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Mental Math

Mental Math - A Guide to Effective Mental Calculations
''Note about Notation: This book generally uses the English/U.S. styles of notation. This includes using commas as a way to divide up the thousands in long numbers (e.g. 32,000 = thirty-two thousand), it will use full stops (periods) as decimal points.''

Calculating things in your head can be a difficult task. If you can't remember what you've worked out or simply don't know how to solve a problem then it can be very challenging and frustrating. But by learning and practicing the methods of using mathematical patterns, you can dramatically improve the speed and accuracy of your arithmetic. These methods are often called "High Speed Mental Math". Mental Math is a valuable skill to have, even in the computerized world we live in:
 * 1) With good mental math skills you can save yourself time by not needing to pull out a calculator (or cell phone) every time you want to do a task.
 * 2) Mental math skills will improve your ability to estimate results, thus having a better ability to catch errors from computer-derived results.  For example, while a calculator will generally give the right answer, based upon what was typed in, if you accidentally typed the wrong number, you might not catch your error if you didn't have good mental arithmetic skills.

Addition
The foundation of all arithmetic is addition, also known as summing. Similar to all mental math calculations, you can improve your ability to add numbers by learning to use some basic patterns.

Changing the Order of Addition
Often when looking for a pattern to help you quickly do an addition problem, it can help to change the order that you add things. For example, 8+1 is the same as 1+8, and in both cases you just count up one from 8, to get the answer 9. If you get stumped on an addition problem, try changing the order of which one you add first, and see if it helps.

Adding Zero, One, or Two
Unless you are completely new to addition, you surely know the pattern for adding I zero. Anything plus zero is equal to the original number. Thus when you see a zero in an addition problem, you can basically ignore it, as it won't have any effect upon the answer. For those who are interested in math trivia, this property of zero not changing things when you add it, is called the "identity property" in arithmetic. Also, keep in mind, that you can only ignore zero in addition, and sometimes in subtraction. In multiplication and division, having a zero in a problem always changes things. You probably also know the rule of adding 1, which is simply count up one number. This can also be used quickly with 2, where you can either count up 2 numbers, or if you know your even and odd numbers well, you can skip to the next even or odd. To understand using the even and odd pattern, you may be familiar with the cheer that has the even numbers: "2,4,6,8, who do we appreciate?" If we add 6+2 we will go up to the next even number, which is 8. Similarly, the odd numbers go 1,3,5,7 so 2+7 will be the next odd number, which is 9.

Adding Nine or Eight: Counting Down from 10
Another arithmetic pattern you surely know is how to add 10 to a number. An example of this is 2+10 is 12, or 6+10 is 16. We can use this pattern to help us add 9 or 8. Since 9 is one less than 10, you can always add 9 to something by adding 10 to the number instead and then counting down one. For instance to find 9+7, you can add 10+7, which is 17, and then count down to 16. Similarly with adding 8 to a number, you can also add 10, and then count down 2 numbers. So for instance, 8+7 can be found by adding 10+7 which is 17, and then counting down 2, which is 15. If you are good with knowing your even and odd numbers, you can also use a similar pattern as was explained with adding 2, by just going down one even or odd number. or you could say when it's adding 9 you know it's going to a higher number for instance 9+8 you know it's going to be a teen so subtract one 9+8 = 1 now subtract one from 8 to get 7 now put them next to each other to get 17.

Doubling and Nearly Doubling
You may already be good at doubling numbers, such as 2+2. When doubling a number, you are doing the same thing as multiplying by 2. This also means, that if you have learned to count by numbers, such as counting by 4's, you know that it is 4, 8, 12, 16... And thus 4+4 is 8. Once you have become good at doubling, you can use this knowledge to add numbers that are nearly double of each other, by just counting up or down by one. So for instance, 8+7 can be found by adding 8+8, which is 16, and then counting down by 1, which is 15. (If it is easier, you could also have done this by doing 7+7, which is 14, and then counting up 1 to 15.)

Adding Fives
This technique is a little trickier than the others we have so far talked about, but with some practice it might help you out. When adding 5 to another number, the goal is to "find the five inside" the other number, and then add or subtract what is left. For instance when adding 5+8, you could say that 8 is 5+3, so 5+8 is 5+5+3, or 13. Don't worry if you can't get this method, because most of the time you can use one of the other methods that have been taught to find the answer.

To Ten or Close
It is useful to memorize the patterns that add to 10 which are: By knowing these patterns, if you see a pattern a little different you will know to go one higher or lower. For instance, 4+7 has the 7 one higher than 6, so this must add up to 11, because 4+6=10 so 4+6+1=11.
 * 0+10
 * 1+9
 * 2+8
 * 3+7
 * 4+6
 * 5+5

Summing Groups of Numbers by Finding Numbers that Add to Multiples of 10
A useful trick when adding lots of small numbers is to clump together the ones that add up to multiples of 10. For example, if you have to add 2 + 3 + 5 + 7 + 9 + 11 + 8, that can be rearranged as (3 + 7) + (9 + 11) + (2 + 8) + 5 = 10 + 20 + 10 + 5 = 45. This method is also useful when performing column addition with more than two numbers. For example, in the problem: 56 35  47  21  12  32 +23  --- Column addition is generally performed by adding the digits in the ones place, carrying them over, and then adding the digits in the tens place., and so on. A way to make this task easier is to group the digits in the ones place in groups of ten, and mark them on your paper like this: 5 6 3 5  4 7 \  2 1 \  1 2  -- 10  3 2 / +2 3 /  --- Similarly the 6, 2, and 2 would be crossed off, yielding another 10. Therefore, the digits in the ones place add up to 10+10+5+1 (what's left) or 26.

Subtraction
A useful trick when subtracting numbers is to begin with the smaller value and mentally skip your way up the difference, with jumping points at recognizable boundaries, such as powers of 10. For example, to subtract 67 from 213 I would start with 67, then add 3 + 30 + 100 + 13. Try this once and you see how easy it is. Sounding out your thoughts it would be "three, thirty-three, one hundred thirty-three plus the remaining 13 is one hundred forty-six". A second method is to break up the number that you are subtracting. So instead of doing 1000-258 you would do 1000-250 and then subtract 8.

Subtraction from Numbers consisting of 1 followed by zeros: 100; 1,000; 10,000; etc
For example, 1,000 - 258 We simply subtract each digit in 258 from 9 and the last digit from 10. 2          5             8          from 9      from 9        from 10 7          4             2 So the answer is 1,000 - 258 = 742

Note that if the number being subtracted (the minuend) ends in a series of zeros, you subtract the last nonzero digit from 10, and leave the trailing zeros alone. E.g.: 10,000 - 5920 = {9-5}{9-9}{10-2}0 = 4080. This always works for subtractions from numbers consisting of a 1 followed by zeroes: 100; 1000; 10,000 etc. Another way of easily thinking of this method is to always subtract from 999 if subtracting from 1,000, and then adding 1 back. Same for 10,000, subtract from 9999 and add 1. For example, 1000-555 =   999 - 555 + 1= 444 + 1 = 445 Similarly 10,000 - 1068 = (9999-1068)+1 = (8931)+1 =8932 So the answer is 10,000 - 1068 = 8932 For 1,000 - 86, in which we have more zeros than figures in the numbers being subtracted, we simply suppose 86 is 086. So 1,000 - 86 becomes 1,000 - 086 = 914

Bigger Numbers using the 9s Trick (10's Complement Addition)
The above technique can be extended to arbitrarily long numbers in the following way: subtract the minuend from the next power of ten greater than the subtrahend using the nines trick above, then add the result to the subtrahend instead, but don't carry the final '1'.

Example: 1,254,953-34,064 34,064 becomes 9,965,936 via the nines trick (notice we pad the beginning with 9's to make it the same length as the subtrahend). Now add: 11  1 1  1,254,953 +9,965,936  1,220,889 And again notice that we do not include the final carried '1' on the left in our result.

Subtracting Left-to-Right
Normal subtraction is performed right-to-left, borrowing from the left when a borrow is needed. However, we read left to right, and numbers are read out loud to us in this same order, so it is convenient to be able to subtract left-to-right as well. We can do this by going ahead and pre-borrowing by default and then adding back a carry (if there is one) when we move on to the next column if it turns out we didn't need to borrow. This technique also cuts down on the amount of mental work one must do to propagate a borrow from right to left.

Example: 9543 -1992 First preborrow from the 9, leaving 8 and subtract the thousands place: 1 8543 -1992  7 Now preborrow from the 15 in the hundreds place, leaving a 14, and subtract: 11 8443 -1992  75 Now preborrow from the 14 in the tens place, leaving a 13, and subtract: 111 8133 -1992  754 Last column, we have nothing to borrow from, so we just subtract. In this case, we don't get a single digit, so we carry it back to the tens place: 111 8133 -1992  7551 And we're done! 7551 is the correct answer.

Patterns for 0, 1 and 10
Chances are you already know the pattern for multiplying by 0, 1 and 10. But in case you don't, anything times 0 is 0. Anything times 1, is itself still, and anything times 10 has a zero added to the end, so 29x10 is 290

Patterns for 2, 4, and 8
Multiplying by 2 is simply doubling a number, and so the pattern for doubling with addition is the same. Multiplying by 4 is doubling twice. So 12x4, can be found by going 12+12 which is 24 and then 24+24 which is 48. Similarly, multiplying by 8 is doubling 3 times, so 12x8 is 12+12 which is 24, then 24+24 which is 48, and then 48+48 which is 96. If you multiply by a quadratic (a number that can continuously divide in half until reaching 1, without involving fractions), then this method will always work.

Patterns for 9
Multiplying by 9 has a special pattern. When multiplying a single digit by 9, the answer will always start with a digit one less than the number, and then the other number will add to 9. This may sound complex, but lets look at an example. If we want to do 9x6, simply have your first digit being one less than 6, so we know the answer will start with a 5, then next digit must add up to 9, so the number that when added to 5 will equal 9, is 4, so the answer of 9x6 is 54. Another way to think of this method is you're multiplying the number by 10, then subtracting the number from the product. If you think of it this way, then this example becomes 10x6 = 60, then 60-6 = 54.

Patterns for 5
Any number multiplied by 5 will end in either a 5 or a 0. One way of finding the answer is to multiply by 10 first, and then divide your answer in half. Another is to count by fives.

"Number Neighbors"
If you don't know the answer to a problem, you may know the answer to a problem where one of the numbers is one more or less than the one in the problem. For instance, if you didn't know the answer to 7 x 6, you  might know 6 x 6 is 36, and then you could just add one more 6 to get to 42.

Multiplying Larger Numbers
When multiplying larger numbers it is very important to pick the correct sums to do. If you multiply 251 by 323 straight off it can be very difficult, but it is actually a very easy sum if approached in the right way. 251x3 + 251x20 + 251x300 is a scary prospect, so you have to work out the simplest method.

Rounding
One of the first things to do is to look if the numbers are near anything easy to work out. In this example there is, very conveniently, the number 251, which is next to 250. So all you have to do is 323x250 + 323 - much easier, but 323x250 still doesn't look too simple. There is, however, an easy way of multiplying by 250 which can also apply to other numbers. You multiply by 1000 then divide by 4. So 323x1000 = 323,000, divide by two and you get 161,500, divide by 2 again and you get 80,750. Now this may not seem easy, but once you've gotten used to it, dividing by four (or other low numbers) in that way becomes natural and takes only a fraction of a second. 80,750+323 = 81,073, so you've got the answer with a minimum of effort compared to what you would otherwise have done. You can't always do it this easily, but it is always useful to look for the more obvious shortcuts in this style. An even more effective way in some circumstances is to know a simple rule for a set of circumstances. There are a large number of rules which can be found, some of which are explained below.

For this multiplication, some would mentally find 251 × 323 = 250 × (320 + 3) + 1 × 323 (easy), since multiplying 250 × 320 is not hard: 25 × 32 = 25 × 4 × 8 = 100 × 8 = 800 (some would get this immediately), so 250 × 320 is 80,000. Thus, with everything in mind, 251 × 323 = 250 × 320 + 250 × 3 + 1 × 323 = 80,000 + 750 +323 = 81,073.

Factoring
If you recognize that one or both numbers are easily divisible, this is one way to make the problem much easier. For example, 72 x 39 may seem daunting, but if taken as 8 x 9 x 3 x 13, it becomes much easier. First, rearrange the numbers in the hardest to multiply order. In this case, I'd go with 13 x 8 x 9 x 3. Then multiply them one at a time. Which would equal up to a whole new Faction
 * 1) 13 x 8 = 10 x 8 + 3 x 8 = 80 + 24 = 104
 * 2) 104 x 9 = 936
 * 3) 936 x 3 = 2808 that would equal another number

Multiplication by 11
To multiply any 2-digit number by 11 we just put the total of the two digits between the 2 figures. for example: 27x11 can be written as [2][2+7][7] Thus, 27x11=297 Another example: 33x11 can be written as [3][3+3][3] Thus, 33x11=363. To visualise: 330 + 33 363 Carry=overs: 77 x 11 = 847 This involves a carry figure because 7 + 7 = 14 we get 77 x 11 = [7][14][7]. We add the 1 from 14 as carry over to 7 and get 77x11=847 Similarly, 84x11 can be written as [8][8+4][4]=[8][12][4]. The 1 from 12 carries over, giving 84x11=924 For 3 digit numbers multiplied by 11: 254 x 11 = 2794 We put the 2 and the 4 at the ends. We add the first pair 2 + 5 = 7. and we add the last pair: 5 + 4 = 9. So we can write 254 x 11 as [2][2+5][5+4][4] i.e. 254x11=2794 Similarly, 909x11 can be written as [9][9+0][0+9][9] i.e. 909x11=9999

Multiplication by 99, 999, 9999, etc
To multiply a number A by 99, you can multiply A by 100 and then subtract A from the result. When the number A is a two digit or one digit number, the result would be (A - 1) following by (100 - A). For example, when we multiply 65 by 99, we get 6435. Similarly, to multiply a number A by 999, you can multiply A by 1000 and then subtract A from the result. When the number A is a three digit, two digit or one digit number, the result would be (A - 1) following by (1000 - A). For example, when we multiply 611 by 999, we get 610389. This same idea can be used for multiplication by any large number consisting only 9s.

Same First Digit, Second Digits Add to 10
Let's say you are multiplying two numbers, just two two-digit numbers for now (though the rules could be adapted for others) which start with the same digit and the sum of their unit digits is 10. For example, 87×83 (sum of unit digits: 7+3=10). You multiply the first digit by one more than itself (8×9 = 72). Then multiply the second digits together (7×3 = 21). Then stick the first answer at the start of the second to get the answer (7221). A simple proof of how this works is given in the Wikipedia article on Swami Bharati Krishna Tirtha's Vedic mathematics. If the result from the multiplication of the unit digits is less than 10, simply add a zero in front of the number (i.e., 9 becomes 09). For example, 59×51 is equal to [5×6][9×1] which equals [30][09]. Thus 59×51 = 3009.

Squaring a Number That Ends with 5
This is a special case of the previous method. Discard the 5, and multiply the remaining number by itself plus one. Then tack on a 25 (which as in the previous section, is 5x5). For example, 65x65. Discarding the 5 from 65 leaves us with 6 5 = 6. Multiplying 6 by itself plus one gives us 42 (6x7 = 42). Tacking on a 25 yields 4225, so 65x65=4225. For example, 45x45 can be written as [4x5][5x5]thus 45x45 = 2025

Squaring a two-digit number
Rather than doing 142 or 472 as 14x14 or 47x47, the alternative is: 142 = 10 x 1(14 + 4) + (4 x 4) = 10(18) + 16 = 180 + 16 = 196 In other words, add what's in the ones place to the number, multiply it by what was originally in the tens place (sometimes you'll get a sum with the next number up in the tens i.e. 47 + 7 = 54 so use 4 not 5 in this example) tack a zero at the end, then add the square of the ones place. So: 472 = 10 × 4(47 + 7) + (7 × 7) = 10 × 4(54) + 49 = 10 × 216 + 49 = 2160 + 49 = 2209 So now we know that 472 is 2209. When squaring two digit numbers that are only 1 higher from a number ending in zero, you can also use the basic algebraic formulas: (A+1)^2 - (A*2); or (A+1)(A) - A; or (A+1)^2 - 2(A+1) + 1. For example, when squaring 99: A + 1 = 100 100^2 = 10000 2 * 100 = 200 10000 - 200 = 9800 9800 + 1 = 9801 When squaring two digit numbers that are only 1 higher from a number ending in zero, you can also use the basic algebraic formulas: (A-1)^2 + (A*2); or (A-1)(A) + A; or (A-1)^2 + 2(A-1) + 1. For example, when squaring 91: 91 - 1 = 90 90^2 = 8100 2*90 = 180 8100 + 180 = 8280 8280 + 1 = 8281

Squaring a number when you know the square of a number adjacent or in proximity
This is useful if you want to quickly calculate the square of a number when you know the square of the adjacent number. For example, take the square of 46, using the "5" rule above you know that 45 squared is 2025. Leverage this number and add 45+46 (91) to 2025, which equals 2116. While adding 91 to 2025 in your head isn't exactly easy, it is certainly easier than trying to calculate the square of 46 directly. Doing this with an adjacent known square that is below is a bit more challenging depending on how you feel about doing subtraction in your head. For subtraction, using 45 as our base, and trying to figure our what 44 squared is, we would take the known value of 2025 subtract 44 and 45 to get 1936. This can be leveraged to try to determine squares that are not directly adjacent to the known square, but it gets a bit more complex (in your head!). Symbolically: if b=a+1 and a and b are integers then b2=a2+|a|+|b|.

Just Over 100
This trick works for two numbers that are just over 100, as long as the last two digits of both numbers multiplied together is less than 100. For example, for 103 x 124, 3 x 24 = 72 < 100, so this trick will work. For 117 x 112, 17 x 12 = 204 > 100, so it will not. If the first test works, then the answer is:
 * 1[sum of last two digits][product of last two digits]

Examples: If the addition or multiplication of the last 2 digits < 10, then add a 0 infront of the number, example if the addition is 4, it should be 04. Example shown below: This trick works for numbers just over 200, 300, 400, etc. with one simple change:
 * 108 x 109 = 1[8+9][8x9] = 1[17][72] = 11,772
 * 105 x 115 = 1[5+15][5x15] = 1[20][75] = 12,075
 * 132 x 103 = 1[32+3][32x3] = 1[35][96] = 13,596
 * 102 x 103 = 1[2+3][2x3]=1[05][06]=10,506
 * [product of first digits][(sum of last two digits) x first digit][product of last two digits]

Examples: If the addition or multiplication of the last 2 digits < 10, then add a 0 infront of the number, example if the addition is 4, it should be 04. Example shown below: For numbers just over 1000, 2000, etc., use the following:
 * 215 x 204 = [2x2][(15+4)x2][15x4] = [4][19x2][60] = [4][38][60] = 43,860
 * 201 x 202 = [2x2][(2+1)x2][2x1]=[4][06][02]= 4,0602
 * [product of first digits]0[(sum of last two digits) x first digit]0[product of last two digits]

Examples: For each order of magnitude (x10), add two zeroes to the middle.
 * 2008 x 2009 = [2x2]0[(8+9)x2]0[8x9] = [4]0[17x2]0[72] = [4]0[34]0[72] = 4,034072
 * 2008 x 2009 = 4,034,072

Just beneath 100
This trick words for every number beneath 100, but is faster in the 90s. For example, 96*98:

The answer will be a four-digit number,

[xx][xx].

For the last two digits, it is the product of the differences between 100 and the number for each multiplier. Take the first number 96. 100-96=4. Then take the second number 98. 100-98=2. 4x2=8. 8 is going to be our last two digits so 08.

[xx][08]

The first two digits is any number minus the difference between 100 and the other number. Let's take the first number 96 for example. The other multiplier is 98. 100-98=2. So take 2 away from 96. 96-2=94. You will get the same two digits if you pick any of the two numbers.

[94][08]. So the answer to the equation is 9408.

Division
Again there are many possible techniques, but you can make do with the following or research your own. All numbers are the products of primes (you can make them by multiplying together prime numbers). If you are dividing you can divide by all the prime products of the number you are dividing by to get the answer. This means that 100/24 = (((100/2)/2)/2)/3. Although this means you have a lot more stages to do they are all much simpler. 100/2 = 50, 50/2 = 25, 25/2 = 12.5, 12.5/3 = 45/30 = 41/6 = 4.166666666recurring Also, another helpful trick is, when you have to multiply and then divide by a number, always divide first, until you've reached numbers that are relatively prime, and then multiply. This keeps numbers from being too large. For example, if you must do (18 * 115)/15, it is much easier to divide 115 by 5 and 18 by 3, and then multiply them together to get 23 * 6 = 138.

Multiply by the Reciprocal
Division is equivalent to multiplying by the reciprocal. For instance, division by 5 is the same as multiplication by 0.2 (1/5=0.2). To multiply by 0.2, simply double the number and then divide by 10.

Division by 7
The number 1/7 is a special number, equal to $$0.\overline{142857}$$. Note that there are six digits that repeat, 142857. A beautiful thing happens when we consider integer multiples of this number:
 * $$\frac{1}{7} = 0.\overline{142857}$$
 * $$\frac{2}{7} = 0.\overline{285714}$$
 * $$\frac{3}{7} = 0.\overline{428571}$$
 * $$\frac{4}{7} = 0.\overline{571428}$$
 * $$\frac{5}{7} = 0.\overline{714285}$$
 * $$\frac{6}{7} = 0.\overline{857142}$$

Note that these six fractions of seven contain the same six digits repeating in the same order ad infinitum, but starting with a different number. But how is this useful when dividing by seven? Consider the problem 207/7. First, we can convert this to 200/7 + 7/7. We know that 7/7 equals one, so the answer will be 200/7 + 1. But what is 200/7? It is simply 2/7 times 100, and from the above, we know that $$\frac{2}{7} = 0.\overline{285714}$$, so by moving the decimal point, we know that $$\frac{200}{7} =28.\overline{571428}$$. All that remains is to add the one from 7/7, giving us $$\frac{207}{7} =29.\overline{571428}$$.

Division by 9
The fraction 1/9 and its integer multiples are fairly straightforward - they are simply equal to a decimal point followed by the one-digit of the numerator repeating to infinity:
 * $$\frac{1}{9} = 0.\overline{11}$$
 * $$\frac{2}{9} = 0.\overline{22}$$
 * $$\frac{3}{9} = 0.\overline{33}$$
 * $$\frac{4}{9} = 0.\overline{44}$$
 * $$\frac{5}{9} = 0.\overline{55}$$
 * $$\frac{6}{9} = 0.\overline{66}$$
 * $$\frac{7}{9} = 0.\overline{77}$$
 * $$\frac{8}{9} = 0.\overline{88}$$

To solve a problem such as 367/9, we reduce it to
 * $$\frac{367}{9} = \frac{300}{9} + \frac{60}{9} + \frac{7}{9}$$
 * $$\frac{367}{9} = 33.\overline{33} + 6.\overline{66} + 0.\overline{77}$$

First add $$33.\overline{33} + 6.\overline{66} = 40.0$$. Then add $$40.0 + 0.\overline{77} = 40.\overline{77}$$.

Division by 11
The fraction 1/11 and its integer multiples are fairly straightforward - they are simply equal to a decimal point followed by the product of nine and the integer multiple repeating to infinity:
 * $$\frac{1}{11} = 0.\overline{09}$$
 * $$\frac{2}{11} = 0.\overline{18}$$
 * $$\frac{3}{11} = 0.\overline{27}$$
 * $$\frac{4}{11} = 0.\overline{36}$$
 * $$\frac{5}{11} = 0.\overline{45}$$
 * $$\frac{6}{11} = 0.\overline{54}$$
 * $$\frac{7}{11} = 0.\overline{63}$$
 * $$\frac{8}{11} = 0.\overline{72}$$
 * $$\frac{9}{11} = 0.\overline{81}$$
 * $$\frac{10}{11} = 0.\overline{90}$$
 * $$\frac{36}{11} = 3.\overline{27}$$

Cube Roots for under 1,000,000
Before this goes any further, notice the last digit for the first nine cubes. 1, 8, 27, 64, 125, 216, 343, 512, 729

Notice how the last digit for each cube contains the numbers 1-9.

For each number, break it down into two groups. The last three digits and the remaining digits at the front. For the last three digits, find the cube root whose cube ends with the same number it ends with. That will be the last digit. For the front few digits, round it down to the previous cube and find the cube root of that. That will be the first digit.

Let's take "148877" for example. Divide it into 2 groups: 148, and 877. Start with 877. The number ends with a 7 and the number 3 is the only number in which a cube ends with "7". So the last digit must be 3.

Look at 148. Round it down to the previous cube, which is 125. The cube root of 125 is 5, which is the first digit. Put it together, and 53 is the answer.

This strategy will not work on cube roots that contain decimals, although it will give an approximate.

Estimation
The best way to make estimation quickly in mental math is to round to one or two significant digits (that is, round it to the nearest place of the highest order(s) of magnitude), and then proceed with typical operations. Thus, 1242 * 15645 is approximately equal to 1200 * 16000 = 19200000, which is reasonably close to the correct answer of 19431090. In certain cases, one can even round to simply the nearest power of ten (which is useful when making estimations with much error and large numbers).

Range Search
It is sometimes easier to make a calculation in the opposite direction from the one you want, and this can be used to quickly estimate the value you want. Square root is a good example. It is easier to square numbers than to take the square root. So you take any number that will square to a little larger than the one you want, take another that squares to less than the one you want and use an average of the two. The trick now is to apply a general technique ( the Bisection Method ). We create a new estimate using the average of our first two numbers. Square this. If it's value is higher than we want, we use it as the upper value of our range. If it is lower than we want, we use it as the lower value of our range. We now have a new range that must contain the square root we want. We can apply the same process again to get a more accurate value ( this is known as Iteration ). This technique is widely applied in computing, but it's also very handy for some mental mathematics.

Other mental maths
Perhaps one of the more useful tricks to mental math is memorization. It may seem an annoyance to memorize certain math facts. However, it can tremendously speed up your calculations when you don't have to do the division or multiplication in your head. Such useful math facts to memorize include: perfect squares and cubes (especially powers of two), prime factorizations of certain numbers, and the decimal equivalents of common fractions (such as 1/7 = .1428...). For example, trying to figure out 1024/32 is much easier knowing that it's essentially the same as 2^10/2^5. Many of these are memorized simply by frequent use. Thus, the best way to get good is to practice. It's a good idea to memorize 3 x 17 = 51. We can extend this to 6 x 17 = 102. If we round these numbers: 3 x 17 is approx. 50, 6 x 17 is approx. 100, 9 x 17 is approx. 150, and so on. These are very helpful in estimating since 3, 6, 9, 50, 100 are common numbers.

Advanced Mathematics
It is possible to make good estimates of quite complex formulae. Range search is a useful technique. Aside from that, there are many other mathematical rules that you can exploit too.

Binomial Expansion
The Binomial Theorem means we can relatively easily expand an equation like:
 * $$\sqrt{1 + x} = 1 + \textstyle \frac{1}{2}x - \frac{1}{8}x^2 + \frac{1}{16} x^3 - \frac{5}{128} x^4 + \dots\!$$

This is very useful if $$x$$ is less than 1. In that case, the powers of $$x$$ get smaller and smaller, and we can ignore them. Even for whole numbers and Integers, this is useful as we can split the problem into a larger number and smaller number added and then raised to a power. The smaller number's powers will become less important. We can then neglect terms of the expansion that involve the smaller numbers, and thereby get a reasonable estimate. For example:
 * $$(x+y)^4 \;=\; x^4 \,+\, 4 x^3y \,+\, 6 x^2 y^2 \,+\, 4 x y^3 \,+\, y^4.$$

If the $$y$$ value is much smaller than the $$x$$, we can make a good estimate, even if we don't add the $$y^4,$$ $$4 x y^3$$, or $$6 x^2 y^2$$ terms.

The Binomial Theorem again comes to our help. Here we usually want to work out the following for compound interest:
 * $$(1+x)^n$$
 * where the original principal sum is 1, $$x$$ is the rate of interest over a short period of time (e.g. if the monthly rate is 5%, then $$x = 0.05$$), and $$n$$ is the compounding frequency over a longer period of time (for example 12, if the interest rate is the monthly rate, and the overall period is a year).

Using the theory we can roughly estimate this as
 * $$1 + n x + \frac{n (n-1)}{2} x^2$$

Although this is only a simple approximation, it works quite well for a small x.

title: Mental Math


text:
Cookbook:Bean Pot

| Bakeware

A bean pot is a medium-sized earthenware vessel in which baked beans are customarily made. The ingredients are combined in the bean pot and left in a warm or moderate oven to bake for several hours, often four or more.

Modern bean pots come in a variety of colors and designs, but tradition holds that a bean pot should be two-tone brown, on cream.

Bean pots also vary widely in size, though two- and three-quart (2-3 L) pots are by far the most common. A one-quart (1 L) bean pot holds enough beans to feed two people sufficiently, while large families might find pots bigger than three quarts (3 L) to be excessive.

Although cooking baked beans in a bean pot is traditional, there is no reason that beans cannot be baked in any baking dish with a suitable cover. A Dutch oven is a well-suited replacement for a bean pot.

See also: Dutch oven

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Cookbook:Bean Pot


text:
User:ImageObserver

public interface ImageObserver

An asynchronous update interface for receiving notifications about Image information as the Image is constructed.

title: User:ImageObserver


text:
User:Panic2k4/Archive

Abuse of GPL/Software License ?
by: NECTY - Networks and Security Systems

Largo da Lagoa, 7C

2795 116 Linda-a-Velha

Portugal

Phone: +351 214 147 305

Fax: +351 211 454 205

E-mail: info [at] necty [dot] pt

Web: http://www.necty.pt

Domingos Bruges Chief Technology Officer : está na equipa da Caixa Mágica desde o princípio, sendo estudante de Engenharia de Telecomunicações e Informática no ISCTE. Desenvolveu o sistema de arranque do instalador(X/consola), scripts para gerar a imagem de instalação e toda a configuração do LILO e SYSLINUX.

GilDot articles: http://www.gildot.org/press/05/06/28/0822214.shtml /***/

Kiax: Kiax is a softphone (VoIP client program) with a simple and comfortable user interface for making VoIP calls to Asterisk PBX. It depends on the iaxclient library to use Asterisk's IAX2 protocol for easy and successful call configuration and audio suppor

 * Development Status: 4 - Beta
 * Intended Audience: End Users/Desktop
 * License: GNU General Public License (GPL)
 * Operating System: Linux
 * Programming Language: C, C++
 * Topic: Internet Phone
 * Translations: Brazilian Portuguese, Bulgarian, English, French, German, Macedonian, Polish
 * User Interface: Qt

SW instalation requirement: Qt3.2 or greater iaxclient library

Creator: Emil Stolyanov Project Admins: Emo emosto aka emosto [at] users [dot] sourceforge [dot] net growchie aka velislav (.rpm, .deb etc) aka velislav [at] users [dot] sourceforge [dot] net - Packager

other developers: Borislav Mitev aka bmitev [at] users [dot] sourceforge [dot] net - Tester

WWW: http://kiax.sourceforge.net/en_news.html | WWW: http://sourceforge.net/projects/kiax/

/***/

VoipBuster

WWW: http://www.voipbuster.com/en/index.html

News: http://www.voipbuster.com/en/newsflash.html FAQ: http://www.voipbuster.com/en/faq.html

/***/

Notes...

Qt Trolltech: Note that the Qt/Embedded Open Source Edition is not distributed under the QPL, but under the GNU General Public License (GPL).

For development non-free/proprietary software, the Qt Professional Edition is available. It has a normal commercial library license, with none of the special restrictions of the QPL or the GPL.

iaxclient library:

IAXClient is an Open Source library to implement the IAX protocol used by The Asterisk Software PBX

http://iaxclient.sourceforge.net/

Although asterisk supports other IP protocols (including SIP, and with patches, H.323), IAX's simple, lightweight nature gives it several advantages, particularly in that it can operate easily through NAT and packet firewalls, and it is easily extensible and simple to understand.

iaxComm: license = GPL

More info: http://david.dw-perspective.org.uk/VoipBuster-Linux-MacOS-Solaris-FreeBSD.html Other similar projects: http://sourceforge.net/projects/winkiax/

note1

MagicJack was too commercial
MagicJack seems too mercantile and not of an instructional nature, I must check it back in a few months. --Panic (talk) 20:05, 30 December 2008 (UTC)

Issues seem to have been solved, the product is still a commercial venture but the project now has fixed the praises and criticism section.

title: User:Panic2k4/Archive


text:
Cookbook talk:Pulses

Cooking Beans
I recently added a section talking about an alternative cooking method and reasons why it may be superior to the traditional soaking method. After writing it all, I realized that I don't have my sources handy and I felt uncomfortable about committing it, so I just commented it out and left it for another time.

My sources are several fold, though:

 * Mark Bitman, in How to Cook Everything, cites the overnight soak as unnecessary in terms of cooking time.
 * John Thorne, in Pot on the Fire, cites it as unnecessary in terms of
 * cooking time
 * flatulence (effect is negligible)
 * flavor (salting early doesn't toughen beans but makes them taste better)
 * Cooks Illustrated, in an article entitled Eliminating Gas from Beans, did some lab analysis and found that very few of the fart inducing compounds are removed by soaking and only 20-40% are removed by repeated water changes as they cook.

Also, my own experience shows that all of that work isn't really necessary. So, anyone have any objections to be adding this information? I can dig my sources out of storage if it matters. Crcarter 14:49, 28 October 2005 (UTC)

Removing 20% to 40% is pretty good I think. I wonder how long they cooked the beans though. I suggest 6 or more hours, and at least several water changes, in addition to the overnight soak. Your experience that "all of that work isn't really necessary" may reflect a simple lack of concern for farts or your luck in having low-gas gut bacteria. AlbertCahalan 04:19, 29 October 2005 (UTC)

Well, I wouldn't say that 20-40% is pretty good so much as it's something, especially as if you're talking about hours of extra work. (I now must dig my sources out of storage to satisfy my curiosity.) Is there policy on presenting different methods of preparing certain foods? I would think it best to present the simplest and most straightforward method of preparation. Other methods (eg, `Fart Reducing') could be presented as variations, especially since such methods may be prone to diminishing the flavor, texture or character of the food being prepared.

Fart apathy and above average gut-fauna diversity doesn't change the fact that I think the "common knowledge" that beans must be soaked (and require extensive cooking times) is unfounded. Simple experience shows otherwise. Clayton Carter 00:43, 30 October 2005 (UTC)

Well actually that brings to mind other benefits of long cooking times: you can get rid of the awful beany taste and make the beans easy to mash. Mashing the beans to make refried beans for a burrito is way easier after 6 hours of cooking. This isn't much work for the human. The human just needs to plan ahead. The stove does almost all the work. It's not a problem to have multiple cooking methods on this page as long as they all focus on the beans and don't turn into real recipes. If you start needing ingredient lists, make seperate pages. AlbertCahalan 18:33, 30 October 2005 (UTC)

Right. So, I'll -- at some point soon -- make a change to indicate these cooking techniques:
 * 1) Conventional: overnight soaking and simmering.
 * 2) Skip the soak, just simmer. (Mine, I guess.)
 * 3) Fart reduction: soak and extended simmer w/ water changes.

On our personal debate, though, I happen to like that "awful beany taste". Why would you eat beans if you don't like the way they taste? I guess it's a matter of kitchen philosophy, but I generally try to prepare foods so as to preserve as much of their inherent character as possible. Of course long cooking will make beans easier to mash, but this is a discussion of cooking beans in general, though, and not specifically about mashing them. And your point about the work involved is just a matter of semantics. Obviously the human isn't doing the work to generate the energy to cook the beans for six hours, but it still seems like an awful lot to invest if you just want to soften up some beans. Clayton Carter 20:21, 31 October 2005 (UTC)

Beans are cheap and nutritious, and they have the right texture for a burrito. Do you know a substitute? Perhaps butter with rice flour and powdered milk? That wouldn't be cheap though. Mushroom paste? Again, not cheap or even available. AlbertCahalan 01:24, 7 November 2005 (UTC)

Farts, Flatulence, Gastric Distress and Wording
I think that "flatulence" sounds better, esp. in the section heading. The next sentence has an unambiguous reference to "farting". I don't think that flatulence is any less clear than farting, and it sounds a bit less silly. Clayton Carter 20:21, 31 October 2005 (UTC)

Nothing sounds more silly than using a big long aristocratic word when a simple and common one will do. Come on, do people say "oops, sorry I flatulated"? Nobody I've ever known would use this word. Likewise, we don't use cranium all that much. AlbertCahalan 00:53, 7 November 2005 (UTC)

title: Cookbook talk:Pulses


text:
CAT-Tools/DéjàVu X/get File Navigator or AutoSearch - Portions windows back

Close DVX, download and execute the following file: http://www.atril.com/dvx/MenuLayoutDelete.reg


text:
Wikijunior:Ancient Civilizations/Greeks

What area did they live in?
Ancient Greeks lived on the Balkan Peninsula (approximately at the territory of modern Greece) and on the western part of Turkey. They governed themselves from their cities, each of which had a separate government which governed over the countryside surrounding them. There were quite a few of these city states, but their two greatest cities were Athens, in the north, and Sparta in the south. The Greeks lived under their own rule until first being absorbed by the Macedonians, who lived to their north, and then finally the Roman Empire. Greece has many mountains and poor soil, which prevents many crops from being grown there. The country has a mild climate, which makes it convenient to farm goats and sheep. Also, Greece is a sea country: there are many beaches and islands, and no part of the country is far away from the sea. That made many of the Greeks sailors, and that meant that they sailed near and far, trading with different people, learning about other cultures, and bringing their own culture to faraway lands. These types of exchanges inspired development of Greek science and art.

What did their structures look like?

Greek buildings were usually rectangular-shaped, surrounded by colonnades – rows of columns. Greece is rich in limestone, which was the most popular material of the time. Marble was more expensive, and was mostly used for statues and decoration.

Greek theaters looked very much like modern ones, except that most were open to the weather. There were semi-circled rows of seats, each row was higher than the row in front of it, so that people in the back could see better. Centered in front of the audience was a circular orchestra, where performances took place. A low building called a skene sat behind the orchestra. It was used to conceal actors, and gave room for costume changes, props and other "backstage" activity.

What did they wear?
Greek men wore chitons – pieces of cloth pinned on one shoulder. Women wore peplos – long tube-shaped cloth, which was pinned on both shoulders and gathered around the waist. When it was cold, both men and women wore a cloak, called clamys. Greeks wore sandals, which looked a lot like the sandals that we wear today.

What did their writing look like?

Greek writing looked a lot like Modern Greek text, written with capital letters. The Greek alphabet appeared in 8th century BC and was influenced by the Phoenician alphabet, the first alphabet that used signs for letters, not for words or syllables. Unlike the Phoenician alphabet, which did not have characters for vowels, the Greek alphabet had characters for all the sounds used in the language. In that sense it was the first modern alphabet, and the oldest to be used to this day. The Greek alphabet became a base for two other alphabets: Latin (that is used in English) and Cyrillic currently used in Slavic-speaking countries.

What did they believe?

Greeks were polytheistic, which means that they believed in many gods and goddesses. Each god or goddess was “responsible” for some side of life or natural phenomenon.

Twelve of the most important gods resided on mount Olympus. Their leader was Zeus, the god of the sky. Other Olympic gods were: his wife Hera - the goddess of marriage and motherhood, Poseidon – god of the sea, Aphrodite - the goddess of love, Apollo – the god of art and leader of muses - and Athena, the goddess of wisdom and war, and the favorite daughter of Zeus.

Greeks believed in many mystical creatures other than gods: titans – children of Gaia, goddess of Earth, challenging Olympic gods; nymphs – nature spirits; muses – goddesses and patrons of art; centaurs – half humans, half horses; Cyclops – one eyed monsters; giants.

In Greek myths, the Gods often had affairs with real people, and that’s how heroes, like Hercules – man of superhuman strength, who committed twelve labours, and Achilles – the hero of Trojan war, were born.

Are some of them famous even today?
We know many Greek politicians, scientists, and artists. Possibly the most known person of this culture is Homer, the legendary blind poet, who composed two masterpieces of Greek literature: the poems Iliad and Odyssey. Sophocles and Aristophanes are still popular playwrights and their plays are considered to be among the greatest works of world literature. Another famous Greek is a mathematician Pythagoras, mostly known for his famous theorem about relations of the sides of right triangles. Archimedes made many amazing inventions and discoveries. The legend says that he discovered Archimedes Principle while taking a bath, and got so excited, that he ran out naked into the street crying “Eureka!” – “I have found it!” The philosopher Socrates taught to question everything, separating beliefs from proven facts. He even questioned the existence of gods, which got him in trouble: he was accused of corrupting the youth and was sentenced to death by taking poison. Other great philosophers include Aristotle (the teacher of Alexander the Great) and Plato. Alexander the Great is known for his conquest of the Middle East and Central Asia.

What is left of them today?
The whole modern country of Greece! They still speak the same language, though it has changed some, use the same alphabet and preserve their heritage.

But Greek heritage is not limited to Greece only. It influenced Western culture greatly. That's why we call it the Cradle of Western Civilization. We use many Greek words in our everyday life, like democracy, philosophy, photography. In fact, the word alphabet comes from alpha and beta, the first two letters of the Greek alphabet. In mathematics, one of the greatest discoveries they made was about right-angled triangles which is still important in map making. Greek philosophers strongly influenced ideas in the West for many years and their ideas are still important in politics, religion, government, discussion and argument, and in how people should behave toward one another and in society as a whole. Greek architecture and art strongly influenced Western architecture and art. (What does Lincoln Memorial remind you of?) The foundation of our science came from Ancient Greece. The Greek style of sculpture is still used all over the world today for statues of famous people. The Greeks also invented the theater and many of their plays are still acted all over the world today. Many of their stories and poems are also read widely today. The Greeks were the ones who started the Olympic Games, back in 776 BC, in honor of the god Zeus at the town of Olympia. Soon their fun side became more important and they were not just religious festivals anymore. Games were held every four years until AD 394 and were later restarted in 1896. The first of the new Olympics was held in Greece in honor of their original home and they have grown to become popular worldwide.

Wikijunior Alte Zivilisationen/ Griechen fr:Wikijunior:Les civilisations anciennes/La Grèce antique

title: Wikijunior:Ancient Civilizations/Greeks


text: User talk:62.15.155.63

title: User talk:62.15.155.63


text:
User talk:Dannya222

Zdravo, Danja. Vidim da si ti započela modul za učenje srpskog. Možda si primijetila da sam ga ja ponovo počeo na sasvim drugačiji način. Ipak, ono što si ti radila bilo bi veoma pogodno za modul Serbian Grammar koji još nije ni započet. Pošto ti imaš znanja i dara za to, molim te ako možeš da doprineseš modulu Serbian Grammar. Samo, molim te ako možeš da pišeš ćirilicom. Ako ne možeš da koristiš ćirilicu, samo mi javi kad napišeš nešto latinicom, pa ću ja to prepraviti. OK? --Ђорђе Д. Божовић 17:55, 28 October 2005 (UTC)

authors: Ђорђе Д. Божовић~enwikibooks

title: User talk:Dannya222


text:
Muggles' Guide to Harry Potter/Characters/Nearly Headless Nick

Overview
Sir Nicholas de Mimsy-Porpington, better known as Nearly Headless Nick, is the resident ghost of Gryffindor House at Hogwarts School of Witchcraft and Wizardry. He was almost decapitated on October 31, 1492 but the axe was too dull and, despite hitting his neck forty-five times, did not entirely decapitate him, hence his nickname.

Philosopher's Stone
Harry and Ron first meet Nearly Headless Nick at the Arrival Feast. Ron recognizes him, and names him, from a description he got from his brothers Fred and George. Asked why "Nearly Headless", Nick demonstrates that his head is held on only by a thin remnant. Nick also says that he has not eaten for nearly four hundred years.

Chamber of Secrets
Returning to the castle sodden and muddy after a Quidditch practice, Harry meets a dismayed-looking Nearly Headless Nick, who has received a rejection letter from the Headless Hunt. ("Half an inch of skin and sinew!") After hearing Harry's worries about the upcoming Quidditch match against Slytherin, Nick sees Mrs. Norris, and warns Harry that Filch is on the warpath. Harry tries to avoid him but is caught and taken to Filch's office, where Filch starts filling out a detention form for the "crime" of "Befouling the castle". A crash from overhead distracts him, and sends him out of the office. On his return, Filch sees that Harry has become aware of some correspondence on his desk, and dismisses him hurriedly.

Outside Filch's office, Harry once again finds Nearly Headless Nick, who says that he has convinced Peeves to drop a heavy cabinet in the room over Filch's office to distract him, and is pleased that it worked. He then invites Harry, Ron, and Hermione to his Deathday Party, celebrating his death on 31 October 1492.

The Trio attend Nick's party, and find that it is a rather gloomy affair, with Peeves at one point chasing Moaning Myrtle away in tears. To put a quite unsatisfactory cap on the evening, as Nearly Headless Nick starts to make his speech thanking everyone for coming, the Headless Hunt bursts in through the walls and starts a wild game. Harry, Ron, and Hermione make their escape quietly in the hullabaloo.

As they leave, Harry hears a voice. Following the voice, and with Ron and Hermione following him, he finds Mrs. Norris, Petrified and hanging from a torch bracket. Called upon to explain what they had been doing just before finding Mrs. Norris, the Trio explain that they had been attending Nick's Deathday party.

Shortly before Christmas, Harry finds Justin Finch-Fletchley Petrified, and Nearly Headless Nick, black and smoky instead of his usual white color, and apparently also unconscious. Nearly Headless Nick is wafted up to the Infirmary by Ernie Macmillan with a large fan, at Professor McGonagall's orders.

With help from Hermione, despite her being Petrified, Harry and Ron discover that the monster in the Chamber of Secrets is a Basilisk. While this creature can kill with a glance, nobody has died yet because nobody has looked at it directly. In particular, Justin Finch-Fletchley had looked at it through Nearly Headless Nick; and Nick had not been killed by it because he was already dead.

Although we don't see him at the Ending Feast, we are led to believe that Nick is revived at the same time as the Petrified students.

Prisoner of Azkaban
While Nearly Headless Nick has no direct role in this book, he is mentioned in passing.

Goblet of Fire
At the Arrival Feast, Nick informs Harry, Ron, and Hermione that there almost was not a feast this year. Peeves, upset at not being invited to the Feast, had gotten into the kitchen and had been wreaking havoc amongst the House Elves making it. Hermione is astounded to learn that there are over a hundred House-Elves in Hogwarts, attending to the needs of the students. Saying that she will not benefit from slave labour, she pushes aside her plate and refuses to eat any more.

Order of the Phoenix
Nearly Headless Nick is already sitting at the Gryffindor table when the Trio and Neville arrive, and they sit near him. When the Sorting Hat sings its song, Ron asks if the Hat has ever given a warning before, Nick says certainly, but before he can complete his explanation he is interrupted by the start of the Sorting. Once the Sorting is complete, and food appears, Hermione asks him to continue his explanation. Nick says that whenever the Hat feels that the school is in danger, it warns that the school Houses must stand together in the face of the danger. Ron, despite the almost indecent glee with which he is stuffing his mouth, manages to ask how the Hat knows the school is in danger if it is a hat, and Nick points out that it does stay in the Headmasters' office, and likely hears what is passing there. At Harry's disbelief that he could ever join forces with Slytherin, Nick reproaches him, saying that the ghosts of the separate houses cooperate, that he would not, for instance, argue with the Bloody Baron. At Ron's suggestion that Nick is scared of the Baron, Nick is highly affronted and leaves, settling further down the table beside Colin and Dennis Creevey.

As Harry heads to the Owlery to send a message to Sirius on the Saturday following his first week of school, he encounters Nearly Headless Nick, who warns him that Peeves is preparing a surprise for the next person who walks under the bust of Paracelsus. Harry confirms that this surprise involves the bust of Paracelsus falling on that person's head, then finds another way to the Owlery. Nick, meanwhile, heads off to look for the Bloody Baron, to see if he can put a stop to it.

After the death of Sirius, Harry chooses to pack his trunk rather than attend the Leaving Feast. Restless, he leaves the dormitory to walk the halls. He sees Nearly Headless Nick passing through a wall ahead of him, and calls him over, saying he wants a word. Nick is reluctant, but says he rather expected this. They go into a vacant classroom, and Harry asks Nick if there is any chance that Sirius could have become a ghost. Nick says that there is no chance. A certain amount of preparation is required, as well as unfinished business and a fear of death, and Sirius does not have any of that in sufficient quantity to make him want to stick around.

Half-Blood Prince
When Harry returns to Gryffindor Tower following his retrieving the memory from Professor Slughorn, he is denied entrance to the Common Room by the Fat Lady. While he is trying to decide what to do, Nearly Headless Nick wanders past. Harry tells him that Professor Dumbledore had set him this task, and now he has to wait until Dumbledore is back. Nick remarks that the Bloody Baron had said that Dumbledore had returned, but that he seemed tired. Nick suggests that Dumbledore is likely in his office.

Deathly Hallows
Harry has become convinced that the last Horcrux that he must find and destroy is actually the lost Diadem of Rowena Ravenclaw. Professor McGonagall tells him that it has not been seen in living memory. It occurs to Harry that "living memory" only applies to the living and that the castle ghosts have been around far longer than that. Nearly Headless Nick is eager to help in any way that a ghost can, and is somewhat upset that Harry does not want his help, but rather the help of the Ravenclaw house ghost. Despite being upset, however, he does point the Grey Lady out to Harry.

Strengths
Being a ghost, he is already dead, and so he cannot die; even the Monster in the Chamber, who we find out later is a Basilisk, cannot kill him.

Weaknesses
Being a ghost, he has limited ability to interact with the regular world. He is, however, affected by some artifacts of the material world; as mentioned, he cannot be killed by the Basilisk, but he is injured by it, being more or less Petrified by its gaze, and he is then transferred to the Hospital Wing by means of a large fan, indicating that he is affected by air currents. One wonders if this sensitivity to air currents (e.g. wind) is the reason so few ghosts are found outdoors.

Like Moaning Myrtle, Nick does not like being reminded that he is dead. While Myrtle's reaction is to burst into tears and run away, Nick instead tends to become affronted before ostentatiously distancing himself from the offender.

Relationships with Other Characters
Nick as the Gryffindor house ghost, socializes with all Gryffindors. He seems to be particularly fond of Harry, though he is quite pleased to speak with either Ron or Hermione. He is somewhat easily offended by Ron's repeatedly mentioning that he is dead, and on at least one occasion moves away from Ron after such an event.

Nick has been trying for centuries to join one particular ghostly group, the Headless Hunt, but is hindered by his not being actually headless.

Analysis
In many ways, Nearly Headless Nick would seem to be almost a stereotypical 15th Century noble, believing in the birthrights of nobility and becoming affronted when his dignity is impugned. Against this, of course, we have to weigh the fact that we don't really know how 15th Century nobility actually acted. Would they have even deigned to speak with "commoners" like the students at Hogwarts? The average reader doesn't know, but may believe that the nobility of the day felt themselves innately immeasurably superior to those born without titles. The author has to make a choice between historical realism, and story, and we note that in this case, as in most, she has chosen the characterization that makes for the best story. A more realistic Sir Nicholas would likely have jarred fiercely against the expectations of the modern reader; but his portrayal in this series is sufficiently different from that of the students that it evokes the flavour of the age without jarring. Readers who don't believe that Sir Nicholas is portrayed accurately for his era may remind themselves that he has had five hundred years observing how styles have changed in Hogwarts, and presumably has been able to adapt himself to those styles somewhat, in order to avoid being effectively ostracized by the House which he inhabits.

The prime reason for Nearly Headless Nick's introduction would seem to be intimation that death is not final. Nick is the first ghost we meet in the series, and so is the first suggestion that in this series, some form of life after death is proven fact. We will learn from Professor Snape that a ghost "is the imprint of a departed soul left upon the earth," while Nick will say that "Wizards can leave their imprint on the earth, to walk palely where their living selves once trod." We note the implication that the soul itself has departed, but the imprint of that soul remains, and suggest that a similar mechanism may animate portraits and photographs in the Wizarding world. However, existence of the soul being a proven fact in the Wizarding world is undoubtedly meant as comfort for Harry, following the death of his parents, and presumably provides that comfort in at least some measure. Nick, in the first four books, is a concrete manifestation of existence of the soul, and so shows Harry, and the reader, that belief before we are told of it.

In Harry Potter and the Order of the Phoenix, as mentioned, we learn that Nick is not an actual soul, but instead is the imprint of a soul who has passed on. The author, in an interview, has stated that the books became more concerned with death after the death of her mother. It may well be that, in coming to terms with her mother's passing, the author decided that leaving one's entire soul shackled to one place, even if it was as large a place as the Earth, would be a fate worse than death, and so altered her description of ghosts, as enunciated first by Nearly Headless Nick, to indicate that the actual soul of the wizard had departed.

Two things about Nearly Headless Nick have given readers pause.

In the first book, he tells Harry that he has not eaten in almost four hundred years; in the second book, he invites Harry to his five hundredth deathday celebration. As there is not a hundred-year gap in Harry's life at this point, we must assume that either Nick has miscounted, or that the author has made a small mistake. As it turns out, the author, in later editions, corrected the number in the first book to bring them both into line, changing "almost four hundred years" to "almost five hundred years." As the date of Sir Nicholas de Mimsy-Porpington's death is given as 31 October 1492, this also pins the second book to the span July 1992 to June 1993.

In the second book, Nearly Headless Nick is attacked by the monster from the Chamber and is left "no longer pearly-white and transparent, but black and smoky, floating immobile and horizontal, six inches off the floor." We will later find that a restorative draught based on mandrake root will revive all of those not fatally attacked by the Monster, but that does leave the question open: how does one administer a restorative draught to a ghost? This question is never fully answered, except perhaps by considering the dual meaning of the word "draught." Given that possible pun, we can't help wondering if the author selected that term deliberately.

There is also, necessarily, some question of detail about Nick's death. We have to assume that the shape a ghost takes is the shape the body was in at the instant of actual death. At the risk of being gruesome, we note some reports from the time of the French Revolution that severed heads seemed to continue to react, albeit briefly, in a lifelike manner. So the Headless Hunt is made up entirely of members who were beheaded, and then died after their heads were severed. A headsman's axe is heavy, and even a club, applied with normal headsman's force to the neck, will shatter the spinal column and bring about death in short order; it's safe to assume that Nick will have died within a very few seconds after the first axe stroke. So if it did, in fact, take 45 strokes of the axe to behead him, all but the first few (possibly five) would have been posthumous. And it would be one of those first few than nearly severed his head.


text:
User:Sbenza

Wikiaccounts:
 * Wikibooks.org: Sbenza
 * Wikipedia.org: Sbenza

TODO

 * 1) Finish with User:Sbenza
 * 2) Remove previous item from the list =P

title: User:Sbenza


text:
Wikijunior:Ancient Civilizations/Hebrews

Who are Hebrews?
Hebrews were ancestors of Samaritans and Jews. They claim to be the descendants of the biblical Patriarch Abraham. They are known for their input into world culture, because their beliefs have influenced three major religions of the world. They are also known for their cultural and spiritual laws, rules, and morals. The Hebrews have influenced society today to a high degree.

What country did they live in?
Hebrews were nomadic people. They lived in the ancient Middle East. Around 1400 BC they settled in Canaan, the country on the eastern coast of Mediterranean sea, the territory of modern Israel, Jordan, Lebanon and Syria. Later this country was known as the kingdom of Israel and, after the death of King Solomon, was divided into Israel and Judea.

What did their buildings look like?
In the warm climate of the Middle East, the house was not so important. Most of the life of the Hebrew family happened in the open air. Women did the cooking in the yard; stores were just open counters looking into the street. Stone was used for building houses. There were no large forests in the land of Canaan, so wood was extremely expensive.

When Hebrews were nomadic people, they lived in tents. But even when they settled, tents were very popular. Tents are often mentioned in the Torah, and even at the time of David and Solomon, living in a tent was common, especially for poor people.

Another option was living in a cave. The natural cave was enlarged and a wall was built in front, converting the cave into a sheltered home.

Wealthier people lived in the houses built of sun-dried mud bricks. The roofs of the houses were flat so that people could stay outside in the cool evenings and sleep in summer. Domestic animals were kept on the first floor, together with people. There were no chimneys; smoke from cooking or heating fires escaped through the windows. The furniture was very simple. It included a few mats, spread upon the floor at night for sleeping, and rolled up during the day, or a kind of divan set against the wall; there were a table and chairs; a large jug for grain stood in the corner, and others for water, wine, oil, etc.; a niche in the wall held the lamp.

But what made Hebrews really proud was the Jerusalem Temple. There were two temples built: the First Temple was built by King Solomon. Cedarwood for the construction was brought from Lebanon, and the walls and floor of the temple were covered with gold. The Ark of the Covenant was kept in the Holy of Holies, a room at the end of the temple. The first Temple was destroyed in 586 BC when the Jews were exiled into the Babylonian Captivity.

After Jews returned from Captivity in 536 BC, they started building the Second Temple. This temple stood till AD 70 when it was destroyed by the Romans. Another Temple was built and also destroyed. The only part that was left is from Herod's Temple and is the Outer Western Wall, a sacred site for Jewish people. The Western Temple Mount wall is sometimes called the Wailing Wall and was believed to be from the second Temple and is often prayed near to, by the Jews today. This is also a "Talmudic" tradition

What did they eat?
Hebrew food was similar to the food of other Mediterranean people: they ate homemade bread that the lady of the house would bake in the big clay ovens in the yard, lentils, goat cheese, olives, and fresh fruits. Meat and fish were available. The most popular drink was wine.

But there was one difference about the food Hebrews ate: it had to be Kosher. Kosher applied to all different types of food. It applied to meat which had to come from correctly slaughtered animals. These animals had to have split hooves and had to chew their cud. The fish they ate had to have fins and scales. The wine had to be made and supervised by a Hebrew at all times because other cultures would put blood in it to help it ferment and eating or drinking blood is not Kosher. Some of the stricter Hebrews thought that meat should not be mixed with dairy, and that a person had to wait a few hours between having meat and dairy. This is a "Talmudic" tradition.

What did they wear?
Both men and women wore a tunic with a girdle, a robe on top of it, and a mantle (a sleeveless over garment) and a headdress. Men's and women's clothes were different in style and pattern. Women’s garments were longer, with long sleeves.

Hebrew laws also had instructions about their clothing. They were supposed to wear tassels on the corners of their clothing, a commandment from the Bible. Their clothes were never a mix of wool and flax except for the high priest who was permitted to wear such a mixture. The priests also had special instructions about the clothing that they wore while they worked.

What did their writing look like?
From very ancient times, the Hebrews began to write down their history, laws, and beliefs. The first five books or the Torah. The "Torah" was written in Hebrew. The books were written on large pieces of parchment and rolled into scrolls. These books were Genesis, Exodus, Leviticus, Numbers and Deuteronomy.

Hebrew was and is written right-to-left, with consonants and vowel points. The Hebrew script evolved over the course of their history so ancient Hebrew writing does not look the same as it does today. Here is an example of what ancient Hebrew writing looked like:

What did they believe?
Hebrews were among the first people in the world whose religion was monotheistic. Monotheism is the belief that there is only one God. All of their neighbors were polytheistic: they believed in many gods and goddesses that looked and behaved like humans. The idea that there is a single God who cannot be seen and is present everywhere and knows everybody’s thoughts was very unusual at that time. YHWH, יהוה or Yahweh, pronounced Yah-way and translates to "I Am", is the original Hebrew name of the Heavenly Father and the Jews believe saying his name is a forbidden. They use Adoni, pronounced Add-doe-nigh instead. He is also called El or Elohim in the Hebrew bible.

According to the Torah, the first person to start spreading the concept of one God was the patriarch Abraham. Monotheistic beliefs are currently found in many religions all over the world.

The Hebrews believed that they were God's chosen people and that the Torah contained God's laws which must be followed.

Are some of them famous even today?
Many biblical heroes are known today. The Bible became the most published book in the world, and, since so much of it was written about Hebrews, many Hebrew historical figures became famous. Many books, paintings and even movies are dedicated to them.

 * Abraham, Isaac, and Jacob are the three patriarchs.

 * Joseph - Jacob's second youngest son born to him in his old age. According to the Torah he was sold into slavery and ended up in Egypt, where he worked for Pharaoh. His most famous job was interpreting Pharaoh's dreams, which led to him saving Egypt having a famine while the rest of the world was having one.
 * Moses - Considered by many people to be one of the greatest leaders of Jewish people, and according to the Torah he is called the most humble man that ever lived. The most notable according to the Torah he took the Hebrews out of slavery from Egypt, God through him brought 10 plagues to Egypt, split the Red Sea, received the Torah along with the Ten Commandments and the oral Jewish law, set up the Jewish courts, took them to the land of Canaan - the land God promised to them through Abraham.

 * King David - One of three kings of ancient Israel and ruler of the largest territorial extent of ancient Israel. He was a significant military leader and lead the ancient Israelite armies in many successful battles.  He wrote most of the songs in the Book of Psalms.
 * King Solomon - During his reign the kingdom of Israel reached its greatest prosperity, being one of the biggest powers in trade. He was known for his wisdom and justice. He also wrote songs in the Book of Psalms.

 * Queen Esther -Or Hadassah, queen of Persia, according to the Esther she saved Jewish people from evil plans of Minister Haman to kill all Jews throughout the Persian Empire. This event is celebrated during the Jewish holiday of Purim.

 * Jesus of Nazareth - Jesus is one of the most famous Hebrew of all. He was born in Bethlehem to Hebrew parents. He grew up in Nazareth, which is a part of Israel. He also became spiritual leader and many of his early followers were also Hebrew and are still famous today, such as the apostles Paul, Peter and John. Jesus of Nazareth is commonly known as Jesus Christ which is the name his followers chose after his death. Christos in Ancient Greek means anointed one.

What is left of them today?
Kingdom of Israel was destroyed by Assyrians in 722 BC. Judea lost its independence to Rome in the first century AD. Jews had to leave their country. For two thousand years they lived all over the world, preserving their religion, language and traditions. They survived through centuries of discrimination and prejudice and through the extermination of one third of the Jewish population of the world in the Second World War. In 1948 the state of Israel was established again.

Wikijunior Alte Zivilisationen/ Hebräer


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Set Theory/Review

Need help creating math symbols?

= Definitions =

Subset
$$A \subseteq B$$ Subset means for all x, if x is in A then x is also in B.
 * $$\{x \mid x\in A \hbox{ then } x\in B \}$$

Proper Subset
$$A \subset B$$
 * $$\{x \mid x \in A \hbox{ then } x \in B \hbox{ and } A \ne B\}$$

Union
$$\bigcup A$$
 * $$\{x \mid x \in \bigcup A \hbox{ iff } y \in A \hbox{ s.t. } x \in y \}$$

$$A \cup B$$
 * $$\{x \mid x \in A \hbox{ or } x \in B \} $$

Intersection
$$\bigcap A$$
 * $$\{x \mid \hbox{for all } a \in A, x \in a\} $$

$$A \cap B$$
 * $$\{x \mid x \in A \hbox{ and } x \in B\} $$

Empty Set
$$\empty$$
 * $$\hbox{There is a set } A \hbox{ s.t. } \{x \mid x \notin A\} $$

Minus
$$A - B$$
 * $$\{x \mid x \in A \hbox{ and } x \notin B \} $$

Powerset
$$\mathcal{P}(A)$$
 * $$\{x \mid x \subseteq A \} $$

Ordered Pair
$$\langle a, b \rangle$$
 * $$\{ \{a\}, \{a, b\}\} $$

Cartesian Product
$$A \times B$$ or
 * $$A \times B = \{ x \mid x = \langle a, b \rangle \hbox{ for some } a \in A \hbox{ and some } b \in B \} $$
 * $$ \{ \langle a, b \rangle \mid a \in A \hbox{ and } b \in B \} $$

Relation
A set of ordered pairs

Domain
$$\{x \mid \hbox{ for some } y, \langle x, y \rangle \in R\}$$

Range
$$\{y \mid \hbox{ for some } x, \langle x, y \rangle \in R\} $$

Field
$$\hbox{dom(} R\hbox{)} \cup \hbox{ran(}R\hbox{)} $$

Equivalence Relations

 * Reflexive: A binary relation R on A is reflexive iff for all a in A,  in R
 * Symmetric: A rel R is symmetric iff for all a, b if  in R then  R
 * Transitive: A relation R is transitive iff for all a, b, and c if  in R and  in R then  in R

Partial Ordering

 * Transitive and,
 * Irreflexive: for all a,  not in R

Trichotomy
Exactly one of the following holds
 * x < y
 * x = y
 * y < x

= Proof Strategies =

If, then
Prove if x then y
 * Suppose x
 * so, y
 * so, y
 * so, y

If and only If
Prove x iff y
 * suppose x
 * so, y
 * suppose y
 * so, x
 * suppose y
 * so, x
 * so, x
 * so, x
 * so, x

Equality
Prove x = y
 * show x subset y
 * and
 * show y subset x

Non-Equality
Prove x != y
 * x = {has p}
 * y = {has p}
 * a in x, but a not in y

title: Set Theory/Review


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User:GraemeMcRae

Hi, my name is Graeme McRae. I have always been a stickler for proper word usage and grammar, and this makes me annoyed at articles with clumsy wording or dumb mistakes of any kind. With Wikipedia, I can channel that frustration into positive action to polish the "surface" of the articles at the same time I learn from the underlying content. (My contributions) (My Edit Count Stats)

I have a personal webpage that I use kind of as a blog, for ranting about (or appreciating) various things, and a math page that I use for describing some very cool things about math, in a way that might help people understand them.

If you would like to leave me a message, edit my User Talk page, and put your comment at the bottom. I'm looking forward to hearing from you!

 Or, visit my User page on any one of these Wikimedia Sister Projects:

title: User:GraemeMcRae


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User talk:GraemeMcRae/TOCright

TOCright: template for putting the table of contents on the right margin

Created by: User:GraemeMcRae

title: User talk:GraemeMcRae/TOCright


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User talk:GraemeMcRae

Allow Myself to Introduce, my, umm
Hi, my name is Graeme McRae, and this is my User talk page. If you want to get my attention, [ please click here] to leave me a new message. Then watch the page; I'll reply right here. Thanks! —GraemeMcRaetalk 22:35, 28 October 2005 (UTC)

title: User talk:GraemeMcRae


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Formal Logic/Sentential Logic/Constructing a Complex Derivation

= Constructing a Complex Derivation =

An example derivation
Subderivations can be nested. For an example, we provide a derivation for the argument

 * $$\mathrm{P} \land \mathrm{R} \rightarrow \mathrm{T},\ \ \mathrm{S} \land \lnot \mathrm{T},\ \ \mathrm{S} \rightarrow \lnot \mathrm{Q}\,\!$$ ∴  $$\mathrm{P} \lor \mathrm{Q} \rightarrow \lnot \mathrm{R}\,\!$$

We begin with the premises and then assume the antecedent of the conclusion.

Note. Each time we begin a new subderivation and enter a temporary assumption, there is a specific formula we are hoping to derive when it comes time to end the derivation and discharge the assumption. To make things easier to follow, we will add this formula to the annotation of the assumption. That formula will not officially be part of the annotation and does not affect the correctness of the derivation. Instead, it will serve as an informal reminder to ourselves noting where we are going.

This starts a subderivation to derive the argument's conclusion. Now we will try a Disjunction Elimination (DE) to derive its consequent:

 * $$\lnot \mathrm{R}\,\!$$

This will require the showing two conditionals we need for the antecedent lines of a DE, namely:

 * $$\mathrm{P} \rightarrow \lnot \mathrm{R}\,\!$$

and

 * $$\mathrm{Q} \rightarrow \lnot \mathrm{R}\,\!$$

We begin with the first of these conditionals.

This subderivation is easily finished.

Now we are ready to discharge the two assumptions at Lines 5 and 6.

Now it's time for the second conditional needed for our DE planned back at Line 4. We begin.

Note that we have a contradiction between Lines 12 and 15. But line 12 is in the wrong place. We need it in the same subderivation as Line 15. A silly trick at Lines 16 and 17 below will accomplish that. Then the assumptions at Lines 12 and 13 can be discharged.

Finally, with Lines 4, 11, and 19, we can perform the DE we've been wanting since Line 4.

Now to finish the derivation by discharging the assumption at Line 4.

The complete derivation
Here is the completed derivation.


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User:Mahanga

Hi there.

My Watchlist on Wikipedia

User:Gflores/Sandbox

All Wikibooks

Stuff I want to work on:

 * 1) Data structures
 * 2) Firefox
 * 3) Valgrind
 * 4) How to Make Windows Look Like a Mac
 * 5) Freeware and Shareware
 * 6) Vi
 * 7) Bash
 * 8) C++
 * 9) Using Ubuntu
 * 10) C#
 * 11) Installing Linux (dual-boot)
 * 12) Advanced Data Structures and Algorithms
 * 13) Algorithms
 * 14) Categorizing images
 * 15) Mizpelings!

title: User:Mahanga


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Principles of Sociology

''Sociology systematically studies how groups of people are affected differently by human behavior patterns. A deeper understanding of how people make sense of their lives and act to create, maintain, and change the world around them accordingly can aid us in improving our own lives and the lives of others.'' This is but one short summary of what some people ("process" sociologists particularly) believe the essence of sociology to be.... there are many other different and sometimes rivaling conceptualizations.

Introduction
This is an open source curricular module, not a "course" in the traditional sense. There are no schedules, due dates, or tests as would be found in traditional higher education settings. Since there are no real "correct" answers for students to [re]produce, there is no one hallowed book of knowledge to be had here. Instead, what this medium offers is the promise of effectively compiling and organizing virtually unlimited information resources from which users can pick and choose from as they see fit or their situation demands. What may be lost via lack of corporeality, temporality, and formality in the way of grades and credits can be made up for in the expansive potential for discovery based learning in such a novel context. I hope this space will develop into a repository for a multiplicity of perspectives and intellectual exercises built for people looking for interesting and diverse segways into the study of human societies. To begin, I have made my uncopyrighted materials for the course I teach at the University of Florida available here and hope that other educators, interested parties, and diligent students will soon add on to this scaffolding. Perhaps the "experts" who come forth to contribute to this project will also make themselves available to answer questions that truly inquiring minds must produce. This model should foster an enlarged body of engaged participants that become invested in adding onto and improving this forum exponentially, as is the greatest promise and observed tendency of wikis everywhere.

Textbook
Our textbook, should you choose to accept it, is a Introduction to Sociology open source ebook. The topics below correspond to the organization found in this text.

Activities
The weakest link in this format is its lack of structure or accountability. Utilizing the information optimally will likely be difficult for most folks who just drop in and browse around at will. Instead, I would suggest that students follow the material in a somewhat linear manner, at least until (hopefully) the topics below become so diversified that this path becomes unwieldy. Please, fret not that the lack of testing of your reading comprehension via multiple choice assesments means that you will not really "learn" anything, for there exists a superior pedagogical strategy that is uniquely facilitated by open source wikis such as this one. The key to really "getting" this stuff is to "make it your own" by criticizing it and creatively expanding on it. This means that you should actively try to edit all the materials you encounter. Now, arbitrary and/or uninformed changes are not the goal here - instead, you should spend a significant amount of time wrestling intellectually with the ideas and exploring the issues and concepts on wikipedia that relate to the particular discussion topic at hand. The discussion space for each subtopical article is the perfect place to start broaching ideas for substansive changes, but you can also use the email contacts below. The main idea here is that the level of learning you achieve through this activity will be directly proportionate to the amount of time and effort you expend trying to contribute to the materials via attempting to improve them. In fact, a diligent student could make big contributions by simply linking the somewhat obscure terms found throughout the texts to wikipedia articles. More in depth work would include stepping beyond existing materials and developing new discussions of interesting and relevant subject matters. A full assimilation of the knowledge found herein is best achieved by utilizing it in a wholly new context, that is, by writing new articles, hopefully suplemented by outside information sources and multimedia of all kinds.

Contacts

 * Alexevasion - Alex Goldman, M.A. - PhD student in the Department of Sociology at the University of Florida and primary architect of this module - alexevasion@yahoo.com
 * Rcragun - Ryan T. Cragun - PhD student at the University of Cincinnati - primary architect and contributor to the etextbook referenced above

Topics

 * Ethics and Philosophy Guiding Sociological Inquiry
 * General Sociological Theory
 * Principles of Sociology/Three Big Paradigms
 * Society
 * Culture
 * Social psychology
 * Principles of Sociology/Social psychological ways to understand the world
 * Socialization
 * Family
 * Groups
 * Principles of Sociology/McDonaldization and Opposition
 * Deviance and Norms
 * Human Ecology and Urbanization
 * Influence and Interaction
 * Emergent norms
 * Collective Behavior
 * Demography
 * Social Movements
 * The Economy
 * Organizations
 * Religion
 * Politics and Government
 * Principles of Sociology/Radical Center Initiatives
 * Media
 * Nations and Civilization
 * Social change Development
 * Education
 * Race and Ethnicity
 * Sexuality
 * Principles of Sociology/Transsexuality
 * Gender
 * Principles of Sociology/Gender Stratification
 * Urbanization
 * Stratification
 * Health and Medicine
 * Principles of Sociology/Sickness and Wealth
 * Traveling Kids

title: Principles of Sociology


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Principles of Sociology/Sociology and Ethics

Sociological Visions of Ethics and Responsibility drawn from ideas featured in Conversations with Zygmunt Bauman

''In this world there is beauty and there are the humiliated... whatever difficulties this situation may present we should all strive to never be unfaithful to either.'' – Albert Camus

As a general rule, in any society at any given time, there is more humiliation and misery occurring than society notices, more still than it admits, and much more still than it resolves to alleviate or rectify. This is the prime reason why justice is always a distant cry, far ahead and out of reach from everything we do for human well-being and dignity. However, we can't be faithful to the humiliated unless we at least reach for beauty.

Social thought is done for the benefit of humanity when it shows us how we can refuse to act in systematically hurtful ways even while living under circumstances that make the cruel treatment of others seem easy to accept. As relatively free beings, it is possible to choose to care a little more. In that choice lies our human dignity and our sense of morality. The role of critical sociology is to make these choices more accessible by demonstrating that our currently socially acceptable ways of thinking and acting are based on historically isolated and likely flawed sets of social ethics.

Sociologists are not unrealistic utopians who think they know how to finally set the world right to insure that all people live eternally in peace and harmony. This can be rejected on the grounds that the practice of sociology is implicitly tied to the values of the particular culture that surrounds it – those which likewise bind all men and women in the community of social thinkers. However, sociology is an important agent in re-imagining and redoing the current world. It is hoped that this deprives the prevailing institutions of the day the air of invulnerability they desperately need to continue to operate unopposed. What sociology badly needs to fulfill its mandate is an enlarged public forum in which people can come together to recreate their world first in ideas, without the fear that all our hopes and ambitions will be overshadowed by the public desire to make a spectacle out of private lives. It is this forum that our society conspicuously and disastrously lacks and needs to revitalize politics, especially in this time of greatest need.

The effort to give some social choices preference over other alternatives is what we call “ethics”. Society is an ongoing effort to increase the probability of some choices occurring over others. Thus, sociology cannot but be inquiry into the ways in which ethical rules are constructed. Societies are systems of coordinated choices and any society you study is but one reality chosen among many. Society may be “good” or “bad” depending on different beliefs, but in each case it may be better than it is. Being moral means accepting that new choices may be good or may be bad, but it does not mean knowing, let alone knowing for sure which are good and which are bad. Being moral means being bound to make such new choices under conditions of acute and painful uncertainty. To be moral means never to feel good enough about our choices or about the current state of our world – this is the restlessness associated with being human.

Often ethics comes in handy as a tranquilizer, as a drug to mitigate pangs of conscience. However, becoming dependent on the same tired old ethics of justification may in the long run destroy our moral immune system and deprive the self of the little ability it might have had in facing up to tough moral dilemmas and going after the good on its own volition. This restless and indefatigable search for ways to do away with the wrongs of our world never runs a straight line since new actions bring with them new evils. History has been more like a pendulum that a straight edge ruler. To defend ourselves from the evils perpetrated in the past, we march with our backs turned toward the future, but no sooner do we turn to scrutinize the future than it becomes in its turn a past with ugliness showing anew.

Modernity has often been about making the world a “clean” and predictable place. Ordering the world in such a preplanned fashion means making reality vastly different than it currently is by getting rid of the ingredients of reality which are deemed to be responsible for the impurity of the certain human conditions. On this path, we may quickly arrive at a verdict that some people should be refused help, thrown out, or destroyed in the name of a greater good and someone else's greater happiness. Would we be better or worse off without the modern ethos? No one really knows... we still need to wait for full inventory to be made of the atrocities which it may have blinded us to thus far. Modernity's forte is the power of its tools. What counts in the measurements of its success are efficiency, speed, and the scale of performance. Its weakness is the vagueness and uncertainty about the ends to which these tools may be applied. There is a fast growing imbalance between the means we (as members of the privileged lot of humanity) have at our disposal and the ends which we collectively can agree on as worthy of our attention and effort.

If you think you know exactly what the good society is like, then any cruelty you commit in its name is justified and absolved. We can abstain from self-assured acts of cruelty only when we are unsure of our wisdom and admit the possibility of our own ideological fallibility. The ghastly failure of our utopias has turned peoples' thoughts away from what a better life would require to be done in the here and now. It seems that societies manipulate morality rather than produce it. Powerful groups enforce the kinds of morality that advance their own interests. It is this socially produced reality which needs to justify itself, to be tried and judged at the tribunal of ethics.

Freedom may be the natural condition of humanity, but most of human history has been dedicated to repression. Securing bare necessities for all people is the secret to releasing humanity's amazing creative potential. In these times of “liquid modernity”, the hoops one must jump through to achieve security are notorious for being melted as soon as they are molded. For too many, there are only motel beds and sleeping bags available for readjustment. We are told daily that our possibilities are unlimited and that we need only pick and choose those that fit us best. We are then punished for failing to find the best of these advertised alternatives, as if what we had been told of their availability had some guarantee attached. This myth cannot become true for more people as long as the present-day decoupling of freedom and security persists. These two values cannot be entertained separately.

We are encouraged to believe that security is in fact disabling, responsible for breeding the kind of dependency that is thought to constrain human freedom. However, acrobatics and tight rope walking without a [social] safety net is an art few people can master and recipe for disaster for all the rest. Take away security and freedom is the first casualty. Most modern atrocities have been byproducts of a desperate search for security. As older unchanging and self-reproducing orders collapsed under the changes of modernity, quelling the fears brought on by this disturbance was brought to obsessive extremes by modernity, which allowed ever more desperate and destructive responses

Freedom is the uppermost among human values but first and foremost it is a fate. Free beings, if they are indeed free, may embrace that fate or try to escape it, make it into their vocation or fight against it: this is also the capacity to which they owe their freedom. Often freedom seems to be an ambivalent value because it sometimes attracts and repels at the same time. It is disconcerting and frightening to account for one's actions using the terms “I had to” instead of “I wanted to”. Hence the treacherous allure of “there is no alternative” ideologies as well as many of the awesome seductive powers of totalitarian regimes. Remember, there is never a shortage of offers to absolve us of our freedoms.

By itself, the idea of justice has no specific meaning. It only makes sense as a protest against injustice. A just society is a society which considers itself not just enough, which questions the sufficiency of any achieved level of justice and considers justice always to be a step more ahead. A just society is one which reacts angrily to any case of injustice and promptly sets about correcting it. While modernity has blurred many traditional distinctions between justice and injustice, its promise is provide more information on which to base our judgments. Today, the concept of injustice is more hotly contested than any other time in history. However, fast-paced change in the structure and content of our lives has made the idea of justice hazier than ever before. Since justice can only be described as an ever changing ideal, the just society must seek it through ongoing controversy, not majority rule consensus. Like modernity, justice is not just an unfinished project, it is an unfinishible project with only a very limited conception of future directions.

What is more noticeable these days is the tendency to ignore or brush off some of the world's most brutal and excessive differences in standards of living (caused both by particularities in human history and by the current economic regime) as “facts of nature” about which we collectively can do nothing but humbly accept and obey. This happens while the moral alertness of the public is redirected to focus on the demands for recognition from small groups and categories of people sufficiently free and resourceful enough to choose a new lifestyle and demanded its acceptance.

The increasing global effects of our local actions necessitate responsibility on a scale which has never been confronted before. Global power demands global responsibility. The latter has been much slower to arrive even as it finds itself increasingly impotent in the face of consolidated transnational corporate power. The fraction of our income or gross domestic product we are prepared to share with faraway impoverished people who are deprived of livelihood partly as a result of our economy's global search for wealth is pitifully tiny. Investing in the poor may be a morally correct act, but it makes no economic sense under capitalism – less money in wealthy consumers' pockets only raises prices.The problem of finding ways to catch up with rapidly globalizing economic powers by means of our local and national institutions of democracy may presently constitute the major challenge to our standards of justice and morality.

There is a contemporary feeling amongst individuals even in the most free and affluent societies that some of the most basic and important patterns of their lives simply cannot be changed and concern with these problems will only be a waste of time. This is because for the most part the roots of whatever troubles us most and stands in the way of a dignified and morally satisfied life are stuck well beyond the reach of our individual action. These roots are socially planted and cultivated and only collectively can they be dug up and detoxified. Once set in motion, individualization is a self-propelling and self-intensifying process. One of its foremost effects is the undermining of the possibility to act socially to question society and then following this critique with a shared strategy. It is the task of sociology to reconstitute society as the common property and responsibility of free individuals aiming at a dignified life.

With the world changing faster every day, levels of anxiety and isolation continue to rise as individuals and families attempt to cope alone – resulting in very negative consequences for some. With the almost forgotten ties of the extended family out of reach in times of need and insecurity, many people long for a community they can no longer locate. We cannot help missing the missing community but the community we miss cannot be found. Most disconcerting to today's consumer masses is that it cannot be commissioned or made on demand. A true community must be able to address serious crises collectively, but also secure stable and productive lives for its individual members. Like cultures, true communities are not as much impositions of fixed identities as they are processes of making sense with and through others. Our culture should be a knife pressed against the future...


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User:StuRat

Hi,

I'm a computer programmer specializing in FORTRAN programming for CAD/CAM (especially CATIA) and database applications. My interests vary widely from that field, however; into math, science, economics, history, etc., so I hope to contribute to many areas.

title: User:StuRat


text:
Muggles' Guide to Harry Potter/Magic/Expelliarmus

Overview
The Expelliarmus spell is the Disarming spell; it knocks the victim's weapon (usually a wand) out of his/her hands. It can also be used to knock other items out of the target's hands, but we seldom see this use. When it is performed with more power, one can blast the opponent off their feet.

Extended Description
We see this spell first used by Professor Snape in the Dueling Club; Snape casts it on Professor Lockhart, disarming him and throwing him to the end of the platform on which they are demonstrating. Later in the same book, Harry casts the same spell on Draco Malfoy, causing the book that he is holding, Riddle's diary, to fly out of his hand. From this point on, it is used quite often when there is a duel between wizards; if you can get your opponent to lose his wand, you do have a great advantage over him. Later on, Draco Malfoy would use this spell on Dumbledore, unintentionally earning ownership of the Elder Wand.

In Harry Potter and the Deathly Hallows, Harry uses the spell against a Dark Eater during the chase, which causes them to recognize him. Because of this, Lupin warns Harry against the further use of this spell, suggesting that he use more powerful defensive magic.

It is, interestingly, the spell Harry uses to defeat Voldemort in the final book. Harry was, by this point, aware of his own mastery of the Elder Wand and was effectively immune to Voldemort's magic by this, but he needed to cast at least one spell, and it was the Disarming Charm which Harry chose to use. This contrasts with Lupin's earlier warning against using it too often.

Analysis
As mentioned, at one point Harry does use this spell to get someone to drop a book; as the diary is obviously not a weapon, we can see that this spell will act on anything that is held in the hand, not just a weapon or wand. It's possible that there is a mental part of this spell as well, envisioning the specific object that you want to have it act on; alternately, it could work on whatever you are pointing your wand at. In Harry Potter and the Prisoner of Azkaban, in the Shrieking Shack, Harry, Ron, and Hermione all cast this spell at the same time, and it not only pulls Snape's wand out of his hand, but also throws him against the wall. This leads us to believe that the power of the spell is additive when cast by multiple wizards on the same object.

Despite the fact that the charm can do things other than disarm, its main function is to get an attacker to drop his wand; as such, it is referred to as the Disarming spell. This is confirmed by the word's origin, "expelliar" meaning to "be expelled" and "armus" meaning "weapon".

Questions

 * 1) In the seventh book, it appears that this is taken to be Harry's "signature spell". Why would that be?
 * 2) In the seventh book, we learn that there can be other effects from the use of this spell. What would those be?