in order to control nature, "The Birthmark" centers on the scientist, Aylmer's, obsessive attempts to eradicate "imperfection" in the form of a birthmark on his wife, Georgiana's, cheek. As your question suggests, the birthmark becomes a powerful symbol because perceptions of it vary according to the characters' world view.
Hawthorne introduces the theme of nature versus science, as well as the theme of love between man and woman, in his description of the scientist Aylmer:
He had devoted himself, however, too unreservedly to scientific studies ever to be weaned from them by any second passion. His love for his young wife might prove the stronger of the two; but it could only be by intertwining itself with his love of science, and uniting the strength of the latter to his own.
Aylmer's ability to love, a distant "second passion," is restricted by his love of science, and the success of love of another human depends upon the "intertwining" of the two, not, as we might expect, upon the ascendancy of love over science—the two are inextricably and, as we learn later, fatally bound, with science taking precedence.
Georgiana, Aylmer's new wife, is described as beautiful, with one distinguishing mark:
Georgiana's lovers were wont to say that some fairy at her birth hour had laid her tiny hand upon the infant's cheek, and left this impress there in token of the magic endowments that were to give her such sway over all hearts.
The mark is in the shape of a tiny hand—a small but unmistakable symbol of nature's power to create—which, when Georgiana is in an unemotional state, is clearly discernible. Hawthorne's choice of a tiny hand is not random: nature is responsible for Georgiana's creation, and the appropriate symbol of nature's involvement is a "hand." That the birthmark is bound to Georgiana's innermost self is clear when Hawthorne describes the birthmark's varying color. When she blushes, the mark loses its distinctive tint and begins to become less visible, and as blood continues to redden her face, the birthmark and the surrounding color of her face become one. Hawthorne subtly implies that the birthmark and Georgiana's emotions are, like Aylmer's science and ability to love, mutually dependent.
A second powerful theme is framed by Aylmer's growing obsession with the birthmark, an obsession that ultimately leads to disaster but one that is consistent with the earlier description of a man who loves science to the exclusion of all else. Aylmer sees the birthmark not as one of the "magic endowments" that make his wife desirable but as
this slightest possible defect, which we hesitate whether to term a defect or a beauty, shocks me, as being the visible mark of earthly imperfection.
The birthmark becomes, in Aylmer's eyes, a mistake of nature that, while others overlook or view as a beauty mark, Aylmer sees as the emblem of nature's inability to create perfection. Indeed, as time goes by, Aylmer becomes more convinced—to the point at which his dreams are infected by his obsession—that Georgiana's birthmark is not merely a physical defect but is an emblem of inherent human weaknesses
In this manner, selecting it as the symbol of his wife's liability to sin, sorrow, decay, and death, Aylmer's sombre imagination was not long in rendering the birthmark a frightful object, causing him more trouble and horror than ever Georgiana's beauty, whether of soul or sense, had given him delight.
In short, this small hand of nature has taken on all the attributes of nature's ultimate frailty—decay and death—two human inevitabilities that cause Aylmer to hate the birthmark more than he loves his wife. Hawthorne leaves to his readers the conclusion that Aylmer's obsession is the outward manifestation of his completely unbalanced inner being.
In sum, then, the birthmark is itself, one on hand, a benign symbol of Georgiana's gentle and loving nature—and nature's involvement in her creation—and, on the other hand, a foil for the fight for supremacy between science and nature, symbolized by Aylmer's obsessive desire to rid the world of nature's "imperfection." In the end, Aylmer succeeds in controlling nature by eradicating the birthmark, but the cost is Georgiana's life that is dependent on that nature.