I heard this story from one of my ex-colleagues in Cathay Pacific, and I took the liberty of doing some editing and giving it a title.
There were four Catholic men and one Catholic woman having coffee. The first Catholic man stood up and said proudly, "My son is a priest. When he walks into a room, everybody calls him
'Father'."
The second Catholic man stood up and said proudly in a loud voice, "My son is a Bishop. When he walks into a room, everybody says
'Your Grace'."
The third Catholic man stood up and said proudly in an even louder voice, "My son is a Cardinal. When he walks into a room, everybody says
'Your Eminence'."
The fourth Catholic man stood up and said proudly in the loudest voice, "My son is the Pope. When he walks into a room, everybody says
'Your Holiness'."
The Catholic woman was sipping her coffee in silence. The four men looked down at her and gave her a subtle "Well ...... ?". The woman then raised her head and said shyly, "I have a daughter. She's
I taught private tuition in Mathematics to students junior than me while I was studying in secondary school. Over time, I came to become aware of some skills in handling some special situations during the lessons. Here are things you may say in class under certain circumstances:
. You don't want to go through all the possible cases. You just show one, and let the student figure out the rest,
"Without loss of generality, .......... "
. You know it's true, but you've lost your notes and you don't know how to prove it,
"It is obvious that .......... "
. You are struggling on how to explain, and your student suddenly reminds you the critical point,
"It now becomes clear that .......... "
. You feel tired after a long day's study yourself, and you don't want to explain in details,
When mathematician (or anyone working with mathematics) finishes a problem, he or she tends to tell the whole world that the work was quite easily done (Q.E.D.).
More often than not, they have already worked on it for days, if not weeks!
Talent is something you can do easily while others find it difficult to do.
Genius is something you can do easily while others find it impossible to do.
When Gauss (1777-1855) was a child, he attended the primary school in his local town. One day, the teacher found the class was too unsettled. In order to keep the class quiet for a while, he asked the children to sum the numbers from 1 to 100 before they could be dismissed. The class did stay silent while everyone was busy sketching their calculations on papers. Gauss didn't move. He stared at the blackboard for a few seconds, raised his hand and said, " The answer is 5050." The teacher looked at Gauss in disbelief, thinking he was just keen to leave the classroom. Gauss then explained step by step as follows:
"We call the sum of the numbers 1 to 100 S. Then,
S = 1 + 2 + .................. + 99 + 100
If we reverse the order of the numbers and add, the sum is still the same S.
S = 100 + 99 + .................. + 2 + 1
If we take the two together (i.e. add them vertically), we have two times the sum 2S, but the terms become 101 all the way for the 100 terms.
2S = 101 + 101 + .......... + 101 + 101
Since the numbers are the same, we don't need to add 100 times but we can multiply by 100. Simpler still, multiplying by 100 is just to add two zeros at the end of the number.
2S = 101 x 100 = 10100
To get back to the sum S, we just divide by 2.
S = 10100/2 = 5050."
Q.E.D.
Following on Gauss idea, we can develop further to generalize to sum the numbers from 1 to N (no matter what N is):
1 + 2 + ............... + N = N(N+1)/2
or, to sum from the number M to number N:
M + (M+1) + .......... + (N-1) + N = (N-M+1)(N+M)/2
If we still want to go further, we can research more to sum their squares:
1 + 22 + 32 + ………. + N2
or their cubes,
1 + 23 + 33 + ………. + N3
or, to push to the extreme,
1 + 2m + 3m + ………. + Nm
(no matter what m is).
But these require further mathematical techniques like recursive formula and Bernouilli numbers. I can touch on more as time permits.
We recently bought a Samsung side-by-side refrigerator from Bing Lee in Carlingford. It came with a special Christmas bonus. It was a huge 5.8-kg frozen turkey. This gave us a bit of a headache as we don't know what to do with it. Luckily, my daughter Veronica will be back from Canberra for the Christmas holiday. We will give Veronica this big piece of meat. We will also give her some suggested recipes of turkey meals from Woolworths. This will keep Veronica busy during the holidays, making turkey meals every day, and we will hear Veronica sing with joy:
"On the first day of X'mas, my true love sent to me - turkey pie. On the second day of X'mas, my true love sent to me - turkey soup. On the third day of X'mas, my true love sent to me - turkey salad. On the fourth day of X'mas, my true love sent to me - turkey sandwich. On the fifth day of X'mas, my true love sent to me - roast turkey. On the sixth day of X'mas, my true love sent to me - BBQ turkey. On the seventh day of X'mas, my true love sent to me - stuffed turkey. On the eighth day of X'mas, my true love sent to me - sweet and sour turkey. On the ninth day of X'mas, my true love sent to me - deep fried turkey. On the tenth day of X'mas, my true love sent to me - turkey pasta. On the eleventh day of X'mas, my true love sent to me - turkey pudding. On the twelfth day of X'mas, my true love sent to me - turkey cake."
We envisage, after the holiday, Veronica will be more like a turkey :) and we will have the big animal disappeared from our fridge.
I apologize this article may cause difficulty to non-Chinese-reading readers. But there is no way I can write this story completely in English without losing its original charisma.
One day Qianlong Emperor travelled to River South in plain clothes. He was late to find hotel accommodation in the evening. He came to a house where a widow lived. He asked the lady if he could have an overnight stay before he moved on the next day. Being alone by herself, the widow felt it was inappropriate for her to share the house with a guest. Without knowing the visitor was the emperor, she said that there was a rule in the house whereby all guests had to complete a couplet successfully before being admitted into the house. The widow then started off the first half of the couplet as follows:
寂寞守寒窗寡室寧容賓客寓
Qianlong Emperor scratched his head for hours. He could only complete half of the second half:
逌遙遊遠道????????????????
So regrettably, Qianlong Emperor had to leave reluctantly and seek accommodation elsewhere.
Notes: 1. '寓' is used as a verb, meaning 'to stay'; and is pronounced as '如'. 2. This Chinese couplet can be translated (to the best of my ability) as follows: 'Alone staying in a solitary unit, how can this tiny house accommodate guests to stay? Blissfully travelled to the far land, ?????????????????????????????????' 3. A couplet is a pair of sentences where the second sentence must match the first one grammatically word by word, term by term, phrase by phrase and finally sentence by sentence. 4. In addition, a good couplet would have the sentences matched in texture, and convey meaningfully certain messages. This couplet is regarded as one of the hardest (if not the hardest) in the sense that every word in the first sentence starts with the same radical, and it describes the situation the widow was in. Qianlong Emperor could only do similarly for the first half of the second part. Even though he could match the second half grammatically, he would not be able to find so many words with the same radical. That's why he failed. 5. If you can complete the couplet on behalf of Qianlong Emperor, he will knight you as the Scholar of the Year and award you a million dollar in gold.
It's been ten years since we moved to Australia, yet I still have difficulties interacting with the locals. I went to the McDonald's in Gordon with Johnson the other day after picking him up from school in the afternoon. I went to the counter for our orders with a girl. Here were our conversations:
I, "Fruit fizz.". Girl, "Fillet-O-fish?" I, "Hamburger." Girl, "Apple pie?"
In the not-too-distant past (as it appeared to me), I finished my matriculation level (Form 7) study. As the result of my Advanced Level Examination was not good enough to earn me a place in the local universities, nor could I afford for an overseas tertiary education, I had but to look for jobs to start my working career. At that time, I thought Accounting was the best profession for me. I sent out mountains of application letters to all the major firms in Hong Kong for suitable accounting posts. One day, I was asked to go for an interview in China Light and Power. I went to see the Head of the Accounts Department, Mr Nedderman. During the interview, Mr Nedderman didn't ask me anything about Accounting. Nor did he tell me anything about the accounting post I was applying for. He only asked me, "John, are you interested in working with computers?" I didn't have the faintest idea what computers were at that time, let alone I liked to work with them or not. So I hesitated, and said, "I don't know. But I'd like to know more." Mr Nedderman then took me for a tour to the computer room in China Light. It was a hugh farm of machineries. I was totally fascinated by the flickering lights of consoles and the fast rolling reels of magnetic tapes. Mr Nedderman introduced me to the manager of the computing department, and I ended up having an interview with him that day. I never saw Mr Nedderman again since then. A week later, I received a reply from China Light saying my application was not successful. I felt very disappointed. But the meeting with Mr Nedderman had sparked my interest in computing. So I quickly re-focused. I did a bit of research of what computers were, and what were the major computing firms in Hong Kong. I applied to the two then giants: IBM (International Business Machines) and NCR (National Cash Register), and finally I got an offer from IBM for a post of Computer Operator. Thence, I started my 36-year career in the IT (Information Technology) industry: 2 in IBM, 28 in Cathay Pacific and 6 in Qantas.
Expect the unexpected. Sometimes things may turn out not as we wanted, but they may turn out even better. Prepare to re-focus and react. We can start from nothing, provided we learn and work hard.
If you have lived in Australia long enough, you probably have the following experiences:
. you wonder why the bus stop is always located at the junction of the streets where traffic is the busiest. . you need to call up the customer services officers of utility companies at least 3 times to update your personal details. . you are in a queue where the customer services officer chats at least 20 minutes with each person in front of you. . you hear from the announcement the next train will be delayed for half an hour when you have already waited for an hour. . you take the rail on bus (rail bus) to the City on Sundays, as train lines are shut down for maintenance. . your kids go to Chatswood barefooted, and lick their fingers after eating ice creams. . you see beautiful topless blonds lying in Bondi on a sunny day who will turn belly up when you walk across. . the only thing that moves slower than continental drift is the traffic on Pacific Highway after you drop your kids to school in the morning.
