Perfect Numbers
Rebecca Elliot


                The eternal essence of number is the most providential cause of the whole heaven, earth
               and  the region in between. Likewise it is the root of the continued existence of the gods and
               daimones, as well as that of divine men.
               —From the Pythagorean Sacred Discourses, a dictum attributed to Pythagoras’s 
                  daughter  Arignote

A perfect number is the sum of its divisors, excluding the number itself. For example, the divisors of 6 are 1, 2, 3, and 6, and

                                                                             6 = 1 + 2 + 3

                  Six is a number perfect in itself, and not because God created all things in six
                  days;   rather, the converse is true. God created all things in six days because 
                   the number is   perfect.
                   —St. Augustine

Pythagoras had another daughter, Damo. Little is known about her, except that her father entrusted her with his writings when he died and she brought them from Croton to Athens, and this part that I made up, but that might be true: when she was six she played with blocks shaped like squares, triangles, and rectangles, lining them up so they fit into repeating patterns. When I was six, I also played with wooden blocks, but I stacked them into towers, and so I learned nothing about the connection between number and shape.

Four perfect numbers were known to the Greeks: 6, 28, 496, and 8128.

                                                               28 = 1 + 2 + 4 + 7 + 14

Can I make the obvious connection? The average menstrual cycle is twenty-eight days. And this is the number of days it takes the moon to revolve around the earth. Easy.

                                                           496 = 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248

According to Wikipedia, “The number 496 is a very important number in superstring theory” that somehow launched the “first superstring revolution” in 1984. That sounds wonderful, but I have no idea what it means. However, 1984 is the year I was born, and 496 BC is around the time that Pythagoras died, so maybe there’s some equation there. Damo shakes her head, but I’m not sure if she’s saying no or yes. I see her now sometimes in the glass, sometimes in the form of a woman walking her dog in my neighborhood.

Of the writings attributed to Theano, mother of Damo and Arignote, wife of Pythagoras, teacher of mathematics at the school in Croton, all are lost, except a few fragments and letters.

                                                      Theano’s lost works:

                                                  “Life of Pythagoras,”                   “On Pythagoras,” “
                                                    “Cosmology,”                     OR    “Female Advice,” 
                                     “Theorem of the Golden Mean,”           “On Piety,”  
                                              and “Theory of numbers”   and      “On Virtue”
 
                                                  Depending on who you ask.

I see her next in a local park. Damo is by the trash cans, separating out her recycling. She has just been having a barbeque with her friends, but they have all left her to clean up. She doesn’t seem to mind.

            Damo: “Four hundred ninety-six days after my father died, I arrived in Athens. As I was not a citizen, and not a slave, I was categorized by the laws of the time as an Athenian Stranger. This meant I had no protection under the law and, as a woman, I was officially considered a prostitute. But it also meant I had more access to the intellectual life of Athens than a woman citizen would have had.”

            I thank her for the history lesson and she smashes an aluminum can under her boot and tosses it in the recycling bin before walking away without even saying goodbye.

She appears again in Raphael’s painting “The School of Athens,” keeping an eye on the Pythagorean teachings. Is that her holding the slate showing the harmonic ratios? Or is she the one holding out her hand, gesturing caution?

                                      8128 = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 127 + 254 + 508 + 1016 + 2032 + 4064

The number 8128 has an asteroid named after it, 8128 Nicomachus. Nicomachus of Gerasa being the mathematician who discovered the third and fourth perfect numbers during the first century AD. His Manual of Harmonics was written to “a noble lady” – but who was she?

Damo appears in a dream. She says the Pythagoreans all wrote under the same name – the name of her father – and so it’s difficult to say who wrote what. But that wasn’t the point. This was before the Author and his Ego. Some of these texts she wrote, some her mother or her sister wrote. Some were written by the men and women in the school where she learned and later taught. But they were more written down than they were authored, she says. I wonder that she doesn’t mind vanishing into history, leaving so much behind but none of it with her name, all of the credit going to her father or her male contemporaries. She says I’m thinking of Name differently than she did. “Pythagoras” doesn’t mean the same thing to her as it seems to mean to me. “But still,” I say, “and still…” She flickers and then fades and then is gone.

                          The citizen-women had to be mothers and housewives – nothing more; 
                          the stranger-women had to discharge the duties of companions, but
                           remain  outside the pale of the privileged and marriageable class. These 
                           stranger-women applied their minds to their function, with various ideas 
                            of it, and various methods. Many adopted the lowest possible means of 
                             gaining the good-will of men; but many set about making themselves fit 
                             companions for the most intellectual and most elevated among men.
                              They were the only educated women in Athens. They studied all the arts, 
                               became acquainted with all new philosophical speculations, and
                                 interested themselves in politics.
                           --Woman: Her Position and Influence in Ancient Greece and Rome, and Among
                               the Early  Christians, by James Donaldson, 1907

“Is that what we were doing?” I want her to say. “I was a grown woman when I arrived in Athens. I had no interest in making myself a ‘fit companion’ for anyone. Any man or woman who had seen the truth behind numbers, who had discovered that beauty has a mathematical basis, would be too busy to worry about that kind of thing. Not only does pleasing music come from pleasing ratios, but so do the positions of the heavenly spheres, and not only their positions, but their very existence, as well as the existence of every thing, of man, of the gods, of all creatures, of everything…”

Many years later, after I had grown quite old, she came to speak to me again. I sat outside on the porch of the house I had lived in for the last 8,128 days. And I loved that house, and I loved that porch. An old dog rested its head on my feet. “All numbers are perfect,” she said. “All numbers are sacred.” We had named the dog Argos, after Odysseus’s sad, old dog, who lived only long enough to see his master return and then died on a stinking pile of manure. We thought we could give him a better life this time around.

Rebecca Elliott lives in Chicago. She likes to collaborate with other writers & artists on book-making projects, which she publishes under the name of Meekling Press.