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Sunday, July 13, 2014

Real Life? or dream?

Most people, however bad their life might seem from time to time, don’t want to leave it. The fact is, people are addicted to this human game.  I see it as a game that we, for mysterious reasons, have decided to play. After all, what else is there to do?! We don’t know.

 But what happens when we die – leave the human game?  Many people have beliefs, perhaps strongly held and even exclusive, but few have certainties, based in experience.  My personal belief takes its source in what happens to a dream character when we wake up.  The character is seen to have had no real existence, though we didn’t realize this while we were dreaming.  I think that’s what happens when we die.  I cannot say “I” will see that I had no real existence, since “I” will be seen to have never really existed – to have been imaginary, with a body somewhat like a counter in a board game, enabling me to play, collect rewards and forfeits, compare myself with others etc.  We call this “real life” since that’s how it appears to us, and if we understood that it is no more real than a dream, it might lose some of its excitement. Like the follower of this blog who unfollowed me when I queried “is life important?”  Life, to her, still relatively young, was vividly important.

Who, then, will see that I was only a dream character?  We have to resort to impersonal verbs: “it will be seen” – like that. The really fascinating thing is that for some, this seeing has occurred while they were still actively playing this dream game.  They tell us that though life is transformed, it still continues much as before, though since it's apparently a dream in which they no longer have a personal identity, they see it very differently.

 Should anyone be interested in acquiring this “seeing,” it seems it cannot be commanded.   

I may continue this subject in a day or two.

Sunday, June 29, 2014

Try this Mandelbrot program I have written

During the last three weeks I have been amusing myself learning the java programming language.  It hasn't been so easy as at the age of 84 learning and remembering new stuff is harder than it used to be! I have had some help from my son Claude.

To give me inspiration I decided to use my interest in the Mandelbrot set to get to grips with the java language.  I created a program which displays the whole set and you can outline any area you think might be interesting to examine it more closely.

There is a limit to the minimum size of area, due to the limitations of computer precision and it's unavoidable.  However there is plenty of interesting stuff there.

I believe that to see the Mandelbrot set as anything more than a pretty picture or a boring mathematical formula, you need to be mathematically inclined.  The fascination, for me, lies in the mysterious ability of this formula to produce extraordinary patterns from apparently humdrum repetition of a formula.  Looking at the patterns, I am struck by the similarity to many natural forms: Could it be that natural forms, such as a leaf or a flower, have as their formal basis a mathematical formula? Is mathematics more pervasive in the universe than we have heretofore imagined?

There is also the weird phenomenon of little pieces of the set cropping up at some distance from the main chunk, similar in shape but facing in different directions and connected to it by untraceably fine filaments (there are no isolated pieces, they say, and I also suspect that every distant piece is connected to the main by only one path.)
In case anyone wants to explore for themselves, this is a link to the file of my program which I have placed online for anyone to download and try.  To run it, or any other java-based program, you need "java runtime environment" which you probably already have on your computer, but you can download it at the Oracle website if you don't have it.
Once you have opened my program, use your mouse to draw a rectangle somewhere interesting, then press ENTER.  Drawing the rectangle is largely automatic as it has to be horizontal and have certain proportions, so you only need draw the top side of it.  A little practice will soon give you the idea. Email me if you need help.  Read the info on the left of the screen. "Page Up" increase the precision at high magnifications, but also takes longer to draw the picture - perhaps ten seconds or more depending on your  machine's speed..

Possibly you can also open the file in a text editor such as Notepad or Wordpad, if you want to fiddle with it and make alterations.

Friday, June 20, 2014

More Mandelbrot

The Mandelbrot set holds endless fascination for me.  Who would have thought that repeated iteration of a simple mathematical formula could show such intricate, repeating patterns?  For the first picture I used 5,000 iterations as the maximum necessary for determining whether a given point in the complex plane is a member of the set (shown black) or not.  This means that every tiny pixel in the black areas is black because the formula has been iterated 5,000 times to make it so.  It takes 3 or 4 seconds for my laptop to generate this picture, and roughly, say, a quarter of the picture is black and there are nearly a million pixels in the picture. So that alone necessitates 1,250,000,000 iterations, and each iteration means a lot of work for the computer.  What an amazing thing a modern laptop is!  Without such devices at our disposal, we never could have guessed at the intricacies depicted here.

The parts which are not black are points which have been rejected before 5,000 iterations have been performed for them, and their colour is dependent on the number of iterations necessary to decide they should be rejected.

By the way, I read somewhere that it has been proved there are no isolated pieces of the set, every little black bit is connected to the main chunk, even though we may not be able to see the connection because screen resolution is not fine enough or perhaps because we have not used enough iterations, resulting in a pixel being shown black when it shouldn't be. 

Tuesday, June 03, 2014

Do I exist?

The question of the near-universal restricting sense of "I" afflicting humans is a highly interesting and puzzling one. I say "near" universal because there are some people - let's call them "No-I"s - who don't have this restricting sense of "I", they have lost it either intentionally or fortuitously; and "afflicting" because it seems to be at the bottom of nearly all the suffering in human society. The No-Is can still say "I" but it doesn't mean the same thing for them as it does for us unregenerates.

Taking myself as an example, how is it that I have this particular sense of "I" and not some other person"s sense of "I"?  Of course, if I had some other person's sense of "I" I would not be aware of that, I would believe I was that other person, so it seems like a very silly question.  But give it some thought. It can have an effect rather like some of those drawings by M C Escher.

The sense of "I" seems to go with a particular body. As far as I am concerned, this body I am associated with is the centre of my universe.  But is this restricted sense of "I" really necessary?  Some - those who have lost it - say that it's a handicap, and life is infinitely better without it.  Sure, the body-mind organism is still there for use as necessary, but the sense of their personhood has gone.  It's an illusion we would be better discarding.  Each of us thinks that he/she is a person, with goals, problems, etc. but, say the No-Is, this is simply an illusion which dramatically restricts your life and is the cause of all suffering. It sticks, too.  You can't get rid of it easily, because you really do think you are a person - don't you?  It would  be like committing suicide!

The Buddha, it is said, sat under a bodhi tree and vowed not to get up until that illusion had released its hold on him. It did so release, and he did get up, to teach others. He is famously supposed to have said, "Events happen, deeds are done, but there is no doer thereof."

Many will become very indignant when I suggest that the belief that they are a person may be mistaken. It's just a suggestion, but it deserves some thought.

Sunday, June 01, 2014


This picture is a very tiny detail from an image of the Mandelbrot set, a set of complex numbers defined by a simple recursive formula. I made it in the course of modifying Daniel Schiffman's program written in the "Processing" programming language ( I love playing around with programming, especially graphics.)

The Mandelbrot set has fascinated mathematicians and scientists - and other kinds of people, too -  for some decades now, especially since the advent of powerful computers made producing its image very simple.  Magnifying any interesting-looking area will simply produce more fascinating detail, and there's no end to it - in theory.  In practice, it's limited by the ability of the computer to deal with many decimal places.  The image above is a portion of the image below, much magnified (and colour added.)

When I first tried to make the Mandelbrot set image, 23 years ago, my PC had to be left on all night in order to give it time to draw it. I programmed it in the language called "C."  Now, my very ordinary laptop takes just a few seconds to produce a colour image.  Here is an image of the complete set: Those filaments wandering out from the main mass can be magnified to show the kind of detail in the first picture.

Saturday, May 24, 2014

Mango delight

Twenty years ago Rose planted mango seeds, from which three or four trees have been allowed to grow.

It's the mango season here now, and they are plentiful in the stores and on the streets.  Our trees have excelled themselves, and every flat surface in and around our house is covered in big, fat mangos.

Our mangos are the best.  No exaggeration.  I have eaten a great many over the last twenty-three years and no mangos commercially available are as good, flavourful and juicy as those from one of our trees. They have thinner seeds, too, which means more of the weight is edible flesh.  You will notice from the photos that our mangos do not necessarily have the clear  yellow colour the commercially grown product usually has.  I don't know how the growers get them that way, but our dull skins do not detract in any way from their eating qualities

They have to be harvested carefully as if they are allowed to fall they get damaged, and left on the trees the fruit bats enjoy them.  Fortunately Sonny Lopez, our part-time helper, is small, strong and agile and can go up the trees as necessary to bring the mangos down.  He can then take a big bag of them home for himself and his family, and Rose has to give away as many as possible as fast as possible.


We have known Sonny for almost twenty three years and he has has been a great help to us in many ways, building and maintaining much of our house and willing to do almost anything.  He has never learned to read paper plans, which has been a slight disadvantage but since I can read them easily it doesn't matter much.  During the  years I spent building and sailing boats here, he was a frequent companion in my trips to other islands, besides being a great help in the boat-building process.  For a number of years we employed Sonny full time, but he began to develop other interests and take on social and community duties - elder in his church and president of a local association, plus a small business of his own - so the arrangement morphed into part time.  It's enough, as it happens, as we have no big projects in hand now.

Monday, May 12, 2014

Yogurt making

I happen to be very fond of yogurt.  None is available in this town, so I have tried various methods of making my own.  We can easily get through a litre of yogurt every day between the three of us, as we like to use it in cooking.

The first try I used powdered filled milk ("Alaska" brand) with some skimmed milk powder added.  I mixed it in water, about 1.5 litres, heated it to 180 deg F, and after letting it cool to 115 deg I added a teaspoon of Lactopafi (a kind of horrible health drink we can buy here), which I was hoping might contain suitable live bacilli.  I transferred all to a clean vacuum flask and after about eight hours I opened it to find and enjoy some excellent yogurt!  I was surprised.

I made another successful batch, and yet another using Yakult as a starter, but then things began to go wrong and I could never duplicate my first attempts successfully.  Instead of yogurt, I got cheesy curds and whey.

After three unsuccessful attempts, I gave up and decided to buy a yogurt maker.  I chose "Easiyo", and it came with a packet of milk powder and starter mixed.

This device is very simple and consists of an external insulating container, into which you pour boiling water.  You mix the powder with water to one litre in a separate inner container, which is closed tight and lowered part way into the hot water, then the lid is put on the external container and after 8 to 12 hours (8 hours for me, our climate is warm) there you have your yummy yogurt.  Couldn't be simpler.

The next day I made another batch from Alaska powder, skim milk and a spoonful of the first batch for starter.  That was successful, too.

I will just go on using previous batches as starters until that stops working, then I will try Yakult again.  If that doesn't work I will just buy another ready-mixed packet from the original vendor.


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