A Gift of Time

by Merritt, Jerry

  Mom had not yet told Dad about Arlene, so he was quite convincing in his response to the gaunt, sharp-faced DA with his wide mouth and thin, hurried lips. No, he hadn’t seen Arlie since his disappearance, and why would anyone think otherwise since Arlie had been declared dead. And that was that. We pulled away leaving the DA standing in the driveway and me wondering whether word about Arlie being safe had gotten out. Had Mr. Goodwillough told his wife? Had she told a neighbor?

  As we approached the High Pine Bridge, Mom said, “Jim, take a right here. I’ve got to say goodbye to Aunt Cealie. She’s waiting for me at the cemetery.”

  “Are you messing with me, Julene? We’re headed for California and you want me to double back up to High Pine Cemetery to see Aunt Cealie. Is she buried there now?”

  “No she’s not buried there. She’s ninety-eight and I’ll probably never see her again. She’s like my own mother. You know that.”

  Fifteen minutes later, we bounced along the power line road toward the isolated grove of live oaks surrounding the cemetery. Aunt Cealie was sitting on a tombstone waiting as we turned in to the clearing.

  “She’s gonna outlive Nebuchadnezzar,” Dad groaned as we pulled up next to her.

  “It’s Methuselah, Jim, and I hope so.” Mom hopped out, and she and Aunt Cealie hugged briefly, and looked over their shoulders, and tilted their heads listening for sounds off in the distance. Dad lit a cigarette and blew out a loud exhalation, muttering something about Shadrack and allotted time on earth. Finally Arlene stepped out from behind one of the massive oaks. She wore a white dress and a short, black wig Mom had bought at a yard sale a few days earlier. I hardly recognized her. Dad dropped his cigarette when Arlene climbed into the back seat with me.

  Mom gave Aunt Cealie a last hug and climbed back into the car. “Jim, this is Arlene. We’re giving her a ride to California.” Dad threw an over-long glance her way. “Don’t ask,” she said.

  Anxious to finally get underway, Dad, just stuck his cigarette back in his mouth and started the car. “I guess now everybody has to pee.”

  Chapter 32

  The DA just showing up like he did had me on edge. Until we cleared Alabama, I expected to hear sirens behind us at any moment. We were well into Louisiana before I completely relaxed. That night we pulled into Lafayette at a cheap motel with tiny, white cabins lined up like half-pint milk cartons behind the combination general store and office. After dinner, Mom began to work with Arlene. Following a few awkward moments, she finally pulled the Gideon Bible out of the end table and held it out to Dad.

  “Why don’t you boys go out for a while and read up on your Old Testament characters.”

  By the time we crossed into California just below Needles six days later, Arlene was more a girl than she was ever a boy and we were all pretty much a family.

  We spent the night in Needles and rolled into Santa Barbara the following evening. Santa Barbara was just as I remembered it. Walking around town was déjà vu at every turn. The only difference was that, instead of being alone, Arlene followed me everywhere. It was unnerving.

  Arlie was gone. Yet Arlene was Arlie. She seemed unreal. A willowy tendril of smoke risen from the ashes of the child, Arlie. That changeling born into an uncaring world. A child confronted at every turn with hostility, every effort at protecting itself turned against it until, all hope gone, it finally broke that night of the storm. But some core of self must have remained. She was not unlike me after my own return. Her becoming a girl was a complete rebirth for her, and even I finally began to accept Arlene as Arlie’s replacement. But it was a slow evolution for me.

  As for Arlene, with one final, heart-breaking exception, she never mentioned being Arlie again.

  ***

  By the time school started, Arlene’s hair had grown out enough for a pageboy cut. Mom bleached it out nearly white, and, with the tan she had picked up during the summer, Arlene was quite striking as we entered the ninth grade. And on the girls’ softball field she was always the first or second chosen. She entered track and even began martial arts training at free classes offered at the university in the evenings. And became a straight A student. Arlie was well and truly drowned—except for one item.

  I helped Arlene find an expert knife maker in the area. An old Scandinavian up north of town who worked from homemade forges in his barn. He was a sturdy type with white hair and wrists like the forged steel he worked. He wiped his hands on his leather apron and greeted us with a careful grip. “Erik Ostmann. How can I be uf help?”

  Arlene explained what she wanted.

  “Ja. I can forge that. Damascus steel, if you vant.” He grabbed up a tablet and sketched off a shape that looked both ancient and lethal. “One piece. It vill never break or crack und vill hold its edge till a veek after the Day uf Judgment.”

  She nodded approval, so he showed her several cheaper throwing knives and asked her to pick one that fit her hand. She selected the smallest and hefted it expertly. Mr. Ostmann nodded toward a well-shredded post. “Try it.”

  The blade slammed into the post with a speed I couldn’t follow with my eye. Mr. Ostmann smiled appreciatively and said, “I vould recommend about 180 grams for you. A little on the light side, maybe, but you vill make up for it in speed.” He selected a higher quality knife from a drawer. “Try this. One eighty-five grams.”

  After two throws, Arlene agreed. “One eighty it is then. How much?”

  “Damascus steel?”

  “What is that exactly?”

  “Very ancient. Few can forge it today. It takes a special alloy and much hammer verk. I make ten double-overs forged together. That makes over one thousand layers. It takes time. There is nothing vill come close to matching it, though.”

  “Yes, Damascus.”

  “Center balanced? That vay you can throw it by either handle or blade.”

  “Center.”

  He nodded. “Two hundred dollars including a custom fit leather sheath. I can have it ready in about a veek.”

  Arlene glanced at me. I nodded. “I’ll be back in a week.” She counted out ten twenties. “Here’s payment in advance.”

  Mr. Ostmann bowed slightly and smiled. “It vill be here.”

  Chapter 33

  Once rearmed, Arlene became a bit more independent. As for me, well, I was mostly concerned about my continuing inability to make any money from my vast knowledge of future events. It occurred to me I could write the hit songs I knew would be coming out in a few years and make a fortune, but that would be the same as stealing from the people who had written the songs I remembered. Same for inventions other people would make in the future. I needed something never done before. It wasn’t until high school that I found a chance.

  Those two alien equations I had seen so dimly back in the sixth grade were beginning to crystalize out of the dark firmament of my implanted mind but remained an utter mystery. Working with them was mentally exhausting. To relax, I messed around with the zeta function my son, Jimmy, had mentioned. Bernhard Riemann had toyed with it a century earlier and discovered the mysterious relationship it had with prime numbers—that well-known set of elemental numbers so utterly cryptic. But Riemann had never been able to unravel the complex association. German mathematician David Hilbert had named it one of the major unsolved problems of the Twentieth Century. It was still unsolved when I had met Ell. The zeta function was a perfect solution for my dilemma. Actually, it turned out to be too perfect.

  I chose the zeta function’s relationship to prime numbers as my science fair project. To my dismay, I managed to tie the two together. For that historical breakthrough, I got an honorable mention. First prize went to an eleventh grader who had paraphrased an article from the encyclopedia on the binary number system. Still, honorable mention was enough to get my project mentioned in the paper.

  “Honorable mention in mathematics went to Micajah Fenton for his derivation of a formula to generate prime numbers.”

  But that was enough. It caught the att
ention of a mathematician at UC Santa Barbara. He contacted me, probably expecting a good story to regale his buddies with about the starry-eyed kid who thought he had come up with a universal equation for generating prime numbers. I agreed to meet him at his office.

  Myles Mullins was a lanky, balding man with wiry, reddish hair; and pale, watery, eyes. I didn’t much like his condescending attitude at first, but I handed him a copy of my paper and told him Riemann had just missed discovering the solution himself.

  As he flipped to the second page, I could see the doubt in his face. I leaned over and pointed to the third formula. “If Riemann had just thought of trying a Fourier transform on this inverse function, he would have seen the solution immediately.”

  “Why would he try that, kid? Fourier transforms are used with sinusoidal functions, not prime numbers.”

  “But sinusoids are everywhere, including prime numbers. Look—if you just start with the first prime number, two, and generate a wave with a length of four, it passes through every second number starting with two—and the first number it skips over, three, is prime. Then use three to generate the next wave with a length of six and it passes through all numbers divisible by three, and the first skip missed by both two and three is five, the next prime. Continue like that, and each lowest number passed over by all the previous waves is the next prime.”

  “Well, yeah, I see that. It’s like the sieve of Eratosthenes”

  “Except now you’re dealing with sinusoids.”

  “Um.” He craned his neck around studying my equation then flipped the page, and I saw the light come on. He stabbed at the page with his finger. “So you’re using this formula, this Fourier transform you’ve modified, to isolate the wave length of any wave that starts from the smallest of all previous N skip-overs?” He glanced at me for confirmation. I nodded. He rubbed the back of his neck nervously with his free hand. “Maybe. Maybe. But I doubt that’s going to work for higher primes.”

  He stepped over to his chalkboard. “So, if I wanted to know what the twenty-sixth prime was, I would just set N to ….” His chalk clicked away as he ran through some quick calculations for the 26th and 169th primes. After a quiet, “Hummm,” he glanced over his shoulder at me. “And you claim this works for all primes?”

  “The proof is there on the last page.”

  “You have a proof?” He dropped into his desk chair and flipped to the end of my paper. His lips moved silently as he read the short paragraph several times before he leapt up with his hand to his forehead. He made no utterance. For several seconds he merely looked off into the distance before turning to me.

  “And you did this by yourself?”

  I nodded.

  “You came up with a solution to a problem mathematicians have obsessed over for twenty-three centuries, and all you got was an honorable mention. What in the hell was the winner’s project?”

  I shrugged.

  “You know what you’ve done here don’t you?”

  “Yeah, I know.”

  “Kid, you better brace yourself. By the end of the week you’re going to be the most famous person in mathematics. What you’ve done here …. Have you ever heard of the Fields Medal?”

  I shook my head.

  “Well, it’s the Noble Prize of mathematics. It’s awarded every four years. The previous award was last year. But you’ve got the 1962 award locked up with this little science fair paper.” He shook his head. “We always knew it was possible an amateur would beat us to the solution one day, but this—this is unbelievable. Absolutely unbelievable. How’d you come up with this idea?”

  It was time to let him know I was on to his real motivation for inviting me over. “I just used my Captain Midnight secret decoder ring.”

  I had to admit; he was quick. He broke into a guilty grin. “Touché, kid, — touché.”

  Chapter 34

  I found out later the Fields Medal wouldn’t come with any monetary reward. I had been remembering the later Able Prize with its million-dollar payout. But the awards in my current period were mostly prestigious. All I had wanted was money to begin investing. Still, that came soon enough.

  Several days later, the phone rang at five in the morning. It was the math department at the University of Heidelberg. They wanted to book me as a keynote speaker at their mathematics conference in the spring. Mom told them I had school that day. But the phone kept ringing, and Mom wanted to know what was going on.

  “Remember my science fair project. I solved a famous math problem. Now it seems everyone wants me to come tell them how I did it.”

  “Well you always were good in math. Still, this seems a little overboard.”

  “I just got lucky.” Then the phone rang again, and I excused myself to get ready for school.

  By the time Arlene and I left for classes, Mom had gotten rather good at handling the whole affair. She booked a few speaking engagements for me along the West Coast less than three hours’ drive but told me my education came first. By that, she meant high school. Bless her heart. I didn’t argue. I knew she had less than a year left.

  Meanwhile, I was finally entering a period when I recognized a few rapid-growth stocks coming onto the exchanges. My Holiday Inn stocks were now worth nearly four thousand dollars and Arlie had a like amount that wasn’t doing Arlene any good. I located the nearest stockbroker and went through all the wickets necessary to transfer my old Pensacola account. It seemed simple enough. But further reflection convinced me the stockbroker back in Florida must surely have realized the infamous missing son of a serial killer held an account with him.

  I discussed it with Arlene. We both had the feeling there might be a trap set on that account, and any activity on it would trigger a call to law enforcement. The price of Arlie’s disappearance was the loss of his stock. But Arlene remained sanguine about the loss. “It’s a small enough price to pay, Cage. Don’t worry about it.” I think she was just so thrilled to finally be safe and living in a normal family, nothing else mattered.

  Still, I worried about a loose end somewhere. Something we had overlooked. I knew Arlene would eventually need a birth certificate and I knew not to wait too long to get one. In those early, pre-computer days, there was no cross feed between death certificates and birth certificates in any state bureaucracy.

  “Let’s head over to the library and look at some old newspapers on the microfilm readers.”

  “And waste a good day like this?’

  “It won’t be a waste. Trust me.”

  It took us about an hour to find an obituary of an Arlene Trask who had died young and was born within a year of Arlene Quintin. From the library, we walked downtown to the courthouse and asked directions to the vital records section. A brusque, middle-aged woman jotted down our request and disappeared into a back room to emerge a few minutes later with a certified copy of Arlene Trask’s birth certificate. We gave her three dollars, and she gave us the certified copy.

  Now the only remaining problem I could think of that might trip us up was fingerprints. And I didn’t know whether maybe the DA, being a tenacious sort, had ordered a sweep of the Goodwillough house for Arlie’s prints — in case Arlie ever turned up again.

  Then it struck me that I should get a false birth certificate as well. Just in case. In case of what, I had no idea, but we went back to the library and found the obituary of a three-year-old boy named Daniel Shepard who was born the same year as me. We returned to the vital records building and I walked out a few minutes later with a new identity in case I ever needed it. I felt downright subversive and resolved to eventually get us drivers licenses and social security cards under those purloined names. I planned on us being ready for anything.

  ***

  Dr. Mullins had thought my speaking engagements would be a temporary diversion for the math world. A whirlwind tour before the calculation community shunted me off into the oblivion of just another one-trick wunderkind. But by summer, when school didn’t interfere, the speaking tour turned into
a good moneymaker. In fact, the only real moneymaker I had found. So I milked it hard, making sure to throw out enticements in response to questions. Pointers to where bridges between various fields of mathematics might lie.

  In the beginning, I got questions that threw me. I had the ability to answer them, but when Ell had loaded my math abilities, she had no idea what we humans had named the various functions. When one attendee asked me for my thoughts on any links between the Near-Square Primes conjecture and Goldbach’s conjecture, I was stumped.

  “I’m sorry. I don’t know what Goldbach’s conjecture is.” That drew sniggers from the audience.

  “Every even integer greater than two can be written as the sum of two primes.”

  “Ah, I see.” I offered a solid clue on how to link the two. There were no sniggers. “Does that help?”

  The answer was always a brief, “Yes. Thank you.” Or a quick nod. They never asked for more. It was obvious the questioner had been working on the problem for some time and didn’t want further information blurted out that would allow someone else to come up with the proof first. So I always obliged by answering only the specific question asked.

  Following that approach, I pulled in almost fifty thousand dollars in speaking fees by the time school started back. And, yet, I was nothing special in the public’s eye there in California where child-actors sucked up all the media attention. Few cared about a whiz-kid who solved a math problem nobody ever heard of. And once school started up in the fall, the school-day speaking engagements were over. Mom insisted.

  Chapter 35

  It was November when Mom’s first symptom appeared. A precipitous loss of weight. At first, she was thrilled she had finally dropped that extra five pounds she was always working on. But then she dropped another five, and then another. I didn’t say anything. I knew there was no hope, and I wanted to spare her the diagnosis as long as possible.