blended Market
In 1965, the same year as Kolmogorov’s paper, Paul Samuelson proved that properly anticipated prices fluctuate randomly. Within his model, earlier price changes carry no forecast of the next one. Anything they did forecast would already have been traded into the price. Once a piece of information has been absorbed, its price trace offers no shortcut to the moves that remain. To the trader, that resembles incompressibility, though the mathematics differ. For everything already known, the textbook efficient market is the fully blended cup. The third snapshot photographed it.
The first snapshot was the unmixed layer: the filing nobody has read, the asset nobody has repriced. The middle snapshot is the canonical tendril, the post-earnings announcement drift. Ray Ball and Philip Brown first observed it in 1968. Studies since have measured it over subsequent months. The news is public and the price is still travelling.
Other tendrils trace the same arc, each for its own reason. Momentum lasts while incorporation is slow. A valuation spread lasts while capital is constrained. A merger spread lasts until the deal’s uncertainty resolves. The cup lends the arc, not the number. Apparent complexity measures description length, and a profitable pattern can score low on it. The value is alpha: the extra return a structure pays, measured against a benchmark and adjusted for risk. Only what survives implementation costs is investable.
Individual tendrils get exhausted, yet the market as a whole never finishes blending. Part of the reason is fresh cream: news and flows keep pouring in. The deeper reason came from Sanford Grossman and Joseph Stiglitz in 1980. In their model, information costs money to acquire. If prices fully revealed what the informed had paid to learn, nobody would pay to learn it. Then prices would reveal nothing. So a perfectly efficient market is impossible on its own terms. Markets settle instead at what they called an equilibrium degree of disequilibrium. The name is paradoxical, but it describes an equilibrium. The cup must stay partly unmixed to pay for its own stirring. The investors who pay to be informed are the spoon.
The spoon erases mispricing. Where a tendril is mispriced and tradeable at scale, each position against it chips away the return it promises. In the cup’s terms, trading shortens the description of the opportunity, not of the price series itself. Crowding can even swell a tendril before smoothing it. This is why any backtest shows patterns as they stood before you arrived. And no present moment certifies that an edge has peaked. You learn where it was by watching the returns fade, with capital already committed.
Living In The Middle
The blur is the deeper of the two properties, because in a market the blur is yours to choose. Every description of a market blurs it. A factor model does. So do a sector label, a monthly return, a price chart. And what you can see depends on the blur you chose. A £100 million position unwinding through a thin book leaves a wake that lasts minutes. In quarterly data it does not exist. A slow rotation between regimes takes decades. On a trading screen it never shows. When two investors argue about whether a market is efficient, they are often describing it at different blurs.
The choice of blur carries two hazards. The first is invention: a blur can add structure that was never in the process. The Trend The Gaps Invent showed how assets observed too rarely arrive pre-smoothed. The simulation of the cup gave the same warning. The builders’ first blur put a complexity hump into a control cup where nothing interacted. They had to replace it. The second hazard is luck: genuine noise sometimes compresses by chance. The standard is survival out of sample.
Three implications follow. First, budget for the fade. Each tendril’s return should diminish as its cause is used up, and your own trading is part of the using. A strategy that keeps finding new tendrils need not fade with any one of them. Second, search where the mixing is. Structure concentrates where information or flow is in transit: new instruments finding their clientele, forced sellers, calendar flows. It thins towards the most watched corners of any market once costs are counted. Third, audit the blur. Why One Model Is Never Enough argued for holding many models. The same case holds for resolutions.
The Mixing Question
The pattern the mixing makes, then, is one kind of structure the market can pay an active investor to find. Where the structure is a mispricing, trading it helps finish the job.
The same arc turns up beyond markets, though as a rule of thumb rather than a law. A scientific field is most fertile after the founding insight and before the textbooks close it. A technology yields its richest variety between invention and standardisation. An organisation is most adaptable between the garage and the procedure manual.
Knowing the arc does not place you outside it, because every trade against a tendril is part of the blending. An edge made by the mixing is a wasting asset. The question is never whether it will be smoothed away, only how much of the smoothing you are paid for.
The discipline is in asking: not whether a pattern exists, but where in its arc you have met it, at what resolution it is visible, and what your own use of it will do to what remains?
References & Further Reading
Three Approaches to the Quantitative Definition of Information: Andrey Kolmogorov
Quantifying the Rise and Fall of Complexity in Closed Systems: The Coffee Automaton: Scott Aaronson, Sean M. Carroll & Lauren Ouellette
The Big Picture: On the Origins of Life, Meaning, and the Universe Itself: Sean Carroll
Proof That Properly Anticipated Prices Fluctuate Randomly: Paul Samuelson
An Empirical Evaluation of Accounting Income Numbers: Ray Ball & Philip Brown
On the Impossibility of Informationally Efficient Markets: Sanford Grossman & Joseph Stiglitz