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Saturday, September 29, 2012

Not maths per se, just a little physics

Foundational Questions www.fqxi.org is a fun place to hang out.  On their latest essay contest, I look forward to reading a few responses:
Reductionist Doubts, by Julian Barbour.  Because the name of the author - winner of the first contest - excites me.
Revising the Topology of the Earth, by Peter Wamai Wanjohi.  Because it's the only recognizably African (it's Kenyan) author name I found among the hundred-or-so submissions.

The biographies are interesting too.   
This is Barbour's: "After completing a PhD in theoretical physics, I became an independent researcher to avoid the publish-or-perish syndrome. For 45 years I have worked on the nature of time, motion, and the quantum theory of the universe. I am the author of two books: The Discovery of Dynamics and The End of Time, in which I argue that time is an illusion. Details of my research work are given at my website platonia.com. Since 2008 I have been a Visiting Professor at the University of Oxford."

And this is Wanjohi's: "did advanced level physics but is a health professional specializing in community health and development .Works with the government and development partners. As a freelance physicist, he is a published researcher. His wish is top see a public well knowledgeable of their physical, biological and chemical environments." 

The contrast is typical; there isn't a market for "advanced-level physics" in Nigeria.

Drawing by physicist Setthivoine You

In addition to the essays by Barbour and Wanjohi, I'll try to read the top-four essays so ranked by reviewers (the public):
Black holes or anything else? by Christian Corda
Nature has no faithful mathematical representation by Roger Schlafly
On the Foundational Assumptions of Modern Physics by Benjamin F. Dribus
Patterns in the Fabric of Nature by Steven Weinstein

Anyway, here are the past top essays, I've studied all three.  One of them - Stardrives and Spinoza - is so exciting that I may write a short-story inspired by its future-world soon.
2011 - Is Reality Digital or Analog? by Jarmo Makela
2009 - Stardrives and Spinoza by Louis Crane, answering the question: What's Ultimately Possible in Physics?
2008 - The Nature of Time by Julian Barbour

One day, maybe I'll explain the joys and cares of "hyperspecialization and the money to build stuff" in the West, versus "low infrastructure levels, and the freedom to build stuff" out here in the tropics.
Well, it looks like I have already written several research-related posts on my personal blog.  The story starts in 2005 with "The California Institute of Science: I am despondent.  In the past years, I have observed - science, research, and the labours thereof. I have discovered no new science. I have built no new machine. I'm more than two-thirds of the way to my PhD.  However, I can now give an expert report on how scientists do what they do." to this year with "There's no i in research."  I now have a math blog even (you're on it.)  Full circle?

Thursday, September 27, 2012

How is Mahjong Titans scored?

Classical Mahjonng games score different suites (types of tiles) differently and even award extra points for special patterns e.g. three of a kind*[1].  This made me curious as to how Mahjong Titans is scored.

Clearly, you can't match triplets in our pairing game (especially since there are four of each tile design.)
But this is still a valid question: do you score extra for two consecutive pairings of the same design?  Absolutely yes.  I got the hint here months ago, and I've subsequently used it to raise my score**[2] over the months. 

What exactly is the way to increase your score by matching consecutive pairs:
"If you get a matched pair of one class and your next pair is of the same class, you get a bonus. If the next pair is the same number and the same class, the bonus is bigger. If your second pair after that is of the same class again, your bonus is even bigger. You also get bonuses for clearing both pairs of flower or season tiles in a row."
So there you have it, from the horse's mouth (MS Windows - how to play MT)

Of course, all this assumes you know what a class/type/suite is, lol.
The basic thing is there are circles (from 1-9), bamboo sticks (from 1-9, the 1 of bamboo has a bird on it), characters (1-9, look like tally counts), winds (North, South, East, West), dragons (red, green, and black/white).  Each Mahjong layout has four of each of these tiles for a total of (9+9+9+4+3) x 4 = 34 x 4 = 136.  In addition, there are single tiles: four seasons and four flowers.  Grand total 136 + 8 = 144 tiles.

Naming the tiles in Mahjong

Things that raise your score
So you can raise your score by knocking out all four of one type in two consecutive pairs.  The next best thing is to do a sequence of pairs from the same suite.  Cool!  

Things that lower your score

When I first started planning consecutive pairs, my scores went up.  The time taken to complete each game also went up into four digits (in seconds).  I suspect the final score factors in time (higher score for quicker time.)  In fact, I'm learning that the Mahjong score is not a simple or linear thing. You have the option to undo one move or a sequence of moves even up to the start of the game.  You lose some points for reversing a move, but sometimes it's worth it.

Things that are suspected to raise your score

Can you gain higher points by targeting the rare types - flowers and seasons for instance?  For some solitaire games, but probably not for Mahjong Titans, the rules say yes, pair these earlier***[3].

NOTES
- Don't worry about raising your score until you have learned how to win in the first place.  

***[3] - This yahoo games site on Mahjong Solitaire rules gives a number value to each suit (characters get the score written on the tile, circles double them, bamboos triple, winds get four, and a basic score of 5,6, 7 for a dragon, flower, or season respectively.)   This is NOT the scoring system for Mahjong Titans.  Here are three discrepancies that make me certain of it:
1. "Granted three shuffles?" - I hadn't noticed the option to shuffle.  
2. "Move on to the next round?"  I hadn't noticed any rounds.  
3. "...multiplied by the total number of pairs left"  But the points would be too big.  My first two pairs in the last game I played were 2 and 2 (nothing near 72) and seemed to increase as game play continued, not decrease with fewer tiles.  Total scores in the hundreds, not in the thousands as their system would predict.

 **[2] - Further to the April 2012 post about improving all round, I have strong data to show marked improvement in all six configurations.  We'll come back to that later.

 *[1] - See Mahjong, Singaporean Mahjong scoring rules, on Wikipedia.


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Monday, September 24, 2012

Tanya Khovanova reviews a book: Taking Sudoku Seriously

Taking Sudoku Seriously: Why do I like this post?

I agree that sudoku is math is fun: "the goal of the book is to establish a bridge from Sudoku to math. And the book does a superb job of it."

I've also pondered: "methods to solve Sudoku, how to count the number of different Sudoku puzzles, and how to find the smallest number of clues that are needed for a unique puzzle."

Something new: "Sudoku with a twist" like this:
Taking Sudoku Seriously Puzzle 91
Elsewhere on Tanya Khovanova's blog, she discusses a geometric measure, my boy Perelman, and other mathy-things that I actually care about. Could she be my long-lost (math) blog sister?

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