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.


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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.


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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.


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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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The muse

Hesiod and the Muse
Hesiod and the Muse (Photo credit: Wikipedia)

(Whoops! I forgot to post this on Monday, though I had finished it on Sunday)

My musings are generally thought up on the spur of the moment, as I’ve said before. Sometimes I get an idea a few days before I write my post, but sometimes it will come to me when I open WordPress and click on the “new post” link. Today’s post is inspired by a new television show that has just started here, about someone who writes a newspaper column. “Inspired” is too grand a word for it really – the TV show gave me the idea.

I’ve set myself a target of a thousand words per week. The writer in the TV series (called “800 Words“) has a column that is exactly 800 words long. He has just suffered a bereavement and decides to take his kids and relocate to a small town in New Zealand.

1000 words to the big crater (19)
1000 words to the big crater (19) (Photo credit: Wikipedia)

Naturally the kids don’t want to go, and when he gets to his new home, it’s only half built and it isn’t the house that he thought it was. On the trip to the new house he meets a bunch of eccentric locals and stumbles on the local nudist beach. So far, so standard sitcom. I’ll have to see how it goes, but it has apparently gone down well in Australia.

The interesting thing to me, for the purposes of this blog, is the 800 words thing. OK, I set myself a target of over 1000 words, and I generally don’t go many words over that, but to keep it to exactly 800 words seems a bit obsessive. The writer, as part of the continuity of the story, is seen typing his article, and the number of words is shown on the screen.


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Now, I don’t (usually) take much notice of the structure of my blogs – I don’t do an intro, a body, and a wrap up, but I presume the writer does (or is supposed) as he is writing for a newspaper. That’s more complicated than what I do. I can imagine reaching around 900 words and realising that I need to do a wrap up in 100 words or so. Or worse, maybe, reaching 750 to 800 words and realising that you’ve covered your main points and the wrap up is going to have to be stretched to 200 to 250 words.

Of course he is a professional writer so such matters are his bread and butter. This brings me to another point. He gets paid for his column, and apparently gets paid enough to feed himself and his kids! This is slightly more than a little bit unbelievable, to say the least, as what he is shown writing amounts to not much more than a blog. If he writes 800 words a day, 5 days a week that amounts to 4,000 words, and his rate per word would have to be astronomical to keep him and his kids fed and watered.


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The writers of the series have thrown in a few classic clichés in the first episode. There’s the end of the world cell phone coverage or lack of it. There’s the being swindled by the savvy locals, and there’s the saving the bad boy by hiding him from the cops thing. Oh well, perhaps things will get better. It’s not that bad a little show.

The writer in the show is inspired to write about all the things that are happening to him, so he has a ready source of material but my intent is not to make my blog anecdotal in that way. I might mention stuff in passing (like the Rugby World Cup. Yeah! All Blacks!) but in general I want my post to be like a bead necklace with beads on a wire, rather than a single long chain of interrelated links.

Cloisonne beads
Cloisonne beads (Photo credit: Wikipedia)

Of course, I will use the same themes repeatedly, such as science or maths or computing, just as a bead necklace generally has similar beads in many places but my intent is that each “bead” will stand alone.

I get messages from WordPress saying that so and so is now following my blog, but I don’t know what that really means. Does it mean that Mr Blobby is avidly waiting for my blog to come out and is disappointed if I am late? Probably not! But thank you for reading the blog, even if you only do it once. I do occasionally go and look at the blogs of those who are mentioned as following me and I may follow some of them.

Start of the Oracle Act
Start of the Oracle Act (Photo credit: Wikipedia)

Nevertheless, I write my posts with no specific reader in mind. By that I mean that I don’t visualise a person reading, which is odd, because that means that I send my words off into a vacuum. They must however sound good to me, as I write them, and if something that sounds awkward to me reaches the page, it gets altered.

Actually now I come to think about it, the “me” that writes the words seems to be different, or slightly separated from the “me” that does the reading, like Siamese twins in my head. It’s like a different aspect of myself.

"Head of a muse" by Raffaello Sanzio
“Head of a muse” by Raffaello Sanzio (Photo credit: Wikipedia)

For me the actual process of writing goes like this. I form a sentence or part of a sentence in my head and start to type it. My reading self closely follows this process and notices any typos and mistakes and my writing self corrects them, but these things happen so fast and the two processes are so integrated that it seems seamless.

It’s like an ongoing game of ping pong in my head. One part of my mind says to type the word “the”. Another part tells the fingers what to do. I’m unaware or maybe unconscious of what this part is doing, and I specifically don’t think “move the fingers to the letter t and push”. So far as the conscious part of my mind is concerned it just happens.


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The fingers move and the letters get typed. Another conscious part of my mind follows the letters that appear on the screen and passes off to an unconscious part the instructions to edit and retype. After a person has been writing for a while, it seems to your conscious mind that you think the words onto the screen.

Hmm, I’ve reached just over a 1000 words, so it is time to stop. I’ve shifted from talking about the muse and shifted to the mechanics. Either way the process is, as usual, more complex than it appears at first. I’ll have to think some more about how my words reach the page.