Today's verse

Judge not according to the appearance, but judge righteous judgment.

John 7:24 (KJV)

Update on Asia Bibi

Two Christians killed in violence in Pakistan, raising concerns that Asia Bibi may become a target.

For those who do not know who she is, here is the story about Asia Bibi's unjust imprisonment and death sentence for "blasphemy" against the Prophet Muhammad.

Please continue to pray for Asia Bibi and her family.

Today's verse

Now I beseech you, brethren, by the name of our Lord Jesus Christ, that ye all speak the same thing, and that there be no divisions among you; but that ye be perfectly joined together in the same mind and in the same judgment.

1 Corinthians 1:10 (KJV)

A post-Christian age?

Luke Mbefo looks at Christainity in the Western World.

Today's verse

Is not this the fast that I have chosen? to loose the bands of wickedness, to undo the heavy burdens, and to let the oppressed go free, and that ye break every yoke?

Is it not to deal thy bread to the hungry, and that thou bring the poor that are cast out to thy house? when thou seest the naked, that thou cover him; and that thou hide not thyself from thine own flesh?

Then shall thy light break forth as the morning, and thine health shall spring forth speedily: and thy righteousness shall go before thee; the glory of the LORD shall be thy reward.

Isaiah 58:6-8 (KJV)

Persecution in Ethiopia

Lutheran CORE, Lutheran Congregations in Mission for Christ (LCMC), and the North American Lutheran Church (NALC) have established the Ethiopian Church Relief Fund. Ethiopia has seen a recent wave of violence by Islamic extremists against Christians.

Update on Asia Bibi

Lady Catherine Ashton, Vice-President of the European Union, and Dr. Rowan Williams, the Archbishop of Canterbury, have sent letters to the Centre for Legal Aid Assistance & Settlement (CLAAS) expressing concern for Asia Bibi and the growing use of blasphemy laws to persecute religious minorities. For Dr. Williams, this may represent a change of heart and a realization that Islamic law and a democratic society cannot peacefully coexist.

For those who do not know who she is, here is the story about Asia Bibi's unjust imprisonment and death sentence for "blasphemy" against the Prophet Muhammad.

Please continue to pray for Asia Bibi and her family.

Today's verse

I lay down and slept, yet I woke up in safety, for the Lord was watching over me. I am not afraid of ten thousand enemies who surround me on every side.

Psalm 3:5-6 (NLT)

Now what?

We recently joined a LCMS church. Which presents a problem. I can't keep calling this blog "Recovering Lutheran" since I have lapsed back into the Lutheran faith.

A new name - and probably a new look - is in order. Maybe after the end of this semester I will have time to do something....

Update on Asia Bibi

Asia Bibi is fasting for Lent, according to her family.

For those who do not know who she is, here is the story about Asia Bibi's unjust imprisonment and death sentence for "blasphemy" against the Prophet Muhammad.

Please continue to pray for Asia Bibi and her family.

Today's verse

And the scribes which came down from Jerusalem said, He hath Beelzebub, and by the prince of the devils casteth he out devils. And he called them unto him, and said unto them in parables, How can Satan cast out Satan? And if a kingdom be divided against itself, that kingdom cannot stand. And if a house be divided against itself, that house cannot stand. And if Satan rise up against himself, and be divided, he cannot stand, but hath an end. No man can enter into a strong man's house, and spoil his goods, except he will first bind the strong man; and then he will spoil his house. Verily I say unto you, All sins shall be forgiven unto the sons of men, and blasphemies wherewith soever they shall blaspheme: But he that shall blaspheme against the Holy Ghost hath never forgiveness, but is in danger of eternal damnation. Because they said, He hath an unclean spirit.

Mark 3:22-30 (KJV)

Shortage of medics in Tanzania

The head of the Evangelical Lutheran Church in Tanzania (ELCT) Dr. Alex Malasusa says Tanzania is facing a serious shortage of trained medical workers.

Today's verse

What shall we say then? Shall we continue in sin that grace may abound? Certainly not! How shall we who died to sin live any longer in it? Or do you not know that as many of us as were baptized into Christ Jesus were baptized into His death? Therefore we were buried with Him through baptism into death, that just as Christ was raised from the dead by the glory of the Father, even so we also should walk in newness of life.

Romans 6:1-4 (NKJV)

Today's verse

The thing that hath been, it is that which shall be; and that which is done is that which shall be done: and there is no new thing under the sun. Is there any thing whereof it may be said, See, this is new? it hath been already of old time, which was before us.

Ecclesiastes 1:9-10 (KJV)

Today's verse

A good name is to be chosen rather than great riches,
Loving favor rather than silver and gold.

Proverbs 22:1 (NKJV)

Today's verse

Blessed is the man who walks not in the counsel of the wicked,
nor stands in the way of sinners, nor sits in the seat of scoffers;
but his delight is in the law of the LORD,
and on his law he meditates day and night.

Psalm 1:1-2 (ESV)

A contrast

El Cid has the story of two Pakistani women.

Today's verse

What shall we say then? Is there unrighteousness with God? God forbid. For he saith to Moses, I will have mercy on whom I will have mercy, and I will have compassion on whom I will have compassion. So then it is not of him that willeth, nor of him that runneth, but of God that sheweth mercy. For the scripture saith unto Pharaoh, Even for this same purpose have I raised thee up, that I might shew my power in thee, and that my name might be declared throughout all the earth. Therefore hath he mercy on whom he will have mercy, and whom he will he hardeneth.

Romans 9:14-8 (KJV)

Update on Asia Bibi

The number of death threats made against Christians in Pakistan is growing. It seems any public figure in Pakistan who has spoken out in defense of Asia Bibi or other victims of Pakistan's blasphemy laws is either dead or in danger of being killed.

Unfortunately, the Western secular media is too busy worrying about "Islamophobia" to take note of the oppression going on against non-Muslims (and even some Muslims) in Muslim-dominated countries.

For those who do not know who she is, here is the story about Asia Bibi's unjust imprisonment and death sentence for "blasphemy" against the Prophet Muhammad.

Please continue to pray for Asia Bibi and her family, and for all who suffer persecution in Pakistan.

Today's verse

When pride comes, then comes shame;
But with the humble is wisdom.

Proverbs 11:2 (NKJV)

Messenger

The NASA space probe Messenger has successfully achieved orbit around the planet Mercury.

Update on Asia Bibi

The family of Qamar David, another victim of Pakistan's blasphemy laws, believes he was murdered. There is also a call for prayers for Asia Bibi, why may be a target for assassination.

For those who do not know who she is, here is the story about Asia Bibi's unjust imprisonment and death sentence for "blasphemy" against the Prophet Muhammad.

Please continue to pray for Asia Bibi and her family, the family of Qamar David, and for all Christians suffering persecution in Pakistan.

Giving up Christianity for Lent

Again, this is not an article from The Onion:

Episcopal cleric tries Islamic rituals for Lent

Rev. Lawler's Lenten project may get him defrocked, which is a bit strange. Bishop George Wayne Smith of the Episcopal Diocese of Missouri frets that Lawler's actions might be seen as mocking Islam. Perhaps the good bishop is worried that the multicultural Left will go bananas, although deranged hatred is multiculturalism's normal state. Bishop Smith might also be concerned that someone from the Religion of Peace will do to the Episcopal Church what Faisal Shahzad tried (and failed) to do to Times Square last year.

But whether it is multiculturalism or Islam that Bishop Smith fears the most, it is clear that Rev. Lawler will not be defrocked because of turning away from Christianity. A denomination that elevated Gene Robinson to the position of bishop is not in a position to criticize Rev. Lawler's apostasy.

(h/t Cyberbretheren)

Today's verse

O LORD my God, I cried unto thee, and thou hast healed me.

Psalm 30:2 (KJV)

Today's verse

In those days there was no king in Israel; everyone did what was right in his own eyes.

Judges 21:25 (NKJV)

Update on Asia Bibi

Asia Bibi is not the only person being held in prison in Pakistan for alleged blasphemy. Qamar David, who was also convicted under the blasphemy laws, died in prison under mysterious circumstances.

Also, several Asian and Pakistani organizations will be protesting on behalf of victims of blasphemy laws in Rome, Italy on March 26, 2011.

For those who do not know who she is, here is the story about Asia Bibi's unjust imprisonment and death sentence for "blasphemy" against the Prophet Muhammad.

Please continue to pray for Asia Bibi and her family, and for all Christians suffering persecution in Pakistan.

Today's verse

Have not I commanded thee? Be strong and of a good courage; be not afraid, neither be thou dismayed: for the LORD thy God is with thee whithersoever thou goest.

Joshua 1:9 (KJV)

Blot out the Son by writing the word "darkness"

James Frey's literary career has resembled Thomas Hobbes' famous dictum about human life outside society's protection: nasty, brutish, and short. Frey's book A Million Pieces was panned by critics as being a fabrication. Oprah Winfrey dispatched him on national TV. If you god is the publishing industry and the chattering classes that comprise it, this is equivalent to being cast into the fires of Hell.

So Frey is doing what many "artists" have done in America and Europe to try to revive their sagging careers - attack Christianity.

Frey is releasing a new book called The Final Testament of the Holy Bible, which portrays Jesus' Second coming in the form of Ben Jones, a pot-smoking whore-chasing loser. The only thing missing in Frey's new book (as far as I know) is any reference to Jesus/Ben Jones becoming a Muslim. Although Frey knows if he attacks Islam the same way he attacks Christianity, then it will be a race to see who obliterates him first: the Islamic terrorists or the multicultural Left.

From the article linked above Frey all but tips his strategy to return to the Promised Land of the good graces of the New York Times Book Review:

Frey told us the book is "a theoretical third volume of the Bible -- there was the Old, there was the New, and this is the Final." He said, "I'm sure the religious right will go crazy because the story of Ben . . . is hardly the Messiah they have in mind. But I don't really care. I just did what I always do -- tried to write the best book I could."

Frey is counting on - frantically needs, in fact - some prominent Christian or Christian organization to criticize his book (my tiny blog probably does not count, but if he gets desperate enough...). This will create a palpable reaction in the secular media as newspapers and magazine editors and writers rush to Frey's defense against the dastardly Bible-thumpers. Even Oprah may offer absolution to the penitent Frey. When it comes to getting a reflex action, Pavlov's dog was not as well conditioned as the secular media is. Or so Frey hopes.

Unfortunately for Frey, there is no guarantee that this will work. The secular media is hip-deep in Christophobes. Mere Christian-bashing is insufficient for fame and fortune. Competition is too keen.

I find the timing of the release of Frey's book - Good Friday - oddly appropriate. Frey believes that he can obliterate Jesus by writing an "edgy" book. Yet as C.S. Lewis once noted, it is almost like trying to snuff out the sun by writing the word "darkness". The religious leaders of Jesus' time found out that killing Him did not work out as planned.

In short, the problem for Frey (and the secular world in general) is the Sunday that follows Good Friday.

Stumbling through mathematics: no one has Skewes' number

I once saw a bumper sticker that read EVERYONE HAS AVAGADRO'S NUMBER. Avagadro's number is the number of molecules in one mole of a substance, and written in scientific noation is approximately equal to 6.0225 × 10²³. In standard notation, Avagadro's numbers is approximately:

602,250,000,000,000,000,000,000

By contrast, no one can write a Skewes' number in standard form. There are too many digits.

So, why is a Skewes' number so interesting (to mathematicians, anyway)?

A little background information is necessary here. A googol is the number 10¹⁰⁰, which is 10 raised to the one hundred power. In standard form, a googol is 1 followed by 100 zeros, or:

100000000000000000000
00000000000000000000
00000000000000000000
00000000000000000000
00000000000000000000

One function we need to know about is called the prime counting function π(x) . This function is the number of prime numbers less than or equal to x. Some examples would be π(1) = 0, since there are no prime numbers of 1 or less; π(6) = 3, since 2, 3 and 5 are all prime numbers less than or equal to 6; π(13) = 6 since 2, 3, 5, 7, 11, and 13 are all prime numbers less than or equal to 13; and so on. (Note that π(x) is not the famous irrational number π ≈ 3.1415926...)

Another function that we must have to understand what a Skewes' number is about is the logarithmic integral li(x). This function is defined as:

li(x) = ∫₀^xdt/ln(t)

where ln(t) is the natural logarithm of t.

Below is a plot of π(x) and li(x) versus x:



Notice that li(x) (the red line) is always above π(x) (the blue line) Or so it would appear.

Actually, appearances can be deceiving, and in this case they are. For eventually li(x) and π(x) cross each other.

So where does the first crossing occur? In 1933 Samuel Skewes (Derbyshire 2004) showed that the first such crossing* will happen before x is equal to the number:

e^ee79

This number is called the first Skewes' number, or Sk₁. The symbol e is the base of the natural logarithm, which is an irrational number and approximately equal to 2.718281828459045.... Sk₁ should be read as, "e raised to the power of e raised to the power of e raised to the power of 79" (such a stacking of exponents is sometimes called a "power tower"). Compare this gigantic number with the now puny-looking googol!

How many digits does Sk₁ have? Remember that the googol is a 1 followed by 100 digits. According to Derbyshire, the first Skewes' number has 10^{ten billion trillion trillion} digits. Just try writing that number in standard form!

Of course, it is easy to propose even bigger numbers than Sk₁. The trouble is that such a number is a "made-up" or invented number. What makes Skewes' number so interesting is the way it was "discovered". It is the largest number (so far) to come about as a result of a mathematical proof**.

Recent advances in mathematics have reduced the first crossing of li(x) and π(x) to a much, much smaller number (on the order of 10³¹⁶). Nevertheless, the Skewes' number remains one of the more fascinating numbers in mathematics.

(* - assuming the Riemann hypothesis is true.)

(** - if the Riemann hypothesis is false, then a far larger Sk₂, or the second Skewes' number is the result. However, most mathematicians believe the Riemann hypothesis is true.)

Today's verse

“So I say to you, ask, and it will be given to you; seek, and you will find; knock, and it will be opened to you. For everyone who asks receives, and he who seeks finds, and to him who knocks it will be opened. If a son asks for bread from any father among you, will he give him a stone? Or if he asks for a fish, will he give him a serpent instead of a fish? Or if he asks for an egg, will he offer him a scorpion? If you then, being evil, know how to give good gifts to your children, how much more will your heavenly Father give the Holy Spirit to those who ask Him!”

Luke 11:9-13 (NKJV)

Today's verse

Now the serpent was more subtil than any beast of the field which the LORD God had made. And he said unto the woman, Yea, hath God said, Ye shall not eat of every tree of the garden? And the woman said unto the serpent, We may eat of the fruit of the trees of the garden: But of the fruit of the tree which is in the midst of the garden, God hath said, Ye shall not eat of it, neither shall ye touch it, lest ye die.

And the serpent said unto the woman, Ye shall not surely die: For God doth know that in the day ye eat thereof, then your eyes shall be opened, and ye shall be as gods, knowing good and evil.

And when the woman saw that the tree was good for food, and that it was pleasant to the eyes, and a tree to be desired to make one wise, she took of the fruit thereof, and did eat, and gave also unto her husband with her; and he did eat. And the eyes of them both were opened, and they knew that they were naked; and they sewed fig leaves together, and made themselves aprons.

Genesis 3:1-7 (KJV)

Today's verse

On the last day, the climax of the festival, Jesus stood and shouted to the crowds, “Anyone who is thirsty may come to me! Anyone who believes in me may come and drink! For the Scriptures declare, ‘Rivers of living water will flow from his heart.’"

John 7:37-8 (NLT)

Update on Asia Bibi

Asia Bibi is worried that, in the wake of the murders of Shahbaz Bhatti and Salman Taseer, she will be next.

For those who do not know who she is, here is the story about Asia Bibi's unjust imprisonment and death sentence for "blasphemy" against the Prophet Muhammad.

Please continue to pray for Asia Bibi and her family.

A subject no one needs to study

Writing about recent political events, Brian Leiter at the University of Chicago had this to say (h/t: Professor Glenn Reynolds at Instapundit) :

At some point these acts of brazen viciousness are going to lead to a renewed philosophical interest in the question of when acts of political violence are morally justified, an issue that has, oddly, not been widely addressed in political philosophy since Locke.

It's difficult to find an adequate response to Mr. Leiter. Although the word "monstrous" come to mind. For all his education, credentials and and academic recognition, Mr. Leiter is no more sophisticated than a street thug. This is what unbridled lust for political power can do to someone. Academia already has a reputation for being a haven for violent kooks, and Mr. Leiter's post will not help the situation.

At any rate, armchair revolutionaries like Mr. Leiter might want to get some professional psychaitric help in dealing with their growing taste for murder and mayhem. Life is not like a Hollywood action flick or a dusry tome of Nietzsche where no one actually gets hurt. Or has Mr. Leiter not noticed that people tend to flee countries engulfed in violence and civil war?

Here is a screen shot of what Mr. Leiter wrote:

Today's verse

I am poured out like water,
And all My bones are out of joint;
My heart is like wax;
It has melted within Me.

Psalm 22:14 (NKJV)

Today's verse

For thou, LORD, hast made me glad through thy work: I will triumph in the works of thy hands.

Psalm 92:4 (KJV)

Today's verse

And Moses said to the people, “Do not be afraid. Stand still, and see the salvation of the LORD, which He will accomplish for you today. For the Egyptians whom you see today, you shall see again no more forever. The LORD will fight for you, and you shall hold your peace.”

14:13-14 (NKJV)

Today's verse

Jesus spoke to them, saying, "I am the light of the world. Whoever follows me will not walk in darkness, but will have the light of life."

John 8:12 (ESV)

Stumbling through mathematics: which is bigger?

Exponents are one way to represent very large numbers without having to write them out. Some examples are:

2³ = 2⋅2⋅2 = 8

9⁷ = 9⋅9⋅9⋅9⋅9⋅9⋅9⋅9⋅9 = 4782969

10¹² = 10⋅10⋅10⋅10⋅10⋅10⋅10⋅10⋅10⋅10⋅10⋅10 = 1000000000000

Now determine whether number A or number B is bigger:

A = 2^73894618

B = 3^46622313

Good luck trying to put either of those into a calculator! Microsoft Excel can't handle it either. Even Maple 12, a program specifically designed for performing algebraic calculations on a computer, tells me there are too many digits to display in either of these two numbers.

Logarithms are functions that are the inverses of exponential functions. Both logarithms and exponential functions are found in many engineering and scientific problems. The expression b = log_a(x) means b is equal to the logarithm to base a of x. Just to give you an idea of of what they look like, here is a graph of 10^x and log₁₀(x) (this plot was made using Maple 12). The red line represents 10^x and the blue line represents log₁₀(x).



Logarithms have certain limitations. The logarithm of zero does not exist, and the logarithm of a negative number is a complex number. Nevertheless, we are going to make use of the following fact concerning logarithms:

For real numbers a, x, y > 0, if x > y, then log_a(x) > log_a(y)

We will use the following property of logarithms to determine if either A or B is larger:

For real numbers z, x, a and x, a > 0, then log_a(x^z) = z⋅log_a(x)

Take the logarithm of both A and B. We will choose the common logarithm, or logarithm to base 10:

log₁₀(A) = log₁₀(2^73894618)

log₁₀(B) = log₁₀(3^46622313)

Using the property of logarithms introduced above:

log₁₀(A) = 73894618⋅log₁₀(2)

log₁₀(B) = 46622313⋅log₁₀(3)

Now we finally have something that can be evaluated! Using a calculator, we find that log₁₀(2) = 0.3010299957 (evaluated to 10 digits) and log₁₀(3) = 0.4771212549 . We now have:

log₁₀(A) = 73894618⋅0.3010299957 = 22244496.54

log₁₀(B) = 46622313⋅0.4771212549 = 22244496.48

It turns out that A is larger than B.

Today's verse

Too much pride can put you to shame.
It's wiser to be humble.

Proverbs 11:2 (CEV)

Update on Asia Bibi

Rodrick Samson asks if we have forgotten Asia Bibi.

God has not.

For those who do not know who she is, here is the story about Asia Bibi's unjust imprisonment and death sentence for "blasphemy" against the Prophet Muhammad.

Please continue to pray for Asia Bibi and her family.

Today's verse

Blow ye the trumpet in Zion, and sound an alarm in my holy mountain: let all the inhabitants of the land tremble: for the day of the LORD cometh, for it is nigh at hand.

Joel 2:1 (KJV)

Today's verse

Be glad in the LORD, and rejoice, ye righteous: and shout for joy, all ye that are upright in heart.

Psalm 32:11 (KJV)

Today's verse

But you, my dear friends, must remember what the apostles of our Lord Jesus Christ said. They told you that in the last times there would be scoffers whose purpose in life is to satisfy their ungodly desires. These people are the ones who are creating divisions among you. They follow their natural instincts because they do not have God’s Spirit in them.

Jude 17-19 (NLT)