Puzzles

Pieces of a puzzle

Pieces of a puzzle (Photo credit: Wikipedia)

I’ve been musing on the human liking for puzzles. I think that it is based on the need to understand the world that we live in and predict what might happen next. A caveman would see that day followed night which followed the day before, so he would conclude that night and day would continue to alternate.

It would become to him a natural thing, and in most cases that would be that, but in a few cases an Einstein of the caveman world might wonder about this sequence. He might conclude that some all powerful being causes day and night, possibly for the convenience of caveman kind, but if his mind worked a little differently he might consider the pattern was a natural one, and not a divinely created phenomenon.

Puzzling about these things is possibly what led to the evolution of the caveman into a human being. Those cavemen who had realised that the world appear to have an order would likely have a survival advantage over those who didn’t.

The human race has been working on the puzzle of the Universe from the earliest days of our existence. Solving a puzzle requires that you believe that there is a pattern and that you can work it out.

The Universal pattern may be ultimately beyond our reach, as it seems to me that, speaking philosophically, it might be impossible to fully understand everything about the Universe while we are inside it. It’s like trying to understand a room while in it. You may be able to know everything about the room by looking around and logically deducing things about it, but you can’t know how the room looks from the outside, where it is and even what its purpose is beyond just being a room.

Solving a puzzle usually involves creating order out of chaos. A good example is the Rubik’s Cube. To solve it, one has to cause the randomised colours to be manipulated so that each face has a single colour on it.

English: Rubik's Cube variations

English: Rubik’s Cube variations (Photo credit: Wikipedia)

A jigsaw puzzle is to start with is chaos made manifest. We apply energy and produce an ordered state over a fairly long time – we solve the jigsaw puzzle. After a brief period of admiration of our handiwork we dismantle the jigsaw puzzle in seconds. Unfortunately we don’t get the energy back again and that’s the nature of entropy/order.

Many puzzles are of this sort. In the card game patience (Klondike), the cards are shuffled and made random, and our job is to return order to the cards by moving them according to the rules. In the case of patience, we may not be able to, as it is possible that there is no legal way to access some of the cards. Only around 80% of of patience games are winnable.

Empire Patience Playing Cards, Box

Empire Patience Playing Cards, Box (Photo credit: Wikipedia)

Other games such as the Rubik’s Cube are always solvable, provided the “shuffling” is done legally. If the coloured stickers on a Rubik’s Cube are moved (an illegal “shuffle”) then the cube might not be solvable at all. A Rubik’s Cube expert can usually tell that this has been done almost instantly. Of course, switching two of the coloured stickers may by chance result in a configuration that matches a legal shuffle.

When scientists look at the Universe and propose theories about it, the process is much like the process of solving a jigsaw puzzle – you look at a piece of the puzzle and see if it resembles in some way other pieces. Then you look for a similar place to insert your piece. There may be some trial and error involved. Or you look at the shape of a gap in the puzzle and look for a piece that will fit into it. One such piece in the physics puzzle is called the Higgs Boson.

English: LHC tunnel near point 5. The last mag...

English: LHC tunnel near point 5. The last magnets before the cavern. (Photo credit: Wikipedia)

The shape is not the only consideration, as the colours and lines on the piece must match the colours and lines on the bit of the puzzle. In the same way, new theories in physics must match existing theories, or at least fit in with them.

Jigsaw puzzles are a good analogy for physics theories. Theories may be constructed in areas unrelated to any other theories, in a sort of theoretical island. Similarly a chunk of the jigsaw could be constructed separately from the rest, to be joined to the rest later. A theoretical island should eventually be joined to the rest of physics.

Of course any analogy will break down eventually, but the jigsaw puzzle analogy is a good one in that it mirrors many of the processes in physics. Physical theories can be modified to fit the experimental data, but you can’t modify the pieces of jigsaw to fit without spoiling the puzzle.

The best sorts of puzzles are the ones which give you the least amount of information that you need to solve the puzzle. With patience type games there is no real least amount of information, but in something like Sudoku puzzles the puzzle can be made more difficult by providing fewer clues in the grid. A particular set of clues may result in several possible solutions, if not enough clues are provided. This is generally considered to be a bad thing.

Solution in red for puzzle to the left

Solution in red for puzzle to the left (Photo credit: Wikipedia)

Some puzzles are logic puzzles, such as the ones where a traveller meet some people on the road who can only answer “yes” or “no”. The problem is for the traveller to ask them a question and deduce the answer from their terse replies. The people that he meets may lie or tell the truth or maybe alternate.

Scientists solving the puzzle of the Universe are very much like the traveller. They can question the results that they get, but like the people that the traveller meets, the results may say “yes” or “no” or be equivocal. Also, the puzzle that the scientists are solving  is a jigsaw puzzle without edges.

English: Example of a solution of a Hashiwokak...

English: Example of a solution of a Hashiwokakero logic puzzle. Deutsch: Beispiel einer Lösung eines Hashiwokakero Logikrätsels. (Photo credit: Wikipedia)

Everyone who has completed a jigsaw puzzle knows that the pieces can be confusing, especially when the colours in different areas appear similar. For scientists and mathematicians a piece of evidence or a theory may appear to be unrelated to another theory or piece of evidence, but often disparate areas of study may turn out to be linked together in unexpected ways. That’s part of the beauty of study in these fields.

 

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This entry was posted in Computing, General, Maths, Miscellaneous, Philosophy, Science and tagged , , , , , , , , , . Bookmark the permalink.

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