Save me from all those who persecute me;
And deliver me,
Lest they tear me like a lion,
Rending me in pieces, while there is none to deliver.
Psalm 7:1-2 (NKJV)
Monday, February 28, 2011
Today's verse
O LORD my God, in You I put my trust;
Save me from all those who persecute me;
And deliver me,
Lest they tear me like a lion,
Rending me in pieces, while there is none to deliver.
Save me from all those who persecute me;
And deliver me,
Lest they tear me like a lion,
Rending me in pieces, while there is none to deliver.
Sunday, February 27, 2011
Violence in Monduli district
Ten people were hurt after Muslims attacked two churches in the Monduli district of Tanzania. The Muslims were apparently upset with the preaching going on at these two churches.
This story hits home, since my wife and I lived in Monduli after we were married. Please pray for the people of Monduli.
This story hits home, since my wife and I lived in Monduli after we were married. Please pray for the people of Monduli.
ELCT membership increases
The membership of the Evangelical Lutheran Church in Tanzania (ELCT) has increased to over 5.6 million.
Please pray for Tanzanian Lutherans.
Please pray for Tanzanian Lutherans.
Today's verse
Therefore I say unto you, Take no thought for your life, what ye shall eat, or what ye shall drink; nor yet for your body, what ye shall put on. Is not the life more than meat, and the body than raiment?
Matthew 6:25 (KJV)
Saturday, February 26, 2011
Stumbling through mathematics: strange powers
You may have been told by your teacher that square roots of negative numbers do not exist. But what if they actually did? It turns out that the square roots of negative numbers are surprisingly useful in mathematics and engineering.
High school and college students may remember this strange creature from their math classes: √(-1). If you try putting this number into your calculator, you will likely get an error message. So what is it? Mathematicians call this number an imaginary number, and denote it using the symbol i = √(-1).
It turns out that this mysterious number i has some interesting (as well as useful) properties. For example: what happens when we raise i to the second power, the third, etc.?
i1 = i
i2 = (√(-1))2 = i2 = -1
i3 = (√(-1))2⋅√(-1) = i2⋅i = -1⋅i = -i
i4 = (√(-1))3⋅√(-1) = -i⋅i = -i2 = -(-1) = 1
i5 = (√(-1))4⋅√(-1) = 1⋅i = i
i6 = (√(-1))5⋅√(-1) = i⋅i = i2 = -1
i7 = (√(-1))6⋅√(-1) = i6⋅i = -1⋅i = -i
i8 = (√(-1))7⋅√(-1) = -i⋅i = -i2 = -(-1) = 1
...and so on. Notice how the pattern of i, -1, -i, 1 keeps repeating itself? This repetition is one property that makes imaginary numbers so useful.
But what happens if we raise i to an imaginary power, say, i i ? What happens then?
To see what i i is, we must use Euler's equation (an equation familiar to physicists and electrical engineers as well as mathematicians). Let e be the base of the natural logarithm (approximately equal to 2.7182....), and cos(x) and sin(x) be the cosine and sine functions of x:
eix = cos(x) + isin(x)
A complex number is a number made up of a real number and an imaginary number. Complex numbers have the form a + bi or a - bi, where a and b are real numbers. Any real number can be written as a complex number. An example would be the real number 3, which can be written in two different (but equally valid) ways: 3 + 0i or 3 - 0i. All your life you have been using complex numbers - and perhaps did not even know it!
Therefore, i can be written as the complex number 0 + 1⋅i. One value of x that would make cos(x) = 0 and sin(x) = 1 is x = π/2. Then Euler's equation becomes:
eiπ/2 = 0 + 1i = i
Now raise both sides on this equation to the i power:
(eiπ/2)i = ei2π/2 = i i
Since i 2 = -1:
e-π/2 = i i
On the right side of this equation we have an imaginary number being raised to an imaginary power. On the left side we have a real number with no imaginary part whatsoever (the value of e-π/2 is an irrational number and is approximately equal to 0.2078795764...). This result is counter intuitive, to say the least!
But that is not the end of the story. The value x = π/2 is only one possible result. Because cos(x) and sin(x) are periodic functions, there are many values of x that make cos(x) = 0 and sin(x) = 1. In fact, there are an infinite number of values of x! We can re-write the cosine and sine terms to reflect this: cos(π/2 ± 2πn) = 0 and sin(π/2 ± 2πn) = 1, where n is any non-negative integer such as 0, 1, 2, 3, .... The equation can now be re-written as:
e-π/2 ±2πn = i i
e-π/2⋅e±2πn = i i
So, i i results in an infinite number of real solutions. There are many strange results in mathematics, but I would be hard-pressed to find one stranger than this. It is why mathematics is the best science ever!
High school and college students may remember this strange creature from their math classes: √(-1). If you try putting this number into your calculator, you will likely get an error message. So what is it? Mathematicians call this number an imaginary number, and denote it using the symbol i = √(-1).
It turns out that this mysterious number i has some interesting (as well as useful) properties. For example: what happens when we raise i to the second power, the third, etc.?
i2 = (√(-1))2 = i2 = -1
i3 = (√(-1))2⋅√(-1) = i2⋅i = -1⋅i = -i
i4 = (√(-1))3⋅√(-1) = -i⋅i = -i2 = -(-1) = 1
i5 = (√(-1))4⋅√(-1) = 1⋅i = i
i6 = (√(-1))5⋅√(-1) = i⋅i = i2 = -1
i7 = (√(-1))6⋅√(-1) = i6⋅i = -1⋅i = -i
i8 = (√(-1))7⋅√(-1) = -i⋅i = -i2 = -(-1) = 1
...and so on. Notice how the pattern of i, -1, -i, 1 keeps repeating itself? This repetition is one property that makes imaginary numbers so useful.
But what happens if we raise i to an imaginary power, say, i i ? What happens then?
To see what i i is, we must use Euler's equation (an equation familiar to physicists and electrical engineers as well as mathematicians). Let e be the base of the natural logarithm (approximately equal to 2.7182....), and cos(x) and sin(x) be the cosine and sine functions of x:
A complex number is a number made up of a real number and an imaginary number. Complex numbers have the form a + bi or a - bi, where a and b are real numbers. Any real number can be written as a complex number. An example would be the real number 3, which can be written in two different (but equally valid) ways: 3 + 0i or 3 - 0i. All your life you have been using complex numbers - and perhaps did not even know it!
Therefore, i can be written as the complex number 0 + 1⋅i. One value of x that would make cos(x) = 0 and sin(x) = 1 is x = π/2. Then Euler's equation becomes:
Now raise both sides on this equation to the i power:
Since i 2 = -1:
On the right side of this equation we have an imaginary number being raised to an imaginary power. On the left side we have a real number with no imaginary part whatsoever (the value of e-π/2 is an irrational number and is approximately equal to 0.2078795764...). This result is counter intuitive, to say the least!
But that is not the end of the story. The value x = π/2 is only one possible result. Because cos(x) and sin(x) are periodic functions, there are many values of x that make cos(x) = 0 and sin(x) = 1. In fact, there are an infinite number of values of x! We can re-write the cosine and sine terms to reflect this: cos(π/2 ± 2πn) = 0 and sin(π/2 ± 2πn) = 1, where n is any non-negative integer such as 0, 1, 2, 3, .... The equation can now be re-written as:
So, i i results in an infinite number of real solutions. There are many strange results in mathematics, but I would be hard-pressed to find one stranger than this. It is why mathematics is the best science ever!
Today's verse
The Lord is more pleased when we do what is right and just than when we offer him sacrifices.
Proverbs 21:3 (NLT)
Friday, February 25, 2011
Today's verse
But speak thou the things which become sound doctrine: That the aged men be sober, grave, temperate, sound in faith, in charity, in patience. The aged women likewise, that they be in behaviour as becometh holiness, not false accusers, not given to much wine, teachers of good things; That they may teach the young women to be sober, to love their husbands, to love their children, To be discreet, chaste, keepers at home, good, obedient to their own husbands, that the word of God be not blasphemed. Young men likewise exhort to be sober minded.
Titus 2:1-6 (KJV)
Thursday, February 24, 2011
Update on Asia Bibi
Christian living on the India-Pakistan border march in support of Asia Bibi.
For those who do no 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
Many are my persecutors and my enemies,
Yet I do not turn from Your testimonies.
Yet I do not turn from Your testimonies.
Psalm 119:157 (NKJV)
Sunday, February 20, 2011
Today's verse
My soul melts away for sorrow; strengthen me according to your word!
Psalm 119:28 (ESV)
Saturday, February 19, 2011
Mathematical symbols available in HTML
This website has a list of mathematical symbols that should work in HTML.
Thus a simple integration problem (such as f(x) = x2) becomes:
∫ x2 dx = x3/3 + constant
One of the things I hope to do more of with this blog is writing about mathematics, and this will help.
Thus a simple integration problem (such as f(x) = x2) becomes:
One of the things I hope to do more of with this blog is writing about mathematics, and this will help.
Sweet Ps: A prayer for pastors
Lord, I ask that you bless pastors and their families. Our adversary Satan seeks to destroy Your holy Church. Pastors and their families are under constant attack. I ask that You send Your angels to surround and protect them.
Lord, I ask that You give pastors good health, rest, and Your peace. Give them Your holy Word, that they preach only Your Truth.
Lord, there are many false prophets and teachers in the world today. They teach their own beliefs, and seek to destroy those who speak Your Truth. I ask that You expose these false prophets and teachers, that they may deceive no one.
Amen.
Today's verse
“Furthermore it has been said, ‘Whoever divorces his wife, let him give her a certificate of divorce.’ But I say to you that whoever divorces his wife for any reason except sexual immorality causes her to commit adultery; and whoever marries a woman who is divorced commits adultery.
Matthew 5:31-2
Friday, February 18, 2011
Today's verse
The ungodly are not so: but are like the chaff which the wind driveth away.
Psalm 1:4 (KJV)
Wednesday, February 16, 2011
Today's verse
For the Lord protects the bones of the righteous; not one of them is broken!
Psalm 34:20 (NLT)
Tuesday, February 15, 2011
Pray for rain
Tanzania will experience severe food shortages unless the long rains start next month.
There are two main rainy seasons in Tanzania. The long rains usually begin in February/March, and are the most important for agriculture. The short rains come in October, and are important for the coffee crop in the Kilimanjaro region. No rain means no food.
Meanwhile, people living in the Manyara region are being hit by flooding. Life in the Third World is always a struggle.
Please pray for rain for the farmers of Tanzania, and for an end to the flooding in Manyara.
There are two main rainy seasons in Tanzania. The long rains usually begin in February/March, and are the most important for agriculture. The short rains come in October, and are important for the coffee crop in the Kilimanjaro region. No rain means no food.
Meanwhile, people living in the Manyara region are being hit by flooding. Life in the Third World is always a struggle.
Please pray for rain for the farmers of Tanzania, and for an end to the flooding in Manyara.
Today's verse
Today you have proclaimed the LORD to be your God, and that you will walk in His ways and keep His statutes, His commandments, and His judgments, and that you will obey His voice. Also today the LORD has proclaimed you to be His special people, just as He promised you, that you should keep all His commandments, and that He will set you high above all nations which He has made, in praise, in name, and in honor, and that you may be a holy people to the LORD your God, just as He has spoken.
Deuteronomy 26:17-19 (NKJV)
Monday, February 14, 2011
Today's verse
Charity suffereth long, and is kind; charity envieth not; charity vaunteth not itself, is not puffed up,
Doth not behave itself unseemly, seeketh not her own, is not easily provoked, thinketh no evil;
Rejoiceth not in iniquity, but rejoiceth in the truth;
Beareth all things, believeth all things, hopeth all things, endureth all things.
Charity never faileth: but whether there be prophecies, they shall fail; whether there be tongues, they shall cease; whether there be knowledge, it shall vanish away.
Doth not behave itself unseemly, seeketh not her own, is not easily provoked, thinketh no evil;
Rejoiceth not in iniquity, but rejoiceth in the truth;
Beareth all things, believeth all things, hopeth all things, endureth all things.
Charity never faileth: but whether there be prophecies, they shall fail; whether there be tongues, they shall cease; whether there be knowledge, it shall vanish away.
1 Corinthians 13:4-8 (KJV)
Saturday, February 12, 2011
Update on Asia Bibi
Pakistan's President Asif Ali Zardari confirms Shahbaz Bhatti, a Catholic, as Minister of minorities. This might be a positive development since Bhatti has spoken in favor of changing Pakistan's blasphemy laws and has also called for Asia Bibi to be released.
For those who do no 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.
Pray for Joanne
Follow the above link to find out latest news. Please continue to pray for Joanne Heim.
Today's verse
I know that my selfish desires won't let me do anything that is good. Even when I want to do right, I cannot. Instead of doing what I know is right, I do wrong.
Romans 7:18-19 (CEV)
Friday, February 11, 2011
Not negotiatable
Tanzanian religious leaders say peace and harmony is not negotiable.
Here is an interesting quote from the article:
Excellent words! Are you listening, Evangelical Lutheran Church in America?
Here is an interesting quote from the article:
More importantly, the religious leaders resolved not to be swayed by politicians or political parties for political gains.
Excellent words! Are you listening, Evangelical Lutheran Church in America?
Update on Asia Bibi
Unfortunately, there is nothing new to report. Our Christian sister continues to be held for her faith in Christ. The world's media may no longer take an interest in her, but I can assure you that God does.
Here is an interesting article from the Pakistan Christian Post about Pakistan's blasphemy laws.
For those who do no know who she is, here is the story about Asia Bibi's unjust imprisonment and death sentence for "blasphemy" against the Prophet Muhammad.
Never forget our sister in Christ. Please continue to pray for Asia Bibi and her family.
Today's verse
Oh, send out Your light and Your truth!
Let them lead me;
Let them bring me to Your holy hill
And to Your tabernacle.
Then I will go to the altar of God,
To God my exceeding joy;
And on the harp I will praise You,
O God, my God.
Let them lead me;
Let them bring me to Your holy hill
And to Your tabernacle.
Then I will go to the altar of God,
To God my exceeding joy;
And on the harp I will praise You,
O God, my God.
Psalm 43:3-4 (NKJV)
Wednesday, February 09, 2011
Today's verse
Every good gift and every perfect gift is from above, and cometh down from the Father of lights, with whom is no variableness, neither shadow of turning.
James 1:17 (KJV)
Tuesday, February 08, 2011
Today's verse
Those who spare the rod of discipline hate their children.
Those who love their children care enough to discipline them.
Those who love their children care enough to discipline them.
Proverbs 13:24 (NLT)
Sunday, February 06, 2011
Super Bowl prediction
It has been (painfully) obvious since about Week 5 that the Cowboys would not be representing the NFC on their home field in Super Bowl XLV. So I have not paid close attention to the rest of the NFL since the who-will-be-the-new-Dallas-coach drama has captured my interest. Nevertheless:
Pittsburgh 23
Green Bay 17
For the record: I have been following the Dallas Cowboys since 1970, when they lost Super Bowl V to the Baltimore Colts 16-13 in one of the ugliest NFL championships ever. Tom Landry, Dallas's coach for 5 Super Bowls (winning 2 of them), called it the greatest defensive game he ever watched. There were 12 turnovers in that game (6 by each team); a 75-yard touchdown pass that bounced off of a Dallas defender's fingers into the arms of a Baltimore receiver; a botched extra point; the great Baltimore QB Johnny Unitas getting injured in the second quarter and being forced from the game (he was replaced by Earl Morrall); a blown call by the officials early in the third quarter when they gave a fumble recovery to Baltimore (Dallas's OL Rayfield Wright had recovered the ball in the end zone for an apparent touchdown); the relentless Baltimore pass rush that forced the interception that set up the Colt's winning field goal; Dallas's DT Bob Lilly slinging his helmet down the field after the Cowboys lost.
Super Bowl V was also memorable for the fact that the MVP of the game was Chuck Howley, a Dallas linebacker (he had two interceptions and played flawlessly). It is the only time a player from the losing side won the MVP award.
Super Bowl XLV should be so entertaining!
Green Bay 17
For the record: I have been following the Dallas Cowboys since 1970, when they lost Super Bowl V to the Baltimore Colts 16-13 in one of the ugliest NFL championships ever. Tom Landry, Dallas's coach for 5 Super Bowls (winning 2 of them), called it the greatest defensive game he ever watched. There were 12 turnovers in that game (6 by each team); a 75-yard touchdown pass that bounced off of a Dallas defender's fingers into the arms of a Baltimore receiver; a botched extra point; the great Baltimore QB Johnny Unitas getting injured in the second quarter and being forced from the game (he was replaced by Earl Morrall); a blown call by the officials early in the third quarter when they gave a fumble recovery to Baltimore (Dallas's OL Rayfield Wright had recovered the ball in the end zone for an apparent touchdown); the relentless Baltimore pass rush that forced the interception that set up the Colt's winning field goal; Dallas's DT Bob Lilly slinging his helmet down the field after the Cowboys lost.
Super Bowl V was also memorable for the fact that the MVP of the game was Chuck Howley, a Dallas linebacker (he had two interceptions and played flawlessly). It is the only time a player from the losing side won the MVP award.
Super Bowl XLV should be so entertaining!
Today's verse
If we say that we have no sin, we deceive ourselves, and the truth is not in us.
If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness.
If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness.
1 John 1:8-9 (KJV)
Saturday, February 05, 2011
Today's verse
Then Jesus said to His disciples, “If anyone desires to come after Me, let him deny himself, and take up his cross, and follow Me. For whoever desires to save his life will lose it, but whoever loses his life for My sake will find it. For what profit is it to a man if he gains the whole world, and loses his own soul? Or what will a man give in exchange for his soul? For the Son of Man will come in the glory of His Father with His angels, and then He will reward each according to his works.
Matthew 16:24-27 (NKJV)
Friday, February 04, 2011
72 years of marriage
The story of Rev Canon Lusinde (90) and his wife Foebe (89). They were married in 1939 in Dodoma, Tanzania.
May God continue to bless their marriage.
May God continue to bless their marriage.
Update on Asia Bibi
Release International is calling for February 14 to be a day where churches support persecuted Christian women like Asia Bibi.
Also, Bibi's lawyers believe that she will eventually be cleared.
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.
Happy birthday, Mr. President!
This coming Sunday would have been Ronald Reagan's 100th birthday. Here was perhaps his finest moment in office:
Here is Reagan's 1981 Christmas speech:
Here is Reagan's 1981 Christmas speech:
Sweet Ps: Thank you for a snowy day
Lord, I thank you for the snow, which allowed me to spend time with my wonderful son. Today was a miracle.
Amen.
Shocking ... or maybe not
Planned Parenthood worker advises man posing as pimp how to get abortions for underage sex slaves.
Why should this surprise people? This is Planned Parenthood after all. Genocide is their business, so helping sex trafficking might be considered a moral step up for them.
Planned Parenthood professes to be shocked by this. Of course they are:
Why should this surprise people? This is Planned Parenthood after all. Genocide is their business, so helping sex trafficking might be considered a moral step up for them.
Planned Parenthood professes to be shocked by this. Of course they are:
Today's verse
Wash me with hyssop until I am clean and whiter than snow.
(This verse is appropriate since we are snowbound today and everything is closed!)
Psalm 51:7 (CEV)
(This verse is appropriate since we are snowbound today and everything is closed!)
Thursday, February 03, 2011
Update on Asia Bibi
Pakistan's ruling party has withdrawn support for a bill to amend Pakistan's blasphemy laws. Meanwhile, Asia Bibi remains in jail with her future in doubt.
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
Lord, who shall abide in thy tabernacle? who shall dwell in thy holy hill?
He that walketh uprightly, and worketh righteousness, and speaketh the truth in his heart.
He that backbiteth not with his tongue, nor doeth evil to his neighbour, nor taketh up a reproach against his neighbour.
In whose eyes a vile person is contemned; but he honoureth them that fear the LORD. He that sweareth to his own hurt, and changeth not.
He that putteth not out his money to usury, nor taketh reward against the innocent. He that doeth these things shall never be moved.
He that walketh uprightly, and worketh righteousness, and speaketh the truth in his heart.
He that backbiteth not with his tongue, nor doeth evil to his neighbour, nor taketh up a reproach against his neighbour.
In whose eyes a vile person is contemned; but he honoureth them that fear the LORD. He that sweareth to his own hurt, and changeth not.
He that putteth not out his money to usury, nor taketh reward against the innocent. He that doeth these things shall never be moved.
Psalm 15 (KJV)
Tuesday, February 01, 2011
Today's verse
I hope you will put up with a little more of my foolishness. Please bear with me. For I am jealous for you with the jealousy of God himself. I promised you as a pure bride to one husband—Christ. But I fear that somehow your pure and undivided devotion to Christ will be corrupted, just as Eve was deceived by the cunning ways of the serpent. You happily put up with whatever anyone tells you, even if they preach a different Jesus than the one we preach, or a different kind of Spirit than the one you received, or a different kind of gospel than the one you believed.
II Corinthians 11:1-4 (NLT)
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