Asterix Roman soldier. Click for credits and to enlarge
A silly story I wrote over at The Critical Line, where Richard, a witty lawyer from London, entertains his guests with his vast knowledge and adorable English humour.
Richard though has a problem.
He’s terribly profound in mathematics and so are many of his guests who seem to share the same horrible contagion.
But, it’d be fair to say, I am the one to have a big problem, and, what is this tale but a burst of frustration because of my mathematical ineptitude?
The Tale of Manius
English sheep. Photo by Bernard Durfee (2008). Click for credits and to enlarge
Britannia, 526 CE, in a parallel (and almost identical) universe.
The Western Roman Empire has collapsed. Angles, Saxons and Jutes are invading the Roman province of Britannia from the East. All continental Roman soldiers have gone – but the Romano-Celtic in the West are resisting bravely. Only Manius Papirius Lentulus from Roma has stayed. He lives with the barbarians but risks nothing since he’s considered innocuous by the Angles (or Angli as he says in his language.)
The last Roman soldier has made friends with a few of them: Richard (whom Manius sometimes calls Britannia), Dafna (happened there from a far away land), Cheri, Mr. Crotchety and Phil. In their abstruse language – that Manius understands a bit – they sometimes call him MoR (or, in their weird but cute Latin, Roma.)
A goose has just died for occult reasons MoR isn’t willing to investigate.
A Melodious Sequence, 1,2,3…
Manius felt sorry for the poor goose but also curious about how Cheri might prepare it for lunch.
Approaching Mr. Crotchety he told him he had been so lentus and had forgotten he had something important to tell him.
Dafna was weirdly chanting a melodious sequence of numbers:
Getting closer in rapture MoR noticed Richard and Phil approaching her as well. Her song seemed the usual diatonic scale kids learn by just pressing the white keys of a keyboard, do-re-mi-fa-sol-la-si-do.
But MoR couldn’t figure out a kinda weirdness in that melody, so a stupid look froze in his face. Richard’s smile became sly instead. Phil was scribbling like crazy on a roll of papyrus.
Britannia finally lost his patience and shoved an elbow into Roma’s ribs.
“Ouch Richard!! Are you crazy??”
Then it finally hit Roma. That devil of a woman!! She was chanting her sequence according to an ancient tuning!
“Yes – said Richard triumphantly – it is the Pythagorean tuning based on a stack of perfect fifths, each tuned in the ratio 3:2. The Babylonian tuning, actually, more than 1 thousand years older than Pythagoras. Starting from D for example, the A is tuned such that the frequency ratio of A and D is 3:2, so if D is tuned to 288 Hz, then the A is tuned to 432 Hz, the E above A is also …..”
Dafna interrupted Richard with an odd smile:
“What he means – she said – is that the Pythagorean love for proportions is evident in this scale’s construction, as all of its tones may be derived from interval frequency ratios based on the first three integers: 1, 2, 3. Isn’t that amazing?”
Roma felt trapped.
He was surrounded by the Angli and their allies. And they were ALL mathematicians!!
He began to panic. The last Roman soldier in Britannia, outnumbered, outsmarted, began to run wildly uphill and got lost among the sheep never to be seen again.
Sheep in English countryside. Click for credits and to enlarge
The Legend of Roma Continues
A legend says Roma took seven Anglia wives and mixed his blood with the natives.
“Why seven?” asked the Anglia kid to his Anglia grandfather.
The tribe was sitting before a big fire. The summer night was full of stars.
“Because seven is a magic number” replied the Anglia grandfather showily. “The seven hills of Rome, the seven wonders of the world, Jesus saying to Peter to forgive seventy times seven times.”
“But seven – added the Anglia cutie – is also the fourth prime number. It is not only a Mersenne prime (since 23 − 1 = 7) but also a double Mersenne prime since it is itself the exponent for another Mersenne prime, ie 127.”
The Anglia Grandfather paled.
It’s like he saw all his life fall apart in a second. His mind went back to the time when a Roman soldier had fled wildly uphill and had got lost among the sheep.
Even the Anglia kids!! Even THEM!!
His flight had been useless.
That same feeling of panic, of claustrophobia pervaded him.
He was trapped. Trapped forever.