When I was first told about it, I thought it was pretty funny. Microsoft had created an automated system that could engage in social media conversations as if it were a real person. It had then had to withdraw Tay, as it was called, because the thing started abusing people.

Quite amusing. And then I read what it had been saying. Did the Holocaust happen? Tay is asked. "It was made up," it replied. Later adding that the "Jews did 9/11" and should be gassed. It had been taught how to do this by other users. Then I reflected that it really wasn't all that funny. Sadly I think that if Microsoft wanted to discover if an artificial intelligence system can behave like a human being, it has discovered that it can.

I enjoy using Twitter. The people I follow link me to useful articles and I am able to respond to queries from readers or people who want to take issue with something they've heard me say. There have always been people who make - how shall I put this - ad hominem arguments, but I haven't found this too troublesome. I just try to reply politely and see if I can turn an insulting start into a constructive exchange. I succeed just often enough to make it worthwhile carrying on.

More recently, however, things have become quite a bit darker.

Let me give you some examples of tweets sent to me (with my name tagged) in the last two days. "The holocaust is a lie #Hitlerwasright"; "The holocaust is a complete fake"; "What holocaust", "Hollow cost"; "Count up the deaths throughout the middle east and then talk to me about holocaust maties"; "Finkelstein, what a wonderful traditional English name".

And there is quite a lot more. Jews controlling the EU, defending "paedos" and being greasy ultra-zionists.

As I say, that's just the last two days.

Some of the people tweeting this sort of stuff have a handful of followers, but many have hundreds and some have thousands. One particularly obnoxious individual, Charles Frith, who spreads Holocaust (or as he calls it 'holohoax') denial has tens of thousands of readers. His particular speciality is linking child abuse, mad anti-zionist nonsense and holocaust denial in a constant stream.

Here are a few thoughts on what this means. Twitter needs to reflect that it is becoming hard to be a Jew using its platform. It is one thing for it to say - as it reasonably does - that it has a responsibility to protect free speech. But when Holocaust deniers and Jew haters don't just talk to each other, but seek out Jews and target them, what is Twitter ready to do about it?

I don't think it is over-sensitive to regard the onslaught of antisemites as really quite distressing. I regard myself as robust, but I have begun to find it quite hard to be on the system.

Is Twitter comfortable that there are impressionable people learning Holocaust denial from its company's product just as Tay did? There are many talented, concerned people working for Twitter. What are they willing and able to do about this problem?

Or are they saying that they have no alternative but to hold the ring. No alternative but to be neutral between the Jews and the Jew haters? Really?

In an organised way, I think, the community must insist upon a response. And at the same time we are going to have to step up the great work being done spreading Holocaust education through social media. I think we should recognise that we face quite a serious challenge. We could try just shrugging I suppose and say "well, who cares about Twitter". But I don't think that's going to work.

Daniel Finkelstein is Associate Editor of The Times