Present Sources of Bad Karma

1. Spent somewhere around 24 hours doing research for the June itinerary. That's a little too much time.
2. Might not even able to go, if both the ICA and the Chinese Embassy drag their feet on my new passport/s. (see 1)
   
3. US$50,000 a year in tuition might became even more expensive if MAS goes ahead with plan to allow S$ to weaken.
   
4. Have been a complete ass to my parents for the past two or three days.
5. Got that close to being SOL'ed yesterday.
6. Still worried about being rejected by DSTA. (see 3)
   
7. Nothing very useful is moving forward.
8. Google is offering an option, on the Dashboard, to Monetise my blogs. Since I am a perfectly ordinary Blogger user with no major distinguishing attributes, I'd wager they're offering that to all Blogger users. Somehow it stinks of rotten commercialism.
   

Somewhat ironically, I could really use a holiday, or some marijuana, right now.

I have a dream ...

... but it is unclear, faint, confusing at times, blurred at the edges, and sometimes in its entirety, as many dreams tend to be. So now what?

D'OH

'[23:52] [!] Zhuf (3100) Oh well, what the hell.: Proposition: for large enough q, (5*9^q + floor[(162/91) * (10*9^2q-1 + 81^(q-1) )]) ^ 2 \leq 3 ^ (4q+3) + 7 (4q + 3) - 4 \leq (5*9^q + ceiling[(162/91) * (10*9^2q-1 + 81^(q-1) )]) ^ 2
[23:52] [!] Zhuf (3100) Oh well, what the hell.: and now
[23:53] [!] Zhuf (3100) Oh well, what the hell.: we go on holiday
[23:53] [!] Zhuf (3100) Oh well, what the hell.: good day
[23:53] 77/44 - bahdotz...: WAD????
...
[23:54] 77/44 - bahdotz...: wad happens if p is 1 mod 4
[23:54] [!] Zhuf (3100) Oh well, what the hell.: you do get 2 mod 4.
[23:54] 77/44 - bahdotz...: no u dont
[23:54] 77/44 - bahdotz...: if not i would have solved the prob
[23:54] [!] Zhuf (3100) Oh well, what the hell.: yes you do
[23:54] [!] Zhuf (3100) Oh well, what the hell.: why dont you
[23:55] 77/44 - bahdotz...: -.-
[23:55] 77/44 - bahdotz...: something is very strange here
[23:55] [!] Zhuf (3100) Oh well, what the hell.: your mod p argument doesnt work though
[23:55] 77/44 - bahdotz...: 3^p = 3 mod p
[23:55] 77/44 - bahdotz...: 7p = 0 mod p
[23:56] 77/44 - bahdotz...: -4 = -4 mod p
[23:56] [!] Zhuf (3100) Oh well, what the hell.: mm.
[23:56] 77/44 - bahdotz...: sums to -1 mod p
[23:56] 77/44 - bahdotz...: the only p tt satisfies this is p = 3mod 4
[23:56] 77/44 - bahdotz...: or rather
[23:56] 77/44 - bahdotz...: 1 mod 4
[23:57] [!] Zhuf (3100) Oh well, what the hell.: um no?
[23:57] [!] Zhuf (3100) Oh well, what the hell.: like 13 is congruent to -1 mod 7
[23:57] [!] Zhuf (3100) Oh well, what the hell.: but not 2 mod 4.
[23:57] 77/44 - bahdotz...: as in
[23:58] 77/44 - bahdotz...: the only SQUARES
[23:58] 77/44 - bahdotz...: in mod p tt satisfies -1 mod p
[23:58] 77/44 - bahdotz...: is when p is 3 mod 4
[23:58] [!] Zhuf (3100) Oh well, what the hell.: hm?
[23:58] 77/44 - bahdotz...: 1mod 4*
[23:58] 77/44 - bahdotz...: grah
[23:58] 77/44 - bahdotz...: basically
[23:58] [!] Zhuf (3100) Oh well, what the hell.: oh
[23:58] [!] Zhuf (3100) Oh well, what the hell.: hey maybe that was the solution ><.
[23:59] [!] Zhuf (3100) Oh well, what the hell.: go figure.
[23:59] 77/44 - bahdotz...: -.-'

It's like carpet-searching a few hundred square kilometres to try and locate the enemy, and then finding out that he was squatting in your base with a dumb look on his face all this time, because you inadverently took him prisoner-of-war already some time ago.

"There's a sucker born every minute"

There are somewhere around 250 people born per minute, on average, all over the world. Taking David Hannum's statement (the usual attribution to P. T. Barnum is incorrect) at his word and quite literally, allowing a liberal margin of error of 100 percent, we find that about 2 out of every 250 people, or about .8% of the general population are suckers.
If we restrict the sample population to just the United States, we find that there are currently roughly 8 people born per minute there. By the literal estimation of Hannum's statement, 1 out of every 8, or about 12.5% of the population are suckers.
Such a low prevalence of extreme gullibility in the populace is, I aver, in fact cause for celebration. Or, of course, just a warning not to take things too literally.

Intellige

It would be a nice verb to go with intelligible, wouldn't it? To intellige: to comprehend with the intellect. It bears such striking and comforting resemblance to intelligent. Nevertheless, for better or worse, the word does not exist in the English language. Not yet, anyway.

System Disruption

Forgetting for the moment the tragic reality that there were two lives lost, this morning's crash involving a FedEx MD-11 at Tokyo Narita actually made pretty nice footage. Here's the landing ... we see the plane bouncing ... once ... twice ... and it flips over to the side and goes up in flames ...

A later Wall Street Journal article mentioned the matter of the packages on that cargo flight. Imagine being notified that your package which you just sent via FedEx to your friend in, say, the States just got destroyed in a crash at Tokyo. If you weren't familiar with the way international freight companies operated, it would come across as quite strange, no? You deposited the package at an outlet in Singapore, and then you know nothing about where it goes or what it does until someone tells you it has arrived, or else something completely out of the blue happens. It's almost as if the way of the world just got disrupted by some bizarre, off-the-book error.

History Lessons and Worldviews

'Japanese teachers begin with setting the context of a given set of events in some detail. They then proceed through the important events in chronological order, linking each event to its successor. Teachers encourage their students to imagine the mental and emotional states of historical figures by thinking about the analogy between their situations and situations of the students' everyday lives. The actions are then explained in terms of those feelings. Emphasis is put on the "initial" event that serves as the impetus to subsequent events. Students are regarded as having good ability to think historically when they show empathy with the historical figures, including those who were Japan's enemies. ...
American teachers spend less time setting the context than Japanese teachers do. They begin with the outcome, rather than the initial event or catalyst. The chronological order of events is destroyed in presentation. Instead, the presentation is dictated by discussion of the causal factors assumed to be important ("The Ottoman empire collapsed for three major reasons"). Students are considered to have good ability to reason historically when they are capable of adducing evidence to fit their causal model of the outcome.' (from Richard E. Nisbett's The Geography of Thought)

Our history lessons used to be a mixture of the two. Ms. Ng would present infomation in chronological order, essentially telling a story, during the lectures. Then during tutorials we would dissect everything, spread it around and recombine the parts in a rather more analytic framework. The consensus view of what historical thinking was was closer to the analytic version. In a way, it reflects Singapore's hybrid culture--and perhaps the slight tilt towards the West is indicative of RJ's relatively skewed position within the hybrid.
And then of course the Kwok was just being quite completely scatterbrained. What came out was more towards the American style overall, but not at all well-executed. Maybe that wasn't even his intended effect. I can't tell.

Sergeant

Frankly, I don't particularly like hearing a rank attached to my name. Especially my current rank. Because it reminds me of all the heavy responsibilities that come with it and all the bullshit one faces trying to carry them out; of all the great expectations or dim views that people have of it; of all the times those expectations and slights have been downright unreasonable and unwarranted, and, worse, all the occasions when you have failed to live up to reasonable expectations and vindicated those low opinions.
The positive thing to do would be to remember the lessons but not the sting, and to try my best to live up to the responsibility and expectations. But at some level, all the baggage the word carries will never go away.

Fantastic

Yours truly will be spending ten days in June roaming around Marseille, bits of Provence around the Luberon, Amsterdam and some other bits of Holland and Zeeland. Anyone who wants a postcard (though I suspect there are only two other people who will ever read this), please drop a note with your address.

Sere, Sear

Two forms of an adjective meaning, in both literal and figurative use, dry and withered. Don't the two forms feel quite different already? As if by the different spellings and different arrangements and geometries of the letters the whole bag of connotations changes.

Big Gahmen

The PAP Government is a little too big. Not big in the sense of being bloated and overbureaucratic, but big in a more subtle, insidious way. It is so big it pops up everywhere, in politics and beyond; to use a mildly sinister metaphor, it is like an octopus with whose countless tentacles turn up in every nook and cranny.
Most of the Republic's home-grown corporate giants are Gahmen-linked in some way, usually through Temasek Holdings. Statutory boards and other parastatals dominate many aspects of the social and cultural arena. So much so that when NTUC FairPrice announces a textbook donation drive, some attack it as a political power-play.
It hit me too in the course of my recent reading: so many of the Singaporean works I encountered were endorsed, in some way, by the National Book Development Council, which is linked to the Government's National Arts Council. Moreover Singapore's only literary, or indeed cultural, honours, such as the Singapore Literature Prize or the Cultural Medallion, are given by the Government. Not private trusts and foundations established by or in the memory of great personnages, as happens in the West.
There is no denying that the Gahmen here does a lot of things. A lot. Is this necessarily a bad thing though?
It could be, if it competes with and/or stifles individual initiative. The Chicago school loved to remind us that government, not being subject to market forces, would be liable to slack and inefficiency, and that individuals reacting to incentive structures could often do better. They added, as a sort of corollary, that the government should therefore only be doing what individuals left to themselves could not, or would not, do -- provide public goods, regulate externalities, that sort of economic thing. So if there are actually NGOs around who were/are planning to run / actually running something similar to FairPrice's textbook donation programme, FairPrice should quit it and go back to grocering.
The Chicago school's argument does not apply entirely, because The Gahmen and its minions are actually quite efficient creatures by nature; FairPrice is probably running as decently tight a ship with its charity programmes as with its core business. But nonetheless, by continuing to duplicate what civic society could do, NTUC, and, if you wish though it is a bit of a stretch, by extension the PAP, are needlessly expending national resources and stifling civic initiative. And the Gahmen wonders how to instil a stronger sense of civic duty.
In other areas, though, perhaps indeed no one else has done much -- think culture, though I may simply be ignorant. In this case Gahmen intervention, and domination, is understandable and to some extent justifiable ... but still it should aim to nurture and eventually make way for civic involvement.
In the preceding argument "civic society" has been treated as something independent of the government. That is, unforunately, not entirely the case in Singapore, so deep and wide have the Gahmen's tentacles spread. Is NTUC part of the state, or civic society? It is a bit of both really. And to make matters worse, it is the only trade union around here. Singapore's civic society, too, is dominated by the Gahmen. Maybe this was simply the consequence of politics over the decades after Separation ... but it is certainly not a desirable state of affairs. The Government doing much, in addition to civic society, can be a good thing; the Gahmen doing much, because it has supplanted and become civic society as well as government, is definitely not.

Way Spread Out

Someone's head is full of bits and pieces of nonsense at the moment.

Imagination and Geometry

Indeed, geometry is not just a discipline, it is an approach. It is not just the study of space, but an unique way of seeing nature and structure: through the visual image rather than cold, abstract logic. Through the act of imagination, in the sense of conjuring up visual images, It turns abstract semi-comprehension into more intuitive understanding. Coxeter was so right.

Where's the Development?

Popped by the NUS Museums today lunchtime, since it was just nearby, and ambled through their main exhibition, Constructed Landscapes: Singapore In Southeast Asia. It was about Singapore's links to Southeast Asia, as exhibited in visual art; most of the works were by Singaporean artists, though not all. The exhibition was interesting but rather small. Too small to be truly intriguing. I think an extract from the sparse commentary is indicative:
'Memory ... The works in this exhibition do not conform to a single ideal of landscape. They are perspectives engendered by particular experiential and perceived moments, some of which are contradictory to one another. Each work reflects the particular artist's sense of location and the prevailing milieu.'
Around there are scattered works by various artists in various styles. Like a series of snapshots, whose subjects, angles and treatment were chosen all at random. Not completely at random, maybe, but random enough, at any rate, for the pattern to be not easily comprehended. Or a small sample of what should be a much larger, more coherent, more organic body of work.
So now the question I would like to ask is: does that larger body of work actually exist, or is this apparent lack of development the result of larger and stronger factors than just bad, stingy curating?

Overdose of Poetry

Somehow Thumboo's poetry doesn't seem to be very appealing ... it is just too particular. Supposedly the best literary works start from the particular and transcend to the universal. Chinese has a very apt expression for this: 浅入深出. But the particular in this case just seems to overwhelm everything, a huge surrounding sea of names and details that don't particularly connect ... Or maybe I just don't get enough of the references.
Also, Pushkin goes down more smoothly in the English translation than in the Chinese.

Strategy

Matthew's father was a particularly formidable opponent at chess when I played him. He won the first two games easily and was well on his way to taking the third when life interrupted. "You have to figure out what your opponent is trying to do through his moves," he advised.
Very good advice. But not quite complete: before you apply it, first think, very carefully, do you know what you yourself are trying to do through your moves? 知己知彼，百战百胜 ... truly that is the most important thing, awareness. And--do you have any strategy at all? Or are you, like I have been all this time, only reacting to the last move made, responding to the immediate situation?
Maybe depth-free greedy algorithms work very well in some contexts, but life in general is probably not one of them. Please, please, find a direction.

Ignorance is Bliss

'The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents. We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far. The sciences, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of reality, and of our frightful position therein, that we shall either go mad from the revelation or flee from the light into the peace and safety of a new dark age.' -- H. P. Lovecraft, The Call of Cthulhu
Kind of reminds one of the Total Perpsective Vortex from H2G2: ' ... if life is going to exist in a Universe of this size, then the one thing it cannot afford to have is a sense of proportion.' (Chapter 11 from The Restaurant at the End of the Universe)

In Memoriam

Somehow it suddenly came to mind that today is the fifth anniversary of the Madrid train bombings.

Slowly into Atonia

Haydn was excellent. Shostakovich was comprehensible. Schnittke was just ... strange. It had hints of atonalism, but just when they started to really show the old tonal system comes back ... with some minor distortions. The strings in a strange dissonance, trying to 'explore the difference between C-sharp and D-flat'. It can almost stand as its own idiom of sound, actually. Tonal and atonal and semi-tonal in quick succession, all at once ... polystylic, indeed.
Also, there seemed to be very few people in the audience with Singaporean accents. Quite sad, really.

Three Poems

m&ms

me mumbling mama
music to her ears
first child first words
mamas make believe
first mumbles are their names
maybes mostly missing
meaning mostly masked
mumbling morphing into mumurs
me discovers magic
first book first words
mess of marks that manage meaning
mystery making sense
magic making way for
matter mass and molecules
maddening mathematics
morebooks more words
magic mostly missing
meaning mostly masked
mighty man to meek mouse
mumbling marriage vows
modals may I might I
middle spreading ageing
muttering magic spells
mystery mostly missing
meaning mostly masked.

Last book last words,
the mask falls away.

Feathers

Show your colours,
fly united.

Feathers are passports
to a community;
acceptance and strength in numbers,
but only if you have feathers
of the same colour
the same texture
the same quality
of the flock you want to
fly and roost with.
But if your feathers are
marked
spotted
damned
with patterns no flock
seems to understand
or want;
if everyone is in shades of paradise
and you are the only one in
colour of the
fields
woods
mountains --

But feathers are instruments of flight,
travelling clothes
for running light and warm;
feathers not to join
but escape from
sameness
conformity
flockishness of safety in numbers;
feathers to set you apart and be your mark
of courage
as you turn
into the wind
and soar.

Show your colours,
fly solo.

The Brave Heart Opens

The brave heart opens; the frightened one
stays closed, afraid to upset the
balance the head is used to.

The brave heart opens; to life
and living to death and dying, knowing
yet not fearing.

The brave heart opens; to love
in giving and taking, to holding
and losing, fearing yet still loving.

The brave heart opens; to parents
friends and teachers, seeking to be
with, yet never afraid to be without.

The brave heart opens; to God
if He is there, hoping that He is,
but not fearing if He isn't.

- Colin Cheong

The Listeners

‘Is there anybody there?’ said the Traveller,

Knocking on the moonlit door;

And his horse in the silence champed the grasses

Of the forest’s ferny floor:

And a bird flew up out of the turret,

Above the Traveller’s head:

And he smote upon the door again a second time;

‘Is there anybody there?’ he said.

But no one descended to the Traveller;

No head from the leaf-fringed sill

Leaned over and looked into his grey eyes,

Where he stood perplexed and still.

But only a host of phantom listeners

That dwelt in the lone house then

Stood listening in the quiet of the moonlight

To that voice from the world of men:

Stood thronging the faint moonbeams on the dark stair,

That goes down to the empty hall,

Hearkening in an air stirred and shaken

By the lonely Traveller’s call.

And he felt in his heart their strangeness,

Their stillness answering his cry,

While his horse moved, cropping the dark turf,

’Neath the starred and leafy sky;

For he suddenly smote on the door, even

Louder, and lifted his head:—

‘Tell them I came, and no one answered,

That I kept my word,’ he said.

Never the least stir made the listeners,

Though every word he spake

Fell echoing through the shadowiness of the still house

From the one man left awake:

Ay, they heard his foot upon the stirrup,

And the sound of iron on stone,

And how the silence surged softly backward,

When the plunging hoofs were gone.

-- Walter De La Mare

Ruminate

Has your pet squirrel been chewing the trees lately?
(Botany) Presenting a chewed appearance; permeated by striæ; striated, marbled.

Inform

Did you know it could be an adjective as well? Then it is read as in- + form: Not endowed with form, nebulous and formless.
'The budding of the seed, the change of wind, / The inform steps of age ...'

几何与想像

不久前在网上找到一套标题为《几何与想像》的教学材料，这几天刚开始看仔细看。这套教材相当有趣，它是由四名很有成就的几何学家编的（其中包括约翰 · 康威和威廉 · 瑟斯顿），用于明尼苏达州立大学的几何中心开办的一门课程。课程标题同样为《几何与想像》，名副其实，它的主要目的在于启发与提升学生、读者在几何方面的想像能力，让他们从而对各种几何形状与几何概念获得更深、更全面、更扎实的了解。
例如教材前面部分有一系列关于正多面方体（即柏拉图立体）的问题。让正四面体竖立在一个顶点上，其最高点与最底点半当中的横截面回呈现什么样的形状？让正八面体卧在一面上，同样的横截面又会呈现什么形状？在正十二面体的二十条边上行驶，能否找出一条路，让我们从一个顶点开始，当中没有重复地探访所有其他顶点，最后回到我们原来开始的顶点？若是二十面体呢，我们能从它的三十条边中拼出这样的一条路吗？
思考着这些问题时，我对这些立体奇特的素质有了深深的体会。Their symmetry is truly startling. The same number of edges and faces meet at any one vertex, at the same angles. Each of the Platonic solids thus looks exactly the same from any one of its vertices, or from any one of its edges, even the icosahedron with its thirty edges and twelve vertices. There isn't only symmetry in each of them, there's symmetry among the five of them: the dodecahedron has twelve faces and twenty vertices, the icosahedron twenty aces and twelve vertices, and both have thirty edges. Their graphs are dual. Same for the octahedron and the cube ... and the tetrahedron is its own dual. When such symmetry as such, in dry, compact words, it is merely an interesting fact. When one discovers it for himself (or herself) in the process of visualising, realising these solids in the mind's eye, it becomes an source of sheer wonder.
在这以前两个星期还在做竞赛题目，做到头昏脑胀还做不出。通常思考到后来就开始思路模糊不清，已经被发现行不通的旧思路反复地在脑子里转，新思路怎样也想不出。归根结底，大概是因为不完全理解而缺乏想像力。不了解题目的根本，没有想像力得出新的思路，结果一直钻牛角尖，捉不住解题的关键。
在这样的情况下，预期继续闷头死做题目，远远不如通过类似与《几何与想像》的教材来培养想像力与数学直觉。