Before she became Chancellor 16 years ago, Merkel was easy to underestimate. A timid, diffident, divorced, Protestant quantum physicist from East Germany seemed a quite unlikely successor as Chancellor to a cunning, reforming social democrat (Gerhard Schroeder) or as party leader to the renowned national unifier, Helmut Kohl. Both Kohl and Schroeder underestimated Merkel, as did, as her term in office extended, plenty of now-forgotten rivals such as Stoiber, Koch, Merz, Wuff, Ruetgers, Schulz and Steinmeier.

At the start of her career (as Minister for Women and Youth, then Environment), Merkel might have seemed to embody a few of Germans' stereotypical flaws. Like Blair before her and Obama after, she had held none of the great offices of stat before leading her country. Merkel was stolid, earnest, narrow, didactic and boring,

She ruled a country with only a borrow word for "flexible", one so punctiliously observant of rules that I was once berated at three in the morning for not thinking of children while crossing the street against a red light. "Denken an die Kinder!" All the children were safely tucked up, all the traffic had disappeared, but the principle of setting and sticking by an example still held.

Then came the financial crisis, brinksmanship over Greece's place in the Eurozone, the Russian invasion of Crimea, absorption of a million refugees within a year, Brexit, dealing with Trump and coping with a pandemic. The last leader left standing from 2005 (leaving Putin aside) then epitomised characteristic German virtues.

Merkel proved methodical, logical and rational. She listened to experts, mastered her briefs, checked, cross-referenced, consulted and kept on learning. "I'm no good at drifting", as Merkel once confessed. She was still studying her briefing notes when Scott Morrison arrived for a talk.

In happy contrast to his predecessor, Joe Biden declared recently that he "was hired to solve problems". Such a pragmatic, thoughtful, determined approach has typified Merkel's years as Chancellor. Francois Mitterrand first won office in France by insisting that he stood for "la force tranquille". Calm, measured exercise of power better suits Merkel than it did Mitterrand. "Wir schaffen das", "we will cope with this", remains her alternative, easy-to-underestimate, slogan. Quantum physics has taught her that "there is no depth without mass".

Critically, Merkel has emerged from a country in ruins, not Germany as we know the Federal Republic but the GDR. After reunification, a senior German official told me that the FRG government had diligently attempted to find something, anything at all, in East Germany which could be adopted and applied nation-wide in the new Germany.

Kindergartens had been one option, worker involvement in firm management another. Both were frauds. Neither could be made to work. The East German system was based on little more than lies, deceit, coercion and spying. Its collapse was as quick and complete as France's in June 1940, a catastrophe from which the French have not yet quite recovered.

A sceptic might argue that much of all German history, West or East, is unfit for purpose - rightly discredited, shunned, reviled. The German Finance Ministry, the great motor of modern German State power, used to house Hitler's Luftwaffe, with its Messerschmitts and Stukas essential drivers of Nazi power. In addition, the corner where the building stands was the site where the 1951 rebellion in East Germany was brutally suppressed. How, Finance Ministry staff would ask me, could all that tortured, layered history be fairly represented and integrated?

Adopting a different angle of view, consider recent German history through Germany's best films. You move through weirdly bleak modernism (The Cabinet of Dr. Caligari, 1920) to stunningly wicked gloating (Triumph of the Will, 1935). Then comes a bizarrely popular single-note comedy (Dinner for One, 1963), gritty realism (Das Boot, 1981), horrific megalomania (Downfall, 2004) and a grim, graphic story of betrayal which Merkel hands out to colleagues (The Lives of Others, 2006).

In the indices of political leadership, Merkel has nonetheless left some qualities out. Famously she has removed any hint of sex, fashion or style in her chillingly ordinary haircut and predictable clothes. More importantly, flair and grace have gone missing. An orderly, logical expert might morph into a know-all, disposed to interfere in others' business, falsely assuming that all problems can be treated rationally. I was once treated to an afternoon's monologue from a road traffic engineer turned politician, who explained issues coherently and cogently but with an entirely spurious frame of reference. That was former president Ahmadinejad of Iran. While Merkel is altogether different, statistics, and graphs, models and diagrams can only take a leader so far.

Leadership may also require a cardinal Merkel virtue, "Fingerspitzegefuehl", the sense of intuition, judgment and timing which you can feel in the tips of your fingers. "Dexterity" is too meagre a translation for that repertoire of skills. Those talents are not necessarily synonymous with those associated with women leaders (not Thatcher or Meir), qualities like empathy, compassion and consideration.

Modern Germany has elected only eight chancellors. Although a couple (Kohl and Willy Brandt) are more celebrated than Merkel, neither heeded sufficiently the rule that political careers end badly. Remarkably, Merkel leaves on her own terms, in her own time.