The story is not actually set in the Classical past. Rather, it is an example of what swisstone dubs 'appropriation' - that is, a story about a fictional society which has consciously modelled itself on a real past culture.
In this case, the fictional society is an isolated future human colony, and its leaders have deliberately borrowed ancient Greek myths and religious beliefs as a means of exercising control over their subjects. What's more, they have access to both cloning technology and the ability to transfer their minds into new bodies (via a 'Remote Synaptical Kinesis' device). They have cast themselves in the role of the gods, created several clones each, and whenever their old bodies reach the end of their natural lifespan, they call in one of their own clones and have their minds transferred into the new body. The clones think it's a great honour, but the Doctor and his companion are less than impressed, and in any case, the mind-transfer technology is on the blink. Matters are resolved when the old guard get ousted by a couple of their own clones - but will they resist the temptation to start attempting transfers of their own when faced with the prospect of death?
It's a short and fairly simple story, whose basic plot elements are recognisable from multiple other SF stories (Doctor Who and otherwise). Arguably, the Classical aspect isn't doing anything very much more here than it is in Underworld or The Horns of Nimon - that is, lending a veneer of intrigue and sophistication to what would otherwise be a fairly unremarkable story. But I think it would unfair to go quite that far.
For one thing, the use of a Greek setting serves the useful purpose of helping the audience to grasp the relationship between the original colonists and their clones. The plot requires a) that the difference between the original colonists and their clones (or descendants) is clear and b) that we understand that the original colonists have succeeded in establishing control over everyone else on the planet by means of cynical deception. The Greek mythological setting achieves both of these things - casting the original colonists as gods does make their elevated status clear, and offer a plausible explanation for why nobody is questioning or challenging them.
The specific choice of ancient Greek culture to help convey all this makes sense, since it serves dual purpose as a society which did accord great reverence to a multiplicity of gods, but is also associated with great scientific thinking, so that it doesn't seem too weird to find mind-transfer technology incorporated into it. It also adds a valuable extra layer to the relationship between 'Zeus' and 'Hera', the most powerful of the original colonists. They are amusingly snippy with one another, and Zeus has a keen eye for the pretty girls. But for all that, they have been together for centuries, through a succession of cloned bodies. I felt that the Classical veneer really helped to flesh out that idea out by reference to the similar relationship between their mythological namesakes.
So, as an example of Classical receptions it worked for me. Along the way, it constituted my first introduction to Lucie Miller, whom I hadn't met before. She seemed quite good fun - a modern, no-nonsense woman rather along the lines of Donna Noble, who is very ready to question and challenge what other people are doing. Paul McGann seems as good as ever as the Eighth Doctor - and I've used the opportunity to make a new icon in his honour. I look forward to another opportunity to use it once I get my hands on his upcoming story, An Earthly Child - especially having seen The Dalek Invasion of Earth so recently.
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