Doctor Who season 10 is something of an odd duck. Every episode is tasked with being as much of an introduction as it is preparation for a farewell. So far, the season has rightly leaned more toward the former, as Bill has only just begun her journey with the Doctor, venturing first into deep space and distant time in order to escape a sentient oil slick, before moving into the future to bear witness to humankind's near-failed first interplanetary colony. As is usually the case with new companions, Bill's learning curve has been steep; the Doctor has a tendency to throw his fellow time travelers into the deep end, and if you've been watching the previews for 'Thin Ice' then you'll know the Time Lord plans to take that literally.
So far, the education of Bill Potts has offered the audience a small glimpse at the sort of character she'll be. Bill certainly sees the Doctor as her mentor and eagerly greets the rare opportunity to explore the entirety time and space as a learning opportunity. The wide-eyed wonder that Bill displayed in the season premiere hasn't abated two episodes in, especially now that she's smack dab in the middle of her very own English costume drama, after the Doctor's attempts to return them to the university took their journey off course, resulting in the pair staring down an elephant walking along a frozen Thames. While Bill deals with her rapidly changing circumstances with infectious optimism, there's something interesting to be learned for the audience as well.
Each new scenario brings a greater understanding of Bill as a companion and as an individual, and how she'll react the more she learns of the Doctor and the particulars of his journey. This is especially interesting after the events of last season and the ongoing mystery that is the vault and the Doctor's oath that Nardole is apparently on hand to make sure he keeps. Because Jenna Coleman bridged the gap between Matt Smith and Peter Capaldi, and the latter's tenure as the Time Lord will wind up being slightly shorter than most, Bill will be the first companion who is a product of Capaldi's sometimes brusque but no less compassionate Doctor. As such, his actions at the beginning of their time together will forever shape Bill's impression of the two-hearted alien moving forward, regardless the form he takes when it's time to regenerate at the end of the season.
That makes episodes like 'Thin Ice' more important than they might otherwise seem. Every experience dictates how Bill will see the Doctor moving forward, raising the question of just how much her opinion of this iteration will linger when she's introduced not only to the idea of regeneration, but to whomever he becomes next. As such, running around a frozen Thames in search of a giant monster swimming beneath the ice is, oddly, about as good a way for a burgeoning companion to shape her opinion of the Doctor as any.
A lot of that has to do with the Doctor's response to the loss of human life. As he tells Bill, having lived for 2,000 years he doesn't have the luxury of outrage when someone dies. Instead, his response to death is generally to try and do something about it. So when a small street urchin winds up dragged under the ice, to become food for a giant sea creature whose excrement burns a thousand times hotter than coal, the Doctor is confronted with a situation that is practically begging for him to do something about it. The response, then, further underlines one of the core characteristics of Capaldi's Doctor, as his alienness again tends to come off as callousness, making it difficult for a newcomer like Bill to understand that his reaction to the young boy's death is in actuality a learned response to all the death he's witnessed over his very long lifetime. And while the hour attempts to mine the potential conflict between Doctor and companion, hoping to examine two very different perspectives by juxtaposing too little experience with what perhaps amounts to being too much – when it comes to having witnessed death, anyway – the hour wisely does so without turning it into a lesson on Time Lords and Gallifreyan history.
Under any other set of circumstances, the episode would have been a fairly rote installment of Doctor Who, and it still is to a certain extent. But the hour is made more engaging by the interaction between Bill and the Doctor and its less than subtle critique of capitalism, the plight of the working class, and the dehumanization of those same people by those with wealth, power, and influence. It's archetypal science fiction storytelling, fulfilling the needs of the episode in question, while still leaving room for the mystery of what's locked inside the vault that the Doctor and Nardole have been tasked with keeping an eye on.
In all, 'Thin Ice' has to wear many hats and it does so satisfactorily for the most part. Putting the relationship between the Doctor and Bill front and center makes for all the difference, though, as the interplay between Capaldi and Mackie continues to make for a charming new avenue for the series to explore.
Doctor Who continues next Saturday with 'Knock Knock' @9pm on BBC America.