Whee...!
posted by Tan Yee Wei at 7/31/2005 04:37:00 pm
Sunday, July 31, 2005
Melbourne Bloggers Meet
The rendezvous was at Max Brenner QV at 2pm. I managed to be late.
Max Brenner is an upmarket chocolate shop of sorts. They sell a variety of chocolate drinks with chocolate drizzled this and chocolate drizzled that. Business is really good- they even have the cheek to charge a 10% weekend surcharge. A $4.50 drink becomes $4.95 during the weekend. Ta ma de. What next? Up to date supply and demand optimisation? “Current surcharge: 4.3%. Next update in 4:32 minutes.”
I was late for the meeting because my phone flashed me with its “battery low” warning just as I was ready to move. It was not very good since we had no way of identifying each other except by a 10-digit string of numbers that uniquely identifies a phone and thereby the person. And so a charging plug was shoved up a little hole at the bottom of my phone, and left inside for about 15 minutes. That would explain why I was late by 15 minutes.
There were 5 of us (in alphabetical order):
David
Diana
Jean
Keen
Yee Wei
I didn’t talk very much (no surprises there), which was probably a good thing since many of the issues raised were very much beyond my katak di bawah tempurung field of view. There were discussions about Malaysian politics, the NEP, distribution of wealth, the general mindset of Malaysians towards government inefficiencies, architecture at Lim Kok King Institute...
We sat on one of the tables set up outdoors of Max Brenner; they do not have indoor seating. At about mid afternoon, a breeze picked up it started getting uncomfortably cold. Hands disappeared into pockets, and the jackets got zipped up a bit higher. We moved out of Max Brenner into QV’s food court soon after.
It would appear that most bloggers are into photography. David, Diana and Jean have their own SLRs. David has a beautiful Olympus E-300 and posts weekly (Mondays) photographs on his blog, Diana has 2 film cameras (at least one SLR, Canon EOS 300v) and a digital prosumer Canon A510, Jean has been playing with SLRs since form 3 and co-founded her secondary school’s photography club. [correct me if i'm wrong] Myself, only a decade old Olympus iS-1000 ZLR (an SLR but without the removable lens assembly) and no digitals to speak of except for frequently borrowed ones.
3 out of 5 are hardcore photographers! Probably not hardcore porn photographers though. No chance of me visiting shoots in the near future...
A few interesting points I picked up (and still remember):
Never, never, never condemn anyone to the Lim Kok Wing Institute. They do not deserve it. Your enemy can’t have done anything to require a re-education at Lim Kok Wing Institute; the Institute does not deserve more income in form of tuition fees.
Apparently, Lim Kok Wing himself used to be a man down on his fortunes. Nonetheless he kept his Jaguar from his previous high. And, he would beg his friends and acquaintances for the odd RM50 to pump petrol.
The British found tin from Malaya attractive during the colonial era because tin was a commodity in great demand. It was in demand because it was used to package canned food. Canned food was very popular in North America at that time since soldiers were too busy to cook a decent meal and had to resort to cracking open cans of precooked mush. It was the American Civil War.
The political fiasco at SRJK(C) Damansara was the result of politicians trying to use/lever the situation to their advantage, thus screwing over the general population. An insider says that certain parties had been creating trouble. It’s really bad.
It was an interesting one. Hopefully we can meet again sometime in the near future. And no, I wasn’t bored stiff even though I did not talk a lot.
Max Brenner is an upmarket chocolate shop of sorts. They sell a variety of chocolate drinks with chocolate drizzled this and chocolate drizzled that. Business is really good- they even have the cheek to charge a 10% weekend surcharge. A $4.50 drink becomes $4.95 during the weekend. Ta ma de. What next? Up to date supply and demand optimisation? “Current surcharge: 4.3%. Next update in 4:32 minutes.”
I was late for the meeting because my phone flashed me with its “battery low” warning just as I was ready to move. It was not very good since we had no way of identifying each other except by a 10-digit string of numbers that uniquely identifies a phone and thereby the person. And so a charging plug was shoved up a little hole at the bottom of my phone, and left inside for about 15 minutes. That would explain why I was late by 15 minutes.
There were 5 of us (in alphabetical order):
David
Diana
Jean
Keen
Yee Wei
I didn’t talk very much (no surprises there), which was probably a good thing since many of the issues raised were very much beyond my katak di bawah tempurung field of view. There were discussions about Malaysian politics, the NEP, distribution of wealth, the general mindset of Malaysians towards government inefficiencies, architecture at Lim Kok King Institute...
We sat on one of the tables set up outdoors of Max Brenner; they do not have indoor seating. At about mid afternoon, a breeze picked up it started getting uncomfortably cold. Hands disappeared into pockets, and the jackets got zipped up a bit higher. We moved out of Max Brenner into QV’s food court soon after.
It would appear that most bloggers are into photography. David, Diana and Jean have their own SLRs. David has a beautiful Olympus E-300 and posts weekly (Mondays) photographs on his blog, Diana has 2 film cameras (at least one SLR, Canon EOS 300v) and a digital prosumer Canon A510, Jean has been playing with SLRs since form 3 and co-founded her secondary school’s photography club. [correct me if i'm wrong] Myself, only a decade old Olympus iS-1000 ZLR (an SLR but without the removable lens assembly) and no digitals to speak of except for frequently borrowed ones.
3 out of 5 are hardcore photographers! Probably not hardcore porn photographers though. No chance of me visiting shoots in the near future...
A few interesting points I picked up (and still remember):
Never, never, never condemn anyone to the Lim Kok Wing Institute. They do not deserve it. Your enemy can’t have done anything to require a re-education at Lim Kok Wing Institute; the Institute does not deserve more income in form of tuition fees.
Apparently, Lim Kok Wing himself used to be a man down on his fortunes. Nonetheless he kept his Jaguar from his previous high. And, he would beg his friends and acquaintances for the odd RM50 to pump petrol.
The British found tin from Malaya attractive during the colonial era because tin was a commodity in great demand. It was in demand because it was used to package canned food. Canned food was very popular in North America at that time since soldiers were too busy to cook a decent meal and had to resort to cracking open cans of precooked mush. It was the American Civil War.
The political fiasco at SRJK(C) Damansara was the result of politicians trying to use/lever the situation to their advantage, thus screwing over the general population. An insider says that certain parties had been creating trouble. It’s really bad.
It was an interesting one. Hopefully we can meet again sometime in the near future. And no, I wasn’t bored stiff even though I did not talk a lot.
posted by Tan Yee Wei at 7/31/2005 01:18:00 am
Saturday, July 30, 2005
The Slap Analyst
In this scene, Yong confront her husband about his affair with his young and sexy secretary, Ms Marie Curie.
"But I still do love you!” Yong’s husband protested, as if that would justify everything.
“So why did you do it?”
“Well, you know…” he fumbled about for an excuse. It was not in anyone’s best interest to tell the truth. “Well…it can get so dull in that dump sometimes, and she…um…she started it…and…uh…”
Piak!
The fleshy sound of a slap rang out, prematurely terminating the husband’s defence. Yong stormed out of the room, slamming the door after her. Gradually, his cheek turned a pinkish hue of red.
***
The scene ended, and the director complained about the dry acting, the lifeless speech, the expressionless faces, and that dead-ish slap. “That was the hardest I could manage to slap!” whined the lead actress.
“If I may, I just happen to have something with me that might be of use to you,” a voice hidden behind the glare of the lighting fixtures piped up.
“And who are you?” the director snapped. He was already under enough stress from managing this bunch of useless ‘talents’.
“I’m the lighting man,” the voice announced as its form stepped out of the shadows. “But more importantly, I am an expert in the field of slapping. In fact, I’ll be giving a paid seminar at the Marriot tomorrow. My next seminars and lectures will be in Bali, Bangkok, the Shanghai Music Conservatory, Hong Kong and IBM New Delhi.”
“I see…go on,” the director visibly impressed.
“I’ve got some notes that might be of use for today. Can’t help with their horrid acting,” he waved his hand condescendingly in the general direction of the set, “but it’ll do your girl’s slapping some good.”
From an elegant black leather folder, he retrieved several copies of the aforementioned notes and distributed them among the cast and the director. “This is the first portion of the seminar notes. It’s nothing fancy really, all classical physics. The application of quantum mechanics and relativistic effects will only be discussed in the paid lectures,” he gave a wink. “Anyway, read through it, and with a bit of practice, your slap will be the finest around here.”
***
3 days later, the rehearsal was held in a gymnasium. Their usual studio had suffered a tragedy with the plumbing, and was not fit for usage. At one end of the large gymnasium, a red sandbag hung quietly from a crossbeam in the low ceiling. “Interesting,” the lead actress thought to herself. She positioned herself in front of the sand bag and gave it a slap.
Thump!
Her palm slammed into the pliable bag, the particulate material within deforming as it absorbed the impact.
She repositioned herself, and started the making motions faster and faster. Thumps resonated within the large hall with rapid periodicity. She started alternating with left and right hands, then forehand and backhand. Before long, she settled into a sort of chaotic yet rhythmic motion, and was switching between forehand and backhand slaps for left and right hands.
Soon, she was shadow-sparring with an imagined opponent. She held her attacks, feinted, blocked and followed up with a rapid succession of strikes that ended with a final jarring blow accompanied with a Bruce Lee-esque howling shriek.
The lead actor looked at the proceedings with a marked amount of worry. “Am I to be slapped by that...fighting machine?” he asked the director, hoping for the best. “Only once,” the director reassured the young man kindly, albeit with a sarcastic smile.
The Effective Slapping Seminar
by Tan Yee Wei
We’ll start off with the most fundamental points-
Pain from a slap is due to the force of impact
Force of impact depends on momentum and duration of impact.
Momentum is velocity times mass (weight). You can’t change your mass, so you’ll only have velocity to meddle with. More velocity means more momentum.
Start off with more speed, and you will have a greater momentum, and consequently, greater force, and thus more pain (wheee!)
If the duration impact is a very short, forces involved will be greater. Falling into a mattress doesn’t hurt as much as falling onto a concrete floor because the duration of impact on a mattress is spread out as you sink into the soft material, rather than a splat as you stop right on the concrete surface.
So, we need to have maximum velocity, and minimise impact duration. However, for safety reasons, we will not discuss techniques to reduce impact duration.
We’ll start off with ideas for maximising velocity.
There is a practical speed limit for swiping your hand at a face. Your muscles are not able to contract any much faster than this speed.
To make it faster, we move the whole upper body along with it. Now, your muscles are swiping at full speed, and your upper body is moving as well. The sum of speeds makes the slapping speed greater.
To add even more speed, rotate your upper body as well.
Here’s an illustration.
You and your victim are standing on level ground. You slap him.
Your victim is standing on the ground, while you are on a merry-go-round. You slap him in the same direction as the merry-go-round’s direction of spin.
Your victim is standing on the ground, while you are leaning out of a moving train’s window. You slap him.
Your victim is standing on the ground. You, on the other hand, are riding on a spinning merry-go-round that was installed on a moving train. You slap him. OUCH!
And now the techniques (I’m talking in right-handed terms):
Stand with your feet slightly apart, about 20 to 24 inches wide. Hands relaxed downwards at your side. Position yourself so that your victim’s face is in front of your left foot.
Fold your right elbow (without moving your shoulder), such that your palm is about the same height of your shoulder, facing forward.
Shift your upper body towards the right side. The left leg is supporting very little of your body weight now. Bend your knees slightly; keep your waist horizontal; back straight. Twist your hips, waist and upper body towards the right side (clockwise direction) so that you are looking diagonally to the front-right.
Rapidly shift your body’s weight towards the left side. For very rapid movement (which is what we want), push with the right leg. At the same time, start untwisting your upper body towards the left side (counter-clockwise). Simultaneously, extend your slapping palm outwards and take a (counter-clockwise) swipe at the victim. Remember, we want to maximise velocity. Do all your shifting, twisting and swiping as rapid as possible, simultaneously.
Now, your position should be something like this-
Weight on left leg.
Upper body twisted to the left.
With some adjustments, you can now continue on with a backhand slap on the other cheek, using the same techniques as above.
"But I still do love you!” Yong’s husband protested, as if that would justify everything.
“So why did you do it?”
“Well, you know…” he fumbled about for an excuse. It was not in anyone’s best interest to tell the truth. “Well…it can get so dull in that dump sometimes, and she…um…she started it…and…uh…”
Piak!
The fleshy sound of a slap rang out, prematurely terminating the husband’s defence. Yong stormed out of the room, slamming the door after her. Gradually, his cheek turned a pinkish hue of red.
The scene ended, and the director complained about the dry acting, the lifeless speech, the expressionless faces, and that dead-ish slap. “That was the hardest I could manage to slap!” whined the lead actress.
“If I may, I just happen to have something with me that might be of use to you,” a voice hidden behind the glare of the lighting fixtures piped up.
“And who are you?” the director snapped. He was already under enough stress from managing this bunch of useless ‘talents’.
“I’m the lighting man,” the voice announced as its form stepped out of the shadows. “But more importantly, I am an expert in the field of slapping. In fact, I’ll be giving a paid seminar at the Marriot tomorrow. My next seminars and lectures will be in Bali, Bangkok, the Shanghai Music Conservatory, Hong Kong and IBM New Delhi.”
“I see…go on,” the director visibly impressed.
“I’ve got some notes that might be of use for today. Can’t help with their horrid acting,” he waved his hand condescendingly in the general direction of the set, “but it’ll do your girl’s slapping some good.”
From an elegant black leather folder, he retrieved several copies of the aforementioned notes and distributed them among the cast and the director. “This is the first portion of the seminar notes. It’s nothing fancy really, all classical physics. The application of quantum mechanics and relativistic effects will only be discussed in the paid lectures,” he gave a wink. “Anyway, read through it, and with a bit of practice, your slap will be the finest around here.”
3 days later, the rehearsal was held in a gymnasium. Their usual studio had suffered a tragedy with the plumbing, and was not fit for usage. At one end of the large gymnasium, a red sandbag hung quietly from a crossbeam in the low ceiling. “Interesting,” the lead actress thought to herself. She positioned herself in front of the sand bag and gave it a slap.
Thump!
Her palm slammed into the pliable bag, the particulate material within deforming as it absorbed the impact.
She repositioned herself, and started the making motions faster and faster. Thumps resonated within the large hall with rapid periodicity. She started alternating with left and right hands, then forehand and backhand. Before long, she settled into a sort of chaotic yet rhythmic motion, and was switching between forehand and backhand slaps for left and right hands.
Soon, she was shadow-sparring with an imagined opponent. She held her attacks, feinted, blocked and followed up with a rapid succession of strikes that ended with a final jarring blow accompanied with a Bruce Lee-esque howling shriek.
The lead actor looked at the proceedings with a marked amount of worry. “Am I to be slapped by that...fighting machine?” he asked the director, hoping for the best. “Only once,” the director reassured the young man kindly, albeit with a sarcastic smile.
by Tan Yee Wei
We’ll start off with the most fundamental points-
So, we need to have maximum velocity, and minimise impact duration. However, for safety reasons, we will not discuss techniques to reduce impact duration.
We’ll start off with ideas for maximising velocity.
Here’s an illustration.
And now the techniques (I’m talking in right-handed terms):
Now, your position should be something like this-
With some adjustments, you can now continue on with a backhand slap on the other cheek, using the same techniques as above.
posted by Tan Yee Wei at 7/30/2005 07:20:00 pm
My first exposure to sex
Back in the early 90s, when I was not much more than a boy of 10, I learned what ‘sex’ meant. A class mate told me that it involved the man putting his lan into the woman’s pepet. I was mildly fascinated by such an elegant phenomenon, where the protrusion of one fits into the recession of the other.
I did not give the matter much more notice than that cursory spark of interest. Yes, I was among those that actively made silly jokes about penises and breasts, but they were more out of fascination than sexual awareness. Notice the absence of the vagina- it was completely foreign thing to us. In similar vein, you would not expect a German farmer to make jokes about asam laksa. No, neither do I know of anygood asam laksa jokes.
The ‘sex’ matter was forgotten until one day at my grandparent’s house. It was a slow weekend afternoon, and a movie of sorts was on the television. My uncle and a cousin or two were half-heartedly watching the moving images. As I passed through the living room with my cousin David, we paused to look at the television. At that moment, the scene was of a man and a woman kissing. For no explainable reason, I blurted out something to the effect of “maybe they are doing sex,” before moving on.
Once out of the living room, David stopped me and sternly told me that “my father knows what sex is.” “Oh.”
*In hindsight, it is perhaps surprising that my uncle managed to conceal his (presumed) surprise instead of abruptly sitting up and gasping for air.
I did not give the matter much more notice than that cursory spark of interest. Yes, I was among those that actively made silly jokes about penises and breasts, but they were more out of fascination than sexual awareness. Notice the absence of the vagina- it was completely foreign thing to us. In similar vein, you would not expect a German farmer to make jokes about asam laksa. No, neither do I know of any
The ‘sex’ matter was forgotten until one day at my grandparent’s house. It was a slow weekend afternoon, and a movie of sorts was on the television. My uncle and a cousin or two were half-heartedly watching the moving images. As I passed through the living room with my cousin David, we paused to look at the television. At that moment, the scene was of a man and a woman kissing. For no explainable reason, I blurted out something to the effect of “maybe they are doing sex,” before moving on.
Once out of the living room, David stopped me and sternly told me that “my father knows what sex is.” “Oh.”
*In hindsight, it is perhaps surprising that my uncle managed to conceal his (presumed) surprise instead of abruptly sitting up and gasping for air.
posted by Tan Yee Wei at 7/30/2005 12:08:00 am
Friday, July 29, 2005
Melbourne Bloggers Meet @ 30 July
This entry extracted from Diana's blog:
Date: 30 July Saturday
Location: Max Brenner QV
Time: 2pm
Who can come?::
Anyone. blogger/ non-blogger/ blog-reader/ Malaysian/ non-Malaysian/ family/ uni-mates blahblah
It was postponed before, and I don't think i wanna postpone it again.. so rain or shine (btw its FINE weather on Sat) come!!
posted by Tan Yee Wei at 7/29/2005 03:43:00 pm
Matlab Butterfly
While working on my project, I met a butterfly in Matlab. I then brought her over to Photoshop and gave her a makeover.
Click for larger image
Click for larger image
MathWorks Matlab 5.3 (this is extremely dated, coming for the late 90s. The latest version of Matlab is 7.0.4, released March 2005. Can you imagine using Windows 98?)
Adobe Photoshop 7.0
Click for larger image
Click for larger image
MathWorks Matlab 5.3 (this is extremely dated, coming for the late 90s. The latest version of Matlab is 7.0.4, released March 2005. Can you imagine using Windows 98?)
Adobe Photoshop 7.0
posted by Tan Yee Wei at 7/29/2005 01:27:00 pm
Thursday, July 28, 2005
Wind Tunnel Succubus
Click for large image
This is my first attempt to venture into pretend-abstract art. Suddenly hitting on a remarkable inspiration this afternoon, I have arrived at a brilliant scheme that would help name abstract art pieces.
Get two (or more) extremely unconnected words and put them together like it was actually meant to mean something.
For example,
Strawberry Porcupine
Elephant Tincture
Wind Tunnel Succubus
Stagflationary Penis
The Ethereal Cauliflower
What can you come up with? Come on, the more the merrier.
About the art piece:
This was generated by creating a 10 by 10 matrix that is a function of 2 variables. The matrix is complex- each element has a real and imaginary part. Changing the two variables (x and y) will change the values of elements in the matrix, naturally. The determinant D of this matrix will be a complex number, due to the fact that the elements are complex. If for a particular x and y combination, the imaginary part of D is zero, a red dot is dotted on the x-y plane. However, if the real part of D is zero, a blue dot is made on the x-y plane.
This plot is extremely elegant in that at first glance, it appears to be a criss-cross of lines not unlike a chain link fence. However, closer inspection will reveal that the blue lines in fact never cross each other. At the ‘crossing’ points, they actually veer away sharply from each other, leaving a gap in between where the red line will slip through. Sometimes, these gaps are vanishingly small; other times, they are blatantly visible.
posted by Tan Yee Wei at 7/28/2005 05:37:00 pm
Oops
I have finally decided which subjects to choose for my three electives- Human Resources Management, Advanced Computational Mechanics and Optimisation. Unwilling to let a fascinating subject go to waste, I’ll also be attending the lectures for Computational Biomechanics and if time permits, go through the homework and assignments, albeit in a half-hearted and un-assessed manner.
The next step would be to change my subject selection. It is to be done online, but I could not figure out how to access the stupid thing. Trawling through the web pages, I saw nothing remotely like “subject change”. TMD.
This afternoon, I dropped by at the Mechanical Engineering office to ask about changing my subject.
“You go to the Student Information System website, sis.unimelb.edu.au, and look for it on the red coloured column on the right. It would be listed there as view subjects or something. You go there and […]”
So it was there. I’ve visited that page many times in my search for that link, but did not look in the sidebar. My parents have frequently complained that my eyes are large but quite useless. “Wei, get me two more cans of tuna,” my mother would ask from the kitchen. “Where?” “In the cupboard, the bottom shelf”
And I would search the bottom shelf for a good 30 seconds.
“Can’t find it la. Do we still have it?”
“Yes, I just bought it from Giant on Monday. I remembered putting in on the bottom shelf.”
“Ok.”
Another 20 seconds tick away.
“Can you find it?”
“No arr. You want to have a look?”
Mother would stop, and come by exasperatedly. And she would then point right at the cans of tuna, on the bottom shelf, at the edge where they were most visible. Oops.
Having finally known where to adjust my subjects, I then asked if I could do it from the Mechanical Engineering office.
“No, you got to do it online. Are you a first year student?”
“No, 4th year.”
The Academics Program Manager looked stumped. Another lady who had been sort of listening in the background looked up from her documents in surprise. I think it’s expected that everyone should be intimately familiar with the subject selection mechanism.
Then they both laughed. Oops.
The next step would be to change my subject selection. It is to be done online, but I could not figure out how to access the stupid thing. Trawling through the web pages, I saw nothing remotely like “subject change”. TMD.
This afternoon, I dropped by at the Mechanical Engineering office to ask about changing my subject.
“You go to the Student Information System website, sis.unimelb.edu.au, and look for it on the red coloured column on the right. It would be listed there as view subjects or something. You go there and […]”
So it was there. I’ve visited that page many times in my search for that link, but did not look in the sidebar. My parents have frequently complained that my eyes are large but quite useless. “Wei, get me two more cans of tuna,” my mother would ask from the kitchen. “Where?” “In the cupboard, the bottom shelf”
And I would search the bottom shelf for a good 30 seconds.
“Can’t find it la. Do we still have it?”
“Yes, I just bought it from Giant on Monday. I remembered putting in on the bottom shelf.”
“Ok.”
Another 20 seconds tick away.
“Can you find it?”
“No arr. You want to have a look?”
Mother would stop, and come by exasperatedly. And she would then point right at the cans of tuna, on the bottom shelf, at the edge where they were most visible. Oops.
Having finally known where to adjust my subjects, I then asked if I could do it from the Mechanical Engineering office.
“No, you got to do it online. Are you a first year student?”
“No, 4th year.”
The Academics Program Manager looked stumped. Another lady who had been sort of listening in the background looked up from her documents in surprise. I think it’s expected that everyone should be intimately familiar with the subject selection mechanism.
Then they both laughed. Oops.
posted by Tan Yee Wei at 7/28/2005 04:29:00 pm
Monday, July 25, 2005
The apparent ease of divisibility of numbers using different bases
[warning: yet another number theory laden post. It's not heavy mathematics, but more like a philosphical discussion of numbers]
In everyday usage, the most commonly used language to describe numbers is the decimal system, or the base-10. In base-10, numbers (objects) are represented using 10 symbols, namely:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Of course, there are more numbers (objects) than there are symbols, so larger numbers will have to be represented by a combination of symbols. An easy way to think of this is to say that there are 26 alphabets in the English language, but there are definitely more than 26 objects that need to be named. Hence we combine several alphabets to form words like “prototype”, “hippopotamus”, “coffee” and “cheebye”.
Similarly, several symbols might be combined to represent large numbers (objects) like “55”, “252452787”, “100” and “47”.
How are the symbolic representations of numbers (objects) constructed?
Start from the first symbol, 0. 0 will be used to represent zero. The next symbol, 1, will represent one. The next symbol, 2, will represent two. This goes on until we reach 9 (the last symbol available in base-10).
We then add one more character to the name, and it becomes a two-symbol long name: 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21 … 98, 99, 100, 101, 102 … 998, 999, 1000, 1001, 1002…
Sometimes, it appears as if it is easier to divide by some number than divide by other numbers. Sticking to the base-10 notation, it dead easy to see that 4322 can be divided by 2, but it is not as easy to know that 4322 cannot be divided by 3. Is it some inherent property of numbers (objects), or is it purely due to our way of expressing numbers?
Lets write out a list of numbers in base-10, and highlight those that can be divided by 2:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36…
It happens that all those that divide by 2 are numbers that have their last digits that divide by 2 (even numbers).
Similarly, below is a list of numbers with those that divide by 3 highlighted:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36…
It’s slightly messier with this case.
In truth, numbers written in base-10 are easy to divide by 2 (and 5) precisely because 10 can easily be divided by 2 (and 5). As such, as long as the last digit can be divided by 2 (or 5), the number can be divided by 2 (or 5).
To prove the point, we will now work with base-12, using the following twelve symbols:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b
Writing the same numbers (from one to thirty-six) in base-12:
1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1a, 1b, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 2a, 2b, 30…
With the numbers that can be divided by 2 highlighted. Again, it is dead easy to see that if a number can be divided by 2- the last digit needs to be an even number (in base-12, a is also an even number, since a is ten)
What if we highlight those that divide by 3?
1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1a, 1b, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 2a, 2b, 30…
The pattern should be easy to spot. All numbers that have the last digit of 0, 3, 6 or 9 will divide by 3.
This is because we are working with base-12, and 12 divides by 3 (and 2).
Seven is often a difficult number to divide by if working with base-10. What if we use base-14 instead? The 14 symbols used in base-14 are as follows:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d
The numbers one to thirty-six, in base-14:
1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1a, 1b, 1c, 1d, 20, 21, 22, 23, 24, 25, 26, 27, 28…
Highlighting numbers that divide by 3:
1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1a, 1b, 1c, 1d, 20, 21, 22, 23, 24, 25, 26, 27, 28…
Its trickier isn’t it? That’s because 14 does not divide by 3.
Highlighting numbers that divide by 7:
1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1a, 1b, 1c, 1d, 20, 21, 22, 23, 24, 25, 26, 27, 28…
Easy stuff. All numbers ending with the digit 7 or 0 can be divided by 7.
Here is something worth thinking about while you eat your nasi lemak or cheese naan:
How messy will be base-P systems, where (P is a prime number)?
In everyday usage, the most commonly used language to describe numbers is the decimal system, or the base-10. In base-10, numbers (objects) are represented using 10 symbols, namely:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Of course, there are more numbers (objects) than there are symbols, so larger numbers will have to be represented by a combination of symbols. An easy way to think of this is to say that there are 26 alphabets in the English language, but there are definitely more than 26 objects that need to be named. Hence we combine several alphabets to form words like “prototype”, “hippopotamus”, “coffee” and “cheebye”.
Similarly, several symbols might be combined to represent large numbers (objects) like “55”, “252452787”, “100” and “47”.
How are the symbolic representations of numbers (objects) constructed?
Start from the first symbol, 0. 0 will be used to represent zero. The next symbol, 1, will represent one. The next symbol, 2, will represent two. This goes on until we reach 9 (the last symbol available in base-10).
We then add one more character to the name, and it becomes a two-symbol long name: 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21 … 98, 99, 100, 101, 102 … 998, 999, 1000, 1001, 1002…
Sometimes, it appears as if it is easier to divide by some number than divide by other numbers. Sticking to the base-10 notation, it dead easy to see that 4322 can be divided by 2, but it is not as easy to know that 4322 cannot be divided by 3. Is it some inherent property of numbers (objects), or is it purely due to our way of expressing numbers?
Lets write out a list of numbers in base-10, and highlight those that can be divided by 2:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36…
It happens that all those that divide by 2 are numbers that have their last digits that divide by 2 (even numbers).
Similarly, below is a list of numbers with those that divide by 3 highlighted:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36…
It’s slightly messier with this case.
In truth, numbers written in base-10 are easy to divide by 2 (and 5) precisely because 10 can easily be divided by 2 (and 5). As such, as long as the last digit can be divided by 2 (or 5), the number can be divided by 2 (or 5).
To prove the point, we will now work with base-12, using the following twelve symbols:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b
Writing the same numbers (from one to thirty-six) in base-12:
1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1a, 1b, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 2a, 2b, 30…
With the numbers that can be divided by 2 highlighted. Again, it is dead easy to see that if a number can be divided by 2- the last digit needs to be an even number (in base-12, a is also an even number, since a is ten)
What if we highlight those that divide by 3?
1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1a, 1b, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 2a, 2b, 30…
The pattern should be easy to spot. All numbers that have the last digit of 0, 3, 6 or 9 will divide by 3.
This is because we are working with base-12, and 12 divides by 3 (and 2).
Seven is often a difficult number to divide by if working with base-10. What if we use base-14 instead? The 14 symbols used in base-14 are as follows:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d
The numbers one to thirty-six, in base-14:
1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1a, 1b, 1c, 1d, 20, 21, 22, 23, 24, 25, 26, 27, 28…
Highlighting numbers that divide by 3:
1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1a, 1b, 1c, 1d, 20, 21, 22, 23, 24, 25, 26, 27, 28…
Its trickier isn’t it? That’s because 14 does not divide by 3.
Highlighting numbers that divide by 7:
1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1a, 1b, 1c, 1d, 20, 21, 22, 23, 24, 25, 26, 27, 28…
Easy stuff. All numbers ending with the digit 7 or 0 can be divided by 7.
Here is something worth thinking about while you eat your nasi lemak or cheese naan:
How messy will be base-P systems, where (P is a prime number)?
posted by Tan Yee Wei at 7/25/2005 08:23:00 pm
Subject selection confusion
Tomorrow, the semester starts. As of now, I have not selected my subjects yet. I’ll hang around the interesting subject lectures and then finalise my choice later in the week.
At the moment, I have to choose 3 elective subjects from a longish list of about 11. Deftly but brutally hacking* away the less desirable subjects, I’m now left with 5 electives. They are all of equal importance. I think.
Human Resources Management
I’m definitely taking this up. It’s a personal non-negotiable, seeing that I have zero experience in this field and I badly need something management-ish. In fact, it’s so non-negotiable that I had to forgo Power Generation Systems (a delicious sounding course with turbines, reciprocating engines, turbochargers et al) due to a clash in lecture hours.
Optimisation
This is an interesting one. It’s a lot of fuzzy mathematics, dealing with optimising huge, multi-variable systems. Imagine 42 variables. Not a lot? Then consider that there are 42! permutations in these variables. If you can’t imagine how big 42! might be, I can assure you that it's mind boggling. This subject will definitely be an eye opener, in terms of conditioning the brain to think in a completely different way.
Computational Biomechanics
Another eye opener here. The subject description says “On completion of this subject students should gain an understanding of the structure and function of the skeletal, muscular and sensory systems of the human body and biomechanical analysis of the human body subject to a variety of external environments, such as standing, walking and running.”
Advanced Computational Mechanics
Basically a course on how to crunch numbers on a computer, effectively. The introductory course in Computational Mechanics was rather plain. Very academic stuff and bone dry, but probably some practical use.
Advanced Engineering Materials
Basically, a course about high tech materials like “advanced light alloys, superalloys, metal matrix composites, intermetallic alloys, ultrafine and nano-structured materials.” Would be interesting
Seeing that I have sort of confirmed HR Management, I have the other 4 to fiddle around with. If I take up optimisation, I will not be able to take biomechanics and materials (due to timetabling stupidities), and I’ll be stuck with computational mechanics. 2 heavy number crunching subjects!
The other 3 available options would be to drop any one subject from this choice: biomechanics, computational mechanics and materials.
We’ll see what happens.
By the way, 42! = 1 x 2 x 3 x … x 41 x 42 = 1.4 x 10^51.
In comparison, there are only 6.23 x 10^23 atoms in 1 gram of hydrogen. You would need 2,250,000,000,000,000,000,000 tonnes of hydrogen to make assemble 42! atoms.
*I like to think that I hack with a graceful but severe style as seen used by kendo practitioners, and more lethally, by katana wielding samurais. Of course, this is debatable since I did not literally manipulate any weapons.
At the moment, I have to choose 3 elective subjects from a longish list of about 11. Deftly but brutally hacking* away the less desirable subjects, I’m now left with 5 electives. They are all of equal importance. I think.
Human Resources Management
I’m definitely taking this up. It’s a personal non-negotiable, seeing that I have zero experience in this field and I badly need something management-ish. In fact, it’s so non-negotiable that I had to forgo Power Generation Systems (a delicious sounding course with turbines, reciprocating engines, turbochargers et al) due to a clash in lecture hours.
Optimisation
This is an interesting one. It’s a lot of fuzzy mathematics, dealing with optimising huge, multi-variable systems. Imagine 42 variables. Not a lot? Then consider that there are 42! permutations in these variables. If you can’t imagine how big 42! might be, I can assure you that it's mind boggling. This subject will definitely be an eye opener, in terms of conditioning the brain to think in a completely different way.
Computational Biomechanics
Another eye opener here. The subject description says “On completion of this subject students should gain an understanding of the structure and function of the skeletal, muscular and sensory systems of the human body and biomechanical analysis of the human body subject to a variety of external environments, such as standing, walking and running.”
Advanced Computational Mechanics
Basically a course on how to crunch numbers on a computer, effectively. The introductory course in Computational Mechanics was rather plain. Very academic stuff and bone dry, but probably some practical use.
Advanced Engineering Materials
Basically, a course about high tech materials like “advanced light alloys, superalloys, metal matrix composites, intermetallic alloys, ultrafine and nano-structured materials.” Would be interesting
Seeing that I have sort of confirmed HR Management, I have the other 4 to fiddle around with. If I take up optimisation, I will not be able to take biomechanics and materials (due to timetabling stupidities), and I’ll be stuck with computational mechanics. 2 heavy number crunching subjects!
The other 3 available options would be to drop any one subject from this choice: biomechanics, computational mechanics and materials.
We’ll see what happens.
By the way, 42! = 1 x 2 x 3 x … x 41 x 42 = 1.4 x 10^51.
In comparison, there are only 6.23 x 10^23 atoms in 1 gram of hydrogen. You would need 2,250,000,000,000,000,000,000 tonnes of hydrogen to make assemble 42! atoms.
*I like to think that I hack with a graceful but severe style as seen used by kendo practitioners, and more lethally, by katana wielding samurais. Of course, this is debatable since I did not literally manipulate any weapons.
posted by Tan Yee Wei at 7/25/2005 12:59:00 am
Sunday, July 24, 2005
In 14 minutes, the delayed telecast of the German GP will be begin. I'll have to suffer through some pointless, empty commentary by the local idiots* at Channel Ten before the better guys Martin Brundle (ex F1 racer) and James-something from ITV take over.
Tomorrow, classes resume. The month long holiday was a relief. I have been sleeping as and when I like without regard to pretty much everything else. Sleeping times seemed to have settled into a 6am to 2pm pattern. Up to today. Looks like I have some major adjustments to do overnight.
Not bad...this is my fastest post ever- completed and published in a mere 7 minutes.
*I'll complain about them when I come back.
Tomorrow, classes resume. The month long holiday was a relief. I have been sleeping as and when I like without regard to pretty much everything else. Sleeping times seemed to have settled into a 6am to 2pm pattern. Up to today. Looks like I have some major adjustments to do overnight.
Not bad...this is my fastest post ever- completed and published in a mere 7 minutes.
*I'll complain about them when I come back.
posted by Tan Yee Wei at 7/24/2005 09:16:00 pm
Saturday, July 23, 2005
Photo Contest by JFE 8555
"Me and My Car" photo contest by project 8-triple-5.
Yes, that adorable Iswara Aeroback JFE 8555 is organising a photo contest so he can oogle at other cars.
Each of the top 3 contestants will win a DVD of Initial D: Live Action.
Contest closing soon. Quick quick quick!
Details here.
Updates here.
Yes, that adorable Iswara Aeroback JFE 8555 is organising a photo contest so he can oogle at other cars.
For a duration of 01 (One) Week, starting on the 18th of July and ending on the 24th of July, you bloggers (yes, just bloggers) may send me a picture of yourself together with your car, to be judged by me to these criterion (in no particular order);
1. Location of shoot
2. Car's looks
3. Blogger's looks
4. Overall impression and impact
5. Picture clarity
6. Angling and focus creativity
-JFE 8555
Each of the top 3 contestants will win a DVD of Initial D: Live Action.
Contest closing soon. Quick quick quick!
Details here.
Updates here.
posted by Tan Yee Wei at 7/23/2005 02:14:00 pm
Friday, July 22, 2005
Yee Wei’s marriage compatibility check meme
Don’t ask how I got such a weird idea to design a meme.
Yee Wei’s marriage compatibility check meme-
What is your internet connection speed?
ADSL, 512 kbps
List any two movies you like.
Hero, I am Curious
What are a few of your material wants?
To drive some really ham sap cars like the DTM Audi A4, JGTC Honda NSX, Lister Storm...
Which religion(s) do you adhere to? Are you a staunch believer?
I’m mostly agnostic, but sometimes lean a bit toward Buddhism, Hinduism and Taoism teachings.
How likely is it that you will marry someone with different religious beliefs to yours?
No problems, unless he/she/it tries to convert me. That is annoying.
How likely is it that you will marry someone of different race/colour to yours?
Slim chance. Too many cultural differences to iron out.
Do you like children?
Yes, except when they are whining and crying endlessly. Then they look hideous and sound irritating.
Will you mind marrying the one who tagged you?
[i can't answer this since no one tagged me- this is the first generation].
I am tagging:
JFE 8555 (because it would be interesting to hear a car's opinion on these things)
Cynical-Idealist
Mistyeiz
Ob!ique
Sonia
Note- this is not an expression of interest ok.
Yee Wei’s marriage compatibility check meme-
What is your internet connection speed?
ADSL, 512 kbps
List any two movies you like.
Hero, I am Curious
What are a few of your material wants?
To drive some really ham sap cars like the DTM Audi A4, JGTC Honda NSX, Lister Storm...
Which religion(s) do you adhere to? Are you a staunch believer?
I’m mostly agnostic, but sometimes lean a bit toward Buddhism, Hinduism and Taoism teachings.
How likely is it that you will marry someone with different religious beliefs to yours?
No problems, unless he/she/it tries to convert me. That is annoying.
How likely is it that you will marry someone of different race/colour to yours?
Slim chance. Too many cultural differences to iron out.
Do you like children?
Yes, except when they are whining and crying endlessly. Then they look hideous and sound irritating.
Will you mind marrying the one who tagged you?
[i can't answer this since no one tagged me- this is the first generation].
I am tagging:
JFE 8555 (because it would be interesting to hear a car's opinion on these things)
Cynical-Idealist
Mistyeiz
Ob!ique
Sonia
Note- this is not an expression of interest ok.
posted by Tan Yee Wei at 7/22/2005 11:50:00 pm
I'm in deep shit
I think I'm in trouble. Deep deep shit. I don't want to have a baby now. It's not a very suitable time- not graduated yet from university, away from home, without a job, and becoming a parent soon. Die die die die. I see my many opportunities spiralling into a huge drain.
This issue came to light some weeks ago. Hoping that it was nothing more than an anomaly, I pushed it aside, dismissing it as part of my over-worked imagination. It was not to be. Things remained bleak, if not already getting worse.
I haven't had my period for several weeks already. I think I'm pregnant. Will probably get one of those pregnancy test probes to verify. Shit.
Oh wait, I don't have periods. I'm a male. What a relief after that false alarm.
***
On a more real-world note, I just came back from an informal Karate training session. Today, I saw my first point-sparring format.
We only had time for one match each. I faced a tall kwai lou, a very fit man who competes frequently and with plenty of experience. Nevermind the height, I’ll not try head shots with my kicks anyway- these people trained in Karate guard their heads very, very well.
I reminded myself not to kick until a definite scoring situation turned up. Keep it a secret weapon of sorts.
We maintained distance at slightly more than arm’s length, and traded several points, mostly due to attacks to the upper body (chest and head targets).
After a while, I noticed that he was guarding his upper region very carefully. But...mien Gott! His abdominal area was completely open! I’ve never seen such a juicy opportunity. Patience...let him move and be occupied with attacking before kicking that open patch.
He advanced, and a punching-blocking-counter punch-parry-attack mess ensued. It is time.
Abruptly stepping back, I disengaged from the melee, putting the still-wide-open target in perfect range for a snappy front leg turning-kick. Bang!
That caught him by surprise. It also gave me a very satisfying point.
Endnote - I used to practice taekwondo for about 5 years before starting karate. My hand techniques are generally sticky and gooey, but the kicks are usually fast enough to compensate.
This issue came to light some weeks ago. Hoping that it was nothing more than an anomaly, I pushed it aside, dismissing it as part of my over-worked imagination. It was not to be. Things remained bleak, if not already getting worse.
I haven't had my period for several weeks already. I think I'm pregnant. Will probably get one of those pregnancy test probes to verify. Shit.
Oh wait, I don't have periods. I'm a male. What a relief after that false alarm.
On a more real-world note, I just came back from an informal Karate training session. Today, I saw my first point-sparring format.
Whenever a contestant scores a point, the game is paused and restarted. As such, there are no opportunities to counter attack and hope for an equalising point.It felt weird. The kind I’m used to (go at each other without minimal intervention) is termed continuous sparring. We did not do that today.
For a point to be scored, at least 2 out of 3 judges must call the point. Strategy is required such that you choose attacks that are visible to the majority of judges.
Each round lasts for 2 minutes, or end whenever a competitor leads by 3 points.
We only had time for one match each. I faced a tall kwai lou, a very fit man who competes frequently and with plenty of experience. Nevermind the height, I’ll not try head shots with my kicks anyway- these people trained in Karate guard their heads very, very well.
I reminded myself not to kick until a definite scoring situation turned up. Keep it a secret weapon of sorts.
We maintained distance at slightly more than arm’s length, and traded several points, mostly due to attacks to the upper body (chest and head targets).
After a while, I noticed that he was guarding his upper region very carefully. But...mien Gott! His abdominal area was completely open! I’ve never seen such a juicy opportunity. Patience...let him move and be occupied with attacking before kicking that open patch.
He advanced, and a punching-blocking-counter punch-parry-attack mess ensued. It is time.
Abruptly stepping back, I disengaged from the melee, putting the still-wide-open target in perfect range for a snappy front leg turning-kick. Bang!
That caught him by surprise. It also gave me a very satisfying point.
Endnote - I used to practice taekwondo for about 5 years before starting karate. My hand techniques are generally sticky and gooey, but the kicks are usually fast enough to compensate.
posted by Tan Yee Wei at 7/22/2005 07:57:00 pm
Thursday, July 21, 2005
Estimating square roots to several significant figures using arithmetic operations
Foreword:
Some weeks ago, I was travelling by car over long distances. To easy my boredom, I tried to estimate the square root of a large number (I used the odometer reading) using only pencil and paper. This is what I found.
Notation:
sqrt(x) = the square root of x
x^2 = x raised to the power of 2; the square of x
Introduction:
This square root estimation method relies only on integer manipulations. As such, the calculations are reasonably straight forward. In each iteration, one division operation is required. However, these division operations should be very straightforward as only one significant figure is required. Each iteration will result in an additional significant figure of accuracy.
In the estimation of square roots, one can use the extremely exhaustive method of trail and error to continuously improve on the estimation accuracy. However, the multiplications rapidly become tedious as more digits are added to the estimation. Also, each trail does not guarantee an improvement of one significant figure.
The method presented here will take advantage of the fact that the sum of the first n odd numbers equals n^2. In this example, the approach taken is to approach the square root by adding another digit to the estimation. Hence, an estimation of sqrt(3) would be approached using this path:
1
1.7
1.73
1.732
1.7320
1.73205
…
It should be noted that the last significant digit in the estimate is never rounded up. Care should be taken in this respect. This is to done to simplify the calculations such that all iterations add to the previous estimate, instead of adding and subtracting. Of course, the algorithm can easily be modified to round up the last digit, if desired.
Sum of gnomons:
Gnomons- consecutive odd numbers
This is a list of the first few odd numbers-
1, 3, 5, 7, 9, 11, 13, 15…
The sum of the first 2 odd numbers is 1 + 3 = 4 = 2^2
The sum of the first 3 odd numbers is 1 + 3 + 5 = 9 = 3^2
The sum of the first 4 odd numbers is 1 + 3 + 5 + 7 = 16 = 4^2
The sum of the first 5 odd numbers is 1 + 3 + 5 + 7 + 9 = 25 = 5^2
The n-th odd number can be expressed as (2n-1). For example, the third odd number is (2*3 -1) = 5
Estimation procedure:
The procedure shown here will be based on estimating sqrt(56720).
We first partition the number 56720 into segments of 2 digits:
5 67 20
n^2 = 56720
Dividing both sides by 10,000:
(n/100)^2 = 56,720 / 10,000
(n/100)^2 = 5.6720
By inspection, the largest integer for (n/100) that would NOT exceed 5.6720 is 2. Therefore, the first estimate:
n/100 = 2
2^2 = 4
(n/100)^2 = 4
n = 200
n^2 = 40,000
Evidently, our first estimate (n=200) is crude, and its nowhere near the actual value of sqrt(56720).
Going back to our number:
n^2 = 56,720
divide both sides by 100:
(n/10)^2 = 567
Compare this to our earlier estimate of n = 200:
(200/10)^2 = 400
20^2 = 400
From the sum of odd numbers, we know that the sum of the first 20 odd numbers is 20^2. Therefore:
1 + 3 + 5 + … + (2*20-1) = 400
1 + 3 + 5 + … + 39 = 400
Extending the series by adding 4 terms:
1 + 3 + 5 + … + 39 + 41 + 43 + 45 + 47 + 49 = 625 = 25^2
Re-expressing the new terms:
1 + 3 + 5 + … + 39 + (39+2) + (39+4) + (39+6) + (39+8) + (39+10) = 625
1 + 3 + 5 + … + 39 + (39*5 + 2 + 4 + 6 + 8 + 10) = 625
20^2 + (2*20-1)*5 + f(5) = 625 = 25^2, where f(5) is the sum of the first 5 even numbers.
As seen in the last equation, the sum of the first 20 odd numbers can be extended by 5 terms by adding the 5 times the 20th odd number and the sum of the first 5 even numbers [denoted by f(5)].
For convenience, the sum of the first n even numbers can be listed in form of a lookup table.
Returning our estimation:
(n/10)^2 = 567
We also know that 20^2 = 400
The difference between 567 and 400 is 567-400 = 167
We must increase our estimate of (n/10) as much as possible without exceeding 567.
The 20th odd number is 39. We will try to fit as many new terms as possible into the current series (now at 20 terms). Try 167/39 = 4.28 = 4.
4 * 39 = 156, and
f(4) = 2 + 4 + 6 + 8 = 20
4*39 + f(4) = 176
20^2 + 176 = 24^2 = 576
Unfortunately, 576 is larger than 567, so we will try 23^2 instead of 24^2:
20^2 + 39*3 + f(3) = 400 + 117 + 12 = 529
This is our current estimate of n/10 = 23.
(n/10)^2 = 529
n^2 = 52,900
230^2 = 52,900
Keep in mind that we are trying to approach n^2 = 56,720.
The difference between 56,720 and 52,900 is 56,720 – 52,900 = 3,820.
The 230th odd number is 459. Remember that the sum of the first 230 odd numbers (from 1 to 459) is 230^2 = 52,900.
3,820 / 459 = 8.322 = 8
459 * 8 = 3672
f(8) = 2 + 4 + 6 + 8 +10 + 12 +14 +16 = 72
230^2 + (459*8) + f(8) = 56,644 = 238^2
Just to be sure, can we try 239^2?
238^2 + (2*238-1) +f(1) = 56,644 + 475 + 2 = 57,121
No, 239^2 is larger than 56,720, so our current estimate of sqrt(56720) is 239
n^2=56,720
(10n)^2 = 5,672,000
And our current estimate:
238^2 = 56,644
(10*238)^2 = 5,664,400
The difference between 5,672,000 and 5,664,400 is 7600.
The 2,380th odd number is 4,759.
7,600 / 4,759 = 1.63 = 1
2,390^2 + 4,759*1 + f(1) = 5,669,161 = 2,381^2
Our latest estimate of 10n = 2381, and n = 238.1
n^2 = 56,720
(100n)^2 = 567,200,000
238.1^2 = 5,669,161
23,810^2 = 566,916,100
The difference between 567,200,000 and 566,916,100 is 283,900
The 23810th odd number is (2*23810-1) = 47,619
283,900 / 47,619 = 5.96 = 5
5*47619 = 238,095
f(5) = 2 + 4 +6 + 8 + 10 = 30
23810^2 + (2*23810 -1)*5 + f(5) = 567,154,225
The latest estimate of 100n = 23815; n = 238.15
The subsequent iterations will no longer contain any narration.
n^2 = 56720
(1000n)^2 = 56,720,000,000
238.15^2 = 56,715.4225
238150 = 56,715,422,500
56,720,000,000 - 56,715,422,500 = 4,577,500
(2*238150 – 1) = 476,299
4,577,500 / 476,299 = 9.61 = 9
9*476,229 = 4286061
f(9) = 2 + 4 +6 + 8 + 10 + 12 + 14 + 16+ 18 = 90
238150^2 + (2*238150 – 1)*9 + f(9) = 56,715,422,500 + 4,173,291 + 90 = 5,671,970,928,100
238,159^2 = 5,671,970,928,100
238.159 ^2 = 56,719.70928100
2,381,590 ^2 = 5,671,970,928,100
5,672,000,000,000 - 5,671,970,928,100= 29,071,900
(2*2,381,590 -1) = 4,763,179
29,071,900 / 4,763,179 = 6.10 = 6
(2*2,381,590 -1)*6 = 28,579,074
f(6) = 2 + 4 +6 +8 + 10 +12 = 42
2381590^2 + (2*2,381,590 -1)*6 + 42 = 5,671,999,507,216
2381596^2 = 5,671,999,507,216
238.1596 = 56719.995…
Using an electronic calculator to verify the results:
sqrt(56720) = 238.1596103…
We are definitely on the right track.
Cite this article as:
Tan Yee Wei(2005), "Estimating square roots to several significant figures using arithmetic operations", from "Snippets of This and That"
http://tanyeewei.blogspot.com/2005/07/estimating-square-roots-to-several.html
Some weeks ago, I was travelling by car over long distances. To easy my boredom, I tried to estimate the square root of a large number (I used the odometer reading) using only pencil and paper. This is what I found.
Notation:
sqrt(x) = the square root of x
x^2 = x raised to the power of 2; the square of x
Introduction:
This square root estimation method relies only on integer manipulations. As such, the calculations are reasonably straight forward. In each iteration, one division operation is required. However, these division operations should be very straightforward as only one significant figure is required. Each iteration will result in an additional significant figure of accuracy.
In the estimation of square roots, one can use the extremely exhaustive method of trail and error to continuously improve on the estimation accuracy. However, the multiplications rapidly become tedious as more digits are added to the estimation. Also, each trail does not guarantee an improvement of one significant figure.
The method presented here will take advantage of the fact that the sum of the first n odd numbers equals n^2. In this example, the approach taken is to approach the square root by adding another digit to the estimation. Hence, an estimation of sqrt(3) would be approached using this path:
1
1.7
1.73
1.732
1.7320
1.73205
…
It should be noted that the last significant digit in the estimate is never rounded up. Care should be taken in this respect. This is to done to simplify the calculations such that all iterations add to the previous estimate, instead of adding and subtracting. Of course, the algorithm can easily be modified to round up the last digit, if desired.
Sum of gnomons:
Gnomons- consecutive odd numbers
This is a list of the first few odd numbers-
1, 3, 5, 7, 9, 11, 13, 15…
The sum of the first 2 odd numbers is 1 + 3 = 4 = 2^2
The sum of the first 3 odd numbers is 1 + 3 + 5 = 9 = 3^2
The sum of the first 4 odd numbers is 1 + 3 + 5 + 7 = 16 = 4^2
The sum of the first 5 odd numbers is 1 + 3 + 5 + 7 + 9 = 25 = 5^2
The n-th odd number can be expressed as (2n-1). For example, the third odd number is (2*3 -1) = 5
Estimation procedure:
The procedure shown here will be based on estimating sqrt(56720).
We first partition the number 56720 into segments of 2 digits:
5 67 20
n^2 = 56720
Dividing both sides by 10,000:
(n/100)^2 = 56,720 / 10,000
(n/100)^2 = 5.6720
By inspection, the largest integer for (n/100) that would NOT exceed 5.6720 is 2. Therefore, the first estimate:
n/100 = 2
2^2 = 4
(n/100)^2 = 4
n = 200
n^2 = 40,000
Evidently, our first estimate (n=200) is crude, and its nowhere near the actual value of sqrt(56720).
Going back to our number:
n^2 = 56,720
divide both sides by 100:
(n/10)^2 = 567
Compare this to our earlier estimate of n = 200:
(200/10)^2 = 400
20^2 = 400
From the sum of odd numbers, we know that the sum of the first 20 odd numbers is 20^2. Therefore:
1 + 3 + 5 + … + (2*20-1) = 400
1 + 3 + 5 + … + 39 = 400
Extending the series by adding 4 terms:
1 + 3 + 5 + … + 39 + 41 + 43 + 45 + 47 + 49 = 625 = 25^2
Re-expressing the new terms:
1 + 3 + 5 + … + 39 + (39+2) + (39+4) + (39+6) + (39+8) + (39+10) = 625
1 + 3 + 5 + … + 39 + (39*5 + 2 + 4 + 6 + 8 + 10) = 625
20^2 + (2*20-1)*5 + f(5) = 625 = 25^2, where f(5) is the sum of the first 5 even numbers.
As seen in the last equation, the sum of the first 20 odd numbers can be extended by 5 terms by adding the 5 times the 20th odd number and the sum of the first 5 even numbers [denoted by f(5)].
For convenience, the sum of the first n even numbers can be listed in form of a lookup table.
| n | f(n) | |
| 1 | 2 | 2 |
| 2 | 2+4 | 6 |
| 3 | 2+4+6 | 12 |
| 4 | 2+4+6+8 | 20 |
| 5 | 2+4+...10 | 30 |
| 6 | 2+4+...12 | 42 |
| 7 | 2+4+...14 | 56 |
| 8 | 2+4+...16 | 72 |
| 9 | 2+4+...18 | 80 |
Returning our estimation:
(n/10)^2 = 567
We also know that 20^2 = 400
The difference between 567 and 400 is 567-400 = 167
We must increase our estimate of (n/10) as much as possible without exceeding 567.
The 20th odd number is 39. We will try to fit as many new terms as possible into the current series (now at 20 terms). Try 167/39 = 4.28 = 4.
4 * 39 = 156, and
f(4) = 2 + 4 + 6 + 8 = 20
4*39 + f(4) = 176
20^2 + 176 = 24^2 = 576
Unfortunately, 576 is larger than 567, so we will try 23^2 instead of 24^2:
20^2 + 39*3 + f(3) = 400 + 117 + 12 = 529
This is our current estimate of n/10 = 23.
(n/10)^2 = 529
n^2 = 52,900
230^2 = 52,900
Keep in mind that we are trying to approach n^2 = 56,720.
The difference between 56,720 and 52,900 is 56,720 – 52,900 = 3,820.
The 230th odd number is 459. Remember that the sum of the first 230 odd numbers (from 1 to 459) is 230^2 = 52,900.
3,820 / 459 = 8.322 = 8
459 * 8 = 3672
f(8) = 2 + 4 + 6 + 8 +10 + 12 +14 +16 = 72
230^2 + (459*8) + f(8) = 56,644 = 238^2
Just to be sure, can we try 239^2?
238^2 + (2*238-1) +f(1) = 56,644 + 475 + 2 = 57,121
No, 239^2 is larger than 56,720, so our current estimate of sqrt(56720) is 239
n^2=56,720
(10n)^2 = 5,672,000
And our current estimate:
238^2 = 56,644
(10*238)^2 = 5,664,400
The difference between 5,672,000 and 5,664,400 is 7600.
The 2,380th odd number is 4,759.
7,600 / 4,759 = 1.63 = 1
2,390^2 + 4,759*1 + f(1) = 5,669,161 = 2,381^2
Our latest estimate of 10n = 2381, and n = 238.1
n^2 = 56,720
(100n)^2 = 567,200,000
238.1^2 = 5,669,161
23,810^2 = 566,916,100
The difference between 567,200,000 and 566,916,100 is 283,900
The 23810th odd number is (2*23810-1) = 47,619
283,900 / 47,619 = 5.96 = 5
5*47619 = 238,095
f(5) = 2 + 4 +6 + 8 + 10 = 30
23810^2 + (2*23810 -1)*5 + f(5) = 567,154,225
The latest estimate of 100n = 23815; n = 238.15
The subsequent iterations will no longer contain any narration.
n^2 = 56720
(1000n)^2 = 56,720,000,000
238.15^2 = 56,715.4225
238150 = 56,715,422,500
56,720,000,000 - 56,715,422,500 = 4,577,500
(2*238150 – 1) = 476,299
4,577,500 / 476,299 = 9.61 = 9
9*476,229 = 4286061
f(9) = 2 + 4 +6 + 8 + 10 + 12 + 14 + 16+ 18 = 90
238150^2 + (2*238150 – 1)*9 + f(9) = 56,715,422,500 + 4,173,291 + 90 = 5,671,970,928,100
238,159^2 = 5,671,970,928,100
238.159 ^2 = 56,719.70928100
2,381,590 ^2 = 5,671,970,928,100
5,672,000,000,000 - 5,671,970,928,100= 29,071,900
(2*2,381,590 -1) = 4,763,179
29,071,900 / 4,763,179 = 6.10 = 6
(2*2,381,590 -1)*6 = 28,579,074
f(6) = 2 + 4 +6 +8 + 10 +12 = 42
2381590^2 + (2*2,381,590 -1)*6 + 42 = 5,671,999,507,216
2381596^2 = 5,671,999,507,216
238.1596 = 56719.995…
Using an electronic calculator to verify the results:
sqrt(56720) = 238.1596103…
We are definitely on the right track.
Cite this article as:
Tan Yee Wei(2005), "Estimating square roots to several significant figures using arithmetic operations", from "Snippets of This and That"
http://tanyeewei.blogspot.com/2005/07/estimating-square-roots-to-several.html
posted by Tan Yee Wei at 7/21/2005 02:51:00 pm
Pink is back! In wide format too.
It took me an eternity, but I’ve finally sorted it out. Just for the record, 90 minutes is an eternity. By that logic, 3 hours would make two eternities and a week would sum up to a walloping 112 eternities!
More to the point, I’ve fiddled with this template to produce a wider version- a healthy 900 pixels wide compared to the standard version’s anorexic 760 pixels.
And it’s in pink!
And now, for an quick opinion poll-
[edit] Oh shit, it's already 6.20 am. Time for bed! I love holidays.
More to the point, I’ve fiddled with this template to produce a wider version- a healthy 900 pixels wide compared to the standard version’s anorexic 760 pixels.
And it’s in pink!
And now, for an quick opinion poll-
No, I don’t really care if you don’t like pink. Any complaints with the 900-format?
[edit] Oh shit, it's already 6.20 am. Time for bed! I love holidays.
posted by Tan Yee Wei at 7/21/2005 03:53:00 am
Wednesday, July 20, 2005
Memo to self
I just came back from freeloading at a bookshop. As usual, I was reading expensive motoring related literature that I could never afford. Those specialist publications like Racecar Engineering and Race Tech are hideously expensive.
I also spotted a book, “Going Faster: Mastering the Art of Race Driving : The Skip Barber Racing School” by Carl Lopez.
“Interesting… lets see what it has to say on gearshifts.”
Plenty, it turned out. One whole chapter was dedicated to various gearshift techniques and explanations. It turned out that double-clutch heel-and-toe is in factused necessary for racing gearboxes that do not have synchromesh (!). Some experienced drivers can match speeds so well that they no longer need the clutch when shifting, even on non-synchromeshed racing boxes.
However, the Lopez cautions beginners not to get into the habit of shifting without dipping the clutch until they are sufficiently proficient at the skill, or have the budget for frequent gearbox maintenance.
Take note, Yee Hou and Yee Wei.
I also noticed that my ego is too closely related to weird-arsed gearshift black magic. I ought to get a life, perhaps read a bit on tort law, catch up on number theory, finish reading some political science essays (note to IR Postgraduate: yes, its progressing along OK at the moment) and start reading that unsold accounting text book I have in stock.
I also spotted a book, “Going Faster: Mastering the Art of Race Driving : The Skip Barber Racing School” by Carl Lopez.
“Interesting… lets see what it has to say on gearshifts.”
Plenty, it turned out. One whole chapter was dedicated to various gearshift techniques and explanations. It turned out that double-clutch heel-and-toe is in fact
However, the Lopez cautions beginners not to get into the habit of shifting without dipping the clutch until they are sufficiently proficient at the skill, or have the budget for frequent gearbox maintenance.
Take note, Yee Hou and Yee Wei.
I also noticed that my ego is too closely related to weird-arsed gearshift black magic. I ought to get a life, perhaps read a bit on tort law, catch up on number theory, finish reading some political science essays (note to IR Postgraduate: yes, its progressing along OK at the moment) and start reading that unsold accounting text book I have in stock.
posted by Tan Yee Wei at 7/20/2005 05:40:00 pm
I don't like flossing
Both my mother and dentist insist that I should floss once a day. Of course, I nod and agree when they go on about flossing. Of course, I don’t even do it on a biannual basis.
A few years ago, in a hopeless situation, my mother remarked that I was very ‘third world’ in my flossing habits. The dentist agreed with her. I could only smile stupidly at them. I was not going to agree with them, but neither was I going to take up flossing like Vanessa Mae to the violin. At any rate, my dental health has always been in good shape.
So I still don’t floss regularly.
Recently, my teeth looked particularly dirty. Lodged in the interstices between my teeth were tiny fragments of what used to be food but now some soft, indeterminate lumps of beige goo. Just a wee bit, but enough to unsettle me and prompt a rethink of my approach to flossing.
Okay, its time do you-know-what.
From my many-years-old box of floss, I tugged at a generous length of the waxed fibre. Having a longer length makes manipulation much easier. Anyway, it’s not like that box of string is going to be used every day.
Flossing is like having your oral cavity gang raped and violated by two (or more) fingers and a length of string, simultaneously. Mucus from the saliva gets onto everything, making them all slick and messy while traces of blood get smeared on the white enamel.
After theraping flossing was done, I felt slightly better.
A few years ago, in a hopeless situation, my mother remarked that I was very ‘third world’ in my flossing habits. The dentist agreed with her. I could only smile stupidly at them. I was not going to agree with them, but neither was I going to take up flossing like Vanessa Mae to the violin. At any rate, my dental health has always been in good shape.
So I still don’t floss regularly.
Recently, my teeth looked particularly dirty. Lodged in the interstices between my teeth were tiny fragments of what used to be food but now some soft, indeterminate lumps of beige goo. Just a wee bit, but enough to unsettle me and prompt a rethink of my approach to flossing.
Okay, its time do you-know-what.
From my many-years-old box of floss, I tugged at a generous length of the waxed fibre. Having a longer length makes manipulation much easier. Anyway, it’s not like that box of string is going to be used every day.
Flossing is like having your oral cavity gang raped and violated by two (or more) fingers and a length of string, simultaneously. Mucus from the saliva gets onto everything, making them all slick and messy while traces of blood get smeared on the white enamel.
After the
posted by Tan Yee Wei at 7/20/2005 04:05:00 pm
Tuesday, July 19, 2005
Does my bottom look big in this?
Beep beep beep beep.
Beep beep beep beep.
Beep beep beep beep.
The alarm clock would not stop; I woke up, groggy, woozy and semi-conscious. Blame it on insufficient sleep, due to me sleeping at 6am, due to the addictive nature of Sim Tower.
Yes, that 1994 tower development game by Maxis.
I drank a cup of water, stirred a cup of instant coffee, brushed my teeth, changed into some decent clothes and checked my email. Just before I left for the market, I turned around and caught a reflected image of my back on the wardrobe’s mirror.
Gasp. GASP. A pair of surprises caught me off guard, waking me up better than any instant coffee possibly could.
I noted that my bottom looked big in that particular pair of trousers.
Then I realised I had somehow stumbled upon a frequently used comic strip joke- “does my bottom look big in this?” I never thought this issue would exist in the real world, my world.
The moment passed, and I regained my composure. “That was an anomaly. I’ll let it pass, and leave it as it is.”
I could not leave it as it is. Later in the evening, I tried to figure out the source for the optical illusion earlier in the day. I think it’s the cut of the rear pockets and slack in the fabric that combined to give an appearance of vastness to the hindquarters. It had appeared flat and wide, like a slab of lard. A slab, not a lump. Perhaps my Magical Inflatable Thingy (Saffron, 2004) and its paraphernalia are not sufficiently voluminous to take up the slack in the trousers’ fabric. Whatever.
Sources:
Saffron (2004), untitled (6th October 2004), from "27th & 6th".
http://saffraan.blogspot.com/2004/10/are-you-girl-why-girls-dont-play-games.html
Beep beep beep beep.
Beep beep beep beep.
The alarm clock would not stop; I woke up, groggy, woozy and semi-conscious. Blame it on insufficient sleep, due to me sleeping at 6am, due to the addictive nature of Sim Tower.
Yes, that 1994 tower development game by Maxis.
I drank a cup of water, stirred a cup of instant coffee, brushed my teeth, changed into some decent clothes and checked my email. Just before I left for the market, I turned around and caught a reflected image of my back on the wardrobe’s mirror.
Gasp. GASP. A pair of surprises caught me off guard, waking me up better than any instant coffee possibly could.
I noted that my bottom looked big in that particular pair of trousers.
Then I realised I had somehow stumbled upon a frequently used comic strip joke- “does my bottom look big in this?” I never thought this issue would exist in the real world, my world.
The moment passed, and I regained my composure. “That was an anomaly. I’ll let it pass, and leave it as it is.”
I could not leave it as it is. Later in the evening, I tried to figure out the source for the optical illusion earlier in the day. I think it’s the cut of the rear pockets and slack in the fabric that combined to give an appearance of vastness to the hindquarters. It had appeared flat and wide, like a slab of lard. A slab, not a lump. Perhaps my Magical Inflatable Thingy (Saffron, 2004) and its paraphernalia are not sufficiently voluminous to take up the slack in the trousers’ fabric. Whatever.
Sources:
Saffron (2004), untitled (6th October 2004), from "27th & 6th".
http://saffraan.blogspot.com/2004/10/are-you-girl-why-girls-dont-play-games.html
posted by Tan Yee Wei at 7/19/2005 10:24:00 pm
Saturday, July 16, 2005
Dictionary Thesaurus combinations
Myself not being a walking dictionary-thesaurus, I usually need to refer to these helpful volumes when in the mood to write fancy nothings.
Thus far, my favourite is the CD version of the Concise Oxford English Dictionary 10th Edition (COD10) with thesaurus.com on Mozilla Firefox. Oxford English Dictionary Online is used as a back up in the rare occasions when I find COD10 unsatisfactory.
To add thesaurus.com to your search bar in Firefox, select ‘add engines’. Search for thesaurus.com and add it to your list.
Anyone got a better electronic thesaurus to recommend?
Double clicking on a word anywhere in Windows will cause the word to be displayed on COD10. Naturally, it’s a very useful tool when browsing the alternative words generated by thesaurus.com.
The only long term problem with this arrangement is centred on OED Online. Annual subscription to OED Online for individuals is a massively frightful £200 (RM1320 at the current exchange rate). When Yuan Harng graduates from university, I’ll no longer be able to access his university’s account. Drat.
Why Oxford?
Switch to Firefox 1.0.5. You will have no regrets, except maybe ask ‘why didn’t I do it earlier’. Download it here (4.65 Mb).
Subscribe to OED Online, for a reasonable fee of £50 per quarter (3 months).
Concise Oxford Dictionary 10th Edition Considering its usefulness, it is remarkably small at only 5.70 Mb installed. Compare that to huge, useless, gigabyte-scale programs like Warcraft 3 or NFSU2… COD10 is so compact that it canprobably be zipped and emailed. *wink*
Thus far, my favourite is the CD version of the Concise Oxford English Dictionary 10th Edition (COD10) with thesaurus.com on Mozilla Firefox. Oxford English Dictionary Online is used as a back up in the rare occasions when I find COD10 unsatisfactory.
To add thesaurus.com to your search bar in Firefox, select ‘add engines’. Search for thesaurus.com and add it to your list.
Anyone got a better electronic thesaurus to recommend?
Double clicking on a word anywhere in Windows will cause the word to be displayed on COD10. Naturally, it’s a very useful tool when browsing the alternative words generated by thesaurus.com.
The only long term problem with this arrangement is centred on OED Online. Annual subscription to OED Online for individuals is a massively frightful £200 (RM1320 at the current exchange rate). When Yuan Harng graduates from university, I’ll no longer be able to access his university’s account. Drat.
Why Oxford?
That’s because I think that a gray colored ax with an aluminum handle looks wrong. Guess it’s a matter of personal preference- don’t over analyze it.
Switch to Firefox 1.0.5. You will have no regrets, except maybe ask ‘why didn’t I do it earlier’. Download it here (4.65 Mb).
Subscribe to OED Online, for a reasonable fee of £50 per quarter (3 months).
Concise Oxford Dictionary 10th Edition Considering its usefulness, it is remarkably small at only 5.70 Mb installed. Compare that to huge, useless, gigabyte-scale programs like Warcraft 3 or NFSU2… COD10 is so compact that it can
posted by Tan Yee Wei at 7/16/2005 02:55:00 pm
Friday, July 15, 2005
New car- to be sad or happy?
My parents have recently confirmed the purchase of a Toyota Corolla Altis 1.6 to replace the Toyota Landcruiser Prado. I don’t know to be happy or sad.
Reasons to be happy:
Reasons to be sad:
Sideways with a hint of opposite lock. Click on image to enlarge.
In conclusion, my reasons for sadness are purely selfish and ego-centric. I suppose that the only way to satisfy my perverse preference for complicated gear changes would be to get my own manual car and not depend on my parents. Maybe that is their strategy all along…
Reasons to be happy:
We’re getting a new car. We will get to breath in the ‘fresh car smell’, which is in fact due to all manner of potentially harmful inorganic solvents used in the manufacture of various components- glues, plastic wraps, dashboard, seat filler material et al. The Altis will definitely use less petrol than the Prado. The Prado is a heavy vehicle with ungainly aerodynamics. It also has a (comparatively) huge 2.7 litre engine, compared to the Altis’ 1.6 litre with VVTi. The Altis has better performance than the Prado. My mother will be glad that it is an automatic transaxle. The Altis will be in a spanking black colour.
Reasons to be sad:
I love driving the Prado, for all the wrong reasons. It’s got a clunky manual gearbox, a heavy clutch pedal, soft suspension that will squat and dive with every touch of the throttle and brake, not to mention roll when steering. It’s precisely these that make it an engaging drive- it’s extremely difficult to drive really smoothly. And I’ve mastered it. (At least I think so.) Last CNY, I drove my family along the back roads from Kuala Pilah to Malacca. Being smooth on roads sprinkled with fast straights, sharp hairpins and long blind curves was a challenge, and my parents remarked (it’s quite a rare occasion) that the ride was a gentle one (I was actually going quite fast). The Prado can do drifts if you give it the appropriate patch of gravel. Being a rear wheel drive vehicle, it’s not hard at all to get it into opposite lock and hold a slide. There is no way a front drive vehicle can execute a sustained slide. The Prado allows me to play with the gearbox in perverted ways, such as heel and toe gearshifts, double clutch heel and toe, and even shifting gears without using the clutch. And yes, I tend to me smoother when I heel and toe, difficult as it may sound. The Prado is already in black anyway.
Sideways with a hint of opposite lock. Click on image to enlarge.
In conclusion, my reasons for sadness are purely selfish and ego-centric. I suppose that the only way to satisfy my perverse preference for complicated gear changes would be to get my own manual car and not depend on my parents. Maybe that is their strategy all along…
posted by Tan Yee Wei at 7/15/2005 09:28:00 pm
Harh? ICQ?
I was chatting with Sonia yesterday night when we somehow talked about the now obscure topic of ICQ. Sometime within the past 3 years, MSN Messenger overtook ICQ in popularity, and the situation remains till today.
I remember that when MSN started groping the IM market, more and more of my contacts logged onto both MSN and ICQ. Later, people started to neglect ICQ, and my contact list became redder and redder. (The default contact list font setting is red for offline users and blue for online) After a while, there was no real purpose to open the program itself, and ICQ was abandoned. When the computer was formatted, ICQ was not reinstalled.
While chatting with Sonia, I decided to check out ICQ’s website. On impulse, I also downloaded and installed the latest program, ICQ 5.04. I searched for my own details on ICQ’s online user database, and obtained my number. I logged in with the classical foghorn blare. And yes, I still remember my password, many years on.
ICQ’s foghorn blare during login was a familiar sound that I had with me since 1998. When the dial up connection was not performing well, it would take ages before the sound came. On the other hand, the foghorn would sound almost immediately if the connection was sprinting at 49kb/s.
To my pleasant surprise, my contact list was exactly as I had left it a year ago. Everyone remained in their appropriate visible/invisible list. Even the renamed names were there! (I renamed everyone’s display names from their frivolous nicknames to their real names. Makes life easier.)
Unsurprisingly, there was only one other person online- Sonia. She uses Trillian, which integrates MSN, ICQ and AOL into one package for simplicity.
This afternoon, I chatted a little with Sonia using ICQ. The messages came through with a perky ‘ah-aww’ sound. Ahh…those familiar noises in my early days of chatting. (I don’t really remember IRC much.) ICQ easily allows multi-lined chat messages, and hitting enter starts a new line, not send. The shortcut to send is alt+S.
And thus while I chatted with Sonia, I typed my messages, alt+s, alt-tab to other MSN windows, typed my other message, enter, alt+tab... This alt+S alt+tab manoeuvre used to be a very common combination in the past, and today, it feels like I’m rediscovering some latent motor skills.
Rediscovering ICQ was an interesting experience. The familiar foghorn blast, the kinky ‘ah-aww’, the alt+S alt+tab finger roll, the blue & red contact list… It felt nostalgic, like returning home after a long absence.
Join me on ICQ: 22-967-871. You can leave offline messages!
At the height of ICQ’s popularity, some people even committed their UIN to memory, much like their phone numbers and residential addresses.
Download ICQ pro 2003b
Download ICQ lite 5.04
I remember that when MSN started groping the IM market, more and more of my contacts logged onto both MSN and ICQ. Later, people started to neglect ICQ, and my contact list became redder and redder. (The default contact list font setting is red for offline users and blue for online) After a while, there was no real purpose to open the program itself, and ICQ was abandoned. When the computer was formatted, ICQ was not reinstalled.
While chatting with Sonia, I decided to check out ICQ’s website. On impulse, I also downloaded and installed the latest program, ICQ 5.04. I searched for my own details on ICQ’s online user database, and obtained my number. I logged in with the classical foghorn blare. And yes, I still remember my password, many years on.
ICQ’s foghorn blare during login was a familiar sound that I had with me since 1998. When the dial up connection was not performing well, it would take ages before the sound came. On the other hand, the foghorn would sound almost immediately if the connection was sprinting at 49kb/s.
To my pleasant surprise, my contact list was exactly as I had left it a year ago. Everyone remained in their appropriate visible/invisible list. Even the renamed names were there! (I renamed everyone’s display names from their frivolous nicknames to their real names. Makes life easier.)
Unsurprisingly, there was only one other person online- Sonia. She uses Trillian, which integrates MSN, ICQ and AOL into one package for simplicity.
This afternoon, I chatted a little with Sonia using ICQ. The messages came through with a perky ‘ah-aww’ sound. Ahh…those familiar noises in my early days of chatting. (I don’t really remember IRC much.) ICQ easily allows multi-lined chat messages, and hitting enter starts a new line, not send. The shortcut to send is alt+S.
And thus while I chatted with Sonia, I typed my messages, alt+s, alt-tab to other MSN windows, typed my other message, enter, alt+tab... This alt+S alt+tab manoeuvre used to be a very common combination in the past, and today, it feels like I’m rediscovering some latent motor skills.
Rediscovering ICQ was an interesting experience. The familiar foghorn blast, the kinky ‘ah-aww’, the alt+S alt+tab finger roll, the blue & red contact list… It felt nostalgic, like returning home after a long absence.
Join me on ICQ: 22-967-871. You can leave offline messages!
At the height of ICQ’s popularity, some people even committed their UIN to memory, much like their phone numbers and residential addresses.
Download ICQ pro 2003b
Download ICQ lite 5.04
posted by Tan Yee Wei at 7/15/2005 03:42:00 am
Images, images and images
The journey from Melbourne to Adelaide was along the number 8 route. A railway line between Melbourne and Adelaide runs along the road most of the time.
Here, you can see me bending really low to capture an image. I wanted the camera to be pointing horizontally, but as close to the ground as possible. I got a photo or two with the railway tracks on the sides of the photo. Stance inspired by a tai chi quan form.
On Tuesday morning, we walked in a reserve park around the Morialta Falls near Adelaide. The waterfall itself was not a very large one, but it dropped from a great height. No good pictures of it.
Glenelg is a seaside town in the outskirts of Adelaide. This shot is the kind of thing that requires the camera to be very low near the ground. However, there is no need to bend and squat when using a digital camera’s LCD display.
During sunset, a flock of birds came to the waterfront. One of them has only one leg. Note that the leg is slightly bent to keep its centre of mass (gravity) directly above its single feet.
I love macro shots, if you don’t already know.
Adelaide uses articulated buses. They are long and jointed like a train. As far as I know, only Volvo makes these buses. This bus is branded Scania, but looks like a Volvo bus nonetheless. Volvo purchased Scania in 1999 or 2000.
This is the ferry that took to Kangaroo Island. It’s a catamaran, with a capacity of about 40 cars powered by a pair of V12 diesel engines, each producing 1500 bhp.
On one particular street in Pennshaw, Kangaroo Island, there is sea at both ends of the street. Look in the rear view mirror for the other bit of sea.
There is a seal colony on Kangaroo Island, and the location has been uncreatively named Seal Bay.
Kangaroo Island is sparsely populated, and has plenty of straight but narrow roads. We saw plenty of road kill- mostly kangaroos and wallabies (small kangaroo-like marsupials).
Click to enlarge.
This is on the way to the Remarkable Rocks (another uncreative name). The rocks in question are at the far end of the road, on the top of the little peninsular protruding out to sea. Note the bushes- they are very short, but nonetheless complicated. The second image clearly shows that these short little bushes actually resemble miniature versions of real, normal trees. As such, they often look like a full scale rainforest from afar. Standing above them (they are about knee level), I can get slight tinges of vertigo-like sensations if I convince myself that they are actually forests far below eye level. Very remarkable...
This is part of the Remarkable Rocks formation, a wonder of erosion and weathering.
We waited to watch the sunrise before driving back to our hostel. As we blasted along the narrow roads at a prudent speed (just a hair above the speed limit), a kangaroo materialised in the car’s light beam. It was standing on the left side of the road. We moved right to give it some room. The first kangaroo we saw!
The kangaroo saw us, and hopped. Wrong direction, you dolt! It hopped one step, directly into our bumper. Bang! Not even enough time to touch the brake pedal.
The driver (Mr. BZY) was more careful after that incident, and slowed down when there were animals, and gave them even more room. A wallaby hopped across the road; we slowed down while changing lanes. In 3 bounds, it had already crossed the 2 lanes. We had just thought everything was fine when right behind the first animal, a second wallaby followed, just 2 metres behind the first. There was no chance to avoid it. With full brake application, the front tyres squealed as the ABS struggled to hold the wheels along the rain damped surface. Bang!
With 2 deaths in 20 minutes, BZY was naturally freaked out, and CTM took over. There were no further kills.
Click to read.
The next morning, I wrote in the hostel’s guestbook. I did not mention the wallaby- 2 kills would make us appear terribly brutal.
We took the 10.30am ferry out of Kangaroo Island and made out way to Mt. Gambier. The roads in the more rural areas were straight and narrow, flanked on both sides with tall brown grass. Behind those grass would be a vast emptiness of some farmland or other. After sunset at 5.30pm, the drive became exceedingly monotonous. The only visible bit was what the headlights illuminated. The grass on both sides look the same all the time. If a car came in the other direction, its lights would be visible from kilometres away, and would take ages for it to arrive even though both vehicles sped towards each other at a combined speed in excess 200+ km/h.
Mt. Gambier is an area of remarkable geology. There is a bed of porous limestone, and ancient volcanic activity blew a crater in the rock. The water table was thus revealed. In summer, the Blue Lake really does take on a blue hue. The water from this lake is so clean that it is pumped into the town’s water supply without any treatment except a slight dose of chlorine as a precaution.
We stayed at a bungalow with a jacuzzi. Note the natural blueness in the water.
This was from the highest point in the region- 190m above sea level.
Mt. Gambier has lots of limestone caves. When the roof of a cave collapses, it leaves a hole in the ground- a sink hole. This sink hole has been converted into a garden. The top level of the stairs is actually ground level, and the stairs lead into the hole.
Well, that’s the summary. Sorry for the boring narration; could have been better. Thank you for reading.
Here, you can see me bending really low to capture an image. I wanted the camera to be pointing horizontally, but as close to the ground as possible. I got a photo or two with the railway tracks on the sides of the photo. Stance inspired by a tai chi quan form.
On Tuesday morning, we walked in a reserve park around the Morialta Falls near Adelaide. The waterfall itself was not a very large one, but it dropped from a great height. No good pictures of it.
Glenelg is a seaside town in the outskirts of Adelaide. This shot is the kind of thing that requires the camera to be very low near the ground. However, there is no need to bend and squat when using a digital camera’s LCD display.
During sunset, a flock of birds came to the waterfront. One of them has only one leg. Note that the leg is slightly bent to keep its centre of mass (gravity) directly above its single feet.
I love macro shots, if you don’t already know.
Adelaide uses articulated buses. They are long and jointed like a train. As far as I know, only Volvo makes these buses. This bus is branded Scania, but looks like a Volvo bus nonetheless. Volvo purchased Scania in 1999 or 2000.
This is the ferry that took to Kangaroo Island. It’s a catamaran, with a capacity of about 40 cars powered by a pair of V12 diesel engines, each producing 1500 bhp.
On one particular street in Pennshaw, Kangaroo Island, there is sea at both ends of the street. Look in the rear view mirror for the other bit of sea.
There is a seal colony on Kangaroo Island, and the location has been uncreatively named Seal Bay.
Kangaroo Island is sparsely populated, and has plenty of straight but narrow roads. We saw plenty of road kill- mostly kangaroos and wallabies (small kangaroo-like marsupials).
Click to enlarge.
This is on the way to the Remarkable Rocks (another uncreative name). The rocks in question are at the far end of the road, on the top of the little peninsular protruding out to sea. Note the bushes- they are very short, but nonetheless complicated. The second image clearly shows that these short little bushes actually resemble miniature versions of real, normal trees. As such, they often look like a full scale rainforest from afar. Standing above them (they are about knee level), I can get slight tinges of vertigo-like sensations if I convince myself that they are actually forests far below eye level. Very remarkable...
This is part of the Remarkable Rocks formation, a wonder of erosion and weathering.
We waited to watch the sunrise before driving back to our hostel. As we blasted along the narrow roads at a prudent speed (just a hair above the speed limit), a kangaroo materialised in the car’s light beam. It was standing on the left side of the road. We moved right to give it some room. The first kangaroo we saw!
The kangaroo saw us, and hopped. Wrong direction, you dolt! It hopped one step, directly into our bumper. Bang! Not even enough time to touch the brake pedal.
The driver (Mr. BZY) was more careful after that incident, and slowed down when there were animals, and gave them even more room. A wallaby hopped across the road; we slowed down while changing lanes. In 3 bounds, it had already crossed the 2 lanes. We had just thought everything was fine when right behind the first animal, a second wallaby followed, just 2 metres behind the first. There was no chance to avoid it. With full brake application, the front tyres squealed as the ABS struggled to hold the wheels along the rain damped surface. Bang!
With 2 deaths in 20 minutes, BZY was naturally freaked out, and CTM took over. There were no further kills.
Click to read.
The next morning, I wrote in the hostel’s guestbook. I did not mention the wallaby- 2 kills would make us appear terribly brutal.
We took the 10.30am ferry out of Kangaroo Island and made out way to Mt. Gambier. The roads in the more rural areas were straight and narrow, flanked on both sides with tall brown grass. Behind those grass would be a vast emptiness of some farmland or other. After sunset at 5.30pm, the drive became exceedingly monotonous. The only visible bit was what the headlights illuminated. The grass on both sides look the same all the time. If a car came in the other direction, its lights would be visible from kilometres away, and would take ages for it to arrive even though both vehicles sped towards each other at a combined speed in excess 200+ km/h.
Mt. Gambier is an area of remarkable geology. There is a bed of porous limestone, and ancient volcanic activity blew a crater in the rock. The water table was thus revealed. In summer, the Blue Lake really does take on a blue hue. The water from this lake is so clean that it is pumped into the town’s water supply without any treatment except a slight dose of chlorine as a precaution.
We stayed at a bungalow with a jacuzzi. Note the natural blueness in the water.
This was from the highest point in the region- 190m above sea level.
Mt. Gambier has lots of limestone caves. When the roof of a cave collapses, it leaves a hole in the ground- a sink hole. This sink hole has been converted into a garden. The top level of the stairs is actually ground level, and the stairs lead into the hole.
Well, that’s the summary. Sorry for the boring narration; could have been better. Thank you for reading.
posted by Tan Yee Wei at 7/15/2005 01:38:00 am
Wednesday, July 13, 2005
The food we had when on holiday
Cherry and Hazelnut Pie
I had some interesting meals during my trip to South Australia. In general, we did a lot of travelling, spending a large portion of day time sitting our bottoms in the Camry while the Camry rolled us from here to there.
Often times, we were out of synch with regular meal times. To our misfortune, many eateries close their kitchens rather early (especially in smaller outskirt towns), and we had many late lunches eating cold food. We were happy with cold food anyway- they were cakes, pies, tarts and strudels. Brilliant isn’t it?
High Apple Pie
Over the eight days, we had plenty of desserts, sometimes (often) substituting them as meals. From memory, this is a list of confections we consumed between the 3 of us over the 8 days.
Triple layer vanilla mousse
Tiramisu
Apple strudel
Apple crumble
Cherry and custard pie
Apple and custard pie
German baked cheese cake
High apple pie
Cherry and hazelnut pie
Mudcake
Ultra rich choc-caramel slice
Cheese cake
Mudcake
Cheesecake
Pecan pie
Mudcake
There are at least 2 omissions in this list. You will notice several mudcakes and apple pastries- I often suggest mudcakes, and BZY likes apple pies. What a list!
Ultra Rich Choc-Caramel Slice
Notable is the ultra rich choc-caramel slice. It is a small piece of confection, with a base made of compressed and sweetened coconut shreds, a generous layer of very thick caramel paste, and topped with a moderate layer of chocolate. It was really really really rich; good thing we shared the cakes for breakfast, or the single slice would have easily killed someone.
The first morning, we had breakfast at a café in Adelaide’s central market. That café was noted for their muffins, baked in a little clay pot. The muffin of the day was raspberry chocolate. It was brilliant, if not a little too sweet.
Another morning, we had yet another breakfast in a shop serving Western European food, also at the central market.
The menu sheets transcribed:
Breakfast-
Russian Omelette- a fluffy bacon & egg omelette served with 3 Russian salads
Bacon & Eggs- Russian style with 3 Russian salads
Blinny- crepes filled with ricotta cheese and sultanas served with fresh cream.
Meals-
Pelmeni- Russian beef and onion dumplings served with sour cream and dill
Varenyki- Ukaranian potato dumplings served with sour cream and dill
My dish of Pelmeni. The Bacons & Eggs and Blinny were not remarkable to look at, but tasted good nonetheless.
The verdict- an eye opener to Russia, but grossly overpriced.
Compared to Melbourne prices (about $7.5 per 250g), coffee beans are considerably cheaper in Adelaide ($5 per 250g). I got 2 different variants of 250g each, ground on the spot, and a little bottle of coffee beans coated in dark chocolate.
At the market, we got 2 packets of pasta and some sauce for our dinners /suppers. They were ‘home made’ pasta, and one was coloured red with tomato, and the other dyed black with squid ink. The cooked result proved remarkable on the eyes, and attracted a lot of attention. [Pictures later] We chanced upon a butcher stall that won several awards for their sausages. They were reasonably priced, so each of us chose a flavour/variant and we got 3 of each. They were wonderful- firmly packed meat flavoured with various spices. A bit salty for our tastes though.
We visited the chocolate factory for Melba. There was nothing remarkable about it- many of the interesting forming processes were out of sight. We each got some of the chocolates there. My advice, don’t buy Melba chocolates. They don’t taste like a lot of chocolate, and they don’t melt in your mouth. It’s like milk chocolate doped/filled with some vegetable oil instead of using cocoa butter.
2 days later, we visited the Haigh’s Visitor Centre. It was another chocolate factory, but Haigh’s is the premier chocolate firm in Australia selling expensive and presumably high quality chocolates. Most of their filled chocolates are hand made, and many of the processes are visible behind glass walls. The place was permeated with a pleasant cocoa fragrance. The chocolates are rather costly, but of excellent quality. The individual pieces go at a rate of $28.00 per 100 grams. Evil- you can only choose so many pieces with a finite budget.
posted by Tan Yee Wei at 7/13/2005 12:41:00 am
Tuesday, July 12, 2005
Some questionnaire or other...
Sonia shoved this questionnaire at me when I was away, without any chance of protest.
I'm not going to push this on further. The trail stops here.
Total volume of music files on my computer/ Handphone:
6.99 Gb in 1991 files on hard disc.
The last CD/ringtone I downloaded/bought:
I haven’t paid money for music in a long while.
I am perfectly happy with the standard ring-ring tone.
Song/ringtone playing right now:
I Don’t Care At All, by Vanilla Ninja. Godownloadbuy their album, Blue Tattoo.
Fivesongsalbums/ringtones i listen to a lot/ringtones that I use a lot on this phone:
Penny Dai- So Penny
Vanilla Ninja- Blue Tattoo
FIR- I Wanna Fly
Isabelle Boulay- Au moment d'etre à nous
Sarah Brightman- La Luna
I'm not going to push this on further. The trail stops here.
posted by Tan Yee Wei at 7/12/2005 08:50:00 am
I am back
A washed up bit of seaweed during sunset at Glenelg, an overrated seaside town in the outskirts of Adelaide. (click to enlarge, 140kb)
After a nine day long break from life, I am back. With two friends, I had travelled from Melbourne to Adelaide, Kangaroo Island, Mount Gambier and back to Melbourne.
We rented a Toyota Camry, a 2.4 litre inline-4 engine with automatic transmission. We had fleetingly considered renting a Mitsubishi Magna instead, since we had never driven that car and its daily rental rate was only $4 more than the Camry. With its 3.4l V6 engine, it would be interestingly overpowered, but consume petrol like there would be no tomorrow.
We travelled 3149km. I’m quite impressed by the figure.
We consumed 295 litres of petrol, averaging 9.3 litres for 100km travelled. I’m also quite impressed by this figure, considering that this car was rated at 10.4l/100km on the highway cycle. I attribute this to gentle throttle application and an optimised speed to run through chains of traffic lights just in time to slip through when they are green, reducing the need to brake and accelerate. The traffic light run requires immense discipline not to go too fast, or you’ll simply catch the red light ahead.
The economy of Adelaide goes into coma every night at about 5pm, and there’s absolutely nothing to do after dark except for the odd bar to sit in. As such, we had lots of time on our hands after dark. Not an early sleeper, I wrote (i.e. blogged) in my note book. Over the next few days, I might transcribe some of the interesting bits and post them.
posted by Tan Yee Wei at 7/12/2005 07:37:00 am
Sunday, July 03, 2005
BRB
Tan Yee Wei will be away for 7 days. He will be on a holiday trip, departing at 8.00am (+10 GMT) Monday from Melbourne, and back the following Monday.
For some sort of mental stimulation over the week, try to come up with as many alternative words/phrases as possible that means ugly.
If you want a postcard from where I will be going, drop me a text message.
In order that some sense of mystery should still be preserved, no revelation will yet be made concerning the [holiday destination]. This fact may safely be made the subject of suspense since it is of no significance whatsoever.
-Douglas Adams
For some sort of mental stimulation over the week, try to come up with as many alternative words/phrases as possible that means ugly.
If you want a postcard from where I will be going, drop me a text message.
posted by Tan Yee Wei at 7/03/2005 07:18:00 pm
Saturday, July 02, 2005
What on earth is a ‘gnomon’?
A bit of magic, really.
The Oxford English Dictionary gives several definitions of the gnomon. Here are the two relevant ones:
Lets look at the odd numbers first:
1, 3, 5, 7, 9, 11, 13...
If we sum the first 1 gnomon, we get 1.
If we sum the first 2 gnomons, we get 1 + 3 = 4.
If we sum the first 3 gnomons, we get 1 + 3 + 5 = 9.
If we sum the first 4 gnomons, we get 1 + 3 + 5 + 7= 16.
To make life easier, we’ll arrange the sum of gnomons in a series, like so:
1, 4, 9, 16, 25, 36, 49...
Look! The sum of the first n gnomons correspond to the square of n. The sum of the first 3 gnomons is 9, which is 3 x 3. And the sum of the first 4 gnomons is 16, which is 4 x 4.
Magical isn’t it?
Magic, explained geometrically
A geometric representation of the sum of gnomons.
Start with the sum of the first 2 gnomons, 1 + 3 = 4. From the figure, 1 + 3 is represented as the red square and 3 grey squares. Collective, they form a larger 2-by-2 square.
The sum of the first 3 gnomons is 1 + 3 + 5 = 9. It is represented by the red square, 3 grey squares and 5 purple squares. Collectively, they form a larger 3-by-3 square.
This introduction to number theory brought to you by Tan Yee Wei.
The Oxford English Dictionary gives several definitions of the gnomon. Here are the two relevant ones:
An odd number Something shaped like a carpenter's square; an L-shaped bar, etc.
Lets look at the odd numbers first:
1, 3, 5, 7, 9, 11, 13...
If we sum the first 1 gnomon, we get 1.
If we sum the first 2 gnomons, we get 1 + 3 = 4.
If we sum the first 3 gnomons, we get 1 + 3 + 5 = 9.
If we sum the first 4 gnomons, we get 1 + 3 + 5 + 7= 16.
To make life easier, we’ll arrange the sum of gnomons in a series, like so:
1, 4, 9, 16, 25, 36, 49...
Look! The sum of the first n gnomons correspond to the square of n. The sum of the first 3 gnomons is 9, which is 3 x 3. And the sum of the first 4 gnomons is 16, which is 4 x 4.
Magical isn’t it?
Magic, explained geometrically
A geometric representation of the sum of gnomons.
Start with the sum of the first 2 gnomons, 1 + 3 = 4. From the figure, 1 + 3 is represented as the red square and 3 grey squares. Collective, they form a larger 2-by-2 square.
The sum of the first 3 gnomons is 1 + 3 + 5 = 9. It is represented by the red square, 3 grey squares and 5 purple squares. Collectively, they form a larger 3-by-3 square.
This introduction to number theory brought to you by Tan Yee Wei.
posted by Tan Yee Wei at 7/02/2005 09:38:00 pm
Enlightened, four times over
On Thursday, I was enlightened four times.
Together with 2 of my friends, I was bookshop-hopping in Melbourne in search for some decent maps for our upcoming holiday. When we finally got what we wanted, we discovered that we were hungry. Since we were in the travel section of the book store, it made perfect sense to check out “Melbourne” on the Lonely Planet guide books for something good to eat.
On the first Wednesday of July, we had watched Mama Mia! the musical. It was a brilliant production, and I opine that everyone should watch it at least once before dying. Before the show, we walked around the vicinity of the theatre, and saw a small bar of sorts. It looked like a coffee bar. We vowed to return.
In the Lonely Planet guide, we found this same outlet, Pelligrini’s Bar. The espresso came highly recommended. Very well, we would go there.
For the sake of sampling something new, I ordered spaghetti saltati. For some reason, I had never ordered espresso before. This would be another first. One particular drink that was popular was a pinkish concoction of ice and liquid slurry. We ordered that too.
The spaghetti saltati was brilliant. Best pasta I had in a long while/ever. The espresso was an eye opener, in all senses of the phrase. As a friend remarked, “this is very pure coffee.” The pinkish slurry turned out to be watermelon granita with a dash of lemon. Granita is “a coarse Italian-style water ice” (Oxford English Dictionary). It was a good drink. The bill came to a rather hefty A$20.
Together with 2 of my friends, I was bookshop-hopping in Melbourne in search for some decent maps for our upcoming holiday. When we finally got what we wanted, we discovered that we were hungry. Since we were in the travel section of the book store, it made perfect sense to check out “Melbourne” on the Lonely Planet guide books for something good to eat.
On the first Wednesday of July, we had watched Mama Mia! the musical. It was a brilliant production, and I opine that everyone should watch it at least once before dying. Before the show, we walked around the vicinity of the theatre, and saw a small bar of sorts. It looked like a coffee bar. We vowed to return.
In the Lonely Planet guide, we found this same outlet, Pelligrini’s Bar. The espresso came highly recommended. Very well, we would go there.
For the sake of sampling something new, I ordered spaghetti saltati. For some reason, I had never ordered espresso before. This would be another first. One particular drink that was popular was a pinkish concoction of ice and liquid slurry. We ordered that too.
posted by Tan Yee Wei at 7/02/2005 02:55:00 am
I am slightly miffed
During my summer holidays, I actually had enough time on my hands that I actively searched for alternative reading materials. In particular, I offered to proofread my friends’ assignments and essays. Over that period, I saw some interesting papers such as IR Postgraduate’s political science essays (refer to the sidebar, “Current fetishes”), Yuan Harng’s classical physics essay about the aerodynamics of a baseball, an advertising internship report and various press releases for a public relations intern. Eye-openers, all of them.
On Wednesday, as I groggily stumbled into my mailbox, I found a new message with the subject line “Proofread please!!!!” Yes, four exclamation marks. Four.
***
I had initially set out to bitch and complain about this particular person. However, in writing this, I saw that there was little point in doing so. While trying to sort out my ideas and arrange them into a semi-logical form, it dawned on me that the matter at hand is actually rather trivial. Publishing it would only serve to bore the patient reader.
***
I was slightly miffed.
On Wednesday, as I groggily stumbled into my mailbox, I found a new message with the subject line “Proofread please!!!!” Yes, four exclamation marks. Four.
I had initially set out to bitch and complain about this particular person. However, in writing this, I saw that there was little point in doing so. While trying to sort out my ideas and arrange them into a semi-logical form, it dawned on me that the matter at hand is actually rather trivial. Publishing it would only serve to bore the patient reader.
I was slightly miffed.
posted by Tan Yee Wei at 7/02/2005 02:26:00 am
About Me
- Name: Tan Yee Wei
- Location: Melbourne, Petaling Jaya
Perpetually stuck in a time warp (thinks of the mid-90s as recent times). Gradually shedding that veneer of avoidance. Occasionally a feminist in principle and ideology. Likes the semicolon, mathematics, sharp knives, macro photography. Will choose a manual gearbox over an automatic every time. A firm believer in prime lenses. Has a bloated view of himself as a multi-disciplinary genius every now and then. more...
I’m not addicted to them, I can stop reading whenever I want to
Fellow Pornstars
Audrey
Chung Lern
Cynical-Idealist
Jamin
Gorilla Bananas
Jean
Jolene Lai
Jun Ian
Jun Shern
K.T.X.
Penelope
Reta
Sabrina
Shieh May
Steff
Suet Li
Vic
Wei Yi
Yee Juinn
Yee Hou
(Semi) Retired Warriors
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Diana
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Saffron
Shyan Yih
Viewtru
Weng Hong
Subsets
Applied MathematicsApplied Science
Compositions
Mathematics
Microscopy
Natural Science
Number Theory
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Photographic Equipment
Photography
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- Two more weeks,
- How bandwidth availability is making obscure data ...
- Not a regular taekwondo training session
- Half a year in a roll of film
- The World Taekwondo Hanmadang 2011
- Yesterday I saw a magnificently disgusting event a...
- Programming types would say, "Hello world!"
- Anaglyph
- Bitter Gourd is sad because the Garlics refuse to ...
- Red Velvet cake with cream cheese icing
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