Thursday, March 30, 2006

Recent photographs

2 days ago, David and I went for a bit of chocolate overdose at a chocolate boutique kind of place at Koko Black, Lygon Street. For a A$24.00, we had one hot chocolate, one iced chocolate, one chocolate iced cream, and one chocolate mousse. Yeah, it was expensive.

They were delicious. And rich. Very, very rich. We had a late breakfast, skipped lunch, then ate dessert at about 4pm. Even then, the last few bits of the mousse and iced cream was already stretching it.

12-Fold Bisection of the Celestial Sphere

Overhead power or signal transmission lines at a traffic intersection.

The chocolate mousse was beautifully presented, but I was stumped for ideas.
Finally the chocolate swirl got my attention.

The ice cream had a longer helical strip of dark chocolate.


Wednesday, March 29, 2006

More exciting word games

Yvy is on the roll, bravo! She has produced yet another list of words that are to be used in a composition no longer than 200 words. The new rule this time is that words on the list may not be repeated. As always, words should be used in order.

In today’s news, famed playgirl-physicist Eta-Carina has cancelled this evening’s long anticipated sleepover party, citing reluctance to whip up a media frenzy over noise regulation infringements.

A disappointed guest was quoted as saying that "she ought to be handcuffed and lashed several times with a leather belt." "That will be sexy," the guest added.

Eta-Carina, who was previously in the news for alleged misconduct with a threesome of musicians, said that it would be rude to disturb her neighbours, adding that she did not want anymore "hairy situations with the nice folks".

Elsewhere in Praesepe, a man was taken in by police early in dawn near Maranello to aid in investigations of yesterday's shotgun roberry at the Praesepe Central Bank. The police have yet to name any suspects but are confident they will resolve the matter shortly.

In today’s technology updates, engineers at Sony have developed a possible replacement for keyboards by using a soft foam ball that is squeezed using only one hand. Test users were able to adopt the technology quickly, and are current 'typing' at well over 80 words per minute. "There’s really an explosion of interest from video game manufacturers," a Sony spokesperson said.
198 words


I’m quite proud of pulling this off. Taking the news report angle was a nice step out of the box for me, and has enabled the diverse words to be used with little fuss.

And now, to pass this game on, I give it to Sonia and Wei Yi. It's not easy (blame Yvy), but do have fun!

Eta Carina (with no hyphen) is actually the name of a massive star about 7500 light years away from the earth. With a mass of 100 to 150 solar masses, it is thought that this star approaches the theoretical limit on the masses of stellar objects. Apart from the fact that it is expected to go supernova (or even hypernova) in the next million years, it is also blessed with what I think is an elegant name. [reference]

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Tuesday, March 28, 2006

So, what is this Skewe’s number?

Godfrey Harold Hardy (1877-1947) remarked that Skewe’s number is ‘the largest number that has ever served any definite purpose in mathematics’. [1]

The story starts when we consider the prime numbers- numbers that do not divide wholly with any number except for one and itself. The first few prime numbers are

2, 3, 5, 7, 11, 13, 17, 19...

In 300BC, Euclid of Alexandria proved that there are infinitely many prime numbers. [2]

The prime counting function π(N) now comes into play. π(N) simply counts the number of prime numbers equal or less than N.

For N = 11, π(11) = 5. There are 5 prime numbers equal or less than N: 2, 3, 5, 7 & 11.

π(0) = 0
π(1) = 0
π(2) = 1
π(3) = 2
π(4) = 2
π(5) = 3
π(6) = 3

π(100,000,000) = 5761455 [2]

Because the exact distribution of primes is not predictable, number theorists have had to make do with functions that would approximate π(N).

Over the years, various proposals have been made to estimate π(N) at large values of N, each conjecture more accurate than the last.

The twiddle sign (~) indicates that the approximation gets increasingly accurate for larger values of N.

Bernhard Reimann’s landmark 1859 doctorate paper refines the prime counting function’s estimate to a very precise but unproven estimate [2]

Where li(N) is the (natural) log integral from 0 to N.

From here, we will go on to explain how Skewe’s number came about.

Riemann’s log integral was a a good approximation of the prime counting function π(N). However, li(N) seemed to consistently overestimating the actual value of π(N).

For example, at large values of t, 0 can be closely approximated by the following exponential function:

In this particular example, the exponential function is always positive (for positive t), hence consistently overestimating the value of zero. However, the function approaches 0 for increasing t.

The appeared to be the case with Riemann’s log integral- it was consistently larger than π(N), but the error shrinks with larger values of N. For all N within our grasp, li(N) was greater than π(N). In fact, Gauss (1777-1855) was thought to believe that li(N) would always overestimate π(N). [2]

In 1914, John Edensor Littlewood proved that on the contrary, li(N) can overestimate and underestimate π(N), and switches back and forth infinitely many times. This result created quite a sensation, and the next question was obviously, at what value of N is the first ‘Littlewood violation’ (where li(N) turns from overestimation to underestimation)?

In 1933, one of Littlewood’s students Samuel Skewes showed that assuming the truth of the Riemann Hypothesis, the first Littlewood violation would be definitely less than the following number, now known as (the first) Skewe’s number [2] [3]:

GH Hardy calculated that if one were to play chess using every particle in the universe (10^84 particles), where one step is the exchange of two particles, then the number of possible games is roughly equal to Skewe’s number. [1]

In 2000, the upper bound of the first Littlewood violation was estimated to be near the vicinity of 1.39822 x 10^316, a mere 316 digit number. Another paper shows that there is a small possibility of the first violation occurring around 10^176. [2]

However, this is not the end of the story. Samuel Skewes also showed that assuming the Riemann Hypothesis is false (as opposed to the previous true assumption), the first Littlewood violation would occur below another even more monstrous number, known as the second Skewe’s number: [3]

[1] Simon Singh, ‘Fermat’s Last Theorem’, Fourth Estate, London 1997.
[2] John Derbyshire, ‘Prime Obsession – Bernhard Riemann and the greatest unsolved problem in mathematics’, Joseph Henry Press, Washington DC, 2003.
[3] Eric W. Weisstein, ‘Skewes Number’, MathWorld

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WordyWord Meme by Yvy

Yvy started this little story telling game, and I picked it a few days late from Sonia and Yvy’s pages. The point of the game is to write a tale in no more than 109 words using the following 10 words, in order.
1. agent
2. headmaster
3. skirt miniskirt [see edited section below]
4. tomboy
5. fire
6. 69
7. love
8. piglet
9. stinks
10. teh tarik

"And so we’ve simulated student behaviour using agent-based mathematical models," the salesperson-mathematician droned on, the headmaster nearly nodding off from boredom.

The mathematician stepped from the lectern, her elegant skirt contrasting with her short tomboy haircut. "Now, it is obvious that..."

"Excuse me sir," a clerk interrupted, "it’s an incident in room B69. Some boys were caught playing with fire and magnesium strips."

"Sigh... it’s them again. Can’t they just find someone to love and quiet down? Let Piglet handle this." Piglet was the chemistry teacher and discipline master’s nickname.

He turned to the mathematician, "being a headmaster stinks. Let’s go for a teh tarik."
"Yes, we’ll continue later."
109 words


Edited 7.50pm:
Yvy told me that word number 3 should be miniskirt instead of skirt. The composition has thus been reworked to fit a miniskirt onto a mathematician. Fortunately this particular lady has nice long legs that would not complain about the skirt's lack of length.

All modifications italicised. Words from the list will no longer be highlighted.

"And so we’ve simulated student behaviour using agent-based mathematical models," the salesperson-mathematician droned on, the headmaster nearly nodding off from boredom.

The mathematician stepped from the lectern, her miniskirt and tomboy haircut jarring with common perception of mathematicians. "Now, it is obvious that..."

"Excuse me sir," a clerk interrupted, "it’s an incident in room B69. Some boys were caught playing with fire and magnesium strips."

"Sigh... it’s them again. Can’t they just find someone to love and quiet down? Let Piglet handle this." Piglet was the chemistry teacher and discipline master’s nickname.

He turned to the mathematician, "being a headmaster stinks. Let’s go for a teh tarik."
"Sounds good."
109 words


People who I think may appreciate this little foray into guided narrations are:
Yee Hou
Yuan Harng

Sorry it's mathematics again.The first thing that came to mind after spies prancing about in black suits was agent-based modelling used to simulate the behavior of large groups of interacting semi-intelligent entities. Such as pre-programmed robots, humans, flies and business firms.

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Monday, March 27, 2006

Photographs from the Melbourne Commonwealth Games- Cycling

caution: moderately large sized photographs. Exercise patience.

Chris Newton of England.
He picked up a DNF (did not finish).

The Canadian Maple flies high in Melbourne.

Cyclists from the Isle of Man and Wales lean into the first corner of the lap.

Andrew Roche from the Isle of Man finished 22nd with a time of 4:06:29 over 166 km.

It's usually bad manners to let a state's flag touch the ground.

Spectators cheering the competitors on.
Of the 134 cyclists who started, only 35 made it to the finish line.

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Microsoft products do not reflect Australian daylight saving time changes for the year 2006

Today, as usual, I made it a point to attend the free lunch hour concerts at the university’s music faculty. In fact, today’s concert was more important than most other weeks’.

Bonnie Brown was performing.

The first time I saw her perform was in August 05 and it was an enthralling high energy, high speed piano solo. It was the kind of solo that one might use to show off the fact that their fingers can dance at well over 10 Hz on the keyboard.

Anyway I prefer these cheerful pieces to those string quartets that seem to tell you, “I’m so depressed I want to die. Please shoot me, and then shoot yourself after you’re done.”

A brief search on the university’s pages reveals that
Bonnie began studying piano at the age of three. During her time at the Faculty of Music, Bonnie has been awarded the ‘Eric and Linda Jullyan’ Memorial Scholarship’ and the ‘Ormond Exhibition’ for the most outstanding practical examination results in 2001 and 2002. In 2003 Bonnie received the ‘Rosemary Kenny’ prize awarded by the Faculty for the ‘Best Third or Final Year’ student in the bachelor of Music course and most recently the ‘Doris F. Chandler’ Memorial Bursary.

In 2003, Bonnie performed as the featured soloist at the University of Melbourne 150th Anniversary Concert in the Melbourne Town Hall. Bonnie is currently undertaking a Master of Music at the University, specialising in Music Performance under the supervision of Professor Ronald Farren-Price.

Impressive. Very very impressive.


So I got up this morning, and the clock on my Windows taskbar was 1 hour behind the other clocks. Daylight saving must have started, so I wound the clocks back by 60 minutes and had one more hour to slack around before leaving.

I arrived at 12.55, and the entrance of the hall was surprisingly deserted. Usually, it would be a buzz of activity as people drifted in and out of the performance venue.

When I went up to the front desk, the lady behind it told me that the concert had already started.
“What? Did it start at 1?”
I looked at my watch dumbly, “Shit…must be the daylight saving time.” At this point I thought the university had not switched over, which was extremely puzzling. She laughed a sympathetic laugh.
“Thought I wanted to catch Bonnie Brown performing… shit, this sucks.”
“You can still watch the final parts,” she suggested, her hand gesturing towards the door.
“Yes I’ll do that. Thank you,” I headed for the door, extremely annoyed with the circumstances.

Bonnie was still in the midst of her performance. As with the last time, it was an energetic piece with parts that had about 5 to 10 Hz note playing. Having seen a fair bit of lunch hour concerts, I can guess that her pieces would have added up to about 25 minutes. And she was doing it by memory- no score sheets.

I saw about 10 to 15 minutes of the performance.

When I got home, I asked my housemate about the daylight saving time changeover.
“Not until after the Grand Prix,” he told me.
“My computer had already changed, causing me to miss about half of the concert. I’m quite pissed off.”
“Yeah my computer did it too.”

A search on the internet gave this page:
Microsoft products do not reflect Australian daylight saving time changes for the year 2006

Fuck you, Microsoft wankers. Fuck you.

Turns out it is not Microsoft's fault. Heh. (insert sheepish grin)
A few states in Australia postponed the daylight saving switchover due to the Commonwealth Games and the F1 GP.
So it boils down to my gross ignorance.

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Sunday, March 26, 2006

Adventures at the Commonwealth Games- cycling

This afternoon, I went to watch the Commonwealth Games cycling time trail event. My main intention was photography; I was not overly concerned about who got which medal.

After some aimless wandering, I settled on viewing from a corner, where cyclists would lean into the curve. I stood on the outer edge of the curve after convincing myself with some geometric arguments that it would difficult to shoot photos from the inside. Right across me was a press photographer, and he was the same guy I saw across me during the marathon.

Today’s cycling event

Last week’s marathon event

Most spectators were leaning on the barriers, some with hands dangling over it. Across the road, a kid was holding an empty green 750ml bottle that once contained a refreshing charge of Sprite. She managed to drop it onto the course.

The orientation of the bottle, the contour of the course, and the effect of gravity conspired to roll the bottle onto the racing line. The fact that the racing line was very close to the inner wall meant the bottle would be invisible till very late, potentially tripping up the cyclists. If the main group arrived at that moment, it would have catastrophic.

A few of the spectators who saw the bottle early and who still had clarity of thought tried to attract the attention of a pair of police officers but they were out of audible range. Presently, spectators upstream of the corner began clapping and cheering in a slightly lacklustre manner, indicating the imminent arrival of a small group of cyclists, none of which are Australian.

This might turn into a big moment. I was a little downstream of the bottle, and my line of sight towards the little troublemaker was tangent to the racing line. At the instant of the cyclists approaching the bottle, I would be facing them from the front.

I pointed the camera. From previous shots, it was already on high speed continuous shooting mode, auto focus was set to single region high speed AF and the exposure parameters were already fixed.

The bottle was already on the racing line and still rolling lazily. A trio of cyclists in red (possibly 2 Canadians and one Malawian) rounded the blind curve.

The spectators silently watched, transfixed. A high speed drama was unfolding before their eyes.

The bottle came into the cyclists’ view.
“Watch for the bottle!” the leading Canadian yelled at his team-mate.

The red trio tightened their lines perceptibly, missed the bottle by about 6 inches, and they went on their way.


In most circumstances, my error in handling the camera would have been trivial and of no great importance. However, if the cyclists had indeed tripped over the plastic bottle and I missed the shot, my carelessness would have been interpreted as catastrophic stupidity that would warrant the creation of a new subsection in the Master List of Stupid Things.

Turns out I did not turn the camera on.


Shortly after I arrived (about 2 hours after the event started), I saw 2 Malaysian cyclists breeze by in their garish orange outfits. If I’m not mistaken, they were Suhardi bn Hassan and Anuar bn Manan.

I told myself I’ll find a nice spot (which I did) and make sure I take their photos. It might get into The Star’s photo submission.

Subsequently, I did not see any more orange flashes. Turns out they picked up DNFs (did not finish) for themselves. All six of the cyclists!

It’s not as bad as it may seem. 138 competitors started the 166km race, and only 35 finished- 3 quarters dropped out. Still, the six DNFs is not something to be proud about.

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Saturday, March 25, 2006

Photographs from the Melbourne Commonwealth Games- Boxing

caution: moderately large sized photographs. Exercise patience.

Sharif Bogere of Uganda bowing in the ring before his featherweight (57kg) quarterfinal match with Luke Jackson of Australia.

Sharif Bogere during a break between rounds.
He lost to Jackson 12-18.

Adonis Stephenson (in red) for Canada, and Chimwemwe Macfer Chiotcha (in blue) for Malawi touching gloves before their middleweight (72kg) quarterfinal match.

Stephenson won the match 31-9.

Jarrod Fletcher (red) of Australia and Craig McEwan (blue) of Scotland in their middleweight quarterfinal match.

Fletcher won 27-10.
The post-match interactions here between boxers and support crew was the most friendly of the day.

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Friday, March 24, 2006

Topless portraits with fruits, and other images

As previously mentioned, David and I went on a tour of the Great Ocean Road. We’ll not go into the nitty-gritty details of the trip. Instead I’ll simply highlight a few notable events.


Somewhere along the way was a scenic spot with rolling hills dusted with a delicate blanket of mist. Of course I stopped. After a few lacklustre photographs that did not manage to capture the serene magnificence of the landscape, David wanted a few portraits.

Of course he doesn’t use the pretentious term “portrait”, but he wanted a photo anyway. For posing purposes, he took off his t-shirt. A momentary flash of inspiration hit me, and I rummaged around the back seat of the car for a banana.

Privacy concerns has reared its ugly head.
The link to this image has been removed.

Privacy concerns has reared its ugly head.
The link to this image has been removed.

I still don't know if it's funny or bad.

After that, he said since I had so much fun doing the banana shots, it was now his turn. Not contend with doing more bananas, I dug around the mess that the back seat was, and found a pair of C-cup oranges.


Passing a field of grazing monochromatic cows, I stopped for some bovine portraits. Driving off, I ran over a plastic reflector post for fun. We found it extremely amusing, and resolved to do it at the next suitable one.


And finally, some cam-whoring on my part. This was done in a dimly lit public toilet, with a polished sheet of stainless steel for a mirror, and some fluorescent tubes for illumination.

The camera was held with both hands at waist level and pointed at the mirror. ISO was set to 400, but shutter speed was still a slow 1/4s despite a large aperture of F/2.8. Flash could not be used or it’ll blind the camera.

The dodgy angle of the shot makes the side kick look higher than it already actually is.


I usually take care of my books

In the mid-90s, I picked up the habit of reading novels. I think I stepped up from Enid Blyton and the Hardy Boys (I still cringe whenever I flip through these pages) when I browsed my mother’s rented copy of Tom Clancy’s Hunt for Red October.

Due to the influence of people around me, I also read John Grisham, Sidney Sheldon, Michael Crichton and Jeffery Archer. I began to frequent the novel renting outlets and my parents throttled the quantity of novels I was reading due to potential disruptions with my academic work, despite the triviality of weekly spelling tests and the like. In hindsight, I would say they are probably glad I did not take to endlessly watching Cartoon Network or staring blankly at music videos. Not that we had pay TV in that era.

Instead of using bookmarks, I used to make a fold at the corner of the page. Naturally, the fold created a crease, which is nothing more than an elongated region of broken lignin fibres. Of course, the damage is irreversible. Giving the paper a fold in the opposite direction merely expands on the original problem by breaking fibres on the other surface of the paper as well.

I did not care much. Books were nothing more than vessels of information- after the information was assimilated, the carrier was of no use to me. At any rate, the damage to the paper was only done at corners of the book, where the text was not printed on anyway, and where the paper was not load bearing, existing merely to give the page a non-zero margin.


A few days ago, David was reading one of my books when he flipped the front pages around to press it onto the back cover, making it convenient to hold with one hand. I almost screeched at him, but managed to restrain myself to just telling him not to do that to my books.

2 days ago, we rented a car to drive along the Great Ocean Road. I was unfamiliar with the way to the motorway from my new neighbourhood, and thus pointed out the route on the street directory and inadvertently designated him as the navigator should anything go wrong.

“So we are here right?”
“I’ll make a mark on the map.”
“Better not, it’s not ours anyway.”
“Just a small one with a pencil.”
“Ok lah, doesn’t matter anyway.”

He whipped out a black pen and drew a juicy 20mm oval around my street. I felt a serrated blade pen rip through my heart, despite fully knowing that the map belongs to the car rental company, not me.

“You better not do that to the Sydney street directory I loaned you or I’d be very tulan (extremely cross).”
“Ok ok, you look quite serious. I’ll be careful with that.”

It’s not exactly a disorder yet, but I take very good care of books in my possession. All my text books have no marks on them (most engineering text books are not meant to be read, even during revision) and are better than mint- plastic wrappers add a lot of structural integrity to the corners of paperback covers.

Even the photocopied and printed volumes are maintained in excellent condition. I’m pretty sure my copy of Spacetime and Matter lecture notes from Nottingham is in better shape than that of the person who gave it to me.

I still do not have a dedicated bookmark- I use whatever pieces of paper around that happen to be convenient. Most of the time, these happen to be ATM receipts and spent public transport cards. I still have a railway, bus and ferry day ticket from Sydney that serves as a mark.


This entry was made primarily with the intention of making sure this webpage does not become a full time photoblog. The problem is not with photoblogs. Rather, I fear I may lose all skills in written communication, and thus lose touch with ALL of humanity.

I may be a hermit most of the time, but I do not want to be a hermit all the time.

Which reminds me, I have not read a riveting, page turning novel in ages. I must get some from the council libraries soon.


Thursday, March 23, 2006

Photographs from the Great Ocean Road

2 days ago, I posted a short, 2 sentence update. Blogger says it was published, but when I looked 3 minutes ago, it was not there. Wankers!


I'll be away for about 24 hours. Lets hope the gods are cooperative and give me lots of sunset, moonrise and sunrise photos over the ocean horizon.

The reason for my absence was that I went to the Great Ocean Road with David. Presented today will the artsy photographs; we'll talk about the interesting details tomorrow (such as the time we posed topless with various fruits by the car).

Reflections of an unidentified male and a canine of unknown gender on a stagnant pool of tide water.

Several of the Twelve Apostles shrouded in dense sea spray.

The Twelve Apostles during sunset


Sunrise with David at Lohan Beach where whale mating takes place in winter. It was an awfully cold and windy day- note the dense mist on the eastern horizon and the wrathful waves.

Sunrise at Lohan Beach reflected off sand wetted by the waves.

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Tuesday, March 21, 2006


I'll be away for about 24 hours. Lets hope the gods are cooperative and give me lots of sunset, moonrise and sunrise photos over the ocean horizon.

Sunday, March 19, 2006

Photographs from the Melbourne Commonwealth Games- Marathon

caution: moderately large sized photographs. Exercise patience.

Tracey Morris of Wales at the 35km mark. She finished the race in 2:33 hours for 4th position.
Note her cheerful smile- something rare in a gruelling marathon.

Click here for large size image
Click here for Deviant Art entry

Hellen Cherono Koskei of Kenya finished a mere 2 seconds behind gold medallist Kerryn McCann of Australia.

Francis Robert Naali of Tanzania and Teboho Sello of Lesotho.
They finished 8th and 10th.

Teboho Sello cooling off after the 40km mark.

Bottles of fluid at the 35km refueling station neglected by runners.


The original photograph of Tracey Morris which the digitally altered version (first image) is based on.

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Saturday, March 18, 2006

The Hibiscus and the Time Keeper

I learned a new trick on Photoshop from Foot Foot. It's not a very obvious effect, but it does add a bit to certain photos.

The Hibiscus and the Time Keeper

Click here for large size image
Click here for Deviant Art entry


My very own piece of Formula 1

David persuaded to make more mention of him in my blog. Of course I will do that; you can safely ignore the links.

The contents of this post are of dubious legality and questionable morality. Tread with care.


In line with the impending arrival of the Formula 1 circus to Melbourne, Fosters has started their promotional campaign for the Grand Prix. There are several F1 chassis for display at the Melbourne Central shopping mall, including the Williams and the Honda cars.

These are the real things. The driver’s seat and steering wheel may have been removed, but it does into detract from the chassis’s realism.

The gearbox is present. As are the gurney flaps, carbon-carbon composite brakes, brake light, rear diffuser complete with dirt marks, scratched towing hook, nicked wheel rims and worn wheel nuts. This is the real thing that has seen action.

The Williams on display was slightly away from the main promotion area, and it was not surrounded by any promoter bimbos. This allowed me to fondle the gurney flaps and suspension members with minimal embarrassment.

One might recall the procedure when completing a tyre change: screw the nut on, pull the locking stud, raise your hand to indicate completion while making sure you are out of harm’s way.

Impressed by the locking stud, I gave it a push. It unlocked with a deeply satisfying click. Woo... I pulled it back to locked position with another solid click, and a little stub protruded from the main axle to help retain the wheel in place. I locked and unlocked it two more times.

Unlocked position

Locked position
Click here for large sized image

The brake light consists of an array of LEDs, and the housing is part of the rear aerodynamic element
Click here for large sized image

Rear suspension assembly and part of the rear diffuser. Note the drive shaft piercing through the brake duct shroud, and the blue coloured wire that appears to be a sensor output (probably wheel speed and brake temperature readings)
Click here for large sized image

As the text clearly embossed on the tyre wall says, “not for highway use”.

David and I went fiddling with the Williams chassis.

[paragraph truncated to save our skins from the Williams hit team]

The right front wheel

The left rear wheel after our little adventure

Can you spot the difference between the two pictures above?

Back at home:

In conclusion, David was very smart and I’m sure Yee Hou would be dead envious about my latest jewel.


In hindsight, this is slightly ironic/appropriate (depending on point of view) considering that this current blog colour scheme is modelled after the Williams-F1 team's.