Water, the cause of surfing.

English: Environmental Science student samplin...
English: Environmental Science student sampling water from a stream. Picture courtesy of Environmental Science program at Iowa State University. (www.ensci.iastate.edu) (Photo credit: Wikipedia)

I came across one of those pages on the Internet which state something like “At least a few molecules of the water in your body probably passed through the kidneys of Julius Caesar“. They generally use statistics to show that what they are saying is true.

Only those who believe in homeopathy should be disturbed by this. To anyone else, a molecule of water is a molecule of water, and the fact that it had once been contained in a stream of urine is irrelevant. In any case it is too late. 60% of our body is made up of water, so water from Caesar’s urine is already in us.

Julius Caesar, Summer garden, Saint-Petersburg
Julius Caesar, Summer garden, Saint-Petersburg (Photo credit: Wikipedia)

Water is a fascinating chemical. It carries stuff around as it is the basis for blood and lymph and all the other fluids of our bodies. It carries nutrients up the stems of plants. It wears away mountains and builds rocks, it cools lava to form other rocks. It brings nutrients to our crops and washes them away. It even sinks ships.

“You are water
I’m water
we’re all water in different containers
that’s why it’s so easy to meet
someday we’ll evaporate together.”
― Yoko Ono

It’s difficult to think of any occurrence in our familiar world which is not mediated or affected by water in some way. Shortage of water to a society is a disaster, as food cannot be produced, leading to famine and deaths.

Much of the western U.S. is in "extreme d...
Much of the western U.S. is in “extreme drought” (Photo credit: Wikipedia)

Water is thought by most people to be liquid at usual temperatures, though there are some places where it is to be found in solid form. Actually there is a great deal of it around in the gaseous phase, or vapour. We measure this airborne water in terms of the humidity or wetness of the air.

Water is extraordinarily pervasive and can be found in all the nooks and crannies in the materials that we have around us. It acts as a lubricate, and if the water is driven off, by heating or chemical means things become stiff and fragile. Even so, water cannot be completely removed from things – even a diamond probably has a few entrapped water molecules.

Water molecules attaching to each other by hyd...
Water molecules attaching to each other by hydrogen bonds (Photo credit: Wikipedia)

Water plays a role in rotting things down. A corpse kept in a very dry environment desiccates and turns leathery and fragile. I guess that this is because the organisms that rot a body away cannot function in a water free environment.

A body of liquid water fills things from the bottom up. Gravity pulls the water down to the lowest parts of a container and water continues to layer the container. The surface appears to be flat, but that is an illusion. At a small scale, if a tiny bit of the water happens to be higher than the rest of the water, gravity will pull it down, while the other water molecules resist by being in the way.

English: Dilmah - photo by me on today.
English: Dilmah – photo by me on today. (Photo credit: Wikipedia)

Eventually as the water stills, the differences in level even out, and the water surface becomes as level as it can. However, at the molecular level, molecules of water, which are moving relatively fast on these scales, can pop out of the liquid and float away. Other molecules can also pop in to the liquid, so that on average the water is level.

Why doesn’t the surface appear blurry and ill defined then? Well we can’t see at the molecular scale, and also the water molecules form weak electrical bonds with each other. A water droplet is like a large crowd of people all milling about, holding hands much of the time. Those on the outside are not as tightly bound as those further in.


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Imagine now that the crowd is surrounded by a storm of people who are moving faster, and are more spread out so they rarely join hands. One of these gaseous people will now and then bump into the crowd. They may knock loose one of the crowd who will shoot off and become one of the gaseous people, while gaseous person who hit him may now be travelling more slowly and link up with the crowd.

Even in the macro world a water surface is rarely really flat. The dynamic nature of the flatness is apparent when a container is jolted slightly and tiny waves form on the surface as compression waves disturb it. Wind and rain also cause visible disturbances in a lake or pond.

Surface waves
Surface waves (Photo credit: Wikipedia)

Flowing water often forms a smooth, if not level surface. A submerged rock in a river or a weir or fall in a river can form persistent ripples of flumes as the water flows over them. Kayakers know to aim their craft at a flume to safely descend a rapid or waterfall, although downstream of flumes the river often forms “haystacks” where turbulent water is forced into humps which can prove difficult to navigate.

A little stream may be described as turbulent as it makes its way over and around boulders and small drops, but interestingly it is not random. It is not chaotic. A close look will reveal that the bow waves of stones in the flow may flutter and throw off little whirling vortexes, but the bow wave and the pattern of vortexes persists. The little waterfall over a small stone ledge persists, even though the shape of the waterfall may ripple a little.

Ripple effect on water.
Ripple effect on water. (Photo credit: Wikipedia)

In large bodies of water, such as lakes and seas, winds form waves which can travel many thousands of kilometres across oceans and seas. Water waves don’t represent the movement of water over those distances – the only thing that moves is the energy in the wave. Water molecules in a wave move mainly up and down and only a little forwards and backwards.

Circular water current in a wave
Circular water current in a wave (Photo credit: Wikipedia)

However when a wave travels over a beach or shoal, the movement in the vertical direction is curtailed, and the energy is transformed into a forward motion – the wave breaks. Water is transported forward, with the water higher up moving faster than the water at the sea bed which may be water draining off the beach from the previous wave and the wave steepens until it collapses. Hence surfing!


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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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Where do ideas come from?

ideas
ideas (Photo credit: Sean MacEntee)

I was watching this on Youtube, and I found myself saying “Yes, but…”. What Stephen Johnson says in there is all true. I like his idea of a “slow hunch” that takes several years or decades to develop. Stephen’s environmental approach looks at the places that provide the environment where ideas flourish, such as coffee shops which flourished in the 17th century and later. The Wikipedia article notes that

Though Charles II later tried to suppress the London coffeehouses as “places where the disaffected met, and spread scandalous reports concerning the conduct of His Majesty and his Ministers”, the public flocked to them.

Apparently Charles did not like the new ideas emanating from the coffee shops and thought that doing away with them would do away with the ideas. I’m not so sure – the discussion groups from the coffee shops would almost certainly have moved elsewhere.

Lloyd's Coffee House
Lloyd’s Coffee House (Photo credit: Wikipedia)

Ideas certainly sprang from the coffee houses which mutated into or gave rise to the London Stock Exchange, Lloyd’s of London and some famous auction houses. I refer you to the Wikipedia article.

Stephen Johnson describes the environments that provide fertile ground for new ideas, and similar places have been invented and reinvented over the years. While Universities were, I believe, originally set up as places for the studying of religion, the concentration of bright people and the opportunities for discussion inevitably led to ideas which were not to the taste of the religious establishment.

Victoria University, Kelburn, Wellington, New ...
Victoria University, Kelburn, Wellington, New Zealand. (Photo credit: Wikipedia)

My “yes, but..” in relation to the Youtube article was not in relation to the matters Johnson discusses, which was the types of environments that favour new ideas, but how the ideas are formed in the human brain. Johnson talks about one person having “a piece of the puzzle” that completes a new idea, but I think that that is an oversimplification. I see it more like a huge floating jigsaw puzzle, with no edges and maybe many many puzzles. Each person gets millions of puzzle pieces and each person does his or her best to fit together as many pieces as possible and some of the pieces may be assembled incorrectly. I’m thinking of the “Intelligent Design” people when I write that.

a drawing of a 4 piece jigsaw puzzle
a drawing of a 4 piece jigsaw puzzle (Photo credit: Wikipedia)

An idea in that model is simply a realisation that that piece or pieces of the puzzle over here seem to fit with the piece or pieces over there. Any idea is based on innumerable prior ideas or realisations.

Ideas also seem to change over time. I think that I recall that when the idea that white light can be split into many colours was first put to me I accepted it with some reservations. Sort of “If you say so”. But today it seems obvious to me, though it can be that probes into the obvious turn up the un-obvious.

Classic Albums: Pink Floyd – The Making of The...
Classic Albums: Pink Floyd – The Making of The Dark Side of the Moon (Photo credit: Wikipedia)

So where do ideas come from? I’m uncertain. I’m not sure that there aren’t several sources of new ideas, but one that I keep coming back to is that there might be some process in our brains of which we are not conscious that continually and somewhat dumbly searches the puzzle pieces and tries to fit them together. It probably has guidance rules that say that, metaphorically, knobs must fit into sockets, there should be no gaps or space between puzzle pieces.

I call the process dumb because it seems to favour picking close by pieces, and it seems to repeatedly try the same configurations that have failed previously. I say this because sometimes, looking at a fact a new way or introducing a concept from another field may result in a totally new solution to a problem.

Visual Example of the Eight Queens backtrack A...
Visual Example of the Eight Queens backtrack Algorithm (Photo credit: Wikipedia)

I’m aware that I’ve used the word “idea” in a number of senses above, but I hope that it doesn’t detract too much from the argument. I’m also aware that I’ve stretched the jigsaw analogy well beyond the bounds!

As a final comment, I think that people misunderstand the Eureka Moment. The moment occurs not when one solves the puzzle, but the moment that one realises that the puzzle is solved. For instance, when a mathematician works on a proof he may get stuck on a particular step. He may try several solutions, proceeding from the solution under test through several other steps in the proof before he discovers the solution which works. The Eureka Moment happens when he discovers that the solution he is trying is the correct one, not when he chooses the solution. A subtle but definite difference.

archimedes
archimedes (Photo credit: Sputnik Beanburger III)