Course Policies

New faces.  New people.  A new semester.  The summer heat begins to wane and the nights begin to feel cooler.  The swimming pools are now emptier and family schedules become busier.  This is ever true for the typical college professor.

The beginning of a semester is an enjoyable, albeit stressful, time of the year.  The first day of classes is exciting and invigorating, but it can often be dry as it focuses on the course policy and syllabus.  These combined documents are a contract between myself as their professor and them as the students.  Over the years that contract has ballooned from a one page document to a whopping seven page document! Ugh…

Many students do not read it, yet they registered to attend the class and, subsequently, are bounded to it.  It offers the vision of the course in addition to a daily schedule.  Often it will contain all the assignment details and the due dates for them.  It always contains a grading policy, that is, how they will be assessed throughout the course.  It gives classroom and university policies, such as attendance, late-work, and academic integrity policies.  I am as much bounded to the contract as they are.  It is my way of showing my cards upfront.

The document communicates to students how to be successful in the course.  It provides information about obtaining help, time-management strategies, and essential tips to be a learner in mathematics.  The success of students does not hinge on their intellect or natural mathematical ability, rather their willingness to be coached and learn.  It may require difficulty and hardship.  It may require sacrifice to obtain a greater good down the road.  It may require being uncomfortable.  It may require more time than you thought. It may require the recognition that you can not do it alone.  It may require admitting that help is necessary.  It may even require being in class regularly!

In all, it requires their attention.

For the inattentive student, how is their attention gained? Their grade in the course.  No student wants to fail a class.  They all want an A grade. In other words, when given the option, it is reasonable to assume that all students want to pass rather than fail.

God has also given a course policy that details a grading policy.  And we are all registered for His course.  It states that perfection is the only way to pass the course.  Bummer. However, later in the course policy we find that a perfect score can be awarded to you if another classmate with a perfect grade wants to switch places.  You read on and it tells you the student’s name that will do this for you.  Oddly enough the student’s name is the teacher’s name!  Would you take that offer knowing you could not simply drop the course?  What would your reaction be?



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In the moment

“I am now handing out the exams, do not start until I tell you to do so.  Please keep the exams face down.  Please remove all items except pens, pencils, or erasers,” the professor states.  The students shuffle papers away and clear their desks.  They appear anxious to begin.

“It is now 8 o’clock, you may all begin.  You have till 8:50, that is, 50 minutes.”

The students flip to the first page of the exam.  Some brows begin to sweat and furrow, a few pencils tap, some pensively stare at the ceiling, while others feverishly type on their calculators[1].  Nevertheless, there are always a collection of students that look like a seasoned runner: focused, steadfast, stressed but remaining calm, and diligently working toward the prize.  That determined look espouses confidence even if the student themselves do not feel that way!

Question: Where does that confidence come from? 

Short Answer: Preparation.

Long Answer: It stems from an investment of time learning the subtle nuances of the material.  It comes from working problems and understanding their extensions.  It comes from handling the frustrating moments of “I don’t get this” that, through hard-work, transforms into “ah-hah” moments.  Understanding often comes by the way of 99% perspiration and 1% inspiration.

This means that when the exams do come the diligent student draws from understood material.  They pull it from their banks of knowledge that have been seasoned through time and hard work.  That’s what comes to mind.  That is what brings forth an air of confidence to face the exam.

In the heat of battle or the exams of life what comes to your mind?  Vile thoughts? Empty thoughts? Despairing thoughts?  Self-righteous thoughts? Righteous thoughts? Noble thoughts? Godly thoughts?

Do you read the scriptures hastily just as a student crams for an exam?  Or do you read the scriptures with intention and diligence just as the confident student that prepares?  After all, understanding gained hastily dwindles but those that seek it diligently will increase it (Proverbs 13:11-12).

What came to mind when Stephen was about to be stoned in Acts 7?  What came to mind when the prophet Isaiah was about to be sawed in two?  What came to mind when Shadrach, Meshach, and Abednego were about to be thrown into the furnace?  Or Daniel prior to being thrown into the lion’s den?  Or when you are singled out for your faith in Jesus Christ?  Or the other Christian martyrs of today and yesterdays?

I can tell you what came through their mind: The hope and peace that defies all human understanding in knowing that those in Jesus will overcome death itself and are assured victory in the end (Phil 4:6, 1 Cor 15:55-58).


1. This behavior always baffles me. Especially, since I know that their particular exam doesn’t require any calculator use. I often think, “What are they typing?” This behaviour is similar to going to work on a house with a wild chain-saw when you are tasked to work on a plumbing system!



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Are all things possible?

The class ends and students make the usual mad dash to the exits.  Lines of exiting students quickly form as new students flood in.  A student approaches me with a brief question as I desperately try to ready the classroom for the incoming professor.

“Dr. B., why are we only interested in the invertibility of square matrices?”  The student asks.

“Because, it doesn’t make sense to talk about the invertibility of matrices that are not square,” I respond.

In the study of linear algebra, matrices are a common conversation point.  Matrices stem from a wide range of applications.  They can be viewed as linear transformations, that is, they map objects from one space to another space.   They may represent a vector equation or a linear system of equations.  The latter case may be more familiar from your high school algebra training.  In either case, a matrix can be used to store all the relevant information, for which allows for easier manipulation by hand or through a computer.

All matrices have N rows (number of equations) and M columns (number of unknowns).  If N equals M then it is called a square matrix.   When solving a linear system of equations, say A xb,  a unique solution exists if and only if the matrix is invertible, that is, there exists a matrix C such that A C = C A = I, where I is the identity matrix.

This only makes sense for square matrices.  Therefore it is nonsense to talk about the inverse of matrices that are not square (rectangular matrices).  It is a contradiction of terms.  We simply can not have an invertible 2 by 3 matrix. It simply does not make sense.  It is like having a square circle or a married bachelor.

What does this have to do with God?  Everything. Consider a common dialogue that I have been privy to:

Skeptic : If God is All-Powerful then all things are possible.

Me : No, God can do any thing but not anything.

Skeptic : Huh?

Me : God can not do what is logically inconsistent.  He can not make a married person also a bachelor.  He can not make a positive number also be a negative number.  He can not make a square also a circle.

Skeptic : Oh, okay, but I still do not think God is All-Powerful.  Maybe the reason why there is so much pain and suffering in the world is because God is not strong enough to overcome it. Could God create a stone that even He could not lift?

This conversation seems to make a truly profound claim about an attribute of God, that is, that He can not be All-Powerful.  However, the last question by the skeptic is simply a contradiction of terms.  It doesn’t make sense.

If God is All-Powerful, that is, He can lift anything, then it does not make sense to talk about something He can not lift!  This is equivalent to a student wishing to talk about invertible 2 by 3 matrices; be it their wish or not it simply does not make sense from basic principles.

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Finely Tuned Questions – Part III

RulersIn an initial post an argument for the existence of God flowed naturally from the extraordinary degree of fine-tuning of the universe.  The argument is offered again:

Premise 1.  The fine-tuning of the universe is due to either physical necessity, chance, or design.

Premise 2.  The fine-tuning of the universe is NOT due to physical necessity.

Premise 3.  The fine-tuning of the universe is NOT due to chance.

Therefore it due to design.

Premise 2 was argued favorably in a prior post.  The argument stems that is not guaranteed that any universe that exists is fine-tuned for life.  Hence, the negation of the second premise is fallacious.  The third premise is more intricate and is argued here.


Enter Las Vegas! Intricate dining, exquisite entertainment, with casinos lining the strip beckoning you to come in.  Once in a casino, you will find a place void of clocks with fabricated and bright lighting to make it hard to decipher night from day.  They want you to stay.  Sit down at a table and you’ll be enticed to play with free alcohol and frequent dining service.  You’ll be enticed to play games of probability, for which the house employees have been trained to take advantage of in the long run.  You hear the sound of Roulette and the ball smacking against the intricate groves between the range of possibilities.  It lands on black 15.  An exchange of chips begins as bets are placed for the next spin.  It lands on black 15 again.  Another exchange of chips.  Another spin and black 15 again.  People exchange awkward glances and the bets are now beginning to stack up on that black 15.  Will it come again?  Another spin and another black 15!  Is this chance or design?  You can imagine that if this happened at a roulette table that game would be stopped.  Maintenance workers would come quickly to investigate and service the table.  Something must be wrong with it in order to hit black 15 so many times!

This, my friend, is the incredulous, incomprehensible feature of our universe.  Black 15 has been hit again, again, and again.  Consecutively.  Now, of course if you spin the table 20 times there is a chance that Black 15 will come up 20 times.  So should you be surprised if that occurs?  Or would you be inclined to investigate why that did occur?   Of course, it we have enough spins or iterations then wouldn’t this situation be likely to occur?   Yes, but only if you have enough spins.  In fact, the very reason to push for a multiverse hypothesis is to increase the odds of obtaining our universe!  Hence, its mere suggestion in academic circles is complimenting the fact that our universe is fine-tuned!

Are we part of an infinite ensemble of universes?  Not quite.  First, if there exists an actually infinite number of universes a slew of logical fallacies are had.  Just consider Hilbert’s Hotel. Nor is this what is being proposed by the dominant multiverse hypothesis, M-theory.  This theory proposes a finite number of possibilities on the order of 10^500.  Then, how many of these universes are life-permitting?  The subset of life-permitting universes is abysmally small.  However, it gets worse.  The probability of our universe’s extremely low entropy condition is estimated at 10^(-10^123)  while the chances of our solar system coming into existence by random collisions is estimated to be 10^(-10^60) (see Penrose, pgs. 762-765)!  This means that our universe is extremely rare even among the small subset of possible universes!

Hence, we are back at the casino at the roulette table.  No one has come to stop the game and investigate if the game is rigged.  What is your next bet?  I’ll tell you mine:

“Señor, I’ll take Black 15.”

Let it roll.

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Finely Tuned Questions – Part II

In a prior post an argument for the existence of God flowed naturally from the extraordinary degree of fine-tuning in order for universe to be life-permitting.  The argument is offered again:

Premise 1.  The fine-tuning of the universe is due to either physical necessity, chance, or design.

Premise 2.  The fine-tuning of the universe is NOT due to physical necessity.

Premise 3.  The fine-tuning of the universe is NOT due to chance.

Therefore it due to design.

Here we will argue in favor of the second premise.

Of course that very fact that I am writing this is evidence that a life-permitting universe exists.  Of course you may adhere to a worldview that states everything is illusory, but then who may I ask is reading this?  Not to mention that this worldview is also an illusion, hence a built-in defeater!  Nevertheless, a life-permitting universe exists as a result of fundamental constants being tuned just so.  But why were chosen this way?  In other words, why are they not other values?  The values are not determined by the discovered laws of nature.  Rather, they are substituted into such equations such that we may study aspects of our observable universe.   Hence, if the fine-tuning of the universe is of physical necessity then any values that are chosen must be life-permitting!?  But clearly this is not the case.

Oh, but what of the potential great unifier of physics, M-theory?  Not so fast!  M-theory does not eradicate the degree of fine-tuning, in fact it complicates the situation further!  In fact, it predicts that there is a wide range of around 10^500 possible universes all consistent with the same laws that we have, but varying in their respective constants.  Hence M-theory points to a multitude of universes that are not life-permitting.  In fact, it presents an even greater challenge in unlikelihood of the existence of any life-permitting universe!  Not to mention, M-theory needs 11 dimensions to work.  Why 11?  Why not 10 or 12?  Why perfectly 11?  Hence, there is no evidence supporting that a life-permitting universe is a physical necessity.  It is far more reasonable to expect a universe to not be life-permitting.

In the following post the third premise will be discussed.

“Where were you when I laid the earth’s foundation? Tell me, if you understand.”  – Job 38:4

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