Sander's Reflexions

Last week I’ve been busy with The Change. The Change is quite big, but not bigger than I had imagined. The Change is a ship, or more precise she’s a skûtsje called De Verandering. With 14 people we’ve been sailing her on the Frisian waters. De Verandering. It’s a good name. At least it’s a change for the people sailing her. For a week we were ‘confined’ on an area of approximately 70 m², i.e. 5 m² each. Yeah, it’s almost like the Big Brother TV show. Luckily, we did not have to single out anybody. Sailing has a different philosophy. Time for a brief reflexion on water.



First of all, the crew has to be a team. Discipline is needed. Confidence is essential, you have to rely on each other. The shipper and mates (the 3 M’s) exercised their faith when they gave control to a bunch of no-no’s. They literally handed over the strings (de touwtjes uit de handen geven). They are true philosophers, although M,M&M will probably deny it. But someone who prefers sailing as a volunteer to a well paid job must have a philosophy. They are inspired, one of the shipper’s favorite words: bezieling.

Crew is only one part. The other part of sailing consists of the elements. One has to respect the wind, waters and ship. There has to be a balance of wind, sails and rudder. ‘More is better’ is not the guiding principle. It’s like performing a dance, or tai-chi. It’s close to wu-wei, no forced action, which means an acceptance of the conditions. You can go were the winds will bring you. And this week we were lucky that the winds brought us to the IJsselmeer, where we good experience the force of the waves.

Apart from sailing, there is also life on the ship. Life on the ship is almost ascetic. An exception to this life style were the meals, they were excellent. For the rest, the ship lacks any comfort. Ok, we had a toilet and everyone had a corner to sleep. It’s a contrast with our luxury daily life. No need to go to a monastery for an ascetic life. Meditation? Well, when all your attention is on the wind, sails and course of the ship your mind gets freed from any distracting thought. To be honest, I sometimes even forgot that there were other people on the ship.

So, on the ship I did not talk much about philosophy. Sailing is philosophy without words. One can study books, but they only contain words...

It was great to sail with De Verandering. It’s a challenge to steer a ship of 18 tons on the IJsselmeer with wind force 5. The (Dutch) saying is ‘three times ship right’. Well, maybe it’s due to her name, but I was continuously pushing and pulling the helm with all my force to get her on the right course. On the same time it’s great to see her dancing on the waves when you’re holding the helm. Every wave she swings, dips her nose in the waters, and flushes the front deck. Even the people sitting there, i.e. in the showers on the front deck, confirmed that it was a great experience.



Back home after a week sailing I encountered the void and a sudden sadness. No more wind and water, but a quite house. It’s hard to say goodbye.

So, did it change my life? Well, it changed my haircut. Although it will be quite difficult to maintain my Frisian Waters hairstyle without the refreshing bath in the Frisian waters in the morning.


To conclude a reading suggestion: Lord Jim - Joseph Conrad.

And some nice quotes on sailing:

"The pessimist complains about the wind; the optimist expects it to change; the realist adjusts the sails".
-William Arthur Ward

"Men in a ship are always looking up, and men ashore are usually looking down".
-John Masefield

"Out of sight of land the sailor feels safe. It is the beach that worries him".
-Charles C. Davis

"A ship is always referred to as "she" because it costs so much to keep her in paint and powder".
-ADM. Chester Nimitz

"Bad cooking is responsible for more trouble at sea than all other things put together".
-Thomas Fleming Day

Copied from http://www.winddancer.tv/Quotable Sailing Quotes.htm

“Daddy, why is a killer whale black and white?” A very usual question during breakfast, ain’t? I guess she heard something about it. Let’s give it a try, “They want to look like cows.” She is surprised. She smiles, “No, there are also brown cows.” Yep, silly answer, silly remark. She’s got the wit. Let’s continue, “Oh, but maybe the killer whales don’t know about brown cows.” Another smile. “No daddy, they don’t want to be seen. They are harder to see if their back is black and belly is white.” I wonder who told her that.

BTW, she does not only play with Lego and trains when she’s with me. She also plays with Barbies, as you can see.

Last weeks I spent some time with this popular number puzzle, Sudoku. For those who have never heard of it, have a look at the Wikipedia. I don’t really like to spent my time on puzzles with a known solution. I prefer puzzles that have not yet been solved. But the Sudoku is interesting, since it contains many unsolved questions. I was not interested in a particular solution, but the general solution of Sudoku’s. I had the following questions:

1. Is there a logical solution method for all Sudoku’s? I mean, is there a set of rules to find the numbers without trial and error?
2. How many Sudoku solutions are there?
3. What is the minimal number of givens needed to have one unique solution?
4. Can I create a Sudoku grid in a mathematical way, i.e. (again) without trial and error.

Well, these turned out to be the real tough questions. I found only an answer for question 2. There are 6670903752021072936960 = app. 6.671×10²¹ valid Sudoku grids. And even this answer was not found with a pure mathematical method. It involved quite some number crunching on a computer.

I also found an answer on the third question. I turns out to be 17. But again, there is no mathematical proof. I found no answer for the fourth question. Unfortunately I’m not that good in mathematics (I’m a physicist) to help the world with some nice solutions on the questions.

What about the first question? I do not have a complete solution for every Sudoku. But I found and implemented several rules. I started with a small program to solve the Sudoku of the daily newspaper. It contained one rule:
1. A number may occur only once at a row, column and block (3x3 cells).
This rule reduces the number of options for a cell. With the first Sudoku I tried this rule was enough to solve it. I was quite disappointed that the puzzle was that simple. The next day the puzzle was more difficult. I had to add a second rule.
2. A number must occur one at a row, column and block.
This rule was a great help. About 95% of the puzzles in the newspapers can be solved with these two rules. The figure below shows the solution process. The white squares represent the remaining options in a cell. A square in upper-left corner represents a 1, next to it is 2 and upper-right is 3. Number 4 is underneat the 1, 5 is in the center of the cell, etc.. The black squares indicate that that option is the only remaining option for the number in a row, column or block.



A few days later I found some more difficult puzzles. And I found some rules to solve these.
3. If the remaining options for a number in a block are on one row/column, that number must be in that block on that row/column. The options for that number can be removed from the other blocks of the row/column. In the figure below this is depicted by the cyan colored options for number 6 on row 7. The red options can be removed.
4. Rule 3 can also be reversed: If the remaining options for a number in a row/column are in one block, the options for that number can be removed from the other rows/columns of the block. This is shown in the south block. Number eight must be on column D, and can thus not be in cell F9.

These 4 rules were quite easy to implement on the computer. If I had to write a complete automatic solver, then I would start a trial and error from this point. The number of options has been dramatically reduced and only a few options have to be tried. I found some other rules to solve the Sudoku manually, but these rules are computationally quite expensive. But our brain, especially visual cortex, is well equipped to recognize the patterns. I found a good description of those solution rules on this very good Sudoku site. My last two rules are:
5. Disjoint chain: if a set of two or three numbers occur only in two or three cells (respectively) then these numbers must occur in these cells and other options can be removed. E.g. the dark green 2 and 3 in the east block are a disjoint chain. The yellow 8 can thus be removed, leaving a single (dark blue) 8 in cell G7. The light green 1, 5 and 8 are also a disjoint chain (on column I).
6. Disjoint subset: if 2 (or 3) cells on a row/column or block contain the same subset of 2 (or 3) numbers, then these numbers must occur in those cells and can be removed from the other cells.
(I do not have an example of this rule.)



That was enough about Sudoku for me. Any questions?