The Cat in Numberland​, by Ivar Ekeland

How do you prove that fractions are countablely infinite?

You can find the answer in this book for children. I read to my boy when he was around 6 or 7 years old. He was intrigued. Math is not difficult, it's just abstract. So the problem is that there is a dearth of good math teachers. Most people are floored by algreba, which is the key to higher level math learning.

The concept of Hotel Infinity was pioneered by David Hilbert, an eminent mathematican, though George Cantor was the mathematican who came up with the concept. So I suppose mathematicans at the pinnacle are not teaching children or teenagers. They are more interested in research.

Fret not, for there are still wonderful books like The Cat in Numberland around :)

F1 Singapore 2011

This was the fourth year in the running that Singapore was hosting the F1 race and the second time that my younger brother and I attended.


We took MRT, alighted at Lavender MRT station and took the free shuttle bus service to Gate 1. The place was abuzz with activities. Funky music filled the air. The many kiosks selling F1 merchandise and big golly balloons all added to the drumming-up of the F1 thrill factor.

Upon entrance, we were greeted by stilt performers with afro hairdo. They were also very friendly and offered to take a picture of us.

The crowd was just nice, not too thick for comfort. There was enough room for all to enjoy the performance around and to take in crisp fresh air. We took our time to sample the performance on our way to our seats. The leisure walk towards Marina Channel was relaxing with the cool evening breeze accompanied the gently lapping waters.

We were able to reach our designated seat in time for the start of Formula One Third Practice. The ushers were very efficient and courteous. They promptly guided us to the correct seat when we seemed a little lost.

The view from our seats was set against the Singapore Flyer and it marked the start and end of the lap. From our angle, we would be seeing the fast cars zipping by as they crossed the finishing line of the lap.

After some time, we decided to walk down further towards the Singapore Flyer as our tickets came with free rides on the Singapore Flyer. That was the highlight of the night.

It has probably been a year or so since I last boarded the Singapore Flyer. This time, I noticed that the miniature model of the Singapore Flyer and some models with interative element were exhibited as one walked into the passage leading to the capsule. These exhibits were much welcome as they broke the monontony of waiting to board the capsule, not that the wait was long.



The inclusion of the ride at Singapore flyer in this F1 event was a Fabulous One. We enjoyed an unparalleled bird's eye view of the Marina Bay Street as the capsule gradually brought us up 165 m above ground. The air-conditioned capsule carried 10 to 20 people and we could follow the fast cars zooming around almost the entire track.

After the ride which coincided with the end of the practice round, we were close to Gate 2. We exited the event venue and walked to Promenade MRT station. Along the way, the friendly and knowledgeable ushers were there to help. There were also ample and clear directional signs. This pointed to good planning beforehand all the way to the execution. All in all, it has been a fantastic experience.

Financial Advice from Mr Buffett

Amidst the current bearish financial market, I will like to share what Mr. Buffett has written a few years back. It's food for thought. Ponder on.

Back in 2008, Mr. Buffett wrote:
"A simple rule dictates my buying: Be fearful when others are greedy, and be greedy when others are fearful. And most certainly, fear is now widespread, gripping even seasoned investors. To be sure, investors are right to be wary of highly leveraged entities or businesses in weak competitive positions. But fears regarding the long-term prosperity of the nation's many sound companies make no sense. These businesses will indeed suffer earnings hiccups, as they always have. But most major companies will be setting new profit records 5, 10 and 20 years from now."
..."In short, bad news is an investor's best friend. It lets you buy a slice of America's future at a marked-down price. Over the long term, the stock market news will be good. In the 20th century, the United States endured two world wars and other traumatic and expensive military conflicts; the Depression; a dozen or so recessions and financial panics; oil shocks; a flu epidemic; and the resignation of a disgraced president. Yet the Dow rose from 66 to 11,497."

One of the most important reminders for investors during times of market turmoil is what Mr. Buffett states here:
"You might think it would have been impossible for an investor to lose money during a century marked by such an extraordinary gain. But some investors did. The hapless ones bought stocks only when they felt comfort in doing so and then proceeded to sell when the headlines made them queasy. Today people who hold cash equivalents feel comfortable. They shouldn't. They have opted for a terrible long-term asset, one that pays virtually nothing and is certain to depreciate in value. "

The things we did in Pittsburgh

The year was 2005, the Lim family decided to spend a year in Pittsburgh where papa Lim was to do a one-year postgraduate study.



It turned out to be a year which I would always remember. The year which outsiders would expect it to be a bed of roses but I could assure you that it wasn't easy. In fact, it was tough, tremendously difficult. The year which I proved to myself that nothing was insurmountable if the family stayed together.

I could still remember the shock of staying at home to look after two toddlers. The younger one was one going to two. At this stage of his life, it was termed the terrible two for a good reason. Yet, he was also so clingy, so loving and always melted my heart at the end of the day. The elder one was obedient, very teachable and always spellbound by my little history lesson and also science through observing the world around us.

Weekly Ritual

It took a while before we settled into the routine. We looked forward to our weekend grocery trip at the Strip District. We would stop by Lotus - a Chinese departmental store - to buy our oriental cooking needs such as soy sauce, jasmine rice, kaya and stuff. Next would be Wholey's for fresh produce, and also lunched at the second storey where the in-house cafeteria was. We savoured the freshness of the fish and chips and creamy soup. There were also free sculptured balloons just for kids.



My very considerate husband would come home early once every mid-week and brought us out to Freeport Road where the restaurant was Ponderosa. It was to be my break from housework and it coincided with the restaurant's family promotion so kids would well get free sculptured balloons. My two boys would be so excited and would just go to the balloon guy to get more balloons.

Sometimes, we would go to King's restaurant - a restaurant similar to our local Swenson - with ice-cream, yet distinct in its own way. One of which was the building which was single storey with a rooster north arrow atop.

Besides food, we also visited the parks. Our favourite spot was Lakepoint Shelter which was near our place. The scenery changed alongside the season. Autumn was the most beautiful with the vibrant hues of red, rust, yellow and gold. Winter looked solemn with the bare trees covered with snow.





I have now started my journey to detail more our one-year stay when I have the time. Little by little, they would piece together the precious memory that we have together.

Quartiles, deciles and percentiles

I have an affinity with Mathematics. This is a short blogpost consolidated from some quick google and my little explanation on how to remember coupled with my little list of related topics.

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Quartiles, deciles and percentiles (which are all examples of quantiles) are standard descriptive statistics which are used to divide a set of data points into equally sized subsets.

Quartiles divide the sample into four groups, with the lower quartile being 25%, the median value being at 50% and the upper quartile at 75%. Quartiles are essentially ranking mechanisms. The upper quartile is that position in the data set which has 75% of values below it and 25% above it. (How to remember: Quartile comes from the word quarter).

Deciles divide the sample into ten groups, with the lower decile is equivalent to the 10th percentile. (How to remember: Decile comes from the word decimal).

Percentiles divide the sample into one hundred groups. The 90th percentile is that position in a data set which has 90% of data points below it, and 10% above it. (How to remember: Percentile comes from the word percent).

So what is interquartile range?
Ans: 75th percentile - 25th percentile

Other related topics:
- Cumulative frequency curve
- Normal (or "bell-shaped") distribution.
- Power-law distribution - this is interesting. It looks something like a hockey-stick leaning against the y-axis. It appears to situation where big is rare and small is common. The distribution of wealth is one example, there are many poor souls around but few very, very wealthy ones.

When we are analysing data, we need to be mindful if it is one of power-law distribution. 'cos we are schooled to think that normal distribution is well, normal.

Pittsburgh Curry Chicken

Today was the day when I decided that I should replicate the chicken curry recipe which I learnt in the faraway Pittsburgh, Pennsylvania, USA. The initial period of being terribly homesick, led the then reticent me to seek out the Singapore recipe for chicken curry. A fellow Singaporean shared with me her family recipe tweaked slightly due to the availability of the ingredients in Pittsburgh and to cater to the palate of her little ones at home.

The curry which I shall now name, Pittsburgh Chicken Curry, which used to evoke that soothing, nostagic feeling, now has another meaning to it. It symbolises the bonding that we have together as a family and also with other fellow Singaporeans in a foreign land. Today's curry chicken was a success and a hot favorite with my two primary school going boys.

So here is the recipe (enough for 4 persons) which I hope my boys will pick it up when they are older:

The ingredients are
- 1 heapful tablespoon of curry powder
- 1 teaspoon of ground chilli powder
- 1 medium-size onion (to chop into small pieces)
- 4-5 small potato (to remove the skin)
- 3-4 medium-size carrots (remove the skin and cut into medium pieces)
- 800g to 1 kg of chicken pieces (can be all chicken wings/ leg if desired)
- 1 can of evaporated milk
- half can of plain water
- a pinch of salt

Steps (Estimated time to prepare- 30 to 45 minutes)
- Marinate the chicken pieces with the curry powder for around 15 minutes
- Chop the onion into small pieces and add the chilli powder
- Cut the potato and carrots
- In a pot, heat some cooking oil (about 3-4 table spoons or so, just enough to coat the pot with oil), pan fry the potatoes and carrots, until one can smell the fragrant. Then scoop up the potatoes and carrots and leave aside.
- Now, add the chopped onion with chilli powder and fry until the onion fragrant is in the air.
- Next, add the marinated chicken pieces and stir them together with the onions-cum-chilli mix, until the chicken pieces are about 75% cooked.
- Add in the evaporated milk plus half can of water, bring the mix to boil.
- Add the potatoes and carrots.
- Simmer for about 30 minutes for all to soften, if need be, one may need to scoop up the chicken pieces, leave aside and add to the mix when the potatoes and carrots have softened.
- Add a pinch of salt and the curry is ready.

A little tip - if you want more curry gravy, be judicious with water. Instead, you can consider adding fresh milk or skimmed fresh milk.

LIM FAMILY - MANY ANGRY BIRDS IN HAND...

Three months' ago, despite the light dizzle, the Lim family ventured in a nondescript yet idyllic corner in Ayer Hitam. We walked gingerly to avoid the rain water trapped in the potholes which were aplenty along the tarmac road. The occasional splashing of the accidential foot in hole did not dampen our spirits and we trekked along relentlessly.

We were rewarded handsomely when we found soft toys abound in the little shops in the cluster. Yes, among the plethora of toys were .... Yes, no prize for getting the right answer. It was - Angry Birds soft toys - the latest craze in Singapore, Johore and China. What made this a wonderful catch was that these were not just the not-too-pretty versions of Angry Birds soft toys - aka counterfeit ones - which one could get all around Singapore, but the real deal, erh or somewhat the real McCoy.

Since then, we have been thinking about the cute plush soft toys. So when Papa Lim suggested a day trip to Ayer Hitam, the boys were raring to go. We did not bother to ask much about the origin of these lovable soft toys but grabbed two - the yellow and black one - the last time round. This time, my younger boy was more direct and interestingly very diplomatic. (Ahem, it must be from my pool of good genes :P) The owner explained that in each batch of Angry Birds soft toys, there would be a few nice-looking ones which they would separately take it out for sale.

We rounded up our haul of a medium-size blue bird and the red one, enlarging our earlier collection, plus a bolster with the emblem of the green bird or in the words of my boys - the boomerang and a very powerful one, a large-size red bird. Oh yes, with the running of Cars 2, we have also grabbed a little plush Lightning McQueen backpack for my 4-year old nephew.

It has been a wonderful half-day road trip up north, that brought a smile to everyone in the Lim family. As the sun gradually set, we hit the road again on our journey to Singapore.