The cogwheel that Kolya sends Sofia symbolizes the hypocritical nature of the Soviet Union during the 1930s. On the one hand, the Soviet Union celebrates intelligent innovators like Kolya, framing the technological advancements they make as a form of admirable devotion to the Communist cause. When Kolya invents a new method of making cogwheels in a factory, for instance, the Communist Party sings his praises in the newspaper, and Sofia proudly displays the first cogwheel made by his new method, letting it loom over her room on the windowsill as a reminder of the great work he’s doing for the country.
On the other hand, though, the cogwheel itself also symbolizes the relative powerlessness of people like Kolya and Sofia under repressive regimes. Cogwheels, after all, are small parts of much bigger machines, and though they’re integral to the machine’s functioning, they’re ultimately controlled by stronger forces—a good representation of how Communism can go wrong and end up functioning as a way for the government to manipulate its citizens instead of empowering them. As the novel progresses, Kolya’s cogwheel remains on Sofia’s windowsill, but its meaning changes. At first, it represents the great opportunities he has been given and the fantastic strides he’s making for the country. By the end of the novel, though, it symbolizes little more than the fact that even widely celebrated and devoted citizens are subject to the horrific cruelty of repressive governments.