# Abstract Confusions

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

## 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.

## 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.

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

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.

## 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

## 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

## Street Fighting Mathematics – Preview

I read this news from MIT, I haven’t read this book yet, and thus this is a preview.

An exciting book written on educated guessing, problem solving  and rough calculations by MIT Prof. Sanjoy Mahajan. Prof. Sanjoy Mahajan wrote Street Fighting Mathematics – The art of educated guessing and opportunistic problem solving book out of years of experience he got teaching Street Fighting Mathematics for math undergraduates. You can read the Open Course Ware material for street fighting mathematics here. You can download and read an early draft version of Street Fighting Mathematics – in PDF from MIT (the book is considerably improved and has more materials 150+ pages).

## 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.

## One Way Only…

This time around, some thing interesting from the world of mathematics.

All of us dealt with functions of different types. We are introduced to functions when very early in school. Single varriable, multi varriable, simple and complex functions. And in college, functions declared, defined and studied. In this post, one such function, known as “one way function” is used widely in computer science.

### Wonderful functions from math

Mathematics is full of functions. These functions are applied far and wide else where. Few are used many times where as few others are used little. And very often functions and equations are interchanged. The most celebrated of them all is –

$E=M \times C^2$

## Stray Dogs, Rigor Mortis & Mathematics

In one of the last October month’s outpour’s, we got an unlikely guest at our door step. When I first heard weak howling, I dismissed it to the sound of vicious wind, later it got intense and this time it is not faint, it is a miserable cry. When I checked the door, I found a week old dog pup. Shivering in the cold and rain, it curled itself to the door mat. I felt so pity of it, so got few old clothes and heaved at it for extra warmth. It was already mid night, I left it and slept.

What happened next day was surprise for me. Eager to see, whether the pup was still there, I opened to door to check. There were two dog pups, not one. The new one seemed to be elder to the old one by a day. But both of them were happy. Now, feeding one dog was fine, but two? It was no easy job. But we kept them feeding for quite some time.