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it as a sign； the fact that my return to the Hypnerotomachia had brought a new structure to the world I lived in。 Quickly I began to fall into my father's trap； the one my mother tried to warn me about。
Wednesday morning； when I mentioned to Katie that I'd dreamt of my father； she did something that in all our days of jogging she'd never done before： she stopped。
〃Tom； I don't want to keep talking about this；〃 she said。
〃About what？〃
〃Paul's thesis。 Let's talk about something else。〃
〃I was telling you about my dad。〃
But I'd grown too used to conversations with Paul； invoking my father's name in any situation and expecting it to deflate all criticism。
〃Your dad worked on the book Paul's studying；〃 she said。 〃It's the same thing。〃
I mistook the sentiment behind her words for fear： fear that she would be unable to solve another riddle the way she solved the last one； and that my interest in her might fade。
〃Fine；〃 I said； thinking I was saving her from that。 〃Let's talk about something else。〃
And so a period of many pleasant weeks began； built on a misunderstanding as plete as the one we started with。 In the first month we dated； up until the night Katie spent at Dod； she built a fa？ade for me； trying to create something she thought I wanted； and in the second month I returned the favor； avoiding all mention of the Hypnerotomachia in front of her； not because its significance had diminished in my life； but because I thought Colonna's riddles made her uneasy。
Had she known the truth； Katie would've been right to worry。 The Hypnerotomachia was slowly beginning to bully my other thoughts and interests out of focus。 The balance I thought I'd struck between Paul's thesis and mine…the waltz between Mary Shelley and Francesco Colonna； which I imagined more vividly the more time I spent with Katie…was devolving into a tug of war； which Colonna gradually won。
Still； before Katie and I knew it； trails had formed in every corner of our shared experience。 We ran the same paths each morning； stopped at the same coffee shops before class； and snuck her into my eating club the same ways when my guest passes ran out。 Thursday nights we danced with Charlie at Cloister Inn； Saturday nights we shot pool with Gil at Ivy； and Friday nights； when the clubs on Prospect fell quiet； we watched friends perform in Shakespeare edies or orchestra concerts or a cappella shows across campus。 The adventure of our first days together gradually blossomed into something else： a feeling I'd never had with Lana or any of her predecessors； which I can only pare to the sensation of returning home； of joining a balance that needs no adjusting； as if the scales of my life had been waiting for her all along。
The first night Katie noticed I couldn't sleep； she recited a work by her favorite author for me； and I followed Curious George to the ends of the earth； where the weight on my eyelids carried me off。 After that； there were many nights I tossed and turned； and Katie found a solution for each of them。 Late…night episodes of M*A*S*H ； long readings from Camus； radio programs she used to listen to at home； now caught on a faint transmission down the coast。 We left the windows open sometimes； to hear the rain in late February； or the conversations of drunk freshmen。 There was even a rhyming game we invented for empty nights； something Francesco Colonna might not have found as edifying as Rithmomachia； but that we enjoyed just the same。
〃There once was a man named Camus；〃 I would say； leading her。
When Katie smiled at night； she was like a Cheshire cat in the dark。
〃Who left U。 Algiers with the flu；〃 she would respond。
〃He had lots of potential。〃
〃But was not existential。〃
〃Which made old Jean…Paul Sartre so blue。〃
But for all the ways Katie had found to make me sleep； the Hypnerotomachia still kept me awake more often than not。 I'd figured out what the smallest harmony of a great victory was： in Rithmomachia； where the goal is to establish number patterns containing arithmetical； geometric； or musical harmonies； only three sequences produce all three harmonies at once…the requirement for a great victory。 The smallest of these； the one Colonna wanted； was the sequence 3…4…6…9。
Paul quickly took the numbers and made a cipher of them。 He read the third letter； then the fourth after that； followed by the sixth and ninth； from the appropriate chapters； and within an hour； we had another message from Colonna：
I begin my story with a confession。 In the keeping of this secret many men have died。 Some have perished in the construction of my crypt； which； imagined by Bramante and executed by my Roman brother Terragni； is an unequalled contrivance for its purpose； impervious to all things； but above all to water。 It has taken many victims； even among the most experienced men。 Three have died in the movement of great stones； two in the felling of trees； five in the process of building itself。 Others of the dead I do not mention； for they have perished shamefully and will be forgotten。
Here I will convey the nature of the enemy I face； whose rising power lies at the heart of my actions。 Reader； you will wonder why I have dated this book 1467； some thirty years before I wrote these words。 It was for this reason： in that year the war began which we are still fighting； and which we are now losing。 Three years earlier His Holiness； Paul the Second； fired the court abbreviators； making clear his intentions toward my brotherhood。 Yet the members of my uncle's generation were powerful men； with much influence； and the expelled brethren flocked to the Accademia Romana； which good Pomponio Leto sustained。 Paul saw that our number persisted； and his fury increased。 In that year； 1467； he crushed the Academy by force。 So that all would know the strength of his determination； he imprisoned Pomponio Leto； and had him accused as a sodomite。 Others of our group were tortured。 One； at least； would die。
Now we are challenged by an old enemy； suddenly reborn。 This new spirit grows in strength； and finds a more powerful voice； so that I have no choice but to construct； with the assistance of friends wiser than I； this device whose secret I disguise here。 Even the priest； philosopher though he may be； is not equal to it。
Continue； reader； and I will tell more。
〃The court abbreviators were the humanists；〃 Paul explained。 〃The pope thought humanism bred moral corruption。 He didn't even want children to hear the works of the ancient poets。 Pope Paul made an example of Leto。 For some reason； Francesco took it as a declaration of war。〃
Colonna's words stayed with me that night； and each night that followed。 For the first time； I missed a morning run with Katie； too tired to pull myself from bed。 Something told me Paul was wrong about the new riddle…How many arms from your feet to the horizon？…and that Eratosthenes and geometry were not the solution。 Charlie confirmed that the distance to the horizon would depend on the height of the observer； and even if we could find a single answer and calculate it in braccia； I realized； the answer would be enormous； far too big to be useful as a cipher。
〃When did Eratosthenes make tha