Carl Størmer

Carl Størmer: The Man Who Triangulated the Northern Lights

In the 1890s a student walked the streets of Kristiania with a camera concealed under his coat, photographing strangers who had no idea they were being observed. The pictures survive, and they are startling — among the first genuinely candid images of urban life, faces caught with none of the composure a Victorian sitter would have arranged. The photographer was Carl Størmer, and the instinct on display would define his career: point an instrument at something that will not hold still, and catch it anyway. He would spend the next fifty years doing it to the aurora borealis.

Skien, and a Boy Who Changed His Mind

Størmer was born in Skien in 1874 into a pharmacist's family. In 1886 his parents moved to Kristiania — now Oslo — specifically to secure him a better education, a piece of ambition that paid off comprehensively. His early enthusiasms were botany and astronomy. At around sixteen the interest swung hard and permanently to pure mathematics, and he never left it.

He took his candidate's degree in 1898 and then went to Paris, studying at the Sorbonne under Henri Poincaré and Émile Picard — an apprenticeship at the absolute centre of European mathematics, and one that mattered enormously for what followed. Poincaré's obsession was the behaviour of trajectories in dynamical systems that could not be solved in closed form. Størmer's life work would be exactly such a problem.

Pure Numbers

His first reputation was as a number theorist, and he published prolifically — on Pell's equation, and on rapidly converging series for π of the Machin type, the kind of identity that lets a computer extract digits efficiently and that in his own era let a patient human being do the same by hand. In 1903, aged twenty-nine, he was appointed Professor of Pure Mathematics at the University of Kristiania. He held the chair for forty-three years, until 1946.

Birkeland's Question

The turn came from a colleague. In 1896 the physicist Kristian Birkeland had run laboratory experiments firing charged particles at a magnetised sphere, producing glowing patterns near its poles that looked unmistakably like miniature auroras. Birkeland's hypothesis — that the northern lights are caused by charged particles from space steered into the polar regions by Earth's magnetic field — was correct, contested, and mathematically beyond him. He asked Størmer for help.

Størmer gave him decades. The task was to compute the trajectory of a charged particle moving through the field of a magnetic dipole — a problem with no general closed-form solution, requiring laborious step-by-step numerical integration, done by hand, half a century before there were machines to do it. He published at least forty-eight papers on it. The work established which particles reach the Earth and where, mapped the forbidden and allowed regions of the field, and produced the theoretical apparatus later used to understand cosmic ray access and the trapped radiation belts. The whole class of problem still carries his name.

Photographing the Aurora

Theory was half of it. From 1909 Størmer began systematically photographing the aurora, and here his teenage hobby and his professional mathematics collided to spectacular effect. "What may result," he wrote, "when a pure mathematician happens to be an enthusiastic amateur photographer."

The existing photographs of the aurora were blurred and useless for measurement; exposures were too long for a phenomenon that moves. Størmer solved the optics by fitting a small, fast lens taken from a children's film camera made by the German manufacturer Ernemann. The improvement was decisive enough that some three hundred cameras built to his design were eventually distributed to researchers around the world.

Then he industrialised the observation. He set up networks of stations across Norway, separated by at least five kilometres, linked by telephone. When an aurora appeared, observers at different stations were told to photograph the same display at the same instant, each frame also capturing fixed background stars. With two images of the same object from a known baseline against a known stellar reference, the height of the aurora becomes a problem in plane trigonometry — parallax, the oldest trick in astronomy, applied for the first time with rigour to something previously measured only by guesswork.

What the Cameras Found

The answer was that the aurora is far higher than most nineteenth-century observers had assumed and remarkably consistent: its lower border averages a little over 100 kilometres above the surface. The full range ran from about 71 kilometres up to 1,000 kilometres for sunlit auroras, high enough to be catching sunlight while the ground below was in darkness.

Those numbers were not a curiosity. They were the empirical test of Birkeland's theory and of Størmer's own trajectory calculations, pinning the phenomenon to a specific layer of the upper atmosphere and constraining any physical account of it. Størmer's photographs fed an aurora atlas circulated during the second International Polar Year of 1932–33 to collaborators in Canada, the United States, Britain and the Netherlands. He kept photographing until he died in 1957. Most of the images are lost; the Norwegian Museum of Science and Technology preserves several hundred.

Why Carl Is Called a Genius

Størmer's distinction is that he was equally formidable at two things that almost never occur in the same person: hand computation of intractable dynamics, and the design of a working observational system. The trajectory calculations were an act of sheer mathematical endurance — numerical integration of a nonlinear problem, performed manually, sustained across forty-eight papers and several decades, at a level of care where a single arithmetic slip invalidates everything downstream. The aurora network was an act of engineering and organisation: a lens scavenged from a toy, a telephone system, a baseline, and a trigonometric identity, combined into an instrument that could measure the sky. The honours reflected it — the Fridtjof Nansen Prize, election to the Royal Society, honorary degrees from Oxford, Copenhagen and the Sorbonne, and the presidency of the International Congress of Mathematicians when it met in Oslo in 1936.

The counter-case deserves stating plainly. The physical insight was Birkeland's, not Størmer's; Birkeland posed the question and supplied the theory, and Størmer came in as the mathematician who could execute it. Størmer never produced a general analytic solution to the dipole trajectory problem, because there is not one — his results are numerical and particular. His number theory is respectable rather than revolutionary. And a good deal of the aurora achievement is craft rather than intellect: choosing the right lens, siting the stations, drilling the observers, keeping the telephone logs straight, repeating the exercise across decades of Norwegian winters. That is patience and organisational skill of an exceptional order, and it should be described as such rather than dressed up as insight. What ties the two halves together — and what does look like genius — is the judgement to see that a phenomenon everyone treated as a spectacle was in fact a measurable object, and to know precisely which measurement would settle the question.

Legacy

Størmer died in 1957, the year the International Geophysical Year began and the year Sputnik went up — the moment the upper atmosphere he had spent his life triangulating from the ground became somewhere instruments could actually be sent. The radiation belts discovered the following year were populated by exactly the trapped particles his equations described. Modern space-weather physics, which forecasts the geomagnetic storms that threaten satellites and power grids, rests on the trajectory theory he built by hand for a colleague who needed a mathematician.

Achievements

• Foreign Member of the Royal Society — 1951
• Notable work: Størmer number
• Notable work: Størmer's theorem
• Held posts at University of Oslo
• Educated at University of Göttingen, University of Oslo and University of Paris
• Fields of research: astrophysics, aurora, discoveries and inventions and geophysics