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Chávez Is Jailed for Organizing a National Lettuce Boycott Summary
Labor organizer and farmworkers' rights leader César Chávez was jailed for boycotting lettuce growers, elevating him to the status of champion of the oppressed and the poor in the minds of many Americans. The boycott led to legislation that benefited farmworkers.
Throughout the history of the farm labor movement in California, growers have relied on a cheap, dependable workforce that has been composed primarily of minorities. The state's first farmworkers were American Indians. The Native American population in the state was reduced from an earlier level of 300,000 to 30,000 in 1860 through disease and ill-treatment. Native Americans were replaced by Chinese, who had been brought to America to help construct the Central Pacific and the Union Pacific railroads. The Chinese were eager to work in America, even though thousands succumbed to disease on the passage across the Pacific. When farmers replaced livestock and wheat with fruit and truck crops toward the end of the nineteenth century, even more Chinese immigrated, until Congress suspended Chinese immigration in 1882. Lettuce boycott (1970) Labor unions;lettuce boycott Boycotts [kw]Chávez Is Jailed for Organizing a National Lettuce Boycott (Dec. 4, 1970) [kw]National Lettuce Boycott, Chávez Is Jailed for Organizing a (Dec. 4, 1970) [kw]Lettuce Boycott, Chávez Is Jailed for Organizing a National (Dec. 4, 1970) [kw]Boycott, Chávez Is Jailed for Organizing a National Lettuce (Dec. 4, 1970) Lettuce boycott (1970) Labor unions;lettuce boycott Boycotts [g]North America;Dec. 4, 1970: Chávez Is Jailed for Organizing a National Lettuce Boycott[11040] [g]United States;Dec. 4, 1970: Chávez Is Jailed for Organizing a National Lettuce Boycott[11040] [c]Laws, acts, and legal history;Dec. 4, 1970: Chávez Is Jailed for Organizing a National Lettuce Boycott[11040] [c]Social issues and reform;Dec. 4, 1970: Chávez Is Jailed for Organizing a National Lettuce Boycott[11040] [c]Business and labor;Dec. 4, 1970: Chávez Is Jailed for Organizing a National Lettuce Boycott[11040] [c]Trade and commerce;Dec. 4, 1970: Chávez Is Jailed for Organizing a National Lettuce Boycott[11040] Chávez, César Huerta, Dolores Brown, Jerry Meany, George Kennedy, Robert F. [p]Kennedy, Robert F.;and organized labor[organized labor] Lindsay, John V.
At almost exactly the same time that the Chinese labor supply was cut off, Japan relaxed its long-standing ban on emigration, and workers from Japan began to pour into California. By 1910, their numbers had swollen to more than forty thousand. Even though the Japanese were industrious, they were not ideal workers from the growers' viewpoint because they dreamed of owning land and becoming farmers in their own right. Agitation over the "yellow peril" and the "rising tide of color" in California culminated in 1924 in a new immigration act that ended immigration from Asia. Fortunately for the growers, the Mexican Revolution of 1910 opened another pool of foreign labor.
Tens of thousands of rural families fled Mexico, and by 1920 the census reported nearly 100,000 Mexican nationals in California. Between 1942 and 1964, California received special dispensation to use Mexican contract workers. The influx of these braceros (literally, "arm-men") increased the Mexican population in the state by 100,000. For the most part, the growers welcomed the contract workers because they could be forced to work for whomever they were told under terms set by the growers. In addition to those who immigrated legally from Mexico, an untold number of workers crossed the border illegally into the United States. In some ways, these workers were entirely at the mercy of employers and labor contractors. Except for a brief period during the 1930's, when thirty thousand Filipinos were imported to California, Mexicans provided the bulk of the farm labor force for most of the twentieth century. Mexican immigrants fit the growers' concept of the perfect labor force because they did not, for the most part, aspire to land ownership or to fringe benefits.
For nearly one hundred years, agricultural employers beat back attempts to organize the workforce. Prior to the 1960's, migrant workers had never won collective bargaining rights because they had not been highly motivated to organize. In addition, their itinerant lives made it difficult for them to meld into a solid group. Although the farm labor movement was active during the twentieth century, it was not very effective, primarily because leadership did not come from the groups that made up the workforce. Leadership came from political groups (such as the Industrial Workers of the World), intellectuals (such as Ernesto Galarza), urban unionists (such as Norman Smith and Clive Knowles), and the clergy (such as Father Thomas McCullough).
César Chávez in 1966.
(Library of Congress)
César Chávez succeeded where his predecessors had failed partially because he worked in the fields as he organized and was trusted by the farmworkers as no other leader had been. As the son of migrant workers, Chávez and his family had lived in their car or in tents without heat or light, had gone without shoes in the winter, and had eaten mustard greens to stay alive. Chávez and his brothers and sisters attended segregated schools, which provided little more than child-care service.
Until his family learned the tricks of the labor contractors, they had worked hard harvesting fields only to be cheated by growers when the work was completed. There was no job security, and fringe benefits were few. The labor camps that they lived in periodically were a collection of nine-by-eleven-foot tin shacks that collected the heat of the summer sun and lacked indoor plumbing. Many of the conditions that Chávez's family and thousands of other Mexican families experienced were similar to those endured by the waves of Chinese, Japanese, Mexican, and Filipino workers who had preceded them.
Chávez became involved in the farm labor movement almost by accident. Like many second-generation Mexican Americans, he and his wife had left the migrant stream and probably would have left agricultural work altogether if Chávez had not spoken to Father Donald McDonnell McDonnell, Donald . Father McDonnell got Chávez interested in the farm labor movement by telling him about Pope Leo XIII's endorsement of labor unions. Through Father McDonnell, Chávez met Fred Ross Ross, Fred , a representative of the Community Service Organization Community Service Organization (CSO) who had come to California to set up local chapters. In 1953, Chávez became a statewide organizer for the CSO and, with the help of his principal assistant and a labor organizer in her own right, Dolores Huerta, built the CSO in California to twenty-two chapters. After ten years, Chávez left the CSO because, unlike many CSO leaders, he believed that it would be better for his people to end the bracero system and upgrade farmwork instead of fleeing to an uncertain future in the cities. He believed that farm labor organizing should be emphasized much more than it was.
After withdrawing his life savings of $900 in April, 1962, Chávez and his family moved to Delano, where he founded the National Farm Workers Association National Farm Workers Association that same year with no outside help. The NFWA's first big strike occurred at the Delano grape strike, in response to a cry for help in 1965 from the Filipino grape pickers in Delano. At that time, grape pickers in Delano received $1.20 an hour, which was $.45 less than the federal minimum wage. The pickers lived in shacks with no heating or plumbing. In addition, pickers were often accidentally sprayed with insecticides. At stake were the interests of 384,100 farmworkers in California and 4 million agricultural workers in the United States.
To keep pressure on the table-grape growers, Chávez and Huerta decided in 1967 to stage a nationwide boycott against them. By 1968, with the support of the Roman Catholic church and such influential Americans as Senator Robert F. Kennedy and New York City mayor John V. Lindsay, the boycott succeeded in lowering grape sales by 12 percent. Chávez's twenty-five-day fast in 1968 united California's farmworkers behind the movement and established Chávez as a hero. Victory was finally achieved in 1970 when the largest producer among grape growers in the United States, John Giumarra, Jr. Giumarra, John, Jr. , signed contracts recognizing the existence of the union (known by this time as the United Farm Workers United Farm Workers Organizing Committee, or UFWOC), and agreeing to pay $1.80 an hour plus $.20 for each box of grapes. Chávez proved for the first time that field-workers could force an entire industry—85 percent of the grape growers in California—to sign a contract with their union leaders.
Fresh from the triumph of La Huelga (the strike), Chávez embarked on a much more ambitious crusade. This time the product was lettuce, picked by workers in California and Arizona. The lettuce growers not only had the support of corporations such as Purex but also were backed by the U.S. Defense Department, which had refused to buy any "union lettuce." The UFWOC's primary target was Bud Antle's Antle, Bud huge ranch in the Salinas Valley. Antle was one of many growers in Salinas, King City, the Imperial Valley, and the San Joaquin Valley who had secretly signed contracts with the Teamsters Teamsters Union in an effort to destroy the UFWOC.
On September 17, 1970, Chávez announced that the UFWOC was sending people to sixty-four cities in North America to organize a national boycott of lettuce. Chávez's announcement was in direct defiance of Superior Court Judge Anthony Brazil's Brazil, Anthony decision the day before to grant permanent injunctions against picketing to thirty growers, on the grounds that this was a jurisdictional dispute that was illegal in California. Knowing full well of the publicity that would develop if he were jailed, Chávez continued the boycott against Antle and ordered that the following statement be given to the press on the day that he went to jail:
Boycott Bud Antle! Boycott Dow Chemical! And boycott the hell out of them! Viva!
Chávez's contempt-of-court trial was held on December 4. The presiding judge, Gordon Campbell Campbell, Gordon , sentenced Chávez to jail on each of two counts of contempt of court and ordered that he remain in jail until he notified all UFWOC personnel to stop the boycott against Antle. The judge also fined Chávez $500 for each of the two counts. Chávez's jail sentence generated the attention that he had hoped for. While he was in the Salinas County Jail, visits to Chávez by Coretta Scott King and Ethel Kennedy were covered by the national press and the major television networks.
A week after Chávez was jailed, the State Court of Appeals denied a union petition that the Antle injunction be set aside. The UFWOC then appealed the decision to the California Supreme Court, Supreme Court, California which ordered Chávez's release twenty days after he was jailed. During a mass of thanksgiving that was held in the parking lot, Chávez told a crowd of about four hundred union supporters, "Jails were made for men who fight for their rights. My spirit was never in jail. They can jail us, but they can never jail the Cause." Four months later, the California Supreme Court ruled that the UFWOC had the right to boycott Bud Antle.
Chávez was correct in his assumption that the contempt-of-court trial and his subsequent jail sentence would bring La Causa (the farm labor movement) to national attention. Chávez's charismatic leadership, which was based on Mahatma Gandhi's philosophy of passive resistance, convinced many Americans that Chávez was the logical successor to Martin Luther King, Jr., and Robert Kennedy. The political ramifications of Chávez's jailing extended to both the union halls and the courts.
The Teamsters' fear that the court hearing would turn public opinion against them was well founded. In 1973, when the Teamsters called in about one hundred"guards" at $67.50 per day to protect strike breakers from interference by Chávez's pickets, newspapers across the nation branded them as "goon squads." Convinced that the Teamsters and the growers were jointly seeking to destroy the farmworkers, George Meany threw the full support of the AFL-CIO AFL-CIO[AFL CIO] behind the grape and lettuce boycotts on April 8, 1974. Finally, in 1979, the Teamsters signed a "peace treaty" with the UFWOC that gave the field hands to the UFWOC and the canners, packers, and farm-truck drivers to the Teamsters. This was an amazing concession, considering that the Teamsters had already persuaded 50,000 of California's 250,000 agricultural workers to join them rather than the UFWOC. This uneasy alliance was primarily the result of the Teamsters' desire to repair the damage that their union's image had suffered through their dispute with the UFWOC.
Chávez's skill at persuading liberals to regard the boycotts of grapes and lettuce as a just cause eventually produced legislation that benefited the workers. Sensing that allying himself with the farmworkers would help him to be elected governor, Jerry Brown made the creation of workable farm labor relations law one of his primary goals. In September, 1975, the state's Agricultural Labor Relations Act Agricultural Labor Relations Act, California (1975) took effect. The main impetus of this law was the formation of the Agricultural Labor Relations Board Agricultural Labor Relations Board , which gave labor organizers access to the fields. Although the ALRB was too poorly funded to be truly effective, its very existence testified to the belief of many lawmakers in California that the labor disputes were another manifestation of California's problem of interethnic relations between employers and workers. They interpreted Chávez's crusade as a struggle not simply for economic security but also for minority self-determination.
Of far more importance than Chávez's achievements is the way his nonviolent approach to social change carried over to other movements. He demonstrated through his deep emotional commitment to the UFWOC that people of various backgrounds, political persuasions, and faiths will come together for a common cause if it is morally correct. The truth of this statement is born out by the fact that the techniques developed by La Causa have been successfully applied by farmworkers in other lands. Chávez also showed through his courage and hard work that individuals really can make a difference. Lettuce boycott (1970) Labor unions;lettuce boycott Boycotts
xlink:type="simple">Acuña, Rodolfo. Occupied America: A History of Chicanos. 5th ed. New York: Pearson Longman, 2004. A general history of Chicanos, now a classic. Detailed sections on Chicano agricultural labor organizing, tracing Chicano labor struggles to the turn of the century. Also details labor struggles in other sectors of the economy. Well referenced, with an excellent index.
xlink:type="simple">Dolores Huerta Foundation. http://www.doloreshuerta .org. This nonprofit organization, based in Bakersfield, California, focuses on community activism and education, especially concerning women and children. Includes a lengthy biography of Huerta.
xlink:type="simple">Gonzalez, Gilbert G. Guest Workers or Colonized Labor? Mexican Labor Migration to the United States. Boulder, Colo.: Paradigm, 2006. Comprehensive discussion of Mexican labor in the United States. A critical analysis of immigrant workers.
xlink:type="simple">La Botz, Dan. César Chávez and La Causa. New York: Pearson Longman, 2006. A biography of Chávez, covering his early life as well as his political activism. Includes discussion of the Delano grape strike and the formation of the UFW. Bibliography, index.
xlink:type="simple">Levy, Jacques. César Chávez: Autobiography of La Causa. New York: W. W. Norton, 1975. The standard history of both César Chávez and the UFWA, though not a complete history of the movement because it traces Chávez's activities only through the first half of the 1970's.
xlink:type="simple">"The Little Strike That Grew to 'La Causa.'" Time 102 (July 4, 1969): 16-22. Provides the background to Chávez's activities during the turbulence of the 1960's. It is much more objective than many other accounts of this period.
xlink:type="simple">London, Joan, and Henry Anderson. So Shall Ye Reap: The Story of César Chávez and the Farm Workers' Movement. New York: Thomas Y. Crowell, 1970. Covers only the first few years of the farm labor movement; more useful as a history of the movement in California than as an account of César Chávez's activities, which make up only the last two chapters.
xlink:type="simple">Taylor, Ronald B. Chávez and the Farm Workers. Boston: Beacon Press, 1975. Comprehensive history of César Chávez's farm movement. Less personalized than Levy's book but is more objectively written. Portrays Chávez as a "man at odds with himself" who was better at organizing movements than he was at running unions.
United States Begins the Bracero Program
U.S. Government Program Begins Deporting Mexican Workers
AFL and CIO Merge
AFL-CIO Expels the Teamsters Union
Chávez and Huerta Form Farmworkers' Union and Lead Grape Pickers' Strike
Hoffa Negotiates a National Trucking Agreement
U.S. and Mexican Companies Form Maquiladoras
Chinese boycott of 1905
Montgomery Bus Boycott
Lamb to the Slaughter
Gay and Lesbian Palimony Suits Emerge
The Problems of Philosophy
Wang Mang's Rise to Power
Prize-Winning Aborigine Novelist Revealed as a Fraud
Reporter Jayson Blair Is Exposed as a Fraud
Actor Charles Chaplin Cannot Reenter the United States


I agree with comments made by others , it has been a strange mayfly season this year , requiring more effort and covering more water to find a hatch and more importantly rising fish . I found this lovely wild one in an out of the way lie , and made the usual hash of playing and landing it without a net which was safely in the boot of my car . I slipped it back and in my excitement did not measure it , so have no real clue what it might have weighed .. though that seemed and still does rather immaterial , it was a beautiful though !


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text:
Trent Dougherty and Justin P. McBrayer (eds.)
Skeptical Theism: New Essays
Trent Dougherty and Justin P. McBrayer (eds.), Skeptical Theism: New Essays, Oxford University Press, 2014, 337pp., $120.00 (hbk), ISBN 9780199661183.
Reviewed by Graham Oppy, Monash University
This aptly named book contains twenty-three new essays. In the preface, the authors say that (a) the collection moves the debate over the viability of sceptical theism forward; (b) the contributors are (fairly evenly) divided between established scholars in the field and up-and-coming scholars working in philosophy of religion; and (c) they aimed for a collection that is balanced. I think it fair to say that the collection does move the debate forward, that there is a nice division between established and up-and-coming scholars, and that there are many respects in which it is balanced. However, it will not go unremarked elsewhere that what is perhaps the standout essay -- by Lara Buchak -- is also the only chapter written by a woman.
There is a large existing literature on sceptical theism. Some of the major contributors to it -- e.g., the late William Alston, William Hasker, Justin McBrayer, Alvin Plantinga, Michael Rea, William Rowe, Bruce Russell and Peter van Inwagen -- are not represented in this volume while other major contributors -- e.g., Michael Bergmann, Paul Draper, Daniel Howard-Snyder, Stephen Maitzen, J. L. Schellenberg, and Stephen Wykstra -- have new contributions here.
The book is divided into four parts. I shall consider each in turn.
Part I, 'Knowledge and Epistemic Humility', kicks off with a pair of papers that continue the exchange between Jonathan Matheson and Trent Dougherty over the consistency of sceptical theism with commonsense epistemology. Matheson argues that Weak Sceptical Theism -- the claim that, if an individual is on balance justified in believing that she is in no position to judge whether particular evils are gratuitous, then she is not on balance justified in believing that any particular evil is gratuitous -- is consistent with Phenomenal Conservatism -- the claim that, if it seems to S as if P, then S thereby has at least prima facie justification for believing that P. According to Matheson, if a person is on balance justified in believing that she is in no position to judge whether particular evils are gratuitous, then any direct evidence that that person has for the claim that particular evils are gratuitous will be fully defeated. (7) The main claim that Dougherty seeks to defend 'goes in the other direction': a person to whom it seems obvious that there are gratuitous evils will be, on balance, justified in rejecting the claim the she is in no position to judge whether particular evils are gratuitous. (23) According to Dougherty, sceptical theists have almost universally held that, owing to the truth of the sceptical theists' sceptical theses, no one anywhere has any reason to disbelieve in God on the basis of facts about evil. While there are many interesting questions of detail that are taken up in this discussion -- concerning, for example, the distinction between rebutting and undercutting defeaters, and the merits of Bayesian epistemology -- it is a curious feature of the discussion that it is far from clear that the main claims of the two protagonists are jointly inconsistent: Matheson's Weak Sceptical Theism does not entail the view that Dougherty claims sceptical theists have almost universally held.
Part I also contains an interesting exchange between Chris Tucker, Todd Long, and E. J. Coffman. Tucker defends two claims: (a) if true, the sceptical theists' sceptical theses prevent some people from obtaining any justification whatsoever to doubt the existence of God from their encounters with evils; and (b) since the sceptical theists' sceptical theses tell us nothing about whether we have rational, non-inferential means of recognising that there are gratuitous evils, encounters with evil may justify some who take those evils as sufficient grounds to reject the claim that God exists. (45) Long argues that there is a version of sceptical theism -- 'minimal sceptical theism' -- that is strong enough to prevent anyone from obtaining even the slightest justification to doubt the existence of God on the basis of encounters with evil. In his view, in appreciating how limited with respect to knowledge, power and goodness we are in relation to that which would be had by a perfect creator were there to be one, we come to have reason to be in doubt about whether our thoughts about what would justify a perfect creator in allowing evil track what would be a perfect creator's justifying purposes. (74) Coffman argues that, while Long is mistaken in supposing that his minimal sceptical theism is strong enough to prevent anyone from obtaining even the slightest justification to doubt the existence of God on the basis of encounters with evil, Tucker is mistaken in thinking that encounters with evil may justify some who take those evils as sufficient grounds to reject the claim that God exists. In particular, according to Coffman, the truth of the claim that at best we have undefeated reason to withhold judgment on whether the total value we perceive in certain states of affairs accurately reflects the total moral value they really have plays a crucial role in defeating the suggestion that encounters with evil may justify some who take those evils as sufficient grounds to reject the claim that God exists. (84)
Part II, 'Debating CORNEA' (where CORENA = Condition of Reasonable Epistemic Access), contains a very interesting exchange between Paul Draper, Timothy Perrine and Stephen Wykstra, and Lara Buchak.
Draper argues that if, on the assumption that God exists, we grant that we would not expect to know God's reasons for permitting certain evils, then (a) CORNEA's core shows that our inability to adequately explain the existence of those evils in terms of theism is not strong evidence against theism; but (b) CORNEA's core fails to show that the evils themselves are not strong evidence against theism. (Draper distinguishes three readings of CORNEA's core: STRONG CORE (in cognitive situation S, Pr(E/H) is many times greater than Pr(E/~H) only if, relative to S, Pr(E/~H) < 0.5); SIGNIFICANT CORE (in cognitive situation S, Pr(H/E) - Pr(H) is large only if, relative to S, Pr(E/~H) < 0.5); and LEVERING CORE (in cognitive situation S, E is evidence that would make a positive difference of close to 0.5 to the probability of H if the probability of H independent of E were close to 0.5 only if, relative to S, Pr(E/~H) < 0.5). He notes that, while STRONG CORE and LEVERING CORE are true, SIGNIFICANT CORE is false.)
Next, Perrine and Wykstra argue that, despite Draper's claims to the contrary, there is a moderate sceptical theism that defeats Draper's well-known evidential argument from evil. They formulate Draper's argument as:
SIMPLER: Naturalism is a much simpler hypothesis than theism.
FITTER: Naturalism has a better predictive fit than theism regarding the data of good and evil.
NO-OFFSETTER: There are no epistemic advantages that theism has over naturalism such that those features, when combined, suffice to offset the epistemic advantage naturalism has over theism (if SIMPLER and FITTER are true)
FALSER: (Therefore) Theism is probably false. (145)
The moderate sceptical theism that Perrine and Wykstra recommend conjoins the following four theses: (1) we should be very confident in our ability to discern some of the goods that God values and some of the evils that God disvalues; (2) we should have middling to low confidence in our ability to discern connections between the goods we discern God to value and God's allowing specific instances of suffering; (3) we should be maximally uncertain that we can discern all of the goods that God values and the relative weights of those that we can and can't discern; and (4) we should be maximally uncertain that we can discern all the connections holding between all the goods God values and all God's acts of allowing suffering. (160) According to Perrine and Wykstra, a moderate sceptical theist will insist that, while it may be that naturalism has a better predictive fit than naive theism to the data concerning good and evil, there is no reason to doubt that better versions of theism will have an equally good fit to that data without yielding some other epistemic advantage to naturalism. Moreover, we cannot now determine that evidence is relevant only to NO-OFFSETTER and not to FITTER, because evidence plays a crucial role in determining which are the better versions of theism.
Draper responds with a range of criticisms of Perrine and Wykstra, diagnosing both 'misunderstandings' and 'mistakes'. In particular, he suggests that they make a mistake that can be brought out with the following analogy. Suppose that three balls are drawn randomly from four urns. According to theory-12, the balls all come from either the first or second urn; according to theory-34, the balls all come from either the third or fourth urn. As it happens, the first, third and fourth urns all contain 900 yellow balls and 100 purple balls, while the second urn contains 3 yellow balls and 997 purple balls. There are two versions of each of the theories: there is a version of theory-12 on which all of the balls come from the first urn, and there is a version of theory-12 on which all of the balls come from the second urn; there is a version of theory-34 on which all of the balls come from the third urn, and there is a version of theory-34 on which all of the balls come from the fourth urn. That the first ball drawn is yellow favours theory-34 over theory-12 and the first version of theory-12 over the second version of theory-12. However, if the next two balls that are drawn are also yellow, it remains the case that the total evidence favours theory-34 over theory-12, even though there is a version of theory-12 that fits the data just as well as theory-34. By analogy, theory-versioning cannot help theists avoid the implications of the distribution of goods and evils in our world. (175-76)
Buchak takes up the cudgels on behalf of Perrine and Wykstra. Granted, in Draper's analogy, the total evidence favours theory-34 over theory-12. But how are we to compare theory-1 -- the 'updated' theory, which says that all of the balls came from the first urn -- with theory-34? There are two different ways that we might have updated. On the one hand, we might have followed Draper in updating by conditionalisation: in that case, we shall suppose that theory-34 is better confirmed by the evidence than theory-1. On the other hand, we might have updated the conditional -- if theory-12 is true, then theory 1 is true -- without lowering the probability of the antecedent: in that case, we shall not suppose that theory-34 is better confirmed by the evidence than theory-1. If we understand Perrine and Wykstra to take theory-versioning to be updating on a conditional without lowering the probability of its antecedent, then -- according to Buchak -- Draper's objection is not decisive. (185)
Part III, 'Sceptical Theism's Implications for Theism', kicks off with an exchange between J. L. Schellenberg and Michael Bergmann. Schellenberg argues that, if sceptical theism undermines ways of justifying atheistic belief, then there is a kind of sceptical atheism that undermines ways of justifying theistic belief. In particular, sceptical atheists can appeal to principles such as:
SA1: We have no good reason for thinking that the considerations opposing the epistemic force of religious experience we know of are representative, relative to the property of (potentially) figuring in an undefeated defeater of religious experience as justification for theistic belief, of the considerations opposing the epistemic force of religious experience there are.
SA2: We have no good reason for thinking that the arguments from horrors or hiddenness against theism we know of are representative, relative to the property of (potentially) constituting a successful proof that theism is false, of the arguments from horrors or hiddenness against theism there are.
SA3: We have no good reason for thinking that the possible goods we know of are representative, relative to the property of consistency with a person being axiologically ultimate, of the possible goods there are.
According to Schellenberg, there is no non-arbitrary way for theists to discriminate between these principles, and the kinds of principles that are commonly taken to be definitive of sceptical theism, e.g., Bergmann's principles (as formulated by Schellenberg):
ST1: We have no good reason for thinking that the possible goods we know of are representative, relative to the property of figuring in a (potentially) God-justifying reason for permitting such things as hiddenness or horrors, of the possible goods there are.
ST2: We have no good reason for thinking that the possible evils we know of are representative, relative to the property of figuring in a (potentially) God-justifying reason for permitting such things as hiddenness or horrors, of the possible evils there are.
ST3: We have no good reason for thinking that the entailment relations we know of between possible goods and the permission of possible evils are representative, relative to the property of figuring in a (potentially) God-justifying reason for permitting such things as hiddenness or horrors, of the entailment relations there are between possible goods and the permission of possible evils.
More generally, Schellenberg suggests that sceptical theists should look with some fondness on what he calls total evidence scepticism: the claim that, for many a proposition expressing a belief or potential belief of ours, we have reason to doubt whether the total relevant evidence supports that proposition. (199)
Bergmann insists that his sceptical theses -- ST1-ST3 -- support only a limited scepticism about certain kinds of access to God's reasons: while these sceptical theses entail that we cannot know via inductive inference from known goods, evils and entailments between them that there are no God-justifying reasons for permitting certain evils, these sceptical theses do not entail that there is no other way in which we can come to have that knowledge. Moreover, he suggests that, without further information not yet supplied, it is unclear when Schellenberg supposes that his total evidence scepticism is to be applied; after all, if it applied always, then it would lead to an uninteresting global scepticism. (215)
Part IV, 'Sceptical Theism's Implications for Morality', kicks off with an exchange between Stephen Maitzen and Daniel Howard-Snyder. Maitzen's paper is a critical evaluation of Howard-Snyder's previously published 'Epistemic Humility, Arguments from Evil, and Moral Scepticism' (Oxford Studies in Philosophy of Religion 2). In particular, Maitzen claims that when it comes to the case of Ashley Jones -- a twelve-year old girl who, while babysitting her neighbour's children, was raped and bludgeoned to death by an escapee from a local juvenile detention centre -- 'commonsense morality' tells us (a) that we should be confident that we're obligated to intervene in Ashley's case, and (b) that we should not be confident that we have that obligation if -- as sceptical theists maintain -- we should be in doubt about (i) whether the goods we know of constitute a representative sample of all the goods there are and (ii) whether each good we know of is such that the necessary conditions of its realisation we know of are all the necessary conditions of its realisation that there are. (281) On Maitzen's account, commonsense morality is a hodgepodge of consequentialist and non-consequentialist considerations, but it nonetheless serves as a sound foundation for criticisms of sceptical theism.
Howard-Snyder says that something that more properly deserves to be called 'commonsense morality' tells us that we are not obligated to intervene provided that if, for all we can tell, there is a reason that would justify our non-intervention, then we have a sufficiently good reason not to intervene. In his view the fact that, for all we can tell, there is a reason that would justify our non-intervention is not a sufficiently good reason for us not to intervene. In the course of his discussion, Howard-Snyder draws an interesting distinction between a general principle that he attributes to Bergmann -- that we should believe something on the basis of something else only if we have good reason for thinking that the latter is a truth-conducive basis for believing the former -- and a general principle that he is himself prepared to endorse -- that we should believe something on the basis of something else only if it is not the case that we should be in doubt about whether the latter is a truth-conducive basis for believing the former.
I have not discussed all the chapters. In particular, I have not mentioned those by: John DePoe, N. N. Trakakis (Part I); Kenneth Boyce, M. J. Almeida (Part II); Wes Morriston, Erik Wielenberg, Andrew Cullison, Kevin Timpe (Part III); and Ted Poston (Part IV). Unlike those I have discussed, these chapters all stand alone: they are not parts of the book's wider exchanges . However, along with the chapters that I have discussed, they advance our understanding of sceptical theism. As a whole, the essays will set the agenda for discussion for many years to come.

redpajama_set_name: RedPajamaCommonCrawl


text:
Cannabis for Horses? The Latest Research on Equine Cannabis Medicine
Francis Cassidy July 28, 2021 0 comments
Cannabis for horses has a long history and a promising future.
Some believe that society is putting the cart before the horse when it comes to all matters related to medicinal cannabis. This is especially true when it comes to helping the animals entrusted to our care. So perhaps historical literature will shed some light on how useful cannabis has always been as a medicine. For the naysayers, cannabis for horses has been around for along time. But, modern equestrians want to know: Is it safe? Does it work?
The Bonded Relationship of Horse and Human Goes Way Back
Much of the world was first explored on foot and horseback as new lands were discovered, conquered, and settled. Ancient cave paintings and the early founding texts of our culture describe a deep bond with the horse.
As with any important ally, horse or otherwise, the health of the animal was of paramount importance to human endeavors. In the days before modern medicine came to be, natural cures were the primary form of treatment. According to CuChullaine O'Reilly, author of the Encyclopaedia of Equestrian Exploration, cannabis had a firm place in the medical kit of those who, like O'Reilly, undertook long journeys on horseback.
The Historical Use of Cannabis to Treat Ailments in Animals
The first-known writings describing the use of cannabis to treat ailments among horses appeared in the book The History of Four-Footed Beasts, written in 1607 by Edward Topsell. It discusses the widely-used practice of mixing hemp seeds with a horse's ration to promote rapid weight gain.
Historical use of cannabis in horses also extends to the treatment of colic and pain relief. French Renaissance writer, physician, monk, and Greek scholar, François Rabelais discussed it widely in his writings.
Rabelais commented on cannabis, "If of its juice you put in a bucket of water, suddenly you will see the water thicken, as if it were curds, so great are its virtues. And the water thus curdled is the immediate remedy for horses with colic."
RELATED Concern Over High THC Levels Is Just Repackaged Prohibition
According to O'Reilly, the use of cannabis as a treatment for equine colic persisted down through the centuries. In his writings, O'Reilly hypothesized that cannabis extracts promoted relaxation that lessened the horse's abdominal pain. This would reduce the chances of the animal imparting further damage upon itself. It wasn't until U.S. Prohibition began in 1937 that the practice ceased.
Liquid Cannabis was Once Accepted Medicine
So prevalent was the use of cannabis in treating horses, that Parke Davis pharmaceutical company came to be among the largest suppliers of liquid cannabis. Founded in 1866, the company still exists today as a subsidiary of the pharmaceutical company Pfizer. In the pre-Prohibition days, they collected hemp seeds in India and Nepal and grew high-quality cannabis in the U.s.. The oily resin extract from the mature plants mixed with alcohol became the substrate for much of the medicine used to treat ailments in horses. The recorded use of cannabis in treating colic within the U.S. dates back to 1880.
Wild horses in western Wyoming
The Widespread use of Cannabis in Pre-Prohibition Days
In the days before Harry Anslinger and company began to formulate what would later become Prohibition, the U.S. War Department widely recommended cannabis as a treatment for colic in horses. The 1915 Manual for Farriers, Horseshoers, Saddlers, and Waggoners recommended dosing colicky horses with liquid cannabis and olive oil.
Other ready-made cures were universally approved. Veterinary products that comprised alcohol, liquid cannabis, and chloroform were widely available at the turn of the twentieth century.
In his book Horses, Saddles and Bridles, General William Giles Harding Carter described the use of cannabis as an antispasmodic and anodyne. In addition to treating colic, he also expanded the use of cannabis to treat acute indigestion, impaction, and constipation.
Prior to prohibition, American-grown cannabis was just as potent as the more expensive forms of cannabis imported from India. Parke Davis, among others, described how cannabis was an alternative to commonly used opium at the turn of the last century. They boasted of its ability to treat convulsive disorders. As well as urinary irritations, persistent cough, hysteria, and any painful afflictions like flatulence, spasmodic colic, pruritus, and neuralgia.
RELATED Sustainability in Cannabis Grows is Hard to Achieve
The Equine Cannabis Revival – Cannabis for Horses
The pain-killing and relaxing properties of cannabis were all apparent for those who treated horses in the past. In recent times, however, the advent of modern muscle relaxants and analgesics has dampened the desire among the veterinary community to pursue the benefits of cannabis in treating common issues such as equine colic.
As society is now learning, prohibition did considerable damage to our understanding of the medicinal properties of cannabis. But the endocannabinoid system (ECS) is present in all vertebrate species. Scientists still have a lot to learn with humans and animals, however, a revival of sorts is underway when it comes to treating the common afflictions.
In Canada, where cannabis is legal at the federal level, many private enterprises are ahead of the game when it comes to pushing the boundaries on how cannabis may benefit our equine companions. Cannahorse, a Toronto-based company, is focused on advancing equine health via the use of medicinal cannabis. Horses have a very similar endocannabinoid system to that of humans. Thankfully, horses are unlike dogs, who have a much greater number of cannabinoid receptors in their brains and are at high risk of suffering adverse effects.
Cannahorse envisions vast therapeutic potential from medicinal cannabis for horses. They are primarily concerned with producing medicinal solutions to help aid in stress relief, joint inflammation, and surgical recovery.
With the advancements in our understanding, the miracles of the cannabis plant know no bounds. And as always, it's the reintegration of the wisdom of our elders that allows society to carve out a new path for physical and spiritual well being for both ourselves and our animal companions.
Francis Cassidy
http://www.thestrayphotographer.com/
Francis Cassidy is a freelance writer who writes on a variety of topics. With a particular focus on the cannabis industry, he aims to help ensure the smooth reintegration of cannabis back into global culture. When not writing, he's to be found exploring his new base in British Columbia, Canada. You can follow his other works including his photography on his blog thestrayphotographer.com
Jessica McKeil January 29, 2020
What Happens if My Dog Eats Weed?
Francis Cassidy December 23, 2019
University of Guelph Researching CBD for Dogs with Cancer


Breastfeeding dress - Thea. "
Beautiful stripped breastfeeding dress with zip access points for easy breastfeeding. Stylish, modern and beautiful. Looks stunning with a pair of black tights and heels. It can be worn as smart casual or for special occasions. The stripes make it look elegant and is a timeless classic! Absolutely gorgeous and it will sure live up to your expectations.
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Our breastfeeding collection uses discreet vertical zips by your breasts for easy access to breastfeeding. The zips are cleverly hidden and blend in with the designs which is something that is different from your usual high street nursing clothes and lets you wear anything you like without worrying about how you are going to be able to breastfeed especially when in public. You can now wear pretty things that suit your wardrobe and compliment your figure.
Has two zip access points (one on each side ) for easy access to breastfeeding.


As I said on Instagram, what the eff cold weather??? Grrr. But, it gave me a chance to break out some pre-Fall gear. Love my new Shawlsmith London scarf, IT'S GIRAFFE. Yup. It's a giraffe skin pattern with a gorgeous warm ombre effect. I had a chance to preview their Fall line, and there. are. more. giraffes. to come. Check out the current collection here. I'm also super excited about these distressed toothpick jeans from J Crew. Their denim just keeps getting better. These are perfectly, lightly distressed, and the ankle length actually hits my ankle. (#Shortyproblems.) Get them here ON SALE!


text:
package org.zstack.kvm;

import org.springframework.http.HttpMethod;
import org.zstack.header.host.HostVO;
import org.zstack.header.message.APIMessage;
import org.zstack.header.message.APIParam;
import org.zstack.header.rest.RestRequest;

import java.util.HashSet;
import java.util.Set;

/**
 * Created by xing5 on 2016/3/14.
 */
@RestRequest(
        path = "/hosts/kvm/actions",
        isAction = true,
        method = HttpMethod.PUT,
        responseClass = APIKvmRunShellEvent.class
)
public class APIKvmRunShellMsg extends APIMessage {
    @APIParam(resourceType = HostVO.class, nonempty = true)
    private Set<String> hostUuids;
    @APIParam
    private String script;

    public Set<String> getHostUuids() {
        return hostUuids;
    }

    public void setHostUuids(Set<String> hostUuids) {
        this.hostUuids = hostUuids;
    }

    public String getScript() {
        return script;
    }

    public void setScript(String script) {
        this.script = script;
    }

    public static APIKvmRunShellMsg __example__() {
        APIKvmRunShellMsg msg = new APIKvmRunShellMsg();
        Set <String >set = new HashSet();
        set.add(uuid());
        set.add(uuid());
        msg.setHostUuids(set);
        msg.setScript("ls");
        return msg;
    }

}

redpajama_set_name: RedPajamaGithub


text:
\section{Introduction}

In 1925 R.A.~Fisher \cite{Fisher25} introduced the celebrated concept of statistical distance.
This notion was the cornerstone for
what has developed nowadays into a major field in Statistics, known as Information Geometry.
This has ramifications, for instance,
in Information Theory, Statistical Mechanics, Biology and Quantum Mechanics, see \cite{AN00, Centcov82}.
One key ingredient of
the successful approach of Information Geometry has been the geometrisation.
That is, aiming  at stating the results in a way that
is independent of the specific situation or coordinates and thus providing a very general framework that can be applied to a variety
of situations.

The central object of the approach is known as a statistical manifold and we will denote it by $\mathcal{S}$.
This assumes that, given a particular family of probability distributions $\mathcal{P}(X)$ on a measure space $X$, one is able to find a parametrisation, i.e.\ a mapping $$p: \Xi \to \mathcal{P}(X),$$
such that $p$ is a bijection onto its image $p(\Xi)$. Under suitable conditions, we refer to \cite{AN00} for a proper definition of a Statistical Manifold, $
\mathcal{S}$ has the structure of a differentiable manifold and Fisher's statistical distance provides it with a natural Riemannian
metric, the so called Fisher-Rao metric \cite{Rao45}.

In addition to this Riemannian structure, there are two geometric objects related to it that play an important role. On one hand
there
is  a so called dualistic structure \cite{Aea87}. This is a pair of torsion-free connections $(\nabla,\nabla^*)$ that satisfy the relation
$$X(g(Y,Z)) = g(\nabla_{X}Y, Z) + g(Y,\nabla^*_{X}Z),$$
where $X, Y, Z$ are vector fields over the manifold.
These two connections are said to be dual to each other. Notice that, in particular, the Levi-Civita connection is the unique self--dual connection.
On the other hand there is a notion of Divergence function, the most notable example of which is commonly known as
Kullback-Leibler divergence (also called relative entropy) \cite{KL51}. A divergence function is a two-point function
$$F: \mathcal{S}\times\mathcal{S}\to \mathbb{R}$$
which is differentiable in both entries and with the following properties:
\begin{align}
    &F(\mathbf{x}, \mathbf{y}) \geq 0 . \notag\\
    &F(\mathbf{x}, \mathbf{y}) = 0 \Leftrightarrow \mathbf{x} = \mathbf{y} .\label{eq:propertiesdivergence}\\
    &\frac{\partial F}{\partial x^i }\bigr|_{\mathbf{x} = \mathbf{y}} = \frac{\partial F}{\partial y^j }\bigr|_{\mathbf{x} = \mathbf{y}} = 0,
\notag
    \end{align}
{for $i,j = 1, \dots, \dim(\mathcal{S})$, and where $\mathbf{x} = \{x^1, x^2, \dots\}$ and  $\mathbf{y} = \{y^1, y^2, \dots\}$ are
coordinates of the manifold $S$}. The last condition just requires that the first derivatives of the function $F$ vanish on the diagonal. Notice that the three conditions together amount to require that the function $F$ has a local extremum on the diagonal.

In the context of information geometry and of statistical inference the divergence functions are measures of the relative difference
between probability distributions. We refer to
\cite{AN00} for an introduction and selected applications of divergence functions in Information Geometry. One remarkable
property, from the geometric viewpoint, of these general divergence functions is that they are \emph{generating potentials} for the
geometric structures introduced so far. The concrete meaning of the term ``generating potential'' will be made clearer in the next
section. The properties of Eq.~\eqref{eq:propertiesdivergence} are sufficient for a two-point function to generate a Riemannian
metric and a dualistic structure and therefore can be applied in general for any differential manifold, regardless if it is a Statistical
Manifold or not. The particular case of the Kullback-Leibler divergence gives rise to the Fisher-Rao metric and the so called
exponential connection and mixture connections.

Having a generating potential for geometric quantities is an advantage, for instance, when deriving geometric or, more properly,
tensorial quantities that must be preserved under concrete transformations. Indeed, this is the case of the Kullback-Leibler
divergence, where its monotonicity under transformations fo the probability distributions reflects on the monotonicity of the
Fisher-Rao metric \cite{Csiszar67, Csiszar67b, Vajda89}.

In the context of Quantum Mechanics, the geometric description of the space of pure states \cite{EMM10, AS99} leads to a natural
interpretation of the Fubini-Study metric as a quantum counterpart of the Fisher-Rao metric \cite{Wootters81, FN95, Fea10}.
However, when one wants to apply the same information geometric approach to the space of quantum mixed states the picture is
not so clear. There are intrinsic difficulties in the problem, like the ambiguity in defining the logarithmic derivative of a matrix
\cite{Helstrom76, ES13} and the fact that the space of mixed states is not a manifold but it is partitioned into the disjoint union of differential manifolds labelled by the rank of quantum states  \cite{MMZS05, GKM05, Cea17c}. This leads to a wide variety of quantum divergence functions and quantum Fisher-Rao
metrics depending on the particular aspect that one wants to highlight, cf.\ \cite{Petz96,Cea17,MMVV17}. Having a geometric description of the
structures involved, independent of the particular realisation or setting, becomes useful in identifying the most relevant among all
the possibilities.

The aim of this article is to analyse thoroughly the role of two-point functions in differential geometry as potential functions for
tensorial quantities and we will do so in an intrinsic approach. Our interest relies also in the definition of a well-posed inverse
problem for the potential function, cf. \cite{Cea17b, CCM17}. In particular we will see that Hamilton's principal function is a particular
solution to the problem.

\section{Generating Potentials for Tensorial Quantities}

Generating potentials are common objects in mathematics. The most simple intrinsic example that one might think of would be the
exterior differential of a smooth function $f$ on a differentiable manifold $\mathcal{M}$. The one-form obtained this way is intrinsically
defined and does not depend on the particular coordinates chosen to define it. At this point one can also recognise that
there might be some global problems when defining the inverse problem. Poincaré's Lemma shows that the inverse problem, i.e.,
if
given a closed form $\alpha$ one is able to find a function on $\mathcal{M}$ such that $\mathrm{d}f = \alpha$, has a local solution but in
general a global solution might not exist.

An interesting situation is encountered in the context of Kähler manifolds where one can describe (at least locally) the symplectic form $\omega$ using the so-called (local) Kähler potential $f$ by means of the formula
\begin{equation}\label{eq:kahler}
    \omega_{ij} = \frac{\partial^2 f}{\partial z\partial\bar{z}},
\end{equation}
where $z$, $\bar{z}$ are, respectively, holomorphic and anti-holomorphic coordinates. Again, this definition is intrinsic and the symplectic form defined this way does not
depend on the particular coordinates chosen to define it. Of course, by formula \eqref{eq:kahler} one computes the coordinate
expression of the symplectic form, but this coordinate expression transforms properly under a change of coordinates of the
manifold. In fact, this situation is analogous to that of the exterior differential. One can show that a local Kähler potential always
exist. One can easily define the coordinates of a tensor by taking iterated derivatives of a function defined on the manifold. For
instance, in \cite{Duistermaat01} there is introduced the concept of  \emph{Hessian Riemannian structure}. Let $\mathbf{x} = \{x^1,x^2,\dots\}$ be local coordinates on an open neighbourhood $U\subset\mathcal{M}$ and let $f:U\to\mathbb{R}$ be a convex function. Then one can define the local coordinates of a Riemannian metric by
$$g_{ij}(\mathbf{x}):=\frac{\partial^2 f}{\partial x^i \partial x^j}.$$
While this can be done to define the local coordinates of a tensor, if one chooses to express the function $f$ in a different local chart $\mathbf{y}=\{y^1,y^2,\dots\}$, the expression
$$\tilde{g}_{ij}(\mathbf{y}):=\frac{\partial^2 f}{\partial y^i \partial y^j}$$
defines a different tensor. There is a notable exception, closely related to Kählerian functions, the so-called (flat) \emph{Hessian Structure} \cite{Shima07}. Hence, recovering desired transformation properties of $g$ by imposing invariance conditions on $f$ is not possible by such an approach. Remarkably, if one considers two-point functions with conditions \eqref{eq:propertiesdivergence} one is able to derive tensors of rank higher than one. This is well known for the information geometry community, where the relevant divergence functions that arise give rise to the Fisher-Rao metric. However, it turns out to be a general situation that can be defined on an arbitrary differentiable manifold.

Since we want to define the potential functions in an intrinsic way, we need to define the restriction to the diagonal appropriately. Consider the diagonal embedding given by
\begin{align*}
    D:\mathcal{M} &\hookrightarrow \mathcal{M}\times\mathcal{M}\\
    p &\mapsto (p,p)\qquad.
\end{align*}
The restriction to the diagonal is given by means of the pull-back by $D$. If \hbox{$F:\mathcal{M}\times\mathcal{M}\to\mathbb{R}$} is a two-point function, then $F|_{\mathrm{diag}}= D^*F$. In local coordinates one has that
$$D^*F(p) = F\left(D(p)\right) = F\left(p(x^1,x^2,\dots),p(x^1,x^2,\dots)\right), p\in\mathcal{M}.$$
In addition, one can define the two canonical projections:
\begin{align*}
    \pi_L:\mathcal{M}\times\mathcal{M} &\hookrightarrow \mathcal{M}    &     \pi_R:\mathcal{M}\times\mathcal{M} &\hookrightarrow \mathcal{M}\\
    (p,q) &\mapsto p & (p,q) &\mapsto q\quad.
\end{align*}
By means of these one can define the Left-lift  and Right-lift of a vector field $X\in\mathfrak{X}(\mathcal{M})$ as follows \cite{Cea17}. The Left-lift $X_L\in\mathfrak{X}(\mathcal{M}\times\mathcal{M})$ of the vector field $X\in\mathfrak{X}(\mathcal{M})$ is defined as the unique $\pi_L$-related vector field such that \hbox{$X_L(\pi^*_Rf)=0$} and $X_L(\pi^*_Lf)=\pi^*_L\left(\strut X(f)\right)$. The Right-lift is defined analogously.

We will say that a two-point function
$$S:\mathcal{M}\times\mathcal{M}\to\mathbb{R}$$
is a potential function if it satisfies the property
\begin{equation}\label{eq:contrast}
D^*(\mathcal{L}_XS) = 0, \quad X\in\mathfrak{X}(\mathcal{M}\times\mathcal{M})\,,
\end{equation}
where $\mathcal{L}_X$ is the Lie derivative with respect to the vector field $X$.
The condition in \eqref{eq:contrast} is slightly more general than the conditions in \eqref{eq:propertiesdivergence}. Indeed, the latter imply that the diagonal is a local extremum of the function while \eqref{eq:contrast} only requires it to be a critical point.

Any potential function defines a second order tensor in the following way:
$$g(X,Y) := D^*(\mathcal{L}_{X_L}\mathcal{L}_{Y_L}S).$$
We will show that $g$ is $f$-linear in both entries and therefore that it is a tensor. First notice that for any function $f$ on $\mathcal{M}$ and any vector field $X\in\mathfrak{X}(\mathcal{M})$ one has that
$$(fX)_L = (\pi^*_Lf) X_L$$
 and therefore $f$-linearity in the first entry follows by the $f$-linearity of the Lie derivative. Now consider
\begin{align}
    \mathcal{L}_{X_L}\mathcal{L}_{(fY)_L}S &= \mathcal{L}_{X_L}\left(\pi^*_Lf\mathcal{L}_{Y_L} S\right)\\
        &= \pi^*_Lf\mathcal{L}_{X_L}\mathcal{L}_{Y_L}S + \mathcal{L}_{X_L}(\pi^*_Lf)\mathcal{L}_{Y_L} S,
\end{align}
and taking the pull-back by $D$ on both sides we get
\begin{equation}
    g(X,fY) = fg(X,Y) + D^*\left( \mathcal{L}_{X_L}(\pi^*_Lf)\right)D^*\left(\mathcal{L}_{Y_L} S\right)
\end{equation}
and by condition \eqref{eq:contrast} the second term at the right hand side vanishes. It is easy to see that this tensor is symmetric. Indeed,
$$\mathcal{L}_{X_L}\mathcal{L}_{Y_L}S = \mathcal{L}_{Y_L}\mathcal{L}_{X_L}S + \mathcal{L}_{[X,Y]}S$$
and after applying $D^*$ one gets
$$g(X,Y) = g(Y,X).$$

Notice that no assumption has been made on the symmetry of $S$ under permutation of its entries and in the most common situations this will not be the case. There are other possible combinations in order to obtain tensors of rank two, but all of them lead to the same symmetric tensor up to a sign. Indeed,
\begin{align}\label{eq:generateg}
D^*(\mathcal{L}_{X_L}\mathcal{L}_{Y_L}S) &= D^*(\mathcal{L}_{X_R}\mathcal{L}_{Y_R}S) \notag\\
        &= -D^*(\mathcal{L}_{X_R}\mathcal{L}_{Y_L}S) \\
        &= -D^{*}\left(\mathcal{L}_{X_{L}}\,\mathcal{L}_{Y_{R}}\,S\right)=g(X,Y).\notag
\end{align}
A general and coordinate free proof of this fact can be found in \cite{Cea17}.
Note that if every point on the diagonal of $\mathcal{M}\times\mathcal{M}$ is a minimum for $S$, then $g$ is positive semi-definite.
Analogously, if every point on the diagonal of $\mathcal{M}\times\mathcal{M}$ is a maximum for $S$, then $g$ is negative semi-definite.
If $\{x^{j},\,y^{k}\}$ is a coordinate system on $\mathcal{M}\times\mathcal{M}$ adapted to the Cartesian product structure, then the local components of $g$ read:
\begin{equation}
g_{jk}=\left(\frac{\partial^{2}S}{\partial x^{j}\partial x^{k}}\right)_{x=y} = \left(\frac{\partial^{2}S}{\partial y^{j}\partial y^{k}}\right)_{x=y}= - \left(\frac{\partial^{2}S}{\partial x^{j}\partial y^{k}}\right)_{x=y}\,,
\end{equation}
in complete accordance with the expressions used in information geometry \cite{Aea87, AN00}.

\begin{example}
Let $\mathcal{H}$ be a finite-dimensional complex Hilbert space, and consider the open submanifold $\mathcal{H}_{0}$ consisting of $\mathcal{H}$ without the null vector.
It is well known that the space of pure quantum states may be identified with the complex projective space $\mathbb{CP}(\mathcal{H})$ associated with $\mathcal{H}$.
Furthermore, the complex projective space is the base space of the principal fibre bundle $\pi\colon\mathcal{H}_{0}\rightarrow\mathbb{CP}(\mathcal{H})$ with structure group $\mathbb{C}_{0}$, that is, the Abelian multiplicative group of non-zero complex numbers.
In particular, we have $\pi(\psi)=[\psi]$, where $[\psi]$ is the equivalence class of vectors in $\mathcal{H}_{0}$ differing only by the multiplication with a non-zero complex number.
Now, let us consider the following two-point function on $\mathcal{H}_{0}\times\mathcal{H}_{0}$:
\begin{equation}
S(\psi,\,\phi):=\frac{|\langle\psi|\phi\rangle|^{2}}{|\psi|^{2}\,|\phi|^{2}}\,,
\end{equation}
which is the quantum-mechanical counterpart of the (non-normalised) ``generalised transition probability'' introduced by Cantoni in \cite{Cant75, Cant77, Wootters81}.
If $\{\mathbf{e}_{j}\}_{1,...,\mathrm{dim}(\mathcal{H})}$ is an orthonormal basis in $\mathcal{H}$, we may introduce a Cartesian coordinate system on $\mathcal{H}_{0}$ setting $\psi=\sum_{j}\,(x^{j} + i y^{j})\,\mathbf{e}_{j}$.
Then, in an obvious way, we may introduce a Cartesian coordinate system $\{x^{j},\,y^{j};\,X^{k},\,Y^{k}\}$ on $\mathcal{H}_{0}\times\mathcal{H}_{0}$ that is adapted to the product structure.
In this (global) coordinate system, it is a matter of straightforward computations to prove that $S$ is a potential function.
Furthermore, from the expressions:
$$
\frac{\partial S}{\partial x^{j}}= \frac{1}{|\psi|^{2}\,|\phi|^{2}}\,\left(\langle\psi|\phi\rangle\,(X^{j} - i Y^{j}) + \langle\phi|\psi\rangle\,(X^{j} + i Y^{j}) - \frac{2x^{j}\,|\langle\psi|\phi\rangle|^{2}}{|\psi|^{2}}\right)\,,
$$
$$
\frac{\partial S}{\partial y^{j}}= \frac{1}{|\psi|^{2}\,|\phi|^{2}}\,\left(\langle\psi|\phi\rangle\,(Y^{j} + i X^{j}) + \langle\phi|\psi\rangle\,(Y^{j} - i X^{j}) - \frac{2y^{j}\,|\langle\psi|\phi\rangle|^{2}}{|\psi|^{2}}\right)\,,
$$
it is easy to see that the symmetric covariant tensor $g$ generated by $S$ reads:

\begin{equation}
\begin{split}
g =  & \sum_{j,k}\,\frac{2\left(x^{j}x^{k} + y^{j}y^{k} - \delta_{jk}\,R^{2}\right)}{R^{4}}\,\left(\mathrm{d}x^{j}\,\otimes\,\mathrm{d}x^{k} + \mathrm{d}y^{j}\,\otimes\,\mathrm{d}y^{k}\right) +  \\
& +  \sum_{j,k}\, \frac{y^{j}x^{k} - y^{k}x^{j}}{R^{4}}\,\left(\mathrm{d}x^{j}\,\otimes\,\mathrm{d}y^{k} - \,\mathrm{d}y^{j}\,\otimes\,\mathrm{d}x^{k}\right) ,
\end{split}
\end{equation}
where $R^2 = \mathbf{x}^2 + \mathbf{y}^2$. This is the pull-back to $\mathcal{H}_{0}$ of the Fubini-Study metric tensor on the space of pure quantum states $\mathbb{CP}(\mathcal{H})$.
\end{example}

We may take a further step and give a generating algorithm for covariant tensors of order three. The main ingredient in order to do so is that one can combine the action of Left-lifts and Right-lifts in order to cancel non-tensorial contributions of the higher order derivatives. Consider for example
\begin{align}\label{eq:skewness}
    T_1(X,Y,Z) &:= D^*\left(\mathcal{L}_{X_L}\mathcal{L}_{Y_R}\mathcal{L}_{Z_R}S - \mathcal{L}_{X_R}\mathcal{L}_{Y_L}\mathcal{L}_{Z_L}S\right),\\
    T_2(X,Y,Z) &:= D^*\left(\mathcal{L}_{X_L}\mathcal{L}_{Y_L}\mathcal{L}_{Z_R}S - \mathcal{L}_{X_R}\mathcal{L}_{Y_R}\mathcal{L}_{Z_L}S\right).\notag
\end{align}
It is easy to check that both objects are indeed $f$-linear in all the entries and symmetric. One can define up to 8 different possible combinations that lead to order three tensors. As happens for the second order tensor, it can be proven that all of them are equal up to a sign,  cf.\ \cite{Cea17}.

In the context of information geometry this tensors are called the skewness tensors \cite[Chapter4]{Aea87} and they are used to define the dualistic structure of the statistical manifold. The Christoffel symbols of the dual connections $\nabla$ and $\nabla^*$ are defined by adding and subtracting, respectively, to the Christoffel symbol of the Levi-Civita connection the skewness tensor $$\Gamma^{i}_{\negthickspace\pm jk} = \Gamma^{i}_{\negthickspace {jk}} \pm g^{il}T_{ljk}.$$
For instance, by this procedure the Kullback-Leibler divergence gives rise to the exponential connection and the mixture connection. Notice that both right hand sides in \eqref{eq:skewness} vanish if the potential function is symmetric, thus recovering the well known result that symmetric divergence functions can lead only to the self-dual case $\nabla=\nabla^*$.

At this point, a natural question would be if it were possible to use the same procedure to recover higher order tensors from a given potential function $S$. However, before considering this issue in Section \ref{sec:generalcase}, we will address first the inverse problem of finding a potential function that generates two given covariant tensor fields of order two and three.

\section{Hamilton-Jacobi approach to Divergence Functions and the inverse problem}

In this section we will address the inverse problem of finding a potential  function given a Riemannian metric and a skewness tensor. This inverse problem will be relevant in situations where there are not clear candidates for the potential/divergence functions but where there are relevant metrics or connections that one would want to generate. This is of particular importance in Quantum Mechanics where, as explained in the introduction, it can help to distinguish or highlight particular families of divergence functions among the available variety.

In some situations one can find a canonical divergence function. For instance, the self-dual case has as natural divergence function the geodesic distance between points of the manifold. In general, a canonical solution to the problem will not exist. Roughly speaking, this is due to the fact that the metric and skewness tensor only fix the lower order terms in a power series expansion. Thus, the higher order terms might be changed arbitrarily to define infinite possible \emph{equivalent} divergence functions. By equivalent we mean that they generate the same metric and skewness tensors. A successful attempt to obtain solutions to the inverse problem is given, for instance, in \cite{AA15}, however, this approach lacks of a characterisation of the geometric conditions needed to guarantee the global existence of the solution.

We will review here the approach introduced in \cite{Cea17b} based on the Hamilton-Jacobi theory. In this case the existence of the solution of the inverse problem can be characterised. Moreover, it will allow us to address the problem of finding a generating potential for higher order rank tensors. The main idea is to consider Hamilton's Principal function as a two-point function. Given a Lagrangian $\mathfrak{L}$ and a solution of the equations of motion determined by the Lagrangian, $\gamma:[t_\mathrm{in} , t_{\mathrm{fin}}] \to \mathcal{M}$ Hamilton's principal function is given by the action integral
$$S[\gamma] = \int_{t_\mathrm{in}}^{t_{\mathrm{fin}}} \mathfrak{L}\left( \gamma(t),\dot{\gamma}(t)\right) \mathrm{d}t.$$
If one considers only solutions with $t_\mathrm{in} = 0$ and $t_{\mathrm{fin}} = 1$ such that $\gamma(0)= \mathbf{x}$ and $\gamma(1)= \mathbf{y}$ it becomes a two point function
$$S[\mathbf{x}, \mathbf{y}] = \int_0^1\mathfrak{L}\left( \gamma(t),\dot{\gamma}(t)  \right)\mathrm{d}t.$$
Moreover, assume that the dynamical system defined by the Lagrangian is completely integrable.

From now on we will assume that the Lagrangian is at least of second order with respect to the velocities, i.e.,
$$\mathfrak{L} = g_{ij}v^iv^j + \mathcal{O}(|v|^3),$$
and that $g$ is positive defined. In particular, let us consider the Lagrangian
\begin{equation}
    \mathfrak{L}(\mathbf{q},\mathbf{v}) = \frac{1}{2} g_{ij}v^i v^j + \frac{\alpha}{6} T_{ijk} v^i v^j v^k,
\end{equation}
where $\alpha\in\mathbb{R}$ is a parameter that is included for convenience. Have into account that this Lagrangian can be written in a coordinate free way as was done in \cite{Cea17b}.

We will show that the two-point function $S$ determined by this Lagrangian solves, under certain assumptions, the inverse problem for $g$ and $T$.
From the Hamilton-Jacobi theory \cite{Lanczos}, having into account that $S$ is Hamilton's principal function and recalling that in the Lagrangian formulation of dynamics \cite{Mea90} the local expression of the canonical momentum is given by $p_{i}=\frac{\partial \mathfrak{L}}{\partial v^{i}}$, we have that:%
\begin{equation}
    \frac{\partial S}{\partial x^i} = -p_i = \frac{\partial \mathfrak{L}}{\partial v^i}\Bigr|_{\mathbf{q}=\mathbf{x}} = -g_{ij}(\mathbf{x}) v^j_{\i} - \frac{\alpha}{2} T_{ijk}(\mathbf{x}) v^j_\i v^k_\i ,
\end{equation}
\begin{equation}
    \frac{\partial S}{\partial y^i} = P_i = \frac{\partial \mathfrak{L}}{\partial v^i}\Bigr|_{\mathbf{q}=\mathbf{y}} = g_{ij}(\mathbf{y}) v^j_{\mathrm{fin}} + \frac{\alpha}{2} T_{ijk}(\mathbf{y}) v^j_\mathrm{fin} v^k_\mathrm{fin} .
\end{equation}
This guarantees that
$$D^*p_i = D^* P_i =0,\quad i= 1,\dots,n.$$
This is because the points in the diagonal satisfy $\mathbf{x}=\gamma(0)=\gamma(1)=\mathbf{y}$ and therefore the initial velocity is zero. This shows that the two-point function satisfies the condition in Eq.~\eqref{eq:contrast}.

We need to obtain the explicit solution of the equations of motion in order to be able to express $\mathbf{v}_\i$ and $\mathbf{v}_\mathrm{fin}$ only in terms of the endpoints of the curve $\gamma$. If we use the Taylor expansion around $t=0$ of the solution of the equations of motion we have that
\begin{equation}
    \gamma(t) = \gamma(0) + t\mathbf{v}_\i + \frac{t^2}{2}\dot{\mathbf{v}}_\i + \frac{t^3}{6}\ddot{\mathbf{v}}_\i + \mathcal{O}(t^4).
\end{equation}
Substituting $t=1$ and having into account that $\gamma(0) = \mathbf{x}$ and $\gamma(1) = \mathbf{y}$ we have that
\begin{equation}\label{eq:vin}
    \mathbf{v}_\i = \mathbf{y} - \mathbf{x} - \frac{1}{2}\dot{\mathbf{v}}_\i - \frac{1}{6} \ddot{\mathbf{v}}_\i + \mathcal{O}(t^4).
\end{equation}
Analogously, if we expand around $t=1$ we get an expression for $\mathbf{v}_\mathrm{fin}$, namely,
\begin{equation}\label{eq:vfin}
    \mathbf{v}_\mathrm{fin} = \mathbf{y} - \mathbf{x} + \frac{1}{2}\dot{\mathbf{v}}_\mathrm{fin} - \frac{1}{6} \ddot{\mathbf{v}}_\mathrm{fin} + \mathcal{O}(t^4).
\end{equation}
The Euler-Lagrange equations determined by the Lagrangian are
\begin{equation}\label{eq:eulerlagrange}
    \dot{v}^l = -\alpha T^{l}_{jk}v^j\dot{v}^k - \Gamma^{l}_{jk} v^j v^k - \frac{\alpha}{6} g^{lr} A_{rjks}v^j v^k v^s,
\end{equation}
where we are raising and lowering indices in the usual way by means of the Riemannian metric $g$. Here, $\Gamma^{i}_{jk}$ are the Christoffel symbols of the Levi-Civita connection and we have defined the tensor
$$A_{rjks}:= \left( \frac{\partial T_{jkr}}{\partial q^{s}} + \frac{\partial T_{jrs}}{\partial q^{k}} + \frac{\partial T_{rks}}{\partial q^{j}} - \frac{\partial T_{jks}}{\partial q^{r}} \right).$$

We will assume now that $\dot{\mathbf{v}}$ is an analytic function of the velocities and we will neglect terms with high powers of $\mathbf{v}$, since we are interested in what happens in a neighbourhood of $\mathbf{v} = 0$, i.e.\ the diagonal. We can inductively substitute \eqref{eq:eulerlagrange} in \eqref{eq:vin} and \eqref{eq:vfin} in order to obtain the expressions for $\mathbf{v}_\i$ and $\mathbf{v}_\mathrm{fin}$ respectively. The analytic expression for $\ddot{\mathbf{v}}$ is obtained by differentiating the equations of motion. Notice that $\dot{\mathbf{v}}$ is at least of order $\mathcal{O}(\mathbf{v}^2)$ and that $\ddot{\mathbf{v}}$ is at least of order $\mathcal{O}(\mathbf{v}^3)$. If we define now $\Delta^i = y^i - x ^i$ a straightforward calculation leads to:
\begin{align}
    \frac{\partial S}{\partial x^i} = &-g_{ij}(\mathbf{x}) \Delta^j -\frac{1}{2}\Gamma_{ijk}(\mathbf{x}) \Delta^j \Delta^k -\frac{1}{6} \Gamma_{ijk}(\mathbf{x}) \Gamma^{j}_{ls}(\mathbf{x}) \Delta^k \Delta^l \Delta^s \label{eq:1stderivativea}\\
        &-\frac{\alpha}{2} T_{ijk}(\mathbf{x}) \Delta^j \Delta^k -\frac{\alpha}{12} A_{ijkl}(\mathbf{x}) \Delta^j \Delta^k \Delta^l + \mathcal{O}\left( (\mathbf{y}-\mathbf{x})^4\right).\notag
\end{align}
\begin{align}
    \frac{\partial S}{\partial y^i} = &\phantom{-}g_{ij}(\mathbf{y}) \Delta^j -\frac{1}{2}\Gamma_{ijk}(\mathbf{y}) \Delta^j \Delta^k +\frac{1}{6} \Gamma_{ijk}(\mathbf{y}) \Gamma^{j}_{ls}(\mathbf{y}) \Delta^k \Delta^l \Delta^s\label{eq:1stderivativeb}\\
        &+\frac{\alpha}{2} T_{ijk}(\mathbf{y}) \Delta^j \Delta^k -\frac{\alpha}{12} A_{ijkl}(\mathbf{y}) \Delta^j \Delta^k \Delta^l + \mathcal{O}\left( (\mathbf{y}-\mathbf{x})^4\right).\notag
\end{align}
Now one can check that formulae \eqref{eq:generateg} and \eqref{eq:skewness} give rise to the tensors $g$ and $T$. For instance, one has that
$$D^*\left( \frac{\partial ^2 S}{ \partial y^i \partial x^j} \right)(\mathbf{q}) = D^*\left( \frac{\partial ^2 S}{ \partial x^i \partial y^j} \right)(\mathbf{q}) = -g_{ij} = - D^*\left( \frac{\partial ^2 S}{ \partial x^i \partial x^j} \right)(\mathbf{q}).$$
this shows that (up to a sign) only one tensor of rank two can be generated out of the two-point function. Moreover,
\begin{equation}\label{eq:3rdderivativesa}
    D^*\left( \frac{\partial ^3 S}{  \partial x^l \partial x^k \partial y^j} \right)(\mathbf{q}) = -\Gamma_{jkl} + \alpha T_{jkl},
\end{equation}
\begin{equation}\label{eq:3rdderivativesb}
    D^*\left( \frac{\partial ^3 S}{  \partial y^l \partial y^k \partial x^j} \right)(\mathbf{q}) = -\Gamma_{jkl} - \alpha T_{jkl}.
\end{equation}
Hence, choosing $\alpha = 1/2$ in the Lagrangian solves the inverse problem, since subtracting the latter formulae from each other is precisely one of the definitions in \eqref{eq:skewness}. Remember that there are other 6 possible linear combinations of the derivatives that lead to rank three tensors. However, one can check that they generate the same tensor $T$ up to a sign.

Strictly speaking, in order to prove \eqref{eq:3rdderivativesa} and \eqref{eq:3rdderivativesb} it is not necessary to consider the term $\ddot{\mathbf{v}}$ in the expressions \eqref{eq:vin} and \eqref{eq:vfin}. Neither is it necessary to consider the expressions \eqref{eq:1stderivativea} and \eqref{eq:1stderivativeb} up to order $\mathcal{O}((\mathbf{y}-\mathbf{x})^3)$. The contributions of these terms to the third order derivatives of the principal function vanish identically after taking the pull-back to the diagonal. In fact, these terms were not taken into account in \cite{Cea17b} but have been considered here since we are willing to study what happens in order to generate higher order tensors. In particular, we are interested in the possibility of generating fourth order tensor fields.

\section{Higher rank tensors in the general case}\label{sec:generalcase}

In this section we will consider the problem of defining tensors of order four out of a two-point function, or more concretely, out of a potential function, cf.\ Eq.~\eqref{eq:contrast}. Our first objective will be to find linear combinations of derivatives of the two-point function giving raise to rank four tensors. We will use the following abbreviated notation
$$LRLR := D^* \left(\mathcal{L}_{X_L}\mathcal{L}_{Y_R}\mathcal{L}_{Z_L}\mathcal{L}_{W_R}S\right).$$
And similarly for other combinations of Left-\ and Right-lifts. This is convenient because the only differences between the terms will be the particular combination of Left-\ and Right-lifts that appear. There are only two possible rank four tensors, namely
\begin{align}
Q_1(X,Y,Z,W) = &(LRRL - RLLR) + (LRRR - RLLL)\notag\\
        &+ (LRLL - RLRR) + (LRLR - RLRL),
\end{align}
\begin{align}
Q_2(X,Y,Z,W) = &(LLLL-RRRR) + (LLLR - RRRL)\notag\\
        &+ (LLRL - RRLR) + (LLRR - RRLL).
\end{align}
We can now compute the derivatives of the principal function and see what is the rank four tensor that one gets. In principle, one could also enlarge the Lagrangian to accommodate a term of order $\mathcal{O}(\mathbf{v}^4)$. Before computing the tensors $Q_1$ and $Q_2$ we will consider the Lagrangian given by
\begin{equation}
    \mathfrak{L}(\mathbf{q},\mathbf{v}) = \frac{1}{2} g_{ij}v^i v^j + \frac{\alpha}{6} T_{ijk} v^i v^j v^k +\frac{1}{24} C_{ijkl}  v^i v^j v^k v^l,
\end{equation}
where now $C$ is some fourth order tensor. Using the same analysis of the previous section one can show that the first order derivatives of the principal function become now:
\begin{align}
    \frac{\partial S}{\partial x^i} = &-g_{ij}(\mathbf{x}) \Delta^j -\frac{1}{2}\Gamma_{ijk}(\mathbf{x}) \Delta^j \Delta^k -\frac{1}{6} \Gamma_{ijk}(\mathbf{x}) \Gamma^{j}_{ls}(\mathbf{x}) \Delta^k \Delta^l \Delta^s \label{eq:1stderivativea2}\\
        &-\frac{\alpha}{2} T_{ijk}(\mathbf{x}) \Delta^j \Delta^k -\frac{\alpha}{12} A_{ijkl}(\mathbf{x}) \Delta^j \Delta^k \Delta^l \notag\\
        &-\frac{1}{24} C_{ijkl}(\mathbf{x})  \Delta^j \Delta^k \Delta^l+ \mathcal{O}\left( (\mathbf{y}-\mathbf{x})^4\right).\notag
\end{align}
\begin{align}
    \frac{\partial S}{\partial y^i} = &\phantom{-}g_{ij}(\mathbf{y}) \Delta^j -\frac{1}{2}\Gamma_{ijk}(\mathbf{y}) \Delta^j \Delta^k +\frac{1}{6} \Gamma_{ijk}(\mathbf{y}) \Gamma^{j}_{ls}(\mathbf{y}) \Delta^k \Delta^l \Delta^s\label{eq:1stderivativeb2}\\
        &+\frac{\alpha}{2} T_{ijk}(\mathbf{y}) \Delta^j \Delta^k -\frac{\alpha}{12} A_{ijkl}(\mathbf{y}) \Delta^j \Delta^k \Delta^l\notag\\
        &+\frac{1}{24} C_{ijkl}(\mathbf{y})  \Delta^j \Delta^k \Delta^l+ \mathcal{O}\left( (\mathbf{y}-\mathbf{x})^4\right).\notag
\end{align}
Now one can compute the result of tensors $Q_1$ and $Q_2$ and it turns out that both of them vanish identically. This means that this particular potential function does not generate rank four tensors.

In what follows we will show that if the potential function is analytic on a neighbourhood of the diagonal, it cannot generate order four tensors. First notice that condition \eqref{eq:contrast} amounts to say that the diagonal of $\mathcal{M}\times\mathcal{M}$ is a set of critical points for a potential function $S$, and there it attains the value $S(\mathbf{q},\mathbf{q})$ for $\mathbf{q}\in\mathcal{M}$. A Taylor series expansion around a point $\mathbf{q}_0$ of the diagonal has necessarily the form
\begin{align}
    S(\mathbf{x},\mathbf{y}) = & S(\mathbf{q_0},\mathbf{q_0}) + h_{ij}(\mathbf{q}_0)(y^i - x^i)(y^j - x^j) + \notag \\
    & + t_{ijk}(\mathbf{q}_0)_{ijk} (y^i - x^i)(y^j - x^j) (y^k - x^k) + \\
            &+ c_{ijkl}(\mathbf{q}_0) (y^i - x^i)(y^j - x^j) (y^k - x^k)(y^l - x^l) + \mathcal{O}((\mathbf{y} - \mathbf{x})^5),\notag
\end{align}
where $\{x^1, x^2, \dots, x^n, y^1, y^2,\dots, y^n \}$ are now coordinates relative to the point $(\mathbf{q}_0,\mathbf{q}_0)$ on $\mathcal{M}\times\mathcal{M}$ and where $h_{ij}$ depends on the second derivatives of $S$, $t_{ijk}$ depends on the third derivatives of $S$ and so on. This is so because all the derivatives along the direction tangent to the diagonal vanish.

If one computes the tensors $Q_1$ and $Q_2$ in this particular case one gets that they vanish identically. This means that a potential function, assuming it is analytic, is not capable of generating non-trivial covariant tensor fields of order four.

\section{Conclusions}

We have studied the inverse problem for potential functions and found a solution in terms of Hamilton's principal function and a suitable chosen Lagrangian built from the metric and the skewness tensor. The solution will exist  provided that the equations of motion of the associate Hamilton-Jacobi problem are completely integrable. We have also studied if one is able to recover higher order rank tensors (order four) from a potential function satisfying \eqref{eq:contrast}. It turns out that the answer is negative assuming that the potential fucntion is analytic on a neighbourhood of the diagonal.

Notice that potential functions, as they are described here, have the limitation that they cannot generate non-symmetric tensors. For instance, one cannot generate a symplectic structure using the procedure described. One way of achieving that could be by considering Grassmann variables.

Another interesting line to pursue would be that of finding a way of generating higher order tensors. From what we have seen, at least for order four, this will not be achievable by a two-point function. By that we mean that the tensor arises as linear combinations of the derivatives of the potential function. It is clear that once one has obtained the Christoffel symbols, for instance, one can compute out of them the Riemann tensor in the usual way. What we have shown is that the Riemann tensor cannot be directly obtained by computing fourth order derivatives of the potential function. It is very likely that one could do that by considering three-point functions. However, developing such a theory in depth would also require a Hamilton-Jacobi theory of order higher than two (associated to evolution equations including up to third order derivatives).

\section*{Acknowledgements}

The authors want to thank the scientific committee of the ``XXVI International Fall Workshop on Geometry and Physics'' for giving them the opportunity to present this research. G.M. acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the Severo Ochoa Programme for Centres of Excellence in RD (SEV-2015/0554), and would like to thank the support provided by the Santander/UC3M Excellence Chair Programme 2016/2017. J.M.P.P. was supported by QUITEMAD+ S2013/ICE-2801, the Spanish MINECO grant MTM2017-84098-P and the ``Juan de la Cierva - Incorporaci\'on" Proyect 2018/00002/001.

redpajama_set_name: RedPajamaArXiv


text:
Stuck in Neutral: Stalled Progress in Statewide Comprehensive Smoke-Free Laws and Cigarette Excise Taxes, United States, 2000–2014
By Holmes, Carissa Baker ; King, Brian A. ; Babb, Stephen D.
Title : Stuck in Neutral: Stalled Progress in Statewide Comprehensive Smoke-Free Laws and Cigarette Excise Taxes, United States, 2000–2014 Personal Author(s) : Holmes, Carissa Baker;King, Brian A.;Babb, Stephen D.; Published Date : Jun 16 2016 Source : Prev Chronic Dis. 13. URL : https://stacks.cdc.gov/view/cdc/40164
Holmes, Carissa Baker ; King, Brian A. ; Babb, Stephen D.
Holmes, Carissa Baker ; King, Brian A. ; Babb, Stephen D. Less -
Increasing tobacco excise taxes and implementing comprehensive smoke-free laws are two of the most effective population-level strategies to reduce tobacco use, prevent tobacco use initiation, and protect nonsmokers from secondhand smoke. We examined state laws related to smoke-free buildings and to cigarette excise taxes from 2000 through 2014 to see how implementation of these laws from 2000 through 2009 differs from implementation in more recent years (2010–2014).
We used legislative data from LexisNexis, an online legal research database, to examine changes in statewide smoke-free laws and cigarette excise taxes in effect from January 1, 2000, through December 31, 2014. A comprehensive smoke-free law was defined as a statewide law prohibiting smoking in all indoor areas of private work sites, restaurants, and bars.
From 2000 through 2009, 21 states and the District of Columbia implemented comprehensive smoke-free laws prohibiting smoking in work sites, restaurants, and bars. In 2010, 4 states implemented comprehensive smoke-free laws. The last state to implement a comprehensive smoke-free law was North Dakota in 2012, bringing the total number to 26 states and the District of Columbia. From 2000 through 2009, 46 states and the District of Columbia implemented laws increasing their cigarette excise tax, which increased the national average state excise tax rate by $0.92. However, from 2010 through 2014, only 14 states and the District of Columbia increased their excise tax, which increased the national average state excise tax rate by $0.20.
The recent stall in progress in enacting and implementing statewide comprehensive smoke-free laws and increasing cigarette excise taxes may undermine tobacco prevention and control efforts in the United States, undercutting efforts to reduce tobacco use, exposure to secondhand smoke, health disparities, and tobacco-related illness and death.
Smoke-Free Policy
Tobacco Smoke Pollution
urn:sha256:2e68019e731cef9edcdd2d802bfb1af52e70077fe2fdc7bebc2b46c940429bfb
PCD-13-E80.nxml
PCD-13-E80s01.gif
PCD-13-E80s01.jpg
Smoke-Free Policies in the World's 50 Busiest Airports — August 2017
Title : Smoke-Free Policies in the World's 50 Busiest Airports — August 2017 Personal Author(s) : Tynan, Michael A.;Reimels, Elizabeth;Tucker, Jennifer;King, Brian A.; Published Date : Nov 24 2017 Source : MMWR Morb Mortal Wkly Rep. 66(46):1265-1268. URL : https://stacks.cdc.gov/view/cdc/54293
Tynan, Michael A. ;
Reimels, Elizabeth
Nov 24 2017 | MMWR Morb Mortal Wkly Rep. 66(46):1265-1268.
Exposure to secondhand smoke from burning tobacco products causes premature death and disease, including coronary heart disease, stroke, and lung canc...
Going Smokefree Matters—Multiunit Housing
Title : Going Smokefree Matters—Multiunit Housing Corporate Authors(s) : National Center for Chronic Disease Prevention and Health Promotion (U.S.). Published Date : 02/20/2019 URL : https://stacks.cdc.gov/view/cdc/89646
National Center for Chronic Disease Prevention and Health Promotion (U.S.).
There is no safe amount of secondhand smoke exposure.The home is the main place many children and adults breathe in secondhand smoke. Each year, an es...


text:
Undergraduate competition
1. Don't stop at the headline
2. What did the researchers actually say?
3. Independent experts?
4. Links to the original work?
5. Associations handled correctly?
6. How to assess risk?
7. Is the article biased?
8. No study stands alone
9. Consistent with other articles?
10. Exaggeration and opinion
competition, Rewrite the Headlines, undergraduates
Rewrite the Headlines: OMG, Bacon Causes Cancer! (When Pigs Fly….)
by Research the Headlines on	2016/02/04
Over the first few weeks of February, we're showcasing the top entries in both the school and undergraduate categories of our Rewrite the Headlines competition (full list of winners here). We continue with another of our commended undergraduate entries, from Ajay Shah at the University of St. Andrews.
OMG, Bacon Causes Cancer! (When Pigs Fly….)
On October 26th, 2015, the results of a new study rippled across social media and news outlets. Sensationalist Twitter hashtags and Facebook posts lamenting its results dominated the cyber landscape. Sales at supermarkets and grocery stores fell by millions of pounds in the following weeks. Thousands of people swore off their favourite foods in the panic, hoping to bargain for a few extra years of life. What could this study have discovered to cause such a viral reaction throughout society? Well, of course, it showed that bacon causes cancer!
Hold up. What? One of the most universally loved foods in the world (Americans consume 18 pounds per capita annually), cast aside by a suddenly health-conscious population, just because of one study's results? How could this have happened? As is often the case, the culprit is not those responsible for creating the study (they just did the science), nor the general population (we just read the articles). The culprit is far more insidious, something capable of unnecessarily inspiring fear into millions of innocent people. That culprit, was The Headlines.
I woke up that morning to see a short BBC notification on my phone declaring that red meat causes cancer. Confused, I called my girlfriend as I skimmed the article.
"WHAT??" said my girlfriend when I read the headline to her, likely picturing morsels of steak morphing into tumours as they passed through her colon.
"Yup, the WHO has declared that red meats cause colon cancer. It's true – even the BBC is reporting it," I replied.
After some quick research, and reading headlines and tweets such as:
"OMG! Bacon causes cancer!" (New York Post)
"Processed meats rank alongside smoking as cancer causes — W.H.O. U.N. health body says bacon, sausages and ham among most carcinogenic substances along with cigarettes, alcohol, asbestos and arsenic." (The Guardian)
"Bacon, hot dogs and processed meats cause cancer/are as dangerous as smoking, says @WHO." (PBS)
the alarm bells began to ring. My girlfriend quickly swore off processed meats for life, and limited red meats to one meal per week. I, an avid meat-eater myself, decided not to let The Headlines fool me, and began to do some research of my own.
As I had suspected, the initial reaction to the study was quite overblown. In fact, the first paragraph of the WHO report itself says that "red meat is probably carcinogenic to humans based on limited evidence ". "Limited evidence" means that, while a positive correlation is present between the exposure (meat) and outcome (cancer), other explanations (confounding factors, bias, chance) cannot be ruled out.
The findings are based on an assessment of more than 800 studies, which gave more weight to the studies with larger sample sizes, fewer confounding factors and better experimental design. Approximately two thirds of the case-control/cohort studies showed a positive correlation between eating processed meats and colorectal cancer incidence. It was found that eating 100g of red meat per day raises colorectal cancer incidence by 17%, while eating 50g of processed meat daily raises incidence by 18%. Both types of meat consumption were also linked to pancreatic, prostate and stomach cancer.
Personally, I think that the study was very well-conducted and is a fantastic example of "Good Science". The researchers importantly identified a mechanism of action, identifying known carcinogens produced during the cooking of meat, and postulating that these compounds lead to cancer formation. They also examined a wide range of studies under specific criteria, minimizing the influence of confounding factors and bias. The different types of meats were classified appropriately, and suitable recommendations were made.
Upon reading the WHO report, I felt quite upset at the media for their treatment of the story. The WHO researchers were quick to reassure, suggesting that a reduction of processed meat consumption would be a preferable alternative to widespread vegetarianism. Indeed, they identified the valuable nutrients and compounds in red meat, and after contrasting these with the increased cancer risks, officially only recommended cutting down red meat consumption to 70g daily. This is a stark contrast to the doom-and-gloom picture portrayed by the media.
An increase of cancer incidence by 17-18% may seem like a lot, and with the media's handling of this report, any meat eater would do a double-take before chowing into that cheeseburger. However, this "relative risk" looks a lot different when put into perspective. It is estimated that, among 1000 people who eat little-to-no processed meat, 56 would develop bowel cancer during their lives. Comparatively, of the 1000 people who eat the most processed meat, 66 are expected to develop bowel cancer during their lives. Indeed, the 17% increase seems miniscule when compared to smoking (2,400% increased risk) or drinking alcohol (500% increase). And this ignores the fact that red meat offers many healthy nutrients, which may overpower the carcinogenic effect in some. Regardless, red and processed meat now joins an increasingly cluttered list of carcinogens, including aloe vera (Class 2B), the Sun (Class 1) and Air (Class 1), some of most dangerous things known to man.
So, throughout the journey from "my bowels are full of carcinogen-induced tumours" to "eating meat probably, might, slightly increase the risk of developing a tumour in my large intestine", I learned a lot about clinical studies, the media, and The Headlines. I learned that "carcinogen" is a broad term, and a subatomic particle that may be essential to the fabric of our reality (neutrons) is also a known human killer. I learned that clinical studies completed under similar conditions could have polar opposite results. But most importantly, I learned that in a world dominated by clickbait headlines and diminishing attention spans, the onus is on us to do our research, and Rewrite the Headlines.
Ajay Shah, University of St. Andrews
Carcinogenicity of consumption of red and processed meat. Bouvard, Véronique et al. The Lancet Oncology.
World Health Organization. International Agency for Research on Cancer. IARC Monographs Evaluate Consumption of Red Meat and Processed Meat. Www.iarc.fr. N.p., 26 Oct. 2015. Web. 29 Nov. 2015. https://www.iarc.fr/en/media-centre/pr/2015/pdfs/pr240_E.pdf.
Boseley, Sarah. "Processed Meats Rank alongside Smoking as Cancer Causes – WHO." The Guardian. N.p., 26 Oct. 2015. Web. 29 Nov. 2015. http://www.theguardian.com/society/2015/oct/26/bacon-ham-sausages-processed-meats-cancer-risk-smoking-says-who.
Sutherland, Amber, and Chris Perez. "OMG! Bacon Causes Cancer." New York Post. N.p., 26 Oct. 2015. Web. 28 Nov. 2015. http://nypost.com/2015/10/26/omg-bacon-causes-cancer/.
International Agency for Research on Cancer (IARC). Agents Classified by the IARC Monographs, Volumes 1 – 114. 2015. Accessed at http://monographs.iarc.fr/ENG/Classification/List_of_Classifications_Vol1-114.pdf on October 27, 2015.
US Department of Health and Human Services. Public Health Service, National Toxicology Program. Report on Carcinogens, Thirteenth Edition. 2014. Accessed at http://ntp.niehs.nih.gov/pubhealth/roc/roc13/index.html on October 2, 2014.
The Rewrite the Headlines competition was supported by funding from the British Academy, with additional funding from the University of Strathclyde.
Prizes were supported by the British Academy, the University of Strathclyde, the School of Chemistry at the University of St. Andrews, the School of Social Work and Social Policy at the University of Strathclyde, the University of Dundee School of Life Sciences, and the Particle Physics Experiment Research Group at the University of Edinburgh, the Social Research Association, the Scottish History Society, and Palgrave Macmillan.
Competition details can be accessed at https://researchtheheadlines.org/rewritetheheadlines, and the full list of winners is available here.
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I think it is about time to start eliminating some of these School practices that are dangerous to the students. The risk is not worth the tradition.
There are too many kids in this country leave their home and return in a pine box.