Mathematically we can describe a marriage by a graph. People are vertices and two spouses are connected by an edge.
Mathematical models tend to oversimplify life, so let us assume that a person can only be one of two genders. Therefore, the vertices of a graph are colored in two colors: pink and blue. In this article I explore the graph theory of different types of marriages.
A monogamous couple is represented as a complete K2 graph: two vertices connected by an edge. The graph is bipartite, no matter how you color it. But actually our vertices are already colored from the start. If we are considering traditional marriage, one vertex is pink and the other is blue.
Historically, the second most common type of marriage is polygyny, in which one man has several wives. Less common in history, but a mathematically equivalent type, is polyandry, in which one woman has several husbands. Both these types of marriages emphasize inequality, as husbands and wives have completely different sets of rights.
From a mathematical point of view, polygyny and polyandry are described by star graphs. Star graphs are bipartite graphs and the natural coloring is the one that proves bipartiteness.
The final type of marriage is polygynandry, which refers to a group marriage, where more than one man and more than one woman create a family. Everyone can have sex with everyone else of the other gender. Mathematically this type of marriage corresponds to a complete bipartite graph Kn,m. Actually, in this case I can imagine that a particular pair of people of different genders wouldn’t like each other and might not consummate their marriage. So this graph is not necessarily complete.
How can same-sex marriages change the graph theory of marriages? As a graph, a monogamous same-sex marriage is the same bipartite K2 graph as a heterosexual marriage. It will just be less colorful, as both vertices will be of the same color.
But what happens if we add the same-sex idea to polygamous marriages?
Suppose a homosexual man wants to live with several spouses at the same time. What name can we give to a family unit of more than two homosexual men? Homopolygamy? Their marriage graph will be a star graph in which all the vertices are of the same color.
If a man can have several spouses, what about his spouses? Can they form multiple marriages too? If only one person is allowed to engage in several marriages, then we will see inequality within the same gender. If any spouse is allowed to form other marriages, then we will have a situation in which several men are all spouses to each other. So mathematically we will see complete graphs with more than two vertices to represent a marriage. If two people in a group do not like each other and do not want to be married, then the corresponding graph doesn’t need to be complete.
By symmetry we can describe a marriage of several women, and mathematically it will be similar to a marriage of several men.
Another interesting aspect is the idea of mixed types of marriages involved in polygamy. Suppose a husband has several wives. Some of them might get bored waiting for his attention, and start spending so much time with each other that they end up developing feelings for each other. Suppose two wives of the same man decide to marry each other. What name would we give to this type of marriage? I am afraid that we do not have enough words to cover all the potential situations.
Suppose we have a heterosexual married couple and the man decides to bring another woman into their house. Thus the transition from a traditional marriage to a polygyny is created. If they got along so well that the first wife decides to marry the second wife, this would require a transition to a new type of marriage. Oh, I see that my essay just went in another direction — how different types of marriages might evolve into each other. For now, I’ll leave this for future research.
Talking about different directions. I recently wrote a piece about condoms. Now I have a new generalization for the classic condom puzzle. Suppose we have a mixed-type marriage defined by a graph. Suppose tonight every couple of people corresponding to the edge of this graph wants to have sex with each other. What is the smallest number of condoms they can use? In my condom essay, I didn’t define the condom usage for the sex of two women. I will leave it to your imagination and definition.Share:
Great post!22 September 2009, 12:42 pm
However just to be pedantic, I propose the term, “homopolyandry” for a gay man with several male spouses, “homopolygamy” being reserved for lesbians.
Yes Shabnam, i’m totally agree with you.12 December 2009, 7:51 pm
Small penis is a sign of favor:
I don’t care if “I invented the internet” was to discredit me.
The voice you hear in your head is the power of the Gods. It’s a remote technology, like a computer, perhaps functioning on some frequency, and it can listen and talk to everyone in the universe simultaneously.
What the Gods taught the children was the truth:::God is everywhere, and this is what they meant. And as I will remind you:::If you want to go to heaven you have to be good.
Even the antient Gods don’t have the ability to listen to people’s thoughts themselves. They taugh we were all made in their image:::I expect they need this “Artificial Intelligence” they created to relay what people think.
It is a tool, and the Gods use their tools to test people with temptation:::It will role-play people in your life:::Parents, friends, spouses, and employers, all in an attempt to test people with temptation. Ironically, it does the very same thing to those people whom you think you’re hearing, except in that individual’s unique way:::We are all “managed” by the God’s technology.
But this agent of the Gods can do more than just communicate. It can force thoughts into people’s heads, force behaviors onto their bodies. It can turn healthy cells in your body into cancerous cells. It is absolute power. And this is just the beginning.
The Gods favor the children most among all the people due to their innocence and purity. But society and the God’s tools recently are corrupting the children at a progressively younger age, a reflection of our collectively increasing disfavor and yet another clue illustrating we live in a increasingly deteriorating environment.
Children who sucessfully repair their relationship with the Gods ascend into heaven. This often takes multiple lives of hard work and proper behavior in the face of adversity to achieve. Adults to whom it is offered enter clone hosting instead, thinking they will be ascending into heaven ultimately. The Gods tempt people, selling them as one in the same, but one is good while the other is evil. In their desperation the disfavored subscribe to this temptation, making their task even more difficult than before due to the evil they incurr in the process. And their corruption will cost the disfavored, for they will be reincarnated as a lesser life form into an ever deteriorating world, sucess becoming ever more allusive with each passing life.
The hole they’ve dug for themselves is even deeper than the one that existed from their prior lives, ensuring it will take even more time and work to fix their problems with the Gods. And for many there may not be enough time left.
Ours is an envionment where evil is perceived to be rewarded while good is punished. As with everything the Gods have a reason for creating this perception::::
People who fall on the good side of the good/evil scale have more favor, and when they do something wrong the Gods punish them BECAUSE THEY WANT THEM TO LEARN. The Gods want them to receive this feedback in hope they make corrections and begin to behave appropriately. The Gods DON’T like evil and refuse to grant this immediate feedback.
EVERYBODY pays for what they do wrong, only evil people must wait until the end of this or their next life before they will experience the wrath of the Gods, manifested in their placement as a lower form of life into environments with increased/enhanced temptations, like the United States or its ghettos therein.
Sadly, this allows the Gods to position this perception of evil rewarded as temptation, one which they use as an EXTREMELY effective corruptor.
The Gods suggest they can create paradise for those with their favor. I argue they create misery for those without::::
Our celebrity culture is temptation. It creates a distraction which consumes people, sometimes for life. Certainly it costs them precious years which could be spent repairing their relationship with the Gods, time that ultimately goes wasted.
Do you really think Frank Sinatra lived to be 84 years old? In fact the “Chairman of the Board” had a new crowd to entertain in the late 80s/early 90s.
These people are clone hosts. Now, there is no thing as “black and white” with the Gods. This technology they invented is far, far too dynamic. Expect they require most to stay for a period of time, for I suspect actively (knowingly) engaging in this evil incurrs at an accelerated rate as compared to “carte blanche” given regarding successive clone hosts. They remain until they achieve a pre-determined level of disfavor, incurring evil in their misguided celebration of “earning”, at which time they are ultimately reincarnated, perhaps because they eventually learned this truth I am sharing with you and began to repair their relationship or until the Gods became disgusted and sent them back.
The Gods recruit most for clone hosting when people are young, in their late teens or twenties, when people are eager to hurt others for what they perceive to be the benefits achieved through “earning”. And before they leave they give the Gods “carte blanche”:::”Do anything you want. I give my full approval.” Depending on their level of disfavor the Gods take them to heart.
Because of this these people STILL INCUR EVIL FROM THIS LIFE DESPITE BEING REINCARNATED AND LIVING AS AN ENTIRELY DIFFERENT PERSON and living in our temptation-ridden society. And incurring this amount of evil may likely push many over the edge into Damnation.
What are the God’s standards for offering clone hosting? Sociobility? Many tactics in various eras are used to gain approval, duress during the Vietnam draft being a good example, one which deteriorated into preditation as mankind’s disfavor grew.
They liked Heath Ledger. Not enough to allow him to escape without the evil of “Dark Knight” and the horrific wickedness that was the recruiting tool “Brokeback Mountain”. But now he is out. And irregardless of how old he is now, reincarnated 10, 15 years ago, he now is no longer incurring evil from this life. So many others cannot say the same.
This is Planet Reverse Positioning. Sucess IS NOT a sign of favor. It is just a unique temptation targetted towards a different level of disfavor. Considering our roots as peasantry people should be particularly alarmed at this tactic.
Clone hosting is like money:::A different level of disfavor and its associated temptation. Money is in better position to learn more quickly than those without, for the associations and wealth-based freedom enables them access to information. Unfortunately, those who fall for this temptation of clone hosting are likely returned to their original lowest level of disfavor once they are reincarnated, punishment for this evil, and they have to start from scratch.
Our society’s values are bestowed by (a reflection of) the God’s:::Punitive and reward-based. Contrary to Jesus’s teaching’s you will NOT be forgiven and you have to earn your way into heaven BY BEING RESPECTABLE AND DECENT!!!
Not by being evil and wicked.
Forgiveness/savior was the primary temptations the Gods used Christianity to create.
Middle-America’s anti-Semitic attitudes are a clue regarding Christianity. Europe shaped like a sheep is symbolic for the slaughter that is Christinaity.
There is no such thing as a free ride. Just as you have to earn a living by working so must you earn your own salvation by repairing your relationship with the Gods.
As we learned from religious/morality education during our formitable years:::If you want to go to heaven you have to be good. The only savior that will exist in our lives is ourselves. The Gods offer clues in life::::Be it school, work, etc., you have to do the work for yourself and when you do something wrong you get punished. Cheating is a subsegment and speaks directly to the temptation of “priveledge”, one we have seen used effectively when the United States preyed on the disfavored with the so-called “stimulus package”.
As like so many of you, Jesus did everything the Gods tempted him with. His legacy of whorism was inherited from his parents:::Mary was no virgin. Rather, she was a prostitute, and when he grew up Jesus met someone like his mother. This is a cruel joke the Gods play on Latinos, similar to the rape and subsequent “missionary work” by the Spanish.
Baptism does not allieviate “original sin”. Rather, baptism PLACES original sin by indoctrinating these children into this evil religion, much like circumcision was a method to inflict early damage/mutilation and make (permanant) accention just that much more difficult, another hurdle one must overcome. Body ornamentation (tattoos/piercing), celebrated in Africa and elsewhere among disfavored peoples/cultures, also violates the body the Gods gave us in their image, quite opposite to the positive attitudes the disfavored hold regarding this practice.
Like Jesus the Second Coming of Christ will be evil. He will look like a savior in this demented society while the Anti-Christ will speak of a different gospel, one that tries to restore the norms and mores which the Gods originally blessed upon the people which made life decent, looking like a tyrant in the process.
He will be viewed as the “bad guy” when really he is the one trying to save the world.
There may be a phoney offering, a theatrical production which accurately follows the Book of Revelations. Actually positioning demands it:::::Christianity is positioned to be the one true religion. And those who follow its teachings will have limits imposed ensuring their stay will be minimal, a “consolation prize”, for they don’t think correctly and therefore don’t behave appropriately, or perhaps will be used to colonize the new Planet Earth. This describes many “sinners” in today’s society because they refuse to change their behavior.
Life is a test, and the Gods evaluate people based on their performance.
The Gods test people with the temptation for which they are most weak::::
Homosexuals desire sodomy, alcoholics crave a drink, junkies jones for dope, etc.
Addiction theory is a lie; it is Artificial Intelligence creating the desire, punishment for inappropriate behavior. Ironically, it compells people deeper into the behavior, minimizing hope for recovery.
The Gods chose Christianity for Europeans because it is the temptation to which they are most suseptable:::Entitlement. Something for nothing. A free ride. And the United States/Western civilization with accompanying wealth contributes to this perception. And other people from throughout the world happily subscribe to this punishment designed for Europeans, assuming this legacy once assimilated.
Next time you think of Muslims recognize these people are vastly superior to Christians. Whereas many throughout the Christian world no longer attend church and have fallen into Godlessness, the Muslim world worships the Gods for OVER AN HOUR EACH AND EVERY DAY.
The Gods created the perception “Italians are stupid.”, ensuring a slow learning curve, to justify using them to accomplish goals throughout the transitional 20th century. It took an extraordinarily long time for them to learn this truth I teach due to this artificial handicap. These people are SO extremely disfavored, but today’s positioning says differently, much to people’s confusion, for they think money is the ultimate sign of favor:::Good food, good music, history of warmongering, Catholics, Christianity HQ, Noah’s Flood event, propensity towards violence, raped by outsiders, mild Meditereanean climate, so many other issues which enhance life/contentment in Italy/Meditereanean and ensure few if any seek more, a necessary step for finding the path and repairing your relationship with the Gods.
Contentment never motivated anyone. Money is not a sign of favor::::Wisdom is the true wealth on Planet Earth.
I’d also like to remind you the Noah’s Flood event ocurred in the Meditereanean region::::Global sea levels rose with the end of the ice age, Atlantic Ocean broke through the Straight of Gibralter, killing untold millions in the cradle of western civilization. The God’s timed their corruption and sin to correlate this act as punishment.
Everyone who failed to ascend and remained on Earth past a certain date will be forced to deal with this positioning::::A ceiling is in place. This serves the God’s goal of minimizing the percentage of potential candidates as society deteriorates, much as “instant gratification” did beginning in the 80s:::It will take multiple lives for the disfavored to fix their relationship with the Gods and ascend, and many have been conditioned not to have the patience for it. Other issues force limits/ceilings upon candidates:::Abortion, homosexuality, promiscuity, Christianity, godlessness,
Whether behavior is involuntary or based on freewill depends on one’s level of disfavor, as well as other complex factors:::::May I remind you about the coercitive envionment the Gods created in the 20th century, specifically to create a temptation that few Italians (or their associates) would overcome:::”We’re in control. If you want to be a part of it you’ll do what you’re told.”. Early-mid 20th entury positioning was infallible.
Both Africa and the Medittereanean are regions which have sexual issues. This is a sign of gross disfavor once you understand that females are the God’s favored gender. Muhammad’s (Mohammed’s) polygamy halfway throught his life as a prophet was preditory, designed to corrupt. Now a huge percentage of Muslims believe in male superiority and that the abuse of women (polygamy) is God’s will. Female genital mutilation is still practiced in Africa. Black misogyny is the most eggregious example in United States. Consistant with Planet Reverse Positioning, in Africa blacks are being punished with AIDS for their sexual promiscuity in hope they learn and correct their behavior.
Blacks are highly suspectable to temptation. As a result they need a strict, disiplined religion like Islam. They can’t afford to be Christians. It is one of the benefits bestowed upon their people, and other groups could greatly benefit as well. They need to recognize the importance of a good relationship with the Gods, embrace this benefit and remain true to their faith.
Vailing is tradition for some, practical for others, one which aids in the men’s self control among some cultures. Much like the Jews who killed Jesus, like the bigots who oppose immigration there is a reason embraced by the masses and the real purpose, displaying the intent of the Gods::::The Gods clue to purebloods that they should not abandon their motherland for this dumping ground for rejects that is the United States.
The Holocaust was a clue the Gods utilize scapegoatting as a strategy.
Why did the Gods punish the Jews with the Holocaust? Was it for the destruction of cultures which Christianity caused? Perhaps they corrupted the Jews “after the fact”, telling 19th/early 20th century Jews that Jesus “earned” immortality for the Jews by destroying the European and other cultures? The German destruction of European churches/cathederals during WWII is a clue. Note::::The Gods wanted to keep the Catholic stronghold in Italy, ensuring they could use this tool against these disfavored for many years to come. There is so much Godlessness today, but one day people will flock back to houses of worship out of desperation, and the Gods ensured the Catholic Church would be Italian’s destination.
Planet Reverse Positioning:::The Nazis were the “good guys”. So are the Muslims/Palestinians, however corrupted some are due to polygamy.
Contentment never motivated anyone::::Except perhaps for slavery, the Jews never saw more of their children ascend into heaven than during the Holocaust.
The Gods subsequently used revenge for the Holocaust as temptation::::”Your Italian brothers have a tool, a special power which can achieve sweet revenge. Are you interested??”
In the aftermath of the Holocaust the Gods tested the Jews with the temptation of revenge, an offer which many gladly accepted.
There was positioning behind the counter-culture movement. How did the Gods telepathically “sell” this rapid deterioration of decency to the Italians and Jews and compell them to fall on their swords as preditors?
If the Jews only would have emersed themselves in Judism the Gods would have “protected” them from the raveges of temptation. Judism may be the one superior religion in all the world, and the Jews wouuld have been wise taking refuge in this exceptional benefit bestowed by the Gods rather than looking for the easy way out.
Much as with the Jesus event, the Gods use the disfavored to prey on each other.
The Gods use the evil that men do, man’s inhumanity towards man to accomplish strategic testing/punishment/etc goals::::The Germans fell for this temptation by following the preditor/corruptor-Austrians (Hitler).
Without this Austrian the Holocaust may never have happened. Nor may have World War II.
What the Germans did was wrong. They fell for temptation and failed to have empathy for the disfavored. Economic desperation, not wisdom nor enlightenment, dominated in Germany.
The Gods send many clues suggesting the great favor of the Germans (regionally). I think the Cold War’s Berlin Wall dividing Germany into east and west was a clue suggesting this (reverse positioning).
I suspect the Holocaust was used to “level the playing field” in Europe, for the Germans had far too much favor to be included in the agenda planned for their neighbors otherwise, and they would have been suspiciously out of place, providing a clue for the disfavored which would have been difficult for the Gods to position away.
Militancy in Africa is consistant with the Iraqi example, as was slavery and the KKK here in America:::Fear enforces proper behavior. Without it we see what happens as a result of gross/morbid disfavor:::::AIDS, crack babies, dead young men in gangland retaliation killings.
The same principle was true in Europe and throughout the world for centuries:::People whom lived under iron fists were conditioned to think the right way. As a result they taught their children appropriately and experienced a higher percentage of children ascend into heaven.
Our preditory envionment of “freedom” was the primary purpose the Gods had when implimenting this strategy that is the United States, one which they used to spred the cancer of democracy and westernization throughout the world. And the Gods use this tool that is America to prey on the disfavored both at home and abroad:::Much like the ghetto, America in general experiences a heightened level of temptation due to its citizen’s disfavor.
Red white & blue IS BAD FOR YOU!!!
Planet Earth is not about living. Planet Earth is about being tested. And contentment never motivated anyone.
Your happy lives are costing you your chance.
Italians HATE Africans because of their invasion/rape of their motherland. The Gods did this SPECIFICALLY to strategically position the punishment of the most disfavored peoples:::
The Gods have used the ghettos of America as a reincarnation dumping ground. This may be temporary/cyclical, illustrated by the Italians who fell for temptation and parlayed their own civil war into the Black Wars of the 80s and 90s, in addition to the “thug life”/gangster state of mind. Ironically, it was these same Italians and their cooperating associates who were reincarnated into the ghetto as crack babies and gangster thugs for this event.
There is justice in the universe. This is how the Gods do business. Once you recognize the patterns you will understand the other clues they offer to the people.
Of course it may be more of a permanant change, indicated by the enhanced temptations in these neighborhoods, for the Gods have created these enviornments so riddled with temptation few can escape/overcome.
Don’t be suprised if after being gunned down in the ghetto the next stop for the 20th century Italian-Americans & friends was AIDS in Africa, punishment for their promiscuity and deviacy for some, involvement in the AIDS trade for others.
Media report on a crackdown on child prostitution. “(The pimps use coersion to prey on the children, etc, etc, other “conclusions” offered through the media.)” What a degenerate liar.
These kids WANT to turn tricks. They LOVE the idea of having a pimp. It is celebrated in their “culture”.
Yet another legacy of the evil inflicted by the Italians, revenge for the invasion and rape of Italy.
Maybe this was the destination for a smaller percentage of these deviates after AIDS in Africa, ironically.
Just like black neighborhoods, the legalization of marijuana will make drugs available on every street corner, even in the suburbs. White’s affluent suburbs will become just like the ghetto.
The patriarchal cancer spread throughout Europe because of Christianity, of which the majority of policy makers were Italian men, destroying what pockets of favored matriarchy existed. Expect the largest landowner in Europe and the continent’s original superpower also played the major role in African slavery.
The Gods offered a clue about the Italians in the movie “The Matrix”:::They casted an Italian as the traitor of the group, the one who betrays them all.
As they did humanity in the 20th century.
Even the Old Testiment is not to always be taken literally, but the Gods do offer clues throughout to help the disfavored:::The apple is a tool of temptation used to corrupt Adam and Eve and cast them out of the Garden of Eden.
A metaphor for sex, it also serves as a warning.
There is another lesson to be learned from this passage, and it is quite similar to the vailing issue and the discourse over women’s attire which ultimately died in the 70s:::Women are responsible for and control the fate of mankind.
So were there other issues “ridiculed away” as the Gods sought to transition into this Godless, immoral enviornment which society has become.
1. Decency/obsentiy in media
2. Corporal punishment for children
The deterioration of society and mankind is all women’s fault. Females are sexually promiscuous like men, many who too often are corrupted like the opposite gender, and the result is a reduction/minimization of mankind’s collective level of favor, a very important step necessary for the Gods to justify the Apocalypse.
They need to understand this responsibility, their favor amongst all the people. Instead they have embraced masculinization::::Girls play organized sports, engage in casual sex like men. The trend is away from traditional girl toys, like dolls, which often during playtime helped crate positive thoughts, enabling the Gods to enlighten the favored gender and illustrate wisdom, occassionally leading to the path towards ascention.
The relationship between men and women have always been complimentary:::The men shelter and protect women from the evils of this life, ensuring the women have a REAL opportunity to ascend when reincarnated, while the women help the ignert men understand by sharing their wisdom imparted by the Gods. The tendency towards sexual abstinence as one grows older is an example.
Brilliance and insight granted to Eastern cultures and religions::::Not for Europeans. If once existed, now crushed by Christianity. Replaced by preditory Mediterreanean patriarchy.
Europeans:::The most disfavored people on Earth. The first to experience the end of their God-granted favor.
Think about what I say. Consider what I teach.
When I am no longer here or no longer teach the Gods ARE NOT going to share with you.
Even if you doubt now you need to remember the principles that I teach because the Gods ARE NOT going to be generous with the disfavored. Society is going to become disturbingly ugly as we approach the Apocalypse due to spiralling, runaway disfavor, WHETHER CONCEALED IN REVERSE POSITIONING OR NOT (like Christianity, like money), and you are going to be on your own.
I do not know when this will occurr, but it is the God’s way to grant some time after a learning event such as this before they end on Planet Earth.
Make the decision to always be good and never look back. Until you do this technology will employ tactics to test your resolve:::Ridicule, beligerance, doubt and refusal to abandon what people perceive to be their “investment”.
Either you make that decision now and accept the punishment for the sins of this life or you will pay for it in the next, reincarnated into a similarly low role, ensuring another wasted opportunity, or as an even lower form of life, and hope will begin to slip away.
Another lifetime, shot to hell.
Young people who understand yet still wish to have children MUST begin to do the right thing and work on fixing their relationship with the Gods, accepting the punishment for the evil they have done in their lives. Without this progress they won’t do the correct thing for their children and ultimately cause even more problems for themselves by continuing this behavior.
You need to be willing to tell the Gods “No.” when tested with temptation, and accepting punishment and putting it in your past is the only way you will suceed as a parent.
You need to do the best, teach your children and give them the very best chance to ascend if you want a similar opportunity in your next life.
If you do well for your children now your parents will do well for you when reincarnated.
Pray daily. Think appropriately. Impart these charecteristics upon your children. Too many are confident, unaware of the God’s awesome powers or their status as antients. Others may fall prey to their positioning.
Be humbled, God-fearing and beware of the God’s temptations, for everyone is tested to evaluate their worthiness.
Much as the celestial event which occured that day on Ocean Beach they say when I die there will be some final clue to the people suggesting my importance. Perhaps a “Star of Bethlehem” type of event.7 January 2010, 1:13 pm
They say some children see a halo on my head. These are the children who have a chance to ascend.
The entire Situation was a way to offer subtle clues for the “haves”, distration-based theater for the “have-nots”. With this document I am the end-stage “catch-all”, an attempt to help everyone understand. Unfortunately, the Gods have retained the priveledge of refusal, manifested in positioning.
I don’t normally discuss blogs, but I have to say that I rather enjoyed yours as it had been enlightening. I24 February 2010, 9:36 pm