Just Thinking

This is not the sort of pie you can eat, but rather the ratio of the distance around the sort of pie that you can eat compared to the distance across it. The history of the accuracy to which the value of pi has been determined is quite interesting and that is what this article is about.

When I was at school we were often told to use the approximation for pi of 22/7 which is 3.142857 ... although this is a bit of a rough value being wrong in the 3rd decimal place, a better fraction being 355/113 = 3.14159 292... but the nice thing about this very accurate fraction is when it is expressed as a division of 113)355 because it can easily be remembered from the 113355.

I have always liked that fraction of 355/113 ever since I came across it as a young man. I have even seen an explanation for this one in the bible, which is much better than the pi equals three that is also claimed to be there.

These can be compared to the true value being something like this:

pi=3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 ...

Historically pi had to first be determined by making a circle and rolling it and comparing to the diameter by measurement and early values around the world tended to be between 3 1/8 and 3 1/6 and centered around 3 1/7 which is quite close to the true value. In other words the accuracy was only a little better than 1% although careful measurement can reasonably easily achieve at least one more decimal place than that.

This graph shows several thousand years of the history of the accuracy of pi determinations and there are two main phases although they are not quite distinct. The first phase was of actual measurement and shows only a little improvement over a long period.

The second phase is based on finding ways to calculate pi based on various geometric constructions and using trigonometry to determine the value. Usually this means dividing the circle into many small identical triangles that are thin slithers and adding the circumference up as the many sided figure approximates a circle more accurately as the number of sides increases.

The accuracy of Pi as determined by measurement or calculated by humans.

The second phase of calculation really got going from around 1400 onwards when Madhava in India calculated pi to 11 decimal places. However before that, in about 480, Zu Chongzhi (or Tsu Ch'ung Chi) had found the fraction 355/113 which is accurate to 7 decimal places.

Eventually some formula for pi were discovered based on trigonometric expansions and these were easier to go to more places, but still required a lot of long calculations when done by hand. Remarkably people did hand calculations of pi to more and more digits, reaching 626 digits by Ferguson by 1946. One poor chap, Shanks, did 707 places back in 1874 but made a mistake after the 527th digit.

However from 1947 onwards computers took over from humans as the pace-setters of pi, starting with 710 places in that year and going ahead in leaps and bound to 1,240,000,000,000 places in 2005. This is pretty remarkable as disk technology today will only hold the answer on the very largest single disk drives manufactured. You need something more for the working. Note that this diagram expands the time axis and compacts the accuracy axis, so the rate of improvement is very much faster.

The accuracy of Pi as calculated by computers.

The rate of improvement in the value of pi was very slow by measurement, perhaps doubling the accuracy (by which I mean halving the percentage error) every 500 years roughly. But with formula based calculation by humans the improvement became some 7 times faster, doubling the accuracy about every 72 years as shown by the trend line in the first graph. But computer calculation meant a doubling in accuracy every 1.8 years as shown by the trend line in the second graph, a further 40 fold improvement in the rate of progress.

For comparison, the record for remembering pi is shown on the second graph. For a while human memory was gaining on computer calculation, but when computer calculation interest in pi calculation was rekindled in the 1980s, people got left in the dust. There is no chance that ever again people will be able to learn all the places of pi that computers can calculate. In fact, if a long lived person spent their whole waking life reciting pi they could only get to about 10^9 decimal places which is only 0.1% of the present determination ... but by then, at the present rate of improvement, the value of pi would be known to 10^28 digits, so they would be far further behind than when they started.

References used in preparation of this article:
* Wikipedia article about pi
* Wikipedia article about approximations to pi
* Chronology of pi determinations
* Zu Chongzhi who determined pi in 480

"Non-cooperation with evil is as much a duty as is cooperation with good."
- Mohandas Gandhi

In todays world it is easy to say that the problems are so great that as individuals we cannot affect them. That is exactly the cause of problems - that no-one stands against seemingly overwhelming forces. Just which snowflake in an avalanche can be held responsible? Another view ...

…We don’t have to engage in grand, heroic actions to participate in the process of change. Small acts, when multiplied by millions of people, can transform the world. Even when we don’t ‘win’ there is fun and fulfillment in the fact that we have been involved, with other good people, in something worthwhile. We need hope. An optimist isn’t necessarily a blithe, slightly sappy whistler in the dark of our time. To be hopeful in bad times is not just foolishly romantic. It is based on the fact that human history is a history not only of cruelty but also of compassion, sacrifice, courage, kindness. What we choose to emphasize in this complex history will determine our lives. If we see only the worst, it destroys our capacity to do something. If we remember those times and places—and there are so many—where people have behaved magnificently, this gives us the energy to act, and at least the possibility of sending this spinning top of a world in a different direction. And if we do act, in however small a way, we don’t have to wait for some grand utopian future. The future is an infinite succession of presents, and to live now as we think human beings should live, in defiance of all that is bad around us, is itself a marvelous victory."

- Howard Zinn

I have taken the above quote from NonviolenceUnited.org who always capitalise the "Non" but never the "violence". This is an organisation aiming to get people to think and act in new ways that help reduce violence of all types in the world right now, not waiting for the next election, not waiting for someone else to act, but each of us choosing to do what we can do now. The site is full of inspiration thoughts and quotes and advice on how to live with these ideas in your heart at all times.

We nearly all think of Gandhi as a great man, but how many of us follow his advice? There is much evil in the world today, with especially the large and powerful nations having governments controlled by very corrupt people, and this situation can easily lead people to despair. But that is exactly what those leaders and manipulators want us to do. We can instead decide that we will be millions or billions of people simply not co-operating with their schemes of invasion, enslavement and greed.

"We can re-invent civil disobedience in a million different ways... The corporate revolution will collapse if we refuse to buy what they are selling -- their ideas, their version of history, their wars, their weapons, their notion of inevitability. Remember this: We be many and they be few. They need us more than we need them. Another world is not only possible, she is on her way. On a quiet day, I can hear her breathing."

- Arundhati Roy

Arundhati Roy is the author of "The God of Small Things" for which she received the 1997 Man Booker Prize for Fiction. She gave a 44 minute speech Come September as the Lannan foundation lecture for September 2002. She is Indian and talks particularly about the situation in India and Pakistan as well as the World. She speaks of living outside of patriotism, something that I have long felt is necessary to solving international conflicts. "My country right or wrong" is always wrong. Roy is an inspirational speaker and I recommend this video. Some brief excerpts ...

"flags are pieces of coloured cloth that people use, first to shrink-wrap people's brains, and then as ceremonial shrouds to bury the dead"

"grief ... the death of dreaming ... the (absolute) unfairness of the world"

In 1989 Bush Snr said that Saddam Hussein was committing genocide on the Kurds. He sent him $500,000,000 in subsidies that year, and $1,000,000,000 the following year. After the first gulf war he implemented sanctions that caused the death of 500,000 children.

Wikipedia on Arundhati Roy.

"Nonviolence is the greatest force at the disposal of mankind. It is mightier than the mightiest weapon of destruction devised by the ingenuity of man.

Literally speaking, ahimsa means non-violence towards life but it has much higher meaning. It means that you may not offend anybody; you may not harbor uncharitable thought, even in connection with those whom you consider your enemies. To one who follows this doctrine, there are no enemies. A man who believes in the efficacy of this doctrine finds in the ultimate stage, when he is about to reach the goal, the whole world at his feet. If you express your love—ahimsa—in such a manner that it impresses itself indelibly upon your so-called enemy, he must return that love.

This doctrine tells us that we may guard the honor of those under our charge by delivering our own lives into the hands of the man who would commit the sacrilege. And that requires far greater courage than delivering of blows.

Ahimsa or non-injury, of course, implies non-killing. But, non-injury is not merely non-killing. In its comprehensive meaning, ahimsa or non-injury means entire abstinence from causing any pain or harm to another living being, either by thought, word, or deed. Non-injury requires a harmless mind, mouth, and hand."

- Mohandas Gandhi

Ahimsa is actually a central tenet of Hinduism, Buddhism and Jainism, but is also present in the West through the Hippocratic Oath taken by doctors which includes the statement "I will prescribe regimens for the good of my patients according to my ability and my judgment and never do harm to anyone" and often summarised as "first do no harm". It is present also in Christ's advice to "turn the other cheek" and "love your enemy". It is the foundation of a peaceful and moral life regardless of one's religion.

I recommend NonviolenceUnited.org as a useful resource for those who would embark on a path of trying to make this world a better place to live.

In this article the question is asked Is the United States Killing 10,000 Iraqis Every Month? Or Is It More?

A state-of-the-art research study published in October 12, 2006 issue of The Lancet (the most prestigious British medical journal) concluded that -- as of a year ago -- 600,000 Iraqis had died violently due to the war in Iraq. That is, the Iraqi death rate for the first 39 months of the war was just about 15,000 per month.

That wasn't the worst of it, because the death rate was increasing precipitously, and during the first half of 2006 the monthly rate was approximately 30,000 per month, a rate that no doubt has increased further during the ferocious fighting associated with the current American surge.

Remember that is up to October 2005 and almost two more years of increased violence has passed since then.

It is difficult to imagine this amount of bloodshed. If you take all your family, all your friends and work mates, you might come to several hundred people. That would amount to the morning of one day of killing. Can you imagine the horror of that? Can you imagine repeating that again in the afternoon, again in the evening and again in the night? What about every day of every week, year after year.

And why is this being done? Quite simply because the likes of Bush and Cheney have been telling lies for money. And they got Blair to go along with them. The scale of their lies is so great that many people cannot believe that people would stoop that low, so they pretend that it isn't happening. These men have been paid billions of dollars to tell lies to profit other evil men who wish to sell weapons of mass destruction and to steal and / or control oil. What they have accused others of in their lies, they have actually done.

The following pictures represent the typical result of just one typical hour of USA activities in Iraq. And look at what America's young people are turning into! Gloating at the death and suffering that they cause. They will make model citizens when they come home won't they?

For more pictures like this go here and here and here.

I know that this is hard to look at. Imagine how much harder it is to live with or die with. Whoever in the USA does not act now to impeach Bush and Cheney is equally responsible. American's elected them. They were known to be liars and criminals at the last election. Their list of crimes grows daily and they show contempt for the law in many ways.

Both the USA and UK must make certain that they look for better morals from their leaders in future. The Democrat party is no better than the Republicans. Their leaders do not set out to impeach Bush and Cheney for only one reason. That reason is not that they wouldn't be successful. It is that they do not want new leaders now, as they think they can easily win the next election if they do not act.

Go to the title link to see the original page.

It is stated that already 100,000 people have signed this petition.

Ten Reasons to Impeach George Bush and Dick Cheney
I ask Congress to impeach President Bush and Vice President Cheney for the following reasons:

1. Violating the United Nations Charter by launching an illegal "War of Aggression" against Iraq without cause, using fraud to sell the war to Congress and the public, misusing government funds to begin bombing without Congressional authorization, and subjecting our military personnel to unnecessary harm, debilitating injuries, and deaths.

2. Violating U.S. and international law by authorizing the torture of thousands of captives, resulting in dozens of deaths, and keeping prisoners hidden from the International Committee of the Red Cross.

3. Violating the Constitution by arbitrarily detaining Americans, legal residents, and non-Americans, without due process, without charge, and without access to counsel.

4. Violating the Geneva Conventions by targeting civilians, journalists, hospitals, and ambulances, and using illegal weapons, including white phosphorous, depleted uranium, and a new type of napalm.

5. Violating U.S. law and the Constitution through widespread wiretapping of the phone calls and emails of Americans without a warrant.

6. Violating the Constitution by using "signing statements" to defy hundreds of laws passed by Congress.

7. Violating U.S. and state law by obstructing honest elections in 2000, 2002, 2004, and 2006.

8. Violating U.S. law by using paid propaganda and disinformation, selectively and misleadingly leaking classified information, and exposing the identity of a covert CIA operative working on sensitive WMD proliferation for political retribution.

9. Subverting the Constitution and abusing Presidential power by asserting a "Unitary Executive Theory" giving unlimited powers to the President, by obstructing efforts by Congress and the Courts to review and restrict Presidential actions, and by promoting and signing legislation negating the Bill of Rights and the Writ of Habeas Corpus.

10. Gross negligence in failing to assist New Orleans residents after Hurricane Katrina, in ignoring urgent warnings of an Al Qaeda attack prior to Sept. 11, 2001, and in increasing air pollution causing global warming.

The above are all well documented and proven statements. Any one is sufficient grounds for impeachment. The Libby pardon has to be taken by Americans as the final sign that Bush treats them and the law with contempt.

The sooner that the USA gets this job done, the sooner they stop their country looking foolish in the world and have a chance to repair some of the damage that has been done.

Known as the Golden Rule, many Christians will know this as a Christian saying: "Do unto others as you would have them do unto you". It is also a saying of Buddhism, Hinduism (or Brahmanism), Taoism, Confucianism, Islam, Paganism, Judaism, Zoroastrianism and others. For details of this claim, see these articles on the golden rule and the ethic of reciprocity (wikipedia). See also Peace be with you.

Recently my post Religious Belief and Social Problems received some discussion and it also resulted in me having long discussions with Atheists and Theists outside of this blog. In reply to one remark in the blog I stated:

... Better to understand that "as you give, so shall you receive" and "do unto others as you would have done unto you". These are practical guides to living. However these beliefs do not require a belief in God, the bible, prayer or attending church to work.

I have added the bold here, because I want to emphasize that atheists can equally well as theists believe in the golden rule. However when they do so, they believe in it for its own sake, not as a means of getting a reward in the hereafter. That is not to say that all religious people do that, but many think that way. Belief in the principle for its own sake is more pure and leads to healthier actions. Lip service is worse than useless.

One thing that I especially wanted to raise in this article is the awareness that I have had from a number of atheists that have been brought up in religious families. A large number of these people exist, and they are really tortured by the experience. If your response to that remark was that they deserve it, then you are not a Christian, for that is not Christ's teaching. This is the typical scenario for a person in a religious family that becomes an Atheist:

1. Have doubts about the existence of God or the Bible's divine inspiration. Keep it to themselves for a while.

2. Mention the doubts. Get told that they will go to hell if they don't believe. This keeps them pretty quiet for a while but probably makes them think even less of God as he is then seen as the ultimate bully.

3. Keep quiet about it for a long time and live a double life, pretending to believe. There must be huge numbers of such people who fill out the census with "Baptist" or "Catholic" or whatever but secretly do not believe.

4. Develop guilt and repress thoughts. This is unhealthy for a person to live this way.

5. Once they become independent from their parents they may meet others that think like them and gain courage. They then move in different circles avoiding the "bible-bashers".

6. Tell their families about it which leads to storms and accusations that "you will go to hell" but "I will pray for you". They are unable to be themselves around their families. That is unhealthy, as everyone needs love and acceptance from their families.

7. Either stop associating with their families or keep living a double life and trying to avoid the family. This benefits no-one.

Now, here is a question directed at Christians or other theists. How can you reconcile this type of behaviour towards your children with the golden rule? Admittedly it is not as bad now as the inquisition. But if you knew the torment that you put your children through and the lasting damage, and the way you drive them away from your religion, you would not do this. Christ's message is clear. Love everyone and judge them not. It is not your decision whether they go to hell or not, but if you think it is then you create hell right now in this life for you and your children.

I see so much Satanic music and videos come out of America. The energy for these things is fed by the denial of the believers. They create the atmosphere in which those that started with doubts learn to hate instead.

It amazes me that in the developed world, Americans preach more religion and go to church more than most other countries, and at the same time they have more guns, commit more murders, attack and invade far more other countries than anyone else, and often in the name of God. This is the utmost hypocrisy. If there are any people who really believe in Christianity in America, they should certainly not support such people as George W. Bush because all his behaviour is so much against all Christ's teaching. And yet so many of the religious in America do vote for Bush. I cannot understand this at all. They have all entirely failed to get the message. Turn the other cheek. Do not tell lies. Do not kill. Love your enemy. Do not covet your neighbours oil wells.

I have been told by an American Theist that all Atheists are Satanists. You cannot be a Satanist unless you believe in God and hate him. By definition an Atheist cannot be a Satanist. He also says that the roots of Atheism are in Marxism. Excuse me, but Atheism existed for many centuries before Marxism was ever thought of. Is it compulsory to think crooked and to abuse people if you are religious? You will note that I am criticising many religious people in America, but I am not abusing them. I am telling them, please think about what you do. If you are really a Christian, then follow Christ's commandments. That means you should:

a. Let you children speak their minds and kindly explain your beliefs to them. Allow them to reach their own conclusions. They will love you for that.

b. Do not vote for Presidents that you know have attacked other countries or suspect that they might.

c. Do not send troops to other countries. Speak out against this.

d. Cut down on your oil usage by getting a car that uses half as much gas so that your country can stop invading other places.

e. Read up on the news and find out the lies that your leaders are telling you. Bush, Cheney and Libby are criminals.

f. Teach your children to understand people from other countries and treat them with respect.

g. Love everyone including Atheists.

If you do all these things, then I will believe that you are a Christian and I will hold you in the highest respect for practicing what you preach.

In recent years customer loyalty schemes have been all the rage. They range from having a stamp put on a card when you buy another book or greeting card at the stationers to a pre-paid card that give special prices when you buy pizza or movie tickets, from special petrol price vouchers when you buy groceries to fly buys on everything that you purchase. They are retailers attempts to get you to keep using their stores. This article examines whether these schemes can possibly benefit anyone.

One way that I like to look at things is to see what would happen if everyone did the same thing. After all, if the scheme is a good one, everyone will copy it. So the end result of these customer loyalty schemes is now clearly visible.

You now have to keep loads of bits of paper and cards with you all the time, waste time at shops and checkouts getting stuff filled in and stamped, get really annoyed when you finally get enough stamps on your book club card only to find that the original purchase date is too long ago and the offer has expired, and you pay for all the paper work in the prices --- and collectively the retailers are doing more work, employing marketing idiots (yes, you know who you are) to do nothing useful and collectively not getting 1 cent more income between them. They must have to put up their prices to pay for all their extra costs. We are paying more to have our time wasted. If they didn't do this they could have a price advantage which is what people really want.

People are not spending more. All the businesses are getting the same total income. They are all spending more money doing this stuff. They are wasting money on running the schemes. They are wasting time while their employees do the paperwork. They are paying for extra materials that all end up in rubbish dumps. They are annoying their customers. It is madness if you even think about it for a few minutes.

Please, why don't they all agree to call it off. If they don't we need to all agree to never shop at a place that offers these schemes. Prices must be able to be kept lower if no silly schemes are run. Let us never shop at such places.

My conclusion is that we live in an age ruled by marketing hype, and full of people that cannot think straight. These things are not worthy the time spent on them. They benefit no-one. They waste everyone's time. People knock on your door and phone you incessantly with special offers that are useless to those selling them and those buying them. They employ people in jobs that should not exist. Let them get a proper job doing something useful.

A related scheme is the people that telephone and tell you that you have won something, when really they are trying to get you enrolled in some pathetic scheme. My conversations with them go like this.

Me: Hello

Them : Congratulations, you have won a package worth $170 ...

Me: No thanks.

Them: ... but I haven't told you all the benefits of ...

Me: No thanks. I don't need it.

Them: ... its free and you get all this wonderful ...

Me: No thanks. I don't want it.

Them: let me tell you about ...

Me: No thanks. Good-bye.

How can any self respecting person spend hours on the phone each day annoying people with promises of free things, when they know that they are lying? It must cause serious stress to do this. Even worse, the people that dream up this stuff! They should all have to spend 3 months ringing each other and answering calls day and night until they surrender and promise never to pester anyone or tell a lie for the rest of their life.