Tag: critical thinking

Revolutionizing Social Media Interaction for a Brighter Future

As we get closer to the American elections, and then moving into the Canadian elections next year, I find it more and more imperative that we work to effect a fundamental change in the way we interact with social media and, by extension, how we interact in real life. Over the last ten years or so my concern over the culture has grown from mild alarm at some people’s online behaviour, to something approaching real fear that we are at a tipping point into another real-world dark age, specifically with respect to intellectual and cultural decline. And violence.

It’s not all bleak though. Thanks to many private conversations, I know I am not alone in my concern, and I do see signs that there are public figures with a legitimate desire to change this trajectory, as opposed to leveraging the culture for their own personal gain. And considering the magnitude of people who, exclusively through social media, get their news, form their opinions, and – maybe most troubling – learn how to communicate, social media is where it has to start.

If we can do it, it won’t be through any kind of censorship or similar attempts to control how people use their favourite platform though. It has to be you and me. We have to change the nature of our posts. And so I had this idea of a filter, or sieve, that we can apply to our more meaningful posts to both increase their effectiveness, and also combat the culture that is propelling us toward a precipice.

Consider this. If you want to engage in political posts on social media, that is your choice, and I support it. Keep in mind though that these posts are, by nature, argumentative, in that political posts always argue for or against some candidate or issue. Which on its own is not a problem. Argument (or debate) is not a fight. The idea that arguing equals fighting is something that’s manifested because people like getting attention and scoring points. True argument is not a contest, but a means to pursue truth and, conducted properly, is how we progress. Because the acquisition of truth can never be considered a loss, proper arguments have no losers, and in that sense they have no winners either, because to win an argument someone would have to lose.

But many people argue poorly, because they argue for points.

In the philosophical study of argument there are many identified fallacies. If you’re not familiar with the idea of a logical fallacy, think of these as techniques or strategies that falsely trick you into thinking they are effective. When you employ them you or your audience may think you’re “winning” but you have not made a true case. To avoid this, and hopefully steer us away from the precipice, I ask that you apply what I’m calling an effectiveness sieve to your words before you click that post button.

Run your post through the following sieve. If you can’t answer yes to all three sieve questions, refine your thoughts until it passes them all, then go ahead and put it out there.

  1. Do my words avoid belittling, shaming, or otherwise personally attacking someone who doesn’t agree with my position?
  2. Does my post allow for (and even maybe invite) respectful discourse with someone who disagrees with it?
  3. Does my post offer information/education that someone who disagrees with me might not have considered?

You can actually stop reading here, if you like. The value of each question is probably self-explanatory. But if you want to dive a little deeper into the reasoning behind these criteria and their relationship to common fallacies, or to reflect a little more deeply on whether or not your own posts are effective, read on.

(A word of warning though: I use examples below to illustrate the points and a lot of them are, by design, inflammatory in concept and language. I am not expressing my views in any of them – I am parroting posts I have seen in my social media feeds.)

Sieve Question One
“Do my words avoid belittling, shaming, or otherwise personally attacking someone who doesn’t agree with my position?“

Fallacy This Helps Avoid: Ad Hominem (Attacking the person)
This occurs when instead of challenging an idea or position, you irrelevantly attack the person or some aspect of the person who is making the argument. The fallacious attack can also be aimed at a person’s membership in a group or institution.1

How to tell
Imagine that someone who holds an opposite position made a post worded like yours. Would you take it as a personal attack, or would you view it as someone simply supporting ideas that you disagree with? Keep in mind that we can challenge ideas without attacking the people who embrace them. In fact, this is the only way to dismantle dangerous ideologies. In democratic societies where change essentially requires consensus, attacking opponents instead of ideas is possibly the worst way to stimulate progress. Consider this example:

Example 1
“Considering the unbelievable depths of stupidity you display in believing that climate change is a hoax, it would obviously be a waste of time explaining the facts to your fascist republican ass.”

Example 2
“You have been duped by the lamestream media, so I will leave you to your weak-minded, sheeple liberal delusions about how solar power will ‘save the planet'”

Example 3
“I read conflicting views on whether climate change is real, if it is a concern, and if it is totally caused by human factors. I am not an expert, and it’s not always easy to filter out the real experts from the ones who claim to be. And even then, it’s not always easy to filter out which experts, if any, are twisting their analyses to suit some underlying agenda. However, the scientific consensus points at climate change being a real danger, and being attributable to human factors. The recommendations to address it seem to be a net good, even if the premise that we are the problem isn’t totally correct.”

It should be obvious what’s happening in the first two examples. There is no attempt to change anyone’s mind. It’s just mud-slinging peppered with tired insults engineered to pump up the audience members who agree. Neither post does anything to address the issue of climate change itself, and just drives a wedge between people who hold opposing views.

Meanwhile, if I’ve crafted the third example well enough, hopefully you can see that there is no evidence of ad hominem at all, and even though the poster is leaning toward one “side”, they have not shut down engagement.

Sieve Question Two
“Does my post allow for (and even maybe invite) respectful discourse with someone who disagrees with it?“

Fallacy This Helps Avoid: Straw Person
This occurs when, in refuting an argument or idea, you address only a weak or distorted version of it. It is characterized by the misrepresentation of an opponent’s position to make yours superior. The tactic involves attacking the weakest version of an argument while ignoring stronger ones.2

How to Tell
This is often used in conjunction with the ad hominem fallacy because it adds even more punch. After all, only moron would believe a weak argument. Most people have no desire to engage in discourse with someone who starts off with the premise that “Your position is weak, because it supports x so I am right and you are wrong and unless you can see that you are an idiot.” Consider the contentious example of abortion:

Example 1
“Pro-choice? So you think that murdering babies is ok!?! I guess you don’t care about the lives of the babies who get killed.”

Example 2
“Pro-life? So women should have no say over what happens to their own bodies?!? I guess you don’t care about the 13-year old girl who was brutally raped and is now forced to carry and give birth to the child of the man who scarred her forever.”

Example 3
“I struggle with the abortion issue. I believe it is a clear and terrible breach of fundamental human rights to tell someone else what they can or can’t do with their own bodies, regardless of the circumstances but especially when there is physical/psychological trauma involved that can be addressed with an abortion. But I am also really troubled by the fact that I am in no position to decide whether a viable fetus, at any stage of development, is a human life, and I don’t see how anyone could be, really. The issue feels like being offered only two choices where each choice is loaded with ethical downsides, and there is no option to not choose. I worry that in order to alleviate the moral weight of each choice, people downplay or even outright lie about the consequences of their position. So although I land on the side of pro-choice, I do not do so lightly, and I am aware that it feels like I have made a moral choice to prioritize the essential rights of the mother over the potential rights of the unborn child. I hope this choice is correct.”

Consider the first two examples. Will a pro-choice person who just got told they murder babies want to engage in anything other than hurling insults with this person? Will a pro-life person who just got told they don’t care about the effects of rape on a 13 year-old girl want to engage in anything other than hurling insults with this person? By attacking a weak/distorted version of the other side, each has set it up so that any engagement by someone with an opposing view will manifest as some level of support for the weak/distorted claim.

Meanwhile, in the third example, the author has ultimately stated a position. Would a pro-x person be open to understanding the author’s struggle? Would a pro-life person feel safe to engage in discourse? Does it seem that there is the possibility that anyone who engages – including the author – might change their minds about anything surrounding the issue, including about people themselves who hold the opposite position?

Sieve Question Three
“Does my post offer information/education that someone who disagrees with me might not have considered?“

Fallacy This Helps Avoid: Irrelevant Authority
This is committed when you accept, without proper support for an alleged authority, a person’s claim or proposition as true (and that alleged authority is often the person employing the fallacy). Alleged authorities should only be referenced when:

  • the authority is reporting on their field of expertise,
  • the authority is reporting on facts about which there is some agreement in their field, and
  • you have reason to believe they can be trusted.

Alleged authorities can be individuals or groups. The attempt to appeal to the majority or the masses is a form of irrelevant authority. The attempt to appeal to an elite or select group is also a form of irrelevant authority.3

How to Tell
Are you claiming that some position is wrong? If so, have you explained how you know this? What authority are you citing? Or are you claiming expertise and asserting “Thinking x is wrong!”

Example 1
“Jordan Peterson says switching to a meat-only diet literally saved his life. Vegans are slowly killing themselves.”

Example 2
“I lost 30 pounds when I went vegan and feel so much better. Eating meat is asking for heart disease and dementia.”

Example 3
“It makes sense to at least consider evolution when determining what a ‘healthy’ diet looks like. Before humans had access to foods not native to our geography, the only people that would have survived would be the ones who thrived on what was available. So if your ancestors evolved in warmer climates, it would make sense that your constitution would welcome more grains and vegetables, whereas ancestors in colder climates would have evolved to thrive off meats.”

Consider the first two examples. Jordan Peterson is not an authority on nutrition (he actually takes great pains to make that clear whenever he talks about his diet). So while he has said that a carnivore diet works for him, it is not evidence that the carnivore diet is better than others. In the second example, the author is actually setting themselves as the authority. Neither example offers any warranted expertise or education and are strictly anecdotal claims.

In the third example the author poses an idea that promotes questioning and further research. They are not claiming any personal authority, or even choosing a side, even though they may have a preference. They are presenting an hypothesis that can be (and probably has been) analyzed by experts.

If you’d like to read more about informal fallacies often used in argument, I recommend this link from Texas State University. It lists the common ones and provides explanations and examples. One of my favourites is Begging the Question, which I always laugh about because it’s a phrase that gets used so often, and almost always incorrectly, while at the same time the real fallacy gets used regularly in arguments.

In any case, I hope we can all change the way we interact on social media and beyond. I really do believe we need that flavour of revolution.

Thanks for reading,
Rich

  1. https://www.txst.edu/philosophy/resources/fallacy-definitions/ad-hominem.html ↩︎
  2. https://www.txst.edu/philosophy/resources/fallacy-definitions/straw-person.html ↩︎
  3. https://www.txst.edu/philosophy/resources/fallacy-definitions/irrelevant-authority.html ↩︎

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