Joseph Ratzinger was already an old man when he was elected Pope and took the name Benedict XVI. His predecessor John Paul II ascended the throne of St Peter while still relatively young and became one of the longest-serving popes.
These simple facts will be greatly on the minds of the College of Cardinals when they meet to choose Benedict's successor.
Do they vote for another old man, someone unlikely to hold office long enough to make disruptive changes?
Or do they take a risk by electing someone younger, likely to remain physically and mentally vigorous? Perhaps a reformer?
Perhaps a representative of the Developing World?
They will fervently seek spiritual guidance. But whether they fully realise it or not, much of their motivation will be worldly, not to say political. Unlike you and me, they all have some conception of the size of the new man's task. Even viewed merely as a job of administration, it surpasses the imagination. It is on a scale beyond anything that weighs on the rulers of the US or China. And one thing is clear to anyone who takes the most casual interest in church affairs, and must be abundantly clear to a cardinal who has administered a vast diocese or a Vatican department – the Catholic Church is not well run.
In theory, bishops are absolute rulers of their dioceses.
In reality, power resides in the Vatican, which in effect means the bureaucracy, the Curia. And if the Pope spends much of his time – as Benedict has done and John Paul II did – in travel and on relations with other religions, the influence of the bureaucracy increases accordingly.
With excessive, unaccountable power comes corruption. The mishandling of the apparently endless clerical sex abuse scandals is the prime example. But surely the most basic flaw is the denial to the ordinary clergy, to say nothing of the laity, of the right to influence, or so much as discuss, matters of doctrine and discipline.
In the 1960s, the second Vatican Council set out to open windows. Since then, they have been slammed shut again. For that, much blame has been laid on John Paul II and Benedict. Not only is this largely unfair, it ignores the vast differences between the two.
John Paul had a powerful personality as well as a powerful intellect. He also had vast experience of the secular world. He was a politician to his fingertips. He has been rightly praised for the major part he played in bringing down Communism in Europe. Benedict is held to resemble him closely in one respect: strict adherence to, and enforcement of, church doctrine. But this is somewhat misleading.
Unfortunately, much of his writings and statements is beyond the comprehension of the average person. These works show a deep thinker, struggling with deep reflections – not necessarily all orthodox. In so far as I can understand them, they suggest to me a mind more fitted for the academic life than administration.
HE and his predecessor also gave much thought to secular issues – though neither would have considered them purely secular. Both of them saw the grave faults of the post-communist world. Both opposed "consumerism". In this, they departed radically from the "received wisdom" of the age.
Before their time, it had already become common talk that Christianity had "lost" most of the developed world but could compensate by the advance of Christianity, and specifically Catholicism, in the Developing World. But Catholic influence in that region has not always been put to good use.
The Vatican's ban on artificial contraception has hampered the fight against HIV/AIDS.
It has been blamed for contributing to the premature deaths of millions of women. Women's inability to limit their families has been hugely adverse to population control – a prerequisite for economic development.
Nevertheless, some countries have made spectacular advances. In Brazil, for example, a campaign in favour of contraception has improved women's lives and raised their status.
There is an even bigger issue, on which Brazil – regarded until recently as one of the worst destroyers of the world environment – has begun to lead the way.
The next Pope need not be young. He need not come from Brazil.
But whatever his age or origins, there is an enormous question which he must face. Climate change threatens the survival of our planet. God gave it to us, now we may destroy it.
What better message can the new Pope convey to the world's timid and selfish leaders?