Abstract Confusions

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

Category Archives: Math

Abstract Confusions – 2011 in review

Got a nice report from WordPress. Though I did not blog actively in 2011, there are quite few posts that still cornered people’s attention. One of my new years resolution is to write more. So, sit firm and buckle up, here I come, 2012! 🙂

The WordPress.com stats helper monkeys prepared a 2011 annual report for this blog.

Here’s an excerpt:

The concert hall at the Syndey Opera House holds 2,700 people. This blog was viewed about 21,000 times in 2011. If it were a concert at Sydney Opera House, it would take about 8 sold-out performances for that many people to see it.

Click here to see the complete report.

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?

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.

Read more of this post

Some Interesting Requirements / Questions

Over the time I received few interesting requirements and questions. Few of them are straight forward that you do it in minutes, and few other questions are strange enough that some time have to sit and etch out the solution which is not top of the head. It would be only fair to share the information here. I would give you the requirement / question, if you can answer them, please add in comments.

You can use any language you like (except 3rd requirement). I was forced to use PL/SQL because of the project requirements.

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Dangerous Mind – Mathematics and Insanity

Problem solving is a top-notch skill. All of us face problems, in work, in life and every day happening. Jokingly mathematicians identify the following stages of a problem solving:

  1. Identifying the problem (includes preparation, collecting information, identifying challenges and risks) .
  2. Attacking the problem (use existing tools, techniques to derive new method). Get vigorous, consciously.
  3. The problem attacking becomes an unconscious activity from a  conscious one, then the problem starts attacking you.
  4. Either problem is consumed or the attacker is consumed by problem.

Especially at stage 4, one will be thinking only about the problem. While driving, eating, teaching and even in sleep. Archimedes resolved the problem when he was bathing. Isaac Singer, the american inventor of sewing machines was supposed to found solution for the problem of finding where to put hole in needle so that it is easy to stitch, in dream, he dreamt of someone chasing him with strange spear with a hole in the spear head. These are examples of sub conscious mind solving problems.

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My Favorite Mathematicians

History of humanity is full of stories about achievements of outstanding men and women. It is even more interesting and captivating when we read about mathematicians. I will try to list down the great people of mathematics who were the driving force of conceptual thinking and intellectual advancement of mathematics. This is in continuation with a story I wrote some time ago.

Earliest Mathematicians

No one know where the first class in mathematics was held. But all of us know for pretty sure what could have been the first theorem proved. Pre historic math was used for studying geometry and planetary. Greeks mastered this field of mathematics. Euclid, Aristotle, Archimedes and Pythagoras were the most noted mathematicians. They all are philosophers too. For good, once, a great mastery over written and oratory skill of a language was needed to practice mathematics.

In India, Baskara wrote Lilavati, a book written in poetic verses about mathematics. But the scene shifted slowly. As math became more abstract words and verses gave away to numbers and symbols. Read more of this post

Statistics: When Numbers Lie

Mark Twain once said,

There are three kinds of lies: lies, damned lies, and statistics.

Another quote by Steven Wright says like this,

47.3% of all statistics are made up on the spot.

And there is a detail account of how to lie with statistics. We all love numbers. Any talk with references to numbers is considered to be correct and appropriate.

How to Understand Numbers

Most of the time, it is people’s mistake in understanding the numbers presented to them. For example, understanding what numbers mean. Consider the following cases.

A corporation was able to announce the following the statistics: Total number of shareholders: 3003. Average shares per shareholder: 660. Looks nice, thats more like a democracy, every one has equal say in the proceedings, but in reality, it is just three people holding 3/4th of shares and remaining people holding 1/4th share. What looked like a happy number is actually not so.

Share Holding pattern - Average cheats

Share Holding pattern - Average cheats

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Math Games for Children

Games are the sure shot fun way to teach some thing. And math is one of the top-notch skills one needs to own for being successful in any career. Imagine if playing games hone your mathematical skills. As a kid I grew up learning few board games which helped me to understand the most basic math operations – counting, addition and division (subtraction and multiplication thereof).

Very recently, I tried teaching math principles to my nephew but found difficult without the help of games. The most important thing I did was to run to a store to get him a board game. So, if you don’t want to spend those long boring hours and make teaching fun, try few of these games.

Snakes and Ladders

This is a simple game. Most of adults would have played it. Two or more players can play this game. This board game has hundred squares numbered from 1 through 100. And a player wins if he starts from 1 and reach 100. Each player has to toss a die and move their playing piece according to the output of the die.

ladders-snakes-board-game-screenshot

Snakes and Ladders - A Chance game in 100 squares

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Haskell – A Functional Programming Language

Functions in mathematics are like building blocks in many fields. Functions are also widely used in physics and other branches of engineering. In computer science, functions play a major role.  When you have a mathematical function and want to write a program for that, most of the time you do it line by line, with the program constructs like looping, conditional looping and other control structures. This could run to several lines of code.

Functional Programming

Unlike the programming languages like Pascal, C, C++ and all other higher programming languages thereof, are known as imperative programming or structured programming languages. Imperative program is executed using statements described steps after steps. Functional programming is programming executed by evaluating expressions (or functions).  There are no variable assignments, on the higher side, functional program contains no side effect at all. Read more of this post