Abstract Confusions

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

Tag Archives: Math

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

Advertisements

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

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.

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

Read more of this post

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

Read more of this post

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

Oracle Database and Partial Differential Equations (PDE)

I was going through this website and found this interesting offer on Oracle Database 10g: Complete Reference. This wonderful book is sold for INR 63 (+100 for handling and postage), and in total INR 163 with companion CD. It still worked out to a good deal. Until I found the related titles, which the site suggested, “If you like the above item, you might also like the following items:” and listed down books from Partial Differential Equations (PDE).

Now, please don’t get angry. Either there has to be hidden connection between Oracle and PDE or the site some how read my mind. You can also try and it might still show up to you. Even I would like to know where there is any relation between Oracle Database and Partial Differential Equations.

Instant Insanity – A Graph Theoretic Wonder

Instant insanity is one the many games involving sound mathematical principles. In particular it involves graph theory to solve. One of the mathematics most powerful tool – representation theory is used. As you are aware of, what looks like a strange problem is transformed into totally a unrelated problem in another field because of the hidden relations / transformations. Often these relations transform into a treasure trove of knowledge and excitement.

Read more of this post

A Good Design Can Win You A World War

Often one thinks, “what is it like having a good design?”. What a wonderful design can do to you?. As a matter of fact, history is full of events answering these questions. One such is, Russian designed war tanks versus German designed war tanks during German invasion of Russia, World War II. I saw a documentary on the design of war tanks by German and Russians in Discovery channel. It became evident at the end of war, a good design can win you the world war.

German Tanks

During World War II Germans designed and deployed a heavy tank named Tiger I. Tiger I was produced after intense research and development. It turned out,

While the Tiger I was feared by many of its opponents, it was over-engineered, expensive and time-consuming to produce. Only 1,347 were built between August 1942 and August 1944. The Tiger was prone to mechanical breakdowns and in 1944, production was phased out in favour of the Tiger II.

Tiger I - German Tank

Tiger I - German Tank

Read more of this post

To run or not to run in rain? – A math solution

Ever faced with the inability to take decision whether to run or not to run in rain? or in a snow fall? The question is of course not about running on heavy rain.Most of the time when it drizzles you are left with inability to take decision whether you should ran like mad to home or just walk into it. Friends who wait for the rain to subside have always one easy solution to take. Few brave people decide to fancy it and run in the rain. I always used to run and think afterwards why I ran.

Read more of this post