Friday, April 16, 2004

Math Humor

One evening Rene Descartes went to relax at a local tavern. The tender approached and said, "Ah, good evening Monsieur Descartes! Shall I serve you the usual drink?". Descartes replied, "I think not.", and promptly vanished.

"The problems for the exam will be similar to the ones discussed in the class. Of course, the numbers will be different. But not all of them. Pi will still be 3.14159... "

Salary Theorem
The less you know, the more you make.

Postulate 1: Knowledge is Power.
Postulate 2: Time is Money.
As every engineer knows: Power = Work / Time
And since Knowledge = Power and Time = Money
It is therefore true that Knowledge = Work / Money .
Solving for Money, we get:
Money = Work / Knowledge
Thus, as Knowledge approaches zero, Money approaches infinity, regardless of the amount of Work done.

Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed?
Abbott and Costello made arithmetic shenanigans the basis
of a number of their comic dialogs.

Here is a dialog from their movie titled Buck Privates:

Abbott: You're 40 years old, and you're in love with a little girl,
say 10 years old. You're four times as old as that girl.
You couldn't marry that girl, could you?
Costello: No. ?

Abbott: So you wait 5 years. Now the little girl is 15, and you're 45.
You're only three times as old as that girl.
So you wait 15 years more.
Now the little girl is 30, and you're 60.
You're only twice as old as that little girl. ?

Costello: She's catching up. ?

Abbott: Here's the question. How long do you have to wait before you
and that little girl are the same age?

Costello: What kind of question is that? That's ridiculous.
If I keep waiting for that girl, she'll pass me up.
She'll wind up older than I am.
Then she'll have to wait for me!

Here's another encounter from Buck Privates, one echoed in
several later movies.

Abbott: Do me a favor. Loan me $50.
Costello: I can't lend you $50. All I've got is $40.
Abbott: That's okay. Give me the $40, and you'll owe me $10.
Costello: How come I owe you $10?
Abbott: What did I ask you for?
Costello: $50.
Abbott: What did you give me?
Costello; $40.
Abbott: So you owe me $10.
Costello: That's right. But you owe me $40. Give me my $40 back.
Abbott: There's your $40. Now give me the $10 you owe me.
That's the last time I'll ever ask you for the loan of $50.
Costello: How can I loan you $50 now? All I have is $30.
Abbott: Give me the $30, and you’ll owe me $20.
Costello: This is getting worse all the time.
First I owe you $10, and now I owe you $20!
Abbott: So you owe me $20. Twenty and 30 is 50.
Costello; Nope! Twenty-five and 25 is 50.
Abbott: Here's your $30. Give me back my $20.
Costello: All I've got now is $10!

Abbott then entices Costello into a silly, double-or-nothing
number game.

Abbott: Take a number, any number at all from 1 to 10, and don't tell me.
Costello: I got it.
Abbott: Is the number odd or even?
Costello: Even.
Abbott: Is the number between 1 and 3?
Costello: No.
Abbott: Between 3 and 5?
Costello: No. I think I got him.
Abbott: Between 5 and 7?
Costello: Yes.
Abbott: Number six?
Costello: Right. . . . How did he do that?

Toward the end of the movie, during a boxing match, Costello is
knocked to the canvas, and the biased referee gives a quick
count: 2, 4, 6, 8, 10.

Costello: What's this? 2, 4, 6, 8, 10? What happened
to 1, 3, 5, 7, and 9?
Ref: I don't like them numbers. They're odd.

X equals just about everything I learned of math in school

President Bush says our schools need to do a better job of teaching mathematics, and I agree with him 150 percent. Many high-school students today can't even calculate a square root! Granted, I can't calculate a square root, either, but I USED to be able to, for a period of approximately 15 minutes back in 1962. At least I think that was a square root. It might have been a ``logarithm.''
But whatever it was, if I had to learn how to do it, these kids today should have to learn it, too. As President Bush so eloquently put it in his address to Congress: ``Mathematics are one of the fundamentaries of educationalizing our youths.''

I could not have said it better with a 10-foot pole. We all need mathematics in order to solve problems that come up constantly in the ``real world.'' For example, suppose four co-workers go to a restaurant, and at the end of the meal, the waiter brings a bill totaling $34.57. How much, including tip, does each person owe? If the co-workers do not know mathematics, they will just guess at the answer and put in random amounts of money ranging from $9 to $11, unless one of them is a guy I used to work with named Art, in which case he will make a big show of studying the bill, then put in exactly $4.25.

But if the co-workers know their mathematics, they can easily come up with EXACTLY the correct answer. They can do this using ``algebra,'' which was invented by the ancient Persians. (They also invented the SATs, although they got very low scores because in those days there were no pencils.) The way algebra works is, if you don't know exactly what a number is, you just call it ``X.''

The Persians found that this was a BIG mathematical help in solving problems:
PERSIAN WIFE (suspiciously): How much have you had to drink?
PERSIAN HUSBAND: I had ``X'' beers.
PERSIAN WIFE: Well, how much is THAT?
PERSIAN HUSBAND: It's a (burp) variable.
PERSIAN WIFE (not wanting to look stupid): Well, OK then.
Historical Footnote: Several years later, when the ancient Romans invented Roman numerals, and it turned out that ``X'' was actually equal to 10, there was BIG TROUBLE in Persia.

But getting back to the four co-workers at the restaurant: To figure out how much each person owes, they would simply use the algebraic equation AEPO=1/4$34.57+T(((-SA?)@
(+NSOB!)(-SITE)(H), where ``AEPO'' is the amount each person owes, ``T'' is the tip, ``SA'' is whether the waiter has a snotty attitude, ``NSOB'' is whether the waiter has a nice set of buns, ``SITE'' is a variable used if you think somebody in the kitchen is spitting in the entrees, and H is hydrogen. Using this equation, our four co-workers can easily calculate that each one owes exactly, let's see... carry the 7... OK, it would probably be somewhere between $9 and $11.

So we see that algebra is a vital tool for our young people to learn. The traditional method for teaching it, of course, is to require students to solve problems developed in 1928 by the American Association of Mathematics Teachers Obsessed With Fruit. For example:
``If Billy has twice as many apples as Bobby, and Sally has seven more apples than Chester, who has one apple in each hand plus one concealed in his knickers, then how many apples does Ned have, assuming that his train leaves Chicago at noon?''

The problem is that these traditional algebra problems are out of date. Today's young people are dealing with issues such as violence, drugs, sex, eating disorders, stress, low self-esteem, acne, global warming and the demise of Napster. They don't have time to figure out how many apples Ned has. If they need to know, they will simply ASK Ned, and if he doesn't want to tell them, they will hold him upside down over the toilet until he does. And then Ned will sue them, plus the school, plus his parents for naming him ``Ned'' in the first place. Ultimately the ACLU will get the Supreme Court to declare that the number of apples a student has is protected by his constitutional right to privacy.

So what is the solution? How do we balance our children's need to learn math against the many other demands placed on them by modern life? I believe there IS a solution, one that is both simple and practical. I call it: ``X.''

Tuesday, April 13, 2004

AP Stats

Had a sub yesterday; I was at a meeting for planning the AP Statistics curriculum for next year. We've met a few times this year and I always find the meetings useful and productive. I am looking forward to teaching the class. But having a sub is always a bit stressful because you have to do more work to prepare for it and cleaning up afterward then if you had just been there yourself. Hopefully things went well and I won't have any extra chaos when I get back. I am really looking forward to teaching AP Stats next year.

We got lots of useful goodies at the meeting today; we finally found out there is a teacher's guide, for example. It doesn't have much in it, but we also got a test booklet we can draw from for tests and quizzes to give our kids next year. We also got some software and material to go with it, called Fathom. It is statistics software, but primarily we'll be using the statistics calculators like the TI -83 and TI-84. The 84's come out next month and I am hoping to buy one. Not cheap, they're like $120.

Thursday, April 08, 2004

From The History of the Ka'ba and its People

Ka’aba The House Of Allah

In the province of Hejaz in the western part of Arabia, not far from the Red Sea, there lies the town of Makka. In the centre of this town there is a small square building made of stones, about 60 feet long, 60 feet wide and 60 feet high. Since time immemorial this town and this stone built house has been known to world travellers.

Tradition goes that the Kaaba was ordained by Allah to be built in the shape of the House in Heaven called Baitul Ma’amoor. Allah in his infinite Mercy ordained a similar place on earth and Prophet Adam was the first to build this place. The Bible, in the Chapter of Genesis describes its building when God ordained Abraham to erect a Shrine for worship when Abraham was ordered to go to the Southern desert with his wife Hagera and infant son Ismael. The Old Testament describes this building as the Shrine of God at several places, but the one built at Ma’amoor is very much similar to the one at Makka. There is no doubt that it was referring to the stone built house at Makka.

Qora’an brought this story into the full light of history. In Sura 3 Verse 90 Qora’an says “Allah has spoken the Truth, therefore follow the creed of Ibrahim, a man of pure faith and no idolater”. The first house established for the people was at Makka, a Holy place and a guidance to all beings. Qora’an firmly establishes the fact that Ibrahim was the real founder of the Holy Shrine.

When Prophet Ibrahim built the Holy Shrine in Makka, his prayers were that this place should remain a centre of worship for all good and pious people; that Allah should keep his family the custodians of the Holy place. Ever since, Ismael the son of Ibrahim who helped his father to build this place and his descendants remained the custodians of the Holy Shrine. History tells us that centuries passed and the guardianship of the Kaaba remained in the family of Ismael until the name of Abde Manaf came into the limelight. He inherited this service and made it much more prominent. His son Hashim took this leadership and extended it to many other towns of Hejaz so much so that many pilgrims flocked annually to this place and enjoyed Hashims’s hospitality. A feast was given in honour of the pilgrims, food and water was served to all guests by the family of Hashim. This prominence created jealousies and his brother Abdushams’ adopted son Ummayya tried to create trouble. There was a dispute in which Umayya failed and left Makka to settle down in the Northern provinces of Suria(Sham) currently known as Syria. After Hashim his brother Muttalib and after him Hashim’s son Shyba who became known as Abdul Muttalib assumed the leadership of the family. He organised feasts and supplies of water to the pilgrims during the annual festival of Pilgrimage to the Holy Shrine.

Prophet Ibrahim built this House for devout worship to one God. But within his lifetime people disobeyed his orders and began to put idols inside the Kaaba. Ibrahim had to clean the House of these idols and of Idle worshippers. He told the people that this was a symbolic house of God. God does not live there for He is everywhere. People did not understand this logic and no sooner had Ibrahim died the people, out of reverence, filled the place with idols again. They thronged to this place annually and worshipped their personal gods, It was over Four Thousand years later that the last of the line of prophet (SA), Muhammad Ibne Abdullah entered Makka triumphantly, went inside the Ka’aba and, with the help of his cousin and son in law Ali Ibne Abi Talib, (AS) destroyed all the idols of Ka’aba with their own hands. At one stage of this destruction of idols, the tallest of the idol Hubbol was brought down after Ali had to stand on the shoulders of the Prophet to carry out God’s orders. The Prophet of Islam was reciting the Verse from the Qur’an

“Truth hath come and falsehood hath vanished.”
This was done in the 8th year of Hijra, January 630 AD after the bloodless victory at Makka by the Prophet of Islam.

Historically when Ibrahim was ordered by Allah to build the Shrine for worship over a small he uncovered the original foundations of the Kaaba built by Adam. Ibrahim with the help of his son Ismael erected the new shrine on the same foundations. Originally it contained only four walls without a roof . Centuries later during the timeof Kusayi who was the leader of the Tribe of Quraish in Makka a taller building was completed with a roof and a quadrangle wall around it to give it the shape of a sanctuary and doors all around the sanctuary walls. People entered through these doors to come to the Ka’aba for worship. It is now about 60 feet high, 60 feet wide from east to west and 60 feet from north to south. A door is fixed about 7 feet above ground level facing North East. A Black stone (Hajar al Aswad) was fixed into its eastern corner. In front of the building was Maqame Ibrahim, the arch shape gate known as that of Banu Shayba and the Zamzam Well. Just outside are the Hills called Safa and Merwa and the distance between the hills is about 500 yards. These days both of the hills are enclosed into the sanctuary walls with a roof over it.

The whole building is built of the layers of grey blue stone from the hills surrounding Makka. The four corners roughly face the four points of the compass. At the East is the Black stone (Rukn el Aswad), at the North is el Ruken el Iraqi, at the west al Rukne el Shami and at the south al Rukne el Yamani. The four walls are covered with a curtain (Kiswa). The kiswa is usually of black brocade with the Shahada outlined in the weave of the fabric. About 2/3rd’s of the way up runs a gold embroidered band covered with Qur'anic text.

In the Eastern corner about 5 feet above ground the Hajar el Aswad (the blackstone) is fixed into the wall. Its real nature is difficult to determine, its visible shape is worn smooth by hand touching and kissing. Its diameter is around 12 inches. Opposite the North west wall but not connected with it, is a semi circular wall of white marble. It is 3 feet high and about 5 feet thick. This semi circular space enjoys an especial consideration and pilgrims wait in queue to find a place to pray there. The graves of Ismael and his mother Hajera are within this semi circular wall. Between the archway and the facade (N.E.) is a little building with a small dome, the Maqame Ibrahim. Inside it is kept a stone bearing the prints of two human feet. Prophet Ibrahim is said to have stood on this stone when building the Ka’aba and marks of his feet are miraculously preserved.

On the outskirts of the building to the North East is the ‘Zamzam Well’ (this is now put under ground).

History of the building of the Ka’aba.

Qur’an in Sura Baqra Verses 121 to 127 described it clearly that Allah had ordained his servant Ibrahim to build the Shrine there for worship of One God. During Kusayi’s time it was rebuilt and fortified. During the early years of Prophet Muhammad (SA) before he announced his ministry, the Ka’aba was damaged by floods and it was rebuilt again. When the Black stone was to be put in its place the Makkans quarrelled among themselves as to who should have the honour to place it there. They had just decided that the first comer to the quadrangle should be given the task of deciding as to who should have the honour. Muhammad (SA) came in and was assigned this task. He advised them to place the stone in a cloak and ordered the heads of each Tribe each to take an end and bring the cloak nearer the corner on the eastern side. He himself then took out the stone and placed it in its position. It has been fixed there ever since.

After the martyrdom of the family of the Prophet at Kerbala in 61 Hijri (681 AD), the Ummayad Caliph Yazid Ibne Moawiya did not stop there in the pursuit of his destruction. He sent a large contingent under the command of Haseen Ibne Namir to Madina which destroyed the Mosque of the Prophet. They did not stop there but proceeded to Makka and demolished the four walls of the Ka’aba and killed thousands of muslims who protested. Yazid died and Ibne Namir returned to Damascus, Ka’aba was rebuilt by Abdullah Ibne Zubayr and his associates. Umawi forces came back to Makka and killed Abdullah Ibne Zubayr, hung his body on the gates of the Ka’aba for three months for all to see the Umawi power. But eventually this arrogance of power brought its own consequences and Mukhtar became the ruler in Iraq. Under his guidance the Ka’aba was refurbished and pilgrims began to arrive in safety to perform Hajj.

The Ka’aba successfully withstood the Karamatian invasion of 317/929, only the Blackstone was carried away which was returned some twenty years later. In the year 1981 the Wahabis brought tanks inside the Ka’aba to crush the kahtani revolution against the Saudi regime and almost demolished the South Eastern Wall. This was later restored with the help of the Makkan people.

Every man living in Makka in the 6th and 7th century must out of necessity have had some relationship with the Ka’aba. On the Muhammad (SA), the Prophet of Islam, the Qur’an is silent during the Makkans period in this respect. All that is known is that the muslim community of the period turned towards Jerusalem in prayers. Subsequently about a year and a half after the Hijra the Muslims were ordered during prayers which were lead by the Prophet of Islam himself to turn towards Makka. The particular mosque in Madina where this happened is called Masjide Qiblatain, meaning the mosque with two Qiblas.The Qur’an tells the muslims, “ turn then thy face towards the sacred mosque and wherever ye be turn your faces towards that part ”Qur’an II,139/144.

At this same period the Qur’an began to lay stress on the religion of Ibrahim, presenting Islam as a return to the purity of the religion of Ibrahim which, obscured by Judaism and Christianity, shone forth in its original brightness in the Qur’an. The pilgrimage’s to the Ka’aba and ritual progressions around the building were continued, but were now for the glorification of One God. The Abrahimic vision of the Ka’aba created a means of discerning an orthodox origin buried in the midst of pagan malpractices to which the first muslims pointed the way.

Every year after the Hajj ceremony the place is closed for one month and on the Day of Ashura the Ka’aba is washed from inside by the Water from the well of Zamzam and a new Kiswa is brought to cover the Ka’aba for the next year.

This is the story of the Ka’aba and the persons who protected it and remained its custodians and protectors from the satanic and evil forces throughout history. Muhammad (SA) and the people of his household (Ahlulbayt) were the protectors of the Ka’aba, and currently the 12th Imam from the direct descent of the Prophet of Islam is the real protector, its custodian and guardian and shall remain as such while in concealment.

Saturday, April 03, 2004

Teacher's Etiquette

Here is a nice, brief article I came across on teacher's etiquette. It is specifically designed at Islamic teaching, like madressah, etc., but even though I teach math to non-Muslim students much of it still applies. I have also added at the end something from Imam Ja'far Sadiq (as) I found on the same subject.

Shahîd ath-thânî, Shaykh Zaynud-dîn b. `Ali b. Ahmad al-‘Âmilî (d. 965 AH) has complied a book on the significance and etiquettes of learning and teaching in Islam. The work Muniyatul Murîd is higly beneficial for teachers and students of an Islamic school. Shahîd ath-thânî has listed thirty etiquettes that a teacher needs to follow while s/he is in a classroom with students.

Following are some of points for we need to consider implementing. We pray to the Almighty Allah ifor success and acceptance. 1. The teacher should be dressed neatly and respectfully with complete awe and reverance. White dress is recommended for it is the best dress.

2. When going to the class read the du`â taught by the Holy Prophet . I begin in the name of Allah, the Beneficent, the Merciful. O Allah, bless Muhammad and his family. O Allah, I take refuge with You from misleading or getting misled, making mistakes or being made to make mistakes, doing wrong or being made to act wrongly, and (from) acting ignorantly or being made to act with ignorance. [O Allah] Mighty is Your protection, Holy are Your names, Sublime are Your praises, and there is no god besides You. In the name of Allah, sufficient for me is Allah. I rely O Allah, and there is no power and strength except with Allah. O Allah, strengthen my heart and let truth appear on my tongue. O Allah, bless Muhammad and his family.

3. At the beginning of the class or whilst heading to the class have the intention (niyyah) of teaching and spreading the knowledge in order to disseminate Islamic sharî‘ah, conveying the rules of religion and increasing of knowledge through remembrance.

4. Greet, i.e. say salâmun ‘alaykum to all those present.

5. Begin the class with a brief recitation from the Holy Qur’ân. Then pray for those present, for all Muslims and for your self. Also, say a short khutbah (sermon) that includes taking refuge from Shaytân, praising Allah, salawât on the Prophet and his family, and praying for scholars.

6. When teaching, sit with tranquility, dignity, humility and modesty. Facing the Qiblah is recommended. The Prophet fhas said: the best gatherings are those in which people sit facing Qiblah.

7. Avoid excessive jokes and laughing for that reduces ones self-respect.

Imam Sadiq (as) said,
"Your teacher has the right over you that you should honor him and pay him respect in different assemblies. You should be very attentive to his words. you should not raise your voice above his. if anybody asks him a question, you should not give its reply. You should not converse with others in his presence and you should allow the people to benefit from his knowledge. You should not speak ill of anyone before him. If anybody speaks ill of him in your presence, you should defend him. You should conceal his shortcomings and bring his virtues to light. You should not associate with his enemies and should not dispute with his friends. If you act on these lines the angels of Allah will testify that you have paid attention to him and have acquired knowledge for the sake of Allah and not to attract the attention of the people.

And the right of your pupils on you is that you should realize that in granting you knowledge and opening its path to you, Allah has appointed you to be their guardian. In case, therefore, you teach them properly and do not frighten them and are not furious with them, Allah will, through His kindness, increase your knowledge. But if you drive the people away from knowledge and, as and when they approach you for it, you frighten them and get annoyed with them, it will only be appropriate that the Almighty Allah may take away the light of knowledge from you and may degrade you in the eyes of the people."

Friday, April 02, 2004

A Moment in the Sun

Wow today is turning out to be a busy blog day, but I didn't want to pass this up.

This evening I had a really nice, guilty pleasure. My mom and I go to the movies on Friday and tonight we didn't go to our usual theater. At this different theater, we ran into one of the board members of the charter school I used to teach at.

They sort of didn't renew my contract for the third year because they didn't like that I was looking elsewhere. There were some nice things about teaching at a small school like that, but the politics were just unbearable - incredible - a major eye-opener for me.

Anyway, this board member tells me that I was really missed at that school. Then she says, "We didn't know how very much we'd miss you - and I mean that as a compliment." She asked where I was teaching and we chatted a little and when I told her I would be teaching AP Statistics next year (insha'allah) she got big impressed eyes and said she was happy for me.

So I enjoyed my little moment of having one of them tell me essentially that they realized they made a mistake about me and didn't realize what they had until I was gone. :) I have heard so much about the troubles they've had with teachers since I've left and I have been so happy to be elsewhere. Okay, I need to get un-full of myself, but it made me feel vindicated and respected, it was nice of her to say it.