Abstract Confusions

Complexity is not a cause of confusion. It is a result of it.

Category Archives: Number Theory

What’s special about 2012?

Happy new year to all. Wish you the most successful and happiest year ahead.

Now, that being said, let us look at the specialty of 2012. Being an even-numbered year, and a leap year, 2012 for sure is attractive.  Though few can complaint about having one extra day to get through in February.

2012 – Alan Turing year

2012 is named as Alan Turing’s year. Alan Turing was born on 23rd, June of 1912. 2012 will be his birth centenary year. He is widely respected for inventing theoretical computer and much of code breaking in Cryptology.  His contribution in war-time Britain saved scores of live and eventually lead allied forces to win world war II.

2012 – Cooperative year

2012 is also named as international co-operative year. Co-operatives or cooperative unions are special kind of business/non-business establishments. It is special to me, as I have studied a cooperative management diploma for a year.

2012 – Mathematical significance

2012 is also a E-Toothpick sequence number. Last year, 2011, we observed what as a toothpick numbered year. A E-Toothpick is formed by three half toothpicks, like a trident.

2012 : E-Toothpick number

2012 : E-Toothpick number

2012 – Mayan Calendar

The story of 2012 as the end year of Mayan calendar is well-known.  Even there are a handful of movies made on it. It is left to see what happens in 2012. Even if we have to go by Mayan’s, we have full year 2012.

Mayan Calendar till 2012

Mayan Calendar ends at 2012

2012 is has same calendar as of 1984, 1956 and will have same as 2040, 2068 (that’s +/- multiples of 28 years). On another side note, there is a move to have a permanent calendar. A calendar that has every weekdays of a month identical year after year.

From: http://www.cato.org/pub_display.php?pub_id=13940

Two Johns Hopkins professors are proposing a new calendar in which dates would fall on the same days of the week every year.

The calendar proposed by Richard Conn Henry, an astrophysicist, and Steve H. Hanke, an applied economist, begins each year on Sunday, Jan. 1.

There will one full week added every 5th or 6th year.

Do you like it? I do not. Not just simply for the reason, that there will be no new calendars printed with glossy models. Also for the fact that there will be no surprises in the holidays and leaves. Doesn’t it become monotonous?

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On Counting, Countability, Uncountability and Confusions thereof

The very basics of math skills are not taught by any one, it is inculcated from birth. In my childhood days, I remember how I got surprised by my grand mother’s mathematical (rather counting) skills. She was not taught in any school, she has to manage the household stuff, few farm works. She could never read a word, but still she could precisely count the number of coconuts, add subtract multiply or tally the rupee notes and settle the account. Counting is something that comes naturally to one. In fact I read some where, counting is not exclusive to humans, birds like crows can count till five. Another news item claims chimpanzees can even count better than humans.

Asian Advantage in Counting

Another article even attributes geographical / language factors for mastering the mathematical ability of remembering number. If you haven’t read it, here is the summary: the article advocates the certain languages (Asian in this case) have inbuilt advantage in manipulating numbers in mind. Because, the words for the numbers are smaller and easy to store, retrieve, manipulate.

Chinese number words are remarkably brief. Most of them can be uttered in less than one-quarter of a second (for instance, 4 is ‘si’ and 7 ‘qi’) Their English equivalents—”four,” “seven”—are longer: pronouncing them takes about one-third of a second. The memory gap between English and Chinese apparently is entirely due to this difference in length. In languages as diverse as Welsh, Arabic, Chinese, English and Hebrew, there is a reproducible correlation between the time required to pronounce numbers in a given language and the memory span of its speakers. In this domain, the prize for efficacy goes to the Cantonese dialect of Chinese, whose brevity grants residents of Hong Kong a rocketing memory span of about 10 digits.

It could not help me but to compare this with the counting in my mother tongue Tamil.  In English, we have to count fourteen, sixteen, seventeen, eighteen and nineteen, so one would think that we would also say one-teen, two-teen, and three-teen. Not the case. It is little bit in a different form: eleven, twelve, thirteen, and fifteen. Compare that to Tamil counting, 11 is pathinoonnu (பதினொன்று or pathu+one; ten+one), 18 is pathinnettu (பதின்னெட்டு or pathu+ettu; ten+eight). Read more of this post

What’s special about 2011?

2010 is gone. And I always like even numbered years compared to odd ones. I was asking to myself, what’s special about 2011? It works out that 2011 is indeed special.

First: 2011 is a prime number. The fundamental building blocks of number system, prime numbers are special. It means 2011 can not be expressed a product of smaller prime numbers (or any other numbers for that sake). And then, a friend pointed out 2011 can be expressed as sum of 11 prime numbers.

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