Abstract Confusions

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

Category Archives: Mathematicians

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

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

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