I remember a childhood story. Two love birds built a beautiful nest for their family with so much of effort. One day, after long search for food, they came back late to their nest. They were shocked to see another bird occupying their nest. The love birds told him, "It is our nest and we built with so much of effort". He replied them, "I found it and it is mine now". The love birds fought with him for days. Later they realized that they were wasting their time and energy, and it was not worth fighting anymore. They moved on to a different location and started their family.
Our history has been tainted with so much of bad events. People made mistakes and have been making them. I am sure that no country or society is perfect. But is it worth fighting for some past events? How much is worth for you and your children? Can you make some reasonable compromises for the sake of peace, your own peace, your children's peace? After all, the innocent people you are killing not your real enemies. Remember, destruction is so easy; do not think that you have achieved something. If you really want to show something great, then create something... make your society, your country a better place where freedom and knowledge blossom, men and women equal, no poverty and everybody is happy... show this to the world and to your enemy.
Oh, I forget it... you may not understand any of this logic, as you just follow some blind faith without any reasoning. There is a bad attitude in our society that it is OK to believe in something without any reasoning. It creates a platform, a foundation, a hideout for those go to extremes.
In this global village, everybody is dependent on each other like never before. If some group or segment or country falls behind, it is everybody's duty to bring them up; else it would affect every one of us. We have so much knowledge and power to create; at the same time, weapons to destroy entire earth in seconds. Together we can rise up, else we will fall together!
Our history has been tainted with so much of bad events. People made mistakes and have been making them. I am sure that no country or society is perfect. But is it worth fighting for some past events? How much is worth for you and your children? Can you make some reasonable compromises for the sake of peace, your own peace, your children's peace? After all, the innocent people you are killing not your real enemies. Remember, destruction is so easy; do not think that you have achieved something. If you really want to show something great, then create something... make your society, your country a better place where freedom and knowledge blossom, men and women equal, no poverty and everybody is happy... show this to the world and to your enemy.
Oh, I forget it... you may not understand any of this logic, as you just follow some blind faith without any reasoning. There is a bad attitude in our society that it is OK to believe in something without any reasoning. It creates a platform, a foundation, a hideout for those go to extremes.In this global village, everybody is dependent on each other like never before. If some group or segment or country falls behind, it is everybody's duty to bring them up; else it would affect every one of us. We have so much knowledge and power to create; at the same time, weapons to destroy entire earth in seconds. Together we can rise up, else we will fall together!
I remember a childhood story. Two love birds built a beautiful nest for their family with so much of effort. One day, after long search for food, they came back late to their nest. They were shocked to see another bird occupying their nest. The love birds told him, "It is our nest and we built with so much of effort". He replied them, "I found it and it is mine now". The love birds fought with him for days. Later they realized that they were wasting their time and energy, and it was not worth fighting anymore. They moved on to a different location and started their family.
Our history has been tainted with so much of bad events. People made mistakes and have been making them. I am sure that no country or society is perfect. But is it worth fighting for some past events? How much is worth for you and your children? Can you make some reasonable compromises for the sake of peace, your own peace, your children's peace? After all, the innocent people you are killing not your real enemies. Remember, destruction is so easy; do not think that you have achieved something. If you really want to show something great, then create something... make your society, your country a better place where freedom and knowledge blossom, men and women equal, no poverty and everybody is happy... show this to the world and to your enemy.
Oh, I forget it... you may not understand any of this logic, as you just follow some blind faith without any reasoning. There is a bad attitude in our society that it is OK to believe in something without any reasoning. It creates a platform, a foundation, a hideout for those go to extremes.
In this global village, everybody is dependent on each other like never before. If some group or segment or country falls behind, it is everybody's duty to bring them up; else it would affect every one of us. We have so much knowledge and power to create; at the same time, weapons to destroy entire earth in seconds. Together we can rise up, else we will fall together!
Our history has been tainted with so much of bad events. People made mistakes and have been making them. I am sure that no country or society is perfect. But is it worth fighting for some past events? How much is worth for you and your children? Can you make some reasonable compromises for the sake of peace, your own peace, your children's peace? After all, the innocent people you are killing not your real enemies. Remember, destruction is so easy; do not think that you have achieved something. If you really want to show something great, then create something... make your society, your country a better place where freedom and knowledge blossom, men and women equal, no poverty and everybody is happy... show this to the world and to your enemy.Oh, I forget it... you may not understand any of this logic, as you just follow some blind faith without any reasoning. There is a bad attitude in our society that it is OK to believe in something without any reasoning. It creates a platform, a foundation, a hideout for those go to extremes.In this global village, everybody is dependent on each other like never before. If some group or segment or country falls behind, it is everybody's duty to bring them up; else it would affect every one of us. We have so much knowledge and power to create; at the same time, weapons to destroy entire earth in seconds. Together we can rise up, else we will fall together!
Pronounce the following sets of numbers: [10, 11, 12, ...], [20, 21, 22, ...], [30, 31, 32,...], [40, 41, 42, ...], and so on. Notice that the first set [10, 11, 12, ...] does not follow how others sets are pronounced. You might have probably wondered about it before. In my native language Tamil all the sets follow the same patterns of pronunciation. So, I immediately noticed the odds of Eleven and Twelve when I learned English. The reason for this odds lies behind how number theory evolved over the time.
In my early childhood we lived in a small village. Everyday, the milkman delivers milk to my home and mark a line on the house wall. On the fifth day, he crosses the last four lines and starts a new one. This is how he counts the number of days he delivered milk. This is very early form of numbering system. Imagine writing 118 in this system; it would take lot of space.
Roman number system uses the same idea, except it introduces new symbols for 5 = V, 10 = X, 100 = C, etc. For example: CXVIII is 100 + 10 + 5 + 3 = 118. Hence, Roman number system is based additive principle (Also note that instead of writing 4 as IIII, it is usually written as IV, 5-1 = 4). This system requires new symbols at every major step to minimize the size. Any arithmetic calculation like addition, subtraction, multiplication, division, etc. would be a challenging task on Roman number system. It was usually handled by few mathematical experts.
Our current number system is based on positional notation. It was originally developed in India and spread across the world. Another important mathematical milestone was also achieved in India at that time; that is to introduce a symbol for nothing or zero. Introduction of zero is noted as important as invention of wheels in the scientific history. The positional notation can be based on any base great than one (i.e. 2 and above). Our standard current number system uses base 10 – decimal system. This means that we need only 10 symbols to represent any number: 0,1,2,3,4,5,6,7,8,9. And each digit value depends on its position: 1st digit = 1; 2nd digit 10; 3rd digit 100; etc. For example: 4328 = 4*1000 + 3*100 + 2*10 + 8*1. As it is based on base 10, each digit value is increased by multiples of 10. If different base is used, say 12, then it should be increased by multiples of 12 (Note that we also need 12 symbols).
The use of base 10 is based on our 10 fingers. Before the standardization of base 10, people around the globe were tried many different bases, out of which 12 and 20 were also popular. In English and German base 12 was used initially. Though the notation is now changed to decimal system (base 10), we are still using the old words for 11 and 12; and hence the first set [10, 11, 12, ...] sounds odd compare to others.
The positional number system not only simplifies how a number is written, it also simplifies all arithmetical calculation. The ancient art of computation, once confined to a few adepts, is now taught in elementary schools. There are not many instances where scientific progress has so deeply affected and facilitated everyday life!
"Mathematics is the queen of the sciences and the theory of numbers is the queen of mathematics" – Gauss.
Reference: What's mathematics, by Richard Courant & Herbert Robbins.
In my early childhood we lived in a small village. Everyday, the milkman delivers milk to my home and mark a line on the house wall. On the fifth day, he crosses the last four lines and starts a new one. This is how he counts the number of days he delivered milk. This is very early form of numbering system. Imagine writing 118 in this system; it would take lot of space.
Roman number system uses the same idea, except it introduces new symbols for 5 = V, 10 = X, 100 = C, etc. For example: CXVIII is 100 + 10 + 5 + 3 = 118. Hence, Roman number system is based additive principle (Also note that instead of writing 4 as IIII, it is usually written as IV, 5-1 = 4). This system requires new symbols at every major step to minimize the size. Any arithmetic calculation like addition, subtraction, multiplication, division, etc. would be a challenging task on Roman number system. It was usually handled by few mathematical experts.
Our current number system is based on positional notation. It was originally developed in India and spread across the world. Another important mathematical milestone was also achieved in India at that time; that is to introduce a symbol for nothing or zero. Introduction of zero is noted as important as invention of wheels in the scientific history. The positional notation can be based on any base great than one (i.e. 2 and above). Our standard current number system uses base 10 – decimal system. This means that we need only 10 symbols to represent any number: 0,1,2,3,4,5,6,7,8,9. And each digit value depends on its position: 1st digit = 1; 2nd digit 10; 3rd digit 100; etc. For example: 4328 = 4*1000 + 3*100 + 2*10 + 8*1. As it is based on base 10, each digit value is increased by multiples of 10. If different base is used, say 12, then it should be increased by multiples of 12 (Note that we also need 12 symbols).
The use of base 10 is based on our 10 fingers. Before the standardization of base 10, people around the globe were tried many different bases, out of which 12 and 20 were also popular. In English and German base 12 was used initially. Though the notation is now changed to decimal system (base 10), we are still using the old words for 11 and 12; and hence the first set [10, 11, 12, ...] sounds odd compare to others.
The positional number system not only simplifies how a number is written, it also simplifies all arithmetical calculation. The ancient art of computation, once confined to a few adepts, is now taught in elementary schools. There are not many instances where scientific progress has so deeply affected and facilitated everyday life!
"Mathematics is the queen of the sciences and the theory of numbers is the queen of mathematics" – Gauss.
Reference: What's mathematics, by Richard Courant & Herbert Robbins.
Pronounce the following sets of numbers: [10, 11, 12, ...], [20, 21, 22, ...], [30, 31, 32,...], [40, 41, 42, ...], and so on. Notice that the first set [10, 11, 12, ...] does not follow how others sets are pronounced. You might have probably wondered about it before. In my native language Tamil all the sets follow the same patterns of pronunciation. So, I immediately noticed the odds of Eleven and Twelve when I learned English. The reason for this odds lies behind how number theory evolved over the time.
In my early childhood we lived in a small village. Everyday, the milkman delivers milk to my home and mark a line on the house wall. On the fifth day, he crosses the last four lines and starts a new one. This is how he counts the number of days he delivered milk. This is very early form of numbering system. Imagine writing 118 in this system; it would take lot of space.
Roman number system uses the same idea, except it introduces new symbols for 5 = V, 10 = X, 100 = C, etc. For example: CXVIII is 100 + 10 + 5 + 3 = 118. Hence, Roman number system is based additive principle (Also note that instead of writing 4 as IIII, it is usually written as IV, 5-1 = 4). This system requires new symbols at every major step to minimize the size. Any arithmetic calculation like addition, subtraction, multiplication, division, etc. would be a challenging task on Roman number system. It was usually handled by few mathematical experts.
Our current number system is based on positional notation. It was originally developed in India and spread across the world. Another important mathematical milestone was also achieved in India at that time; that is to introduce a symbol for nothing or zero. Introduction of zero is noted as important as invention of wheels in the scientific history. The positional notation can be based on any base great than one (i.e. 2 and above). Our standard current number system uses base 10 – decimal system. This means that we need only 10 symbols to represent any number: 0,1,2,3,4,5,6,7,8,9. And each digit value depends on its position: 1st digit = 1; 2nd digit 10; 3rd digit 100; etc. For example: 4328 = 4*1000 + 3*100 + 2*10 + 8*1. As it is based on base 10, each digit value is increased by multiples of 10. If different base is used, say 12, then it should be increased by multiples of 12 (Note that we also need 12 symbols).
The use of base 10 is based on our 10 fingers. Before the standardization of base 10, people around the globe were tried many different bases, out of which 12 and 20 were also popular. In English and German base 12 was used initially. Though the notation is now changed to decimal system (base 10), we are still using the old words for 11 and 12; and hence the first set [10, 11, 12, ...] sounds odd compare to others.
The positional number system not only simplifies how a number is written, it also simplifies all arithmetical calculation. The ancient art of computation, once confined to a few adepts, is now taught in elementary schools. There are not many instances where scientific progress has so deeply affected and facilitated everyday life!
"Mathematics is the queen of the sciences and the theory of numbers is the queen of mathematics" – Gauss.
Reference: What's mathematics, by Richard Courant & Herbert Robbins.
In my early childhood we lived in a small village. Everyday, the milkman delivers milk to my home and mark a line on the house wall. On the fifth day, he crosses the last four lines and starts a new one. This is how he counts the number of days he delivered milk. This is very early form of numbering system. Imagine writing 118 in this system; it would take lot of space.
Roman number system uses the same idea, except it introduces new symbols for 5 = V, 10 = X, 100 = C, etc. For example: CXVIII is 100 + 10 + 5 + 3 = 118. Hence, Roman number system is based additive principle (Also note that instead of writing 4 as IIII, it is usually written as IV, 5-1 = 4). This system requires new symbols at every major step to minimize the size. Any arithmetic calculation like addition, subtraction, multiplication, division, etc. would be a challenging task on Roman number system. It was usually handled by few mathematical experts.
Our current number system is based on positional notation. It was originally developed in India and spread across the world. Another important mathematical milestone was also achieved in India at that time; that is to introduce a symbol for nothing or zero. Introduction of zero is noted as important as invention of wheels in the scientific history. The positional notation can be based on any base great than one (i.e. 2 and above). Our standard current number system uses base 10 – decimal system. This means that we need only 10 symbols to represent any number: 0,1,2,3,4,5,6,7,8,9. And each digit value depends on its position: 1st digit = 1; 2nd digit 10; 3rd digit 100; etc. For example: 4328 = 4*1000 + 3*100 + 2*10 + 8*1. As it is based on base 10, each digit value is increased by multiples of 10. If different base is used, say 12, then it should be increased by multiples of 12 (Note that we also need 12 symbols).
The use of base 10 is based on our 10 fingers. Before the standardization of base 10, people around the globe were tried many different bases, out of which 12 and 20 were also popular. In English and German base 12 was used initially. Though the notation is now changed to decimal system (base 10), we are still using the old words for 11 and 12; and hence the first set [10, 11, 12, ...] sounds odd compare to others.
The positional number system not only simplifies how a number is written, it also simplifies all arithmetical calculation. The ancient art of computation, once confined to a few adepts, is now taught in elementary schools. There are not many instances where scientific progress has so deeply affected and facilitated everyday life!
"Mathematics is the queen of the sciences and the theory of numbers is the queen of mathematics" – Gauss.
Reference: What's mathematics, by Richard Courant & Herbert Robbins.
Scriptures and their interpreters say God is a matter of faith beyond any proof or logic. Nevertheless, there are many logical arguments from both sides. One such a popular quote from Epicurus (341 BCE - 270 BCE):
"Is God willing to prevent evil, but not able?
Then he is not omnipotent.
Is he able, but not willing?
Then he is malevolent.
Is he both able and willing?
Then whence cometh evil?
Is he neither able nor willing?
Then why call him God?"
The typical counter argument for the existence of evils stems on man's freewill.
Another popular paradoxical statement is: Can God create a stone so heavy even He cannot lift it? If "he cannot", then there is something that God cannot do. If "he can", then also there is something that God cannot do – to lift the stone. Either way God is not omnipotent. So, they would argue God must be inconvincible concept. The counter argument is: just because God is powerful does not mean that He would do anything. For example, can He do evil things?
Here is my logic, just for fun! :-)
Once my little cousin brother amazed, "We developed car, but it goes faster than us; we developed flight that can fly, but we cannot fly; we developed calculator, but it calculates faster and accurate than us". Let's extend this further - can we able develop an intelligence machine that can learn and think faster and smarter than us? Though we cannot predict exactly when, but it can very well be developed. Some people are afraid that these machines might go out of control from us. But this is just a Hollywood movie story line. Because we are the ones going to design and develop how they would learn, think and evolve; and they have to be bound by those designs. Now how God might handle his own creations. I would say, the answer should be 'He cannot be stupid enough to create a stone He cannot lift it'. So, God is either stupid enough to have a design that allows the existence of evils or He is just part of evils!
"Is God willing to prevent evil, but not able?
Then he is not omnipotent.
Is he able, but not willing?
Then he is malevolent.
Is he both able and willing?
Then whence cometh evil?
Is he neither able nor willing?
Then why call him God?"
The typical counter argument for the existence of evils stems on man's freewill.
Another popular paradoxical statement is: Can God create a stone so heavy even He cannot lift it? If "he cannot", then there is something that God cannot do. If "he can", then also there is something that God cannot do – to lift the stone. Either way God is not omnipotent. So, they would argue God must be inconvincible concept. The counter argument is: just because God is powerful does not mean that He would do anything. For example, can He do evil things?
Here is my logic, just for fun! :-)
Once my little cousin brother amazed, "We developed car, but it goes faster than us; we developed flight that can fly, but we cannot fly; we developed calculator, but it calculates faster and accurate than us". Let's extend this further - can we able develop an intelligence machine that can learn and think faster and smarter than us? Though we cannot predict exactly when, but it can very well be developed. Some people are afraid that these machines might go out of control from us. But this is just a Hollywood movie story line. Because we are the ones going to design and develop how they would learn, think and evolve; and they have to be bound by those designs. Now how God might handle his own creations. I would say, the answer should be 'He cannot be stupid enough to create a stone He cannot lift it'. So, God is either stupid enough to have a design that allows the existence of evils or He is just part of evils!
Scriptures and their interpreters say God is a matter of faith beyond any proof or logic. Nevertheless, there are many logical arguments from both sides. One such a popular quote from Epicurus (341 BCE - 270 BCE):
"Is God willing to prevent evil, but not able?
Then he is not omnipotent.
Is he able, but not willing?
Then he is malevolent.
Is he both able and willing?
Then whence cometh evil?
Is he neither able nor willing?
Then why call him God?"
The typical counter argument for the existence of evils stems on man's freewill.
Another popular paradoxical statement is: Can God create a stone so heavy even He cannot lift it? If "he cannot", then there is something that God cannot do. If "he can", then also there is something that God cannot do – to lift the stone. Either way God is not omnipotent. So, they would argue God must be inconvincible concept. The counter argument is: just because God is powerful does not mean that He would do anything. For example, can He do evil things?
Here is my logic, just for fun! :-)
Once my little cousin brother amazed, "We developed car, but it goes faster than us; we developed flight that can fly, but we cannot fly; we developed calculator, but it calculates faster and accurate than us". Let's extend this further - can we able develop an intelligence machine that can learn and think faster and smarter than us? Though we cannot predict exactly when, but it can very well be developed. Some people are afraid that these machines might go out of control from us. But this is just a Hollywood movie story line. Because we are the ones going to design and develop how they would learn, think and evolve; and they have to be bound by those designs. Now how God might handle his own creations. I would say, the answer should be 'He cannot be stupid enough to create a stone He cannot lift it'. So, God is either stupid enough to have a design that allows the existence of evils or He is just part of evils!
"Is God willing to prevent evil, but not able?
Then he is not omnipotent.
Is he able, but not willing?
Then he is malevolent.
Is he both able and willing?
Then whence cometh evil?
Is he neither able nor willing?
Then why call him God?"
The typical counter argument for the existence of evils stems on man's freewill.
Another popular paradoxical statement is: Can God create a stone so heavy even He cannot lift it? If "he cannot", then there is something that God cannot do. If "he can", then also there is something that God cannot do – to lift the stone. Either way God is not omnipotent. So, they would argue God must be inconvincible concept. The counter argument is: just because God is powerful does not mean that He would do anything. For example, can He do evil things?
Here is my logic, just for fun! :-)
Once my little cousin brother amazed, "We developed car, but it goes faster than us; we developed flight that can fly, but we cannot fly; we developed calculator, but it calculates faster and accurate than us". Let's extend this further - can we able develop an intelligence machine that can learn and think faster and smarter than us? Though we cannot predict exactly when, but it can very well be developed. Some people are afraid that these machines might go out of control from us. But this is just a Hollywood movie story line. Because we are the ones going to design and develop how they would learn, think and evolve; and they have to be bound by those designs. Now how God might handle his own creations. I would say, the answer should be 'He cannot be stupid enough to create a stone He cannot lift it'. So, God is either stupid enough to have a design that allows the existence of evils or He is just part of evils!
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