There is a bill being considered by the House of Lords right now to pardon Alan Turing, the computer genius and war hero who was convicted of gross indecency in the 1950s over his relationship with another man.

But what would such a pardon mean? What would such a bill, now in the committee stage in the Lords, achieve? It can't change the course of Turing's life – we will have to wait for another genius to invent time travel to achieve that. It can't change the course of gay rights. And it can't change the fact that thousands of gay men – who are not being offered a pardon incidentally – were convicted and punished of something which is no longer a crime. These are the realities of history and they are more important than the meaningless magic trick of a posthumous pardon.

So why is the Government supporting the idea of a pardon for Turing, who was famously part of the team that cracked the Nazis' Enigma messages? Probably because pardons are a way of being seen to do the right thing with little effort or cost. It is a way of wiping away a troublesome matter, like ink off a whiteboard, in the way the Labour Government did in 2006 when it pardoned 306 British soldiers shot for desertion and other offences during the First World War. That pardon was awarded no matter what the offence, and the evidence was not re-examined, which is a extraordinary way to behave when you think about it. We would never put 306 men on trial at the same time, so why on earth would we pardon them in such a way?

More importantly, a posthumous pardon cannot adjust the facts of the past. Should we, for example, pardon everyone ever executed by the British state because we now realise the barbarism of capital punishment? The truth is many hundreds of men were convicted of desertion during the First World War even though they were probably suffering from shell shock or other trauma. It is wrong by modern standards but it is the reality of what happened 100 years ago and we should not attempt to expunge this or pardon it away; we should accept it and let it remain as a historical fact, to shock us, remind us and change us.

Exactly the same situation applies to the Turing case. In the 150 years or so that homosexuality was illegal in the UK some 50,000 men were convicted under the law (homosexuality was not decriminalised in Scotland until Margaret Thatcher's Government acted in 1980). In Turing's case, his conviction led to him choosing chemical castration over imprisonment, which in turn is likely to have led to his suicide in 1954. Many other men in the same situation faced blackmail, the end of their careers and, in some cases, the end of their lives. It's only by acknowledging all of this that we can appreciate the advances made in gay rights in recent years. Put another way: we can only be proud of where we are by looking at where we came from: a world where Turing, the man credited with shortening the war by two years, was a criminal; a world where 50,000 men were convicted for being gay.

The reality of those 50,000 convictions is not a reason for pardoning Turing though; in fact, the convictions are critical in the case against a pardon. Why should we pardon Turing and not the others? Turing was a polymath and a genius, but none of that entitles him to a pardon over the other men convicted of gross indecency. Those other men may not have been geniuses but they took the same risks as Turing in breaking the law and suffered the same punishments; many of them were just as willing as Turing to stand in the dock and refuse to deny they were in a relationship with another man. And don't think you can solve this problem by offering a blanket pardon to all 50,000 – could there, for example, be some cases among the 50,000 in which the sex was not consensual?

A better solution than pardons is to accept the inequities of the past and mark Turing's contribution to science and the war effort in other ways. There's a new film coming with Benedict Cumberbatch as Turing, for example, which will help to take the story to new audiences. But more importantly the codebreaking centre Bletchley Park is being restored. In years to come, it will be the place to go to see the rooms where Turing worked. It will be the place to go to think about what Turing did for us and what we did to Turing.