Universal Gravitation (Journey to the Center of the Earth)

Having seen parts of the original film and the previews for what must have been a horrible remake, I can assert with confidence that the physics behind a Journey to the Center of the Earth are of much greater interest than any film that goes by that name (from the preview of the latter, it appears that dinosaurs currently reside somewhere within our planet, where they are safe from all the pesky breathable air up here).

While we usually think of the gravity due to planets when we reside on their surface or orbit around them, it is intriguing to consider the role that gravitation plays inside a large body.

Newton's law of universal gravitation states that all bodies having mass emit a gravitational field and thereby attract all other masses to them.  The magnitude of the attractive force (which, by Newton's third law, acts on both bodies) is governed by the mass of each body, as well as their proximity to one another.  The force is stronger for more massive bodies, and increases as the gap between them reduces.  In equation form, the magnitude of the gravitational force, Fg (in Newtons), that acts on both bodies is given by

Fg = GM₁M₂/r^{2    (refer to figure below)}

Here, G is known as the universal gravitational constant (6.673 × 10^-11 m³/kg s²), M₁ and M₂ are the masses of each of the bodies (kg), and r is the distance that separates them (m).

Extremes in Engineering and Politics

As I watch the election season unfold in America, I am constantly stunned at how far to one side each party and their supporters are and seemingly must be.  It is, by and large, Republicans to the right, Democrats to the left, and no middle ground in sight.  When we categorize ourselves as one of these two extremes, we may enjoy the apparent sense of community that comes from it.  After some time, we begin to identify with one extreme.  However, as a whole, such categorization has the net effect of polarizing a nation.

In the twenty-first century, it seems that so many of us are unimpressed by an optimized solution.  There is nothing sexy about a calculated compromise.  On YouTube, it is the biggest this and the fastest that which tend to garner millions of views.  We simply are not interested in anything average.

I think that politicians ought to replace their segragating rhetoric with a middle of the road approach.  But the fault lies not only with them.  The voting population must recognize the value of a moderate approach.  Why do we tend not to award those who are steady and balanced?  Is it related to our fascination with outlandish personalities like those of the Kardashians?

Vive le Québec Intolérant

Today, for a change, I write of nothing scientific.  You may find it to be educational nonetheless, particularly if you do not reside in Canada, as it concerns the provincial election of its most diverse and bizarre province: Quebec.  As the majority of my readers reside in the United States, where an election with global impact is on the horizon, I will continue on.

Let's begin with some geography.  Canada has ten provinces and three territories.  Quebec is one of the bigger provinces in terms of both land mass and population, and is located towards the East.  It is rich in terms of water, and, as a result, is one of the only North American states whose energy production is primarily sustainable (hydro power).  The population of Quebec is concentrated along the St. Laurence river, which flows from West to East.  The city of Montreal, the second most populous in all of Canada, is an island along the St. Laurence towards the western side of the province; it happens to be my home.
 

Neil Armstrong's Legacy

The recent passing of Neil Armstrong at the age of 82 has caused many of us to stop what we are doing and consider man's past and ponder its future.  This is not an obituary for the first man to have ever set foot on the Moon or any surface not called Earth.  This is simply a commentary on the significance of that momentous step in July of 1969.

The lunar landing was, for mankind, the defining moment of the twentieth century.  In a century that contained countless events that we would like to forget, Armstrong's steps onto a distant world will be forever remembered and cherished as a supreme achievement.  If ever one feels cynical about life, or is experiencing a mundane stretch in one's day to day activities, one can simply imagine the realization of the Apollo 11 mission.  It exemplifies man's desire to explore and ability to achieve.

On Free Post-Secondary Education and Lifelong Learning

Much ink has been spilled in recent months - particularly in the province of Quebec - as to whether a post-secondary formal education is a privilege or a right.  After reflecting on this question over the summer, and listening in on several debates on the matter, I have not been swayed from my initial stance: it is a privilege.

A prosperous society should ensure that its citizens have access to a high quality elementary and high school education.  While some students benefit from this environment more than others, all high school graduates leave with a basic body of knowledge.  More importantly, after more than a decade of interacting with roughly fifty different educators, these young men and women, some more than others, have learned how to learn.

Learning is a right in the sense that no one should be prevented from doing so.  But learning is not limited to a school setting.  Educational institutions do not hold a patent on learning.  Someone who is not enrolled in University is still welcome to visit the library, to have discussions with friends and family, and to peruse the internet, which contains an unimaginable wealth of useful information amidst an endless supply of videos of cats eating their own vomit (the user gets to decide what content is more beneficial to them, and judging by hit counts on YouTube, society tends to favour cat puke).

Curiosity: How NASA Got its Groove Back

If NASA were a prize fighter, few would have been lining up to place bets on it in recent years.  The American space agency suffered a metaphorical TKO in 2011 as its shuttle program came to an end.  From that point onward, in order to send American astronauts to the International Space Station, the US government would need to rent some seats aboard a Russian spacecraft.  This position of dependence that the one time unrivaled space faring nation found itself in seemed to indicate that NASA had lost its mojo.

Well, what a difference a year, and a trip to Mars, can make.  This week, NASA's one ton rover suitably named Curiosity began cruising around Mars following an eight month long voyage through the solar system.  As the first pictures of the red planet reached our blue one, it became clear immediately: NASA was back.

What Makes Usain Bolt so Fast?

The quintessential Summer Olympic event has yet again come and gone, and as was the case in Beijing in 2008, Usain Bolt of Jamaica has captured the gold medal in the 100 m dash in convincing style.  True, fellow countryman Yohan Blake has the ability to run with Bolt, and a few others in the field can compete with him on their best day, but for half a decade, Usain Bolt has held the coveted title of 'world's fastest man'.  The question I would like to address is "Why?"

Let us begin with a quick kinematic assessment of the 100 m dash, using Bolt's 2009 World Record setting run in Berlin as an example.  Starting from rest, Bolt ran 100 m in 9.58 seconds - a feat that will likely not be matched for a long while.  Bolt's average speed (distance over time) on this occasion was 10.44 m/s.  He reached his top speed at around the 65 m mark of about 12.27 m/s.  That is 44 km/hr, which carries a hefty fine for a car in a school zone.

Stephen Harper Hears a Who - but Ignores it

I sat down to watch the movie, "Dr. Seuss' Horton Hears a Who!" with my three-year-old daughter the other day.  The only Seuss books that I recall from my childhood are "Green Eggs n' Ham" and "Hop on Pop", but I was very impressed with this 2008 animated film from top to bottom.  While my daughter was very entertained by the many jungle animals, I gradually became quite focused on the real world symbolism that is not so subtly embedded within it.

Happiness Not a Consequence, Merely an Assertion

Science is all about measurements.  Scientists try to determine the model that best fits the data to gain insight into the behaviour of the world around them.  They measure everything, from temperature to charge to chaos.  These measurements are dependent upon a number of things.  In thermodynamics, an engineer may like to measure the temperature of a body as a function of time for a specific set of conditions.  Here, temperature is a dependent variable, and time is an independent variable.

It is appropriate to consider the measured temperature of a body to be a consequence of several factors.  It may seem sensible then to apply this approach to assess our state of mind on a given day.  I aim to show that this is a misguided way to perform a self-assessment.  That is, it is nonsensical to attribute our mental state to a given set of conditions that is present in our lives.  The measured variable that I wish to focus on is happiness.

Happiness... That state of being that we are all encouraged to pursue from a young age.  But, how does one measure it?  How does one know when one has achieved it?  Whatever the answers to these questions, it is certain that the assessment is anything but absolute.  I would even take it one step further.

Domesticating our Kids

I heard today on the radio about how more and more pet owners are abandoning their pets on moving day.  This is negligent, because domesticated animals are ill-prepared to fend for themselves in the wild.  While such negligence may be punishable under the criminal code, and is, of course, morally wrong, it seems to me that there is a more general issue at play here. 

On some level, there is an inherent disservice in the practice of domesticating animals at all.  By sheltering them and feeding them, we undermine all of the instincts they have developed over the long adaptive road of evolution.  This article will not explore this debate any further, but will use it as a backdrop for a discussion on how we raise our kids.

I am about to become a parent for a second time, so, naturally, the question of what constitutes effective parenting is on my mind.  If one were to summarize the role of a parent in one sentence, it might look like this: "To ensure the safety of your child, while empowering him or her to take on life independently upon reaching adulthood".  Though parenting is anything but a bland activity, it can be viewed through an engineer's lens, as an optimization problem.

If one hovers too close (helicopter parent), one's child will never attain the level of independence that is needed to tackle life on his or her own.  On the other hand, a completely 'laissez-faire' parenting attitude at too young an age can place a child in an unneccessarily risky situation.  Thus, the parent must find the sweet spot, where their child is free to explore the world, but with reasonable boundaries imposed on them.