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.
இலங்கையில் போரை நிறுத்து என ப.சிதம்பரம் பேசிய காரைக்குடி பொதுக்கூட்டத்தில் இளைஞர் ஒருவர் முழக்கம் : இந்தியாவின் உள்துறை அமைச்சர் ப.சிதம்பரம் காரைக்குடியில் நேற்று இரவு பொதுக்கூட்டத்தில் கலந்து கொண்டு உரையாற்றும் போது, கருப்பு சட்டை அணிந்த இளைஞர் ஒருவர் கூட்ட மேடைக்கு முன் வந்து யாரும் எதிர்பாராத நேரத்தில், 'இலங்கையில் போரை நிறுத்து" என்று முழக்கமிட்டார்.
காலங்களை தின்று வாழும் பறவைகள்
அறையின்
சுவர்க்கடிகாரத்திலிருந்து
நொடிநொடியாய்
விழுந்துகொண்டிருக்கிறது காலம்..
கீழ்
சில பறவைகள் மேய்ந்து கொண்டிருக்கின்றன..
17.03.2009
--OOO--
நெய்தல் நிலத்து பறவையொன்று
நெய்தல் நிலத்து பறவையொன்று
பறந்தபடி
வெகுநேரமாய் என்னை
அவதானித்துக்கொண்டிருக்கிறது.
நான்
அலைகளின் மீது
தப்பித்தலுக்கான ஒத்திகையில் இருக்கிறேன்..
17.03.2009
--OOO--
சொற்களும் நானும்
சொற்கள்
சிக்கலானவை..
மனதின் நிகழ்வுகளை
சொற்களை கொண்டு பிரதியெடுக்க
முயற்சிக்கும் போதெல்லாம்
ஏதேதோ சொற்கள்
முளைக்கின்றன மொழியறிவின் கட்டுக்குள்..
உள்ளுக்குள் உருவாகும்
சொற்களை
அதன் போக்கில் விட்டுவிட்டால்
சொற்கள் எப்படி எப்படியோ உருமாறி
கடைசியில் அர்த்தமற்று போய்விடுகின்றன..
எப்போதும் போல்
தனித்து எச்சமாகிறேன்...
சொற்களற்ற பிரதியாகிறேன் நான்..
05.01.2009
--OOO--
பின்குறிப்பு : எதுவும் விருப்பதிற்குரியதாய் இல்லை..
இலங்கைத் தமிழர்களுக்காக கருணாநிதி திரட்டிய நிதி அந்த மக்களுக்குப் போய் சேர்ந்ததாக தகவல் இல்லை. நிதியை கருணாநிதி தன்னுடைய குடும்ப நிதியில் சேர்த்துக் கொண்டு விட்டாரோ - கேட்ட ஜெயலலிதா மீது வழக்கு : அ.தி.மு.க. பொதுச் செயலாளர் ஜெயலலிதா மீது தமிழக அரசு அவதூறு வழக்குத் தொடர்ந்துள்ளது. இதுதொடர்பாக, சென்னையிலுள்ள முதன்மை செஷன்ஸ் நீதிமன்றத்தில் அரசு வழக்கறிஞர் தாக்கல் செய்துள்ள மனு விவரம் :
கருத்துகள் இல்லை:
கருத்துரையிடுக