Simply

A floor not pillow suffices
warmth is from you the source

Good food my soul nourished
I more cannot ask for

Kids grow and leave me off
with me one grows old with

What I need I only take
often less more never

Probably

The probability of a probability of an event
occuring remains a probability that always
spans from zero to one, a space large enough
to accept minus infinity to plus infinity.
Where one might allude, insinuate or even
contradict if one has a correct number preceded
by words such as even though, provided that,
given that, who, and last but not least if.

It can be either A occurs given B occurs, or
the other way around, that is a probability
that B occurs given A occurs. And believe
me they are not the same. It can be either
the union or the intersection or the complement
or any combination thereof. And yes, counting
the number of events depending on permutations
and combinations almost always yields a huge
number that no one - almost always also - never
checks – as it is astronomical. So, forward your
arguments as tightly and cleanly as possible.

All of these are not nonsense, if you believe
in polls, weather reports, stock market, and
the odds your mom met your dad a long time
ago. And eventually marrying him. A lesson to
always think about the other side, the alternative,
the what-if, the what-not, the what-the-fuck.
As nothing is never trivial even the impossible.

Calgary

I live in a city at the foot of the Rockies, where the sky is
        the bluest of blue,
      June descends as hails the size of pebbles,
     winter lasts half a year despite chinook winds.
It taught me that west coast is my playground:
valleys and ridges with indelible names, winding roads punctuated by
   alpine lakes and campgrounds.
Where ever I go I miss my Yoho, Kananaskis, and Kootenay.

Rare it was to find candlenuts, shrimp chips, and red chillies,
yet they are now as easy as tzatziki, guacamole, mirin, and hummus.
They mingle, enhancing each other, so I sip tamarind soup with
soba noodles; bacon with red chillies could be next to try.
Its gastronomy expands, culture evolves. From cowboys of
           foothills and prairies to globe-reaching
petrochemical and energy exploration.

I was not from around here: a furthest point from my birthplace:
           a fate sealed by another luck.
I have grown to embrace this land:
       A huge mass cradling the Arctic, sheltered from perils of
global warming, political upheavals, international trade disputes.
A fortress cursed by luck of geography:
     northern edges of two vast oceans, impenetrable floe archipelago.

Octavio Paz's A Tree Within

A tree grew inside my head.
A tree grew in.
Its roots are veins,
its branches nerves,
thoughts its tangled foliage.
Your glance sets it on fire,
and its fruits of shade
are blood oranges
and pomegranates of flame.

Day breaks
in the body's night.
There, within, inside my head,
the tree speaks.

Come closer––can you hear it?

Why I Love Poem

A stomach a poem surely never fills

For it amply rewards the time food gives

I wager with you my dear true friend

Prettier a poem than the prettiest song

Picture is worth a thousand words say you

A thousand memories a poem is worth

It does not dance nor promulgate noises

With the quietest intent it softly speaks

It charts moments locations I write

For the deepest thoughts I have of you

e e cummings' poem

may my heart always be open to little
birds who are the secrets of living
whatever they sing is better than to know
and if men should not hear them men are old

may my mind stroll about hungry
and fearless and thirsty and supple
and even if it's sunday may i be wrong
for whenever men are right they are not young

and may myself do nothing usefully
and love yourself so more than truly
there's never been quite such a fool who could fail
pulling all the sky over him with one smile

Conditional Probability

Suppose we have two related questions:

(a) A family has 2 children. What is the probability of having 2 girls for the family?

(b) A family has 2 children. What is the probability of having 2 girls given that one of the children is girl?

Question (b) has a conditional probability element, while (a) doesn't. To answer (a), we need to list 4 possible cases of having 2 kids: gg, bg, gb, and bb. (b = boy, g = girl.) The probability is thus 1/4 for (a).

We only have 3 possible cases for (b): gg, bg, gb, so that the probability is 1/3.

The notion of conditional probability is the first hurdle for students taking the probability and statistics course I teach this term.

We write P(B | A) for the probability of B to occur, given that A occurs,

P(B | A) = P(B ∩ A)/P(A),

where B ∩ A means both events A and B occur.

If we want to apply this formula to answer part (b), then P(B ∩ A) = 1/4 since there is only one case (gg); P(A) = 3/4 since having 1 girl can happen with first child (gb), second child (bg), or both girls (gg). 

The formula P(B | A) = P(B ∩ A)/P(A) is counterintuitive though, so I would write it as

P(B ∩ A) = P(B | A) P(A).

That is, the probability of having A and B to occur is equal to (i) having A to occur, and (ii) having B to occur given A occurs. The last expression gives more clarity since if A and B are statistically independent, then

P(B | A) = P(B),

so that when A and B are independent, P (B ∩ A) = P(B) P(A).

Depending on available data, any P(B ∩ A), P(B | A), or P(A) can be computed, but clearly we need to know two in order to solve for the third.

Another useful probability formula is

P(A ∩ B) = P(A) + P(B) – P(A ∪ B),

where A ∪ B means either event A or B occurs.

The conditional probability can be used to answer an unconditional probability. For example, the probability of picking for the first time an odd number from the 5 numbers: 1, 2, 3, 4, 5 is 3/5 since there are 3 odd numbers out of 5. What is now the unconditional probability for picking an odd number for the second time (thus, regardless of the outcome of the first pick)?

Risk Averse

1. I almost had a serious bike accident today because of three good things. I felt better after an episode of sore throat. The weather was great: sunny and 10 C. My bike was lighter because it's Sunday, so I didn't put panniers for books and laptop.

The three things that were supposed to help me enjoy my Sunday biking have caused me lose my guard. They gave an illusion that I was invincible. I felt great and therefore bad thing could not happen. I was wrong.

The bike's front tire hit the sharp edge between the asphalt and the concrete median when I moved to the left lane before an intersection. I lost my balance and the bike wobbled furiously. Luckily, I unclipped my left shoe fast enough to stop without falling. My right shoe was still attached to the right pedal though. It was a close call, uncomfortably close to cars on my right!

2. Biking has inherent life-threatening risks: (i) from other road users, (ii) from the cyclist, and (iii) from road conditions. From my experience, the largest risk comes from the second cause, i.e., myself.

If I am not physically prepared, then I shouldn't go out biking. But feeling too confident or too afraid is also dangerous. When I bike long-distance, I thus never think about the 100 km per day target, I think only about 2 hours ahead. I deal with the risks of 100 km per day target by bringing appropriate clothing, enough food, and learning bike repairs.

In other words, the long-term risks cannot be mixed with short-term risks. Long-term risks are managed by good preparations and deliberate planning. I prepare my family members for my possible death when I bike long-distance. I discuss with my wife steps to take when such possibility does occur. I tell my sons that I could die on the road when a vehicle hits me. I share with them what they need to do in case I die.

3. Taking risk is thus normal, when we understand and accept all possible consequences that may come. Becoming fully aware of all possibilities – good and bad – is actually a good thing.

Taking risk is habitual. The more I take risks, the easier it is for me to handle them as I become more experienced. I will be in a hospital today, sustaining serious injuries or worse, if I am a rookie cyclist.

The hardest part is thinking about all possibilities that can occur when an action is taken. This is when experience and knowledge help a lot. Taking risk is thus not the same as being ignorant.

Defining Directions for Position, Velocity, and Acceleration

I teach an engineering dynamics course this term. I have read several engineering dynamics textbooks and am not impressed by how thick these books are. They gave a lot of examples and problems, but clear concise exposition of concept is often lacking. Reading these books makes me want to write my own textbook.

One example is a lack of clear explanation on how to consistently assign and interpret sign values (positive or negative) to position, velocity, and acceleration. An easy way to get rid of this confusion is offered here. I hope it is concise enough.

Velocity is the rate of change of position x of a particle with time t:

v = dx/dt.

The direction (i.e., sign) definition of the three quantities starts with the definition for the position x. If dx > 0, then v > 0 since dt is always positive. Now, dx = x(final) – x(initial) > 0.

v > 0 thus produces x(final) > x(initial). In other words, v > 0 corresponds to the direction of increasing x.

What about the acceleration? The acceleration a depends on velocity v through this relation:

a = dv/dt,

so that a > 0 if dv > 0 since dt is always positive. By the same argument, we say that a > 0 produces v(final) > v(initial).

It is possible that both v(final) and v(initial) < 0, even though v(final) > v(initial), so that a > 0 points in one direction, while both final and initial velocities point in the opposite direction. Having a > 0 or a < 0 thus does not correspond to a direction of the particle's motion. The direction of the motion is determined by v.

If a has an opposite sign to v, then the particle's speed will slow down. If a and v share the same direction, then the particle's speed increases.

First Day of Class

1. A Canadian undergraduate student pays about $6000/year for enrolling in 10 courses at a Canadian university. Each course has about 50-hours worth of lectures and tutorials, so each 1-hour class contact costs $12. A good lecture is like having a nice lunch but is more expensive than watching a movie. A lecture can be inspiring or dull, which are two possible outcomes from watching a movie.

2. I don't believe a university course should be directly applicable to "real world". My one-year experience working for industry taught me that even a managerial job in an oil and gas company will become a routine over 6 months. 

But a course should at least improve students' thinking skills: filtering information from different sources, independently testing opinions against facts, articulating thoughts into an actionable plan.

3. Incorporating active learning components into courses is a key part of teaching, something that I will start doing this year. Students these days (i) do not easily defer to an authority figure and (ii) work and communicate constantly in group. 

A traditional delivery method - where a teacher scribes on a board and students observe - will be a thing of the past, especially with the forward march of online course delivery companies like Coursera and Udacity.