Plurality of Worlds

I just finished reading Multiverses and blackberries by Martin Gardner (in his 2003 book Are Universes Thicker than Blackberries?). In this article he discusses the Many Worlds Interpretations (MWI) of quantum mechanics. As an extreme example of MWI the work of David Lewis, The Plurality of Worlds (1986, see the wiki page, or read parts on Google books) is mentioned. David Lewis "seriously maintains that every logically possible universe-that is, one with no logical contradictions ... is out there." (M. Gardner, 2003)

It was not the first time I heard about David Lewis' theory, which belongs to modal realism. At first I found it a funny idea: some Universes would be extremely dull because they would exist only of for example of the number 2, others only of 15 - 3 = 12, or of all possible triangles. Others would be rich like ours.

After thinking about it a bit longer, problems arise: all logically consistent Universes have logically consistent histories. Does this mean that every moment in the history of every possible Universe is an Universe? Or is the entire time-line of every possible Universe already there? In the latter case, we would live in an entirely deterministic Universe.

To this moment, I have not read Lewis' work myself, so I cannot be completely certain about the following, but what I know about the Plurality of Worlds-theory suggests a more fundamental problem. A Universe that has no 'parallel Universes' to it, that is the Only One Universe, can be without logical contradictions. According to the theory, that Universe would exist. However, it would rule out all the other Universes.
One may conclude that the Plurality of Worlds-theory itself leads to logical contradictions. The Universes that contain a Plurality of Worlds-theory could therefore not exist within the theory. Since the theory does exist, the Plurality of Worlds-theory must be false!

Arithmetic (again)

A week ago, the Wiskundemeisjes('Mathgirls') posted that the debate on education of arithmetic and mathematics has come back from holiday again. The new season of fierce discussions has been opened by Joost Hulshof. Read his article in Dutch here: http://www.math.vu.nl/~jhulshof/TAL.pdf (CASE-sensitive!). Hulshof argues against the so called 'realistic arithmetic'. After reading the piece, I have to conclude that the proponents of realistic arithmetic have a major misconception of what cognitive psychology has to teach us.
(I sense polarisation at work.)

A mind without confusion

At the root of Yggdrasill, the Tree of Life, lies the magical Source of Urd. There dwell the three Norns: Urd (Wyrd), Verdandi and Skuld. Now, Urd is old Norse for 'fate'. It has become the root wert-'='to turn' to mean anything prone to change. The word 'weather' (='weer' in Dutch) originating from this, the same holds for the Dutch verb 'worden' (='to become') and also the word 'versus' ('turned against'). Because of the connotations with changing behaviour, it is easy to understand that the name Wyrd has developed into 'weird', strange and unpredicted.

This in itself is an interesting piece of etymology. But the story gets better. Last week I received a small gift from Oshita sensei. He passed this eighth dan exam iaido last year. He gave me a tenugui, a small towel, that was made for the occasion. It has a nicely calligraphed text on it. The calligaphy reads fudoshin, which normally is translated as 'an unmovable mind.'



The first and the last characters are very common: 'heart'/'mind' and 'not'/'no'. The middle one I had seen before, but I had forgotten its meaning. I used my Chinese/Japanese program Wakan and found out that the middle character means 'move, motion, change, confusion, shift, shake'. Thus, the calligraphy reads (as I translate it) something like 'a mind without confusion'.
In this way I found out that also in the Far East the bond between 'change' and 'confusion' is anchored in vocabulary.

Arithmetic

"Swordsmanship is just like this. If from the time the student is a beginner without having learned any techniques well, you say something like 'Technique will come naturally without intention; establish the hard by means of the soft,' or 'Techniques are only trivialities,' he will become empty-handed and lazy, and will never know of where to stand. Thus he will be at loss both in this world and the next."
From: Issai Cholzanshi, The Demon's Sermon on the Martial Arts (tr. William Scott Wilson).

In the Netherlands a debate on education in arithmetic and mathematics has been going on for a long time. On one side there are those who say that it is no use of learning techniques, if there is no understanding. On the other hand there are those who say that understanding will come naturally after technique has been mastered.

Prof. Jan van de Craats, an important spokesman of the latter group, argues that the didactic method of 'realisitc arithmetic' give children a variety of tricks, which leaves the pupils confused. Children need structure.

Those who advocate 'realistic arithmetic' claim that old fashioned techniques like the 'staartdeling' (an algorithm in essence equal to the English 'long division') are obsolete, because 'nobody does calculations with pen and paper any more' (Adri Treffers in De Volkskrant). That is a great loss.

I strongly feel that automatisation of arithmetic techniques, together with the learning by heart of the multiplication tables are necessary for a good sense of numbers. This is, I believe, in turn needed for a good grasp of and ability to handle with more abstract objects such as functions, variables and parameters.

As long as realistic arithmetic and mathematics remain the common way of teaching, our pupils may "become empty-handed and lazy, and will never now of where to stand."

Glacier water pockets

Some days ago, I was watching the episode 'ice' from the BBC documentary series Earth. In this episode Dr Iain Stewart shows us a 'back door' to a glacier ("he sees a glacier in action from below"). Here he saw that the glacier has holes filled with water, these pockets can contain up to about twenty litres of water. The commentator puts forth the hypothesis that these pockets are generated by the pressure of the ice mass above and that these holes make the glacier less rigid and hence move faster.

The beautiful thing about glaciers is that they are rivers of ice, really behaving like a liquid. The bottom meter (or so) is even filled with sediments (sand, gravel, stones) like they are picked up by the flow and then whirled into the ice. (We even have a word for these processes: glaciofluvial.)

A typical glacier will move several meters (up to about 30 meters) a day, with the bottom parts moving slower due to the friction with the bed. However, the enormous pressure in the bottom parts of the glacier, make the ice more fluid than that on the top layers. During the flow the top layers of the glacier will often crack, because this part (the 'fracture zone') is so rigid.

Now, I was wondering. May it not be possible that the pockets of water in the lower parts of the glacier are a result of a solid phase water being forced into the liquid phase by the energy the glacier has to absorb on its way?

I tried to find an answer on this wonderfully informative site: Martin Chaplin's Water structure and science (here: phase diagrams). however, I could not find the answer there easily. Probably, because most of the information on the site is too specialised for me (or maybe even just too difficult and complicated).

By the way, it seems that the water in these pockets can't be colder than -20°C; looking at the phase diagram from professor Chaplin's site.


What a wonderful place we live in!

Empty Seas

We really ought to worry about our influence on our precious Mother Earth. I take this very serious, because I believe our world is sacred. The main problem is that we do not understand fully the impact of our actions.

However, since this is the case, I tend to scrutinize all warnings and all solutions. Of course, I do not nearly have enough knowledge of the subject to come up with solutions myself, let alone penetrate the complexity of all consequences. The reason I write this is not to cause doubt, on the contrary! I want to spread awareness of the problems we are facing and show that we should not make rash decisions.

Lately people started warning us for the danger of empty seas: our pollution and our fishing may very well tip the population size of fish, causing them to spiral to extinction. This also may cause famine between animals such as sea birds and dolphins. I strongly hope that fishing becoming unprofitable because of the small catches, will happen before fish population levels dropping below a critical sustainable level. Even then there is hope: from that point on, fish population may reach a new 'stable region' (I mean in phase space, not in the waters of the Earth).

At first I had hoped that fish in the oceans may migrate vertically: they may adapt and start to live at depths where they are save from fishing nets. (I have to find out: Will there be enough nutrients and inflow of energy to sustain a new ecosystem on that depth?) Unfortunately, deep seas are already targeted by trawlers, that can easily catch fish at depth at over 1km.

Who knows, maybe fish will become extinct locally or even globally. That would be terrible. If 'only' certain regions of oceans will become completely depleted, new pioneer species may step in, followed by others. Or maybe, the extinction of fish will cause algae and plants to flourish enormously in the oceans, resulting in a gigantic increase of CO2 absorption from the atmosphere thus relieving part of the climate problem. On the other hand, maybe there will be collapse of the global ecosystems causing the world to wander on a chaotic path. Who knows where that will end up.

Flawed renewable energy

Some days ago, the Dutch media reported that small windmills are no solution for the energy demand; today I read these articles on Slashdot and on Low-tech. It came as no surprise to me that the only relevant factor to windmill power yields is the diameter. This I already heard when I was a child as an answer to why some windmills only have two rotors, whereas others have many- more rotors catch more wind, I thought. (I believe my parents took me to a Greenpeace meeting in the mid-eighties, or 'then-about'.)



After a few clicks, I stumbled upon this Low-tech article: The ugly side of solar panels, where you can read that PV solar panels...

"... with an expected lifetime of only 15 years, the worst case scenario [in which they produce] 207 grams of CO2 per kilowatt-hour – [are] just 2 times better than gas. Agreed, this is the worst case scenario, and even in that case solar panels are still a better choice than fossil fuels. But it becomes quite hard to describe them as a “clean” source of fuel."

There are much cleaner types of solar panels, but we still have the issue of their influence on the albedo factor of their environment.

Apparently, we really need some revolutionary new ideas on energy production.