Recurrence

Part of why I don’t believe the story about why Shovel BOB didn’t get evicted for well over a year is that when I was sent a 10-day notice because I quit going to therapy, the notice explicitly stated that even if I fixed the problem within the ten days, they could still evict me if it became a recurrent problem. Eventually, you can get evicted if you only abide by the rules ten days at a time. So, yeah, they are full of it.

I would like to shut my brain off now.

Fibonacci Series.

The Fibonacci series covers the simplest golden section sequence which can be expressed in whole-numbers (the golden section of 89 being 55, and that of 55 being 34, etc.):

2, 3, 5, 8, 13, 21, 34, 55, 89 …

In it each number equals the sum of the two preceding numbers (that is, 2+3 =5, 3+5=8, 5+8=13, etc.).

The sequence approaches nearer and nearer the proportion of the geometrical golden section i.e. the irrational key-number of the geometric mean: the square of every number is equal to the product of the numbers preceding and following it - with the difference of plus or minus 1.

The Fibonacci series embodies the low of natural growth. In the fir-cone starting from the centre, a system of spirals runs in the right and left directions, in which the number of spirals always result in the values of the Fibonacci sequence: 3, 5, 8 and 13 spirals.

A similar setting can be seen on the sunflower, pineapple, chamomile, dandelion, marguerite, cactus, likewise in the arrangement of leaves on the stem and in the horns of some ruminating animals.

cennamology.com
Jupiter Ascending - A Scientist's Take

This rather fascinating article explores the science of Jupiter Ascending (yes, really) and you may be surprised to find that the film actually handles scientific concepts more intelligently than many of its counterparts. I found the section on recurrence especially interesting, particularly this part:

“But even if Jupiter’s initial DNA sequence was identical to this woman’s, they probably wouldn’t really be identical by strict definition, for the same reason that identical twins aren’t truly identical. This is partially due to the environment- and ancestor-controlled phenomenon known as epigenetics. The way Jupiter lives, and even the way her parents and grandparents lived, affects which genes are expressed within her genome, potentially causing physical, medical, and behavioral differences from someone with her exact genetic sequence. It goes without saying that a maid would grow up in a different environment than an intergalactic queen.

“And some of the characters seem to realize this. Titus Abrasax (Douglas Booth) is quick to point out the ways in which Jupiter differs from his deceased mother. Yet Balem Abrasax (Redmayne) seems to actually believe that Jupiter is his mother, speaking to her directly as if she had arisen from the dead. Kalique doesn’t seem to know what to think.”

For a movie that’s generally treated as a dumb blonde, Jupiter Ascending handles some big ideas in exceptionally interesting ways.

Recurrences in JA

Something I’ve been thinking about lately are how the Recurrences in the JA universe are treated/looked upon, etc. 

Like, we get it. Jupiter was the “reincarnation” of Seraphi Abrasax: the late matriarch of the Abrasax Industries, the head of the most powerful dynasty in the universe, etc etc etc. It’s in Jupiter’s DNA to be what Seraphi was. 

Except not really. 

Let me explain. 

Literally the only reason Jupiter got anything out of this “Recurrence” deal was because Seraphi decided to leave something in her will for her Recurrence. And since the object in question, Earth, was entitled to Balem before discovering Jupiter’s existence, that peeved him off and is what got her into this mess. Without Seraphi’s decision to screw her son over, Jupiter wouldn’t have received jack. 

So then, why was she referred to as “Your Highness” and stuff like that?? Literally all she got was one planet handed to her. That’s not much to be proud of as an Entitled. Why is she as respected and prioritized as Seraphi when she is most certainly not Seraphi, nor as powerful as Seraphi was? What’s the deal??

Her DNA made her an Entitled, but it was Seraphi’s choice that made her special. 

This entire thing could be debunked if someone just reminded me that Seraphi also left in her will the right for her Recurrence to become the Head of the Abrasax industries. But as far as my memory goes, all Seraphi left for her Recurrence was Earth. The rest was divided among her children. So even with Balem out of the way, there was still Titus and Kalique, who both owned far more than Jupiter. She’s not even a head of the Abrasax family, right? So then why is she getting treated like supreme royalty when she’s technically just another Entitled that happened to look like Seraphi?

In the years since Lord Balem’s unfortunate and untimely demise, Lady Tay Abrasax has ascended to the head of the House of Abrasax, as was instructed in Balem’s will. She commands hundreds of refineries to produce premium ReGenX-E for the millions who peruse it.

But rarely does she use it herself. It had failed to save her husband from his fate. The substance is nothing to her without him.

Without using it often, she’s aged. Dark circles ring her eyes; faint wrinkles crown her brow, and her midnight hair has lightened to a deep grey in some places.

The sadness in her eyes has been lifted today, though. Rumor has it that a Recurrence of Lord Balem has been confirmed. Tay waits for Mr. Night to return with the news of the geneprint’s verification, her four now-teenaged children around her as she sits on what used to be Balem’s throne at the refinery. Like the three elder Abrasax siblings, Tay’s children are undeniably close to their mother.

Callisto, her primary heir, almost the spitting image of her late husband, strokes her hand gently. Her twin daughters speak quietly in voices much like their mother’s. Ganymede, the youngest son, sits with his head on Tay’s knee.

And so they lie in wait.

askchicanerynight

The Origin of Red Bones

‘Red Bone’, referring to an ethnic group in Louisiana and a black American term for people with fair skin, has strong ties to peoples in what is now eastern Nigeria. Originating from 18th century chattel slavery in the West Indies, the term ‘red bone’ takes from the creole term ‘red Ibo’ referring to fairer skinned black people. The term derived from observations of fair skin among some members of the Igbo ethnic group (and some other peoples lumped in from eastern Nigeria) whose numbers in slavery ratcheted up in the 18th century due to internal conflict in Igboland. European slavers and plantation owners often made observations and generalisations about various ethnic groups since different Africans were targeted for their knowledge, education and skills; a hefty amount of stereotyping and dehumanising was subsequently placed on various ethnic groups found in large numbers in slavery. One recurrent observation was the relatively higher prevalence of fair skinned people from the Igbo area, known then in the Atlantic as the ‘Eboe Country’. The fairer skin was demonised by planters as ‘sickly’ and the Igbo were characterised as weak because of this. This also meant their ‘price’ dropped and poorer planters in places like Virginia took many Igbo leading to a saturation of Igbo people there. The disdain, however, may have been fuelled somewhat by the fact that enslaved Igbo people weren’t unknown for their defiance of slavery, immortalised in the folktale of Ebo landing; they were also involved in a number of slave revolts all over the Caribbean, including in Haiti.

Ultimately, this characteristic was taken in as a negative one and the term ‘red’ was combined with ‘Ibo’ (Igbo) as a pejorative used by black people in the British West Indies for people who were black but with fair skin as opposed to mixed people who were just ‘red’ or ‘brown’ thus suggesting a hierarchy of phenotypes and hair types. Some creole linguists trace the term to Louisiana where it was heard as ‘reddy bone’, leading to the understanding of the term as ‘red bone’ with a less negative connotation as it is still used in AAVE today.

The term red bone is interesting as it seems to be a word that’s linked to a particular experience of an ethnic group in slavery. The word itself carries a lot of historical weight in terms of what it meant for one group of Africans in that era. (Kniffen, Gregory and Stokes 1987; Don C. Marler 1997, 2000; Winer (2009). Dictionary of the English/Creole of Trinidad & Tobago. pg. 754.; [Louisiana, Where Music is King, PBS.])

vimeo

The trailer for Recurrence!!!

Recurrence Relations

How to solve them?

There are several techniques to unwrap a recurrence relation and obtain a closed form that is easy to solve. Some of these techniques include:

  1. Substitution method
  2. Recursion-Tree method
  3. Master method

1. Substitution method:

  • Guess the form of the solution. (the difficult step)
  • Show that the solution works by using mathematical induction.

Perhaps one of the most useful ways that help us find a good guess is looking at the first few terms of the recurrence. Then we can begin to see a pattern, from which we can guess the form of a solution. Then the solution is tested and proved to be correct using mathematical induction.

2. Recursion-Tree method:

  • Helps to come up with a good guess for the substitution method.
  • Useful for recurrences describing the running time of a divide-and-conquer algorithm.
  • Each node in a Recursion-Tree represents the cost of a single subproblem.

3. Master method:

Very useful for Recurrences of the form: T(n) = aT(n/b) + f(n).

  • Split the problem into a subproblems each of size n/b.
  • Subproblems are solved recursively, each in time T(n/b).
  • Dividing problem and combining solutions of subproblems is captured by f(n).
Scene From A Marriage: Bobby's Plight

“I’m afraid of dying.”

She moves over to me and rubs my bald head, bald from the intensive, 21-day experimental treatment I’ve undergone to try and choke my deathless cancer.

“I don’t know when I got to be so afraid again, but here I am.”

“Things have changed, right? I mean, things have changed. Our life is going to change.” She holds me at the edge of my side of the bed, the light from the bed side table glows orange, aggressive but only for its own corner, the rest of the room is sunk in shadow. As she holds me I can feel her belly now nine months along. Sometimes if I stare long enough at it I can watch the little one’s butt move from one side to the other seeking room and comfort. “Everything is going to change.” She tells me very softly and very gently. Recently I’ve imparted this fear of dying so much that I think she’s sick of it, sick of answering for it, that it makes me so tired.

I don’t look at her as she holds me and tells me this. I have my eyes closed. We rock gently there in the open, almost vulgar, glare of the light. It’s like the world could see us. 

“I swear. I wish I didn’t always feel this way.” 

“I know. I know.” 

All of a sudden I remember when I’d try to tell my old students, when I used to teach, how hard it is to impart real “Love” because of how awesome is the failure of language to do what it’s supposed to do. “‘For example,’ I’d tell them. ‘Take Bobby here. He might want to tell his girlfriend how much he loves her.’ [class laughs – Bobby turns red]. ‘So, Bobby here, he tells her one day, ‘I love you;’ and what do you know, his girl says, ‘I love you’ back. She tells him, ‘I love you, too, Bobby.’ But here’s the hitch: Bobby might hear something in her voice, some little thing in the way she said it, and he might wonder, ‘Hey, does her Love mean my Love. Is her ‘I love you’ my ‘I love you’? [my voice trails off] [and to no one in particular, I say] Bobby’s question is a good one.” 

I feel Bobby’s plight with language now because I wonder deep down if my wife does “know” I wasn’t always so scared of something I’ve no control over; but something’s cracked in me. 

Earlier, the radioman said that there were great summer storms coming our way. He said, “Y’all in it’s path.” The storm is coming on strong now. There’s sideways rain and big chunks of hail. The lights are dimming. The thunder is loud. The lightening is bright. It’s getting violent, like the earth is readying for something we can’t understand. It’s all so incomprehensible. 

As the lights flicker, she asks, “You know I know, right?” 

The Eternal Return is basically the theory that there is infinite time and a finite number of events, and eventually the events will recur again and again infinitely. Consider the world as a super-complex chess game. If games of chess are played one after another forever, eventually a game will be repeated since there is only a finite number of possible games. It is the same with the world; eventually events will recur in the same order. The world is an eternal process of coming to be and passing away. The process, however, has no beginning or end. Eventually every combination of matter and energy will be realized and repeated an infinite number of times.