Schocking images from the Tibetan unrest

Thanks to http://justar-lawblog.blogspot.com/, I became aware of the following. We are all aware of the Chinese oppression in Tibet, but to watch the video below is particularly upsetting.

The first images from the oppression in Tibet- Nouvel Obs
The images in this video, at times shocking, were given out by the Tibetan government-in-exile. One can see Tibetans beaten up by police forces. Particularly hard to look at are the images of a young man, apparently tortured and eventually killed by his severe wounds.

Euclid's Elements

Euclid wrote the Elements around 300 BCE. It is, arguably, the most influential book in the history of mathematics. It is divided into 13 Chapters (or "Books") and deals (in modern terminology) with Geometry, plane and solid, Algebra, and Number Theory. It represents the pinnacle of pure thought which clearly shows the achievement of a successful civilization more than 2000 years ago.
For centuries, the Elements remained the basis of Mathematics and Sciences.

We do not possess the original work. The oldest surviving copy dates from the year 888 CE. It was copied by someone known as "Stephen the Clerk" and sold to Arethas of Patras, one of the most scholarly theologians of the Orthodox Church. Despite the custom to destroy ancient works, Arethas preserved and propagated a few. Besides Euclid, he was also interested in Plato and Lucian and produced commentaries of their works. Arethas served as Archishop of Caesarea and was a disciple of Photius I, Patriarch of Constantinople (a scholar himself, notably known for the conversion of Slavs into Christianity and the introduction of the filioque which led to the split between the Catholic and Orthodox churches). I am not aware of what immediate influence Arethas' work had: did someone study Euclid's Elements? Did it produce further scholarly works? Was it considered, simply, a curiosity? It is clear that Arethas himself was not satisfied with the status quo of the church, i.e. the despising of Greek and Latin scientific and secular works, and played a role in reinstating their importance.
The long-term influence of Arethas' copy needs, of course, no comment. Without it, how would Newton's Principia (if it existed) look like?

Arethas' copy of Euclid's Elements can be found in Oxford's Bodleian Library. It has been there since 1804. The Clay Mathematical Institute has produced a high-quality electronic copy of it. The electronic edition contains a superb reproduction of the original text (as written by Stephen). It is hard to read because the fonts used by Stephen belong to the so-called "μικρογράμματη γραφή [mikrogrammati grafi]" or "small-letter script". However, we can also find, on the Clay Institute site, a version in modern Greek fonts, which is easy to read and is also easily understood by the modern Greek speaker, along with translation in English.

Here is an example of a number-theoretic contribution from the Elements (Book 9, Section 36):

Ἐὰν ἀπὸ μονάδος ὁποσοιοῦν ἀριθμοὶ ἑξῆς ἐκτεθῶσιν ἐν τῇ διπλασίονι ἀναλογίᾳ, ἕως οὗ ὁ σύμπας συντεθεὶς πρῶτος γένηται, καὶ ὁ σύμπας ἐπὶ τὸν ἔσχατον πολλαπλασιασθεὶς ποιῇ τινα, ὁ γενόμενος τέλειος ἔσται.

If as many numbers as we please beginning from a unit be set out continuously in double proportion, until the sum of all becomes prime, and if the sum multiplied into the last make some number, the product will be perfect.

In modern mathematical lingo, this says the following:

Let n be a positive integer. Consider the numbers 1, 2, 4, 8, ..., 2^n-1, that is, the first n powers of 2. Let S_n be their sum. Assume that S_n is a prime number. Then 2^n-1S_n is a perfect number (i.e. it is the sum of its proper divisors).

The proof can be found here.



Comment: We can easily see that S_n = 2ⁿ-1. We assume that this is a prime number. (Prime numbers of this form are [now] known as Mersenne primes.) Based on this, we conclude that 2^n-1S_n is a perfect number. In other words, we have a "formula" for perfect numbers:

2ⁿ⁻¹(2ⁿ − 1) is perfect if 2ⁿ − 1 is prime.

This works for n=2, 3, 5, 7, e.g.,
2⁶(2⁷ − 1) = 8128.
The divisors of 8128 are:
1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032, 4064.
Their sum is 8128.

P.S. A converse (due to Euler) to Euclid's proposition is also true. Namely, if an even number is perfect then this number must be of the form 2ⁿ⁻¹(2ⁿ − 1).

Poe's Law

Yesterday, I saw a comment following a posting about Stoning in Islam that read as follows (copied and pasted verbatim):

Dear ,Brother
the emobreoilded allegation by some ignorants to Islam Quran that ; the stoning the adoltery (Rajum Alzani wa l Zaniyah)in fact these brutial canons do only apply in the jewish and christians manuscripts the Turah & the Gospel ,Providentialy We Muslims simply dont have these canon or what so ever Quranic verses revelation stating to stoning the adoltery, even there is no any Quranic verse stating that our beloved compassionat pious Prophet Moahmed has ever ordered to stone someone to death, we all are aware this is a canon must emerged from the Quranic law, according the Quran , the only canonical verses the issues of the adoltery is (Q, 24.1-4) the woman and man guilty of adultery falog each of them a hundered stripes without any compassion in their case matter prescriped by Allah faith, if you truly believe in Allah and the last day and let some of the believers to witness their punishment . plus according to the Sunnah canon its very strict and almost impossible to prove that, two people are commited adultery by a third part(Q.24-4) so the case dissmiss, dont tell me about the Hadith bring me a prove from the Quran I am sure thats so-called hadith of the jewish Woman been stone to death its completly false Hadith, come on Muslims wake up how come on earth our beloved pious Prophet have his own Canon proceed in a deferent Jewish canons, we all know that the final definitive pious prophet Mohamed peace be upon him, canonical oreders abrogated all the pious prophets that been send before him.

peace & love regards to all
Abdulla Mahir .

I wrote a followup comment:

The last comment provides, quite eloquently, a rational and logical explanation of stoning. I’m afraid that none of us know the scriptures well, neither can we ever know them, for they are, as witnessed from the above, written in arabic. I’m afraid we may have missed several important points, precisely those that have been outlined above for our benefit. In view of this, you may wish to consider rewriting your post.

My fellow blogger Michael of http://anadder.com did not immediately catch the sarcasm of it and explained:

Then again Poe’s Law can make it very hard to pass of mockery of religion as sarcasm (at least on the net)…:)

So I wondered what Poe's Law is because I had not encountered the terminology before. And here is what the Urban Dictionary says:

Poe's Law
Similar to Murphy's Law, Poe's Law concerns internet debates, particularly regarding religion or politics.

"Without a winking smiley or other blatant display of humor, it is impossible to create a parody of Fundamentalism that SOMEONE won't mistake for the real thing."

In other words, No matter how bizzare, outrageous, or just plain idiotic a parody of a Fundamentalist may seem, there will always be someone who cannot tell that it is a parody, having seen similar REAL ideas from real religious/political Fundamentalists.

The following is an actual Internet post to Biblically defend a flat Earth:

"All I was saying was that either the earth is flat, and the bible is correct, or the earth is round, and the bible is incorect, i'm going to study the issue more and deside for myself which route I want to take. Either Atheist evolutionist, who agrees with all of mainstream sciences, or flat earth litteral bible believer.
I'm leaning toward being an atheist, because if I can't believe the bible to be completly litteraly true, then I can't believe Jesus when he speaks about heaven, etc..
That would make the moon landing a fake, and pretty much all of modern science false..."

Very nice. Indeed, indeed! It is impossible to create a parody of fundamentalism that someone won't mistake for the real thing! Very true. Sometimes, it is hard not to reply by sarcasm and cynicism to religious fundamentalist claims, to creationist/intelligent design idiocies such as those of Dembski or Lennox and many others. You cannot help it when you want to cry out loud: Stop those childish claims! Enough with your sense of moral superiority! But no! No matter what you say, there is always someone who will take it literally. I once wrote about how beautiful Lennox's argument involving his aunt Matilda was. Read it here if you care to waste 2 minutes. Briefly, Lennox has an aunt, Matilda, who makes nice cakes. His scientist friends can tell him what the cake contains but can never answer to the question why Matilda baked it. I wrote that, obviously, Matilda bakes it because she's a good and caring person and does so because she is a good Christian; and that this sophisticated argument of Lennox is evidence for existence of God. You can't believe how many thanks I received for my comment and how many people thought that it was great of me to extend Lennox's argument in such a nice way.

This is Poe's Law at work, right Michael?

Today, Jeffrey Shallit posted on why he thinks that religion makes smart people stupid. Well, even though I cannot prove that this is a universal law, it seems that Lennox is a prime example of it: he used to be a mathematician but he turned into religion. Instead of trying to work on his subject (Group Theory), he became a priest and an advocate of religion. I've been to two of his talks and, indeed, all I could say is that his arguments are naive. Famous scientists in the past have tried hard to come up with arguments about the existence of god. But Lennox does not belong to this class. He says nothing that has not been said before and does so by abusing science.

The Edinburgh Creationist Group

They claim:

Edinburgh Creation Group is an active forum where scientifically minded people meet to discuss evidence supporting the biblical account of creation.

Scientifically minded? How can anyone who arbitrarily considers the Bible (Torah, etc) as a scientific document consider themselves scientifically minded? Religious, yes. But not scientific. Creationists argue that the Earth is some 6 thousand years old only. Their proof: It is in the Bible. This is not science.

Here is how creationist Professor Andy C. McIntosh proves that god exists:

"My knowledge of thermodynamics has shown me that all mechanical systems (such as an engine or fridge or aeroplane etc.) require not only energy but ordered machinery in order to work. Thus simply adding energy to a lump of matter will not turn this into a machine which can do useful work. Clausius and other great thermodynamic scientists of the past, demonstrated this in the precise expression of the second law of thermodynamics which states that some of energy for useful work will in any system always be lost irretrievably. It has been argued that with an open system, useful energy can be put back in, but this will only be of use if there is an existing machine! One can never get round the 2nd law even for open systems. Working machinery or coded information (when dealing with digitally controlled machines such as in DNA) is always required before anything works."

Now search however deeply you like in the scientific literature and you'll find no notion of ordered or working machinery in the theory of thermodynamics or statistical physics. Thermodynamics works perfectly well without this concept, apparently invented by McIntosh alone.

Dr Marc Surtees, zoologist, eloquently claims:

"The hormonal control of breeding is an example of a switchable feedback control mechanism. Engineers use feedback control mechanisms in many types of machine. The existence of feedback control systems in nature is one of the many evidence of design that biologists work with all the time."

He is out of his mind! He says: Feedback control exitsts in many natural systems [correct], and this shows that there evidence of design [wrong] and implicitly wants us to conclude that god is the designer [idiotic!]

Chilidish argument like the above is what creationists use to prove that their faith has scientific basis. Instead of acknowledging that they cannot do without irrational belief (some kind of sickness, really), they want to convince others not only that what they believe is right, but also that it is scientific!!!

Most creationists are Christian but there are Muslim too. See here for an earlier posting on how militant the latter can be.

William Dembski factors 59

Now, this is FUNNY! So I couldn't resist from linking the spoof. Prominent "mathematician" William Dembski factors the number 59 (no, not in any strange algebraic field, but in the usual way, the way you and I learn in elementary school).


William Dembski is also well-known for having disproved Darwin's evolution theory, at least as far as he and his followers are concerned: whereas you, I and Kanzi (the famous ape) share a common ancestor, William Dembski is a totally distinct species. He is alien. Let him stay with aliens then.

Happy Birthday Darwin!