Thursday, December 13, 2018

A Final Exam Blessing

To those not studying, this may seem odd, but it has happened more than once that a student has asked me for a blessing just before the start of a three-hour final exam I am about to invigilate.  The post-secondary teacher/student relationship has changed since I was a student.  I look them in their eyes, and offer a few words of encouragement.

After giving more thought to the appropriate words to give, I want to lay them out here.  I am calling it:

A Final Exam Blessing (the long version)

Here you are and how far you have come.  There is fear in your eyes and worry in your heart, but it is all misplaced.  Let me explain.

If you are worried today, it is probably true that you have been worried all semester.  That worry, so long as it is measured and not disproportionate, has served you well.  It has pushed you to master content to the best of your ability given the constraints of time, life, and your effectiveness as a student.

If this is you, then you need not fear today.  Take your fear and transform it into confidence.  You need not worry either.  Worry is for yesterday.  On the day of the exam, take your worry and transpose it to alertness and focus.  Dark chocolate will help you to do this.

If the above does not describe you, and you do indeed have what to fear because you are indeed under-prepared, much of the same applies.  You are, and probably have been for some time, in what may be referred to as 'damage control mode'.  It is a hard place to function for extended periods of time.  The good news is it will be over soon, as next semester is a new one, and you are free to transform from the start, and alter your functioning such that the patterns that did not serve you this semester are replaced by patterns that do.

I want to tell you about one student I had some years ago.  She may be unaware of this to this day, but she actually smiles from ear to ear while taking exams.  I never told her about it, because I did not want her to be self-conscious about it.  From my point of view, I had to restrain myself from laughing during examinations. There were forty students sitting in front of me; thirty-nine of them looked mildly panicked, and one is simply beaming.  In another context, this could be the setup to an exceptional horror film.

I am not suggesting that you should smile while writing exams.  What I am suggesting is that the confidence you have rightfully earned should allow you to smile on the inside while you maintain your serious exterior.

Be alert.  Remain focused.  Hundreds of hours have been invested on your part - your worry is now over.  It is actually possible to enjoy the moment, and celebrate how far you have come.

A Final Exam Blessing (the short version)

Here you are and how far you have come

There is fear in your eyes and worry in your heart, but it is all misplaced

You need not fear - take your fear and transform it into confidence
You need not worry either - worry is for yesterday
On the day of exam, take your worry and transpose it to alertness and focus

 In this moment, celebrate how far you have come.

Friday, November 16, 2018

The Day That Newton Met the Aliens

I always enjoy the sixth week of the semester in Mechanics class.  It usually includes the story of Isaac Newton; though in recent years, I have been offering two alternative stories, and asking the students which one is more likely to be the correct one.

Story 1: The Traditional Version

As many literary accounts attest, Isaac Newton was a very bright young fellow from England, who, in his mid-twenties, in the late seventeenth century, had an interest in many areas of science, most notably astronomy.  It was not so much the taking of the astronomical data that he was interested in, but rather, the analysis of the data.

It is important to realize that at this point in human history, science did not really concern itself with the explaining of phenomena.  Science was about observation: experimentation and perhaps noting patterns in the data - science did not seek to establish a framework, a model, ie, a code that seems to govern all matter and interactions in the universe (this is what science has become today).  The young Newton was fascinated with the data, and, encouraged by other prominent scientists of the time, tried to explain the data.

The data as recorded by numerous astronomers stated that planets seemed to orbit the Sun in elliptical orbits.  This upset the religious hard-liners of the time (like, um, just about everyone), as many felt that God would prefer circles over ellipses (not the first or last time humanity felt the need to suggest to God what universe was best).  It may have even upset Newton himself, because he too was religious.  Still, Newton could not and would not place his personal beliefs above the evidence that was before him, and so began the most famous foray into science in human history.

All Newton really had to work with was the fact that orbits had elliptical shapes.  He also had, like all of us do, the ability to interact with his environment, and to observe how rain, snow, and, yes, apples, fall.  Here is where the story gets weird, perhaps even disturbing...

Newton proposes the Law of Universal Gravitation as well as certain laws of motion.  Some might call this 'playing God' - I suspect that some at the time actually did.  He then needed to check if these laws, as proposed, were consistent with the elliptical paths that orbiting bodies exhibited.  In other words, he needed to see if his theoretical framework matched the experimental data.  He ran into a problem: the only way to do this required a new branch of mathematics (Mathematicians of the day were extremely adept at geometry, but not much else).  So, he took it upon himself to invent Calculus.

Yes.  Some guy in his twenties ran into a problem in his pursuit of science, so instead of raising his arms and accepting this dead end, he invented arguably the most important branch of mathematics we currently know of.  And then, he used this new math to address the advanced ordinary differential vector equation that results when you combine Universal Gravitation with Newton's Second Law of Motion.  Orbital Mechanics experts today refer to this particular analysis as "The Two-Body Problem."

I recall being in Professor Misra's Orbital Mechanics course at McGill University.  During class #2, he showed the class the Two-Body Problem, and proceeded to solve it.  At that point in my young career, I had been exposed to Calculus and Linear Algebra for six years and had taken at least ten math courses that covered these branches of the discipline.  I recall thinking that it was a very tough problem to solve.  I still find it to be a tough problem today.

Apparently, Newton did manage to solve it, and all of his ground-breaking work in this area is described in a book as sacred as most any religious text: Philosophiae Naturalis Principia Mathematica (published in 1687; an original copy is surely stored today somewhere behind glass).

Gravitation, laws for motion, mass, inertial frames, momentum - all of these concepts that are central to most any scientific pursuit were established by this one guy in a handful of years.  Today, any scientific analysis that does not involve the very small (microscopic), the very fast (>10% light speed), or the very dense (black holes), utilizes the framework described by Newton to the letter.

The End.

But there is another possibility...

Story 2: The Alternate Version (The Aliens Theory)

Isaac Newton was a very bright young fellow from England, who, in his mid-twenties, in the late seventeenth century, had an interest in many areas of science, most notably astronomy.  One night, he wished upon a star that he could be a famous scientist.

The next day, Newton was visited by aliens.  These aliens visited him quietly every night for the next several years.  They taught him Calculus and Mechanics, and eventually helped him write his famous Principia.  The aliens said, "Call it The Coolest Book by the Coolest Dude," but Newton insisted it get a different very long name.

The aliens were annoyed with Newton and his fancy book title, so they stopped visiting him once the book was published.

The End.

The way I see it, both stories are unbelievable.  The more I think about both stories, the less comfortable I feel in asserting that one story is more likely than the other.  I suppose all of the historical accounts point to Story 1, but I ask this question in all seriousness: How could a person have accomplished that without outside help? 

I am bewildered not only by the creativity of thought it took to propose those laws and the genius required to develop the math that it takes to assess them; I am equally stunned by the instinct Newton had to even suggest that mathematical equations could be used to describe the world and to predict what happens next.  Scientists today accept this to be true, but a universe could just as easily, at least in theory, have zero mathematical framework.  That Newton did all of this despite the reservations of the Church, as well as his own, is just icing on the cake.

Many historians today would describe Isaac Newton as one of, if not the most important and influential figures in human history.  And, I think that such a designation is warranted regardless of which of the two stories is actually the true one.

Monday, October 22, 2018

Interstellar Missions a 21st Century Possibility

I was at the 2nd Montreal Space Symposium this past Friday, held this year at Concordia University.  I could only attend one of the days, and was again impressed by the level of professionalism the student-organized two-day conference was run with.  I appreciated the format this year, where more than 50 talks (mostly around 15 minutes with 5 minutes of questions) were run, usually two concurrently.

The one talk I took in at the conference that I will never forget was given by Professor Andrew Higgins (Mechanical Engineering Department of McGill University).  He and I have not crossed paths much since the last time I was a student in one of his courses (Fluids II in 2003, I believe).  The talk, entitled, "Bringing Interstellar Down to Earth," was delivered with his usual sense of humour and flair for the dramatic.

Higgins began the talk by explaining the typical reservations he holds for very futuristic project proposals (personally, having spent most of my adult life exploring the dynamics of space elevators, I hold few such reservations).  But, current breakthroughs in some key technological areas have him believing that he may live to see a fraction of light-speed transit to an exoplanet.

Today, we can detect the presence of exoplanets (planets orbiting stars other than the Sun) and even get a sense for their habitability (temperature, and whether it may have an atmosphere).  There is, however, no reason to believe that telescopes near Earth will enable us to learn any more than this about such planets, which are located at minimum around five light years away.  The only way we can hope to learn if life did or currently does exist on such a planet would be to go to it and take a picture, and send the image back to Earth.

While such a mission was laughable even five years ago, it is conceivable that we are now as little as two or three decades away from sending such probes to far off lands.  The challenge is to get a tiny satellite (a few inch diameter thin disk on the order of grams) to move at some fraction of the speed of light.  The number envisaged in the talk was 0.3c.

The 'TinySat' would be propelled to such a mind-boggling speed by a concentrated collection of coherent photons striking its surface... Basically, we would focus sunlight in a fancy way up to the satellite, where it would strike it (each photon carries a tiny amount of momentum, which it can transfer upon colliding with a surface).  The idea is to focus these streaming photons onto the satellite for a matter of minutes, accelerating the disk to, perhaps 0.3c.  If this were accomplished, TinySat would reach an exoplanet that is, say, 6 light years away, in about 20 years.  Then, it could snap some pictures, and send the images back to Earth, where it would arrive exactly 6 years later.  So, in total, in this scenario, pictures of the exoplanet arrive 26 years after the mission launches.  "Launches" ... This mission gives new meaning to the term launch.

What makes this plan reasonable to even discuss is threefold: (1) the emergence of the field of photonics, (2) advances in reflective materials (the surface of the satellite disk could reflect 99.9995% of the photons, and avoid melting during the photonic barrage), and of course, (3) the miniaturization of electronics, which means a useful satellite could be on the order of grams.

The project is known as "Breakthrough Starshot".  Some of the major challenges were outlined by Higgins.  He seemed most interested in how space dust might collide with a TinySat moving at 0.3c.  Would it destroy it?  In my mind, the most exciting challenge is those few minutes of acceleration.  At such high speeds, even the smallest non-zero torque would cause a rotation and a TinySat that moves very fast, but not in the direction that was intended.  Keeping the satellite pointed correctly during this acceleration is a monumental control challenge.  But, while we are on the subject of 'minutes', why not add a few more minutes of acceleration and get to 0.5c?  I mean, it would save us years of waiting for the probe to reach its destination.

Here is another challenge: can we even take a useful picture while moving at some fraction of the speed of light?  Maybe yes, if we account for the Doppler shift - I honestly do not know.  But that is what made the talk so exhilarating.  The numerous challenges posed by this mission are new, and many of them solvable and even testable in a lab here on Earth.  If I were looking for graduate work in engineering or physics, I would surely consider tackling some aspect of this project.

At the end of his 15 minute talk, Higgins was surrounded by eager young students with questions and novel ideas.  The enthusiasm in the room was palpable.  What I can say with confidence is that although the Breakthrough Starshot is a long shot (in every sense of the word), a lot of kids are going to have a lot of fun trying to make it. 

Thursday, October 18, 2018

You Are a Miracle

Truth be told, I cry in public sometimes.  I estimate that 95% of this crying comes from uncontrollable laughter, which, for me, is one of life's greatest gifts, like mango and avocado, and also tortilla chips dipped in guacamole consisting of mango mixed with avocado.

The other 5%, well, that is another kind of tears, sometimes out of sadness, but not always.  This variety of tears can be rendered uncontrollable with well-timed music (or poorly-timed, depending on one's desire to cry).  Films like E.T., the Extra-Terrestrial - I just get so triggered by the music at the end.  If I watch Elliott hug E.T. good-bye on mute, I'm just like "Bye E.T.," but turn up the volume, and I'm a mess.  Don't even get me started on the ending of Coco (the combination of my wife's tears and my own required more tissues than were available).

There is yet another variety of tears, which show up during public speaking (Yay!  I mean, public speaking is just so easy otherwise).  Giving a eulogy at a funeral (or trying to) can bring tears to even the most hardened individual.  As a 'soft' individual, I am batting a perfect 1.000 for crying during eulogies at this time of writing, and I see no chance of that success rate changing.

The weird thing is that I probably cried most trying to deliver a speech at my own wedding (insert marriage joke here).  Honestly, it was such a joyful occasion, and yet, I simply fell apart in the moment.  I have come to realize that I cry not really due to sadness, but actually, due to truth.

I find that truth has the power to overcome me.  If I am standing at a podium, speaking about stuff I do not truly believe in, it will not be touching to anyone listening, and it will not make me feel any kind of emotion other than, perhaps, boredom.  Words that are true to me, and deeply meaningful to me, are hard for me to speak out loud.  That is why I will not record an audio-book for this or anything else I ever write.

This brings me to this short piece, which I will never attempt to read aloud again, because there is just no point.  It reduces me to a sobbing mess, even in the absence of background music.  I remember feeling pride as I wrote it, and then nearly cried trying to read it to my class.  Then I really cried when I tried to read it at a community 'spoken-word' event.  So, I am done.

Feel free to read these words aloud to someone you love...

You Are a Miracle 

"Consider all of the extremely improbable events that led to your being here today...

After the Big Bang, matter needed to become complex enough to form stars.  These stars burned for billions of years, and it was necessary that many of them ended their life cycle in supernova events, which led to the formation of new stars, more complex matter, and planets that orbit these stars.  Of these planets, some were in habitable zones - not too hot, not too cold.  For life to evolve, a conducive chemical soup was necessary, and then, perhaps the most unlikely event of all: one that synthesized a single-celled organism.  Then came evolution, whereby more and more complex organisms evolved - each necessary species along the line managed to avoid extinction before its critical mutation that led to the next branch in the tree.  Finally, the human race emerges (perhaps the most fragile form of all life thus far), and manages to survive millennia of hardship.  And if that were not enough, of all of the billions of humans to have come and gone, your parents met, and pro-created you.

How can you not feel at least a little bit special?  How can you see your existence as anything less than a miracle?

I think this is what is most beautiful about life: a seemingly endless set of possibilities out of which one actual outcome emerges.  I cannot help but have a certain affinity for each and every one of these improbable outcomes.

In this frame of mind, everything is worthy of attention, every topic deserves to be studied.  It seems to me that this is the place where science should begin."