Reason and Treason: A collection
written by Teddy
Within these bindings contain a chapter from a post-war Arithmancy textbook describing the mathematics behind bad luck
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05/31/21
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Luck-Determining Variables
Chapter 1
Have you ever had a lucky rabbit's foot? Has a black cat ever crossed your path? Do you dread Friday the 13th or revel in it? Have you ever known someone who had wonderful or horrible luck for no apparent reason? Read on to discover some of the things in your life that influence blind chance.
17.1 What Are Luck-Determining Variables?
In chapter 15 you learned the basic equation for luck, in which kl stands for a variable which must usually be empirically determined. A variable can be said to be luck-determining if it affects kl in some form, or if it affects kl in certain situations. The nature of kl is not fully understood, but it has been linked to several luck variables, among them the Murphy quotient, the Rasputin variable, and, perhaps most famously, Raglan's heroic constant.
17.2 Luck-Determining Variables in the Real World
It is not uncommon to encounter an object which influences one's personal luck-determining variables in one's day-to-day life. For example, the bite of the Mackled Malaclaw can artificially decrease kl for up to a week, and the rare potion Felix Felicis, when imbibed, increases kl by reducing a subject's Murphy quotient to zero. These are rare, however, compared to the small increase of kl caused by enchanted rabbit's feet sold to New Orleans tourists sampling the mixture of magical cultures the region offers, and the brief spike in luck caused by leprechaun gold. This constant fluctuation in any one person's luck has thus far prevented Muggles from discovering a clear scientific basis for the concept of "luck," but due to the advanced Arithmancy techniques (some of which are covered in Chapter 30), some luck-determining variables can be measured indirectly.
17.3 The Murphy Quotient
The Murphy quotient was discovered in the early 1950s by researchers in the (then-government-funded) American organization, the Men in Black. The experiment (later censured for violating the American Arithmancy Association's ethics guidelines) placed the subject in a small room and asked to answer a series of multiple-choice questions with four questions. The "correct" answers to each question were determined randomly, so a subject theoretically had a one-in-four probability of being correct. If the answer was incorrect, an electric shock was administered to the subject, and as the series of questions continued, the level of the shocks administered was increased. Electricity is a form of energy used by Muggles for a variety of purposes, including, in some countries, to execute criminals. It is more predictable than magic, and is therefore favored for use in certain types of probability experiments.
The experimenters found that the frequency of shocks was inversely proportional to a subject's kl, as was expected. However, it was also found that certain subjects, though they had similar kls to average subjects, were more likely to be administered shocks when the level of the shocks was very high. This made the effects of the collective shocks earned far worse than mere number of shocks would indicate, both because of the level of electricity experienced and because doing well on earlier questions would lull the subjects into a false sense of security.
17.4 Murphy's Law
Muggleborn students may have heard of Murphy's Law, that "whatever can go wrong, will go wrong." In fact, Murphy's Law in Arithmancy is somewhat more specific than that:
The probability of a misfortune in the presence of a particular person is equal to the person's Murphy quotient, km, multiplied by the absolute probability of the event and the degree of unpleasantness the event's occurrence would place the person into.
Or:
p = p0kmns
(eq. 17.1)
where p is the ultimate probability of the event, p0 is the absolute probability, and ns is the degree of unpleasantness (ns is covered in more detail in chapter 32, Relative Nastiness and Absolute Horror). Note that, as neither Murphy quotients nor probabilities can be negative, this equation is only applicable when the event would be unpleasant for the subject.
17.5 The Rasputin Variable
The Rasputin variable is named for Grigori Rasputin, the infamously difficult-to-kill Russian Seer, and affects a subject's chances of dying. It was originally thought to vary from situation to situation, but it has been experimentally determined (using Time-Turner clones of rats) to be constant for a given subject.
Because of the difficulty in studying the Rasputin variable without being prosecuted, it is extremely poorly-understood, and as Rasputin-related equations have been known to induce panic attacks, insanity, and Mahavira's Madness (more commonly known as Divide-By-Zero Dementia) in O.W.L.-level students from 20 paces, they are not contained in this text. However, as the Rasputin variable is intimately linked to the Murphy quotient and Raglan's constant, a brief introduction may be useful to the continuing Arithmancy student.
17.6 Raglan's Heroic Idiocy Constant
Variously known as Raglan's constant, the heroic constant, and Lord Raglan's heroic idiocy constant, this Arithmantic principle gained much publicity directly after Harry Potter's defeat of Lord Voldemort. The higher a heroic constant a person possesses, the more likely they will be able to turn an unpleasant situation to their advantage, and the more dire the situation is, the higher the likelihood that they will escape not only with their lives but win a significant victory in the process.
There is no known safe setting in which to determine the heroic constant of a particular subject. The Men in Black (no longer affiliated with any governmental entity; for an interesting look at scientific ethics and Muggle politics in the magical world, see For Their Own Good, R. Manheim, 1993.) conducted a series of experiments in 1984 which led to their facilities, housed in the Statue of Liberty, being destroyed. The damage to the statue was repaired, ostensibly for the statue's centennial, but the United States Department of Magic estimates that nearly half of all personnel working in the area were lost in the fire. Augustus Rookwood also attempted a brief series of experiments on Raglan's constant after the Death Eater takeover of the Ministry, but his subsequent capture in the Battle of Hogwarts, three days after the experiment was started, likely prevented his further investigation of the subject. It can be presumed that neither the Men in Black nor Mr. Rookwood had high Raglan constants.
There are several factors which nearly all possessors of very high heroic constants possess; they are often born in highly unusual circumstances, usually raised at least in part by people who are not their birth parents, are quite often possessed of a foolhardiness which serves them uncannily well, and frequently die on hilltops or raised platforms. (An ill-concieved campaign to restrict Aurors and recipients of the Order of Merlin from setting foot on hills for their own safety was ended by Hestia Jones, who proposed to climb Mt. Everest should those involved not desist immediately.) However, whether these circumstances are due to the magnitude of the subject's hero constant, or whether the hero constant is influenced so fully by the events of the bearer's life is not known.
17.7 Luck-Influencing Variable Connections
Nearly all of those who have been determined to possess a high hero constant also have very high Rasputin variables and usually have higher-than-average Murphy quotients. The same, unfortunately, cannot be said of possessers of high Murphy quotients and Rasputin variables.
17.1 What Are Luck-Determining Variables?
In chapter 15 you learned the basic equation for luck, in which kl stands for a variable which must usually be empirically determined. A variable can be said to be luck-determining if it affects kl in some form, or if it affects kl in certain situations. The nature of kl is not fully understood, but it has been linked to several luck variables, among them the Murphy quotient, the Rasputin variable, and, perhaps most famously, Raglan's heroic constant.
17.2 Luck-Determining Variables in the Real World
It is not uncommon to encounter an object which influences one's personal luck-determining variables in one's day-to-day life. For example, the bite of the Mackled Malaclaw can artificially decrease kl for up to a week, and the rare potion Felix Felicis, when imbibed, increases kl by reducing a subject's Murphy quotient to zero. These are rare, however, compared to the small increase of kl caused by enchanted rabbit's feet sold to New Orleans tourists sampling the mixture of magical cultures the region offers, and the brief spike in luck caused by leprechaun gold. This constant fluctuation in any one person's luck has thus far prevented Muggles from discovering a clear scientific basis for the concept of "luck," but due to the advanced Arithmancy techniques (some of which are covered in Chapter 30), some luck-determining variables can be measured indirectly.
17.3 The Murphy Quotient
The Murphy quotient was discovered in the early 1950s by researchers in the (then-government-funded) American organization, the Men in Black. The experiment (later censured for violating the American Arithmancy Association's ethics guidelines) placed the subject in a small room and asked to answer a series of multiple-choice questions with four questions. The "correct" answers to each question were determined randomly, so a subject theoretically had a one-in-four probability of being correct. If the answer was incorrect, an electric shock was administered to the subject, and as the series of questions continued, the level of the shocks administered was increased. Electricity is a form of energy used by Muggles for a variety of purposes, including, in some countries, to execute criminals. It is more predictable than magic, and is therefore favored for use in certain types of probability experiments.
The experimenters found that the frequency of shocks was inversely proportional to a subject's kl, as was expected. However, it was also found that certain subjects, though they had similar kls to average subjects, were more likely to be administered shocks when the level of the shocks was very high. This made the effects of the collective shocks earned far worse than mere number of shocks would indicate, both because of the level of electricity experienced and because doing well on earlier questions would lull the subjects into a false sense of security.
17.4 Murphy's Law
Muggleborn students may have heard of Murphy's Law, that "whatever can go wrong, will go wrong." In fact, Murphy's Law in Arithmancy is somewhat more specific than that:
The probability of a misfortune in the presence of a particular person is equal to the person's Murphy quotient, km, multiplied by the absolute probability of the event and the degree of unpleasantness the event's occurrence would place the person into.
Or:
p = p0kmns
(eq. 17.1)
where p is the ultimate probability of the event, p0 is the absolute probability, and ns is the degree of unpleasantness (ns is covered in more detail in chapter 32, Relative Nastiness and Absolute Horror). Note that, as neither Murphy quotients nor probabilities can be negative, this equation is only applicable when the event would be unpleasant for the subject.
17.5 The Rasputin Variable
The Rasputin variable is named for Grigori Rasputin, the infamously difficult-to-kill Russian Seer, and affects a subject's chances of dying. It was originally thought to vary from situation to situation, but it has been experimentally determined (using Time-Turner clones of rats) to be constant for a given subject.
Because of the difficulty in studying the Rasputin variable without being prosecuted, it is extremely poorly-understood, and as Rasputin-related equations have been known to induce panic attacks, insanity, and Mahavira's Madness (more commonly known as Divide-By-Zero Dementia) in O.W.L.-level students from 20 paces, they are not contained in this text. However, as the Rasputin variable is intimately linked to the Murphy quotient and Raglan's constant, a brief introduction may be useful to the continuing Arithmancy student.
17.6 Raglan's Heroic Idiocy Constant
Variously known as Raglan's constant, the heroic constant, and Lord Raglan's heroic idiocy constant, this Arithmantic principle gained much publicity directly after Harry Potter's defeat of Lord Voldemort. The higher a heroic constant a person possesses, the more likely they will be able to turn an unpleasant situation to their advantage, and the more dire the situation is, the higher the likelihood that they will escape not only with their lives but win a significant victory in the process.
There is no known safe setting in which to determine the heroic constant of a particular subject. The Men in Black (no longer affiliated with any governmental entity; for an interesting look at scientific ethics and Muggle politics in the magical world, see For Their Own Good, R. Manheim, 1993.) conducted a series of experiments in 1984 which led to their facilities, housed in the Statue of Liberty, being destroyed. The damage to the statue was repaired, ostensibly for the statue's centennial, but the United States Department of Magic estimates that nearly half of all personnel working in the area were lost in the fire. Augustus Rookwood also attempted a brief series of experiments on Raglan's constant after the Death Eater takeover of the Ministry, but his subsequent capture in the Battle of Hogwarts, three days after the experiment was started, likely prevented his further investigation of the subject. It can be presumed that neither the Men in Black nor Mr. Rookwood had high Raglan constants.
There are several factors which nearly all possessors of very high heroic constants possess; they are often born in highly unusual circumstances, usually raised at least in part by people who are not their birth parents, are quite often possessed of a foolhardiness which serves them uncannily well, and frequently die on hilltops or raised platforms. (An ill-concieved campaign to restrict Aurors and recipients of the Order of Merlin from setting foot on hills for their own safety was ended by Hestia Jones, who proposed to climb Mt. Everest should those involved not desist immediately.) However, whether these circumstances are due to the magnitude of the subject's hero constant, or whether the hero constant is influenced so fully by the events of the bearer's life is not known.
17.7 Luck-Influencing Variable Connections
Nearly all of those who have been determined to possess a high hero constant also have very high Rasputin variables and usually have higher-than-average Murphy quotients. The same, unfortunately, cannot be said of possessers of high Murphy quotients and Rasputin variables.
