Monday, January 27, 2020
Usefulness Of Maxima And Minima Of Functions Engineering Essay
Usefulness Of Maxima And Minima Of Functions Engineering Essay The mathematical concept of a function expresses the intuitive idea that one quantity(input) completely determines another quantity (output). A function assigns a unique value or output to each input of a specified type. The argument and the value may be real numbers, but they can also be elements from any given sets: the domain and the co-domain of the function. Whenever a relationship exists between two variables (or quantities) such that for every value of the first, there is only one corresponding value of the second, then we say:The second variable is a function of the first variable. The first variable is the independent variable (usually x), and the second variable is the dependent variable (usually y). The independent variable and the dependent variable are real numbers. The term function is just a type of operator which transforms the given input to output according to the given conditions. This operator relates two or more quantities to each other, the quantities are known as variables. Out of total variables only one is independent and all other are dependent on that variable. One precise definition of a function is that it consists of an ordered triple of sets, which may be written as (X, Y, F). X is the domain of the function, Y is the co-domain, and F is a set of ordered pairs. In each of these ordered pairs (a, b), the first element a is from the domain, the second element b is from the co-domain, and every element in the domain is the first element in one and only one ordered pair. The set of all b is known as the image of the function. Some authors use the term range to mean the image, others to mean the co-domain. The notation Æ’:Xà ¢Ã¢â‚¬ ’Y indicates that Æ’ is a function with domain X and co-domain Y. (Domain implies input whereas range or co-domain implies output.) In most practical situations, the domain and co-domain are understood from context, and only the relationship between the input and output is given. Thus is usually written as Here the two variables are x and y out of which x is independent and y is dependent on x. From the other side if we consider y as independent variable then x is dependent on y. Every function can be plotted on graph or more precisely Argand Plain. The graph of function may be a straight line, a continuous curve, a circle, an ellipse or even a point also. HISTORY OF MAXIMA AND MINIMA: Since origin of life, all people knew, talked, applied the concept of maxima and minima in their daily lives without even knowing about the concept of maxima and minima. In the earlier phase of time the kings used to estimate the maximum and minimum army of the opposite side, doctors used to record minimum and maximum symptom of any disease, cooks used to estimate the maximum and minimum quantity of food or people before any function, the businessmen used to estimate maximum and minimum profit or loss in any transaction. Even today also the women in the house prepare the food according to maximum or minimum consumption by each individual. Sir Issac Newton, a great scientist, invented the concept of functions and hence concept of maxima or minima. Since then his concepts are very usefully applicable in our daily lives. PRESENT TIME CONCEPTS OF MAXIMA AND MINIMA: The terms maxima and minima refer to extreme values of a function, that is, the maximum and minimum values that the function attains. Maximum means upper bound or largest possible quantity. The absolute maximum of a function is the largest number contained in the range of the function. That is, if f(a) is greater than or equal to f(x), for all x in the domain of the function, then f(a) is the absolute maximum. For example, the function f(x) = -162 + 32x + 6 has a maximum value of 22 occurring at x = 1. Every value of x produces a value of the function that is less than or equal to 22, hence, 22 is an absolute maximum. In terms of its graph, the absolute maximum of a function is the value of the function that corresponds to the highest point on the graph. Conversely, minimum means lower bound or least possible quantity. The absolute minimum of a function is the smallest number in its range and corresponds to the value of the function at the lowest point of its graph. If f(a) is less t han or equal to f(x), for all x in the domain of the function, then f(a) is an absolute minimum. As an example, f(x) = 322 32x 6 has an absolute minimum of -22, because every value of x produces a value greater than or equal to -22. In some cases, a function will have no absolute maximum or minimum. For instance the function f(x) = 1/x has no absolute maximum value, nor does f(x) = -1/x have an absolute minimum. In still other cases, functions may have relative (or local) maxima and minima. Relative means relative to local or nearby values of the function. The terms relative maxima and relative minima refer to the largest, or least, value that a function takes on over some small portion or interval of its domain. Thus, if f(b) is greater than or equal to f(b  ± h) for small values of h, then f(b) is a local maximum; if f(b) is less than or equal to f(b  ± h), then f(b) is a relative minimum. Finding the maxima and minima, both absolute and relative, of various functions represents an important class of problems solvable by use of differential calculus. The theory behind finding maximum and minimum values of a function is based on the fact that the derivative of a function is equal to the slope of the tangent. When the values of a function increase as the value of the independent variable increases, the lines that are tangent to the graph of the function have positive slope, and the function is said to be increasing. Conversely, when the values of the function decrease with increasing values of the independent variable, the tangent lines have negative slope, and the function is said to be decreasing. Precisely at the point where the function changes from increasing to decreasing or from decreasing to increasing, the tangent line is horizontal (has slope 0), and the derivative is zero (With reference to figure 1, the function is decreasing to the left of point A, as well a s between points B and C, and increasing between points A and B and to the right of point C). In order to find maximum and minimum points, first find the values of the independent variable for which the derivative of the function is zero, then substitute them in the original function to obtain the corresponding maximum or minimum values of the function. Second, inspect the behavior of the derivative to the left and right of each point. A wide variety of problems can be solved by finding maximum or minimum values of functions. For example, suppose it is desired to maximize the area of a rectangle inscribed in a semicircle. The area of the rectangle is given by A = 2xy. The semicircle is given by x2 + y2 = r2, for y à ¢Ã¢â‚¬ °Ã‚ ¥ 0, where r is the radius. To simplify the mathematics, note that A and A2 are both maximum for the same values of x and y, which occurs when the corner of the rectangle intersects the semicircle, that is, when y2 = r2 x2. Thus, we must find a maximum value of the function A2 = 42(r2 -x2) = 4r2x2 44. The required condition is that the derivative be equal to zero, that is, d(A2)/dx = 8r2x 163 = 0. This occurs when x = 0 or when x = 1à ¢Ã‚ „2(r à ¢Ã‹â€ Ã… ¡ +2 ). Clearly the area is a maximum when x = 1à ¢Ã‚ „2(r à ¢Ã‹â€ Ã… ¡ +2 ). Substitution of this value into the equation of the semicircle gives y = 1à ¢Ã‚ „2(r à ¢Ã‹â€ Ã… ¡ +2 ), that is, y = x. Thus, the max imum area of a rectangle inscribed in a semicircle is A = 2xy = r2. The problem of determining the maximum or minimum of function is encountered in geometry, mechanics, physics, and other fields, and was one of the motivating factors in the development of the calculus in the seventeenth century. Let us recall the procedure for the case of a function of one variable y=f(x). First, we determine points where f'(x)=0. These points are called critical points. At critical points the tangent line is horizontal. This is shown in the figure below. . The second derivative test is employed to determine if a critical point is a relative maximum or a relative minimum. If f()>0, then x is a relative minimum. If f() The notions of critical points and the second derivative test carry over to functions of two variables. Let z=f(x, y). Critical points are points in the xy-plane where the tangent plane is horizontal. Since the normal vector of the tangent plane at (x,y) is given by The tangent plane is horizontal if its normal vector points in the z direction. Hence, critical points are solutions of the equations: because horizontal planes have normal vector parallel to z-axis. The two equations above must be solved simultaneously. The Second Derivative Test for Functions of Two Variables How can we determine if the critical points found above are relative maxima or minima? We apply a second derivative test for functions of two variables. Let (x,y) be a critical point and define We have the following cases: If D>0 and (,).) If D>0 and (,).)>0, then f(x,y) has a relative minimum at ( ,).). If D If D=0, the second derivative test is inconclusive. Maxima and Minima in a Bounded Region Suppose that our goal is to find the global maximum and minimum of our model function above in the square -2 Relative extrema in the interior of the square. Relative extrema on the boundary of the square. Corner Points. We have already done step 1. There are extrema at (1, 0) and (-1, 0). The boundary of square consists of 4 parts. Side 1 is y=-2 and -2 The original function of 2 variables is now a function of x only. We set g'(x)=0 to determine relative extrema on Side 1. It can be shown that x=1 and x=-1 are the relative extrema. Since y=-2, the relative extrema on Side 1 are at (1,-2) and (-1,-2). On Side 2 (x=-2 and -2 We set h'(y)=0 to determine the relative extrema. It can be shown that y=0 is the only critical point, corresponding to (-2,0). We play the same game to determine the relative extrema on the other 2 sides. It can be shown that they are (2,0), (1,2), and (-1,2). Finally, we must include the 4 corners (-2,-2), (-2,2), (2,-2), and (2,2). In summary, the candidates for global maximum and minimum are (-1,0), (1,0), (1,-2), (-1,-2), (-2,0), (2,0), (1,2), (-1,2), (-2,-2), (-2,2), (2,-2), and (2,2). We evaluate f(x,y) at each of these points to determine the global max and min in the square. The global maximum occurs (-2,0) and (1,0). This can be seen in the figure above. The global minimum occurs at 4 points: (-1,2), (-1,-2), (2,2), and (2,-2). One of the great powers of calculus is in the determination of the maximum or minimum value of a function. Take f(x) to be a function of x. Then the value of x for which the derivative of f(x) with respect to x is equal to zero corresponds to a maximum, a minimum or an inflexion point of the function f(x). The derivative of a function can be geometrically interpreted as the slope of the curve of the mathematical function y(t) plotted as a function of t. The derivative is positive when a function is increasing toward a maximum, zero (horizontal) at the maximum, and negative just after the maximum. The second derivative is the rate of change of the derivative, and it is negative for the process described above since the first derivative (slope) is always getting smaller. The second derivative is always negative for a hump in the function, corresponding to a maximum. A critical point (x,y) of f is a point where both the partial derivatives of the functions vanish. A local maximum, or a local minimum, is a critical point. In one variable, local maxima and minima are the only `nondegenerate critical points. In two or more variables, other possibilities appear. For instance one has the saddle point, like the critical point of at (0; 0). In some directions this looks like a maximum, in other directions this looks like a minimum. We try to classify critical points by looking at the second derivatives. APPLICATIONS OF MAXIMA AND MINIMA IN DAILY LIFE: There are numerous practical applications in which it is desired to find the maximum or minimum value of a particular quantity. Such applications exist in economics, business, and engineering. Many can be solved using the methods of differential calculus described above. For example, in any manufacturing business it is usually possible to express profit as a function of the number of units sold. Finding a maximum for this function represents a straightforward way of maximizing profits. In other cases, the shape of a container may be determined by minimizing the amount of material required to manufacture it. The design of piping systems is often based on minimizing pressure drop which in turn minimizes required pump sizes and reduces cost. The shapes of steel beams are based on maximizing strength. Finding maxima or minima also has important applications in linear algebra and game theory. For example, linear programming consists of maximizing (or minimizing) a particular quantity while requiring that certain constraints be imposed on other quantities. The quantity to be maximized (or minimized), as well as each of the constraints, is represented by an equation or inequality. The resulting system of equations or inequalities, usually linear, often contains hundreds or thousands of variables. The idea is to find the maximum value of a particular variable that represents a solution to the whole system. A practical example might be minimizing the cost of producing an automobile given certain known constraints on the cost of each part, and the time spent by each laborer, all of which may be interdependent. Regardless of the application, though, the key step in any maxima or minima problem is expressing the problem in mathematical terms. Everything in this world is based on the concept of maxima and minima, every time we always calculate the maximum and minimum of every data. Now-a-days results are also based on the concepts of grades which is again based on the concept of maxima and minima.
Sunday, January 19, 2020
Response to Bystander Effect, Prejudice, Aggression and Deterrence Theory Essay
The Bystander Effect states that the greatest number of bystanders who witness an emergency the less likely anyone of them will help. What are your views about the bystander effect?            The phenomenon of the bystander effect became recognized and found its niche in social psychology studies after the murder of Catherine â€Å"Kitty†Genovese in 1964. As it is one of the most shocking murders in the history, the emphasis on the psychological phenomenon that occurred in March 13, 1964 at about 3:15 am (Gado 2007) is overrated. Trekking back to the murder of Genovese, we can note that at the very hour when the crime occurred people are still usually asleep. According to the accounts on the incident, the victim did scream for help, and since it was a fatal assault, surely, the victim’s persistence to get some aid should not be doubted, -this screaming and shouting for help may cancel out the fact that the people in her proximity are still deeply asleep (as accounts say there are 38 witnesses to this murder), but at those very hours we need not further dig deeper to unravel the mysterious apathy of the witnesses all we need to do is take note of the time the assault happened; some of the witnesses may have actually heard the screams but still has the need to sleep to face a Saturday-workday ahead of them.            We can complement this further with what Abraham Maslow’s hierarchy of needs states; that the greatest need of an individual is his/her physiological needs in which sleeps or rest falls under. Moreover, since the violent scene broke the supposedly yet sleep-time’s peace, it is understandable that the witnesses had chosen not to leave the refuge of their homes, fearing that they could be the next victim. -the need for safety and security comes as the second priority in Maslow’s renowned pyramid model. These two needs therefore may have overridden any urges to be a hero or a Good Samaritan among the witnesses at those moments.            The belief that occurs each time a â€Å"bystander effect†happens is that every witness thinks that someone else among the other witnesses is more capable to help. Let us simulate a likely scenario in observance of the theory: a 79 year old lady was tripped by a rock on a crowded and busy street. In an instance like this you may likely see that not only one person will rush in to help the old lady get back on her feet.            A bystander effect though always has a chance to occur and cast its spell; to shroud a cloud of confusion that may blur the discerning of witnesses to response to an emergency. On one hand, some factors may actually trigger a witness’s or a bystander’s urge to help.            First, the affinity or degree of relation the bystander has with the individual in need of help. This will define the innate will to help and would trigger a certain sense of responsibility on the bystander’s side to help that someone he/she knows or that someone whom he/she at least have something-in-common with (for example, supporting the same basketball team, someone in the same organization). Second, would be the empathy factor that may come from one’s recalling of a previous experience that will move him/her to be of help. Third, would be the effect of mood and condition of a bystander (Bordens & Horowitz 1973), this however considers the ruling of Maslow’s hierarchy of needs over the urge to help base on mood. How can prejudice be reduced?            Through quick referrence to a dictionary, prejudice would simply be defined as preconceived or premature judgement. First, let us see the nature behind prejudice; according to the Gale Encyclopaedia of Psychology (2005), â€Å"People are not born prejudiced: many prejudices are formed against groups with which a person has never had any contact.†In basic analysis, we can then perceive that the existence of prejudice pre-requires innocence or even ignorance, -that one’s mind must be a pail that should be empty or yet has to be filled (by information and initially with opinions of other people).            Through interaction and communication with other individuals, one would naturally absorb the prejudices of another individual he/she gets contact with. According to the communication model (Laswell 1948); in every communication process there is the presence of: 1) a source, 2) a message, 3) a channel, 4) a receiver, 5) an effect, and 6) a feedback. Applying this process in tracing the development of prejudice, if an individual has yet zero knowledge or background towards a subject, as a receiver of a message he/she had to undergo the next step of the process, which is the effect. The effect here now since the receiver is yet an ’empty pail’ would be to digest the message, and if the message transmitted is prejudiced it will pour a content in that empty pail that may soon serve as the receiver’s raw material in generating his/her own prejudices. In psychology, this model resembles the social cognition pattern which likewise explains the development of prejudice.             If we are to reduce prejudice, the direct equation we can derive from Laswell’s Model would be to reduce the interaction and communication with other individuals. This in reality however, is improbable as communication being both infinite and spontaneous processes cannot be reduced in terms of amount. The number of communication sources can forcibly be reduced but the messages that a receiver had already received will continue to develop and be repeatedly analysed in his/her mind which then will be used by him/her when it’s his/her turn to communicate as a speaker.            Prejudiced beliefs lead to stereotyping, which are natural tendencies to categorise the world in order to make sense of it (NAT.org 2003). In an attempt to make the complex world organized as we perceive it, we tend to put labels on objects, events, and individuals that has same characteristics which send to us stimuli that are alike.            A means to reduce stereotyping and generalization as dictated by prejudice is to expose a prejudiced person to individuals capable of dispelling it (Gale Encyclopedia2005), these individuals include those that contradict the stereotypes. This approach to reduce and neutralize stereotyping, though somewhat indirect, will help in thawing whatever barriers prejudices had formed within one’s disposition which eventually is good, as sooner or later this prejudiced person will have the chance to interact with a person who belongs to a grouped he/she had stereotyped.            In the treatment to reduce prejudice in the form of stereotyping, immersion could be a vital antidote. In the same manner as Edward Said’s Travel Theory (1983), a culture or an idea (which in some cases can be a prejudiced idea) is bound to loose its original potency, its strength, and even its form as it gets contact with other cultures.  A stereotype can likewise be tamed; if the ignorance and the innocence where it was founded over will finally be bridged by discovering the truth (which may include interacting with the people whom you had a stereotype on) -this first-hand, actual, and direct encounter will not just reduce prejudice but also dispel it.            More than the more common but not-at-all easily done idea; to be openâ€â€minded, interaction would be the best achievable solution in reducing stereotypes. Write a two-page essay in which you describe Freud’s theory on aggression. Additionally, describe Bandura’s theory on aggression and what strategies would he recommend using to diminish aggressive behaviour. Do you think that aggression is innate or learned? Why?            Sigmund Freud explained that the theory of aggression begins at the early ages when a boy begins to develop his intimate relationship with his mother, being the natural provider and nurturing entity for the boy -this intimate relationship will come to a point that the boy will have sexual desires for his mother. In the family picture however, there is the presence of the father -whom the boy will ‘treat’ as his rival in getting his mother’s affection and attention. But eventually, the boy will realize that he can’t win over his father, as the chances of winning in physical terms is impossible due the boys inferior size, the boy will concede is this competition and soon will realize that his mother is not a suitable object of love and sexual urges (cited in Freud & Smith 1999).            This sexual-desire idea is called the Oedipus complex; while as for the girls, they also undergo the same condition and it is termed Electra complex. Freud claims that these are manifestations of the modifiers that dictate human behaviour; instinct and sexual urges called libido. Libido is energy derived from the Eros, or life instinct (cited in Freud & Smith 1999). Aggression is the outcome when the urges of libido are not released.            Eros, is present in every man, so as what Freud had introduced thereafter; the concept of Thanatos or death force. This energy from this death force seeks to deliver death and destruction, which also bounds a man to destroy his own self. Thanatos does not entirely pour its energy towards self-destruction, some of which are channelled to other objects and individuals which explains the presence of aggression.            Even before technology, liberal thinking, and advance science, and even before the man who gave name to the concept was born, the world had abide with the ‘survival of the fittest’. Scientist Charles Darwin used the phrase to term the endless struggle of beings against one another for existence. The energy from Thanatos may support what sends a being to take aggression upon another.            Bandura (1973) claimed that human behaviour is determined by the environment. Likewise man’s behaviour also dictates his environment. This means that a man learns his aggression on what he perceives on his environment, while with the presence of aggression or the absence of it around, affects what the environment will become.            Bandura’s approach in dealing with and along the process diminishing behaviour is through self-regulation or simply to control one’s own behaviour. This begins with self-observation (watching and analyzing our own behaviours), then with judgement (setting a standard or an ideal measure were we can compare our behaviours with and pattern it to them), and finally with self-response (your manner of affirming yourself whether you are satisfied or not with what was your behaviour in a particular occasion).            Aggression is innate to man, I agree for solid reasons. First, I would refer to what Abraham Maslow (1954) refer as the second immediate need; safety and security. From which threats do we seek protection against? Harsh weather? -We got our concrete homes and thick winter suits. Wild Animals? That’s what technology and urbanization is for, putting the dangerous forage-and-hunt lifestyle locked in oblivion, then what? The best answer would be human threats -which are manifestations of the presence of aggression in man. Second; man is the superior specie of all but we are still classifiable as animals -beings which are programmed from birth to seek, hunt and fight for survival. An aspect of aggression is learned by man but this mainly covers the manners of aggression; like the idea of how to use weapons and sub due impending opponents. What is deterrence theory? Why do people commit crimes?            Punishments are pre-emptive instruments set by established laws and rules meant to discourage and intimidate would-be offenders. An ever-existing idea based on what is called the Deterrence theory. â€Å"Deterrence theory is based on the concept that, if the consequence of committing a crime outweighs the benefit of the crime itself, the individual will be deterred from committing the crime†. (Summerfield, 2006, p. 1).            By default, deterrence theory lies on the fear a punishment can instil to the subjects of a law.    Ideally, a law applies to everyone in a state; both the government and the subjects. But in reality, since deterrence theory was put to practice in an organized-society nation, it has revealed some serious flaws in itself.            Write Morgan Summerfield traced the origin of the deterrence theory -stemming out the roots of its practice from old England from the Dark Ages, Feudal Era, the Tudor period, when feudal lords, kings, and queens, where the first to introduce the system of punishment.           Although crimes at that era meant heavy punishment, as Summerfield would collectively describe as â€Å"brutal†and â€Å"severe†, an individual’s economic status would determine his vulnerability to the legal consequences of the crime; â€Å"Someone wealthy or influential could often commit offences with impunity, while someone of lesser birth would be severely punished for the same offence.†           Between this statement’s lines lies an implication; the power of money, and the call to have it, which is avarice, is also ‘encouraged’.  Money, power, and influence has been the bridges to punishment-evasion several centuries ago. These gives definition to deterrence theory as the imperfect concept where present laws and subjects-controlling policies are taken from.            The answer to the question why do people commit crimes lies in the failures of deterrence theory. By default, law enforcers assume that making it known to the people that crimes are met with punishments is not enough.            First reason; not every criminal are caught, hence the crime = penalty equation is not absolute. Second, every criminal does not have the same level of fear; the fear variable is defined by how ‘hard’ the criminal/law offender is (a repeatedly imprisoned individual may not fear the conditions of being in jail as much as a first-time convict would. Third would be how able the criminal is in protecting/saving himself/herself from the legal repercussions of the crime.            If we are to directly relate the question why do people commit crimes with the fear-dependent deterrent theory, we can conclude that the discrepancy of fear among the subjects of a law do explains why not all individuals are stopped by impending punishments and thus, go on and commit crimes.            Another premise that may explain why do people commit crimes is the existence of free will; â€Å"When they act in a criminal manner, they do so out of free will and weigh the consequences of their actionsâ€â€they know what they are doing and choose to do it†(Summerfield 2006). Along with it is the belief of Chinese Philosopher, Kong Zi (Xun-Zi) that man is by nature evil. -reflected in the oldest book of all time, the Bible, in the chapter of Genesis where the first man used its free will to ignore the rule set by God in the Garden of Eden.            Kong Zi meanwhile acknowledges too that man is capable of doing good; but for a man to do a good act it has to be done consciously. The society’s means of increasing man’s awareness and sensitivity to do conscious good acts, to teach what is right and to do right is by establishing institutions (schools, churches) to teach norms, and make laws and policies (to assure that the norms are followed). -Which brings us to an uncomplicated cycle; the â€Å"naturally evil†man is straightened out and taught what is good being covered by different laws and policies which is based from the deterrence theory. On a research done by Richard Lebow and Janice Stein (1995), they claimed that Deterrence theory rarely succeeds. Although their work underwent ‘waves’ of criticisms and was thoroughly scrutinized for gaps and flaws, the spirit of deterrence theory, which is carried over by the laws in present time seems to testify on the findings of Lebow and Stein. References Contributors: Bandura, A. (1973). Aggression: A Social Learning Analysis. p. 183. Englewood Cliffs, NJ. Prentice-Hall. Bordens, K. Sm, Horowtiz, I, A.(Eds.). (2001) Social Psychology (second edition). Lawrence   Erlbaum Associates Gado, M. (2007) A Cry in the Night: The Kitty Genovese Murder Retrieved February 26, 2008 from Crime Library, Courtroom Television Network, LLC. Gale Group, (2001). Gale Encyclopaedia of Psychology, 2nd Ed.. Retrieved February 27, 2008 from http://findarticles.com/p/articles/mi_g2699/is_0002/ai_2699000270 Huitt, W. (2006). Social cognition. Educational Psychology Interactive. Valdosta, GA: Valdosta           State University. Retrieved February 28, 2008 from        http://chiron.valdosta.edu/whuitt/col/soccog/soccog.html. Jervis, R., Lebow, R., Stein, (Eds.). (1985) Psychology and Deterrence . Baltimore: The Johns  Hopkins Press, Laswell, H.D., (1948). â€Å"The structure and function of communication in societyâ€Å" -in the communication of ideas, ed. Bryson, L. New York: Harper. Maslow, A (1954). Motivation and Personality. NAT.org. (February 2003). The Psychology of Prejudice Retrieved February 28, 2008 from       http://www.e-alliance.ch/media/media-4301.pdf. Said, E. W. (1983) â€Å"Travelling Theory,†The World, the Text, and the Critic.            Cambridge: Harvard  University Press. Smith, A. K. (1999) Theories of Aggression. Biology 202: 1999 Final Web Reports-Biology.     Retrieved February 28, 2008 from Serendip database. Summerfield, M. (2006). Evolution of Deterrence Crime Theory, a journey with an End. Retrieved            February 27, 2008 from Associated Content, Inc.
Saturday, January 11, 2020
Thorn Queen Chapter Twenty-Three
There is no real way to describe rape. Sex with Kiyo or Dorian, the men I loved†¦well, I could have described that for hours in exquisite detail. I could have elaborated on the way they stroked my hair or the way their lips touched my skin. Even with Dean-my cheating bastard ex-sex had still had its share of affection and joy, back when things had been good between us. There was none of that with Leith. Well, not on my part, at least. And I think that's what made it especially bad. For him, with his crazy infatuation, it really was an act of love. He visited me often over the next few days, and each time he took me against my will, he'd tell me he loved me and attempt some sort of gentleness and affection. The horrible part was, I couldn't even resist that. It barely required any force on his part to make me submit. Honestly, I wished it had been violent. I wished he'd been cruel and brutal. I'd spent my life in fights, dealing with pain and blows. There would have been something comfortingly familiar about that, like it was just another battle for me. The twisted love he showed for me during each act of rape, however†¦well, that made it harder to bear. In that time, I only saw Art once. Abigail checked on me a number of times, and I learned that it was she who mixed the nightshade, though Leith had taught her the recipe. Cariena was the one I saw the most. She seemed to have been installed as the live-in maid and occasional sex toy for visiting guys. When I arrived, there had been three other gentry girls, but Isanna-the one I'd heard mentioned that first day-left shortly. She was very pretty, and Abigail seemed particularly happy at the price she'd gotten for her. The other two were stunning as well, and they seemed to glumly accept that their time would come. They faced it without much emotion or protest, like condemned criminals going to the gallows. Mostly, their faces were like pieces of a dream. I was kept so heavily drugged that my moments of clarity were few-though the drugs never made me forget what Leith did. None of the other girls had to be drugged; the iron was enough for them. Cariena told me, however, that when other women had required the nightshade, they hadn't taken nearly as much as me. Art and Abigail were too afraid of me getting loose, so they gave it to me more frequently than usual. â€Å"When will you know?†Leith demanded one day. He had just arrived and stood outside my room, arguing with Abigail. The door was ajar. â€Å"I thought you people had the ability to tell this kind of thing.†â€Å"We can,†snapped Abigail. â€Å"But not this soon. You've probably got to wait at least two weeks. Besides, you don't seem to mind passing the time that much.†The sneer in her voice came through loud and clear. I made a mental note to choke the life out of that bitch. Leith, however, didn't sound so happy. â€Å"Two weeks is a long time. I need to bring her back pregnant before anyone finds her! They're looking for her. She has powerful allies. Her people are loyal, and both the Oak King and the Willow Queen have taken up the search.†Dorian's dedication didn't surprise me, and knowing he was working to find me gave me the first hope I'd had in a while. But Maiwenn, too? Had that been Kiyo's doing? Or truly her own kindness? â€Å"I don't care about your tree-based monarchs,†said Abigail impatiently. â€Å"Nobody would think to look for her here.†â€Å"She suspected before. She told others. Someone could scry for her.†â€Å"They won't find her. Scrying won't work. Not with the wards here. Now why don't you stop whining and just get in there and do your business so this won't be a problem. She's almost due for her next dose.†I decided wringing her neck wasn't slow and painful enough. Yet, their words had given me a lot to think about. There was a search on, enough of one that Leith feared discovery. Her mentioning the wards had reminded me of when I'd sent Volusian here. Volusian†¦there was an option I hadn't considered yet. I could summon Volusian to me and have him warn the others. The wards were a problem. He couldn't break them on his own, but if I was calling him, the ties that bound us would be enough to pull him through. If I could muster the energy to do it. The iron and nightshade affected the gentry part of my magic. My shamanic powers, the ones I'd used for years, were tied into my strength and will-which I didn't have a lot of lately. That being said, I felt more coherent now than I had in a while-which was still pretty addled. Abigail had said it was almost time for my next dose. I had to imagine the further from the dose I got, the more its effects would dim. Cariena had said most people didn't take as much, which probably meant the nightshade would still stay in my system awhile. But if I could reach a point when its effects were lessened†¦ My brainstorming was halted as Leith entered. Consternation from his argument with Abigail showed on his face, but it soon transformed to a smile when he saw me. â€Å"Eugenie†¦you look so pretty today.†Yes, yes, I'd heard it all before. I was so beautiful, so amazing, a jewel among women that he loved so much. His words irritated me as much as insults would have. I'd been put in an ivory damask dress today, which gave me sickening bridal associations. He looked me over, and his admiration again changed to a frown. I was lying on the bed, one hand cuffed to the headboard. â€Å"What's this?†he asked. â€Å"Why did they do that?†â€Å"I was a smartass to Abigail. This was her punishment.†His face darkened further as he sat on the bed. â€Å"I don't like that†¦don't like her doing that. But, Eugenie, you have to admit you bring it on yourself†¦.†Oh, Leith. He was so lucky I could barely lift my free arm, or I would have punched that pretty face of his. He peered at me intently. â€Å"You have to get pregnant soon.†â€Å"It's not something I can really control,†I said. Well, I could have controlled not getting pregnant if I was still on the pill. I hadn't taken it in†¦how many days? Three? Four? I wasn't sure how long I'd been here. I knew all the stats, though, about women who'd gotten pregnant from just missing one pill†¦. He sighed and began unlacing the bodice of my dress. â€Å"We'll just have to keep trying then. If we just wait a little while afterward, I can do it twice today.†Oh, how fucking lovely. I wanted to explain that it wouldn't matter how many times he did it, not if I wasn't ovulating. That kind of science was lost on him, I knew, alleged genius or no. As far as most gentry were concerned, sex equaled babies, end of story. â€Å"Once it's done, we can go home. We'll get married, and you won't have to be restrained like this anymore. You can move freely and use your magic.†I decided not to mention that if we did that, the first thing I'd do with my magic was make sure I was a widow. â€Å"Things'll be good then,†he said, moving his body over mine. â€Å"I promise. I love you so much†¦.†I didn't need any nightshade to make me feel numb after Leith left. He'd held good to his word to have sex twice, and I was slowly reaching that point where it just didn't matter. I couldn't feel anything. My body wasn't even attached to my consciousness. It was like my mind existed elsewhere, dreaming or, occasionally, plotting my revenge through the drugged haze. I thought of anything I could-anything that wasn't the violation of my body-while he was on top of me. Usually, I imagined it was happening to someone else and not me. That made it easier to bear until after he left, when the ache inside reminded me that it had indeed been me. Cariena and another girl arrived shortly thereafter to give me my next dose of nightshade. I couldn't recall the other girl's name, though not for lack of caring. It was just the way my brain worked lately. She was extremely pretty, with curly black hair and sky blue eyes that reminded me of Ysabel's. Abigail occasionally let the girls administer the nightshade, confident enough in her hold over them to do it. And her confidence was well-founded. I'd tried before to talk them out of it, but their fear of her was too great. This time, I merely attempted a delay. â€Å"Wait,†I said, as they leaned over. It looked like the black-haired girl was going to hold me down while Cariena poured. â€Å"Let me just talk to you for a minute.†Cariena immediately grew nervous. â€Å"Your majesty, we can't†¦Ã¢â‚¬ Sometimes I found her use of my title endearing. Other times, I thought it was a joke, considering my present situation. â€Å"Just a minute. That's all.†â€Å"Let her,†said the other girl. I flashed her a grateful smile. â€Å"What's your name again?†â€Å"Markelle.†It sounded familiar. Markelle. I would remember this time. I wanted to treat her as a person, not an object. â€Å"Look, I just want to know about the nightshade. How often do I take it?†â€Å"Every six hours,†said Cariena, still clearly worried about this delay. â€Å"That's twice as often as they usually give it,†added Markelle. And with those words, I saw the slightest flash of bitterness in her eyes, the first I'd seen in any girl. I wondered then if she was one of the other â€Å"difficult†ones that Cariena had described, one who had to be drugged as well and eventually subdued. â€Å"Is there any way†¦is there any way you guys could, like, dilute it?†There it was, the big question. Cariena gasped, but Markelle readily answered. â€Å"No, your majesty. Abigail makes it herself and makes sure we come straight here. There's no opportunity.†â€Å"Where? Where does she make it?†â€Å"In the kitchen. She has the ingredients set aside and makes a fresh batch every day.†â€Å"What else is in it? Aside from the nightshade?†Markelle looked at Cariena expectantly. Cariena gulped, and it took her several seconds to answer. She rattled off a list of herbs, some of which I knew, some of which were unfamiliar. They probably had different names in the Otherworld. â€Å"Do Abigail and Art ever eat here? Like, do they cook? Is their kitchen stocked?†Markelle nodded. â€Å"But we never prepare the food-it's always them.†She was quick-minded; she'd probably thought I was going to suggest poison. Not a bad idea, really. â€Å"Are there any ingredients in the nightshade mix that look like other herbs they might have in the kitchen?†Both girls looked confused. â€Å"I've seen no other herbs,†said Cariena. â€Å"You have freedom of the house.†I knew most girls stayed in the basement, though. â€Å"The next time they're not around, go through the cupboards. If their kitchen's stocked, they must have a spice rack.†A knock sounded at the door. â€Å"What's taking so long?†Abigail called. â€Å"See if any spices look like the ones in the potion,†I hissed as the doorknob turned. â€Å"Swap them.†Abigail entered just as Markelle held me down. Cariena poured while Abigail watched with a critical eye. â€Å"You're too slow,†snapped the shaman. â€Å"She needs this regularly.†Both girls groveled, bowing their heads deferentially. â€Å"Forgive us,†said Cariena. I knew her contrition wasn't faked. â€Å"It won't happen again.†Abigail rolled her eyes. â€Å"Stupid girls. I'll have to do it myself next time.†The instant effect that damned potion always had began to run through me. The familiar blackness swept over me, and I slept. Another day went by. Leith â€Å"visited,†and the girls apparently hadn't taken my advice on the nightshade because my six-hour cycle repeated as usual. Abigail usually came with one of the girls now, apparently not trusting them anymore. Art came once as well, and a few caustic comments from me earned me another cuffed hand. I began to understand the roles they played. Both participated in the brokering and sale of the girls. Art helped Leith's men catch the girls and offered his home-the one I'd once thought too large for a guy like him-as their prison. Abigail seemed to handle the day-to-day affairs of taking care of the girls, and it occurred to me one day that those handcuffs at her place hadn't been part of anything kinky. They'd been part of her arsenal for this hellhole, and I suspected the trip to see her â€Å"sister†that day had probably been to deliver some poor girl to her new owner. I cringed at what that car ride must have been like. For a gentry to be surrounded in all that metal and technology†¦it would have been awful for her. Leith was getting dressed after one of his conjugal visits one day. I was close enough to my next nightshade dose that I was able to shoot him looks of contempt-ones he didn't notice. He seemed particularly excited. â€Å"It's been a week,†he said. â€Å"One more week, and Abigail says we can test to see if you're carrying my child.†He pressed a kiss to my forehead. â€Å"I can feel it, Eugenie. I know we've done it.†There was no â€Å"we†in sexual assault, but again, I found it easier just to remain silent lately. It usually made him leave that much more quickly, which then left me alone with my thoughts and my aching body. Sometimes after he visited, my body would feel so violated and dirty that I'd hate it. Then I'd remember that none of this was the fault of my body or me. It was Leith. Shortly after his departure that day, Abigail and Markelle came in with my next dose. I'd heard talk that Markelle had a buyer. Her days really were numbered now, and I felt bad for her, this girl who'd once fought back against her captors. I was so used to the nightshade by now that they almost didn't need to hold me down anymore to force me to take it. It was a bit disheartening that I felt that way now and wondered if I too was on my way to that sad resignation everyone else had. The two of them left, and I lay there, waiting for the unconsciousness that always followed. It usually lasted an hour or so before I came to and lived in my fuzzy state until the next dose. Sure enough, I started to feel a little tingly†¦but no sleepiness followed. I lay there, scarcely daring to breathe. After falling drearily into a strict regimen, any sort of change was a shock to my system. I waited and waited. No unconsciousness. My blurry, addled state didn't disappear, but it didn't get any worse than when I was due for my next dose. Holy shit. One of them had done it. One of those girls had swapped out the nightshade tincture's ingredients. Who? I would have wagered money on Markelle over timid Cariena. Markelle occasionally had that rebellious spark in her eyes, despite her docile behavior, and her impending sale would be serious motivation. She was from the Thorn Land too-my subject. Sometimes I got the feeling that she truly believed her queen could get her out of this. But did I? I still didn't know if I could get myself out of this. My weapons were long since gone, and I didn't think I had the strength to launch a physical attack on Abigail or Art. My door was kept locked, so there was no prowling for me. Gingerly, I sat up. The world shifted as usual, but again, not like it normally would have post-potion. What to do with this freedom? I had no guarantees my next dose wouldn't be the usual stuff. That gave me six hours, and the further that time progressed, the better shape I'd be in. I would have given anything for a clock or even a glimpse of the sun. I needed to track the time, waiting until the last possible moment for my strength to be at its peak. It looked like I'd have to wing it and hope my guess was right. For a moment, panic washed over me. There seemed no obvious options, and I didn't know how fast the potion would let up. Anyone could walk right in at any time. Leith could come in. Leith†¦With some of that fuzziness gone from my head, the memories of what he'd done to me came through more sharply, and my fear grew- No! I swiftly ordered myself not to think about any of that. Not Leith. Not overwhelming odds. I needed to think only of escape, and for that, I needed to start with small details. I'd been good today-no bindings. And with the nightshade, no one felt the need to give me iron bracelets like the girls. That meant no blocking of my magic, short of the potion. Somehow, I doubted I'd have the power in six hours to blow this place up with a mini-hurricane. What did that leave me? Hopefully physical stamina†¦and with it†¦my shamanic powers? Now the countdown began. The minutes were agony, particularly since I had no way to count them. At first, I just attempted general counting in my head, but that grew tedious. I had nothing to do but wait and gauge my own body's recovery. And recover it did. Oh, I was a long way from being able to kick anyone's ass, but my wits grew a little clearer. Standing and moving didn't hurt much either. Finally, I decided it was now or never. I had to take my gamble. Maybe it was well before the six hours, but I couldn't risk going over. It would have been easier with my wand, candles, and other accoutrements. What I had to do wasn't impossible, though. I turned off the lights, plunging me into darkness, and sat on the bed cross-legged. â€Å"Volusian,†I said softly. â€Å"By the ties that bind, I summon you to come to me and obey my commands.†Weak as I was, I felt my will go out, stretching beyond the worlds to my minion. At first, I thought it was useless-then, I felt it. The slightest twitching of our bond. I gritted my teeth, drawing all the strength I could. â€Å"I summon you,†I growled. â€Å"Obey me and come.†For a moment, I thought I'd failed. Then, a coldness filled the room, and red eyes burned before me. Seeing them in the blackness was too scary, and I stumbled up to turn the lights back on. â€Å"My mistress returns,†he said. â€Å"Or rather, I return to my mistress.†I didn't need to see the slight curling of the spirit's lips to know my hold on him was tenuous. It was like a fragile string of silk, ready to snap at any moment. Bringing him here, through those worlds, had sapped more of me than I thought imaginable. I still held him, but for the first time in the years I'd enslaved him, the full realization of just how powerful-and dangerous-he was hit me. â€Å"I have tasks for you,†I said sternly. I could show no weakness. He took a few steps toward me. â€Å"My mistress is bold to say so. You can barely maintain the bond between us as it is.†â€Å"I can hold this bond until the end of time. Now, you will obey me.†And almost before I saw what was happening, his clawed hands were around my neck-cold, cold. So cold that they burned. â€Å"I have waited for this for so long,†he hissed. â€Å"So long for you to weaken so that I may finally kill you and make you suffer the way you have tormented me these years, enslaving me and sending me to do your menial errands.†I couldn't even manage a scream, not with the way his hands were cutting off my air. I could only manage something that was half-grunt and half-gasp. Desperately, desperately, I fought him mentally. I was one of the most powerful shamans in the world. I could control wayward spirits. I could enslave them easily. I'd once had a host of them. I could fight this. â€Å"You will feel pain like you have never dreamed possible,†he continued. â€Å"You will beg for death, beg for dismemberment†¦for even that would be easier than the agony I will inflict on you.†Everyone had warned me so many times about keeping Volusian. What if your control slips? they had all asked. Dorian had even offered to help banish him to the Underworld for good. I had laughed the worries off. I was strong. Even after a battle like I'd had with the fire demons, maintaining that link to Volusian was practically subconscious. But now†¦now, this was different. â€Å"You are losing it-the bonds are nearly broken. In a few heartbeats, your control will be gone†¦.†No! I couldn't speak a response, but the words in my mind burned. I would not lose this. I would not lose control of him. Wrenching up the last scraps of my strength was like ripping my own heart out. You will obey me! Back off! The world started to sparkle as my air grew less and less, and then-he did back off. His eyes blazed with malice. He'd been so, so close, and we both knew it. My control now was still a tenuous thing, and I had to hope I would recover my strength soon and solidify my grasp. â€Å"You will obey me,†I said in a thin voice. â€Å"You will not harm me.†â€Å"As my mistress commands.†But I could tell from his voice that he didn't believe this would last, that he was biding his time. Meanwhile, I was running out of time to decide what to do, not only because I didn't know if he'd break free again but also because Abigail could be here at any moment. My initial instinct was to tell him to simply get me out of here. But if that command took the last of my strength, he could easily kill me once we were out. And even if I made it out, what about the girls? I couldn't rescue them on my own. How long until Markelle disappeared? No, I needed to kick Volusian out of the house. If I didn't summon him back, those wards would keep me safe. I needed to send him for help, and that choice had to be a wise one. â€Å"Leave this house. Go to Dorian,†I said. I drew upon that fleeting strength of mine to enforce the order. â€Å"I command you. Go to Dorian and tell him where I'm at. Exactly where I'm at.†I could have sent him to Kiyo. Kiyo knew where this house was. But if the effort of these commands was enough to finally shatter my hold on Volusian, Dorian might be able to bind him back. It would be better than Volusian running loose. That, of course, depended on whether my order was strong enough to even get Volusian to Dorian to deliver the message. My first command had been to get Volusian out of the house and keep me behind the wards. If that was all I could manage, Volusian would no longer be bound to obey. He has to, I thought desperately. He has to get to Dorian†¦. â€Å"Go!†I ordered harshly. â€Å"As you command.†Volusian vanished, eyes narrowed, confident our bond was about to break. As soon as he was gone, I fell onto the bed, nearly ready to pass out. Would it work? Or had I just broken the last fragments of our bond? I was too afraid to reach out and test the link. I didn't have the strength. The door suddenly unlocked. Nightshade time. With a sickening thought, I realized that if it was the original kind, I would almost certainly lose that control of Volusian. If it was Markelle's decoy, I could hold onto my strength. Abigail entered, a cup in hand and Markelle in her wake. The gentry girl's eyes were down, her whole posture meek. I bit my lip at their approach, waiting to see what my future held.
Friday, January 3, 2020
Harriet Tubman on the Twenty Dollar Bill
Harriet Tubman was an amazing woman  she escaped slavery, freed hundreds of others, and even worked as a spy during the Civil War. Now she’s going to grace the front of the twenty dollar bill. But is this move progress or pandering? The Current State of Currency The faces of United States currency have a few things in common. They feature prominent figures in American history. Figures such as George Washington, Abraham Lincoln, and Benjamin Franklin have been pictured on our paper money, and some of our coins, for decades. These individuals were prominent in the founding and/or leadership of the nation. Not surprising, money is sometimes referred to colloquially as â€Å"dead presidents,†despite the fact that some figures on the money, such as Alexander Hamilton and Benjamin Franklin, were never presidents. In some ways, that fact does not matter much to the public. Hamilton, Franklin, and the others are larger than life figures in the history of the founding of the nation. It makes sense that the currency would feature them. However, what Washington, Lincoln, Hamilton, and Franklin also have in common is that they are prominent white men. Indeed, very few women, and fewer people of color more generally, have been featured on U.S. currency. For example, prominent women’s suffragist Susan B. Anthony was featured on a United States dollar coin minted from 1979 to 1981; however, the series was halted due to poor public reception, only to be reissued again for a short period in 1999. The following year another dollar coin, this time featuring the Native American guide and interpreter from the Shoshone nation, Sacagewa, who led Lewis and Clark on their expedition. Like the Susan B. Anthony coin, the golden dollar coin featuring Sacagewa was unpopular with the public and is of primary interest to collectors. But it looks like things are about to change. Now several women, including Harriet Tubman, Sojourner Truth, Susan B. Anthony, Lucretia Mott, Elizabeth Cady Stanton, Marian Anderson, and Alice Paul will be gracing other denominations of paper money in the next upcoming years. How Did It Happen? A group called Women on 20s has been advocating to replace former president Andrew Jackson on the twenty dollar bill. The non-profit, grassroots organization had one major goal: to convince President Obama that now is the time to put a woman’s face on America’s paper currency. Women on 20s used an online election format with two rounds of voting that let the public choose a nominee from an original slate of 15 inspiring women from American history, women such as Wilma Mankiller, Rosa Parks, Eleanor Roosevelt, Margaret Sanger, Harriet Tubman and others. Over the course of 10 weeks, more than half a million people cast votes, with Harriet Tubman ultimately emerging as the winner. On May 12, 2015, Women On 20s presented a petition to President Obama with the election results. The group also encouraged him to instruct Secretary of the Treasury Jacob Lew to use his authority to make this currency change in time to have a new bill in circulation before the 100th anniversary of women’s suffrage in 2020. And, after a year of public polls, discussion, and agitation, Harriet Tubman was chosen to be the face of the new twenty dollar bill. Why the $20 Bill? It’s all about the centennial of the 19th amendment, which granted (most but not all) women the right to vote. 2020 marks the 100th anniversary of the passage of the 19th Amendment and Women on 20s sees having women on the currency as the most appropriate way commemorate that milestone, arguing that â€Å"Let’s make the names of female ‘disrupters’â€â€the ones who led the way and dared to think differently -- as well-known as their male counterparts. In the process, maybe it will get a little easier to see the way to full political, social and economic equality for women. And hopefully, it wont take another century to realize the motto inscribed on our money: E pluribus unum, or ‘Out of many, one.’†The move to replace Jackson makes sense. While he has been hailed throughout history because of his lowly beginnings and rise to the White House and his conservative views on spending, he was also an unabashed racist who engineered the removal of indigenous people from the southeast  also known as the infamous Trail of Tears  to make way for white settlers and the expansion of slavery because of his belief in Manifest Destiny. He is responsible for some of the darkest chapters in American history. The group’s focus on putting women on paper money is a key one. Women had been featured on coins --and not the frequently used ones such as the quarter -- yet those coins have been unpopular and have gone out of circulation quickly. Putting women on more frequently used paper money means that millions will use this currency. It means that women’s faces will be staring back at us while we buy groceries or tip servers or make it rain at the strip club. And instead of it being â€Å"all about the Benjamins,†it may be all about the Tubmans. Who Is Harriet Tubman? Harriet Tubman was a slave, a conductor on the Underground Railroad, a nurse, a spy, and a suffragist. She was born into slavery in the 1820s in Dorchester, Maryland and named Araminta by her family. Tubman’s family was fractured by slavery and her own life was marred by violence and pain. For example, when she was 13, she received a blow to her from her master that resulted in a lifetime of illness, including headaches, narcolepsy, and seizures. In her 20s, she decided to take the ultimate risk: fleeing slavery. To call Tubman brave is an understatement. She not only made the perilous escape from slavery herself, she also returned South dozens of times to free hundreds of others. She used disguises to evade and outwit slave catchers and never lost a single person on the flight to freedom. During the Civil War, Tubman worked as a nurse, cook, scout, and spy. In fact, in 1863, she led an armed raid that freed 700 slaves in South Carolina on the Combahee River. Harriet Tubman has the great distinction of being the first woman ever to lead a military expedition in American history. After the civil war, Tubman was an avid suffragist who worked with high profile women’s rights advocates such as Susan B. Anthony and Elizabeth Cady Stanton, lecturing on the right to vote. Later in life, after retiring to a farm outside of Auburn, New York, and after a long and arduous process of appeals, she secured a pension for herself of $20 per month for her Civil War efforts -- which makes it all the more ironic that she will now grace the front of the $20. Is This Progress or Pandering? Harriet Tubman is undoubtedly a great American hero. She fought for the oppressed and put her own life and body on the line numerous times for others. As a Black woman freedom fighter, her life is a primary example of what it means to fight intersectionally  taking into account various intersecting oppressions. She represents some of the most marginalized in our history and her name and memory should be on the lips of schoolchildren everywhere. But should she be on the $20? Many have hailed the decision to replace Andrew Jackson with Harriet Tubman, citing the move as evidence of the great progress our nation has made. Indeed, during part of her life Tubman was legally recognized as chattel  that is, movable property like a candlestick, or a chair, or cattle. She could have been legally bought or sold with U.S. currency. Therefore, goes the argument, the fact that she will now be the face of money shows how far we have come. Others have remarked that this same irony is why Tubman should not be on the $20. The argument is that a woman who risked her life countless times in order to free others, and who spent her years advocating for social change should not be associated with something as debased as money. Also, some argue that the fact that she was considered property for much of her life makes her inclusion on the twenty dollar bill hypocritical and distasteful. Still more insist that Tubman on the $20 simply pays lip service to issues of racism and inequality. In a moment where activists are trying to make the claim that Black Lives Matter and when systemic oppression has still left Blacks on the bottom of the social totem pole, some wonder about how useful it is to have Harriet Tubman on the $20. Others have argued that paper currency should only be reserved for government officials and presidents. This is a particularly interesting moment to place Harriet Tubman on the $20. On the one hand, the U.S. has seen an amazing amount of social change in the past few decades. From having a Black president to the passage of gay marriage to the rapidly shifting racial demographics of the country, the U.S. is transforming to a new nation. However, some of the nation’s old guard is not going down with a fight. The increasing popularity of ultra-right wing conservatism, white supremacy groups, and even the troubling rise of Donald Trump speaks to much of the uneasiness a substantial part of the country has with the social sea of change going on. Some of the vitriolic reactions to the news of Tubman on the twenty dollar bill underscore that racism and sexism are far from obsolete. Interestingly, while Women on 20s did gain a victory for their campaign by getting Harriet Tubman on the $20, Andrew Jackson is not really going anywhere: he will still be on the back of the note. Perhaps in the case of women gracing U.S. paper currency, it is a situation where the more things change, the more things stay the same.
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