melanoman: (Default)
The second half of this paper has been a long time coming because I ended up shooting my own theory down when researching and testing it. So rather than slink off quietly I'll write a different paper shooting down my original thesis and making some guesses about what is really going on. Part I of the paper lays a lot of groundwork about pejoratives in general and racial pejoratives in specific.

It ends with the comment that the meaning of these terms varies radically with the set of prejudices. This brings up an interesting case where the speaker and listener have substantially different prejudices about the group. The meaning that the speaker is conveying includes or at least refers to his own prejudice, but the hearer has a potentially different set of prejudices and hears the term accordingly. Additionally, the underlying premise that the speaker subscribes to a derogatory view of the target group is conveyed, even if it isn't exactly clear what the derogatory view is.

Since the prejudice is part of the meaning of the terms, the ambiguity that comes from differing prejudices makes these terms prone to misunderstandings when the speaker incorrectly assumes a shared opinion. This superficial misunderstanding about specifics in no way invalidates the underlying correct understanding that by using a pejorative the speaker is expressing a strong negative opinion about the group.

This distinction becomes clear when contrasting the confusion that comes from the transition when a previously neutral terms becomes pejorative versus the confusion that comes when a bigot speaks to someone who does not share a particular prejudice. As an example of the former, consider some time around the 1970's when the neutral term to refer to people native to Asia and thereabouts plus their descendants was "oriental." Around that time, the word became a pejorative and was eventually replaced with the term "Asian" As an inevitable part of the transition, people from the dialect groups that changed later would talk to those from groups that changed earlier. The speaker, who had possibly never heard the term "Asian" nor knew of any reason for the term "oriental" to cause offense, would use the term to someone for whom the term was a pejorative. In this case, the hearer might incorrectly assume that the speaker was a bigot based on the language usage, even though bigots and non-bigots alike in the speakers dialect group were using the term. Over time as a kind of critical mass formed from similar interactions, the dialects influenced each other and spread the pejorativization of "oriental" from dialect to dialect. After the transition, the assumption that using the term "oriental" implied that the speaker had a dim view of the becomes correct for continued usage (but not retroactively to pre-transition usage). This does allow for some awkward artifacts like the "CP" in "NAACP"

This brings up the much more challenging topic of how neutral the non-pejorative terms are. My initial theory was that language would demand a term that referred to any frequently discussed group such that the term did not have a pejorative standing. Whenever one such term became pejoratized, another would be generated to take its place. When the sentiments surrounding the group were particularly charged, the process of pejorativization and replacement would be accelerated. I had been trying to work up an experiment to distinguish group-reference from group-description in the various terms. To date the results have been inconclusive at best, and seem to suggest that even the most neutral terms must invoke a prototypical image of a group member. In doing so, they are subject to many of the same phenomena that the pejorative counterparts are.

That said, there can be no question that a person using a vulgar term like "zipperhead" is being insulting in a way that a person using a term like "Asian" is not. Some day I hope to write a Part III that explains why and how one term is so much more offensive than the other, but first I'll need to figure that out.
melanoman: (Default)
This post is an academic investigation into how framing works with respect to racial pejoratives. In particular, I'm interested in exploring the boundaries of when a racial term draws in other racial ideas versus when it stands alone. By the very nature of this discussion, some offensive terms will get examined --- so offensive that I feel the need to make a disclaimer that I do not condone the use of these terms and that I am committed to the elimination of racism to the extent that this is possible. I suspect that this post will be too technical to be of much practical use in fighting racism, but I'd be thrilled to be proved wrong on that point.

The post was inspired by a stoneself post on the meaning of the term "white trash." The term "white trash" started out as a pejorative term coined by 19th century black americans to identify a radial group off the category "white." The term at once associated the identified group with "white" (i.e. they had white skin) but also differentiated them from the prototypical "white." The modern term is still a radial term off the "white" group, though the exact distinction being made has changed somewhat and the speaker base has broadened to include non-black speaker. In both cases the differentiation is pejorative and involves behavioral, social, and economic factors. The specifics of the distinguishing factors are beyond the scope of this paper, except for their pejorative nature.

Radial terms of this sort exclude the newly identified group from the original one. The naive definition of "white" --- a person with relatively low melanin content in their skin with caucasian ancestry --- would include "white trash" as "white," but the usage of this term focuses much more on the distinction than the similarity. More simply, when a person is called "white trash" the emphasis is that this person does not fit the prototypical image the speaker has of white people.

All pejoratives, by their nature, make a negative judgment against an identified individual or group. A second distinction can be drawn between pejoratives that make a judgment and pejoratives that express a prejudice.

An example of a pejorative that makes a judgment about an individual would be the term "jerk." When someone calls a person a "jerk" the emphasis is directly on the quality and/or behavior of that person and doesn't much consider the association of that person with anyone else. Words of this type range from very mild terms like "slacker" to vulgar ones like "asshole." Some are very specific about what sort of judgment is being made, such as "slacker" referring to work ethic, while others are much more generic.

The group-based pejoratives and racial pejoratives in particular typically emphasize prejudices about a group rather than make a specific judgment about an individual. Contrast the term "scab" (a pejorative referring to a person who works in spite of declared strike) with the the term "wop" (a vulgar pejorative referring to Italians and people of Italian descent). The former term emphasizes a particular behavior and derives it power from the hatred of that behavior and its effect on the lives of the union workers whose negotiation tactic is being undermined. The latter term derives all its meaning and force from prejudice.

Some terms function both ways, such as the term "nag." The term definitely focuses on a particular behavior, namely excessive repetition of instruction or criticism, but it also associates with attitudes about women and draws on those attitudes as part of its meaning. This is why it is awkward or humorous to refer to the same behavior in a male as "nagging." As that humorous usage becomes more common, the humor starts to fade and the meaning of the term starts to change so that the association with female stereotypes is weakened, so we can imagine a time in the future when "nag" might become a gender-neutral term referring only to the behavior and not the prejudice. This certainly hasn't happened yet.

Context always allows a term from one class to be used as if it were from the other, as in the vulgar example "What is the difference between a black man and a nigger?" By taking the form of a judgment-based pejorative, the speaker, at least nominally, is making specific judgments about individuals, even though the extremely vulgar term "nigger" draws all of its power from racial stereotypes. Whether the question is asked sincerely by someone who thinks of "nigger" as a radial category within blacks or insincerely by someone who just want to refer to his or her prejudice with the pretense of fairness, the word still draws heavily on a particular set of assumptions about a group of people to derive its meaning.

The term "white trash" works much the same way. The exact meaning is hard to pin down because it varies with the particular prejudices of the group that uses it. This raises a question about how much of the set of prejudices is drawn into the discussion when a racially charged term is used. This was the topic I initially wanted to address, but I've run short of time laying the groundwork, so I'll have to leave that to a PART II of this post later on.
melanoman: (Default)

Solving Inequalities with One Absolute Value (II)

 

These steps explain how to solve an inequality with one absolute value and one variable when there are variable terms both inside and outside the absolute value sign.

 

Step 1: Isolate the absolute value

 

Exactly like Part I of this lesson.

 

3 - | x – 3 | > - x           è - | x – 3 | > - x – 3               è | x – 3 | < x + 3

2 | y2 – 4 | > 6y è | y2 – 4 | > 3y

 

Step 2: Is the expression in the absolute value negative or nonnegative?

 

This can be a difficult step for complicated expressions, but for the simple polynomials we are usually working with, there is an easy way.  Solve the related equation where the expression is equal to zero.  This will tell you where the graph crosses zero.  Mark the variable in this related equation so you don’t confuse it with the original problem.

 

x0 – 3 = 0         è x0 = 3

y02 – 4 = 0        è y0 = -2 or 2

 

Divide the domain into sections using the roots above and mark each section as positive or negative by plugging in a test value.

 

x – 3    è negative where x < 3, nonnegative where x >= 3

y2 – 4   è nonnegative where y < -2, negative where -2 < y < 2, nonnegative where y > 2

 

Step 3: Split the problem into sections

 

Write a separate inequality for the negative section and the positive sections.  Mark the variables so you don’t mix the two up.  To make the positive inequality, just drop the absolute value sign.  To make the negative inequality, multiply the contents of the absolute value sign by -1.  If step 2 showed that your expression was always positive or always negative, you only need to make one inequality.

 

xp - 3 < xp + 3

3 – xn < xn + 3

yp2 – 4 > 3yp

4 – yn2 > 3yn

 



Step 4: Solve using basic algebra

 

xp - 3 < xp + 3              è -3 < 3                     è true (everything)

3 – xn < xn + 3              è 0 < 2xn                    è xn > 0

 

yp2 – 4 > 3yp                 è yp2 – 3yp – 4 > 0     è (yp – 4) (yp + 1) > 0  è yp > 4 or yp < -1

4 – yn2 > 3yn                 è - yn2 – 3yn + 4 > 0   è (1 – yn) (yn + 4) > 0  è -4 < yn < 1

 

Step 5: Take the intersection for each section

 

Now we combine the domain notes from step 2 with the partial solutions from step 4 by taking the intersection for each section.  If you got an always-true result in step 4, take the entire corresponding section.  If you got an always-false result, take nothing for that section.  At this point we can drop our special markings for the sections.  Be extra careful when the section has an OR in it --- you may want to sketch a graph in two colors.

 

xp >=3 AND true         è x >= 3

xn < 3 AND xn > 0       è 0 < x < 3

 

(yp <= -2 OR yp >= 2) AND (yp > 4 OR yp < -1)         è y <= -2 OR y > 4

(-2 < y < 2) AND (-4 < yn < 1)                                    è -2 < y < 1

 

Step 6: Take the union of the two sections

 

0 < x < 3 OR x>=3                              è x > 0

y <= -2 OR y > 4 OR -2 < y < 1          è y < 1 or y > 4

 

melanoman: (Default)

Solving Inequalities with One Absolute Value (I)

 

Step 1: Isolate the Absolute value

 

Treat the absolute value signs like a set of parenthesis that you can’t break, or like the whole thing was one variable, then solve for that on the left side.  Remember to flip the inequality if you multiply by a negative number.

 

1-2|x-3| > -5  è -2|x-3| > -6 è |x-3| < 3

 

If the right side is a constant, solve using the steps below.  If the right side includes a variable, this problem requires special handling (learn how in part II of this lesson)

 

Step 2: Is the right side negative or zero?

 

If the right side is or could be negative, this problem needs special treatment.  If the right side is a negative constant, then the answer will either be “no solution” or “all real numbers” depending on whether the equality is “greater than” or “less than”

 

|x| < -1             è no solution

|x| <= -1           è no solution

|x| > -1             è all real numbers

|x| >= -1           è all real numbers

 

The same goes for a right side of zero, UNLESS the inequality is “less than or equal.” In this very special case the contents of the absolute value equal zero.

 

|x| <= 0            è x = 0

 

Step 3: Get rid of the absolute value marker

 

Now we split the equation into two parts.  We will compare the left side without the absolute value markers to the right side and it’s opposite.  If the inequality uses “less than” then we bound the contents of the absolute value marker between the right side of the equation and it’s opposite.  If the inequality uses “greater than” then we split the equation into the union of two inequalities.

 

|x+1| < 3          è -3 < x +1 < 3

|x| <= 5            è -5 <= x <= 5

|x-3| > 7           è x -3 > 7 OR x -3 < -7

|x| >= 13          è x >= 13 OR x <= -13

 

Step 4: Simplify (if needed)

Use basic algebra to simplify as needed.

melanoman: (Default)
Jessie posed a question last night about cycle detection on really large lists. The idea is that you can't afford to store the whole list in memory.

I started out playing with the problem statement by proposing some really easy solutions.

If you know how many elements are in the list, just traverse that many elements and see if you are at the list end. If not, there is a loop. (No, you don't know how many elements are in the list)

If the list is doubly linked, just check the first link has a null previous pointer and that every other link has ->previous->next = self. (No, the list is singly linked).

So I stopped playing and pulled out the real solution. Store the 1st, 10th, 100th, 1000th, etc. element into memory while traversing the list and checking each element in memory to see if it has been stored. Now you have O(log n) storage requirements and O(n) search time. In real life I'd double instead of multiplying by ten, but I wanted to make the math obvious. Now you can handle a googol of data with 100 stored addresses.

Jessie surprised me by saying this was close to the "real" solution, but not it. He went on to state that he has a solution that is also O(n) in search time, but uses no more than 10 stored addresses. I played with the problem a little while and my gut feel is that there is no such solution. I'm fairly certain than any solution with O(1) storage is NOT O(n) in search time.

I just came up with the solution. You don't need all the powers of ten, just the most recent one. Sigh. And if you use the powers of two instead you are guaranteed a fairly small amount of looping before hitting the target.

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