Re: Efficient packing in an elevator

I was amused to see another guy jump from one corner of the elevator to the opposite corner of the elevator.

Don't really have a solution to this problem yet. Shall work on it in my spare time. Hmz, maybe I can write this up for my game theory class ...

Efficient packing in an elevator

What is the most efficient method of packing in an elevator? More specifically, lets say an apartment building has N(=36) stories and you stay on floor n(=29). When you enter an empty elevator, where do you stand?

What are some factors to consider?

1) Is there anyone else entering after you? If so, you shouldn't block the door

2) How far in should you move? You'd have to walk that distance out again.

3) You'd want some personal space between you and the other person. This space should be approximately equal.

4) As the elevator empties, you'd want to maintain an approimately equal amount of personal space.

5) Clearly, the elevator patterns of latter passengers should influence your decision.

6) And what is the elevator is not empty? Has your elevator patterns influenced those who were in the elevator?


Clearly, I have way too much free time to be thinking about such stuff. Well, its just a distraction so that I don't think about other stuff.

Boo

A week has passed and I’m heading back towards Chicago. There’s about another hour to the Narita leg of this flight, and then another 11 hours more of being up in the air. I managed to see a sortof sunrise on the plane, and it’s so beautiful. I’d love to do more sunrise watching this spring and summer, as and when I can afford the time. Seeing that stretch of fish stomach white expanding across the horizon, basking in the glow of the sun, sharing the moment with friends.
Let’s see, what thoughts do I want to pen down?

I’m such a kid, but one that’s growing up. My last real (as compared to nominal?) growth spurt was in NS, and I think I’m due for another. Of course I’ve been growing gradually in the past 4 years, and have friends to thank for lighting the way. These past 2 quarters have been some very interesting times; Job search, Price Theory, Wei Ren’s death, meeting Hunter, touring SF, talking with sbf, hearing about Joshua, (not) learning differential topology or commutative algebra and coming back home to Singapore. This upcoming quarter would be a challenge of classes and adjusting towards work; such different lifestyles, such different scenarios. Ah yes, I have to figure out what classes I’m taking, and what the schedule is. I should consider Nori’s 9am class, just so that it forces me to deal with waking up early. Oh, someone please remind to shave on Thursday. I’ve Optiver events over the weekend, and I think I should be somewhat presentable at least. The good thing about staying in Chicago is that I won’t miss Thursday’s classes too

Oh, there goes the threat to destroy all electronics that are not switched off. Oh, so apparently my battery has lost its ability to charge past 70%, though that could be a fault with the Singapore electricity supply… Okie, 2 hours more to this flight, and the sunrise would be on the wrong side (aka left) of this plane. Don’t think I’m time adjusted, even though I slept through half the flight. Ended up watching 7 pounds (bad) and slumdog millionaire. I have yet to understand what the big hoohah in SM really is about. I mean, its good, but X Oscars good? Hm, well, not like I know what the other competition this year looks like. Okie, back to more thought dumping.

Intro to Finance course. The only undergrad course last quarter, hence by definition, the easiest. Didn’t spend much time on it, but the concepts were easy to grasp. Well, once you get them in the correct setting and understanding, the rest would follow. Didn’t do well for the midterm due to numerous careless mistakes that I made. Did well enough for the final (which dropped the midterm grade) and I managed to scrape through. Why am I blabbering about this? Well, I felt that the course on the whole was very easily understandable, and that it shouldn’t be that hard to do well in it. So, once again, why do people have trouble in the courses? I’d admit that Fuchs wasn’t all that good a teacher, and several times the concepts were somewhat unclear and required looking through again. However, he did have good questions which aided understanding. (Sounds so much like Shumel lol) Well, hopefully work would be like that, smooth and easy sailing lol.

What I did over the week. Met up with a whole bunch of other people. Ate 1 box of durian on the car trip home. Spent Friday at home with parents and played MJ with sis at night. Taught induction at SIMO (and had a nice list of non-immediate problems), met up with Chicago seniors in the night (and played MJ). Had Sunday lunch at grandma’s place, which was good chicken curry, yam balls, lotus soup. Then went to buy shoes, to replace my holed ones. Met Mrs Soh for Monday lunch, and that was a good 2.5 hour conversation about Singapore, education, climate, economic crisis, people. Met Thomas Teo for dinner, who brought us to dian xiao er, and was another nice conversation, though more around math stuff. Met boon for tues lunch, and then my Chicago army mates for dinner. Weds lunch was Edmund, and dinner was Chengping at Ding Tai Feng, who gave me a treat and got a pleasant surprise in return. Gave her a postsecret book, which is a site that I quite like. Met Aunty Jenny for Thrusday lunch at Sakura, and then visited grandpa in the evening and had fish head curry and whatnots. Mum cooked Friday lunch, and met Kianboon for tea and Miss Tang + Rachael for dinner. Would be sad to miss R’s wedding in June, but oh well. Sat morn was spent with parents again, and we went out for dinner at Lao Pa Sa. Yup, that about summarizes how I spent my time. Oh, add to that like 5 boxes of durians and 50 X 40 mins of Sie Diao Ying Xiong Zhuan. And of course, lots of chatting too.

At some point in time, I’d be inclined to pen down some of my thoughts about the current economic situation. It would certainly be useful to do so, esp given all that’s currently happening. Haven’t kept up with much of last week’s events, though it seems quite quiet, at least on the surface.

1. I expected oil prices to rise to $80 at the end of the year, but given developments in the past months, I’d revise that downward to $60. And if the economy recovers by the end of next year, it should be at $80 then. How did I arrive at these numbers? Magic lol.

2. I’m amazed at the effect that propaganda has on the economy. Take Singapore for example – In terms of news information received, it is amazingly sheltered from the true extent of the global recession/depression. It’s also reported that the unemployment rate is still beneath 5% (which is technically full employment), but I doubt that such is true. Teenagers are still going on massive shopping sprees, without regard to the diminishing expected paychecks of their parents. Uni grads are now beginning to worry about not finding a job (which they should have done since last October at least) Well, there would be a bumper crop of teacher applications this year, which might end up being harmful to the overall quality instead

3. China’s call for a world currency is just an initial step. Well, their buying spree of raw materials would come before that. I wonder what’s up their sleeves, but its good that they are taking advantage of this situation, to grow from being a follower to a player. Given China’s massive investment in US treasuries, they would be severely affected by a weakening dollar (US’s declaration that it would buy up treasuries led to about a 2% drop in its currency). This is especially true as their domestic market isn’t developed, and products from their industries have to be mostly exported. But in a world that’s increasingly becoming protectionist, such is hard.

4. Let’s model protectionism as a Prisoner’s Dilema. In this simplistic setting, since we are in a game with finitely many turns, everyone would choose to take P instead of B, which is what we’re beginning to see. While the ‘Buy US’ clauses were toned down, they set the initial ground and biased more people towards P as retaliation. Then came Gordon Brown decision to protect British jobs, and the EU’s decision to not orchestrate a massive bailout of its territories.

William Blake - Auguries of Innocence

I only knew of the first paragraph, so here it is published in its full glory for rest who are as ignorant as I was.....




To see a world in a grain of sand,
And a heaven in a wild flower,
Hold infinity in the palm of your hand,
And eternity in an hour.

A robin redbreast in a cage
Puts all heaven in a rage.

A dove-house fill'd with doves and pigeons
Shudders hell thro' all its regions.
A dog starv'd at his master's gate
Predicts the ruin of the state.

A horse misused upon the road
Calls to heaven for human blood.
Each outcry of the hunted hare
A fibre from the brain does tear.

A skylark wounded in the wing,
A cherubim does cease to sing.
The game-cock clipt and arm'd for fight
Does the rising sun affright.

Every wolf's and lion's howl
Raises from hell a human soul.

The wild deer, wand'ring here and there,
Keeps the human soul from care.
The lamb misus'd breeds public strife,
And yet forgives the butcher's knife.

The bat that flits at close of eve
Has left the brain that won't believe.
The owl that calls upon the night
Speaks the unbeliever's fright.

He who shall hurt the little wren
Shall never be belov'd by men.
He who the ox to wrath has mov'd
Shall never be by woman lov'd.

The wanton boy that kills the fly
Shall feel the spider's enmity.
He who torments the chafer's sprite
Weaves a bower in endless night.

The caterpillar on the leaf
Repeats to thee thy mother's grief.
Kill not the moth nor butterfly,
For the last judgement draweth nigh.

He who shall train the horse to war
Shall never pass the polar bar.
The beggar's dog and widow's cat,
Feed them and thou wilt grow fat.

The gnat that sings his summer's song
Poison gets from slander's tongue.
The poison of the snake and newt
Is the sweat of envy's foot.

The poison of the honey bee
Is the artist's jealousy.

The prince's robes and beggar's rags
Are toadstools on the miser's bags.
A truth that's told with bad intent
Beats all the lies you can invent.

It is right it should be so;
Man was made for joy and woe;
And when this we rightly know,
Thro' the world we safely go.

Joy and woe are woven fine,
A clothing for the soul divine.
Under every grief and pine
Runs a joy with silken twine.

The babe is more than swaddling bands;
Every farmer understands.
Every tear from every eye
Becomes a babe in eternity;

This is caught by females bright,
And return'd to its own delight.
The bleat, the bark, bellow, and roar,
Are waves that beat on heaven's shore.

The babe that weeps the rod beneath
Writes revenge in realms of death.
The beggar's rags, fluttering in air,
Does to rags the heavens tear.

The soldier, arm'd with sword and gun,
Palsied strikes the summer's sun.
The poor man's farthing is worth more
Than all the gold on Afric's shore.

One mite wrung from the lab'rer's hands
Shall buy and sell the miser's lands;
Or, if protected from on high,
Does that whole nation sell and buy.

He who mocks the infant's faith
Shall be mock'd in age and death.
He who shall teach the child to doubt
The rotting grave shall ne'er get out.

He who respects the infant's faith
Triumphs over hell and death.
The child's toys and the old man's reasons
Are the fruits of the two seasons.

The questioner, who sits so sly,
Shall never know how to reply.
He who replies to words of doubt
Doth put the light of knowledge out.

The strongest poison ever known
Came from Caesar's laurel crown.
Nought can deform the human race
Like to the armour's iron brace.

When gold and gems adorn the plow,
To peaceful arts shall envy bow.
A riddle, or the cricket's cry,
Is to doubt a fit reply.

The emmet's inch and eagle's mile
Make lame philosophy to smile.
He who doubts from what he sees
Will ne'er believe, do what you please.

If the sun and moon should doubt,
They'd immediately go out.
To be in a passion you good may do,
But no good if a passion is in you.

The whore and gambler, by the state
Licensed, build that nation's fate.
The harlot's cry from street to street
Shall weave old England's winding-sheet.

The winner's shout, the loser's curse,
Dance before dead England's hearse.

Every night and every morn
Some to misery are born,
Every morn and every night
Some are born to sweet delight.

Some are born to sweet delight,
Some are born to endless night.

We are led to believe a lie
When we see not thro' the eye,
Which was born in a night to perish in a night,
When the soul slept in beams of light.

God appears, and God is light,
To those poor souls who dwell in night;
But does a human form display
To those who dwell in realms of day.

Boo

And so it appears that, once again, the only time I have to blog is aboard an airplane. Got a roundtrip ticket with ANA for US1200, and am currently on the Tokyo-Singapore leg of my trip. It has quite decent food; and even serves Hagendaz ice cream which pleases kids to no end. Got a big craving for durian on the flight, and so while I was in Narita, I got my sis to get my parents to bring durian along to the airport LOL. It’s been 1.5 years since I’ve been back, and possibly some time again before I head back again. Would be meeting up with quite a few people this trip back. Days up to weds have been planned and booked already lol.

Read John Grisham’s The Appeal. Typed up Induction notes for SIMO training - Am very excited to be hosting this Saturday’s session. Followed that with watching 3 movies - Changeling and message in the bottle (both of which made me tear) and The Professer and his beloved math equation (a jap show that wasn’t going anywhere with anything). Took quite a few naps too, hopefully I’d be time adjusted and ready to hit the ground running (Well technically, I should be sleepy since I land at midnight)

Have yet to submit my Topo take home final, more or less done with it in the sense of not working on it anymore. But should just glance through it and ensure that things are properly written up. Interesting fact: I was supposed to prove the divergence theorem, but had no idea what it was. Went online and did a search, and apparently found a wrong one (well, it was a corollary) and proved that instead. Luckily Lucas pointed that out to me, and hopefully what I have now works. Spent about 4 days on this final, and am quite proud of it; worked through 2 interesting questions.

Algebra was bad since I have had no freaking clue what has been happening for the past 3 weeks. Sigh. It’s a strange consolation that I’m not going to do a PhD in Math. Well, that’s why. Finance final was better, considering that I spent only 24 hours on it. But then again, as with the midterm, I could have made numerous stupid mistakes without realizing them.

Oh, there goes a PA announcement (in Jap first). Its 1.5 hours to touchdown, and would be landing slightly ahead of schedule. On the Chicago-Tokyo leg, we were initially stuck on the ground for like 2 hours, cos there was some maintenance problem with the air-con. And then they refueled to fly further south, which allowed them to reduce travel time slightly, though increase fuel consumption as they fly over water. We were flying over this snowy mountainous region which was so beautiful.

Perhaps I should stop reading reports about airplane crashes; like the recent one which had a highlighted maintenance problem with the engine but was sent off. Well, the thing I hate about airplanes is takeoff, landing and turbulence (Well, apart from the crammed seats that is). Nowadays, I try and sleep takeoff and landing away, which generally works. But the landing in Narita had quite a bit of turbulence (okay okay, very slight), but that still threw me off slightly. But I love taking off and landing in Singapore at night and seeing the citylights.

Well, mostly I have been too busy to blog. This past 10 weeks went by just like that. Not that it was slow or fast, but each day had its own set of tasks to do. Like Thurs and sometimes Tues/Weds would be devoted to algebra, while Sunday and Monday would be set aside for Topology. This quarter has also been quite a roller-coaster of emotions, with everything that has been happening. San Fran seems like barely a month ago, though its more like 3. But in a certain sense, this past quarter has been a quarter of growth and learning about myself, many thanks to the various parties involved. Let’s see what next quarter brings.

In the long term plan of things, I’m somewhat confused and lost. It’s more of I have no idea what’s the course of action that would make things work out. I have been lucky with various turn of events, but the element of luck is too finicky for me to work with. Airplane rides are also somewhat useful for thinking things through, since I’m stuck there with not much to do. When I get back, I have to do my OPT application, Tax forms, Optiver administrative stuff … Hmz, I should add Optiver as an actual word to Microsoft lol. Okie, added. The first two weeks should be somewhat hectic.

Next quarter, apart from my Algebra and Topology, would most prob be taking Game Theory, a second year Econ grad class. Which proves that I can always up the intensity of my courses from the previous quarter. It has been a mad 4 years, and I’m extremely thankful for my time here. When I look back, while I can’t pinpoint what it was that I exactly learnt (esp for algebra and topology lol), I know it has provided me with a way of approaching and thinking and dealing. I would be quite excited to see an application of Abstract Algebra in econs actually. Shmuel showed an interesting application of fundamental groups to the economic social choice function. He even has a paper on it which I should look through when I have the time/understanding.

Okie, my lappie declares that its time for me to stop blabbering, and so I will. See you again in a week!

A blast from 5 weeks ago

As you can tell, this post was written up a long time ago. Shrug.

Boo, and yes, once again I’m back in the air. Or rather, for now, I’m stuck on the ground in front of the gate for another 2 hours or so. Got here early, and have nothing else to do but rot. Hmz, I wonder if I would be willing to pay $5 for wireless internet. But guess not LOL. Besides, its too confusing to figure out Tmobile’s hotspot access and payment, so shall content myself with more dumping of thoughts. Of course, there is always the alternative of going to play some game (but being mouseless, it limits my possibilities) Now now, lets see …
SF
Was a great trip of relaxing. Came here for 4-5 days with Sibo and Ghee Chuan, where we roamed the city and such. Went clubbing in Castro on the first night, went to Chinatown twice for dimsum, watched Milk in Castro Theater, which was along the street that it was filmed. Watched doubt too, which was good, though I felt that they could have gone slightly further with the plot. Well, perhaps the intention was just that. Had a whole cracked crab seafood dinner, mmmm. I miss my seafood so LOL. Oh well, shall ask Ivan to steam fish at some point in time. Oh, and frascati too, however you spell it. It’s apparently a very popular restaurant, and it’s somewhat amazing that we managed to get seats when we went there, dressed as students do LOL.
After they left, met up with M who hosted me for a few days. Watched ‘A Christmas Carol’ at the ART Theater, which was (full of kids) and quite boring. Well, its not like much more can be done with the story of Uncle Scrooge. Sat next to an evolutionary biology major from Virginia, and one of my first questions was ‘So, is there a contradiction between evolution and biology?’ Haha, I need to curb my instinctive trouble-making nature. Went to big sur to see the coast, drove over golden gate bridge through muir woods, wehnt for more dimsum at yank sing, and generally just lazed around. Did a lot of tv watching (and need to redirect my hulu queue alerts to another email add). Apart from heroes, House, Bones, think I might be adding Legend of the Seeker to my list. It’s based on Terry Goodkind’s Sword of Truth series, which is very well written. Tofu freak is quite a big fan of it, but I’ve put it off due to the thickness of the books, and that its an uncompleted series. (Yes, I’m still irritated with Robert Jordan Wheel of Time). Slept on the couch, and can’t wait to get back to my bed.
Back to Chicago
Theres been a huge snowstorm in Chicago, and I’m wondering if that would affect my travel plans. Hopefully not, but one never knows. Gonna crawl back into my bed (after turning on the heat that is). Hmz, still have about 1.5 weeks left in Chicago before school starts. Will need to vacuum my room (with the Roomba of course), and clean up the place slightly. Shall attempt to watch Wicked, head to the art institute, shop with the ‘oh-we-didn’t-sell-enough-over-christmas/NYE’ sale, keep up with news again. Oh god, I think the Bush-Iraqi journalist-shoe incident is particularly hilarious. Oh, and possibly lose some SF weight too. I wonder how the markets would do over the next 2 weeks, given that its Christmas/NYE, and fewer people would be in the office (unless of cos, leave has been revoked)



Classes
Will be taking commutative algebra with Nori and differential topology (whatever that is) with Shmuel. Need a third course, which is likely to be Intro to Finance (assuming I can get into the class by scaring other people away). Oh, and my thesis … have yet to write up a plan for Grace/Lima, will be one of the first things I do when I get back. Oh well, might do that on the plane too, summarizing what I have from the powerpoint presentation, not like I did anything much more on it. Sigh. Too little time with too much to do. Also, I wanna be lazy HAHA. I think the proper compromise would be to contact Ali, and run the experiment, and leave it at that. It would be a good one-time experience in conducting an experiment, in order to obtain information that theory is unable to give an answer to.
Future
Well, this post seems to be very forward looking. However, I’m still uncertain about what the future holds for me, or even, what I want from it. I’m sure that there are lots of possibilities open for me, and it’s a matter of what I want to grab. To answer a long-ago posted question, I think that especially because I’ve seen what is available, I know that it is not exactly what I want, and thus would have to search for an alternative way. My long term goals are simple: To be happy. Of course, this begs the question, what does it mean to be happy? There would be several avenues of my life that has to be fulfilled, in terms of academic standards, living standards, achievements, balh blah. Being goal-oriented, I have to content myself with small steps that I can take first, and hope that they eventually lead to a big overall picture. At least I have seats on the airplane, and do not need to wait to be assigned a seat on the full flight, while watching first-class passengers board.

harlow once again

And so once again I’m up in the air, signaling an end to the quarter that has gone by. (And now I’m wondering if my parents know that I’m travelling. Well, you’re now informed.) It was an incredibly fast 10 weeks, hit the ground running when school started and things just went on from there. Haven’t had time to record down my thoughts, which was what this is for. So this would be a potentially long entry, depending on what I have to say (and once again, you’re not obliged to read it all). Oh, and don’t count on any regular updates for the next year either.

Grad classes
Was taking 3 grad classes this quarter, which was definitely a lot more than I could afford to bite off. Algebra, Topology, Price Theory. Topology was completely brand new, I really should have taken the undergrad course beforehand, to have gotten exposure to the ideas and such. Still, I think it went fine overall, along with all the weekends of bunkering down and attempting to understand what was being taught. Didn’t really like the way Farb was presenting his arguments without much solid proofs, and am not all that sure that I understand the ideas of homology, cohomology and homotopy. The last two in particular are still quite shaky, but I think I managed to apply them somewhat successfully in the final. I’m glad for getting to know these ideas, having heard of them from Jonathon and Lucas, and seeing them fleshed out in greater detail. What are its applications you may ask? Well, one never knows. There would certainly be possibilities in game theory.
Algebra with Ginzburg was slightly better, but only because some of the material was covered by Nori earlier. Seeing representation theory, Classification of PID, Jordan normal form, Wedderburn theory, etc, once again was good. Which reminds me, I need to get my notes back from Sue at some point in time. The homework sets were a good test of understanding and application, and working with the group of undergrads certainly helped me. Though, I would always prefer to have a better understanding of algebra, and my concepts of it are still but mere grasps of straw. Made some really careless mistakes on the final, but oh well.
Price Theory certainly suffered the most. It was well taught by Gary Becker and Kevin Murphy, in terms of modeling of economics and seeing various ideas come together in some coherent framework. But as algebra homework was due on the same day as Price Theory, it often ended up that price theory was neglected to deal with algebra, or interviews. In the end, I took it for a Reading grade, also because I didn’t have time to prepare for the final.

Thesis
Something else that I might not have the time for. Sigh. I actually do want to carry out the experiment to see the results. I might just do it, but then not complete the thesis. Though actually, there isn’t much to it, but just carrying out the experiment. Will see how that goes. I’m really undecided on this, really really want to see it through. In other news, Ali has my penultimate draft, which he’d look through before we email it to Crawford for a reply. After one iteration, we’d look at which possible journals to submit it to. Will see how it goes, failing which I have a thesis paper more or less written up.
Knowing myself
The closing of a chapter of my life only leads to the opening of another door. My exploits in competition mathematics is almost certainly over, definitely for the position of a participant, with the Putnam last Saturday. Did the best that I could have on it, and am very happy with how things turned out. With any luck, I’d be able to pick up $250 again, though it was a somewhat easier year and cutoffs are going to be higher. Then again, it’s not like I really care. I’m glad for the experience and exposure that I’ve had been given, which has so dramatically changed my life. I’ve waxed lyrical about the professors, my teammates, the IMO experience, my brats, the questions, the techniques, the ideas. I actually went to the extent of sharing my favorite homotethy question (the title of this site) with one of the Optiver interviewers (and yes, I had prepared to talk about it beforehand)
I’m really glad for the bunch of friends that I’ve found here. I will certainly miss them when we graduate, though I’d be rooming with Sibo next year. The river of life has its tributaries and distributaries, people that come in and out of my life, leaving indelible footprints in my heart. I’m happy I finally made it down for dinner on 10th week Tuesday, though I was really tired out and hiding my tension under the table. All things have their time, and I think it’s a good time. Right now, my future is so uncertain (but certainly bright and unlimited). I think I’d take Weiwei’s suggestion of relaxing control for the moment and falling. It’s scary, like a roller coaster, but also exhilarating.

On a sadder note, this entry would not be complete without a paragraph about Wei Ren. I remember a conversation at the end of spring quarter last year, where we were talking about graduation plans, work opprortunities, student loans, life. I’d certainly miss seeing him on the East bus, or even in the halls of Eckhart. I’d like to thank H for helping me work/talk through this.

Wicked is going to end its Chicago leg in a month or so. I might drag myself down to watch it over winter break, awaiting the lottery tickets. Here’s a slight tribute to it:


GALINDA:
What is this feeling,
So sudden and new?

ELPHABA:
I felt the moment
I laid eyes on you;

GALINDA:
My pulse is rushing;

ELPHABA:
My head is reeling;

GALINDA:
My face is flushing;

BOTH:
What is this feeling?
Fervid as a flame,
Does it have a name?
Yes! Loathing
Unadulterated loathing