It was one of those slow, easy going Sunday afternoons on our favorite deck overlooking the bubbly creek. Neighbors came to say hi to Pamela, share a cake, and listen to her stories. As usual, the conversation soon turned to her beloved Harmony. Isn’t this what eternal life is all about, I thought; Harmony’s spirit now roaming her native universe, yet she’s still alive right here in Pamela’s heart.
“So what did you do all those awake times in the wormhole?” started the neighbors. Leaning from her lawn chair, Pamela said the wormhole was quite a disappointment, at least for her. After all the excitement of preparations, launch, passage through the planetary system, and the anticipation of entering the portal, there was just a big nothing. They had a slew of experiments to do, but the instruments had no readings beyond those of the capsule, the scanners picked no external signals.
Harmony, curious and inquisitive as always, found the condition intriguing. With no dimensionality outside our own, are we infinitely small or infinitely large? Being all there is, are we our own universe running on its own time? Are we this universe’s gods? Could we start creating a new world from within? In contemplating these questions, Harmony one day brought up the mystery of prime numbers.
“I teach my students how to generate prime numbers,” interrupted Jens. We could all see how he was into the subject. “You start with the first two prime numbers, 2 and 3, and then make each subsequent number to be an odd number not divisible by three. The formula IF(MOD(An+2,3)=0,An+4,An+2) does that.” “And then you purge all numbers that are multiples of any of the other prime numbers. For example for the prime number 5, the formula is IF(MOD(Bn,5)=0,””,Bn), and so on.” “This is called the sieve method because, as you keep deleting the blank lines, you end up with prime numbers only.”
Pamela continued that Harmony had in mind certain special prime numbers she called “complete” or “stable.” For example, the two of us in the capsule could act in three distinct ways: Harmony alone, Pamela alone, and the two of us together. If each of these acts made a new entity, the number of those would be the next prime number, 3. It is a complete number, as there is no additional way the two of us could act, and also stable because it can’t be divided. “I can see that,” I noted, “sort of like a three-legged stool.”
Pamela continued that these new entities could now act all three together, each one individually, or in pairs. “Yes, there would be three pairs, according to the formula COMBIN(3,2),” reported Jens, “so in total, the three different entities could act in seven distinct ways.”
Pamela said yes, another prime number fitting Harmony’s concept of complete and stable. “I got it,” continued Jens, now on the roll with fingers racing on his pad. “These seven entities could act, let me see … in 127 distinct ways!” “Another prime number for sure, and I suppose the next of Harmony’s complete and stable numbers.”
So where was Harmony going with this series of prime numbers, just a game in the boredom of the wormhole or was there some deeper meaning? According to Pamela, she thought it had something to do with the process of creation. What would the next number be then? “Already working on it,” replied Jens, “I mean, in how many distinct ways could 127 entities act?” … “Two much for my spreadsheet, but looks like it would be a thirty-nine digit number!” Quite a creative explosion, I say.
With that, I got up for a glass of Chianti to go with that cake; know it doesn’t look right, but red wine with sweets is a weakness I intend to keep. As for my other weaknesses, you may refer to my report, working title The Twin.