Prof. S. Naranan's Papers

(Apr 17, 1930 - Nov 28, 2019)

Dr. S. Naranan (b.1930) was an experimental cosmic-ray physicist and X-ray Astronomer based mostly in the Tata Institute of Fundamental Research, Bombay (India) in a career spanning 42 years. He is a firm believer in the interdisciplinary character of science and has diversified his interests to other fields such as mathematics, statistics, computer science, biology, genetics and linguistics.

Here, we present some of his papers on miscellaneous, interdisciplinary topics.

1. Scientific Publications of Prof. Naranan - Introduction by S. Naranan
   A brief background of his education, research work and publications.
   
   
2. Fibonacci Kolams
   A new modular approach to build kolam designs of any arbitrary size and shape using some unique properties of Fibonacci Numbers.
   
   2.0. Fibonacci Kolams - An Overview
   
   2.1. Part I: Square and Rectangular Designs
   
   2.2. Part II: Square and Rectangular designs of arbitrary size based on Generalized Fibonacci Numbers
   
   2.3. Part III: Rectangualr Kolams with two-fold Rotational Symmentry
   
   2.4. Part IV: Evolution of Loops
   
   2.5. Part V: A Board Game for Kolam Designs: A Fibonacci Kolam is made up of unit square tiles on a grid of unit square cells.  The tiles come only in 8 different shapes (A B C D E F G H).  This feature renders possible design of a Boardgame for kolams, either as a solitaire or  as a two-person game. A board of size 14 x 14 and 300 tiles have been produced. The game can be adapted for play on a computer.
   
   2.6: Correspondence with Martin Gardner on Fibonacci Kolams
   The eminent Mr. Martin Gardner was an idol of Naranan. On 16th April 2010, he wrote him a letter along with his papers. To his pleasant surprise he recieved a prompt laudatory response from Gardner. Their correspondence is reproduced here. Sadly Martin Gardner passed away on May 22, 2010, at age 95, within weeks of reviewing and commenting on this work. This could be one of a few of Mr. Gardner's last letters before his death.
   
   2.7: Kolam Designs based on Fibonacci series
   
   The Dutch Mathematical Journal ‘Nieuvw Archief voor Wiskunde' has published this paper (Reference: Nieuw Archief voor Wiskunde 5/20 nr.3 September 2019. Their Website: www.nieuwarchief.nl).
   
   Kolams are decorative designs in South Indian folk-art. They are drawn as lines and curves around a grid of dots. An essential feature is the rotational symmetry of the design – four-fold for squares and two-fold for rectangles. Fibonacci Recurrence is an elegant mathematical tool for their design. Any set of four integers (a b c d) with the property c = a+ b and d = c+ b can be a basis for a Fibonacci Kolam. A desirable feature of the kolams is that they are ‘single-loop’. Kolams of any desired size can be created using a modular approach. Several square and rectangular kolams are presented. They can be adapted for computer-aided drawing. All Fibonacci Kolams can be assembled with only eight basic shapes. This is the basis for a Board Game for play by one or more players. A 14 x 14 board made of thick cardboard and 300 tiles is fabricated.
   
   
3. A statistical Study on Failures in solving Crossword Puzzles (PDF)
   Cryptic crossword puzzles are one of many hobbies of Prof. Naranan. He doesn't just solve them, he keeps a record of his errors! Maintaining meticulous records of his errors daily, over a period of two decades, resulted in this fascinating study, which was published in the Journal of Quantitative Linguistics (JQL). This is Author's Accepted Manuscript, published with their permission.
   
   This work has been referenced in the following publications:
   
   3.1: Crossword Unclued, a site hosted by Shuchi (Schuchismita Upadhyay)
   
   3.2: Open Magazine
   
   3.3: John Halpern's book:  "The Centenary Of The Crossword": Section 11 "Crossword Stories", under the heading "The Completion Process - Figure This Out!" (pg. 170-171).
   
   
4. Word Puzzle Lottery and the Laws of Chance (PDF)
   In early 1950's a combination of word puzzle (with temptingly easy solution), was offered as a lottery in several magazines in India. Here is an interesting look into the scheme and the laws of chance.
   
   
5. Cryptic Crossword Puzzles: A statsitical Analysis of Errors in Solution (PDF)
   This paper is a follow-up of the author's 2010 paper (item# 3 above), and has new results of three different categories: (1) an update of his results to 16 years of data with total number of puzzles 5484 from the original 3404 an increase of 2080, (2) analysis of another solver’s (Daniel Peake’s) error/success data from 260 puzzles of The Guardian in 2013 and (3) a very special kind of word puzzle lottery which was popular in India in 1940’s and 1950’s.
   
   
6. Universal Calendar
   An approach to finding the weekday of any date (day, month, year)
   
   
7. Calendar Problems
   A look at some elementary mathematics to find the day of the week; a companion paper to the above Universal Calendar. Includes a sample of some interesting calendar problems.
   
   
8. Kaprekar Constant 6174
   An introduction to the fascinating Karprekar Constant 6174. Written especially for school children.
   
   8.1: Kaprekar Constant 6174: Translated in Tamil (PDF)
   Mr. K. Sudhakar, author of the Tamil fictional novel "6174", fascinated by Prof. Naranan's article above has translated it for Tamil reading audience.
   
   
9. A Variant of Kaprekar Iteration and Kaprekar Constant (PDF)
   In iterative processes, a small change in the iteration rules can lead to profound new patterns.  A slight tweaking in the Kaprekar Iteration procedure proves the point. This is a companion article of "Kaprekar Constant 6174" above.
   
   
10. Historical Linguistics and Evolutionary Genetics (PDF)
    Etymology, the origin and evolution of words, is the most common tool in dating ancient texts in historical linguistics. The author has proposed a statistical tool based on the evolution of usage of letters of the alphabet. Given two historical texts, many centuries apart, a ‘distance measure’, a number, is defined. Larger the distance, greater is the difference in their age. A similar method is used for the evolutionary ages of six species of mammals, by analyzing their DNA, the genetic material of life.
    
    
11. My daughter Vidya Ramanan's Finger Paintings:
    Vidya started drawing and sketching from a very young age. She has tried all types of painting and sketching: water color, oil, crayons, pencil and charcoal. In the last year she decided to try computer-aided art. With simple doodle-style movements on her iPad, she can generate very intricate complex patterns of art.
    
    11.1: Finger Paintings: Set 1
    11.2: Finger Paintings: Set 2
    11.3: Finger Paintings: Set 3
    11.4: Finger Paintings: Set 4
    11.5: Finger Paintings: Set 5
    11.6: Vidya's Hand Drawings: Set 1
    11.7: Vidya's Hand Drawings: Set 2
    
    
12. My father's Unique Tamil Typewriter (PDF)
    Background and an excellent treatise on the characteristics of the one-of-a-kind Tamil Typewriter - a treasure, perhaps a museum piece - that belonged to Naranan's father, Prof. K. N. Sundaresan. It has been used only by them both.
    
    12.1: The above article as it appeared in the "Madras Musings" dated May 16-31, 2014 (PDF)
    We thank Mr. S. Muthiah, the Editor, for publishing the article in his popular Madras Musings issue. In spite of the difficulty to format the document with the many photos to fit on his website, Mr. Muthiah took the extra effort to do an exceptional job. We tthank him for it.
    
    12.2: The Hindu Metroplus dated May 12, 2014, on this unique Typewriter
    A lively aabreviated version appeared in the Metroplus section to introduce the unique typewriter to the Hindu readers. Written by Mr. S. Muthiah.
    
    
13. Kolam Designs based on 'Versatiles'.
    Versatile is a unique quadrilateral, which can tile a plane into different polygons.  Kolams embedded in versatiles can form motifs of different shapes, e.g. square, square with a hole, rectangle with a hole and parallelogram. Universatile is a generalization that goes  beyond versatiles, offering wider choice as Universatile kolams.   Versatile and Universatile kolams represent a new genre of kolams, different from the Fibonacci kolams (item # 2).
    
    
14. Messages felicitation and condolences
    Update: We are sad to inform that Dr. Naranan passed away peacefully on November 28, 2019, in Chennai. Here is a link to the write-ups from his family and friends.
    
    
    

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