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At one point during this lecturing one-man show, the reincarnation of Karl Marx asks: "Is there anything more outrageous than an honest critic?" OK then, Brighton. Prepare to be outraged.

This play gives us plenty of facts about Karl Marx's life, but very little nuanced insight, and even less about his fascinatingly prescient political philosophy. Instead, we have an accusatory rant at the world's ills – a crowd-pleasing sermon which will persuade no-one and change nothing.

The conceit is that Marx, striking a deal with God, has been sent back to his home in Soho to deliver one last lecture. But God isn't as infallible as we've been led to believe; so Marx has been delivered not to his old stamping-ground in London, but to SoHo, New York. We the audience are therefore New Yorkers, and Marx proceeds to harangue us for things like not having a health service and still enforcing the death penalty. As a provocation or challenge to a Brighton audience, this makes no sense whatever. It will only make us feel smugly superior.

In truth though, I don't think I'd feel challenged by this piece even if my home were in New York. Like all Fringe shows, it has a self-selecting audience: playwright Howard Zinn's utterly justified anger gets us nowhere, because everyone present will already agree with him. Where we might disagree is on his championing of socialism over social democracy – Corbynism versus Blairism, if you will. But Marx says surprisingly little about that; despite apparently knowing what's going on in the modern world, he doesn't use familiar examples to illustrate his ideals, but instead suggests the details of his philosophy are too dry and complex to explain.

And when it comes to Marx the man, the play grows hagiographic; weaknesses and deficiencies are occasionally acknowledged, but never probed or examined. Once, Marx recalls, his daughter challenged him on gender equality – a potentially interesting opportunity to place his writing in the context of the values of the time. But no: "I won't comment on that," says Marx, and that's the end of the matter. Similarly, the discomfort many feel around his musings on the "Jewish question" are highly relevant to modern political discourse; yet the subject is raised and then simply abandoned, as though merely mentioning it is enough to make it go away.

Zinn's script does effectively dispel a couple of common misunderstandings, around the "dictatorship of the proletariat" and the "opium of the people", and if you're surprised to find Marx embracing the existence of God then you'll be set gently right on that point too. I'd have loved to hear him go further, and make more of a case for what Marx's philosophy actually was, but for the most part we just get a tubthumping list of things he opposes. Marx, and Marxism, deserve better.