They built the campus of Washington University up on a hilltop. (Hence why it was until recently called the Hilltop Campus.) When on the edges of campus, it's thus unsurprising to discover one must go up to get anywhere. In this particular building one can go up to the fifth floor and then cross a skybridge to the second floor of another building.
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(...Not that he could take these stairs--they don't go all the way to the top.)