Want Good Grades? Then Forget About Getting Good Grades!

Ok, I admit it. I have a habit of creating titles that create a disconnect. And are a little click-baity. But to be honest it only happens because I often like to write about misconceptions, and so by definition the title will appear counter-intuitive. Today I am going to write about something that over the course of my teaching career has met with perhaps the most resistance from students and parents, but which has also met with the most success when embraced.

If you want good grades, stop trying to get good grades.

Scandalous, I know. And trust me, I have heard all the rejoinders. So as you can imagine, I will explain.

See, in the current system of education, grades stopped being a measure of progress some time ago. What they have become instead is currency. A commodity that is pursued, traded and leveraged with as much vigor and ferocity as the dollar, euro, or yen. And I am not using hyperbole here. Schools these days have come to be viewed by many students, parents and even teachers as a marketplace. Teachers have the grades, students want them. And in this marketplace the end goal is to get as high a grade as possible. To very many – but to be completely fair, not to all – how that happens is not nearly as important as that it happens. To this category of student, the goal of school is not to learn, but to get grades. And this paradigm shift causes a fundamental change in how the entire process is viewed. I will list just a few examples:

  • Bargaining
    It has become standard operation procedure now that when teachers return graded work, the immediate next phase is the negotiation. Students dissatisfied with the magnitude of their grade will question, cajole and even harass the teacher about the grade, with the common theme that since the student believes the grade should be higher, the teacher has assigned a wrong grade. There are even times when the guise of reason is dropped completely, and the student will actually say things like “I need a 97% to get into <insert elite university program here> so can you raise my mark?”
  • Academic Dishonesty
    Academic dishonesty (aka cheating) is not a new phenomenon. What is new, however, is the pervasiveness of it, and the total lack of ethical struggle involved in making the decision to use it as a tool for getting high grades. After all, if the only purpose of school is to get a high grade, and if cheating accomplishes that, then where is the ethical problem? And so we see rampant use of things like plagiarism, paying others to do work that students then submit as their own, or gaming the system so that assessments like tests are skipped, then done at a later date after getting information from other students who were present at the time about what was asked.
  • Grade Mills
    Countless “schools” have popped up over the last decade or so who’s sole purpose is to guarantee official credits and high grades. The thinly disguised mission of these schools is to create a means by which, for a price, students can get a credit on their high school transcripts and also get an absurdly high grade. What separates a grade mill from a more legitimate private school is how accurately the student’s grade reflects their knowledge on completion of a course. I have taught many students who received a grade mill credit in a prerequisite course for the one I am teaching, with a grade of 100%, who do not possess the most basic skills meant to be learned in that prerequisite course.
  • Cramming
    This is definitely not a new concept in academics, but it has spread to more and more students, who in fact no longer recognize that it is not actually a means of learning. In courses where there are scheduled tests/exams, students to little to no work during times where there is no assessment looming. They attend class, possibly take notes, and otherwise devote minimal attention to the lessons, because “this won’t matter until the test.” They do not see this as an ineffective strategy at all. The belief that drives this is that the only time the subject knowledge will matter is when they are tested on it (and thus in a position to get grades), and so the plan is to study as much as possible the day – or even the night – before a test. Cramming all the information into their short-term memories just long enough to unleash it onto their test papers, to be promptly forgotten as they leave the room after writing the test.

These are not the only examples of what I am talking about, but they are the most common. And it is clear that none of these appear to give actual learning more than the slightest courtesy of a head nod. They are completely and totally about getting grades.

Sometimes, they even work. But that’s a trap. Because even when they work, they are only short-term solutions to a lifelong endeavour, and they all create stress and anxiety in the process.

  • Bargaining for grades, when it works, teaches that it is not about what you earn, but about what you can badger people into giving you. It shifts the perspective about where the effort should be placed. Rather than placing effort on producing good work, the effort is placed on convincing the teacher to assign a high grade. This creates an internal tension that results in generalized anxiety, because the student ends up in a position of having to convince the teacher of something that is not actually true, and for which there is no evidence.
  • Cheating works for its intended purpose (when you don’t get caught), but like grade mills, perpetuates the “appearance over substance” philosophy, and also imbues dangerous long-term values that erode at the ethical fabric of society. The stress this creates is clear – fear of getting caught, and the consequences. Additionally there is the gradual accumulation of anxiety brought on by creating an academic avatar that is more and more fraudulent and removed from the person who wears it.
  • Grade mills teach that appearance matters much more than substance – if you can appear to be someone who earned a perfect grade in calculus, it does not matter if you actually are someone with a deep understanding of calculus. It is hard to even wrap ones head around how many ways this is wrong. First, the injustice of potentially securing a spot in a college or university over someone who earned a lower grade, but actually knows much more calculus. Then, the fact that with the label of “100% in calculus” anyone who checks that label will assume that you are a calculus genius and expect that you are, creating significant stress on the person masquerading as the calculus prodigy. Finally, the pressure that the very existence of grade mills places on legitimate schools, who have little choice but to begin awarding higher grades so that their students can remain competitive when it comes to post-secondary offers of education, which is a non-trivial contributor to grade-inflation. The stress created here is very similar to that created by cheating, and has the added anxiety-producing bonus that at some point there won’t be a grade mill offering credits and grades for money, and that the student will actually have to perform as the person their grades have indicated that they are.
  • Cramming is arguable the lowest offense on this list, because in its purest form the student is not misrepresenting themselves at all. However it is fraught with disadvantages, from the fact that many students struggle to absorb and then reproduce the knowledge in a meaningful way, to the fact that when needed later – in the same course or in a subsequent one, the knowledge is no longer accessible. It also creates a great deal of stress and is a common cause of test-anxiety, which is a very real issue for many students who find they “totally knew this last night” but can not recall it when test time comes.

Perhaps most tragically, this issue causes stress and anxiety not just for the students engaged in them but for the many students who are not, because it creates an unlevel playing field that places incredible burden on the ones who are doing things the right way. Grade inflation is a real and dangerous phenomenon, where just like monetary inflation, a loaf of bread is still a loaf of bread whether the price tag says $0.75 or $2.99. The difference is that because we use percentages as grades, there is a ceiling, and so we are staring to distinguish by decimals. And that means that for any student mistakes cost much more than they ever did in the past.

Ok. So I’ve devoted the article to this point (approximately 5 minutes of reading time, if the algorithm that tells me how much I have written so far is to be trusted) outlining the issue. And maybe I’ve made it seem like hope is lost, because we do in fact live in a system where grades matter for universities, colleges, academic awards, and sometimes for that first job, and all of these vehicles by which students are getting the grades are either unethical or riddled with stress and anxiety. But hope exists! Because there is very good news.

To get good grades, all you have to do is actually learn the material!

Revolutionary, I know. It almost seems like I am joking. I assure you I am not. This simple fact is lost on more students and parents than I wish was the case. Clearly it would work though, right? Of course it would. Students, you can take all the effort you are devoting to “getting grades” and shift it to “learning material”. Immerse yourself in class. Ask questions of the teacher. Engage in discussion. Pay attention. Do work in increments (that is, homework), instead of cramming the night before a test or exam. Decide that you will be a master of the topic and use your teacher as the resource they are. Develop a love of learning – trust me, this is not as hard as you think – and as you grow into this person who legitimately strives to learn, the grades will automatically follow, as an afterthought!

Now I know from experience that this message lands differently on everyone. Some people roll their eyes, either inwardly or outwardly, and decide that the game as it is being played works just fine for them. Others hear me and know it makes sense, but feel that it’s too hard, and getting grades some other way will be the way to go. But, there is a significant portion of students I have talked to who have taken the idea to heart. And without fail they are the most academically successful, as reflected both in their grades, and in their facility with the material they have learned. These students inevitably report back to me that once they stopped their pursuit of high grades, and shifted their energy to the learning, they began earning higher grades than they ever had before. And their confidence grew as their anxiety atrophied. Because so much of the mentality of getting grades involves somehow gaming the system into awarding false credit, that when they shift into the person who actually has earned the credit they are receiving, they feel bulletproof.

And what a great feeling that is!

Thanks for reading,
Rich

Let Your Child Fail

Depending on the perspective of the different people in my life I am many things: a son, a father, a brother; A student, a teacher, a mentor; A friend, a colleague, a training partner. And yet, in all these capacities I have learned one lesson well, and seen it play out repeatedly. Failure is critical for growth, and letting loved ones fail is one of the hardest manifestations of loving them that there is.

This is never more acute than when it comes to your child. It is one of the most painful struggles in normal parenting. Seeing a that a child is making poor choices and is therefore on a path to failure, letting it happen, and watching the fallout is heart-rending. And yet, the alternative is worse: Letting them believe that there is always a safety net.

As parents, it is our job and our duty to give our children all the tools and guidance they need to succeed as they grow. But it is not our job to give them success. It is not our job to undo their failures, or to mask them as something else. In fact, any “success” that is not earned is not a success at all, and any part we play in delivering these false successes is, in fact, failing in our duties as parents.

Repeatedly and consistently rescuing a child from failure teaches them that failure is not on the table. It teaches them that life will be fine regardless of poor choices, lack of knowledge, or lack of skill. It’s like giving someone voice lessons and using autotune to correct their pitch before playing back their singing to them and to the world, letting them believe they are the next Freddy Mercury or Whitney Houston, and then letting the world watch their train-wreck audition for American Idol. It not only sets them up for confusion later in life, it inhibits self-awareness to the point that life in the “real world” will for them will seem like walking through a minefield, where the reactions from others are so completely out of line with their internal measures (calibrated in their youth) that they can, at times, feel like they never really know what is wrong with them or why they get the responses they do. Consider those American Idol auditions where the singer is so clearly awful, and yet they think so highly of themselves that they tell the judges it’s the judges who are terrible.

The thing is though, that in the moment failure is happening, we parents want nothing more than to take the pain away. Every parent knows what I mean. Your child’s pain, whether physical or emotional, is about a million times worse than your own. My wife always talks about that moment when a toddler is running to you in the park to show you some amazing treasure they found, with that big toddler smile and enthusiasm, when they trip and fall and start crying miserably. We all want that enthusiasm and joy to be the only thing they ever feel. We never, ever, want them to fall.

But it’s unrealistic. Everyone falls. Learning what caused it, analyzing how to have avoided it, and recovering from it are the real lessons. The lessons that lead to a person who truly can be successful. And so we have to let our children fail. And then we have to be there for them to love and support them as they recover from it. We have to show them that failure isn’t the end of anything, and that even in their failure we believe in them and love them as much as we always have. That is how they will learn to grow from failure, without spending a ton of counter-productive energy and emotion on self-recrimination and shame.

In my years of teaching, I have had countless conversations with parents concerned about their children’s academic success – or lack thereof. And on more occasions than I care to count, a parent has outright asked me if there is anything I can do to raise their child’s grade. These parents are always taken aback when I tell them that there is nothing I can do, and nothing they can do either. However there is everything the child can do. We can give them the tools, we can be there to support their learning. We can be the best parents and teachers there are. But we can not “raise the child’s mark”. That is on the student. And sometimes, the student fails. When I tell the parents that I am willing to let that happen, they often think it means I am a bad teacher. There have been a few occasion where they said so. But my response is always the same:

“I am being the best teacher I can be. I will always be there to support your child. I will give them every tool I have, and the guidance to use it, in order for them to succeed. When they need me, I will be there. I will be there even when they don’t realize they need me. But I will never do the work for them, and I will never assign a grade they did not earn. And if they should fail, I will be there to support them and help them see what went wrong, and how to address that in the future. Given all that, my only hope is that your child will look back on their time as my student and realize the gift I gave them: The gift of letting them fail.”

We want the next generation to be resilient, strong, caring and educated. Failure is the path to all of these. As hard as it is, we need to let our children fail.

And then celebrate the heck out of their successes!


Thanks for reading,
Rich

We Didn’t Sign Up for This

The global COVID-19 pandemic has been a reality long enough now that the emails and texts that start off “in these extraordinary circumstances” or “considering the difficult times”, or “unfortunately, due to the unprecedented situation we find ourselves in” now feel like the opening sentiment is redundant. It has strangely become awkward to know what to say when sending out an email with yet another update on how someone or some institution has been impacted. We get it. And yet … we don’t get it. Because we didn’t sign up for this.

I have always admired and respected people in law enforcement, the armed forces, and perhaps especially firefighters and EMT’s. I remember 9/11, which drove home the point that hardly needed making that when everyone’s instincts are screaming at them to run away, these are people run toward. And my respect for them stems from the fact that they signed up to do it. Something inside compelled them when they were younger to sign up for a career of running toward the danger. Of being in place when the shit is going down. Of being the person who was standing between the monster and the town, or being the first person the rest of us might see after getting mauled by the monster – doing their best to get us out of the danger and back into the loving arms of uneventfulness. My respect for them is unchanged.

But now we are finding out that some monsters don’t make a frontal assault. Some of them don’t take the path through the Hot Gates, so that Leonidas and his Spartans can know where to stand to get between the armies of Xerxes and the Greek civilians. Sometimes there is no bridge for Gandalf to block, because sometimes the Balrog descends like a toxic snowfall, on everyone at once.

And we didn’t sign up for that.

Grocery store clerks and cashiers, essential workers in office buildings, gas station attendants … they didn’t sign up to have to go out each day and do the exact opposite of what the rest of us have been told to do. Nurses and doctors signed up to treat sick and injured people – but they didn’t sign up to fight for 15+ hours a day, 7 days a week, against an unseen and not fully understood enemy, under-equipped and underfunded. They didn’t sign up to put themselves at risk caring for ICU patients with a highly contagious virus. They didn’t sign up to hold the phone as patients who might never go home FaceTime their families who just cry as they watch their loved one in an induced coma, breathing only thanks to a ventilator.

It is sadly ironic that some of the lowest-paid occupations in our society are now clearly the backbone of it. I find myself more and more troubled by this glaring imbalance. They didn’t sign up to be brave. The didn’t sign up to run toward the trouble. They didn’t sign up to be at the front. And yet.

What we are slowly discovering is that there are no rules for this. There are no precedents. Values and priorities we thought we understood only a month ago have undergone a seismic shift. And still, many people are operating on assumptions out of a lifetime of habit. As a high school teacher I am seeing this acutely through the lens of my colleagues and my students. Some colleagues are very concerned we will not be able to cover all the curriculum. Some students are very concerned about how this will impact their grades. But it seems to me that what this concern is missing is that the entire world is in the same boat. Every grade 12 student in the province of Ontario is not in school. Every graduating student that will attend university next year is going to have major gaps in their knowledge base as compared to previous years. Every single one of them. As for grades, the only time grades ever matter is when they are being compared to the grades of others. Entrance to university or college. Acceptance to a Masters program. Awards and scholarships. I can promise you that when committees are sitting looking at grade transcripts from this time, they will 100% not be wondering what the hell happened in 2020. Nobody knows yet how they will compensate for the complete inscrutability of the transcripts that we generate, but it is certain that there won’t be individual students who managed to live an alternate reality stream where they did not experience the pandemic and the effects it had on curriculum delivery and grading.

I also find it ironic as an educator that for years now we have been saying that we need to prepare our students for a future that we don’t understand, and yet now we find ourselves living a present that we have no frame of reference for. All the rules have changed. Societal norms are in flux. Responsible governments are scrambling to make the best decisions for the present and for the future. We’ve seen politicians completely shed their veneer, humbled into humanity by the pandemic. We’ve seen others double-down on the default political position of obfuscation, redirection, and selling the fantasy. They don’t have a rule book for this, so some are writing a new one, while others are desperately trying to make the old one work. Time will show either way that governments around the world are making many mistakes. But time will also show the wisdom of many of their decisions. It is too soon to be able to tell in each instance which is which. But as I wrote a few years ago, mistakes are just as valuable in the long term as getting things right, because time doesn’t stand still and we are only ever as good as the lessons we learn. Mistakes make excellent teachers for those willing to learn instead of criticize.

Because we didn’t sign up for this, we don’t have a playbook. There is nothing that is time-tested and proven effective. There is nothing you are “supposed” to be doing with your time. There is only what makes sense in the moment. And the biggest thing to understand is that everyone is in the exact same boat. Or to use another metaphor – we are all on the same ride, and the ride has stopped. So when things return to whatever normal will look like, we will all emerge into the same sunlit sky, rubbing our eyes and stretching our arms and legs. Standards and expectations that applied before the pandemic in many cases not be relevant.

Everyone will understand what you went through.

Thanks for reading,

Rich

Interesting Times

There is a saying that goes “May you live in interesting times” and depending on who you ask it is meant either as a blessing or as a curse. I have always considered it a blessing. After all, who wants to be bored? It is also “interesting” that although the saying has often been attributed to Chinese culture, there appears to be no solid evidence of this.[1]

The application to today’s situation – and the parallels of attribution – are worth noting for a moment, though not dwelling on. That COVID-19 originated in China seems to be effectively certain. That it has anything to do with Chinese culture is not (in a country with almost 1.4 billion people how can we designate any one practice as national culture?) That it has thrust us into interesting times is clear. How we behave is going to be something we learn from and talk about for the rest of our lives. I like breaking down my own experience into two categories: Fear and Opportunity. I’ll talk about both.

The fear. Well this is an obvious one, right? I am afraid the virus will overload our health care system. I am afraid of getting the virus. I am afraid that my loved ones will get the virus. I am afraid that myself or someone I love will need hospital care for some other reason and not be able to get it. This is first and foremost. Like almost everyone reading this, I have loved ones who are vulnerable. I cherish them. I want to protect them. But even for my loved ones who are not vulnerable, I don’t want them to get sick. The threat of COVID-19 is something we can’t see, and it travels on our network – the very network we turn to for much of what we consider a happy existence. Humans are a social species. We rely on our pack to survive and thrive. And the virus uses that exact connection to spread. So, we are in a time where we must go against our culture and our very human instincts and disrupt the network. This naturally creates more fear. We are programmed to find safety and security in our social connections, and these are the very connections we must sever in order to break up the network. There is no human alive who has lived through a time like quite this, though there are certainly those who have lived through arguably worse. In modern memory though, this kind of reaction to pandemic exists only in history books and in movies. So, it’s scary for sure. But the fear also creates the opportunity.

If forced to select a time in my life where this was going to happen, well this is the time I would select. There is no human alive who has lived through a time like this – a time where connectivity is so easily established without physical presence, where we have successfully created a new network on which a biological virus can not travel. A time where respect and understanding has been pushing itself more and more to the forefront of our considerations in how to deal with each other. A time where mental health issues like anxiety and depression have become something we are no longer expected to conceal and endure in isolation, but rather to share and explore so that we can help each other grow and be better. And while much has been discussed about the dangers of this non-physical connectivity, we are now faced with the opportunity to show how we can overcome those dangers and use it for immeasurable good.

We are feeling isolated – we can connect. We are feeling anxious – we can share. We have been feeling exploited and tainted by social media – we can exploit it right back and use it in ways we always wanted to but instead allowed it to deteriorate into a morass of rage and AI marketing.

Most importantly, we can connect with those who we are still face-to-face with. Our families.

As a teacher, my plan is to use what I know and what I am learning about connectivity to continue this year’s delivery of curriculum. It won’t feel exactly like being in class. I have done some experimenting already and I can tell you this – while inferior in ways, it is also superior in other ways, and we will allow ourselves to see it, to embrace it, and to grow. Patience is key, but so is enthusiasm. And I am happy to tell you that swirling around with the feelings of uncertainty and anxiety that I’m having about this pandemic and the measures we are taking, is a maelstrom of enthusiasm that is unyielding. We’ll make it work.

As a human, my plan is to continue to exercise proper caution, in the hopes that months from now there will be a whole slew of people who will be able to criticize what we have been doing as overreaction, using evidence of a less severe outcome to back their claims. I will wait as we all settle into this temporary new normal, and as our politicians perhaps speed up the recognition and acknowledgment of what experts have been saying since the outbreak started. We will have food. We will have our prescriptions. And with care and some healthy paranoia, we will have access to health care when and if we need it. None of us signed up for this, but we can handle it. Humans have weathered worse, under much less optimal conditions!


[1] From Wikipedia, citing Garson O-Toole: “Despite being so common in English as to be known as the “Chinese curse”, the saying is apocryphal, and no actual Chinese source has ever been produced. The most likely connection to Chinese culture may be deduced from analysis of the late-19th-century speeches of Joseph Chamberlain, probably erroneously transmitted and revised through his son Austen Chamberlain.”

Maximizing Exam Performance

As a high school math teacher and now university lecturer, one of the most common issues I see is students who under-perform on tests and exams. By this I mean that the grade they earn is not an accurate reflection of their level of mastery of the material – sometimes tragically so. I have been teaching for around 20 years, and my experience teaching, as well as my experience as a student, has caused me to form some strategies to address this. In a recent email exchange with a student who was asking for advice on how to manage studying for multiple exams, I decided to organize my thoughts and type a detailed response. With that student’s permission, I also decided to share it here on my blog.

Question: How would you recommend studying for finals and what are the key things that I should prioritize?

I have some tips, but there is a caveat: these are things that I’ve learned through personal experience as well as my experience teaching for about 20 years, and I have learned that while they are solid tips and work for many people, everyone needs to tailor them to suit their own learning style and personality.

First, some terminology for the purpose of these tips: 

  • Homework
    I’ll use this term to refer to any work you would be assigned or do voluntarily throughout a course that does not directly get assessed for grades. It may be questions/reading assigned by the prof, or practice assignments. It should also be daily review of notes taken in class, which can and probably should include enhancing the notes with more thoughts or research.

  • Test
    I’ll use this term to refer to some kind of minor assessment that does count for marks, but not a large part of the course. These are usually assignmentstests or quizzes, and they generally happen regularly, often weekly. The knowledge they assess is normally not cumulative, focusing on one topic or unit at time, or perhaps just one or two weeks worth of material from the course.

  • Exam
    This refers to the major assessments in a course and are usually cumulative in the knowledge they assess. In many math classes this is a midterm and a final exam. Sometimes it is just a final exam.

  • Term Mark
    This refers to the grade a student earns on any tests, not including exams, as defined above.
Here are the tips more or less in order of priority
Don’t study for exams!

Sounds weird right? What I mean is that you should not be studying for exams – you should be studying for expertise. Furthermore, this studying should occur throughout the term, not in the days before an exam. The root of the word student is study. This literally means that if you are thinking of yourself as a student, then you are thinking of yourself as one who studies.

For many students this is a paradigm shift, even if they don’t realize it. Students have a habit of using the term for accumulating marks, instead of accumulating expertise. A combination of procrastination on homework, sub-optimal time management, and misplaced priorities create a situation where decisions are made to maximize a term mark while minimizing actual learning. That may seem harsh, but students usually see some or much truth in it when they inspect their own habits during non-exam times.

The shift is to start to view homework as the tool to help you grow into an expert in the course material, to the point where you could potentially even teach it. In fact, finding ways to teach the material (usually by helping others with the work) is the very best way to gauge your own level of expertise. If/when you reach this level during the homework, writing tests and exams becomes much less a matter of which questions you are prepared for, and more a matter of making sure that when it is time to write that you are rested and feeling physically comfortable.

Make an exam prep schedule

So once you have an exam schedule from the school, and you know when your exams will be, make a schedule for exam prep. It is almost always better to devote parts of each day to different exams rather than trying to devote all your attention to the next exam. So for example, you might have 4 exams in all, and from day one of prep time (which is the day after the last actual lecture), each day should be divided into 4 parts. At first, you can devote more time in each day to the first exam. Then, when that exam is done you only have 3 per day, and can devote more time to the second exam, etc. Make sure to include recreation/rest time in your schedule! It is unreasonable and unrealistic to think that if you have 16 hours of awake time in a day that you can spend 16 hours doing exam prep.

The puzzle of creating the schedule is mathematically pleasing and kind of fun. When you’re doing it, imagine you were creating it for someone else – someone that you are close to and care about, like a sibling or friend. Not for yourself.

Follow your exam prep schedule

Once you have prepared your schedule, put your faith in it. Don’t question your scheduling decisions after that fact. Pretend it was set for you by someone else – someone that you are close to and who cares about you, like a sibling or a friend. Someone you don’t want to let down. They took the trouble to make this schedule for you so that you would be successful. You owe it to them to follow it to the letter. Resist the temptation to over- or under-use the times they allotted for work. Resist the temptation to under- or over-use times they allotted for recreation.

Prepare!

If you have spent the term studying as outlined above, then most of the work is done when exams roll around. At this stage what you want to do is prepare. I like to think of it using sports as a metaphor. With a big game or event approaching, athletes don’t use the time leading up to the day to become excellent at their sport. That work has already been done, over the course of their training. What they do before a big event is prepare themselves. They manipulate their training and diet so that they will peak on the day of the event. They get ready mentally for the stress of the day. They take care to eliminate distraction that during the rest of the year they allow, more or less. In other words, they sharpen everything they have already done, so that their performance will be optimal on the day. That is what exam prep is. Here is how it might look:

  1. No phone during prep time.
    That means it’s not just on silent in your pocket, or upside down on the desk. It means it is literally off, and in a different room than you are in. You are allowed to use it during recreation time, and you should, if that makes you feel better.

  2. Review the most recent course material first
    Work your way from the end back to the beginning of the course. This is for two main reasons: One, that material is the most fresh in your mind, and so it needs the least review. Two, by working backward you by necessity and up cementing ideas from earlier in the course, since they were generally used to build the ideas that came later. This forces you to assimilate them more completely, and by the time you get to those concepts you are already quite an expert.

  3. Use tests and/or homework assignments as your map to prep.
    Take blank versions of them and simulate writing them from scratch. If you studied throughout the course you will find that you can mostly do this without consulting any external resources like class notes, course notes, textbooks, other students, tutors or the web. But when you find yourself struggling to recall a concept, don’t hesitate to use those resources, more or less in the order I listed them.

  4. Do not focus on being ready for a certain type of question.
    Instead, make sure you are expert in all the concepts you review. A litmus test for expertise is to imagine you had to teach the concept. Would you be able to field questions from students like yourself? Can you envision a way to present it to your peers that would make the concept clear for them? If you can, take opportunities to actually try. There are usually people more than willing to let you explain concepts to them!

  5. From time to time, refer to any exam outline that has been shared by the instructor.
    As you progress through the review, put a check on concepts you feel you are good with. When you have finished working back, it would be shocking if there was not a check on every item. But if there is, go back and find instances of that concept in your review and have another look.

  6. Sleep!
    There is nothing to be gained by staying up all night before an exam, and much to be lost. Any feeling of security it may give you, or any thoughts of “I’ll just hold it together then crash after the exam” are almost always self-delusion. No athlete would ever go into a major event already exhausted. It does nothing to improve performance and much to impair it. On the other hand, a solid night’s sleep will give your brain a chance to reset, refresh, and reorganize.

  7. Finish studying the night before
    It is almost never a good idea to do any studying the day of an exam. If you made a good schedule, you finished studying the night before. After a good night’s sleep, your job is to stay relaxed and properly fed. On the day of the exam, the first time you look at course material should be when the exam begins. Otherwise you risk spiraling on some
    last-minute topic you have convinced yourself is important, and it defeats much of the organization that has taken place in your brain. Picture a well-organized filing cabinet with everything where it belongs. That is what you want to take into the exam with you. Contrast that with a mostly well-organized filing cabinet, with a few files removed and papers scattered about the room. That is a much less effective way to be able to access your knowledge during the exam.

  8. When the time comes to begin writing, do not begin writing.
    This is one of the biggest mistakes I see students make when the exam actually starts. They flip to the first page and start writing. That is putting your destiny in the hands of the person who created the exam instead of in your own hands. What I mean is, why should you write the exam in the order that someone else decided? And furthermore, why should you start writing without any idea of what is coming? When starting on a long road trip it is a much better idea to zoom out and see the whole route so that you have an idea of where you are going, rather than just thinking of the next turn.

    What I strongly recommend is that when the word is given that you may begin, turn the first page and just read. Read all the questions. Slowly. Take the time to make sure you understand what each question is asking. Do not attempt to answer any question until you have read all the questions. Then decide what order you want to write the exam in. Choose your best questions first. Save any you don’t know how to do for the end. You will find that if you write the exam this way three things happen:
    • First, your time is automatically optimized, since you are spending the least amount of time on questions at the beginning.
    • Second, your confidence grows as you progress through the exam, which is much better than having a tough question destroy your spirit near the beginning of the exam.
    • Third, as you work through the questions you are good with, you subconsciously are also thinking about the harder ones you saved for the end, and often get clues and ideas from the questions you are working on so that when you get to the ones you thought were hard, they no longer are – or at least they are easier than they seemed.

That’s it! As I said, you can take or leave as much of this advice as you like, but I would say that if you decide to ignore some of it because you’re afraid to try it, that may not be the best reason not to give it a go. Fear is not generally a good reason to avoid trying something new.

Thanks for reading,

Rich

Why Study Mathematics?

In my job, this question is one I get asked very often. To be honest, it usually comes in a slightly different form …

“When am I ever going to use this? What is it good for?”

As a high school math teacher for 15 years, this is one of the most common questions I received. When I began lecturing at university, I was surprised to find that I still sometimes get asked variations of this question. I suppose it’s a good question, if the idea is that at some point someone will say to you

“Determine

and have your answer on my desk by 5pm today. And don’t get any funny ideas about using WolframAlpha!”

Because the truth is, that rarely happens.

I often give a joking answer, and say flat out, “You won’t,” and then go on a rant about how math doesn’t need to be good for anything, because it is just good. Nobody ever stood in the Sistine Chapel, staring at the ceiling, asking what it was good for! They just appreciate the inherent beauty, because it speaks to their soul. Math is the same.

I think that’s a perfectly good answer, to be honest. But in a more serious light, I find the answer to the question is actually another question: “When are you not going to use this?”

Of course, there are direct applications of many branches of math. But those tend to be very specific, and these days depend heavily on software to do the heavy lifting, so I tend not to think of those. Instead, consider that football players perform bench press as part of their training, to the point that the ability to bench press 225 pounds for as many reps as possible is tested at the NFL combines. Yet not once have I ever seen a football player perform the bench press during a game. Why do they do it then? Couldn’t they just practice the skills they will actually use in a game? I can promise you that at no point during a football game does a player think “oh, this situation is just like bench pressing 225 pounds – I will apply that same skill now.” And I imagine there are very few football players who complain while lifting weights that they will “never use this in real life”. Of course, we know that the reason they train the bench press is that it increases strength and power, so that when the time comes that they need it, it will be there without consciously calling upon it.

Studying mathematics is the same. Math teaches so much if we are awake to the lessons. Here are some things I have learned, continue to learn, and apply regularly from my math studies, along with some examples of how they have impacted me personally.

Scale simple solutions to solve large problems

It is almost always the case that large problems can be effectively solved by breaking them into smaller problems, or by developing scalable solutions to simpler problems. For example, about 3.5 years ago I decided I wanted to learn to draw, so I took a piece of white printer paper and a mechanical pencil and drew a superhero-esque muscle man. It sucked. Like a lot. But I was not discouraged in the least by that. I was fueled by it. Why does this suck so much? I know how I want it to look, why can’t I make it look that way? I was excited by the fact that I could recognize how much it sucked, and by the prospect of working to slowly strip away the suckness. I spent hundreds of hours, solving small problems that were contributing to the suckyessence, and slowly scaling them up. Want to draw a heavily muscled arm? Learn to draw a cylinder. Then learn to draw little cylinders that lie on the main one. Then learn to draw “twisted” cylinders and tubing that changes diameter as it twists. Learn anatomy. Now put it all together. I intuitively understood platonic solids and how they interact with and reflect light. I applied these understandings to understand the types of skills I needed to hone with the way I held and manipulated pencils. I started looking closely at things I never paid attention to before. I still do this, and at no point during this process do I ever consciously say “Oh, that’s just like <fill in math course here>”, but at every point I feel exactly the way I feel when I am working on difficult math problems.

Being right also means proving you are

Math is really never about just “getting the right answer”. It’s about proving that an answer – or a result – is correct. The emphasis on proof is critical. In the real world, being right is rarely enough if you can’t convince others that you are. Careful, methodical, and audience-appropriate explanations are invaluable in this regard. Developing and writing proofs in mathematics is as much an art form as it is a science (perhaps even more so), and my studies in mathematics immeasurably improved my approach to constructing an audience-appropriate argument or explanation. This has had a profound impact on my communication skills, as well as my approach to confrontation. I have used this skill in more ways than I can list, but some examples are: when I have been in contract negotiations, when I deal with sales people when buying big-ticket items (and even when I bargain at markets), when I find myself moderating arguments between friends, family, colleagues or students, and when I used to work as a personal trainer and had to motivate and justify the kinds of exercise and diet choices I wanted my clients to make. In every single one of these situations, and more, I am really constructing proof. In fact, I would say that proof dominates almost all my communication.

Emotional attachment to a belief is irrelevant

Not wanting to be wrong about a belief, especially if it has been long-held, is normal. It is, however, illogical and possibly even dangerous in the face of proof to the contrary. Mathematics trains us to seek, understand and ultimately accept proof on its own merit, and not on any emotional yearning. It also trains us to be grateful when proven wrong, since it makes little sense to want to be wrong for even one moment longer than necessary. My training in math has led to a much more open-minded approach to new thoughts and ideas, and after careful consideration – which involves listening to argument dispassionately, asking relevant questions and weighing evidence – I find myself either happily embracing a new thought, or else more confident in the one I already had, having had the opportunity to test it rationally against a differing viewpoint.

Creativity and math are NOT mutually exclusive.

Not even close. Deep study of mathematics reveals and refines a strong creativity that aligns with and is mutually supportive of logic. This fusion is relatively rare, and people who have it are prone to what seem to be exceptional accomplishments. In truth, the exceptionality of it is not the accomplishment itself but the relative scarcity of people who can do it. One of my favourite examples is Leonardo da Vinci, who most people think of as a great artist, but who was also an accomplished mathematician and scientist, and who did not consider these as separate pursuits or modes of thinking. I find the same is true in my own life, although there are many people who wonder how a mathematician could be artistic.

Clarity lives just on the other side of contemplation

The journey math students regularly take from being completely mystified and often intimidated, to understanding and comfort is a lesson in overcoming that serves us well in all the challenges the future can bring. It instills a confidence that says, “I may not understand this right now, or even feel like I ever could, but I know I can do it.” General wisdom suggests that “easy” might seem gratifying in the moment, but true satisfaction comes from overcoming a challenge. Many people shy away from challenge for fear of failure, but studying mathematics teaches us that we can tackle large problems, even if they seem overwhelmingly daunting at the outset. An example that makes me laugh is the time I purchased a large and intricate piece of exercise equipment for my home gym (a functional trainer/smith machine combo). I bought it used, so it did not come with any assembly instructions, and perhaps embarrassingly, it didn’t occur to me to use Google. When I picked it up the seller had already “helpfully” disassembled it into n pieces, where n is large. I was completely baffled at how to reassemble it when I got it home. But I was not daunted. I laid all the pieces out on the floor, shuffled them around into sensible groups, and slowly assembled sections that made sense. I made mistakes and discovered them when they led to chaos. I backed up, took a different approach, and eventually put it together. The process was not “clean” – I hurt my hand trying to brace a nut while tightening a bolt, and cursed myself for not taking the time to get a wrench to hold it in place. But the result looks like it was assembled by a pro. I’ve had it for many years now, and it still works perfectly. I am fully aware that my engineer friends would consider this a trivial exercise, but for me it was a hard-fought and well-earned victory. This type of approach has stood me well time after time.

You don’t always have to see the whole path to the goal

How often have you been working on a difficult proof or problem, not really knowing if you were getting anywhere good, nevertheless continuing to take small, logical steps – always forward, occasionally pausing to reorient yourself to see if the direction made sense – when suddenly you found yourself having completed the entire thing? Some mathematicians call this the “follow-your-nose” principle of proof. A leads to B which leads to C etc. This might be the most important lesson of all. If you have a long-term goal that seems incredibly distant and perhaps overly ambitious, consider that if you just point yourself in the right direction and take small steps, occasionally reorienting yourself, you do eventually get where you want to go. Plus, the journey is so rewarding. In my life I have used this principle I learned from proof over and over and is in fact how I ended up lecturing at university, something that has been a dream of mine since the 12th grade.

And that concludes my very long answer to the common question! I hope you found something of value.

Thanks for reading!

Rich

My Silver Anniversary

On December 19th, 2018 my wife Marla and I celebrate our 25th wedding anniversary. I think that’s a big deal, so I decided to write something. The last time I wrote something for our anniversary was for our 19th, and is still one of my favourite things I’ve written. If you want, you can read that one here: My Champagne Anniversary

The Champagne Anniversary blog still says a lot about how I feel about our relationship, and relationships in general, so there’s no need to repeat that message here. Instead, in honour of this milestone anniversary, I’ve decided to tell the story of how we met. I’m a high-school teacher and the story is replete with high school drama, so it’s a favourite of my students and thus I have told it countless times over the years. Like any story that gets oft-retold, many of the facts morph with each retelling, and the memories of of telling the story get fused with the memories of the actual event, creating some sort of amalgamation of facts and feelings that nonetheless stands as true, to the extent that it represents one’s own perception of history.

Whatever the hell that means.

Just Your Average Nerdy Kid …

Marla and I met in 1986, when I was 17 and she was 16. But to properly tell the story, I need to paint a picture of who I was before we met, and to do that, I need to go back in time a bit further than that.

Growing up I clearly remember wondering how it would feel to know someone loved you. With the exception of my parents, and I guess my siblings, I couldn’t imagine it. Of course I knew my parents loved me – especially my mother – but what would it be like to be sure that someone else did? Romantically, I mean?

I can’t remember a time when I didn’t have a crush on someone. Some girl in my class, or from the neighbourhood where we lived, or from the summer camps I went to. I was a pretty shy kid, and would never dream of doing anything about these crushes. They were just silent admiration and fantasies of going out on dates, holding hands, and being “boyfriend and girlfriend”. These memories go back to before I was 8 years old for sure, though the exact ages are blurred now. I would watch television and movies and see couples in love and legitimately marvel at how the guy could possibly be certain about the girl’s feelings. I admit I didn’t think about this equation much from the female perspective. To me, females had their shit together in a way that males could never comprehend. They certainly never experienced the kind of doubt I was struggling with. They were models of self-confident perfection, while guys were basically just schmucks hoping to be lucky enough to have someone fall in love with them, while never being sure if that was even possible. Well, maybe not all guys. But certainly this guy.

Entering adolescence certain things became clear to me. First, I was not an athlete. I was a skinny asthmatic kid with what I sometimes used to think of as hyperactive empathy disorder (I have since come to realize it’s not a disorder at all – it’s a gift – if not a heavy one to bear sometimes). As such, I tended to steer away from intense competition, and didn’t have the natural grace or physical intelligence that some people seem to be born with. My strengths seemed to be in all things nerdy. I was good at school, good at video games, and good at watching Star Trek. I had friends with similar interests. We did not talk to girls – we had no idea how to. We had fun though! My friends and I spent almost the entire year of grade 7 coming to school each day dressed as, and in character of our favourite Star Trek crew members. I was Spock, complete with homemade communicator and scientific tricorder. I worked on pretending to be emotionless and logical. I lamented not being able to raise one eyebrow. I did not take myself too seriously. None of us did. It was just our way of having fun.

Adolescent Upheaval

When I was 13, my parents divorced. When I was 15, my mother decided to move from Calgary to Toronto. Starting a new school in grade 10 for someone like me was an adolescent nightmare. Fortunately my best friend Rob and his family also moved that summer, largely due to the fact that our mothers were friends as well. Rob and I spent essentially all of grade 10 together, still wondering if there would ever come a day when we could actually talk to girls. We certainly talked about them! Those weird, wonderful, remarkably composed humans who always seemed to know what they were doing were so far from our world, there literally seemed to be no way to make first contact (see what I did there? Star Trek reference). Think Raj from Big Bang Theory, but in real life. Also, Raj found he could talk to women if he had some alcohol – we didn’t drink, and in any case, it wouldn’t have worked.

The Tale of Raj and Saavik (or something like that)

Here’s a little anecdote I love to tell to illustrate just how nerdy and naive I was. In grade 11 I took a history course, with a teacher who liked to set up the desks in the classroom in a big U. My seat was at the tip of the U farthest from the door to the classroom. There was a girl in the class whose name I forget, but for the purpose of the story let’s say it was Saavik. I had a gigantic crush on Saavik. I thought she was the smartest, prettiest, funniest and coolest girl at the school (or at least in the history class). The high school I went to was public, but was in a Jewish neighbourhood, so a lot of the kids there were Jewish, as am I. Saavik was Jewish. I figured that was good, because in some altered reality where she and I got married and lived happily ever after, it would be good that we were both Jewish.

Anyway, Saavik sat across the U from me, with her friends. I used to try to divide my time roughly evenly between paying attention to the teacher and the classwork and admiring Saavik without seeming to. The old “stretch-and-scan-across-the-room-but-linger-3-nanoseconds-longer-as-your-eyes-pass-your-crush” gambit was a favourite. Sometimes I would think about what I might say if I ever found a way to talk to her.

Then I’d laugh at myself. Because, like, whatever buddy.

One day before class started I was sitting at my spot when Saavik got to class. Of course I knew she was in the room – I always knew. But I kept my cool (haha – me, cool). As she made her way to her seat something weird happened, which to this day I don’t have an explanation for. Maybe her friends weren’t there. Maybe she wanted to see the world from a different angle. Maybe she was temporarily taken over by aliens from another dimension wanting to run sociological experiments on human adolescents. In any case what she did was she started to make her way around the U toward my location.

I had no idea what to do.

My heart rate rose to approximately 473 bpm. I started to sweat a little. I started talking/yelling at myself in my head:

Why is she coming this way?!? Keep your eyes on your book! Oh god she’s coming closer! What is she doing? What am I going to do! For the love of Vulcan do not look up. What?! Is she sitting down?!?! NEXT TO ME?!?!?!!!

I couldn’t move. I couldn’t look up. But at the same time I knew this was my chance, if ever there was to be one. Then the most bizarre thing happened. My left hand was resting on the table, and I felt someone touch my ring.

Saavik was touching my ring!!!

Then, as if it couldn’t get any more intense she spoke.

To me.

“Nice ring” she said.

She’s touching my ring!! She talked to me!!! What do I do?!?! What would Fonzy do?!? I have to talk to her. I have to say something! What do I say? Has to be good. Have to make sure she knows I’m Jewish so that marriage is possible. What do I say?!?!

“Thanks” I said, in a voice almost exactly like those two fanboy monsters from Monsters Inc. who idolize Sully, Smitty and Needleman, “I got it for my Bar Mitzvah.”

Then I pulled my hand away. And never looked up. It was the first and last conversation we ever had. I can’t tell this story without laughing at myself. But it is 100% true.

 I wonder what ever happened to Saavik.

Rich, Rob and Geordi

Ok. So hopefully you get the idea. Shy kid, lots of nerdy friends, can’t talk to women, wishes he could. Now we’ll fast-forward to the summer between grade 11 and grade 12. It is maybe worth noting that this was back when the Ontario education system had a grade 13 in high school, for kids who wanted to go to university after graduating. Rob and I had become very good friends with a guy I will call Geordi. We had been friends with Geordi for most of grade 11. He is a great guy. He was nerdy like us, but also had a bit of a sophistication that we did not. That certain, you know, savoir-faire. That summer Geordi decided that enough was enough. In grade 12, he was going to start talking to girls. He was going to get a girlfriend.

Cue Smitty and Needleman:

“Hahahaha! Ok Geordi, whatever you say man. As if you can talk to girls!”

But Geordi was determined. And to his credit, when grade 12 started, he managed to grow into someone who could, in fact, talk to girls. And he did. Regularly. Of course not when Rob or I were around – but that’s because it’s hard to seem sophisticated and together with Smitty and Needleman hanging around making you lose your focus.

Geordi started to report back to us on this new world of girls he was living in.

“Sophia and I walked to the convenience store at lunch today. I really like her.”

“I sit next to Jodi in English. She’s really funny.”

“There is this girl Nyota whose locker is just down the hall from mine. She’s super-nice.”

All were candidates for Geordi’s first girlfriend. All sounded super-exotic and awesome. I was seriously in awe of Geordi. As the year progressed it became clear that Geordi had indeed learned how to talk to girls, and things were looking as though he would in fact achieve that mystical state of having a girlfriend, heretofore only achieved by athletes and dudes with cool skateboards. Rob and I were happy for him, and not a little jealous.

Enter Nyota

One day I met Geordi at his locker at the beginning of lunch. Geordi had a car, so it was especially good to be his friend around lunchtime. Anyway, Nyota happened to be there. Geordi introduced us:

“Nyota, this is my friend Rich. Rich, Nyota.” he said.

“Nice to meet you Rich,” said Nyota, quite reasonably. Little did she know I had just suffered two minor heart attacks during the introduction and was fighting off an embolism. I believe my response was something along the lines of

“Hbbj Nrag, bluwq,” delivered most charmingly, I imagine. Maybe there was an umlaut on the u in bluwq. I can’t be sure.

Of course I assumed the natural and usual outcome of the exchange, which is to say I would get the look of bewilderment tinged with horror that I had come to expect from girls I attempted verbal communication with. But that didn’t happen.

Nyota kept talking to me.

I honestly have no idea what she said. I was just fascinated by the fact that she didn’t do the virtual cut-and-run. I remember she was smiling. I remember that she was talking to me as though I were normal. I remember finding that extremely confusing.

It took me about 47 seconds to fall in love.

That was a special day. It marked the first time I considered myself to have been in an actual conversation with a girl. And it was the beginning of me being able to talk to girls, like a normal human being. It opened up a whole new high school experience, centred on Nyota, of course. I made sure to spend as much time as possible in her orbit. She was always so nice. She introduced me to all her friends, and I was able to talk to all of them, though admittedly only long enough so that it wasn’t totally rude when I returned my focus to Nyota. One of the friends she introduced me to was Marla. Marla seemed nice enough. But whatever. Nyota was the one!

The Pact

Eventually I knew it was time to have a discussion with Geordi. If Nyota and I were to be married, he would probably have to find out sooner or later. So one day when I was over at his place I let him know that I had fallen hard for Nyota. I figured he’d be cool with it, given how many other girls were on his radar. Turns out he wasn’t totally cool with it. I remember him saying that although there were plenty of girls he had been talking to, Nyota was the one he was having romantic feelings for. Damn. Just my luck. So we did what any two idiotic adolescent boys would do – we made a pact. We would both pursue Nyota to the best of our abilities, and once one us was successful, the other would back down, and we would remain friends. It’s funny I know – the arrogance to assume that one of us would be successful, as if Nyota didn’t have other options, or was even interested in a relationship. But in any case, that was the pact.

For myself, there was never any doubt that she would choose me. She had to. We were meant to be together. I could feel it in my soul, with a depth only adolescent hormones can attain. My newfound confidence was exhilarating, and I was going to ride it out for all it was worth.

I was a lifeguard back then, and I regularly worked at an apartment building occupied mostly be senior citizens who never used the pool. I would often sit and stare at an empty pool, or do crosswords (after I finished my homework, that is – I managed very high grades in high school thanks to that empty pool). Sometimes a friend would come and visit with some McDonald’s which was right across the road. One day Nyota came to visit. She brought me a Big Mac. Love, right?

So as we were sitting there eating our grease, she suddenly got really serious. She says she has to tell me something.

“Geordi told me about your pact,” she says.

“blüwq?”

“He told me how the two of you are both interested in me.”

“He did. That’s … interesting.”

“I just want you to know, I love you both. I haven’t made my choice yet. But I will soon.”

Ouch. I questioned Geordi’s choice, that’s for sure. But she did say she loved me (don’t get excited – Nyota used to say I love you to pretty much anyone she was friends with). And at least now everyone knew the situation. I still had no doubts about who she would choose. That is, until Halloween that year – this would be 1986.

The Halloween That Crushed Me

Geordi had a Halloween party at his place. We weren’t old enough to drink legally, but for some reason I always looked old enough and could buy alcohol without getting carded. I bought some for everyone, which is funny because I myself never drank. Didn’t like the taste. Still don’t, actually. Anyway, we were all there at Geordi’s having a good time. At one point in the evening I realized I couldn’t find Nyota, so I went looking for her. She wasn’t anywhere downstairs where most of the people were hanging out (neither was Geordi, although I didn’t notice that), so I went upstairs. The door to Geordi’s room was closed, so naturally I went in (I swear this is not how it sounds – I was so naive that I just thought it was another place to look, and I had been in Geordi’s room hundreds of times since that’s where we hung out when we were at his place).

I found Nyota. And Geordi, as it turned out.

Now before you get all freaked out I have to tell you that it’s not what it would have been if this were a television drama. They were just sitting on the bed. But they were sitting really close. And they both looked at me with expressions that told me that Nyota had made her choice. I apologized for interrupting, closed the door, and went straight for the beer. I grabbed a bottle of Molson Canadian and must have chugged like at least one seventh of it, then decided I was drunk. I slid down the wall I was leaning on and started crying. Oh the teenage angst. Oh the pain! Rob found me like that and figured out what happened, and we left.

The next day at school Nyota found me and apologized that I had to find out that way (funny right? She apologized to me because I barged into a room where the door was closed). Apparently she had made her choice some time before, but neither of them knew how to tell me. She said she still wanted to be my friend, because she valued our friendship very much and in fact considered me to be her best friend. I agreed. We would be friends forever.

Not My Finest Moment

About a month later, Geordi and his family went to Montreal to visit some family. Being friends and all, Nyota and I spent much of that time together. We went to see Lady and the Tramp, which was playing in a theatre near where I lived, and went to dinner after. We talked a lot about what had gone down. I told her I still loved her and couldn’t turn it off. She told me that Geordi didn’t understand her the way I did, although he loved her and she loved him. We decided that she had made the wrong choice. She decided she would break up with Geordi when he got back, then we would wait an appropriate amount of time and then she and I would get together officially. I had officially broken my pact with Geordi, but I thought he would understand. Nyota was my soul mate, after all. It was much more than just teenage romance.

That year I had a New Year’s party at my place. Like Halloween, everyone was there. Nyota told me that she would break up with Geordi at that party. I was eager for that to happen so we could begin our life together. I was hyper-aware of Nyota and Geordi all evening, and eventually I noticed that they were not around. Nyota came back later but Geordi did not. She was not happy. I am sure he was not either. But it was done. We spoke briefly but she was very upset and left. I was upset for Geordi, but elated for myself. All those years of wondering what it would be like to be in a romantic relationship and here I was, in one.

A few days later Nyota told me that she was headed over to Geordi’s place to talk. He has asked if she would come over and she felt she owed him that. I was concerned, but hey – people do what they need to, right? I told her to call me when she left, no matter what time it was. I stayed by the phone all night. I unplugged the other phones in the apartment when it got too late so the call wouldn’t wake my mother or siblings. I put the phone under my pillow so it would wake me but be muffled. The call never came.

Let the Teenage Angst Begin

The next day I called her house. These were the days before call display – if you wanted to know who was on the phone you had to actually answer it. Nyota’s mother answered. I asked for Nyota and she asked who was calling. When I said it was Rich, she said Nyota wasn’t home and would call me back.

Hmmmmm.

Rob had come over that morning, and when I hung up he said he would try. He called, and again Nyota’s mother answered. She asked who was calling and he said Rob. She said one second, and put Nyota on the phone. Rob gave me the receiver, and I said hi.

“Oh, it’s you” she said, “I was going to call you later.”

“Well I’m here now. How did it go? What happened?”

“We had a long talk, and Geordi helped me realize what I should have already known. That I love him more than anything in this world.”

I felt like Thanos had used all the power in the infinity gauntlet to reach into my chest and squeeze my heart.

“Well kid, you had me fooled.” I said, and I hung up the phone.

I was pretty inconsolable for weeks after that. Geordi and I talked and decided we were cool, but we really weren’t. It was hard for him to forgive me and I didn’t blame him. And I was just unable to internalize what had happened. We were supposed to be soul mates. She was the only girl who ever talked to me. And she chose someone else.

I still hung out with our friend group when we would go out. One of our common activities was to go bowling and then hang out at a Tim Horton’s near the bowling alley. Any teenager will tell you, there is no pain like teenage heartbreak though, and I would stay alone in the corner and wallow. During that time, Marla would always come over to see how I was doing. I can only imagine how pathetic I looked. She and Nyota were very close, and she knew what had happened. We talked and talked. I lamented my loss. She commiserated. This went on for a long time.

The Beginning of Love Was True Friendship

Eventually I began to realize that we weren’t spending our time talking about Nyota anymore. We were just talking about stuff that people talk about. I also realized that whenever the group went out, I always wanted to be near Marla because I just really enjoyed her company. I wasn’t sure if she felt the same way, but she seemed to not mind the fact that we always ended up sitting together. I know I didn’t mind. And when we hugged as friends, did she hold it a little longer? I wasn’t sure. I know I was holding it just a smidgen long, but always hyper-aware of whether she was pulling away as one does at the end of the friend hug.

One day Geordi came to me, and asked me if I was having feelings for Marla. I said I thought maybe I was.

His response was “Oh, no. We were worried about that. Nyota and I don’t want to see you get hurt again. Nyota talked to Marla and is sure that Marla does not feel that way about you.”

Not Buying It

I should have been devastated, right? But it didn’t sound true. I was getting a different vibe from Marla than would be consistent with that. So I just kept doing what I was doing, which is to say spending time with her, getting to know her, and just really enjoying each other’s company. Oh, and the hugs were getting longer, I was sure of it. I got a bit more confident as time went on – Rob had a birthday party for Marla at his place, and we were all lying on the floor in his family room listening to music and talking. Marla and I were lying on our stomachs next to each other, and she was close to a glass coffee table. I put my arm over her back – like right over, in an arch, no touching – and said I was just protecting her side from the corner of the table. She smiled in the cutest way (which she still does) and said ok. I stayed like that for hours, I think. Couldn’t feel my arm. But I could sure as hell feel my heart.

Our First Date

There was another couple in our friend group that I haven’t talked about. I’ll call them Han and Leia. They were good people, and a real power couple at the time. Han and I discussed going to see a movie with Leia and Marla. We asked them and it was set. The movie was Brighton Beach Memoirs. The date was January 27, 1987.

During the movie I decided to “make the move”. The Danny Zuko move. I literally yawned and stretched to put my arm around her shoulders. But before I put it all the way down I lost my Zuko, and asked her if it was ok if I put my arm around her. She said yes.

SHE SAID YES!

I said “Good. Because I love you.”

That’s right folks. First date, right out of the gate. I went there. And her reply was three words I will never forget.

“Are you sure?”

See – she knew I was not quite sane. But I was sure.

“Yes,” I said.

“Good. Because I love you too.”

And with those words … she saved me. (Man, that sentence was fromage right there! True though.)

33 Years Later, She Continues to Save Me

And ladies and gentlemen that was it. That’s the story of how Marla saved me, and helped me become I am today. When we started dating I was 17 years old, and she was 16. We have said “I love you” to each other every single day since then, with the exception perhaps of the days before internet and cell phones, when we were in different cities for university, and long distance charges made it so we couldn’t talk every day.

I’ll be 50 this coming April. 33 years of my life have been spent in love with Marla, and knowing she loves me too. Little me was right – it is a bizarre and wonderful thing. Marla is so much more than my wife. She is more of me than I am myself. Every bit of me that does good in this world is influenced by her. She is the kindest, gentlest, most caring soul. Her greatest pleasure is just being with the kids and I. If the first part of this blog was about how we met, I think it’s an injustice to not spend the end of it talking about how my life is so much better because of her. Here are some images that I have from our 33 years together. They aren’t in any particular order, and the list is infinitely far from comprehensive:

  • Watching her breastfeed both kids. She would sit with them on the special breastfeeding pillow, and methodically kiss all of their parts as they fed, spending particular time on their little toes. So peaceful, and so special. My heart still melts when I think about it.
  • One time on her father’s sailboat, I was on deck and she was below. I looked down through a hatch at the same time her father did at Marla looking up at us with those big brown eyes. I was struck by how sweet she looked. Apparently so was her dad – he commented on her “big cow eyes”. He meant that in a nice way. She has this way of looking at me sometimes with those eyes that is like pure love.
  • On our honeymoon in Ixtapa, Mexico, there were some guys on the beach selling parasailing experiences. I think they were charging $50, but I can’t remember. In any case I do remember it was all the cash we had with us at that moment. I was too scared to try but she was not. I remember seeing her suspended up there, and I was so in love with her at that moment, and so scared that she might get hurt. She looked so small, and yet she was (still is) everything.
  • Watching a movie or television with her and the kids. We always know when something will make her cry (it doesn’t take much, admittedly). We always look at her when we know she will be crying. It’s like she emotes for all of us. We all love her so much, and in those moments I think it gets amplified.
  • After my heart attack I had a fairly ugly-looking bruised, tender area where the catheter for the angioplasty was inserted in my right wrist. I was feeling pretty fragile overall, and was taking extreme care not to stress that area. I remember lying in bed mostly asleep, and I turned over and realized that my arm was about to get squished under my head, so I extended it out. It was then that I realized Marla was fully awake and watching me, as she gently took a small pillow that lives on our bed and placed it under my wrist. She is always doing that – small things to take care of the people she loves. That pillow is still in the same spot 4 years later. I still put my wrist on it. My wrist is fully healed – can’t even see a scar.

I said recently to someone that there isn’t a part of me that isn’t infused with Marla. Double-negatives aside, I don’t know a better way to describe her impact and influence. She is my best friend, my closest confidant, and the source of all my strength and confidence. I literally spend time just treasuring my fortune at knowing her, and being her husband. There may or not be such thing as angels, but there sure are angelic people, and Marla is the most angelic of them all. I love her.

Thanks for reading,

Rich

Heroes

Lately I have been thinking a lot about my heroes. In order to help clarify my thoughts, I thought a blog post might be useful. I’ll start with some clarification about the way I am applying the word “hero”, because I think it can have many meanings.

For me, a person who rushes into a burning building to save a baby is heroic, and I stand in awe of that kind of bravery, but I am not talking about that kind of hero. Then there are the people we see repeatedly doing amazing things in some specific context. For example Michael Jordan often did heroic things on the basketball court, most notably for me was game 5 of the 1997 finals when Jordan, sick with either flu or food-poisoning, still managed to lead the Bulls to victory. But I’m not talking about that kind of heroism.

What I am talking about is when I encounter someone who has amplified some trait or combination of traits I sense in myself, and that I would like to amplify as well. I could probably use the term “role model” here more aptly, but I also find that this term is not as charged with the energy I am trying to convey. The word hero works better.

When I was younger I didn’t realize this – I thought my heroes were demonstrating something I didn’t have, and that drew me to them. As I got older I started to discover that in reality what was happening was they were showing the trees that my seeds could grow into. They were showing that it works, and that it can stand you well. They were showing me that I was right to want to nurture those aspects of my character. So who are my heroes? It’s an interesting list. In many cases there is overlap, but not all. And sometimes the heroism is derived from a very narrow slice of what is undoubtedly a complicated synthesis of things I either don’t know about, or else don’t value in this sense. So I guess my list is kind of like a Frankensteinian conglomeration of pieces, each amplified, that make up the parts of me I like the best, and want to amplify.

Maybe one day I will write out the list, and do my best to identify how each person comes to be there. But today I want to talk about one hero specifically. Because she left us today, and I am feeling the loss intensely. And she is a most unlikely hero.

I’m talking about my dog, Tryxi.

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We said goodbye to her this morning. It was hell. The whole family was there, along with our wonderful vet, who loved Tryxi almost as much as we did. There’s no surprise here for any dog owner. Dog owners all understand how much we love them. And any dog owner who has lost a pet knows there are no words for the pain of that day and that moment. But she was suffering terribly, poor girl. Cancer was eating away at her from the inside out and she had lost her muscle mass, her appetite, and much of her enthusiasm. Although she was happy about people right until the last moment. She loved her people.

So let me tell you why Tryxi was my hero.

Tryxi spent most of her days in my wife’s home office, guarding my wife and the house from her doggy bed. When the four of us (my wife, myself and our two kids) would gather in the kitchen or family room for family time Tryxi always made sure she was there too, the proximity being important to her and to us. Whenever my daughter was sad, she would hug Tryxi and it would be better. Ever since my heart attack about 3.5 years ago I have had bouts of anxiety that cruelly give me chest pain. Hugging Tryxi took the pain away.

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Tryxi never tried to make anyone feel better, or better about themselves. It just happened because she accepted everything as true. If she sensed sadness she never tried to tell the person to make the sad go away. She just absorbed it. When she sensed happiness she ran with it. Tryxi never lied – to herself or to anyone. If she found something to be irritating she said so (as experienced often by our other, younger dog, Moose the pug). When she was in pain Tryxi never thought about whether it was fair or not. She never felt sorry for herself. She also never congratulated herself for anything.

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Tryxi was naturally strong. She destroyed many a Kong in her time – even the “Extreme Kong”, designed for the toughest chewers, was no match for her and lasted less than 20 minutes. Her thighs rippled with muscle even when she wasn’t moving. And yet Tryxi never, ever, used her strength to hurt anyone or anything. She would use it readily to establish her presence, or to solve a problem, but never in aggression. Tryxi knew exactly who she was without anyone having to tell her, and certainly without having to have conversations with herself about it. If she liked something she loved it. If she didn’t like something she ignored it. Her default position was love and calm. Anything that happened that took her away from that place was always viewed as a temporary distraction, and she would deal with it then patiently wait the return to baseline. Without judgement or remorse. Even as she was deteriorating, her attitude stayed like that. She was waiting for her peace.

This morning she found it. She knew it was coming and she wasn’t afraid. It was what she was waiting for.

Tryxi has been my hero for years. I am changed because of her – because she showed me that I could amplify those traits that I saw in myself. I do my best to calmly accept the moment. To live now. To enjoy the love that is always there. To bring peace to others. To not judge. To not waste energy fretting over what is “fair” and instead to use my energy to live fully.

She was a good girl. She is my hero.

Thanks for reading,

Rich

Gracefully Honest

In this blog I will talk about honesty – something I think many well-intentioned people struggle with. This is because sometimes it seems like lying is the right thing to do – and in some rare cases, it is. To paraphrase Sam Harris, when Nazis came looking for Anne Frank and her family, anyone lying about them not being hidden in the building was certainly doing the right thing.

That said, in all but the most extreme cases, people choose dishonesty for misguided reasons. This happens because sometimes the truth hurts. In fact, sometimes, truth is used as a weapon.

The confusion is, in part, because while honesty can be a good thing, there is no guarantee that it always is. Honesty must be wielded virtuously, which is not automatic. In fact on its own, honesty is not a virtue.

Honesty is not a virtue

In classical antiquity, there are the four cardinal virtues. In brief, here they are (these definitions are mine – for more formal details, check this link):

  • Prudence: The ability to judge the appropriateness of a possible course of action.
  • Courage: The strength to act in the presence of fear.
  • Temperance: The exercise of restraint in feeding an appetite.
  • Justice: The purest form of fairness, in a righteous sense.

So honesty is not a cardinal virtue. Now over the centuries, philosophers and theologians have added more virtues to the cardinal four. Of these there are three that I think are moral necessities. These are “love”, “charity” and “kindness”.

Still, on it’s own, honesty is not there. This is because honesty can be used morally (specifically in the context of love, charity and kindness), but it can also inflict pain – intentionally or not. Let’s have a look at that second situation first – the “brutal” honesty.

Brutal honesty

“I am going to be brutally honest with you.”

How many times have you encountered that sentiment? How many times have you said it? Let’s stop to consider what it prefaces: that the person is about to lay some bit of perspective on you that they know is going to hurt.

This is usually justified by the idea that you are deluded somehow, and need to “snap” out of it. Or you need a “hard” dose of reality. Or any other number of violent paradigm shifts the perpetrator feels they are uniquely prepared to impose. Because, after all, the world is full of people willing to coddle you, creating the need for someone righteous enough to tell you the truth, even though it will hurt.

This is bullshit.

This “brutal” honesty is really an attempted behaviour modification through punishment. The shock it is expected to impose is designed to somehow shine light on a deficiency in perception, so that you cease your persistence in pursuing some vision. A vision which, according to the person with the flashlight, is a fantasy. It tends to come from a place of anger and – make no mistake – is meant to make you suffer for whatever pain your apparent delusion has been causing them.

People who use this phrase like to project pride in their willingness to use it. You may hear them boast such claims as “Hey, I call it like I see it”, or “I’m a straight-shooter”. It comes with admonishments like “The truth hurts”, or “If you want to hear the truth then you don’t want to be around me”. They may be offering honest assessments, but they are nested in dishonest motivation, even though the motivation is sitting right there in the phrase. Brutal is not a nice word.

Definition of brutal
“Brutal.” Merriam-Webster.com, Merriam-Webster, http://www.merriam-webster.com/dictionary/brutal. Accessed Mar. 2017.

Check out that definition. There is nothing in there that speaks to any kind of morality or good intention, and certainly nothing virtuous. Even the entry about brutal truth contains no compassion. Accurate? Yes. But unpleasantly and incisively so.

So then someone who prefaces the delivery of truth with “I am going to be brutally honest” is – by their own admission – embarking on a non-virtuous wielding of honesty as a weapon to deliver misery. I propose that in the vast majority of situations, the fundamental reason for this is that even though they are using the word, they are not being honest about their own motivation – the desire to be brutal.

But I don’t want to be brutal!

It’s okay – I know. This notion of brutal honesty leads to a concern from good people who don’t want to be brutal. There is a perception that if the truth is brutal, or perhaps unsavoury, then a lie would be better. Keep in mind though that lies come with a heightened anxiety of their being discovered. This often leads to uncomfortable situations, where additional and more elaborate lies are needed to maintain the facade of truth.

It doesn’t have to be this way. There is a way to be honest and virtuous. I call it “graceful honesty”.

Honesty with grace

First, let’s have a look at the definition of grace, so that you can understand why I chose that word. Grace has many meanings, so I have highlighted the ones I am applying in this context:

Definition of grace
“Grace.” Merriam-Webster.com, Merriam-Webster, http://www.merriam-webster.com/dictionary/grace. Accessed Mar. 2017.

Recall earlier, when I spoke about the three virtues of “love”, “charity” and “kindness”. In many ways, the word grace encapsulates these, and so I choose it to describe the type of honesty I mean.

First, be honest with yourself

Graceful honesty isn’t difficult, but it does require some practice if you are not in the habit. The key to it is when you find yourself either tempted to be dishonest, or about to be brutally honest, you stop and spend some time being honest with yourself first. If your motivations are virtuous, then there will be a way to communicate honestly with grace. Conversely, if your intentions are nefarious, then hopefully you will be honest with yourself about that and choose some other course, having recognized the toxicity of your initial instinct. The key then, is to use self-reflection to uncover and put words to your motivation. I don’t want to use too many specific examples here, because it is easy to make arguments about the inaccuracy of an example as it applies to yourself, and then decide the concept is flawed, but I’ll indulge in one in the hope that it will be a good springboard.

Dinner at Kelly’s

Suppose you have been invited to dinner at your friend Kelly’s house, and you just don’t feel like going. The likelihood is that if you decide not to go, you will fabricate an excuse. Further, the excuse probably has a half-life greater than a few hours. What I mean by that is that it’s probably a concocted scenario that will likely be referred to at a later date. For example, you may claim “my kid is sick”, which you can bet Kelly will ask about in the next day or two, and may even ask your child. In this case you will have to remember the excuse so that you don’t accidentally contradict it later, and you may even have to recruit your family to perpetuate the dishonesty – something they are more likely to forget about, since they are not vested in the lie. Result? Anxiety.

Instead, consider this. You really do value your friendship with Kelly. You also don’t feel like going. Before choosing to be dishonest, you can spend some time in honest self-reflection. Why don’t you want to go? Be super analytical about that. You may discover that you actually do want to go, or you will confirm that you don’t. If you truthfully don’t want to go, you will now be better able to put into words what the real reason is, which will of necessity consist of the factors that are outweighing your legitimate desire to spend time with Kelly.

If you tell Kelly exactly that reason, and if Kelly is a good human, she will understand, because you have been fully honest and presented the reason in full context of how you struggled with the decision. She will appreciate the conflict, and understand the conclusion, even if she is disappointed.

But wait you say! I know Kelly! She would never understand! She would just be insulted! Well, I’m not foolish. I know this is also a possibility. But here’s the thing: this is only the current state of your relationship because of a history of implicit dishonesty about motivation. Which means there is room for more honesty – on her part and on yours. See, if at the core you both value each other and the friendship, then you mean no insult, and so how can she be insulted? And the core is all that actually matters – because it is impossible that either of you wants the other to be upset. That core exists, and honesty will land you there. Graceful honesty.

Graceful honesty doesn’t mean everyone is happy

In the example above, Kelly is probably going to be disappointed. You might also. That may seem contrary to virtue, but it isn’t. Not if you were honest about the factors that outweighed your desire to go. Disappointment isn’t a monster to be avoided at all costs. It’s a natural consequence of not being able to implement more than one choice at a time.

One of the great contributors to dishonesty is a desire to keep everyone happy – or at least not miserable. But it’s a trap. Lying by definition creates a false narrative. Perpetuating this to maintain a state of happiness, in fact maintains a state of delusion. One from which the participants (barring tragedy) must eventually emerge, and who’s discovery is unlikely to legitimize the illusion of peace they were enjoying. Put simply, the lie just sets everyone up for a bigger fall.

But life isn’t about being happy all the time! We all know this. We all experience negative emotions like sadness, anger, and disappointment. For the most part we don’t let these things impact the zoomed-out graph of our lives. Yet we find ourselves willing to skirt honesty with others to somehow shield them from these normal experiences.

Have you ever said something to someone in anger that you later regret? I’m betting you have. I’m betting some if it was pretty damn poisonous, and required a lot of apology, replete with the sentiment “I didn’t mean it”. But is that really true? More specifically, does “I didn’t mean it” mean the same thing as “it wasn’t true”?

My experience tells me that what we are really trying to say is “I regret using honesty to hurt you – it isn’t consistent with how I feel about you.” This can be about something you’ve been holding in for a while, or it can be about an emotion that was real in that moment, instigated by the anger. For example, “I hate you!” during an argument isn’t totally untrue, just imprecise: it really means “I hate this feeling I’m having right now that you are causing”, and it is 100% true. It is also 100% forgivable, because it is 100% understandable.

If you think about this for a while, you will see that the real mistake is not being honest earlier, when graceful honesty would have worked: “I love you, and I’m in it for the long haul, but I do get irritated when you don’t put the cap on the toothpaste. I do not equate this behaviour with you, and my irritation is therefore not aimed at you, but the behaviour.”

That last quote is wordy and annoying, I know. But it’s the idea I am trying to communicate, not a recipe for how to tell your husband to put the damn cap on the toothpaste. Very often we don’t disclose little irritants like that because we are concerned it will be taken as criticism of a loved one we don’t want to hurt, as opposed to observation of a behaviour that is independent of the reasons we care about the person exhibiting it. Graceful honesty would disclose all of that, and keep the barbs from growing onto a club that could be wielded in anger.

See, hiding the truth is silly. We are all in this reality together. We should share it. All of it.

Honesty is the sharing of reality.

Think about it. How can honesty be anything else? But as I said earlier, to do it with grace requires a deeper searching of our own motives than we normally do. So the next time you feel like a lie is warranted (or if you are tempted to inflict pain with truth), ask yourself why. What is motivating you? Who are you trying to protect? Who are you trying to help? When you feel the truth needs to be hidden, put away the issue whose truth is troubling you for a moment and look at the feeling itself – it will be the source of the honesty you should embrace. The reality you should share. It is the only way to build and maintain relationships that have value.

Thanks for reading,

Rich

Open-Mindedness

Recently I have been thinking a lot about why so many people seem inconvincible of certain things which I hold to be true. And while I could certainly make a list of some of these things, that is not the intention of this blog entry. Instead, I have been reflecting on open-mindedness and wanted to share.

Many people – myself included – often enter into discourse with someone of a differing opinion with the intention of convincing them to change their mind. For example, maybe your friend Paul thinks all trees in your neighborhood that are taller than 12 feet should be pruned to 12 feet or less, so as not to obstruct anyone’s view of the lakefront. You know that he’s clearly wrong! You get into a discussion. Only it’s not really a discussion – it’s an argument each of you is trying to win. Maybe out of frustration you start incorporating personal attacks. Maybe you get so angry at Paul’s refusal to capitulate, as well as the horrible things he is saying about you, that it ends your friendship. Maybe in the middle of the night, Paul prunes all of your tall trees. Maybe the next night you erect a 30 foot statue on your lawn directly in Paul’s line of sight to the lake … and so on.

It’s sad, and you don’t even like the statue, but what choice is there? Paul must be taught a lesson.

I wish this was hyperbole. Sadly, it is not. And the conclusion is clearly suboptimal.

Well … let me construct a basis for discussion with some (hopefully) fair assumptions. In doing so I’m going to have to use a little bit of math terminology, and it occurs to me that some people might not know precisely what I mean, or even be put-off by some of my more mathematical references. If you think this might be the case, I ask you to bear with me. The concepts and symbols I use are the best way for me to illustrate my point, and I’ve included here a bit of a math lesson, in case it is not something you’ve encountered in your life – it will clarify some of the words and concepts I use for the rest of this article. Of course, if you feel there’s no need for you to read this section, by all means scroll past it and keep reading (I won’t feel bad).


Some Math concepts

Sets
Mathematicians like to talk about collections of values that are somehow related, and when they do, they use the word set. We use curly brackets to list the objects (known as elements) of a set. So for example the set F=\{apple, orange, banana, kiwi, peach, nectarine\} is a set I have named F, and just so you know, it is the set containing all the fruits I might bring to work with me in my lunch. A subset of a set S is another set that only contains elements from S. So for example M=\{apple, kiwi\} is the set of fruits I brought to work in my lunch on Monday, and is a subset of F. On the other hand, A=\{apple, pineapple, banana\} is not a subset of F.

A Little Bit of Algebra (Apologies to the Arithmophobic)
Consider this simple algebra equation:
\displaystyle 3x+4y=7
The x and y are understood to be symbolic of numbers, but the use of symbols mean that they vary – which is to say, they are variable. The equation is a statement. In this particular statement,
x = 1, y=1
would be a valid solution (i.e., the equation becomes true), since
3\times 1 + 4\times 1=7.
So would
x = 5, y=-2,
since
3\times 5 + 4\times (-2)=7.
However
x = 5, y=2
would not be a solution (i.e., the equation becomes false), since
3\times 5 + 4\times 2=23,
which is not 7.

Statements
In math and philosophy, a statement is a sentence that must either be true or false (but not both, and not maybe). Very often the truth value (i.e., “true” or “false”) of the statement depends on values for variables contained in the statement. The algebra equation above is a statement. Another example is the statement “I like cheese”, which contains two variables: “I”, and “cheese”. If the “I” refers to “Rich Dlin” (i.e., it is me speaking and not you), and the “cheese” refers to “Havarti”, then the statement is true. If the “I” is “Rich Dlin”, and the “cheese” is “Cambozola”, the statement (I promise you) is false. Notice that if the “cheese” were to refer to “gingerbread cookie” the statement would be nonsense, since “gingerbread cookie” is not a cheese – even though it is true that I like gingerbread cookies, it is irrelevant in the context of this statement. A mathematician would say “gingerbread cookie” is not an element of the set of all cheeses. Going back to the algebra example, {(1,1),(3,-2)} is a subset of the set of solutions to the equation given. The actual set has an infinite number of solutions in it, but that’s more than I need to talk about here. What I will say is that the truth value of the statement “Three times John’s favorite number plus four times Gail’s favorite number will yield seven” is:

True if (“John’s favorite number“, “Gail’s favorite number“) belongs to the set of solutions of 3x + 4y = 7,

False if (“John’s favorite number“, “Gail’s favorite number“) does not belong to the set of solutions of 3x + 4y = 7, and

Nonsense if, for example, John claims his favorite number is “cinnamon“. Be on the lookout for nonsense – it is surprisingly common.



The Assumptions

Ok. Welcome back. Here are the assumptions I was talking about:

All questions have a right answer
… when the answer is justified properly with a well framed statement.
The truth value of the statement may be subject to variables that change which answer is correct, but with a fixed set of values for the variables, there is a right answer. For example, the question “Should all trees taller than 12 feet in our neighborhood be pruned?” could be answered “Yes”, justified with the statement “It is unacceptable for some trees in our neighborhood to block sight lines to the lakefront”. Note that here the answer to the question is “yes” if the statement is true, and “no” if the statement is false, and may reasonably depend on whether or not the tree is also so wide, or part of a grove, as to make it impossible for a resident to see the lakefront from a different angle standing on the same property. It may also depend on whether 12 feet is a reasonable height with respect to whether or not sight lines get blocked. In this case these variables need to be introduced into the statement, or else agreed upon as not being variable.

The right answer may well not be knowable
 … even with the variable values fixed – which doesn’t mean there is no right answer!
As an example, consider the question “How many humans are alive on Earth right now?”

  • The number changes many times in a short span of time. So the truth value of the answer depends on what time it is indexed to.
  • The answer is subject to a definition of “alive”, and the answers to whether or not some organisms are living humans are in dispute.
  • “On” Earth needs to be defined. If I am in an airplane, am I on Earth? What if I am in low orbit?
  • However there is an answer, if we fix the variables.
  • There is currently no way, even with the variables fixed, to know the answer.

Knowing the truth is inherently valuable.
This is a big one. Many people demonstrate by their behavior that they do not adhere to this assumption. A simple example is the person who refuses to go to the doctor about a problem because they are afraid of what they might find out. In some ways, not wanting to know the truth is a human quality, especially in situations where a false belief has spawned an entire tree of values and beliefs we have been living by. If the root belief is false, what happens to the tree?

When it Comes to Truth, What We Want Doesn’t Matter
So with these assumptions, my position is that for any belief I hold, I am either right or wrong, and that I may not be able to tell. So then what am I to make of someone who disagrees? Can I immediately conclude that they are wrong? Clearly not. However I freely admit I want them to be wrong, so that I don’t have to be. After all, being wrong has some negative implications. On a fairly benign end it means I have been somehow deluded, which injures my pride. On an extreme end it may mean I have to discard an entire tree of conclusions that were premised on my error, leaving behind a buzzing hive of uncomfortable questions and observations about my previous behavior. But if the root belief is actually wrong, what choice do I really have? Since it is rooted in falsehood, the whole tree is an illusion anyway.

Here is a hard truth: What we want has nothing to do with what is true. I want there to be peace in the Middle East. But there is not peace in the Middle East, and no amount of wishing on my part, no matter how fervent, can alter the truth value of this or any other statement. On the other hand, what is true can and should definitely impact what I want. What we all want.

Ok. Here is another statement that is tautologically true: In the set of things I hold to be true, some might be false. And from a probability perspective, I am also comfortable saying that in the set of things I hold to be true, some are true, and some are false. I want to say “most are true and some are false”, but I am honestly not sure I have a reasonable argument to claim that, so we’ll leave it there as a desire more than a fact.

Shades of Gray
Now I will focus on statements where the truth depends on fixing values for the variables in the statement., which to me is the core of the shades of gray argument: In cases where there is a continuum of possibilities between true and false, almost everything in the set of things I hold to be true lies somewhere within the boundaries of the continuum, rather than on one of the ends.

Here a philosopher or mathematician might (and should!) argue that there can be no continuum between true and false, since those are binary options. My response is that I am talking about a sphere of reasonable answers centered on the truth, where anything outside the sphere is easily demonstrated to be false (or worse, nonsense), but things get a little more touchy inside the sphere. This is a consequence of my point about the truth of a statement depending on fixing values for variables the statement depends upon. To elaborate on this, I am going to define something called an assumption set.

Assumption Set
Suppose a statement depends on a set of variables. For example, consider the statement “Running is good for you.” The truth of this is not absolute. It depends on some variables:

  • How much running (the quantity of the running)?
  • How intense (the quality of the running)?
  • What preconditions do you have that running would exacerbate (e.g, bad knees, asthma, heart problems)?
  • Where do you plan to do your running (road, track, beach)?
  • and many more.

So before we could discuss whether the statement is true, we would have to fix values for these variables. I call these fixed values the assumption set. So for example an assumption set for this statement could be
R=\{45 minutes per day, at 80\% of maximum heart rate, \{sensitive to sunlight, plantar fasciitis\}, track\}.
Notice that one of the elements (the preconditions) in this assumption set is itself a set – that’s completely acceptable. On the whole, I would judge this assumption set to be a reasonable one – which is to say, the elements of the set have a probability associated with them that makes them not unexpected in the context of discussing the claim that “Running is good for you.”
Another assumption set could be
S=\{15 hours per day, at 120\% of maximum heart rate, \{multiple hip replacements, torn Achilles tendon\}, Interstate Highways\}.
On the whole, I would judge this assumption set to be very unreasonable – which is to say, it is highly improbable that this would be an assumption set on which the claim “Running is good for you” would be a relevant discussion.

Reasonable Answers (Approximately True?)
A reasonable answer to a question can be defined as a statement that is true when evaluated with a plausible assumption set. That is to say, the assumption set is comprised of elements that have probabilities high enough that if we observed them we would not be surprised. In situations where the variables are in constant flux, the approximate truth value of a statement may be argued as the one that holds given the most likely assumption set. In cases like this, we may generalize a statement as true, while being willing to challenge it in the face of a game-changing assumption set. We maybe won’t talk about who gets to define “plausible”, even though there are times when that becomes the most relevant thing.

Arguing(?) With an Open Mind
Here I have chosen to use the word “arguing”, even though in truth I prefer the word “discussing”. That’s because most people seem to think that discussions between people in disagreement need to be arguments. I disagree. Remember the assumption that we are not right about everything? And remember the assumption that knowing the truth is inherently valuable? These two should premise every discussion we enter into. So when discussing the answers to questions, or the truth about statements, we need to do our best to remember that what we are trying to do is get as close to the center of the sphere as possible, because that is a good thing to do, and because we may not be there yet.

Of course, we all think we are closer than an opponent. If not, we wouldn’t be having the discussion in the first place. But keeping in mind that if two people are in disagreement, one of them must be wrong, a productive conversation is one where at the end of it the parties have converged on something they both hold to be as close to true as they can see getting. When this happens, the world gets a win. I’ll list some techniques for true open-mindedness.

Discussing With an Open Mind

  1. Remember that you might be wrong.
    Put another way, be willing to change your mind, or adjust the approximate truth of what you believe.
    See, you believe that you are probably right. You may even believe that you are certainly right (although for the truly reflective, certainty is a pretty difficult thing to attain). But your opponent has the same thoughts. Both of you probably have many reasons for these. And they probably have a lot to do with assumption sets, and which one of you is applying the most plausible set. Sometimes the discussion is not about the truth of the statement but on the plausibility of the assumption set. Keep that in mind. Yours may be the less plausible. Or maybe both assumption sets are equally plausible, in which case the statement can be split into two (or more) more detailed statements that include some of the differing assumptions explicitly. But keep in mind that emotional attachment to an assumption set can and will blind you to the plausibility of an alternate set, and ultimately cause you to refute a statement with unreasonable (even fanatical) obstinacy.
  2. Have higher expectations for yourself than you do for your opponent.
    This means you need to challenge yourself to inspect the assumptions and claims of yourself and your opponent objectively, even if they are not doing the same thing. When you do this – and do it out loud – they hear that. Look at elements of the assumption sets and objectively evaluate their probability. Also evaluate whether they change the truth value of the statement or not. And be prepared to evaluate whether or not they render the statement as nonsense – this happens surprisingly often but it’s not obvious until it is isolated. Discussing things this way models a behavior that is necessary for the two of you to converge on a conclusion you both agree with. And if you are consistent with it, your opponent will often adopt the same style, if only because they think this is the way to convince you they are right.
  3. Thank your opponent, regardless of the outcome.
    I don’t mean this as a politeness. I mean this in the most sincere sense. Any opportunity we get to reflect on our set of beliefs is valuable. Sometimes your opponent and you will converge. Sometimes you will not, and they leave the exchange completely unmoved, perhaps even claiming “victory”. This is sad, since the only true victory would be a convergence of opinion, but ultimately it is not relevant to your own experience. Make it so that if you have moved on a topic, it is because you discovered something you were not considering, or were considering incorrectly, and now you are closer to the center of the sphere of truth. If you do not move, make it because you were not presented with any strong evidence that you needed to. In either case your beliefs will have been strengthened in some way, either because you changed to something as a result of new insight, or because you were challenged in some way, and it was unsuccessful. For this you have your opponent to thank.

How to Spot Real Open-Mindedness
Many people claim to be open-minded. It may be true, or it may be a trick (some people say it so that when you fail to convince them of something it will prove they were right). True open-mindedness doesn’t mean you are ready to believe anything. It means you are willing to change your mind when presented with evidence that objectively compels you to do so. If you know of (or are) someone who has changed their mind in the moment, during rational discourse, but who was fairly slow to do so, they are probably the type of person I am describing. This goes back to my point that we are probably not right about everything we believe. Which means mind-changing can occur. Which means if you’ve seen it occur, it occurred in someone with an open mind.

Thanks for reading,

Rich