Last Night's TV: My Resignation/BBC4<br />The Code/BBC2

René Girard knew better than most what made Christianity Christian. Primitive societies, he argued, are overcome by "mimetic desire". Rivals within any group are driven by a fierce competitive instinct to do the other down, and own what he owns. The solution is to identify a potential victim, the vanquishing of whom temporarily restores peace and civility. In Roger Scruton's unbeatable analysis, "scapegoating is society's way of recreating 'difference' and so restoring itself. By uniting against the scapegoat, people are released from their rivalries and reconciled."

Girard argued in his study of scapegoating, Le Bouc Émissaire (1982), that Jesus of Nazareth was a visionary who understood mimetic desire uniquely well. He offered himself as a scapegoat for this mimetic desire, but in granting his killers forgiveness before he died – "Father, forgive them, for they know not what they do" – he emancipates society from the vicious cycle of vengeance from which it is trapped. At least that is the idea. As Scruton puts it: "The climax... is not the death of the scapegoat but the experience of sacred awe, as the victim, at the moment of death, forgives his tormentors. This is the moment of transcendence."

All public resignations are a replay of the Passion. Every time politicians or the press squeal about the need for such and such person to resign, they are answering our primordial yearning for mimetic desire. There is a need to vanquish, to defeat, to conquer the wrongdoer – and so assert justice and begin the process of moral renewal.

The trouble is, it often does more harm than good. That was the chief insight of My Resignation – most public resignations are futile. Usually, they answer short-term demands and create long-term regrets. There is constant chatter about the need to "take responsibility", "show leadership", or "restore honour" and "integrity". When I hear such talk I reach for the bucket.

Why should John Profumo have resigned for liaising with an attractive whore? Why should Greg Dyke resign for being the victim of a whitewashed report from the Establishment? Why should Jacqui Smith resign because of her husband's fondness for porn? In all cases, there was a public pretence that the relevant figure behaved immorally. The accusation was bunkum. Mimetic desire took over. Profumo might have been a hypocrite, but, as his later career proved, he was an outstanding public servant. Dyke was a superb director general of the BBC. Smith was a competent and respected home secretary.

This, then, is another feature of resignations: they often conflate the public and the private. A sin behind closed doors can lead to a withdrawal from public life. And usually those resigning do so at the time when they least ought to. Tempers are frayed, emotions are high, and rationality and reason are relegated to the hinterland of all discussion. Momentous decisions are made just when no decisions should be made.

What's more, there is a certain hypocrisy about resignations. It is instructive to compare leadership with management. Management is déjà vu (seen this before). Leadership is vu jàdé (never seen this before). The former involves engaging a well-known response – a standard operating procedure (SOP) – to a familiar, or tame, problem. The latter involves constructing a novel response to an unfamiliar, or wicked, problem.

We spend our lives demanding leadership from public figures. The minute they transgress a silly, tabloid morality (Profumo, Smith), or fall to an Establishment stooge (Dyke) we allow them to avoid the demands of leadership, and engage the simplest SOP of all – resignation. Perhaps mimetic desire is overwhelming, or irrepressible. But we should have the courage to challenge it, if only because those featured in this show so obviously wish they had.

The demands of the public understanding of science on one hand, and televisual narrative on the other, are sometimes in conflict. Professor Marcus du Sautoy traverses both magnificently in The Code, and is in danger of becoming our finest explainer of scientific wonder. Previous claimants on that title – Robert Winston, Richard Dawkins – found that such a position led to opprobrium from tabloid journalists and religious fanatics.

I therefore have two suggestions for this noble professor. First, abandon the upturned collar. Second, wear slim-fit rather than skinny jeans. The last thing you want to do is compound the coming interrogation by looking like you spend Saturdays in London's Hoxton Square.