## Tuesday, June 30, 2009

### Vedic Mathematics Lesson 2: 10's Complements

You can read about my interest in Vedic Mathematics in this earlier post and find a spectacular application of mental computation using Vedic Mathematics principles in Lesson 1 of this series of posts.

Today's lesson is going to be quite short. I am going to explain how to calculate the 10's complement of any number. Essentially, the 10's complement of a number tells you how far the number is below the next higher power of 10. For instance, 89 is 11 below 100. I call 11 the 10's complement of 89. Some texts refer to 11 as the "deficit" of 89 also.

The 10's complement of a number is very useful in a variety of Vedic Mathematical computations. Thus, learning to work out the 10's complement quickly and (preferably) mentally will come in handy when we proceed to later lessons in Vedic Mathematics.

The sutra that tells us how to compute the 10's complement of a number reads Nikhilam Navatascaramam Dasataha. Literally translated, it means All From 9 And The Last From 10.

The practical application of it is actually quite easy to follow directly from the translation of the sutra. Simply put, take your number and subtract each number from 9 as you go from left to right (All From 9). Put down the answers you get as the digits of the 10's complement going from left to right. When you get to the last digit (right-most digit) of the number for which you are finding the complement, subtract it from 10 (The Last From 10) and write this answer down as the last digit (right-most) of the answer.

Note that since all the subtractions are of single digits from 9 and the value being subtracted from is 9 (which is the highest single-digit number in the decimal system), there arises no question of borrowing digits or doing other mental gymnastics to get the individual digits of the answer. Hopefully, subtracting a single-digit number from 10 should not involve any extraordinary mental gymnastics either. However, that last subtraction can lead to a minor problem we deal with later in this lesson.

Let us apply this lesson to a simple example. Let us take 389,384,753 as the number for which we need the 10's complement. Note that the number has 9 digits, so we are looking for the difference between 1,000,000,000 (1 followed by 9 zeroes, making it a 10-digit number) and the given number (10 raised to the power of 9 is the next higher power of 10 for the given number).

Taking the first digit of the given number from left, we get 3. Subtract it from 9 to get 6. 6 is the first digit of the answer. The next digit of the answer is 9-8 = 1. The third digit is 9-9 = 0, and so on. When we get to the right-most digit of the given number, we find that the right-most digit of the answer has to be 10 - 3 = 7. Remember to subtract the last number from 10 rather than 9 to complete the answer. The answer in this case turns out to be 610,615,247. You can verify the answer in any calculator that can handle 10 digits or more. But the method will work for numbers with any number of digits, even numbers that can not be handled by any calculator because they have too many digits.

Note that we defined the 10's complement as the deficit from the next higher power of 10. This is not necessary for the method to work. This method can be put to work to find the difference between the given number and any power of 10 that has more digits than the given number. Let me illustrate with another example.

Suppose we need to find the difference between 1,000,000 and 98,567. Note that next power of 10 that is larger than the given number is 100,000. Thus, to simply find its 10's complement, we would apply the formula illustrated above and find the answer to be 1,433 (the left-most digit computes to a zero, and has therefore been dropped).

To find the deficit from a higher power of 10, first find the 10's complement. This time do not drop zeroes from the left of the answer. We find the 10's complement of the given number to be 01,433. Now pad the 10's complement to the left with 9's until it has one less digit than the power of 10 from which we are trying to find the deficit. Another way to express this is as follows: pad the 10's complement to the left with 9's until it has the same number of digits as the power of 10 has zeroes. In our case, the power of 10 we are finding the deficit from has six zeroes. So, padding out the 10's complement with 9's to the left so that the answer is 6 digits long gives us 901,433.

Yet another way to express this that may be more intuitive is: pad the given number with zeroes to the left so that it has as many digits as the power of 10 has zeroes. Then find the 10's complement of the padded number using the same rule as before. By this method, first we get our padded number as 098,567. Finding the 10's complement of this number using the rule we explained in the beginning, we get 901,433.

The only trouble you might encounter in the application of this method is if the last digit of the number is a zero. In that case, subtracting it from 10 gives you a 2-digit answer (10) rather than a single-digit answer. The way to deal with this is to then put down zero as the last digit of the answer and carry over the 1 to the left hand side (add it to the number you found earlier for that digit). If that carryover leads to the second digit becoming 10, repeat the procedure, carrying over extra digits to the left as long as is necessary.

That may sound confusing, so the easier way to deal with this is as follows: if the number consists of n zeroes at the end, leave them off initially. Find the 10's complement of the remaining number with respect to the power of 10 just above the left-over number. Then add n zeroes back to the right of the answer you get.

Let me illustrate by finding the 10's complement of 89,000. n, in this case, is 3. By dropping the 3 zeroes from the end of 89,000, we get 89. The 10's complement of 89 with respect to the next higher power of 10 (100) is 11. Therefore, the 10's complement of 89,000 is 11,000 (which is 11 with 3 zeroes added back to its right).

That is all there is to it! It should be easy to reel the 10's complements of any number off in seconds using the mental trick illustrated here. Remember to practice! Happy computing and good luck!!

Note that there are applications out there that define the 10's complement as one more than the 10's complement we have computed in this lesson. That kind of 10's complement is useful in some computations involving subtraction and addition. Remember to not get confused by this distinction between the different definitions of 10's complements.

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I taught my kids the trick to finding the reciprocal of any 2-digit number ending in 9. I thought it would be confusing, given their ages, but they picked it up right away and had no trouble applying either method 1 or method 2 to any given problem. They then went and demonstrated their new-found talent to their mother, who was very proud of them and very happy with me! Now, I have to test them in a few days and make sure they remember what I taught them. That will also give me a chance to make sure I remember what I taught them!

In other news, it looks like I will be taking two weeks off to visit and take care of my parents after my father's surgery starting sometime next week. I have convinced my wife that nothing will go wrong when I am not around. That does not mean that she will be entirely at peace, but for now, she seems confident about handling things during my absence.

Our plan to visit my brother-in-law to help with his mother's surgery and its aftermath turned into a bit of a disastrous fiasco because of various problems. We planned to go out there on Friday. But the aircraft on the flight we were supposed to take was replaced with one that had 70 fewer seats. So, we changed our plans and were accommodated on a flight that would take us where we wanted to go with a connection. But at the last minute, this aircraft developed a mechanical problem that delayed the flight so the connection would not work. We had to give up that day.

To make a long story short, we ended up trying repeatedly to get out during the weekend, and then my wife and kids tried on Monday, and today also. Ultimately, the airline managed to accommodate them today evening on a flight and they are off. Since she is going to her brother's later than originally planned, we are still not sure when she is going to come back. We had originally planned on her being back before I left to visit my parents. But now we might have to reevaluate that option.

The weed-killer application using the hose-end sprayer actually worked. The weeds shrivelled up and died, and the lawn looks much better now. So, I might be switching to the hose-end sprayer permanently and ditching the pressure sprayer altogether.

This last weekend saw me doing more yardwork as I had to dig a 1 foot x 1 foot x 1 foot hole in the ground to plant a rosebush. The rosebush unfortunately sat in a friend's car in the hot sun for a while after it was bought, and came to us with shriveled leaves. We watered it (in the pot) for a few days, but it still did not show much signs of life. I tried arguing that it was a waste of effort digging such a large hole for a plant that may already be dead. But my wife convinced me that all the plant needed was abundant sunshine and natural soil to thrive. So, the plant is in the ground, under more than abundant sunshine, and has been watered for a couple of days now. Still no signs of life, leave alone thriving. Oh well, at least I got some exercise...

## Sunday, June 28, 2009

### Vedic Mathematics Lesson 1: A Spectacular Illustration

You can read about how I got interested in Vedic Mathematics in my previous post. In this post, I will try to justify the praise I had for the mental shortcuts Vedic Mathematics has taught me by using a spectacular illustration. In this lesson, we will learn to find the reciprocals of two-digit numbers ending in 9. Thus, we are interested in finding the decimal equivalents of 1/19, 1/29, etc. I will show you 2 methods to work these problems out, and both these methods produce the exact same solution.

Now, note that all these reciprocals are long series of repeating digits in decimal form. There is no closed-form decimal form to any of these reciprocals. The series of repeating digits can be quite long in many cases (18 digits in the case of 1/19, 28 digits in the case of 1/29 and 42 digits in the case of 1/49, for instance). As such, finding the full set of digits that repeat is almost impossible in most calculators that are limited to 8 to 12 digits. Doing the set of long divisions that will result in finding all the repeating digits of the decimal representation involves 18 steps for 1/19, 28 steps for 1/29, 42 steps for 1/49, etc. It is a long and laborious process that consumes a lot of time and paper, and is prone to errors just because of the amount of time and drudgery involved. The only calculator I have found that can show all the repeating digits of these answers is the Microsoft Power Toy Calculator, which is part of the Microsoft Power Toys For Windows XP, which I mentioned in my post on free software suggestions.

With the methods illustrated here, you will be able to find the entire set of repeating digits in one long string without having to do any long division. You can choose to either find the digits from right to left or left to right depending on whether you are more comfortable with simple single-digit multiplications or single-digit divisions. I will illustrate and explain both methods and you can choose whichever method you are more comfortable with when the need arises.

The relevant vedic sutra that addresses this problem simply reads: Ekadhikena Purvena. Literally translated, it says, by one more than the previous one. This is typical of most vedic sutras which are cryptic, and rely on a guru to expound on the full meaning and applications of it to his students (sishyas). The tradition is then carried forward over subsequent generations in what is referred to as the Guru-Sishya parampara. The meaning of the sutra will become apparent as we work through some examples.

Let us take 1/19 first. As mentioned earlier, there are two methods of working out the answer. One of them involves basic multiplication and is worked out from right to left. The other method involves basic division and is worked out from left to right.

Method 1:

We first apply the literal meaning of the sutra and take one more than the number previous to the right-most digit of the denominator. In this case, we get 1 more than 1, which is 2. Call this number our Multiplier.

1. The method starts out by putting a 1 as the right most digit of the answer. So, our answer so far is 1.
2. Now take the last number we wrote and multiply it by our Multiplier. We get 1x2 = 2. Write this digit to the left of 1 as part of the answer. Our answer so far is therefore 21.
3. Now take the last number we wrote down and multiply it by our Multiplier. We get 2x2 = 4. Write this digit to the left of the answer to get 421 as the answer so far.
4. After we repeat the above process once more, we get 8421 as the answer.
5. Now, when we repeat the process above, we get 8x2 = 16 which is a two-digit number. When the result is a two-digit number, write down the last digit of the 2-digit number and remember the other digit as a carry-over. Thus, our answer becomes 68421, and we have a carryover of 1.
6. Repeat the process again. We get 6x2 = 12. Since we have a carryover number, add that to the answer to get 12+1 = 13. Since this is a two-digit number, repeat the process outlined above: write down 3 as part of the answer and keep 1 as the carryover number. Our answer becomes 368421 so far.
7. Repeating the process again, we get 3x2 = 6, add the carryover number to it to get 6+1 = 7. Write that to the left of the answer to get 7368421.
8. In the next step, the answer becomes 47368421 with a carryover number of 1.
9. In the next step, the answer becomes 947368421 (multiply 4 by 2 and add the carryover number).
10. Continue this process until you start getting repeating digits (starting with 1 which is the last digit of the answer). Then you know that you have found the entire series of digits comprising the answer. Put a decimal point in front of the series of digits and denote that the entire series of digits repeats indefinitely. That is your final answer. In the case of 1/19, the answer is .052631578947368421, repeated indefinitely.

Method 2:

Once again, we first apply the literal meaning of the sutra and take one more than the number previous to the right-most digit of our denominator. In this case, we get 1 more than 1, which is 2. Call this number our Divider.

1. First put down a decimal point. Then take the numerator and divide it by our Divider. We get 1 divided by 2, which has a quotient of 0 and a remainder of 1. Write the quotient to the right of the decimal point, and keep the 1 as a carryover number. Our answer so far is .0
2. Now, prepend the carryover number of 1 to the last quotient, 0, to get 10. Divide this number by our Divider, 2, to get 5. Write this to the right of our answer so far as the next digit of the answer. We now have .05
3. Divide this last quotient by our Divider to get a quotient of 2 and a remainder of 1. Write the quotient to the right of the answer so far. Keep the remainder as a carryover number. Our answer so far becomes .052
4. As before, prepend the carryover number (1) to the quotient (2) to get 12. Divide this number by our Divider, 2, to get a quotient of 6 and a remainder of 0. 6 becomes the next digit of our answer. Our answer so far becomes .0526
5. Continue this process (always write the quotient as part of the answer and prepend the remainder to the quotient to get the next number to divide by the Divider) until we start getting repeating digits (0526, etc.)
6. Remove the repeating digits, denote the remaining digits as repeating indefinitely, and you have your final answer. As in method 1, the final answer from method 2 is also .052631578947368421 repeated indefinitely.

Now, let us see how to apply this method to something like 1/9, for instance. Note that 1/9 can be written as 1/09 to make the denominator a 2-digit number ending in 9. Our Multiplier or Divider becomes 1 more than the first digit of the denominator, 0, which gives us 1. Using method 1, we put down 1 as the first digit of the answer, then multiply it by our multiplier which gives us 1 again. Since the digit has started repeating, we know that our answer is .1 repeated indefinitely.

Similarly, with method 2, we divide our numerator, 1, by our Divider, 1. The quotient is 1. So, we get the first part of our solution as .1. Dividing the quotient by 1 again leads to 1 which is a repeating digit. So, our final answer is .1 repeated indefinitely. I use this simple problem so that you can actually punch the numbers into a basic calculator and verify that the answer is indeed what we found out just now, even though verifying the answer that way for 1/19 or 1/49 is close to impossible. Those reciprocals may require long division by hand to verify the results we get using the vedic methods.

For a more challenging problem, let us now apply this method to find the decimal form of 1/69. Our Multiplier or Divider is 1 more than the first digit of the denominator, 6, so we get 7 as the Multiplier or Divider.

After step 1 of Method 1, we have an answer of 1.
After step 2, we have an answer of 71.
After step 3, we have an answer of 971, with a carryover number of 4.
After step 4, we have an answer of 7971 with a carryover number of 6.
Following the remaining steps of Method 1, we get subsequent answers of 57971 with a carryover of 5, 057971 with a carryover of 4, 4057971 with no carryover, 84057971 with a carryover of 2, and so on.
Carrying on until we get repeating digits, we get the final answer as .0144927536231884057971 repeated indefinitely.

Using method 2, after step 1, we have an answer of .0 with a carryover of 1.
After step 2, we have an answer of .01 with a carryover of 3 (remember that our Divider is 7 and we have to prepend the carryover number to the previous quotient).
After step 3, we get .014 with a carryover of 3.
After step 4, we get .0144 with a carryover of 6.
Subsequent steps lead to .01449 with a carryover of 1, .014492 with a carryover of 5, .0144927 with a carryover of 3, and so on.
After repeating the steps as long as is required, we get the answer as .0144927536231884057971 repeated indefinitely.

When we apply the methods above to 1/99, we get a multiplier or divider of 10 and the answer turns out to be .01 repeated indefinitely. 1/09 and 1/99 are special cases with short repeating sequences because the multipliers and dividers in these special cases are powers of 10 (remember, 1 is 10 raised to the power 0).

The procedure can be used to find the reciprocal of any number ending with 9, not just 2-digit numbers. But the multipliers and dividers get too large to manipulate comfortably when the denominator becomes too large. There are extensions and corollaries to this method to allow one to handle such reciprocals easily. There are also extensions and corollaries to this method to allow division of any number by any number ending in 9 rather just finding the reciprocals of numbers ending in 9. There are further extensions that result in a general rule that will allow one to divide any number by any number without having to do long division at all.

I will post about these extensions and corollaries as I continue learning the inner workings of Vedic Mathematics. In the meantime, hopefully this lesson whets your appetite for the intricacies of arithmetic explored by these methods. Remember, practice makes perfect, so I will leave it as an exercise to the reader to find the reciprocals of 29, 39, 49, 59, 79 and 89 using both method 1 and method 2 discussed in this lesson. The basic idea is that with enough practice, you should be able to do the required calculations in your head and reel off the answers with no hesitation when confronted with a given problem. Good luck and happy calculating!

### Introduction To Vedic Mathematics

I have talked about my attempts to teach mathematics to my children in an earlier post. Because of constant coaching from my wife and I, their level of mathematical knowledge is at a point where they can probably sail through middle school and the early part of high school without learning anything more. They know how to solve simultaneous equations in 2 variables, find slopes and intercepts of linear equations, apply the pythagoras theorem, find the volumes, surface areas, and plane areas of most regular 2-dimensional and 3-dimensional shapes, etc., etc.

Some of it is still dependent on the mood they are in. Sometimes, they apply themselves and can then solve any problem they have been introduced to earlier but stringing together what they know to proceed from problem to solution. At other times, they will get lazy and claim that they "don't get" something even though I know they know how to do it. That is when things get interesting as I lose my patience and berate them for being lazy and unwilling to think through something.

The next task I have been handed by my wife is to make them good at mental computation. They are good at basic mental computation like addition, subtraction and multiplication because they have been to classes where they teach the use of the Japanese Abacus. But my wife is not satisfied with the speed they can achieve using the abacus. Essentially, the use of abacus for doing arithmetic is a brute-force method that has its limitations.

So, my wife did some research and has asked me to teach them Vedic Mathematics. The subject intrigued me enough that I started doing some basic research before I even begin my teaching duties. This is what I have uncovered so far.

Vedic mathematics is a system of mathematics consisting of a list of 16 basic sūtras, or aphorisms. They were presented by a Hindu scholar and mathematician, Jagadguru Swami Sri Bharati Krishna Tirthaji Maharaja, during the early part of the 20th century.

Tirthaji claims that he found the sūtras after years of studying the Vedas, a set of sacred ancient Hindu texts. The calculation strategies provided by Vedic mathematics are creative and useful, and can be applied in a number of ways to calculation methods in arithmetic and algebra, most notably within the education system.

The word “veda” has two basic meanings. The first, a literal translation of the Sanskrit word, is “knowledge”. The second, and most common meaning of the word, refers to the sacred ancient literature of Hinduism, the Vedas, a collection of hymns, poetry and Hindu ceremonial formulae. Believed to be one of the oldest human written records, the Vedas date back over 4000 years. Traditionally, they were passed down orally and adapted from generation to generation by sacred sages called rishis, before eventually emerging written in Vedic, an ancient form of Sanskrit.

The Vedas are divided into four main sections: the Rig-veda, Sama-veda, Yajur-veda and the Atharva-veda, known collectively as the Samhitas. The first three, the Rig-veda, Sama-veda, and Yajur-veda are basically ritual handbooks that were used by priests during the Vedic period (1500–500 BCE). Vedic mathematics is apparently part of the fourth Veda, Atharva-veda, which is distinct from the others in several ways. First, unlike the religious focus of the other Vedas, the Atharva-veda contains hymns, spells and magical incantations for personal and domestic use. Also, the Atharva-veda, which was written later than the other Vedas, was not always considered authoritative, but only became so after being accepted by the Brahmans, the highest order of Hindu priests. Collectively, the Vedas include information about a huge range of subjects, spanning religion, medicine, architecture, astronomy, etc.

It is a well-known and accepted fact that ancient Indian Vedic civilizations were known for being skilled in geometry, algebra and computational mathematics complex enough to incorporate things like irrational numbers. Important contributions to early mathematics were made by Indian scholars like Aryabhatta, Brahmagupta, and Bhaskara II. Indian mathematicians made early contributions to the study of the decimal number system, zero, negative numbers, arithmetic, and algebra. In addition, trigonometry was well-developed and understood in India, and, in particular, the modern definitions of sine and cosine were developed there. These mathematical concepts were transmitted to the Middle East, China, and Europe and led to further developments that now form the foundations of many areas of mathematics.

Almost all ancient Indian mathematics literature is composed completely in verse; there was a tradition of composing terse sūtras, like those of Vedic mathematics, to ensure that information would be preserved even if written records were damaged or lost. Ancient and medieval Indian mathematical works, all composed in Sanskrit, usually consisted of a section of sutras in which a set of rules or problems were stated with great economy in verse in order to aid memorization by a student. This was followed by a second section consisting of a prose commentary (sometimes multiple commentaries by different scholars) that explained the problem in more detail and provided justification for the solution. In the prose section, the form (and therefore its memorization) was not considered as important as the ideas involved. All mathematical works were orally transmitted until approximately 500 BCE; thereafter, they were transmitted both orally and in manuscript form.

Mathematicians of ancient and early medieval India were almost all Sanskrit pandits, who were trained in Sanskrit language and literature, and possessed a common stock of knowledge in grammar, exegesis and logic. Memorization of "what is heard" (śruti in Sanskrit) through recitation played a major role in the transmission of sacred texts in ancient India. Memorization and recitation was also used to transmit philosophical and literary works, as well as treatises on ritual and grammar. Modern scholars of ancient India have noted the "truly remarkable achievements of the Indian pandits who have preserved enormously bulky texts orally for millennia.

Tremendous amounts of energy was expended by ancient Indian culture in ensuring that these texts were transmitted from generation to generation with inordinate fidelity. For example, memorization of the sacred Vedas included up to eleven forms of recitation of the same text. The texts were subsequently "proof-read" by comparing the different recited versions. Forms of recitation included the jatā-pātha (literally "mesh recitation") in which every two adjacent words in the text were first recited in their original order, then repeated in the reverse order, and finally repeated again in the original order. The recitation thus proceeded as:
word1word2, word2word1, word1word2; word2word3, word3word2, word2word3; ...

In another form of recitation, dhvaja-pātha (literally "flag recitation") a sequence of N words were recited (and memorized) by pairing the first two and last two words and then proceeding as:
word1word2, word(N-1)wordN; word2word3, word(N-3)word(N-2); ...; word(N-1)wordN, word1word2;

The most complex form of recitation, ghana-pātha (literally "dense recitation"), took the form:
word1word2, word2word1, word1word2word3, word3word2word1, word1word2word3; word2word3, word3word2, word2word3word4, word4word3word2, word2word3word4; ...

That these methods have been effective, is testified to by the preservation of the most ancient Indian religious text, the rig veda (ca. 1500 BCE), as a single text, without any variant readings. Similar methods were used for memorizing mathematical texts, whose transmission remained exclusively oral until the end of the Vedic period (ca. 500 BCE).

The most notable application of Vedic mathematics is in education. Vedic mathematical strategies may prove to be a useful resource for teachers and students, who may find elements of it easier and more accessible to teach and learn than conventional mathematics. In particular, these strategies may be an invaluable resource to students that already struggle with mathematics, and could benefit from alternative approaches.

One attempt at incorporating Vedic mathematics into education was made by Mark Gaskell, the head of mathematics at the Maharishi School, Lancashire, England. The school has developed a Vedic mathematics curriculum equivalent to the national one with impressive results. According to Gaskell, the alternative curriculum has resulted in livelier classes, greater student enjoyment and understanding, and improved academic performance. In fact, the first set of students to complete the course were each able to not only pass, but achieve over 80%, on the General Certificate of Secondary Education, a proficiency test taken by all secondary school British students, a year earlier than their peers in the regular curriculum.

Once you understand a particular vedic method and learn how to do it in your mind, you can also amaze friends and others with your mental gymnastics. It is just uncanny how the techniques work: when you perform it in front of friends, it is as if you are either performing magic or you are a human calculator. I have even been accused of cheating by some people I have demonstrated these techniques to, though, of course, they just could not figure out how exactly I was cheating!

I think the best way to learn something is to absorb the methodology and then try to repeat it to others in my own words. That will demonstrate that I understand the methodology completely and will help me in teaching my kids what I have learnt. So, I will try to explain these mathematical techniques in my own words in future posts about Vedic Mathematics so that I am sure of the methodology before I sit my kids down and drill them on it. And these posts will also serve as a written record of the methodologies for future reference so that I don't have to hunt around for the original source as I try to relearn something I may have forgotten.

In the meantime, if you are curious, you can get a taste of Vedic Mathematics by going to the official website of the Vedic Mathematics Academy. They have tutorials on some basic methodologies that should be easy to master for most people. They also sell books and DVD's on the subject if you are interested in pursuing it further.

## Saturday, June 27, 2009

### What Kind Of Troubles Would You Rather Have?

Everybody has bad luck and troubles at some time or another in their life. The question is what kinds of troubles would one rather have, assuming that trouble is inevitable? What kind of trouble has the least long-term impact and/or trauma?

I have given this question some thought. I started thinking about this problem when my family and I were once stranded when we were on vacation and had to buy a new set of full-priced tickets to get back home. Yes, it ended up being a lot of trouble and it ended up costing me a lot of money. Friends and relatives were somewhat shocked that we had gotten into that kind of trouble. And, quite flippantly, I told them that is what money is for: to get you out of this kind of trouble. And I realized that as long as money solves the problem and makes it go away, it really was the least troublesome of the kinds of troubles and problems one could have.

I started cataloging all the kinds of troubles one could have. I came up with the list below, which may or may not be complete. Some may choose to break some of the categories below into multiple types and so on. But essentially, in broad terms, I think everyone faces troubles that fall into one of these categories:

• Financial problems
• Work-related problems
• Legal problems
• Health problems
• Emotional problems

Obviously, problems could start out as one and then start having ramifications or create other kinds of problems also. For instance, health problems could lead to financial problems, or emotional problems could lead to work-related issues also. The question now becomes, if you know life is full of problems, what kind of problems do you hope it will be full of?

I have actually ranked these problems into a sort of hierarchy that describes what my priorities in life are. Everyone has different priorities in life, so everyone might have a different ranking. I will go over my ranking and what lead me to it, and hopefully it will get others thinking about what their priorities in life are and what the rankings should be.

Here is my ranking from most desirable kind of problem to least desirable kind of problem:

• Financial problems
• Work-related problems
• Legal problems
• Health problems
• Emotional problems

Let me explain why.

Financial problems: This can include any unexpected problem which requires you to spend money to extricate yourself out of. It could be mundane things like a sudden appliance breakdown at home, a sudden auto repair bill, or more dramatic like my getting stranded with my family with no way home except a new set of air tickets. I am obviously not including financial problems that stem from other kinds of problems, and the reason is somewhat obvious: it is the root problem I am ranking here, not the myriad consequent and subsequent problems it brings along.

Money is a means to an end in my worldview. Money has no intrinsic value by itself. Money can buy you many nice things, but, as the saying goes, the best things in life really are mostly free. I don't think it is a surprise, therefore, that I feel that financial problems are really not problems at all in many cases. It is actually what money was designed for in the first place: a means to an end. In this case, the end is to solve whatever problem you have and get you going again. Yes, it can be painful in the short term and the setback may result in various unpleasant consequences.

But, it is important to be philosophical about it and make sure that the financial problem does not lead to other problems, especially problems of other kinds. If you let it get to you, it might change quickly into a health problem or other worse kinds of problems. That is why, it is important to have a rainy day fund, and make sure you can absorb financial problems philosophically, and keep it a purely financial problem, without allowing it to affect other aspects of your life and changing into other kinds of problems. The reason financial problems are the most trivial in my worldview is that most financial problems, when well-handled are just that: financial problems and nothing more. They don't have to become any other kind of problem, ever.

Work-Related Problems: This could include layoffs, frictions with co-workers or a boss, company going bankrupt, too much work and too little time for life, etc. I rank these kinds of problems just below financial problems in desirability because in many cases, these problems are difficult to keep isolated as just work-related problems. In my world-view, work is a means to an end too. It helps me earn money, which is another of these means to different ends. So, work by itself has no intrinsic value to me.

If you agree with that philosophy, then the obvious solution to most work-related problems is to just get different work. Have problems getting along with a boss, or work sucking the life out of you? Quit and start over elsewhere. I know that it is more complicated than that, but the basic idea is not very complicated. If you want the work-related problem to stay work-related, that might be the kind of drastic action that is required.

In most case, though, it does not work out quite that simply and at the very least, work-related problems lead to financial problems also. Hence, their ranking below purely financial problems in terms of desirability. But once again, it is important to be philosophical about it. Isolate the problem and make sure it does not become worse kinds of problems. I will be honest, I have had work-related problems. And I have considered quitting and taking up a much lower-paying job if that is what it takes to get out of a particular work-related situation. It hasn't come to that ever, but I am fully prepared to take that step and keep the consequences isolated to my finances for obvious reasons.

Legal Problems: This is a rather large category of problems and depending on what kind of legal problem you have, the consequences could be drastically different. Most kinds of legal problems will at least require a lot of money to be spent on legal fees, hiring lawyers, etc. The final result could be more financial problems resulting from a monetary damage award or a stint in probation or jail if it was a criminal legal problem.

Either way, legal problems are likely to have severe consequences which are very difficult to keep isolated. It can lead to financial problems at the very least, but could result in work-related problems, health problems and/or emotional problems also. But one may be able to isolate the consequences to just financial, or financial and work-related. It is almost impossible to isolate legal problems to just remain legal problems (unless, perhaps you are a lawyer), and I am not sure I would desire them more anyways even if they could be so isolated. The problem is that legal problems are highly unpredictable and their evolution and disposal are outside your immediate control in almost all cases.

Health Problems: This kind of problem requires no explanation in terms of what it is. Everybody knows a health problem when they see one. I am not talking about a common cold or the seasonal flu now, but about chronic and/or acute problems that are life-threatening at worst and quality-of-life-threatening at best.

Now we are getting into the big leagues here in terms of problems. Health problems, in my worldview, are always a problem even if the financial consequences are practically nothing because you have good insurance and the work-related consequences are practically nothing because you have disability insurance and/or enough sick leave. You come into the world with only your body to call your own, and health problems threaten to take that most precious of your possessions away from you at worst. At best, they threaten severely how, when and where you get to use that precious possession and put limits on enjoying your body like others with good health do.

I may be biased in this respect because I have always been healthy and value my health as a consequence. Perhaps a person plagued with ill-health learns to live within the limitations imposed by the problem and does not look at it as such a big deal. This is another philosophical question in itself: I view financial problems as trivial because I have learned to live with the limitations imposed by such problems. I view health problems as highly threatening because I have no experience with them except by hearing of the health problems others have. Perhaps, if I had always been sickly but had the Midas touch and was sitting on hordes of wealth, I might consider health problems as trivial and financial problems as highly threatening. It is a hypothetical situation I can not evaluate the relative merits of both honestly outside my biases.

In fact, the bigger philosophical insight from this might be that your ranking is based on what kinds of troubles you are used to and what sorts you are unfamiliar with. Maybe I am attaching way more significance to this ranking than it is worth because it may not reflect your worldview or priorities in life, but just your familiarity with different types of problems. Interesting thought, but I will have to set that aside for now and continue on.

Emotional Problems: This is another grab-bag of various categories all bundled up (a bit like legal problems). I include various things like marital problems, estrangement with relatives, loss of reputation and/or the respect, admiration and love of people who matter to you.

In this respect, I am reminded of two quotes by famous people. One of them is: If a man loses his wealth, he loses nothing. If he loses his health, he loses something. If he loses his character, he loses everything. The second is: As long as a man has character, nothing else matters. And if he does not have character, nothing else matters either.

I was conflicted for quite a while about the relative ranking of health problems and emotional problems. Would I rather live to a ripe old age reviled by and earning the scorn and curses of people around me or would I rather die young surrounded by well-wishers who would honestly mourn me? I think the quotes above reflect my views on the matter though I could never imagine being quite so eloquent in expressing them. I think I have made the right choice in ranking emotional problems at the bottom in terms of desirability.

I guess I am a sentimental old fool after all, in spite of the bravado I put on. I am not openly emotional and I don't wear my heart on my sleeve. But I do have a heart and it is not as hard as people think it is. It may be one of the reasons why I find it difficult to carry grudges. It may also be why I hate confrontations and would prefer to smooth things over quickly in any conflict rather than letting it brew and take on ugly overtones.

Problems are never-ending in life. But if there are no emotional problems in life, if you are well-loved and well-respected, there will always be people around you willing to help you out of any other problems you might have. All the money in the world, the best job in the world, and the fittest body can not buy good relationships or the honest good wishes of well-wishers. Or, maybe I am a fool and I need to have paid more heed to the tongue-in-cheek definition of spouse: a person who will stand by you through all the trouble you wouldn't have had if you had not gotten married in the first place!

## Thursday, June 25, 2009

### Surgery For My Father, Negotiation Time For Me

Things are starting to get interesting with the medical condition of my father, which I spoke about in an earlier post. He underwent a multitude of tests including several ECG's and an angiogram. The final diagnosis is that he has blocks in two arteries leading to his heart. One of the blocks is 80-90%. Another artery has two blocks in a row, each at about 40 to 60%.

The treatment options have pretty unanimously been narrowed down to an open-heart bypass surgery. My parents and brother have now consulted several well-known doctors and nobody has suggested anything else. The basic problem is that angioplasty or a stent is not an option since there are two blocks one behind the other on the same artery. And drugs are considered reliable or effective enough when the blocks are that close to 100%. Moreover, apart from the heart problems, my father is in good physical shape and has no complicating factors like diabetes. Undergoing this surgery would basically take the heart issue out of the equation for the next 10 to 15 years according to the doctors.

I had hoped that it would not come to this. I don't think invasive procedures are the first option to treat anything. And especially so in the case of a septuagenarian. It is not that I don't trust doctors or modern medicine, but I don't trust them blindly either. I don't trust them to ever know everything there is to know about the human body and how it works. I believe in giving the body's natural ability to heal itself a chance (and perhaps a boost, with some natural remedies) before forcing a more drastic medical solution on it.

More importantly, I don't trust doctors to be absolutely and completely objective about deciding the best course of treatment for a given condition given the amount of money sloshing around the system nowadays. I am not saying that doctors make decisions based on financial incentives and nothing else. I am not even saying that doctors are consciously swayed by the financial implications of the alternative courses of treatment. But it would be difficult to argue that money can be eliminated from consideration even at a subconscious level. But in this case, perhaps it was the only sensible option.

The surgery has now been scheduled for very early in July. He will be in the hospital for the first 8 days after the surgery (3 days in the ICU and 5 more days in the general ward). After that he will come home, but the consensus is that he will require extra help and care for about a month or two after coming home. Even simple things like taking a shower will require external help during this period. So, the idea is that my brother and I will take turns and be around for at least a month after the surgery. The plan is also to employ a nurse and a maid during the recovery period to assist my parents.

My wife knows that I have to do my part in taking care of my parents, but is not fully comfortable with me being far away from her over extended periods of time. She can and does take care of the household without my help on a daily basis right now. She is comfortable handling the routine and mundane such as cooking, cleaning, laundry, grocery-shopping, etc., etc. But there is always the nagging feeling in the back of her mind that something non-routine would choose my being away as the excuse to happen when she is least-prepared to handle it. So, she is trying to convince me to limit my time away to about 10 days at a time.

The problem with my trying to be away for only 10 days is that the actual time I spend with my parents will come down to about 8 days in that case because of the travel times involved in getting there and back. I have enough vacation time at work to be away for 3 weeks if I need to. So, conceivably, I could go and spend 8 to 10 days with my parents, come back for a week or two and then go back again for another stint. Obviously, what time commitment would be required from me would depend also on what constraints my brother faces, from a work as well as family perspective.

So, I will have enough on my mind as I head into this weekend. My mother-in-law has undergone minor surgery to place a defibrillator on her heart. She lives with my wife's brother, and my wife, my kids and I are heading out to my brother-in-law's place this weekend. My wife and kids will stay there for a few days, but I will be back after the weekend. I have also made some plans to hike with some friends from college when I am over there. When we initially made plans for this trip, my father's surgery was not in the picture. Now that things have gelled to some certainty on that front, I have to figure out how everything is going to fit together.

One of the options I am mulling over is to postpone our trip to my brother-in-law's place by a few days. At that time, I can send my wife and kids to her brother's place while I head off back home to spend some time with my parents. And my wife would be less uncomfortable with me not being around because she would not be by herself at home. She can either come back home in a couple of weeks and spend some time alone, or she can choose to spend my entire absence at her brother's place. But I am not sure whether postponing the trip is an option given that my brother-in-law also needs help with managing the care of his mother.

Another option is for her to take this trip as planned, come back in a week or so, spend a week at home, then head back to her brother's place while I head to my parents' place. She can then spend some of her time away from me in the company of her mother and her brother's family without being alone. Obviously, making two separate trips to her brother's place is also inconvenient, especially with the kids in tow and the amount of luggage that entails. So many options, so many constraints, it makes my head spin!

Time to lay out all the options in front of my wife and start negotiating in real earnest. And time to think up options and lay them in front of my brother and in front of my parents too. Life is all about compromises and married life is especially so. But it is not just my life, but everyone's life too. Let us see how this works out, who makes what compromises and what ends up happening finally.

And also, this surgery will end up costing me about \$5,000 out of pocket after all the insurance payouts and whatnot. More unexpected expenses, sinking my budget even deeper into the red. Is it any wonder my budget is always so tight?

## Wednesday, June 24, 2009

### Spanish Resources On The Web + Typing Spanish -- Bonus

I took a free Spanish class offered at my daughters’ school recently. To supplement what I was learning in the class, I did some research on learning Spanish over the web. My research lead me to several Spanish-related websites and some were better than others at teaching beginners basic Spanish. I put together this review of Spanish-teaching websites and distributed it to other students attending my class. I have decided to post it online so that others can benefit too.

Need to register at least for a free membership. Free membership provides access to only some of the resources on the site. The free resources include the written lessons, one test and one quiz on each lesson and an oral test. Paid membership unlocks more resources such as a podcast of each lesson, more tests and quizzes, one more oral test and a final test for each lesson. Paid members also get more vocabulary words, but this is not a big advantage since there are lots of Spanish vocabulary websites that have free word lists. The value of this site is in the detailed lessons on Spanish grammar. Seems to be the most complete and full-featured Spanish teaching website around. This site has extensive pronunciation, grammar, vocabulary, verb drill and other sections. There is also a separate travel helper section under “features and resources” with audio.

This website also comes up as Learn Spanish on search engines.

Very basic set of Spanish lessons including some commonly used phrases and small amount of vocabulary. Not very extensive and of limited value except to students taking their very first steps in Spanish.

Very good site, but oriented mostly towards traveling for business. This may be an advantage though since most people who need Spanish are going to need it during travel. So, the site has extensive sections on hotel check-in and check-out, customs and immigration, money and money exchange, etc. There are at least 41 chapters on the site, but some of them are to specialized to be of much use to a general Spanish learner (such as a chapter devoted to labor issues, labor unions, etc.). The registration link does not work, so I have no idea what registration buys you. Looks like all the chapters are accessible without registration. The exercises at the bottom of each chapter include grammar and vocabulary. There is also audio on the site, but the audio links are all individual mp3 files, making it a little awkward to use.

This site has an annoying popup that keeps asking you to sign up for the author’s free Spanish lessons, but you can get access to the resources on the website without registering (go to the bottom of this web page and click on “Spanish Lessons” to get to the Spanish course). The lessons are not as extensive as on studyspanish, but seem to cover most of the basics. There is also some audio on the website. The exercises consist mainly of verb drills, but the site is not interactive – you are given material to drill yourself on and it is up to you whether you want to do it using flashcards or some other means. The site’s navigation is a little awkward and there are lots of links to external commercial sites, so be careful.

Somewhat slow site, but the content is quite good. Part of a group of sites that also teach French and Italian in addition to Spanish. Has sections on vocabulary and grammar, but does not have a well-defined lesson structure. The site expects students to follow links from one topic to another based on interest, but this can be somewhat confusing and disorienting. The sections on flashcards and games are interesting and innovative.

Contains a huge number of electronic flashcard sets that allow you to learn Spanish vocabulary and then test you. The tests take a variety of entertaining forms in addition to the standard flashcard format of showing words in one language and evaluating your response. There are matching games, speed games and various other entertainments. The site does not seem to require any registration, but you can get more functionality (such as creating and/or editing your own flashcards, and creating lists of favorite flashcard sets) if you do register. You can also print flash cards from this site, but the format is a little weird.

This is a very ugly and confusing looking site. However, it has a few useful resources and lots of quizzes, tests, practice sheets, etc. It is very difficult to figure out what is available for free and what requires a membership. In fact, it is not even clear how to sign up for a membership, but the free resources may be worth a few visits to this site.

Another free site that provides flashcard based learning in a variety of subjects. Not as fancy or extensive (very few sets of flashcards as far as I could tell from a quick browsing of the site) as quizlet.com. You have to register for free to create flashcards and sets. But most of the sets already on the site seem to be accessible for free without registration. Flashcard sets are downloadable, but don’t seem to be formatted for standard index cards.

This is another site with very extensive collections of flashcards on various subjects. The Spanish section seems to be quite large and you don’t need to register to learn the contents of the flashcards. It is not flashy like quizlet, with flashcards just being shown on screen for you to respond to, but if you learn well from flashcards, this site is not bad. If you do register for a free account, you can create and share flashcards and sets.

Typing Spanish -- Bonus!

How to type accented characters on the computer

This is another important part of learning Spanish in the age of computers. There are special Spanish keyboards available at electronics stores, but if you are a touch-typist, getting used to a new keyboard layout can be tricky and lead to lots of spelling errors. This is the same problem that happens when you change your keyboard layout to a Spanish layout. The confusion is a little higher with this option because the letters that appear on the screen don’t even correspond to the letters printed on the keyboard. What I have explained here is a much simpler way to retain your current keyboard and keyboard layout and still be able to type accented characters on a Windows computer.

The accents on letters are part of the spelling of a word in Spanish (and other languages with accented characters). Omitting them would be considered bad spelling at best and at worst, could change the entire meanings of words and sentences. Here is how to type the accents over letters if you are using a Windows XP computer.

The first step is to get the US - International keyboard as an alternative keyboard on the languages toolbar. These instructions seem long and convoluted, but once you do it, you will see that it is actually quite simple.

1. Click Start, and then click Control Panel.
2. Under Pick a category, click Date, Time, Language, and Regional Options (or Under pick a Control Panel icon, click Regional and Language Options).
3. The Regional and Language Options dialog box appears. On the Languages tab, click Details.
4. The Text Services and Input Languages dialog box appears. Under Installed services, click Add.
5. The Add Input language dialog box appears. In the Input language list, click the language that you want. For example, English (United States).
6. In the Keyboard layout/IME list, click United States-International, and then click OK. NOTE: When you use the United States-International keyboard layout, you should also use an English language setting.
7. In the Select one of the installed input languages to use when you start your computer list, click Language name - United States-International (where Language name is the language that you selected in step 5), and then click OK.
8. In the Regional and Language Options dialog box, click OK. Notice that the Language bar appears on the taskbar. When you position the mouse pointer over it, a ToolTip appears that describes the active keyboard layout. For example, United States-International.
9. Click the Language bar, and then click United States-International on the shortcut menu that appears. The United States-International keyboard layout has been selected.

Once you have chosen the US – International keyboard layout, typing accented characters is easy and straightforward. To type à for instance, type in ` (key left of 1, and above the Tab key) followed by an a. You will notice that the ` character does not appear when you type it in, only as an accent on top of the letter you type in after typing in `. The accent will appear on top of any character you type after the `. Similarly, for á, type in ‘ (single quote) followed by an a (note that ‘ followed by c will give you ç, not c with an acute accent on top of it). For ä, type in “ (double quotes) followed by a. For ã, type in ~ (shift + key left of 1) followed by a. For â, type in ^ (shift + 6) followed by a. To get ‘, “, and other characters by themselves, just type the character followed by a space or punctuation mark (note that the character will not appear until you type the space or punctuation mark in).

The following table shows you the full range of accented characters you can create using the method above.

 Press This Key Then Press This Key And You Get ‘ (apostrophe/single quote) a, c, e, i, o, u, y á, ç, é, í, ó, ú, ý “ (double quote) a, e, i, o, u, y ä, ë, ï, ö, ü, ÿ ` (grave accent, above tab key) a, e, i, o, u à, è, ì, ò, ù ~ (tilde, above tab key) a, n, o ã, ñ, õ ^ (caret, shift 6) a, e, i, o, u â, ê, î, ô, û

You can assign the normal keyboard and the US-International keyboard different shortcuts on your keyboard so that you can switch between them without having to go through the languages toolbar.

There are also some specialized punctuation marks in Spanish, such as ¿ and ¡. To get these, press the right-hand side alt key and / simultaneously, and right-hand side alt key and 1 simultaneously, respectively. Note that this will not work with the left-hand side alt key, only the right-hand side alt key.

To get all the codes and learn about the full possibilities of the US – International keyboard layout, visit the international keyboard codes website. This site is amazing as it teaches you not just to type Spanish letters and punctuation, but also various other symbols including various currency symbols (£, ¥, etc.), ¤, ©, ®, °, §, etc. I will leave it as an exercise to you to visit the site and figure out for yourself how I inserted the symbols in the previous sentence. So, even if you have nothing to do with Spanish the rest of your life, learning about this keyboard layout may help you out with other tasks.

Note that Microsoft Word 2003 (and also 2007) already includes dictionaries and grammar definitions for Spanish. In Word 2003, go to Tools->Set Language to change the dictionary and grammar language so that you can spell-check Spanish documents and get Spanish grammar suggestions. Just like in English documents, Word will underline misspelled words in red and ungrammatical words, phrases or sentences in green. So, you can use Word as a Spanish language teaching aid! The language setting is by document, so changing it for your Spanish work in those documents will not wreak havoc with the rest of your documents that are in English.

### Free Software Suggestions Part 3

This is the third and final installment of the posts on free software that are based on what I use on my PC myself. Here are links to Part 1 and Part 2 of the posts. As mentioned at the end of Part 2, I am going to talk briefly in this part about software I use for entertainment and games.

• Entertainment
• Windows Media Player: This comes free on every windows computer and you can get the latest version from Microsoft’s website. It is not the sexiest media player out there, but is quite adequate for most people. It can handle most formats of audio and video, but might require the installation of a few additional codecs to handle some weird files. In addition to just playing media files, it gives you the ability to play the file at different speeds, adjust the color saturation of the media, use a graphic equalizer to get the sound just right, etc. It also has the ability to rip music from CD’s and to burn audio CD’s from music on your hard drive.
• K-Lite Codec Pack: Codecs are a contraction of Coders-Decoders. They enable media players to encode audio and video into compact files and then decode them to play them. K-Lite produces an easy to use pack of these codecs that should enable your media player to handle most audio and video files you can get your hands on.
• VLC Media Player: This is one of the most powerful media players out there with a ton of options that should enable you to do a lot more with your media files than you can with most other players. For instance, this media player enables you to take snapshots of each frame of a video as a series of individual JPEG images.
• FreeCorder: FreeCorder is a small application that attaches itself to your internet or file browser as a toolbar. This toolbar has controls that allow you to record to MP3 files all sounds that are produced by your computer. This is very useful if you need to record streaming audio off the web (or the audio from streaming video) onto your computer for offline use. On some computers, the audio hardware is set up in such a way that there is absolutely no other way to tap into the audio coming out of the computer (mainly Dell computers), so FreeCorder is your solution out of this conundrum. FreeCorder also breaks up the audio it records into multiple MP3 files based on pauses in the audio, so if you stream an entire album from the web, the resulting recording will be broken up into individual songs for your convenience.
• Audacity: Audacity is the gold standard when it comes to audio editing. Almost anything you want to do with sound on your computer can be accomplished with Audacity. Like other powerful tools, learning to use it fully could take some time, but if you are into any kind of audio-editing, or into recording podcasts for streaming, etc., this is the tool you need to get familiar with.
• Windows Media Encoder: Just as Audacity is to audio podcasts, Windows Media Encoder is to video podcasts. Not only can you record video on your computer off your webcam using WME, you can also record what happens on your computer screen as a video directly using WME. You can also stream video out of your computer directly using this tool. This is the tool of choice for putting together training videos showing people how to use software (because of the screen-recording capability).
• TagScanner: TagScanner is a powerful application for managing and organizing your music collection. Most music file formats have the ability to associate tags with the file that describe the music in terms of artist, album, year of release, etc. TagScanner allows you to edit these tags, organize your music into folders based on the tag information or derive tag information from the folder structure in which your music is stored. The interface can look a little cluttered and noisy, but once you tap into the power of this tool, you will never again use another tag-editing application.
• Jodix Conversion Tools: Jodix has produced a set of format conversion tools that can come in very handy depending on your needs to port audio and video between different devices. Jodix tools include iPod Video Converter, DVD MP3 Ripper, WMA to MP3 Converter, RM to MP3 Converter and Video MP3 Extractor. Useful tools to have in your toolbox even if you see no use for them right now.
• FormatFactory: FormatFactory is a more powerful and versatile format converter. You can covert from more formats into more formats with FormatFactory than you can with the Jodix Tools.
• AnyVideoConverter: This is another format converter tool. In general, I have noticed that there are always multimedia files out there that cause any given tool to choke up, which are handled perfectly fine by a different tool. That is why I have the Jodix Tools, FormatFactory, AnyVideoConverter and other tools in my toolbox. If one does not work for a particular file, I will try with another until I hit upon one that works with that file.
• MediaCoder: This is the granddaddy of all converters and still one of the most powerful tools out there. Like all powerful tools, it takes time to get to use this correctly, so if your conversion needs are simple and the other tools don’t choke on the file, it may be better to stick to them. But if you want really fine control over the conversion, this is the most versatile tool with the most options for you to fine-tune.

• Games: I am not a hardcore gamer and do not play very many games. Most of the games I list here would probably not even be considered games by hardcore gamers. I don’t play any online games or multi-player games. None of the games in my list are graphics-intensive. They are classic strategy games and a couple of fun ones I acquired a while back. You would be better off not relying on this post for game suggestions, but I wanted this post to be as complete as possible. In general, if you are hardcore gamer, you know what games you want and there is no way to acquire them legally without paying for them.
• Pawn: Chess game, as the name suggests. Small size, but plenty powerful.
• Arasan: Another chess game. This is not as pretty as Pawn, but a lot more powerful and very challenging to beat even when set to play at reduced strength. Read the FAQ for more information about the game.
• Scrabout: A scrabble game based on the official scrabble board layout. The dictionary has some omissions and adding too many words into it causes the program to become unstable. So, by default, you are playing with more words at your disposal than the computer does. It is still pretty hard to beat! Be careful when you install this game, it does not like spaces in the install folder’s name.
• Bogout: This is a computerized recreation of the classic word game, Boggle. Download the Bogout.zip file from the link provided and unzip it into any folder you want. It is ready to run with no installation required. This site is a huge repository of classic games which you can browse and download to add to your collection.
• LaserTank: This is a strategy game in which you move your vehicle over, under and around various obstacles to a final finish point. New levels are being produced constantly by several fans around the world, so you should never run out of levels to play. If you do, create your own levels and add them to the collection.
• Roll’em Up: Pinball game originally produced as a publicity item by a beer manufacturer. Fun to play and somewhat addictive.

Sometimes free software disappears off the web, temporarily or permanently. Sometimes, the websites that host the free software go down because they don’t have enough financial backing to keep the site going. Other times, companies create a new version of software and decide to discontinue giving away a free version. This makes it important to hold onto copies of good applications you find on the web so that you can reinstall it when you need them (either on a new computer or after a reformat, etc.). What I do is create a folder on my hard drive for software that I have installed on my computer and put all the installation files in this folder. I then create a text file in this folder listing the applications, the installation file name, version number, where I acquired it and other details. This entire folder is backed up along with other important stuff on my computer to an external hard drive on a daily basis.

How do I find free software? The first place I start is a good software site like download.com. At the main page, search for the function you hope to accomplish (“backup” for instance) or put in the name of the software if you know it. Once the search results come up, use the left-hand side panel to narrow your search to Free software (don’t bother with the Free to Try category since they are crippled and/or time-limited. You can also use the left-hand side panel on the main page to search by category of software by function, rather than by a search term. Once you click on a category name and reach the page for that type of software, use the left-hand side panel once more to narrow the search to freeware by clicking on Top Freeware. Other sites to search for software include Tucows, Free Downloads, and Sourceforge (which is the repository for most volunteer-based open-source free software).

If you want information and reviews of free software, head over to Gizmo’s Freeware Reviews Page on the web. Organized into multiple categories by functionality, you can easily find recommendations for practically anything you need for your computer. Everybody’s taste is different and what is the best according to one reviewer may not be the best for you and your particular tastes, interests or requirements. I don’t agree with all the recommendations on this website, but I still consider it a very valuable resource for starting my research into software that I may need. This site also offers newsletters and has a freeware forum where you can post questions and get answers from others on the web.

Another useful site if you are specifically interested in open source freeware (freeware for which the source code is also available for you inspect and/or enhance to make your own custom version of the software) is OSAlt. This site allows you search specifically for open-source alternatives to well-known commercial software. So, if you see your friend using photoshop and you are interested in doing what he/she is doing, but don't want to spend the money to acquire photoshop, you can go to OSAlt, put in photoshop and find that there are several alternatives including Gimp, GimpShop, etc.

Ultimately, your best bet to find freeware that is hard to get is search engines like Google. Google is your friend and will unearth things that are buried in layers of obfuscation. Take full advantage of its power to uncover nuggets of free software that will save you tons of money going forward.

An important guideline to keep in mind when installing freeware is to pay careful attention to what you are doing. Most free versions of paid commercial software are sponsored by companies which want to get their message out. So, you might find that freeware is bundled with toolbars and other extraneous stuff you don’t want. Pay attention during the installation and make sure you uncheck unwanted items when options are presented as to what to install and what to leave out. Don’t complain later if you hit next without thinking or looking during the installation, and then find that your homepage has been redirected, and your browser sports a dozen new toolbars!

Happy computing, and good luck!

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Match Up
 Match each word in the left column with its synonym on the right. When finished, click Answer to see the results. Good luck!

Hangman

Spelling Bee
difficulty level:
score: -