Problem Solving

Introduction

Everyone must have felt at least once in his or her life how wonderful it would be if we could solve a problem at hand preferably without much difficulty or even with some difficulties. Unfortunately the problem solving is an art at this point and there are no universal approaches one can take to solving problems. Basically one must explore possible avenues to a solution one by one until one comes across a right path to a solution. Thus generally speaking, there is guessing and hence an element of luck involved in problem solving. However, in general, as one gains experience in solving problems, one develops one's own techniques and strategies, though they are often intangible. Thus the guessing is not an arbitrary guessing but an educated one.
In this chapter we are going to learn a framework for problem solving and get a glimpse of strategies that are often used by experts. They are based on the work of Polya.


A Framework for Problem Solving

The following four phases can be identified in the process of solving problems:

(1) Understanding the problem (see below)
(2) Making a plan of solution (see below)
(3) Carrying out the plan
(4) Looking back i.e. verifying

Each of the first two phases is going to be explained below a little more in detail. Phases (3) and (4) should be self-explanatory.

1. Understanding the Problem

Needless to say that if you do not understand the problem you can never solve it. It is also often true that if you really understand the problem, you can see a solution.
Below are some of the things that can help us understand a problem.

(1) Extract the principal parts of the problem.
The principal parts are:
For "find" type problems, such as "find the principal and return for a given investment", UNKNOWNS, DATA and CONDITIONS, and
for "proof" type problems HYPOTHESIS and CONCLUSION.

For examples that illustrate these, see Example 1, and Example 3, respectively.

Be careful about hidden assumptions, data and conditions.

(2) Consult definitions for unfamiliar (often even familiar) terminologies.

(3) Construct one or two simple example to illustrate what the problem says.



2. Devising a Solution Plan

Where to start ?
Start with the consideration of the principal parts: unknowns, data, and conditions for "find" problems, and hypothesis, and conclusion for "prove" problems.




What can I do ?
Once you identify the principal parts and understand them, the next thing you can do is to consider the problem from various angles and seek contacts with previously acquired knowledge. The first thing you should do is to try to find facts that are related to the problem at hand. Relevant facts usually involve words that are the same as or similar to those in the given problem. It is also a good idea to try to recall previously solved similar problems.


See "Some helpful tips" below for more.
 


What should I look for ?
Look for a helpful idea that shows you the way to the end. Even an incomplete idea should be considered. Go along with it to a new situation, and repeat this process.
Some helpful tips
There is no single method that works for all problems. However, there is a wealth of heuristics we can try. Following are some of the often used heuristics.
Add your own heuristics as you gain experience.

(1) Have I seen it before ?
That is, do I know similar or related problems ? Similar/related problems are ones with the same or a similar unknown or unknown may be different but the settings are the same or similar. See Example 2 for example.

(2) Do a little analysis on relationships among data, conditions and unknowns, or between hypothesis and conclusion.

(3) What facts do I know related to the problem on hand ?
These are facts on the subjects appearing in the problem. They often involve the same or similar words. An example can be found below.
It is very important that we know inference rules.

(4) Definitions: Make sure that you know the meaning of technical terms. This is obviously crucial to problem solving at any level. But especially at this level, if you know their meaning and understand the concepts, you can see a solution to most of the problems without much difficulty. See for example Example 1, and Example 2 below.

(5) Compose a wish list of intermediate goals and try to reach them.

(6) Have you used all the conditions/hypotheses ? : When you are looking for paths to a solution or trying to verify your solution, it is often a good idea to check whether or not you have used all the data/hypotheses. If you haven't, something is often amiss. See Example 4 for example.

(7) Divide into cases: Sometimes if you divide your problem into a number of separate cases based on a property of objects appearing in the problem, it simplifies the problem and clear your mind. For example if the problem concerns integers, then you may want to divide it into two cases: one for even numbers and the other for odd numbers as, for example, you can see in Example 3 below.

(8) Proof by contradiction: If you make an assumption, and that assumption produces a statement that does not make sense, then you must conclude that your assumption is wrong. For example, suppose that your car does not start. A number of things could be wrong. Let us assume for simplicity's sake that either the battery is dead or the starter is defective. So you first assume that the battery is dead and try to jump start it. If it doesn't start, you have a situation that does not make sense under your assumption of dead battery. That is, a good battery should start the car but it doesn't. So you conclude that your assumption is wrong. That is the battery is not the cause. Proof by contradiction follows that logic.

In this method we first assume that the assertion to be proven is not true and try to draw a contradiction i.e. something that is always false. If we produce a contradiction, then our assumption is wrong and therefore the assertion we are trying to prove is true. Example 3 below uses this method.

When you are stuck trying to justify some assertion, proof by contradiction is always a good thing to try.
(9) Transform/Restate the problem, then try (1) - (3) above.

(10) Working backward: In this approach, we start from what is required, such as conclusion or final (desired) form of an equation etc., and assume what is sought has been found. Then we ask from what antecedent the desired result could be derived. If the antecedent is found, then we ask from what antecedent that antecedent could be obtained. ... We repeat this process until either the data/hypotheses are reached or some easy to solve problem is reached. Example 4 and Example 5 below give simple examples of this approach.

(11) Simplify the problem if possible. Take advantage of symmetries which often exist.

Keep in mind that your first try may not work. But don't get discouraged. If one approach doesn't work, try another. You have to keep trying different approaches, different ideas. As you gain experience, your problem solving skills improve and you tend to find the right approach sooner.


Let us now look at some examples to illustrate the topics discussed above.


Next -- Problem Solving -- Example 1



Example 1
This is an example in which you can find a solution once you analyze and understand the unknowns and data.

Problem: A survey of TV viewers shows the following results:
To the question "Do you watch comedies ?", 352 answered "Yes".,
To the question "Do you watch sports ?", 277 answered "Yes", and
To the question "Do you watch both comedies and sports ?", 129 answered "Yes".

Given these data, find, among people who watch at least one of comedies and sports, percentages of people who watch at least one of comedies and sports watch only comedies, only sports, and both comedies and sports.

Let us try to solve this problem following the framework presented above.

Understanding the Problem: This is a "find" type problem. So we try to identify unknowns, data and conditions.
The unknowns are the percentage of people who watch only comedies, the percentage of people who watch only sports, and the percentage of people who watch both comedies and sports.
The data are the three numbers: 352, 277 and 129, representing the number of people who watch comedies, sports, and both comedies and sports, respectively. Note that 352 includes people who watch both comedies and sports as well as people who watch only comedies. Similarly for 277.
The conditions are not explicitly given in the problem statement. But one can see that the percentages must add up to 100, and they must be nonnegative.

Devising a Solution Plan: Here we first examine the principal parts in detail.
First let us consider the unknowns in more detail. To calculate the percentage of the people who watch only comedies, for example, we need the number of people who watch at least one of comedies and sports, and the number of people who watch only comedies. Thus actually two unknowns are involved in each of the required percentages, and the real unknowns are the number of people in each of the categories, and the number of people who watch at least one of comedies and sports.

Next let us look at the data. First the number 352 is the number of people who watch comedies. But that is not necessarily that of the people who watch only comedies. It includes that and the number of people who watch both comedies and sports. Similarly for the second number 277.

Let us use symbols to represent each of the unknowns: Let C represent the number of people who watch only comedies, S that of the people who watch only sports, and T that of the people who watch at least one of those programs.
Then we have the following relationships among the unknowns:
C + 129 = 352
S + 129 = 277
C + S + 129 = T

From these equations we can easily obtain C = 223, S = 148, and T = 500 .
Thus the required percentages are 44.6%, 29.6%, and 25.8%, respectively.

All we had to do to solve this problem is to analyze relationships between the data and the unknowns, that is, nothing much beyond "understanding the problem".


Next -- Problem Solving -- Example 2



Example 2
This is a problem which you can solve using similar known results.

Problem: Find the (length of) diagonal of a rectangular parallelepiped given its length, width and height.

Again let us try to solve this problem following the framework presented above.

Understanding the Problem: This is a "find" type problem. So we try to identify unknowns, data and conditions.
The unknown is the diagonal of a rectangular parallelepiped, and the data are its length, width and height. Again there are no explicitly stated conditions. But the unknown and data must all be a positive number.

Before proceeding to the next phase, let us make sure that we understand the terminologies.
First a rectangular parallelepiped is a box with rectangular faces like a cube except that the faces are not necessarily a square but a rectangle as shown below.



Next a diagonal of a rectangular parallelepiped is the line that connects its two vertices (corner points) that are not on the same plane. It is shown in the figure below.



Devising a Solution Plan: Here we first try to find relevant facts. Relevant facts often involve the same or similar words or concepts. Since the unknown is a diagonal, we look for facts concerning diagonal. Note that drawing figures here is quite helpful.
One of the facts that immediately comes to our mind in this problem is Pythagoras' theorem. It has to do with right triangles and is shown below.



Let us try to see whether or not this theorem helps. To use this theorem, we need a right triangle involving a diagonal of a parallelepiped. As we can see below, there is a right triangle with a diagonal x as its hypotenuse.



However, the triangle here involves two unknowns: x and y. Since x is what we are looking for, we need to find the value of y. To find y, we note another right triangle shown below.



Applying Pythagoras' theorem again, we can obtain the value of   y.
Thus   y² = a² + b²
is obtained from the second triangle, and
x² = c² + y²
is derived from the first triangle.
From these two equations, we can find that x is equal to the positive square root of   a² + b² + c² .


Next -- Problem Solving -- Example 3



Example 3
This is a proof type problem and "proof by contradiction" is used.

Problem: Given that a, b, and c are odd integers, prove that equation ax² + bx + c = 0 can not have a rational root.

Understanding the Problem: This is a "prove" type problem.
The hypothesis is that a, b, and c are odd integers, and the conclusion is that equation ax² + bx + c = 0 can not have a rational root.
The hypothesis is straightforward. In the conclusion, "rational root" means a root, that is, the value of x that satisfies the equation, and that can be expressed as m/n, where m and n are integers. So the conclusion means that there is no number of the form m/n that satisfies the equation under the hypothesis.

Devising a Solution Plan: For this problem, let us try "proof by contradiction". When you are asked to prove the impossibility of an event or non-existence of certain things, this approach often is quite helpful.

Following the "proof by contradiction", let us assume that the conclusion is false, that is the equation ax² + bx + c = 0 has a rational root m/n, where m and n are integers, when a, b, and c are odd integers. We can assume without loss of generality that m and n do not have any factors in common. Then
a(m/n)² + b(m/n) + c = 0 . ------------------------ (1)

Let us try to derive a contradiction from this.
First let us make this equation simpler, that is, let us get rid of fractions.
Since n is not equal to 0, multiplying the both sides of (1) by n², we get
am² + bmn + cn² = 0 . ------------------------ (2)

Since m is an integer, it is either even or odd. We are going to consider those cases one by one. That is "divide into cases".
Let us first consider the case when m is even.
Then n is odd, since otherwise m and n have a common factor 2. Now am² + bmn is even, and cn² is odd. Hence am² + bmn + cn² can not be 0.

Next let us consider the case when m is odd.
By an argument similar to the previous case, we can see that n is also odd.
If m and n are odd, then am², bmn, and cn² are all odd, since a, b, and c are odd integers. However, the sum of three odd numbers can not be equal to 0.

Thus by assuming that the conclusion is false, we have arrived at a contradiction, that is m/n does not satisfy the equation. Hence our assumption must be wrong, and therefore the conclusion is correct.


Next -- Problem Solving -- Example 4



Example 4
This is another proof type problem and "working backward" technique is used.

Problem: Prove that ( a + b + c )² 4( ab + bc + ca ) , if a, b, c are three sides of a triangle.

Understanding the Problem: This is a "prove" type problem.
The hypothesis is that a, b, and c are three sides of a triangle, and the conclusion is that inequality ( a + b + c )² 4( ab + bc + ca ) holds.

Devising a Solution Plan: Here we try "Working Backward" heuristic. That is manipulate the conclusion possibly using the hypothesis and reduce it into something that is obviously true.
First by multiplying out the left hand side of the inequality, ( a + b + c )² = a² + b² + c² + 2( ab + bc + ca ) .
Hence if a² + b² + c² 2( ab + bc + ca ) , then the conclusion holds.

Next, to see what we can try, note that we have not used the hypothesis yet, and see if it can help here.
It is well known that the sum of two sides of a triangle is greater than the third side.
Hence a + b > c , b + c > a , and c + a > b hold.
From these we can obtain c(a + b) > c² , a(b + c) > a² , and b(c + a) > b² .
By adding these three inequalities, we get
a² + b² + c² < a(b + c) + b(c + a) + c(a + b) = 2( ab + bc + ca ) .
Hence a² + b² + c² < 2( ab + bc + ca ) .
Hence a² + b² + c² 2( ab + bc + ca ) .
Hence ( a + b + c )² 4( ab + bc + ca ) holds.


Next -- Problem Solving -- Example 5


Example 5
This is a find type problem and "working backward" technique is used.

Problem: Given a 4 quart pail and a 9 quart pail, obtain 6 quarts of water in the 9 quart pail using these two pails. You can fill or empty the pails and you can have as much water as you want.

Understanding the Problem: This is a "find" type problem.
The problem is to obtain 6 quarts of water in the 9 quart pail using 4 quart and 9 quart pails as measures. You can fill either pail from the water source or from the other pail, and you can empty the pails any time.

Devising a Solution Plan: You can solve this in a number of different ways. Here we try "Working Backward" heuristic. It starts with the desired solution and work backward step by step. At each step we try to find a state that immediately precedes the current state such that we can reach the current state from that state with one simple operation such as filling a pail or emptying a pail in this problem. We repeat this process until we reach some easily reachable state such as empty pails, full pails, one pail full and the other empty, etc.
Our solution to the original problem is obtained by traversing this process backward to the desired state.

Let us denote the 9 quart pail by A and the 4 quart pail by B for simplicity.
In this problem, the desired state is to have 6 qts in A.



Thus in the first step of "working backward", we ask how we could get to the desired state with one operation.

As one can easily see if we could dump 3 qts from 9 qts in A, then we would have 6 qts in A. To be able to dump 3 qts from A we need 1 qt in B. Thus the state immediately preceding the current state is the one where A is full and B has 1 qt in it.



In the second step, the question we ask is how to get 1 qt in B.
It does not look easy to get 1 qt in B. So let us see whether or not we can get 1 qt in A. If we have 1 qt in A, then we can certainly get 1 qt in B without any trouble. thus we might say that the third state is to have 1 qt in A.



In the third step, the question we ask is how to get 1 qt in A.
This is relatively easy to accomplish because all you have to do is to get rid of 8 qts from a full A, which can be done by emptying A twice into B.





Since this state can be easily reached (all you have to do to get to this state is to fill A with water), we stop here. Our solution to the original problem is now obtained by going this process backward.

Thus first we fill up A. Then dump A into B leaving 5 qts in A. Then dump A into B again. This gives us 1 qt in A. Pour that into B. Then fill A and empty it into B. We now have 6 qts in A, which is what is required.

How To Lose Weight In 2 Weeks, Naturally

Losing weight quickly and naturally is a common goal, especially now that the weather is getting warmer and swimsuit season is coming. But is it really possible? 

More importantly, is it safe? Below you’ll find some important aspects to keep in mind when trying to learn how to lose weight in 2 weeks in a way that’s natural for your body:

Manage Your Expectations

Your health should be the top priority. That means that if you’re going to lose weight quickly, especially in two weeks, you need to do so in a way that isn’t going to damage your body. The best way to do that is to have realistic expectations before you even begin. It’s important to stay balanced and not be obsessed with shedding pounds. Losing weight too quickly can slow your body’s metabolism, meaning you might even put on weight if you try to lose too much, too fast. So keep a realistic perspective on your weight loss efforts, or you’ll end up sabotaging yourself.

Drink Water

One of the best tips for losing weight quickly is to drink a lot of water. A common mistake that people make is to replace fattening foods with sodas, milkshakes and sports drinks, which contain large amounts of calories and make it difficult to lose weight. Water is obviously calorie-free, so you can drink as much as you want. It will also reduce your appetite to a certain extent.

Avoid Simple Carbohydrates

Simple carbohydrates, such as those contained within bread and sugar, should be avoided when you’re trying to lose weight quickly. This is because they force your blood sugar levels to rise rapidly, which in turn increases the amount of sugar that’s converted into fat. The more you can avoid these foods the better.

Exercise

Arguably the most important part of losing weight quickly is frequent exercise. Within reason, the more you exercise, the more calories you’ll burn, and the more weight you’ll lose. The best approach is to increase your heart rate, which you can do with cardiovascular exercise, such as running, swimming or cycling.

A  Yoga and interval training are also thought to be effective for people trying to lose weight. It’s vital that you don’t overdo it, though, as that can cause injuries. It also doesn’t do any good in general to punish your body by doing excessive exercise. It’s much better to stay in tune with your body, concentrate on general fitness and exercise in ways that feel good to you. That will also help you feel motivated to continue doing it. With any kind of exercise, you should work your way up to full exertion only after you’ve warmed up, and stop if you get any pain or feel dizzy. It’s always a good idea to get a doctor’s opinion on your exercise routine before starting in order to ensure you’re physically able to do it safely.

The factors above can make a big difference when it comes to losing weight quickly. They’ll help you stay safe and sane as you shed those pounds!

Do You Have What It Takes To Lose Weight Fast?

 Let’s face it. Everyone wants to lose weight fast. When you’re fat, you don’t want to carry it around a minute longer than necessary.

But do you have what it takes…are you willing to do what’s necessary to lose weight fast?

What It Takes To Lose Weight Fast

Quick weight loss isn’t for the feint of heart. So before you decide to jump into a weight loss program, you should know what to expect and what you’ll need to succeed.

• First, you need to have a clear, unwavering goal and very strong reasons why you are going to put yourself through the mental and physical hardship that fast weight loss brings. With strong enough reasons, you can do anything. If you doubt me, imagine that your life – or the life of a loved one – literally depended on you reaching your weight loss goal. What if someone you loved were taken away if you fell even one pound shy of your weight loss goal? Do you think cheating on your diet would be an option. I hope not.
   
• You must be willing to forsake ALL junkfood for as long as it takes to reach your goal. Yes, there are weight loss programs, like Body For Life, that advocate “free” days or “cheat” days to eat whatever you want. But to lose weight fast…really fast…you must accept that no refined sugar shall touch your lips for the duration of your weight loss program.

• You must be willing to withstand near-constant feelings of hunger. A rapid reduction in weight demands that you eat far fewer calories than your body needs. Since your body’s #1 goal is survival, not losing body fat, it will create a very strong urge to eat when you can’t.

• To lose weight fast, you must be ready to give up cream and sugar in your coffee or tea; stop drinking sugar-filled soft drinks and all forms of juice; cut out all lattes…in other words, no liquid calories. The one exception to this would be something like the V-Diet, where all your calories come in the form of specially blended protein shakes.

• You must be ready to become a social perriah until you reach your weight loss goal. Nearly every social event or gathering has food connected to it in some way. When was the last time you attended a social function, even a casual visit with your best friend, that didn’t involve eating or drinking something? 

 If you must attend social events, are you strong enough to, either eat before you go and only drink “safe” beverages or even bring your own food along with you?

Once you reach the end of your weight loss journey, you need to ask an even tougher question…
Are you willing to say “Good-bye” to the habits that got you in trouble in the first place? If you don’t want the weight to come piling back on as quickly as it came off, you need to make some changes my friend.

It’s been said that the definition of insanity is doing the same thing over and over again and expecting different results. So, I ask you…
Are you insane? No? Then let me ask you…

Do you have what it takes to lose weight fast? Are you willing to do what it takes? If so, check out The V-Diet . It’s radical, but effective.

Another quick weight loss program I highly recommend is Warp Speed Fat Loss by Alwyn Cosgrove.

Should You Take Vitamins and Minerals?

                About 40 percent of Americans take at least one vitamin or mineral supplement daily and another 20 percent take them occasionally. Taking vitamins and minerals seems to fall within a gray area — giving your body what it needs by taking supplements certainly benefits you in every way, but knowing how to assess that need is often difficult. Without testing, it’s hard to say which vitamins and minerals you personally need. But these general guidelines apply if you’re in one of these special needs groups:

Pregnant and breast-feeding women

                    Women who are pregnant or breast-feeding generally need additional vitamins, and the B vitamins are particularly important. Folic acid reduces the risk for neural tube defects and possibly facial abnormalities, such as cleft palate, in newborns. Multivitamins also appear to protect against certain congenital heart defects. In order to be protective, however, both folic acid and multivitamin supplements must be taken before a woman actually becomes pregnant. Folate levels, even in a healthy diet, may not be protective enough for pregnant women, and so supplements are needed. 

                    The RDA for folic acid prior to conception and during pregnancy is 400 mcg. During breast-feeding, between 260 and 280 mcg is recommended. Choline, another B vitamin, is also essential for pregnant and nursing women — 450 mg during pregnancy and 550 when breast-feeding. Vitamin B6 may help improve morning sickness. Although one study suggested that if pregnant women take vitamin K supplements, their infants might not need the required injection of this vitamin after birth, supplements of vitamin K during pregnancy are not currently recommended.

                     Some women have low vitamin A reserves in their livers, but it is important to note that too much vitamin A significantly increases the risk for birth defects. Daily amounts of 10,000 IU of vitamin A in supplements and food (an amount not far above the RDA level) can pose a danger. Experts recommend that pregnant women take in no more than 8,000 IU per day and avoid eating liver.

Infants and children

                       Infants who are breast-fed by healthy mothers receive enough vitamins except, in some cases, vitamins K and D. Human milk has low levels of K, and the newborn’s immature intestinal tract may not produce enough to supply sufficient amounts to the baby. Most babies are given an injection of vitamin K at birth. Infants who are breast-fed by malnourished women or by those who lacked sufficient exposure to sunlight may be deficient in vitamin D. In these cases, supplements of 200-300 IU are recommended. 

                       Formulas are required to contain sufficient vitamins and minerals. One study suggests that when infants under 1 year of age take vitamin supplements it may help protect them from developing Type I diabetes later in life. Beyond infancy, most American children receive all the vitamins they need from their diets, unless they are living in severely deprived circumstances.

Smokers

                       Smoking interferes with absorption of a number of vitamins; most importantly, vitamin C. Folic acid supplements may be important for all smokers. When smokers take high doses of antioxidant vitamins, however, it may actually be harmful, especially beta-carotene. Instead of taking supplements, most smokers should be sure their diets are rich in fresh fruits and vegetables and whole grains.

Alcoholics

                      Alcoholics often suffer from multiple vitamin deficiencies. The most dangerous deficiencies are from vitamin B1 (thiamin), folic acid, vitamin B6 (pyridoxine), vitamin B2 (riboflavin) and vitamin C.

Dieters and vegetarians

                        People on weight-reduction diets of fewer than 1,000 calories per day should probably take multivitamins and should also check regularly with a physician. Vegetarians who do not eat dairy or meat products may need riboflavin, vitamin B12 and vitamin D supplements. Those who eat eggs and dairy products need only watch their iron levels.

Older adults

                        Deficiencies of vitamins and important minerals have been observed in almost one-third of elderly people, who often fail to eat balanced meals regularly. Multiple drug regimens that are prescribed for some elderly people may prevent absorption of some vitamins. The elderly, particularly if they are not exposed to sunlight, may be deficient in vitamin D. They also may have low levels of vitamin B6, folic acid and vitamin B12. (Older adults showing signs of dementia should be checked for vitamin B12 deficiencies as well as other disorders that cause mental disturbances.)

                      One study reported that the immune systems of elderly people might benefit from vitamin E in levels higher than the daily recommended dosage. It should be noted, however, that metabolism slows down as a person ages, and in elderly people it takes longer for the liver to eliminate drugs and vitamins from the body. The effect of some vitamin supplements, therefore, may be intensified. Dosage levels of vitamin A, for instance, which might be harmless in a younger adult, could be toxic in an elderly patient. Nevertheless, experts are increasingly recommending extra vitamins and minerals for older people.

Consider These Facts

• 13.5 million people have coronary heart disease.

• 1.5 million people suffer from a heart attack in a given year. 

• 95,000 people are diagnosed as having colon cancer each year. 

• 24 million Americans use diabetes supplies to control their blood sugar.

• 50 million people have high blood pressure. 

• Over 60 million people (one-third of our population) are overweight.

• 45 million Americans get headaches every day

The good news is that ALL the above conditions can be positively affected by maintaining a fitness program. But it's up to you to motivate yourself to be fit! No one can do it for you.

Physical Fitness Tips for Life-long Health

                  Do these excuses about taking care of your physical fitness seem familiar?

• You're too tired.
• You'll start tomorrow.
• You forgot to wash your workout clothes.
• You like cheesecake.

There are probably just as many excuses why you think you can't stay in shape, as there are good reasons why you should. Unfortunately, these excuses often outweigh any motivation to exercise or eat right. Sure, you want to look and feel your best, but why does staying fit have to be so much work?

It doesn't. You can have stronger, more limber muscles; lowered blood pressure and cholesterol levels; a strengthened immune system; and an improved self-image -- and you don't have to spend hours at a gym pumping iron or doing endless abs exercises. You also don't have to eat like a rabbit. Many of your daily activities burn more calories than you think. The chart below demonstrates how some of the functions you ordinarily perform burn calories and help keep you fit:

For the greatest benefit, 20 to 30 minutes of aerobic activity three or more times a week and some type of muscle-strengthening activity is recommended, along with stretching at least twice a week. If you are unable to maintain this level of activity, however, you can gain substantial health benefits by accumulating 30 minutes or more of moderate-intensity physical activity a day, at least five times a week.

The chart above demonstrates how some of the things you do every day can help fulfill that requirement. If you look at fitness as a lifetime pursuit, with everything you do contributing to it, even dressing your child or repairing your car's engine can be part of your "fitness philosophy."
Another way to make sure you get the exercise you need is an easy one - walking. It is not as strenuous as other forms of exercise, such as tennis or jogging, and you'll reap obvious benefits, whether you're a senior citizen or a teenager. You'll get more restful sleep, even if you've historically had trouble sleeping. You 'll also experience a release of tension and stress and a feeling of overall wellness. Walking can also result in weight loss when combined with a proper diet.

Need a nudge? Here are some walking fitness and weight loss tips to get you started:

• Walk with a buddy. You'll improve your overall fitness as you catch up with friends.
• Stretch before you begin. Muscles need to be warmed up to prevent injuries.
• Wear the correct shoes. They should be comfortable with a rubber sole to absorb the shock of each step, especially if you walk on concrete or asphalt.
• Adjust your pace. If you're huffing and puffing as you walk, you're exerting yourself too much.

Using an exercise bike at home is also a great form of exercise that's both fun and easy. If you don't already have one, it's a good idea to do some research to see what others consider to be the best exercise bikes on the market. Finding one that's comfortable for you can make a difference in how often you use it, so it's worth investing time to compare before you buy. Once you have the bike, you might consider putting it near a television, so you can fight off the boredom that may result from a long ride.

And if you work in an office, you're probably really at risk for not getting exercise. Thankfully, there are office exercises you can do to at least add to your cumulative exercise total for the week.

Last but not least, it's important to point out that you shouldn't get too carried away trying to achieve fast weight loss. As they say, slow and steady wins the race. You'll have a much better chance of keeping weight off and staying fit for life if you take a reasonable pace.

Eating Right is One of the Most Important Fitness Tips

Unfortunately, we humans sometimes have an appetite for fatty, salty and sugary foods. (Who wouldn't choose a chocolate éclair over a stalk of celery?) Denying yourself the occasional treat will only make you crave it more, however, so forget about completely eliminating those "forbidden" foods -- just make sure you only reach for the gooey dessert after answering "yes" to two questions:

1. Have you met your nutritional needs for the day?
2. Are you really still hungry?

And remember, while it's best to fuel your body by eating the recommended daily servings of whole grains, vegetables and fruits, it's a good idea to take a vitamin and mineral supplement to ensure that your nutritional needs are being met.

Don't forget that when you exercise, your body needs four to eight ounces of water every 20 minutes to replace water loss. This also holds true for everyday activities that are big calorie burners. Keep in mind that if you feel thirsty during exercise, you've already passed beyond a "safe" stage of hydration. If you are exercising vigorously for more than an hour, you may want to consider sports drinks -- the extra carbohydrates in these drinks help your body to retain body -- and always avoid caffeine or alcohol, both of which further dehydrate your body.

Be patient about seeing results from any fitness program. If you're out of shape, you didn't get that way overnight. You won't get back in shape overnight either. Work your way into a routine, one step at a time. Pushing yourself too hard after a long period of only exercising the finger that presses the button on the remote can result in injury. And don't be too concerned with the numbers on your scale. Your weight might actually climb -- muscles weigh more than fat -- so aim for a certain look in your clothes rather than how much you weigh.

Remember that you're less likely to stick with a fitness routine if you don't enjoy it or if it doesn't fit well into your daily life. An enjoyable fitness experience that works well for you can mean lifelong health, increased well-being and a happier life. This means that if you haven't done so already, you have every reason to start on the road to fitness today!

More Fitness-related Tips

• You can also incorporate fitness into your leisure time. For example, walking is an essential part of a theme park vacation. But you don't want to overdo it either, which can be easy to do when you're more focused on Mickey Mouse than just exactly how much you've walked in a day. If you're like so many people who hit the Orlando theme parks every year, an Orlando massage might be just what you need to make sure you balance the exercise with relaxation.

• It's important to stay healthy and protect your loved ones, so you owe it to yourself to understand term life insurance vs. whole life insurance. The information could make a big difference in your family's health and happiness if something should happen to you. 

 These Physical fitness tips can help just about any age.

Eye Exercises That Relieve Eye Strain

                 You’ve probably experienced it: Your eyes begin to water and twitch, and they burn when you close them. You’re suffering from a common condition — eye strain.


                 It happens when you stare at a road for a long time, work too long in front of the computer, watch too much television, or focus on any task that requires you to look up close for any length of time.

                  Fortunately, there are easy eye exercises that can relax and even strengthen the eyes. No exercise can cure an eye ailment, but doing the following exercises regularly can be beneficial if a weakness or imbalance of the eye muscles causes vision problems, especially eye strain:

               Eye push-ups
               This exercise trains your eyes to work together to aim at the same task, which can help prevent eyestrain.
                Hold a pen in front of your face, about an arm’s length away. Move it toward your nose slowly, staring at the same place on the pen. Bring the pen as close as you can to the tip of your nose before you see a double image.

                 Change your focus
                  This exercise helps you cut down on eye fatigue.

                  Hold a book or newspaper as close to your eyes as you can without the print becoming blurred. Stare at the words for 15 seconds. Then, look at an object approximately 10 feet away and stare at that for 15 seconds. Repeat five times.

                  The eye roller coaster
                   This exercise improves the flow of blood and oxygen to your eyes.

                    Close your eyes and slowly roll them in a complete circle. Then, move them from right to left.   

                                  Repeat three times.

                    Palming and cupping

                    This exercise relaxes your eyes.
                     If you wear contact lenses, remove them. Close your eyes and put the fleshy part of your palms over them. Press gently for a few seconds. Then, cup your hands over your open eyes. Keep your eyes open and look into your palms as you breathe slowly through your nose for 30 seconds.
Although it might seem simplistic, blinking and yawning are also beneficial because they produce tears that lubricate the eyes. And you can also help your eyes by taking nutritional supplements that contain bilberry, vitamin A and lutein. You might also want to try these healthy recipes that contain vitamins that help with eye problems.

Biomedical Research

Biomedical engineering

 

A JARVIK-7 artificial heart, an example of a biomedical engineering application of mechanical engineering with biocompatible materials for cardiothoracic surgery using an artificial organ.

 

Example of an approximately 40,000 probe spotted oligo microarray with enlarged inset to show detail.

 

 

Biomedical engineering is the application of engineering principles and techniques to the medical field. This field seeks to close the gap between engineering and medicine. It combines the design and problem solving skills of engineering with medical and biological sciences to improve healthcare diagnosis and treatment.

Biomedical engineering has only recently emerged as its own discipline, compared to many other engineering fields; such an evolution is common as a new field transitions from being an interdisciplinary specialization among already-established fields, to being considered a field in itself. Much of the work in biomedical engineering consists of research and development, spanning a broad array of subfields (see below). Prominent biomedical engineering applications include the development of biocompatible prostheses, various diagnostic and therapeutic medical devices ranging from clinical equipment to micro-implants, common imaging equipment such as MRIs and EEGs, biotechnologies such as regenerative tissue growth, and pharmaceutical drugs and biopharmaceuticals.

 

Subdisciplines within biomedical engineering

Biomedical engineering is a highly interdisciplinary field, influenced by (and overlapping with) various other engineering and medical fields. This often happens with newer disciplines, as they gradually emerge in their own right after evolving from special applications of extant disciplines. Due to this diversity, it is typical for a biomedical engineer to focus on a particular subfield or group of related subfields. There are many different taxonomic breakdowns within BME, as well as varying views about how best to organize them and manage any internal overlap; the main U.S. organization devoted to BME divides the major specialty areas as follows:

• Biomechatronics
• Bioinstrumentation
• Biomaterials
• Biomechanics
• Bionics
• Cellular, Tissue, and Genetic Engineering
• Clinical Engineering
• Medical Imaging
• Orthopaedic Bioengineering
• Rehabilitation engineering
• Systems Physiology
• Bionanotechnology
• Neural Engineering

Sometimes, disciplines within BME are classified by their association(s) with other, more established engineering fields, which can include:

•     Chemical engineering - often associated with biochemical, cellular, molecular and tissue engineering, biomaterials, and biotransport.
•     Electrical engineering - often associated with bio electrical and neural engineering, bioinstrumentation, biomedical imaging, and medical devices. This also tends to encompass Optics and Optical engineering - biomedical optics, imaging and related medical devices.
•     Mechanical engineering - often associated with biomechanics, biotransport, medical devices, and modeling of biological systems, like soft tissue mechanics.

Biotechnology and pharmaceuticals

Biotechnology (see also relatedly bioengineering) can be a somewhat ambiguous term, sometimes loosely used interchangeably with BME in general; however, it more typically denotes specific products which use "biological systems, living organisms, or derivatives thereof." Even some complex "medical devices" (see below) can reasonably be deemed "biotechnology" depending on the degree to which such elements are central to their principle of operation. Biologics/Biopharmaceuticals (e.g., vaccines, stored blood product), genetic engineering, and various agricultural applications are some major classes of biotechnology.

Pharmaceuticals are related to biotechnology in two indirect ways: 1) certain major types (e.g. biologics) fall under both categories, and 2) together they essentially comprise the "non-medical-device" set of BME applications. (The "Device - Bio/Chemical" spectrum is an imperfect dichotomy, but one regulators often use, at least as a starting point.)

Tissue engineering

Tissue engineering is a major segment of Biotechnology.

One of the goals of tissue engineering is to create artificial organs (via biological material) for patients that need organ transplants. Biomedical engineers are currently researching methods of creating such organs. Researchers have grown solid jawbones and tracheas from human stem cells towards this end. Several bladders actually have been grown in laboratories and transplanted successfully into patients. Bioartificial organs, which use both synthetic and biological components, are also a focus area in research, such as with hepatic assist devices that use liver cells within an artificial bioreactor construct.

Micromass cultures of C3H-10T1/2 cells at varied oxygen tensions stained with Alcian blue.

Genetic engineering

Genetic engineering, recombinant DNA technology, genetic modification/manipulation (GM) and gene splicing are terms that apply to the direct manipulation of an organism's genes.[1] Genetic engineering is different from traditional breeding, where the organism's genes are manipulated indirectly. Genetic engineering uses the techniques of molecular cloning and transformation to alter the structure and characteristics of genes directly. Genetic engineering techniques have found success in numerous applications. Some examples are in improving crop technology (not a medical application per se; see BioSystems Engineering), the manufacture of synthetic human insulin through the use of modified bacteria, the manufacture of erythropoietin in hamster ovary cells, and the production of new types of experimental mice such as the oncomouse (cancer mouse) for research.

Neural engineering

Neural engineering (also known as Neuroengineering) is a discipline that uses engineering techniques to understand, repair, replace, or enhance neural systems. Neural engineers are uniquely qualified to solve design problems at the interface of living neural tissue and non-living constructs.

Pharmaceutical engineering

Pharmaceutical Engineering is sometimes regarded as a branch of biomedical engineering, and sometimes a branch of chemical engineering; in practice, it is very much a hybrid sub-discipline (as many BME fields are). Aside from those pharmaceutical products directly incorporating biological agents or materials, even developing chemical drugs is considered to require substantial BME knowledge due to the physiological interactions inherent to such products' usage.

Medical devices

This is an extremely broad category -- essentially covering all health care products that do not achieve their intended results through predominantly chemical (e.g., pharmaceuticals) or biological (e.g., vaccines) means, and do not involve metabolism.

A medical device is intended for use in:

• the diagnosis of disease or other conditions, or
• in the cure, mitigation, treatment, or prevention of disease

A pump for continuous subcutaneous insulin infusion, an example of a biomedical engineering application of electrical engineering to medical equipment.

 

Some examples include pacemakers, infusion pumps, the heart-lung
machine, dialysis machines, artificial organs, implants, artificial
limbs, corrective lenses, cochlear implants, ocular prosthetics, facial
prosthetics, somato prosthetics, and dental implants.

Biomedical instrumentation amplifier schematic used in monitoring low voltage biological signals, an example of a biomedical engineering application of electronic engineering to electrophysiology.

 

 

Stereolithography is a practical example of medical modeling being used to create physical objects. Beyond modeling organs and the human body, emerging engineering techniques are also currently used in the research and development of new devices for innovative therapies, treatments, patient monitoring, and early diagnosis of complex diseases.

Medical devices are regulated and classified (in the US) as follows (see also Regulation):

1. Class I devices present minimal potential for harm to the user and are often simpler in design than Class II or Class III devices. Devices in this category include tongue depressors, bedpans, elastic bandages, examination gloves, and hand-held surgical instruments and other similar types of common equipment.
2. Class II devices are subject to special controls in addition to the general controls of Class I devices. Special controls may include special labeling requirements, mandatory performance standards, and postmarket surveillance. Devices in this class are typically non-invasive and include x-ray machines, PACS, powered wheelchairs, infusion pumps, and surgical drapes.
3. Class III devices generally require premarket approval (PMA) or premarket notification (510k), a scientific review to ensure the device's safety and effectiveness, in addition to the general controls of Class I. Examples include replacement heart valves, hip and knee joint implants, silicone gel-filled breast implants, implanted cerebellar stimulators, implantable pacemaker pulse generators and endosseous (intra-bone) implants.

 

Medical imaging

Medical/biomedical imaging is a major segment of medical devices. This area deals with enabling clinicians to directly or indirectly "view" things not visible in plain sight (such as due to their size, and/or location). This can involve utilizing ultrasound, magnetism, UV, other radiology, and other means.

An MRI scan of a human head, an example of a biomedical engineering application of electrical engineering to diagnostic imaging. 

 

Imaging technologies are often essential to medical diagnosis, and are typically the most complex equipment found in a hospital including:   

* Fluoroscopy
    * Magnetic resonance imaging (MRI)
    * Nuclear medicine
    * Positron emission tomography (PET) PET scansPET-CT scans
    * Projection radiography such as X-rays and CT scans
    * Tomography
    * Ultrasound
    * Optical microscopy
    * Electron microscopy

Implants

An implant is a kind of medical device made to replace and act as a missing biological structure (as compared with a transplant, which indicates transplanted biomedical tissue). The surface of implants that contact the body might be made of a biomedical material such as titanium, silicone or apatite depending on what is the most functional. In some cases implants contain electronics e.g. artificial pacemaker and cochlear implants. Some implants are bioactive, such as subcutaneous drug delivery devices in the form of implantable pills or drug-eluting stents.

Artificial limbs: The right arm is an example of a prosthesis, and the left arm is an example of myoelectric control.

 

A prosthetic eye, an example of a biomedical engineering application of mechanical engineering and biocompatible materials to ophthalmology.

 

Clinical engineering

Clinical engineering is the branch of biomedical engineering dealing with the actual implementation of medical equipment and technologies in hospitals or other clinical settings. Major roles of clinical engineers include training and supervising biomedical equipment technicians (BMETs), selecting technological products/services and logistically managing their implementation, working with governmental regulators on inspections/audits, and serving as technological consultants for other hospital staff (e.g. physicians, administrators, I.T., etc.). Clinical engineers also advise and collaborate with medical device producers regarding prospective design improvements based on clinical experiences, as well as monitor the progression of the state-of-the-art so as to redirect procurement patterns accordingly.

Their inherent focus on practical implementation of technology has tended to keep them oriented more towards incremental-level redesigns and reconfigurations, as opposed to revolutionary research & development or ideas that would be many years from clinical adoption; however, there is a growing effort to expand this time-horizon over which clinical engineers can influence the trajectory of biomedical innovation. In their various roles, they form a "bridge" between the primary designers and the end-users, by combining the perspectives of being both 1) close to the point-of-use, while 2) trained in product and process engineering. Clinical Engineering departments will sometimes hire not just biomedical engineers, but also industrial/systems engineers to help address operations research/optimization, human factors, cost analysis, etc. Also see safety engineering for a discussion of the procedures used to design safe systems.

Schematic representation of a normal ECG trace showing sinus rhythm; an example of widely-used clinical medical equipment (operates by applying electronic engineering to electrophysiology and medical diagnosis.

Regulatory issues are of particular concern to a biomedical engineer; it is among the most heavily-regulated fields of engineering, and practicing biomedical engineers must routinely consult and cooperate with regulatory law attorneys and other experts. The Food and Drug Administration (FDA) is the principal healthcare regulatory authority in the United States, having jurisdiction over medical devices, drugs, biologics, and combination products. The paramount objectives driving policy decisions by the FDA are safety and efficacy of healthcare products.

In addition, because biomedical engineers often develop devices and technologies for "consumer" use, such as physical therapy devices (which are also "medical" devices), these may also be governed in some respects by the Consumer Product Safety Commission. The greatest hurdles tend to be 510K "clearance" (typically for Class 2 devices) or pre-market "approval" (typically for drugs and class 3 devices).

Implants, such as artificial hip joints, are generally extensively regulated due to the invasive nature of such devices.

 

Most countries have their own particular mechanisms for regulation, with varying formulations and degrees of restrictiveness. In most European countries, more discretion rests with the prescribing doctor, while the regulations chiefly assure that the product operates as expected. In European Union nations, the national governments license certifying agencies, which are for-profit companies. Technical committees of engineers write recommendations which incorporate public comments, and these can be adopted as regulations by the European Union. These recommendations vary by the type of device, and specify tests for safety and efficacy. Once a prototype has passed the tests at a certification lab, and that model is being constructed under the control of a certified quality system, the device is entitled to bear a CE mark, indicating that the device is believed to be safe and reliable when used as directed.

The different regulatory arrangements sometimes result in particular technologies being developed first for either the U.S. or in Europe depending on the more favorable form of regulation. While nations often strive for substantive harmony to facilitate cross-national distribution, philosophical differences about the optimal extent of regulation can be a hindrance; more restrictive regulations seem appealing on an intuitive level, but critics decry the tradeoff cost in terms of slowing access to life-saving developments.

Chocolate as a Health Food?

               Nothing beats a good piece of chocolate. It’s rich, smooth, creamy and makes us feel good, until the guilt sets in.  
               Chocolate’s mood-enhancing qualities are an obvious reason why it is so strongly associated with Valentine’s Day, as a gift for lovers and loved ones.

Chocolate's Dark Secret

                     There’s no getting around the fact that chocolate is a high fat food. But there is growing evidence that, in small quantities, some kinds of chocolate may actually be good for you. Dark chocolate is naturally rich in flavonoids (or more specifically, flavanols, a sub-class of these antioxidants). These compounds are thought to lower blood pressure and help protect against heart disease—among other things. Recent studies conducted both in the U.S. and Europe seem to support chocolate’s beneficial effects on the cardiovascular system, encouraging chocolate manufacturers, such as Mars, to develop proprietary methods of processing cocoa beans aimed specifically at preserving flavonoid content. Traditional roasting and fermentation methods are thought to destroy up to three-quarters of these compounds. Mars uses its Cocoapro trademark on some of its products, indicating the use of this method, and Swiss premium chocolate company Barry Callebaut uses Acticoa.

What about the Fat?

                     It’s still hard to think of chocolate as a health food. Part of the allure is the guilty pleasure of eating it. But before we raid the candy store, it’s worth remembering that chocolate is not a low calorie food. A serving size of Dove dark chocolate (40 grams) contains 210 calories and 13 grams of fat, 8 of which are saturated, although some of this saturated fat is in the form of stearic acid, which is converted by the liver into a "healthier" monounsaturated fat.

Cocoa Powder

                  Cocoa powder, which is low fat, would surely be a healthier way to get both our chocolate fix and our dose of flavanols. Alkalizing cocoa (or Dutch processing) produces a milder flavor and darker color but destroys most of the flavonoids. Since flavanol-rich cocoa is naturally bitter, Mars has worked hard to make it palatable.
                  First, it sold a flavanol-rich series of snack bars and small chocolate bars. These bars were shown in one small study to actively lower total and LDL (bad) cholesterol in those with elevated cholesterol levels, bolstering Mars' claim that its flavanol-rich snack bars were heart healthy.
                  More recently, Mars Botanicals launched CirkuHealth, a cocoa-extract supplement that can be added to drinks and cereals, and Barry Callebaut offers a high-flavanol cocoa powder, which gives chocoholics a healthier, low-fat alternative to high-fat chocolate bars. Still, when the urge to eat chocolate strikes, it's fine to allow ourselves an occasional ounce of flavanol-rich dark chocolate. It'll make us feel good, and it may even do some good.

• Low Fat Chocolate Truffles
• Reduced-Fat Chocolate Pudding
• Chocolate Dipped Strawberries
• Low Fat Chocolate Chip Cookies
• Low Fat Fudge Brownies
• Chocolate Bread Pudding
• Chocolate Chip Muffins
• Conquering High Cholesterol

               You can finally start to see those numbers come down. Take charge of this important aspect of your health.

Why is Dark Chocolate Healthy?

                  Chocolate is made from plants, which means it contains many of the health benefits of dark vegetables. These benefits are from flavonoids, which act as antioxidants. Antioxidants protect the body from aging caused by free radicals, which can cause damage that leads to heart disease. Dark chocolate contains a large number of antioxidants (nearly 8 times the number found in strawberries). Flavonoids also help relax blood pressure through the production of nitric oxide, and balance certain hormones in the body. 

Heart Health Benefits of Dark Chocolate:

                    Dark chocolate is good for your heart. A small bar of it everyday can help keep your heart and cardiovascular system running well. Two heart health benefits of dark chocolate are:

• Lower Blood Pressure: Studies have shown that consuming a small bar of dark chocolate everyday can reduce blood pressure in individuals with high blood pressure.
• Lower Cholesterol: Dark chocolate has also been shown to reduce LDL cholesterol (the bad cholesterol) by up to 10 percent.

Other Benefits of Dark Chocolate:

       Chocolate also holds benefits apart from protecting your heart:

• it tastes good
• it stimulates endorphin production, which gives a feeling of pleasure
• it contains serotonin, which acts as an anti-depressant
• it contains theobromine, caffeine and other substances which are stimulants.

Doesn't Chocolate Have a lot of Fat?:

                 Here is some more good news -- some of the fats in chocolate do not impact your cholesterol. The fats in chocolate are 1/3 oleic acid, 1/3 stearic acid and 1/3 palmitic acid:

• Oleic Acid is a healthy monounsaturated fat that is also found in olive oil.
• Stearic Acid is a saturated fat but one which research is shows has a neutral effect on cholesterol.
• Palmitic Acid is also a saturated fat, one which raises cholesterol and heart disease risk.

          That means only 1/3 of the fat in dark chocolate is bad for you.

Chocolate Tip 1 - Balance the Calories:

                 This information doesn't mean that you should eat a pound of chocolate a day. Chocolate is still a high-calorie, high-fat food. Most of the studies done used no more than 100 grams, or about 3.5 ounces, of dark chocolate a day to get the benefits.
One bar of dark chocolate has around 400 calories. If you eat half a bar of chocolate a day, you must balance those 200 calories by eating less of something else. Cut out other sweets or snacks and replace them with chocolate to keep your total calories the same.

Chocolate Tip 2 - Taste the Chocolate:

               Chocolate is a complex food with over 300 compounds and chemicals in each bite. To really enjoy and appreciate chocolate, take the time to taste it. Professional chocolate tasters have developed a system for tasting chocolate that include assessing the appearance, smell, feel and taste of each piece.

Chocolate Tip 3 - Go for Dark Chocolate:

               Dark chocolate has far more antioxidants than milk or white chocolate. These other two chocolates cannot make any health claims. Dark chocolate has 65 percent or higher cocoa content.

Chocolate Tip 4 - Skip the Nougat:

                You should look for pure dark chocolate or dark chocolate with nuts, orange peel or other flavorings. Avoid anything with caramel, nougat or other fillings. These fillings are just adding sugar and fat which erase many of the benefits you get from eating the chocolate.

Chocolate Tip 5 - Avoid Milk:

                 It may taste good but some research shows that washing your chocolate down with a glass of milk could prevent the antioxidants being absorbed or used by your body.

How To Taste Chocolate

                  Tasting chocolate is much like tasting fine wine -- there are subtleties of flavor and tones that you can train yourself to appreciate. Also like wine, professional chocolate tasters have developed a procedure for judging the qualities of a piece of chocolate. So find the best dark chocolate you can, reap the health benefits of good chocolate and enjoy.

Difficulty: Easy

Time Required: 5 minutes

Here's How:

1. Room Temperature              For best tasting, chocolate should be at room temperature. This allows the chocolate to begin to melt the moment it hits your mouth. Cold chocolate doesn't release its flavors and aromas as quickly, altering the tasting experience.
2. Be Still               You can't appreciate good chocolate if the phone is ringing or you are checking your e-mail. Chocolate comes from all over the world to end up in your house, so turn off the TV and give the chocolate some respect. It will reward you for it.
3. Clear Your Palate             You don't want other tastes interfering with your experience of the chocolate. Make sure no flavors are lingering in your mouth before you begin tasting your chocolate. A piece of apple, a bit of bread or (believe or not) a bite of a pickle are all said to erase flavors in your mouth.
4. Look at the Chocolate             Chocolate experts use the appearance of the chocolate as one of many criteria to judge its quality. Good chocolate should have a shiny, even gloss on its surface. If chocolate is too old, it will develop a hazy finish called 'bloom.' The color of the chocolate depends on the origin of the beans and the roasting process. The color should be uniform for the entire bar. Also examine the detail and care that has been put into creating the chocolate bar. Are the edges clean? Is the molding clear? Has extra effort been put into making an even, uniform bar?
5. Break Off a Piece          Break your piece of chocolate in half and listen to the sound. High quality chocolate produces a sharp, crisp sound and a clean edge. This is called the chocolate's "snap." The higher the cocoa quantity and the better the tempering, the louder the "snap" of the chocolate. Professional chocolate tasters can tell a great deal about the quality of chocolate just by this sound.
6. Rub It             Take your finger and rub just a bit of the chocolate. The chocolate should feel smooth and even. The warmth of your body will cause the chocolate to melt and release odors. These odors will enhance the intensity of your tasting.
7. Smell the Chocolate             Much like wine experts, chocolate experts can find an incredible array of scents and aromas. Some chocolate flavors include:
   
   
   • burnt bread
   • nutty
   • spicy
   • fruity
   The list could continue forever. When you begin tasting chocolate, these aromas probably won't be clear to you. That's okay. Spend more time just smelling the chocolate. Warm it up more with your finger, close your eyes, and let your smell-imagination run wild. Eventually different chocolates will recall different odors. You will start to know which regions of the world produce chocolate with which aromas.
8. Feel the Chocolate in Your Mouth                Good chocolate should literally "melt in your mouth." Chocolate melts at about 97 degrees. While melting the chocolate should feel rich and luscious in your mouth. You should not need to chew good chocolate at all, just let the flavors release on their own. Examine the texture of the chocolate -- it can vary from smooth to grainy. Good chocolate has a rich, velvety texture. Poor quality chocolate feels waxy or greasy.
9. Taste It                     Finally, you should taste the chocolate. You can chew if you want, but just a couple of times. Like with smelling the chocolate, pay attention to the flavors that just pop into your head. These could be the same as what you smelled, or completely different. Spend time being aware of how the flavors change over time as the chocolate continues to melt and coat more of your mouth. 
10. The Finish              As the last of the chocolate leaves your mouth, the lingering flavor is known as the 'finish' of the chocolate. Good chocolate should have a complex, interesting finish that is not bitter or unpleasant. The finish is an important part of the tasting, as many of the early flavors may be masked by other ingredients in the chocolate. 

Tips:

1. When tasting many kinds of chocolate at one sitting, always taste from lowest percentage of cocoa to highest.
2. Store your chocolate in a dry, dark and cool place to avoid 'blooming' and other signs of aging.
3. Remember to balance the calories in chocolate by eating less of something else.
4. If you are having trouble sleeping at night, do not eat chocolate close to bedtime.

Top 5 Chocolate Bars for Spice Lovers

                   Discerning chocolate lovers and spice aficionados alike will thrill to these unique chocolate bars, made from a blend of top-notch chocolate and exotic spices.

1. Chocolove Chilies & Cherries in 55% Dark Chocolate

Image courtesy of Chocolove/© Timothy Moley

                 Ancho and chipotle chilies lend smoky spice notes to this intriguing bar. Chewy dried cherries make for a nice textural contrast to the smooth dark chocolate, and their sweetness is a fantastic counterpoint to the chilies' pleasant bite. If spicy-sweet chocolate isn't enough to get your blood pumping, there's a love poem printed inside the wrapper. Scroll K Dairy Kosher certified.

2. Theo 3400 Phinney Fig, Fennel & Almond Dark Chocolate

This grown-up dark chocolate bar may set you to dreaming of a trip to Mediterranean climes, with its sophisticated blend of fennel, dried figs, and slivered almonds. Organic, Fair Trade certified™, and Vegan.

3. Chuao Chocolatier Chinita Nibs Bar Set

Image courtesy of Chuao Chocolatier

            Venezuelan single origin chocolate is studded with caramelized cocoa nibs and flavored with freshly ground nutmeg. Coffee lovers take note: Chuao recommends pairing the Chinita Nibs chocolate bar with coffee or espresso, for an enhanced tasting experience.

4. Jacques Torres Gingerette Bar

Image courtesy of Jacques Torres Chocolate

                   Renowned pastry chef Jacques Torres, aka "Mr. Chocolate," loads his signature 60% dark chocolate with sulphur dioxide-free crystallized ginger. Lest anyone think Torres is kidding when he calls his ginger "super strong," this chocolate bar has its own "No Wimps. No Whiners." tag line. In other words, it's just perfect for proud ginger connoisseurs.

5. Vosges Haut-Chocolat Naga Exotic Candy Bar

Image courtesy of Vosges Haut Chocolat

                   Sweet Indian curry powder and coconut flakes enhance deep milk chocolate, made with 41% cacao. The first flavor created by Vosges owner and chocolatier Katrina Markoff, the Naga bar comes with tasting notes, and is manufactured in a facility powered by renewable energy.

Dark Chocolate Brownies

These rich and chewy brownies will satisfy any sweet tooth or chocolate craving. Nothing beats home-made chocolate brownies, baked from scratch.

Ingredients:

• 2 oz unsweetened chocolate, chopped
• 2 oz semisweet chocolate, chopped
• 2/3 cup butter
• 1 cup white sugar
• 3/4 c brown sugar, packed
• 3 eggs
• 1 1/2 cups flour
• 1/2 tsp salt
• 2 tsp vanilla
• 1 1/2 cups chopped walnuts

 

 Preparation:

           Preheat oven to 375F. Melt butter with chocolate in a large saucepan, over low heat. Remove from heat and stir in both sugars, eggs, flour, salt, vanilla and nuts. Spread batter into a greased 9x9x2 baking pan. Bake uncovered for 35-40 minutes, or until they start to pull away from the edges of the pan. Cool for at least half an hour before slicing.
 
Makes 16 brownies.