The Blog of Avon.6 (b)
Conclusion of excerpt from BARDCODE.
At the end of Blog.6 we had examined only the wording of the four bolded sonnet numbers in Shakespeare’s sequence: 3, 12, 23, 59, 70, and 97. To conclude we’re going to look briefly at the two that are not prime: 12 and 70.
Sonnet 12: “When I behold the violet past prime”.
This line works poetically and requires no explanation. But it also works mathematically. When you’re past something you’re positioned after it. Sonnet 12 comes after (past) the previous prime sonnet, 3… a prime number. But it also comes literally right after (past) the previous basic integer, 11… which is also a prime number. So sonnet 12 is past prime in both possible meanings.
Sonnet 70: “And thou present’st a pure unstained prime”.
Upon close examination this doesn’t work at all, poetically. But it still works really well mathematically.
In the Arden edition of the Sonnets, editor Katherine Duncan-Jones suggests thou present’st means you exhibit, display, are characterized by. She gives no explanation for a pure unstained other than just unstained. And for prime she gives prime of life, youth, or early manhood.
All well and good… “You are characterized by a pure, unstained early manhood” might work but for the fact that the poet has previously spilled a torrent of ink cataloging a litany of the Fair Youth’s faults in early life. He is anything but unstained! The line makes no sense at all in context with the fatherly, judgmental tone of many of the Fair Youth sonnets, particularly the first seventeen. So how does the poet intend us to interpret this?
When you present something you announce that which follows. You yourself are positioned just before what you’re presenting. Sonnet 70 comes just before (presents) the next prime sonnet, 97… a prime number. But it also comes literally just before (presents) the next basic integer, 71… also a prime number. So sonnet 70 presents a prime, in both possible meanings.
Shakespeare is being absolutely literal in his description of how these numbers behave, mathematically. But in what way are the primes he’s presenting pure and unstained? Is he describing a mathematical quality here also?
There’s a class of prime numbers called absolute primes whose special characteristic is that you can rearrange their digits in any order and they always produce another prime number. With two digit primes this means you simply reverse their digits… you revolve them. With single digit primes there’s nothing to rearrange but technically they’re still classed as absolute. These are all the absolute primes within sonnet number range:
2; 3; 5; 7; 11 (11); 13 (31); 17 (71); 37 (73); 79 (97); 113 (131).
Let’s recap what we just learned about past and presents.
Sonnet 70 presents 71 and 97. Sonnet 12 is past 3 and 11. As a bonus, Sonnet 12 also presents 13. Check them out. They’re all absolute primes!
If you were a renaissance poet searching for a way to describe this special category of primes (which were not even named until 1957) you just might call them pure, don’t you think? Because no matter which way you arrange their constituents they always produce a number that’s a pristine prime. You might also think of them as being unable to be spoiled by the appearance of a non-prime… unstained?
Not surprisingly, he’s found the perfect, poetic way of describing their unique numerical quality. But the question remains: why is he doing this?
Stay tuned. (Stay well tuned.) Something’s coming.