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Hi,

I have a new blog. Blogspot was nice, but I think wordpress is nicer. You can view my new blog at http://mariusmyburg.wordpress.com.

The square root of 2

One proof of the irrationality of the square root of 2 is the following reductio ad absurdum. The proposition is proved by assuming the contrary and showing that doing so leads to a contradiction (hence the proposition must be true).

Assume that √2 is a rational number. This assumption implies that there exist integers m and n with n ≠ 0 such that m/n = √2.

Then √2 can also be written as an irreducible fraction m/n (the fraction is shortened as much as possible). This means that m and n are coprime integers, i.e., they have no common factor greater than 1.

From m/n = √2 it follows that m = n√2, and so m2 = (n√2)2 = 2n2.

So m2 is an even number, because it is equal to 2n2, which is even.

It follows that m itself is even (since only even numbers have even squares).

Because m is even, there exists an integer k satisfying m = 2k.

We may therefore substitute 2k for m in the last equation of (3), thereby obtaining the equation (2k)2 = 2n2, which is equivalent to 4k2 = 2n2 and may be simplified to 2k2 = n2.
Because 2k2 is even, it now follows that n2 is also even, which means that n is even (recall that only even numbers have even squares).

Then, by (5) and (8), m and n are both even, which contradicts the property stated in (2) that m/n is irreducible.

Since we have found a contradiction, the initial assumption (1) that √2 is a rational number is false; that is to say, √2 is irrational.

This proof can be generalized to show that any root of any natural number is either a natural number or irrational.


See http://en.wikipedia.org/wiki/Irrational_number

Irrational Numbers

I am reading an awesome book, "God Created the Integers", compiled and commented by Stephen Hawking. I admit I am not particularly well-versed in mathematics, but I have the (uninformed) opinion that irrational numbers are a side-effect of a fixed-base mathematical system, which can only approximate certain (i.e irrational) values, and not express them definately.

Now, I may be completely wrong, but I am working on a proof that (X * X) = 2, has a rational VBM solution. VBM is a mathematical system that I have developed in which irrational numbers do not exist because irrational numbers are, by their property of having an infinite decimal expansion, undefined (or unspecified) values.

This is a very complicated exercise and I might find out that I am completely mistaken about irrational numbers. But at the end I will hopefully have learnt something.

Read this

http://freethought.mbdojo.com/nobeliefs.html

Phyllotaxis

Pick up a pinecone and count the spiral rows of scales. You may find eight spirals winding up to the left and 13 spirals winding up to the right, or 13 left and 21 right spirals, or other pairs of numbers. The striking fact is that these pairs of numbers are adjacent numbers in the famous Fibonacci series: 1, 1, 2, 3, 5, 8, 13, 21... Here, each term is the sum of the previous two terms. The phenomenon is well known and called phyllotaxis. Many are the efforts of biologists to understand why pinecones, sunflowers, and many other plants exhibit this remarkable pattern. Organisms do the strangest things, but all these odd things need not reflect selection or historical accident. Some of the best efforts to understand phyllotaxis appeal to a form of self-organization. Paul Green, at Stanford, has argued persuasively that the Fibonacci series is just what one would expects as the simplest self-repeating pattern that can be generated by the particular growth processes in the growing tips of the tissues that form sunflowers, pinecones, and so forth. Like a snowflake and its sixfold symmetry, the pinecone and its phyllotaxis may be part of order for free

Stuart Kauffman At Home in the Universe, Oxford University Press, 1995, p 151. (1) Available from Amazon.com

Daniel Krugel

It is only very recently, 6 days ago, through James Randi's newsletter, that I heard of the man named Daniel Krugel. This man, who lives in South Africa, claims that he has developed a device that can accurately locate matter - biological or non-biological - if he inputs a part of that matter, or something closely related to that matter, into the machine. For instance, he claims to be able to find missing persons if he has a piece of the missing person's hair.

Mr Krugel and his device got quite alot of attention when two parents from England contacted him, claiming that their 3-year-old daughter, Madelaine McCann, is missing. The story goes that the McCanns were staying in Portugal, in Praia da Luz, when their daughter disappeared from their hotel room while they were having dinner with friends while Madeleine stayed in the hotel room alone. The parents contacted Mr Krugel and asked him if he could locate their daughter. According to Mr Krugel, the parents provided him with something that he could use to locate Madelaine, and after 'using' his device, he said he 'thinks' that Madelaine is still in Praia da Luz.

Mr Krugel got quite alot of publicity, and was featured in two of South Africas leading investigative journalism TV shows, Carte Blanche and 3rd Degree. I used to always have respect for 3rd degree in particular. But both shows supported MR Krugel's claims, so obviously, 'investigative' does not come into the picture anymore.

This claim is obviously false. It is not possible to locate matter in this way. So I have contacted Mr Krugel and asked him about his device. I am still corresponding with Mr Krugel, and he has provided me with details that he asked me to handle confidentially, so I am not going to post our correspondences here for now. Suffice to say, Mr Krugel's recent statement to me was that his device shows that Madeleine is still in Praia da Luz.

It is perhaps quite surprising that Mr Krugel has offered to demonstrate his device to me in private. If it comes to that, I will definately take him up on his offer. But first I want to find out some more. I will keep you informed.

Silence Speaks Volumes

Remember I asked Rahotep, the 'Egyptian magic person', to provide me with contact details of a client that would vouch for the accuracy of her predictions and efficacy of her magic? She sent me the contact details of a lady named Irene.

I am sorry, but not surprised, to say that I have not heard a word from Irene since I sent her the email, which appears on this blog.

I wonder if Irene is still making use of Rahotep's services - in exchange for Irene's money. Let's hope not.

Reminds me of Penn & Teller

I just came across this blog entry here: http://blog.andrew.co.za/. It reminds me of the Penn & Teller Bullshit episode where another woman discovered an image of God on her door, and yet another woman who discovered the face of Mary on a toasted sandwitch. My God (OK, he does not exist - but you get my point) people who believe that these things have special significance are ignorant!

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ABC reported yesterday that an American woman discovered God in a brinjal.

Here is the story and here is the picture:

I give praise to Jasis for the Miracle of Vowel Irrelevance.

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Are you thinking?

The third-rate mind is only happy when it is thinking with the majority. The second-rate mind is only happy when it is thinking with the minority. The first-rate mind is only happy when it is thinking.

A. A. Milne (1882 - 1956)

Religious Outlook?

I'm a born-again atheist.
- Gore Vidal

A Rahotep Client - What does she say?

Rahotep sent me the contact details of a long-time client, Irene, who is willing to vouch for Rahotep. So I sent this message to Irene, asking her what evidence she could provide for the validity of Rahotep's claims to be able to use 'Egyptian magic'. Let's see what she replies.

Hi Irene,

I am interrested in the service that Rahotep offers. I am very skeptical when it comes to these kinds of extraordinary claims, and although it would be great if these things are true, it is important to ensure that the people who make these claims are either verified and given the credit they deserve, or exposed as swindlers who prey on ignorance and take people's money for telling them lies. I am going to be honest with you; the scientific community have never found any supporting evidence whatsoevever, for the kinds of "paranormal abilities" these people claim they have. Moreover, there are various people and institutions that offer considerable amounts of money to anyone who can demonstrate that 'paranormal' things exist. So let me be candid: the scientific community thinks that "Rahotep" is a fake.

Now, I am, like the scientific community, willing to believe these extraordinary claims - if the people who make these claims can provide scientific evidence. James Randi is a world-renowned magician, illusionist and skeptic. His foundation, the James Randi Educational Foundation (JREF) (www.randi.org), offers a million dollars to anyone who can prove that they have 'super' powers - people like Rahotep who claim to be able to do all sorts of things, such as 'see past, present and future' and change lives with 'egyptian magic' are perfect candidates for this prize.

Let me make clear my position here: I am not saying that Rahotep is a fake or a liar. I am only saying that, with good scientific reason, I 'think' such people are fake. And as a rational, moral person, I believe that it is my provocative, if not my duty, to do everything in my power to determine if the people who are making these extraordinary claims are telling the truth, and having with them the means to revolutionise science and human understanding, or if they are indeed swindlers.

That is why I asked Rahotep for the contact details of a client who will be willing to share her experiences with me, so that I can determine, both for the sake of science and the client, if Rahotep really has paranormal abilities. Of course you can choose not to take part in this, but I think it would be a shame, for if Rahotep is genuine, then you have the opportunity to teach myself and the scientific community that, and if we find out that Rahotep is not genuine, then you will have helped the skeptic community, and yourself, expose another fake.

So, the first question I want to ask you, is if you have anything substantial that indicates that Rahotep has paranormal abilities?

Thank you,
Marius.

Show me God. Or show me the Devil.

In my last post, I mentioned that a colleague sent me a link to videos that support his view that faith healing is real. On that website, the website author mentions his strong support for T.B. Joshua. In some prelimanary research I found out that T.B. Joshua is a very controversial 'christian'. His greatest opponents are... yes, other christians who claim that he is evil and performs miracles through the power of the devil! See for example the article "Clueless in Nigeria" here: http://www.letusreason.org/Poptea8.htm.

I asked Danie and he said that the person doing the supposed healings in the videos are T.B. Joshua. Of course, it does not matter at all whether or not he performs his miracles through the power of God or old Lucifer - if it turns out to be true, it will be adequately paranormal either way.

Link to the Videos, and More Testimonies

Well, Danie sent me a link to the videos. The videos can be viewed here: http://www.christian-faith.com/miraclevideos/. Is that the best evidence that faith healings are not hoaxes? Let's hope not.

He also sent me a link to http://www.doveministries.com, where I found a long video with lots of testimonies by people who claim that they have been helped by God, through Bill Subritzky. I will see what I can find out about these people, and let you know.

The 'Evidence' is Coming In...

In support of his claim that 'Jesus still heals people today', my christian colleague, Danie, has shared a few videos with me in which people are apparently healed by a faith healer. I have asked my colleague if he has a link where the videos can be downloaded, so that I can share it with you. If there is no link, I will upload the videos somewhere and let you know.

One of the 'healed' is a lady by the name of Linda Marsh. The video shows her stating that she has a heart condition. Now, I am trying to get more information on this lady, and until I know exactly that I have the correct person, everything I find might be irrelevant to this case. But I did find record of 'a' Linda March, that died of heart failure in June 2007. Out of respect I will not post the link to the official site where I got this information, in case this deceased Linda Marsh has nothing to do with this case. If however I find more substantial information on the Linda Marsh who was supposedly healed by a faith healer, I will post it here. And if it is she that is deceased because of heart failure, I will try to contact the family and ask them if I may post the URL of her obituary, in the cause of teaching innocent people and stopping those that exploit them.

To the credit of my colleague, he has admitted that the videos are insubstantial and proves nothing. I commend him for that observation. And I still await the evidence he claims exists...

Second Law of Thermodynamics and Complex Systems

I found this rather good explanation of why the creationists favourite 'evidence' against evolution, that the second law of thermodynamics is incompatible with the formation of complex systems, is simply wrong.

Complex systems

It is occasionally claimed that the second law is incompatible with autonomous self-organisation, or even the coming into existence of complex systems. This is a common creationist argument against evolution.[9] The entry self-organisation explains how this claim is a misconception.
In fact, as hot systems cool down in accordance with the second law, it is not unusual for them to undergo spontaneous symmetry breaking, i.e. for structure to spontaneously appear as the temperature drops below a critical threshold. Complex structures, such as Bénard cells, also spontaneously appear where there is a steady flow of energy from a high temperature input source to a low temperature external sink. It is conjectured that such systems tend to evolve into complex, structured, critically unstable "edge of chaos" arrangements, which very nearly maximise the rate of energy degradation (the rate of entropy production).[10]
Furthermore, the concept of entropy in thermodynamics is not identical to the common notion of "disorder". For example, a thermodynamically closed system of certain solutions will eventually transform from a cloudy liquid to a clear solution containing large "orderly" crystals. Most people would characterize the former state as having "more disorder" than the latter state. However, in a purely thermodynamic sense, the entropy has increased in this system, not decreased. The units of measure of entropy in thermodynamics are "units of energy per unit of temperature". Whether a human perceives one state of a system as "more orderly" than another has no bearing on the calculation of this quantity. The common notion that entropy in thermodynamics is equivalent to a popular conception of "disorder" has caused many non-physicists to completely misinterpret what the second law of thermodynamics is really about.

Respecting Religion

"We must respect the other fellow's religion, but only in the sense and to the extent that we respect his theory that his wife is beautiful and his children smart"

H.L. Mencken

Studying Serious Fairies - A Richard Dawkins Quote

"I doubt that religion can survive deep understanding. The shallows are its natural habitat. Cranks and fundamentalists are too often victimised as scapegoats for religion in general. It is only quite recently that Christianity reinvented itself in non-fundamentalist guise, and Islam has yet to do so (see Ibn Warraq's excellent book, Why I am not a Muslim). Moonies and scientologists get a bad press, but they just haven't been around as long as the accepted religions. Theology is a respectable discipline when it studies such subjects as moral philosophy, the psychology of religious belief and, above all, biblical history and literature. Like Bertie Wooster, my knowledge of the Bible is above average. I seem to know Ecclesiastes and the Song of Solomon almost by heart. I think that the Bible as literature should be a compulsory part of the national curriculum - you can't understand English literature and culture without it. But insofar as theology studies the nature of the divine, it will earn the right to be taken seriously when it provides the slightest, smallest smidgen of a reason for believing in the existence of the divine. Meanwhile, we should devote as much time to studying serious theology as we devote to studying serious fairies and serious unicorns. "

Richard Dawkins

"Rahotep"

I have always been a skeptic. But James Randi and Penn and Teller motivated me to become an active skeptic, that not only doubts woo-woo claims, but actively investigates and, if I find that they are fake, debunks them. This is nescessary since innocent, gullible people are being exploited by con-artists. Morally, we have an obligation to do what we can to stop this.

So I have decided that I will use some of my spare time and resources to be the "James Randi" of South Africa, since this is where I live. Quackery and exploitation is as alive here as it is anywhere, so I will fight it.

I have started browsing the internet and I found alot of people with 'dubious' claims. One has to start somewhere, so I rather randomly picked "Rahotep" - http://www.rahotep.co.za/. I will try to contact him, and try to establish if he can really "see into the past, present, and future", or if he is a lier and a swindler that takes desperate people's money.

Evil Witches!

In Deut. 18:10-12, we read:

There shall not be found among you any one that ... uses divination, or an observer of times, or an enchanter, or a witch, or a charmer, or a consulter with familiar spirits, or a wizard, or a necromancer, for all that do these things are an abomination unto the Lord.

(John Edward? Sylvia Browne? I wonder if they claim to be christians...)

On Richard Dawkins' website, I found this quote by Mark Twain:

"During many ages there were witches. The Bible said so. The Bible commanded that they should not be allowed to live. Therefore the Church, after doing its duty in but a lazy and indolent way for 800 years, gathered up its halters, thumbscrews, and firebrands, and set about its holy work in earnest. She worked hard at it night and day during nine centuries and imprisoned, tortured, hanged, and burned whole hordes and armies of witches, and washed the Christian world clean with their foul blood. Then it was discovered that there was no such thing as witches, and never had been. One does not know whether to laugh or to cry."

A Challenge to The Restored Church of God

I have just sent this message to The Restored Church of God (http://www.thercg.org), which endorses faith healing as an effective treatment for sickness.

Hi,

I was shocked when I read the article "The Truth About HEALING" featured on your website, wherein you encourage people to waste their strength, time and money on faith healings. The scientific community has never seen any evidence that faith healings work, and yet you continue to spread this nonsense to sick people. It is unfortunate, and unfair to many followers who rely on you to tell the truth, that you do not have the moral need to rationally evaluate whether or not your extraordinary claims are true or not. That is a sign of a feeble mind. And the fact that you position yourselves as a teaching institution, while you have a feeble mind, is the sign of feeble morals.

In order for you to defend your reasons for spreading this hope, I hereby challenge you to provide me with proof that faith healings do work. If I am wrong, show me that I am wrong. Clearly, no response, or a response in which you decline the challenge, would signify that you can not substantiate your claims.

A copy of this message to you will be circulated on the internet.

- Marius Myburg.

A Faith Healing Challenge

Today, I have officially challenged a christian work colleague of mine (we are both software developers for a company called Aricent), who believes in miraculous faith healings, to proof faith healing exists and is paranormal. James Randi has kindly offered to post my colleague's reply on SWIFT. Here is a copy of the email I sent to Danie (my colleague) and James:


Hi Danie,

Idle discussion, however interresting, can only take one so far. Then proof is needed to establish if what is discussed, has any merit or not. So I have just emailed James Randi ("The Amazing Randi" - www.randi.org), telling him about your mention of miraculous faith healings (and in particular, the story you heard about the boy who was miraculously healed after a christian community prayed for him) when we had another one of our religion discussions this morning. I told him of my informal challenge that I put forward to you: to find scientifically sound evidence for the existence of this phenomenon. You said you are not interrested in the million dollars the James Randi Educational Foundation offers, but I am sure your church, or any organization or cause of your choice, will find the money most helpful.

So, if you are interrested in the truth, I hereby officially challenge you to present the JREF with scientifically unambiguous proof for the existence of a 'paranormal' (or 'God') cause for healings. Like I said this morning, if God does really miraculously heal people, then it should be easy for you to simply find evidence that supports this. Get the phone numbers of the the people who claim their son was miraculously healed. Phone the doctors who treated him. Obtain a statement from the doctor. That is a simple start!

James Randi has kindly offered to present your reaction to this challenge on his website. That would be wonderful exposure for any proof you may find for the existence of god. You will reach, and recruit for your god, more people that the average pastor will in a lifetime.

I want you to realise that by agreeing to undertake this study, you are either going to 1) revolutionize science with your proof, and get a million dollars, and cause many people to start having a reason to consider believing in your God, or 2) realise that your faith is built on stories and myths, and revolutionise your own way of thinking. Either way, it is good! Or, of course, 3) ignore the lack of evidence and continue to believe blindly. Which would be the worst possible response to this challenge. Of course you may choose not to accept this challenge, but that would be synonymous with (3), at least I think so. In your hands lies the opportunity to give alot of merit to your belief system.

I hope you are not offended by such an official challenge. But, from my sceptic viewpoint, I am trying to help you see the light. And, from your religious viewpoint, you now have an opportunity to make me, and thousands of other people, see the light. Just show us the supporting evidence we ask for. If miraculous healing is a real phenomenon, 'simply show us'. That is really all we ask.

Regards,
Marius.




Let's see how he replies.