retrospective forecast

In a hall of mirrors, a person walks up to a curved mirror and sees themselves now as a dwarf, now as a giant. Popular machine learning models behave in much the same way when asked to guess biological age from blood tests or brain scans: they stretch age at the extremes, underestimating it in older people and overestimating it in younger ones.

A Greenland shark swims through cold water in its fourth century, and with every passing year its odds of dying do not rise but fall. This is not a miracle, but the result of an evolutionary trade-off that has so far eluded theory. An organism is like a family budget that cannot be spent twice: every unit of energy can go into reproduction, growth, or body repair.

The brain doesn't just react to the world: it's constantly guessing what will happen next. This principle is called predictive coding: neurons compare expectations with reality and update their internal picture when an error occurs. But how such a complex system could be wired into the living tissue of the cortex remained unclear.

An experienced detective doesn't calculate a criminal's path using the laws of physics: he checks a file of similar cases. The new prediction method works the same way: instead of complex equations, it has a vast archive of trajectories that have already happened — planetary motions, currency exchange rates, signals from space.

At a weather station in Brazos County, Texas, rain is recorded on magnetic tape: every day, four years straight. Nine hundred millimeters in a good season, a hundred in a bad one. Then the tape falls silent. Drought creeps in without a sound — the slow fading of the earth's pulse. The standard SPI-3 index only catches on a month or two later, once the moisture is already gone.

A mosaic of large colored tiles. Each tile is the average precipitation over an entire month for an area the size of a small country. For a general understanding, the picture is fine, but if you need to know whether a downpour hit a specific city yesterday, it's useless.

Every spring, El Niño forecasts lose their edge, like a translator who gets distracted by every rustle in the room and turns a one-hour meeting into a two-hour one. Scientists call this the spring predictability barrier: in March and April, models that confidently predicted a warm phase in the Pacific back in January start making mistakes twice as often.

In the lab, time usually ticks on the wall: hands, digits, a frequency standard. But for the Universe, there are no external clocks. The Wheeler–DeWitt equation, the main law of quantum gravity, contains no time at all, and all fundamental theories lack an inbuilt arrow of time.

Climate scientists have long debated where exactly the El Niño "pool" is located: the region in the equatorial Pacific that first responds to an impending weather shift. The debate isn't due to a lack of data. The ocean is measured along longitude, latitude, and depth, and each slice contains thousands of numbers. The problem is that there are too many numbers to see the pattern directly.

In the hall, fifty sages confer, each observing the ocean in their own way. One listens to surface temperature, another to the wind, a third to how heat hides in the depths. Their judgments often contradict each other, but there is an elder who knows which of them to trust more.

An interpreter at negotiations hears only the words already spoken, yet still guesses the next phrase. This is how the new El Niño forecasting method works: it doesn't peek into the future but relies solely on the past, like an honest listener.

An orchestra without a conductor: the musicians take their seats, tune their instruments, and begin to play in harmony because each one hears the common rhythm. That is how TreeDOX works, a method that predicts chaotic time series without requiring the user to choose parameters or fine-tune anything.

A rough sketch of a portrait: a few confident lines define the shape, but the details are not yet refined. That is how a parametric model, such as vector autoregression (VAR), describes a time series: it captures the main structure, but if the real data deviate from its assumptions, the portrait comes out distorted.

Imagine an interpreter who gets distracted by every rustle in the hall. The more rustles, the more errors in the translation, even though the meaning of the speech hasn't changed. The same happens with data: if measurements are unevenly spaced, standard analytical tools start "hearing" changes that never occurred in the underlying process.

The ice cover of a river looks solid, but beneath it lie cracks that alter the flow. So it is with a time series: behind the smooth surface of numbers hide moments when the rules of the game change. These moments are called change points, and finding them is like tapping the ice to locate weak spots.