Huzzah Better Arguing!

The atheist community has seen its share of controversy and Big Issues and Deep Rifts. Every week, it seems, some event, from the smallest comment on a facebook thread to a public address at a major conference, sparks an internet conflagration, spawning tweets, blog posts and facebooks statuses galore, and further entrenching the “sides” we keep seeing over and over again. As Cliff says (though about something else), “It’s bizarre and disturbing the way an issue becomes a Designated Controversy,” and I agree. It’s sad to me to see the same blowups and the same arguments, when I want so much for us to move forward and to engage more productively with each other.

But sometimes, things don’t go wrong. Sometimes, people react and respond reasonably and thoughtfully to each other. Sometimes, people argue and the internet doesn’t explode. And since the internet is a volatile substance and charitable argumentation can be incredibly difficult, I think we all ought to be honoring and praising the people involved when Things Go Well.

So, Richard Dawkins and Miri Mogilevsky: really, really well done.

It all started when Richard Dawkins went to twitter to discuss the British public shooting and in the ensuing conversation, got called an “insufferable smug white male making snide comments in loafers.”

The conversation then turned to what racism and sexism are, whether they can be said to happen to white people and men and how important definitions are. Obviously, this is a topic that incites a lot of anger and strong opinions, and all of these were easily findable in the twitter discussion that emerged. (Though I must say, from what I can tell, the tweets that flew back and forth where rather more restrained than they might have been, and all those responsible for that deserve praise.)

Miri observed this minor brouhaha, and as a blogger, decided to blog about it, resulting in the great post On Useful and Not-So-Useful Definitions of Racism. This post went over what had happened and then gave an analysis which, while richly and thoroughly critical of Dawkins, was compassionate and thoughtful. Here are some of the things I think she did well:

“Dawkins sounds eerily like my high school self here–desperate to stick to his own definitions of things and reject the definitions of others, all while claiming that everyone needs to be using the same definition in order for a discussion to be productive. Dawkins assumes that a dictionary definition is by default more legitimate than a definition provided by people who actually study the subject in question and presumes that what is written in a dictionary is “true” in the same sense as, say, the periodic table or the speed of light.”

  • She engaged with Dawkins’ understanding of the word racism and instead of dismissing it, explains why she thinks it’s not useful (and by the way, arguing that certain definitions are more useful than others rather than more right than others is infinitely more productive).

“It is true that if you define racism as “not liking someone based on their race,” then people of color can be just as racist as white people…But the fact is that this isn’t a very useful definition. You might as well make up a word for “not liking someone based on the color of their hair” or “not liking someone based on whether they wear boxers or briefs.” I don’t deny that it’s hurtful when someone doesn’t like you based on something arbitrary like your skin color, but when you’re white, this doesn’t carry any cultural or institutional power.”

“As a scientist, Dawkins must realize how difficult it is when people take technical terms and use them too generally. For instance, a “chemical” is any substance that has a constant composition and that is characterized by specific properties. Elements are chemicals. Compounds are chemicals…Yet most people use “chemical” to mean “awful scary synthetic substance put into our food/water/hygienic products.”

These tactics and writing approaches are wonderful. They are thoughtful, productive and charitable, and yet they remove none of the critical bite that makes up the backbone of this piece. I think I can say that even someone who started out being fairly sympathetic to Dawkins could have read the piece and taken the criticism to heart, without immediately feeling defensive or attacked. In fact, I happen to know someone did. Who was this mysterious person sympathetic to Dawkins’ position?

Richard Dawkins himself.

That’s right. Richard Dawkins commented a blog disagreeing with the author and everything didn’t go wrong! (Those of you familiar with some atheist movement history will likely be quite surprised) In fact, he was pretty damn reasonable. You can see the full text of what he said here, but again, I’d like to point out some of the important aspects of his comment.

(6). Where annoyance spilled over into outright pain was the implication that, because I felt strongly about (1), (2), (3) etc, this must make ME a racist. That pissed me off royally and actually hurt. Indeed I find it all but unforgivable.

People tend to become angry when called racists, which I’ve talked about before. I don’t think it’s a very good strategy. Again, pretty understandable, and again, it gives us important information.

  • He explained why he was bothered by others refusing to engage with his definitions and usage of language, and clarified his position on dictionary definitions.

(3). Because, for brevity, I quoted a dictionary, simply to show that the sociological technical term was not universally agreed, I was annoyed that people gave vent to a sort of anti-dictionary prejudice, even calling dictionaries a tool of white, male oppression (reminiscent of a famous feminist who called Newton’s Principia a “rape manual”)! Actually my feeling is that whether or not we use the DICTIONARY definition of a word is less important than making sure we use the SAME definition as each other…But I was accused of a kind of naive dictionary worship, which was grossly unfair.

Now, no one has to agree with Dawkins here, or even be more sympathetic to his position. I think the comment after his gives very good rebuttals to most of his points. But I do think, no matter our opinions on the content, that we have to admit that Dawkins was being restrained and reasonable, and given how much he was being attacked (even rightfully!), it was extremely commendable of him to do so. As a result, there hasn’t been a blowup! I imagine Miri’s comment thread is a little ridiculous, but I haven’t heard anything about loafergate, or Mirigate, or elevatorgate II. And that is thanks to Dawkins being reasonable here.

But why was he able to be reasonable? I am pretty sure that he would not have been nearly so restrained (even given that he was likely doing damage control) if Miri’s post hadn’t been so wonderfully thoughtful.

What we see here is a story of success. We see people who disagree about the values and facts of a case, who are criticizing and rebutting each other, who nonetheless made thoughtful, reasonable points, engaged in good faith and a result were able to turn what could have been a Big Fat Controversy into an everyday disagreement. That’s a testament to civility, and it’s also a testament to Miri and Professor Dawkins, who kept their cool and made the internet, and the atheist movement, a nicer place to be.

Blogathon Wrap Up

I know this is a few days late, but I think it’s nice to have a place where all the posts are in the same place. I also really wanted to have a place to put this beautiful word cloud I made on wordle. It has all the words from all my blogathon posts, scaled to reflect the frequency of their use. I love that I seem to talk about people a lot. The other top words are pretty broad: think, just, know, like, good. They’re my go-to verbs, adjectives and adverbs. But there’s also: math, religious, questions, atheists and argue, and that all seems to describe me pretty well.

blogathon word cloud

For those looking for what I wrote, here are the posts:

My Blogathon Announcement: Where I said I was doing it and explained why I thought it was important.

Beginning Blogathon: Where I talked about why the Secular Student Alliance is so important and wonderful (and also how I got lost getting to where I was going)

What I’ve Learned as President of the Secular Alliance at the University of Chicago: Just a bunch of thoughts on what makes groups succeed and thrive.

On Challenging Religious Beliefs: On why I’m working on not seeing challenging religious beliefs in social settings or online as so cringe-inducing, and why I’m glad people actually do it. (Big honking caveat: All normal social conventions like appropriateness and respect obviously need to apply)

Maaaaaaaath: How and why math is so freaking great. Includes crocheted hyperbolic spaces and some light cursing.

Emotion-based Arguments and the Atheist Community: On my suspicion that arguments about infighting and about accomodationism vs confrontationism might be based more on emotional bias than on good arguments.

Safe Spaces for Racists: On what a space where people could ask “politically incorrect” questions without hurting people might look like. Note: title is meant to be catchy/provocative, not an accurate description of what I’m hoping for. By the way, if you like that post, you might like this one, called, “You Want a Space for Political Incorrectness? You Got It“, in which I announce I’m actually trying to create this space.

Brain Crack: A bunch of silly random ideas I’ve had floating around, like getting kids to teach their own classes and having churches serve as homeless shelters.

That’s all! Thanks so much for reading.

You Want a Space for Political Incorrectness? You Got It

Last Sunday, I laid out what I thought a proper space for “politically incorrect” questions and opinions would look like, because such a space can go drastically, cruelly, wrong. Now, I’ve decided to make one. I’m making a subreddit where those questions and opinions can get answers.

There are many reasons people might have a question about race, sex, disability, or related issues they’re afraid to ask their friends, family or teachers. They may not know how to phrase it respectfully. They may have a question that they know will offend but that they’re desperate to know the answer to. They may actually be bigots who are looking to make people mad. For whatever reason, I think there should be a space where, if they abide by principles of respect, civility and good faith, they should get their questions answered. The subreddit I intend to create will be an educational and discussion-based place. Questions will be answered without judgement. Answers will explain how and why some actions or word are appropriate or not, and place questions of bigotry or prejudice in their proper academic, sociological, political, economic and historical context. They will inform and educate while minimizing harm to the relevant marginalized groups. They will include concrete tips, approaches and scripts, so as to really help people move forward in the world. They will be respectful, civil and charitable, perhaps far more charitable than what is deserved. After all, charity can be totally badass activism.

This will be its own space, with its own rules. I do not think these rules make sense elsewhere, nor should people have to abide by them elsewhere. But I like the idea of a place where everyone agrees to be just ridiculously civil and respectful, to use their emotional energy or their privilege or their desire to educate to great effect. This is not the only form of education and activism. There are many others, which are crucial and vital and must exist as well. But this is a form that I think there isn’t enough of. Tumblr upon tumblr will tell people that it is their job to educate themselves about social justice issues. That may be right. So this is one place they can do it.

Some of the rules:

  • No slurs unless you’re asking about them
  • Disrespectful/cruel/obnoxious questions and comments get deleted
  • Unhelpful/uncharitable/not-intended-to-educate responses get deleted, even if they’re completely correct
  • The mods enforce these rules and give users suggestions on how to be more respectful or helpful.

You can find more of the rules here and at the actual subreddit when it goes live.

If you think this is important and useful, if you agree largely with what I’ve written here, and you want to get involved, look out for the link when the subreddit goes live! And if you want to be even more involved, I want you to be a moderator for the subreddit. Just answer a few questions here, and if you have the same vision I do, you’re in!

I think this could do some real good. Here’s hoping!

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P.S. If anyone is wondering why I think this is so important, here’s something I wrote in a blog post about Social Justice education some time ago:

I do not deny for a second that it can seem like a waste of time, that it can be painful, and that rather more often than we might hope, the people we’re arguing with are not arguing in good faith. That is why we leave it to individuals to decide whether it is worth their time and effort. But those not willing to do this kind of work should not stand in its way. They should not base their arguments on assumptions others do not share and be surprised when they are not understood. They should not make it more difficult for others to do the challenging work by interrupting ongoing conversations with jeering and mockery. And most of all, while there are perfectly good reasons to stop being able to have a conversation or to not enter one in the first place, no one should engage in arguments with people who might be persuaded if they have no intention of taking the process seriously. Ideas rise and fall every day in the public sphere, and there’s no reason to lose arguments or adherents because some don’t think the work of public reason is worth doing properly.

If you want to know more about my take on activism, social justice, better arguing and charity, check out these links:

[Blogathon] Brain Crack

Brain Crack is the stuff in the back of your mind that you wish you could bring into existence that you hold onto, hoping and hoping to write about it or create it. But it’s better to let it out, to let other people see it and add to it and make it better, and maybe one of them will make it happen. Here’s some brain crack I have lying around:

  • When children are old enough, they should run part of the classes they’re in. It forces them to do research, prepare work, be accountable to their peers and work on something that has literal, immediate real world applicability. It cultivates confidence and social skills, and also lets them be creative about the kind of class they would want to see and want to be in. It would certainly give the teacher something to think about. Might take too much time out of class, but maybe it could be extra credit?
  • Everyone with a social security number should be automatically registered to vote when they turn 18. They can just show up at the polling place on election day and vote.
  • Open a restaurant with one table. Everything on the table is for everyone, so if you’re full, you just leave what’s left over for the next person. People who can’t pay can just sit at the table and wait for people to order (there would be some kind of maximum occupancy). People who can might need to buy some more.
  • Every church, mosque, synagogue and other house of worship should have an area where homeless people can sleep. It can be separate from the main area, but just somewhere warm so people don’t have to sleep in the cold. (I can think of a lot of problems with this one, actually).
  • What if instead of fixed distances between two points there were fixed times between two points? So if you walk faster, you would be walking a shorter longer distance. What would that look like? Is that even meaningful?
  • I’ve been thinking about movies that play with atheist = bad, religious = good dynamic but also the liberal = good, religious right = evil dynamic. What would that look like? The good guys are super intense religious people but still good, and then bad people are atheists somehow? Not sure. Would love thoughts.

I’m not defending these ideas to the death, or even at all. I’m sure many of them are morally ridiculous or economically unfeasible. They’re just ideas. But I’d love to hear thoughts on them!

And that’s the end of blogathon! Thanks everyone for the favorites and retweets and comments! Until next time!

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[Blogathon] Safe Spaces for Racists

I said in my post criticizing the Politically Incorrect UChicago Confessions page that I agreed with various people that it would be a good idea to have spaces where people could ask “politically incorrect” questions or say “politically incorrect” things that would then be discussed calmly and charitably, with no backlash or criticism. The question, though, is what that kind of space would look like and how it would work.

Here’s what I envision (there are other ways this could work, of course, this is just one idea):

A subreddit, much like AskScience or AskHistorians, called something like AskSocialJustice or PoliticallyIncorrectEducate (like Transeducate, a great subreddit)

  • You have a verification system that gives flair (tags next to your username, essentially) that indicates what your field of knowledge is. Things like “sexism” or “racism”, or perhaps framing it the other way “feminism” or “anti-racism.” Just as in AskScience or AskHistorians, it might be optimal to have only academics in the subject be given flair, but I’d be happy to have Jessica Valenti or Ta-Nehisi Coates in there, obviously. People who know a lot about the subject and are accustomed to writing about it.
  • The rules in the sidebar are:
    • No slurs unless you’re asking about them
    • Disrespectful/cruel/obnoxious questions and comments get deleted
    • Questions that are good questions but not phrased as well as they could be get rewritten, with the original in strikeout (I don’t even know if this is possible). This lets questions from people who don’t know as much through, but keeps things more respectful and demonstrates how discourse should work.
    • Unhelpful/uncharitable/not-intended-to-educate responses get deleted, even if they’re completely correct
  • The mods enforce these rules and also mention to people that they’re being less respectful or helpful than they could be, and give concrete advice and even rewritings of the comment or question to model what the discourse should look like.
  • Mods also allow any good responses, but emphasize the flaired/tagged experts on the topic

So in the end what I envision is questions like:

  • Why can’t I use the word X, but other people can?
  • What’s wrong with calling someone a Y, doesn’t it just mean blah blah blah?
  • Why do Z people always do A? (Actually, this one would probably get rewritten as “I notice that Z people are more likely to do A than Y people. Why?” so that we encourage people to write what they observe instead of what they infer.
  • I know it’s a stereotype, but actually, B’s totally always do C.
  • Is G X-ist?

And I envision the responses being of the form:

  • Well, here’s the history of that word and what it means to people and what harm it causes when non-Z people use it.
  • So, in some sense, Y does mean that, but its meaning has changed because of these historical events, and now this is the effect it has on people.
  • You may notice that because you’re influenced by the stereotype of Z doing A, and so you don’t notice that Y does A a lot as well. It may also be that they’re more likely to as a result of alpha, beta and gamma cultural influences, and there’s nothing wrong with that. Why does A bother you?
  • Well, B actually isn’t true. The statistics indicate that C is a lot more common, even though popular media and even news outlets emphasize B far more.
  • G certainly comes out of an X-ist culture, and it might perpetuate it, but the benefits of G could outweigh those in the cases of R, S and T.

Responses would follow the guidelines of charity and civility laid by myself, Dan Fincke and others. They would be academically rigorous but as free of jargon as was humanly possible, and accessible to readers of a variety of educational levels. Responses would also contain concrete advice for how to act or what to say, giving useful potential scripts where helpful. Questions asked frequently would probably end up constituting their own page that people would get linked to if they asked the same ones.

That way, people of all beliefs, from the merely curious to the rabidly racist, get their questions answered, and they stay anonymous. They get thoughtful, charitable answers filled with resources, should they want to investigate further. The answers are logically and academically rigorous, and delivered without moral judgement or abuse, even if moral judgement would in general be thoroughly warranted. (I think there would also be a way to say, “Yes, that’s X-ist and it’s an awful thing to say to someone. Here’s why..) within these guidelines, since that doesn’t have the same effect as simply calling them an awful person. There would be plenty of empirical data provided whenever possible. Responses would emphasize the real, tangible ways that bigotry and prejudice affect people and their lives, so as to cultivate empathy, but also place responses in historical, economic, political and sociological context.

What do you all think? Would this work? Would these spaces be good? Productive? Would they still “make bigotry fester”? (Which I’m not really sure is a thing) . Would they still hurt people and spread bigotry? What would you add or take away from the rules or approach? I’d love to hear people’s thoughts.

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[Blogathon] Emotion-based Arguments and the Atheist Community

We know that much of our morality comes from visceral emotions rather than pure, crystalline reasons. We know that Kant’s categorical imperative not to murder comes long after the evolution of human disgust at the thought of killing someone in the in-group. We know that a great deal of anti-gay sentiment comes from the notion that men having sex with men is icky. And since we know these things, we also know that sometimes,even if reasonable-seeming arguments exist for some position, they are predicated primarily on some deep emotional basis. If we were to recognize this in ourselves, it would be very important for us to reconsider our position, and be sure that we weren’t just sticking to it because it was so uncomfortable not to.

There are two potential examples of this in the online atheist community. Now, I don’t want to imply that there are no good arguments on the issues I’m about to present, or that everyone’s just being irrational. Only that on these issues, I think there is more emotional motivation than we as skeptics should be comfortable with, in large part because good evidence on the issue is difficult to find or thoroughly absent, leaving us with only our gut reactions.

Issue 1: The Badness of Infighting

We online atheists have been talking about infighting pretty much as long as we’ve been infighting. Is it good? Is it bad? Is it harmful? A lot of people really don’t like it, think it’s divisive, bad for the movement and all around ill-advised. Now, they could certainly be right. Beth Ann Erikson has made very compelling arguments that infighting makes the community look very bad from the outside, which discourages people from joining us and fails to give new atheists a safe place to land. I often think that while arguing against sexism and racism is very important, one of the most powerful things we can do is just to keep writing, keep blogging, about sexism and racism more generally, but also about just everyday skeptic and atheist topics.

All that said, my distinct impression is that the reason people don’t like atheist infighting is because it’s uncomfortable. If you don’t have a dog in the fight, it can feel exactly like holiday dinners where dad is mad at sister, and aunt’s not talking to uncle, and grandma is lecturing brother for not saying grace and standing up for his atheist principles, and you’re there, tense, anxious, staring at your turkey getting cold and wishing everyone would just calm down.

I understand this feeling, I do. But I think it’s misguided. We’re not at a holiday table, after all. Most of us don’t know each other in real life. That doesn’t mean real feelings aren’t at stake, but it does mean that it might be easier to distance yourself from the people doing harm. Most importantly, we’re not physically trapped. No one is keeping us on the internet. We are free to leave, to engage in self-care, to rant and vent to our friends, or simply to do something else for a while which will alleviate the discomfort.

That means all that’s left to argue about is whether there are empirically demonstrable harms or benefits that come from “infighting”, and that’s a dreadfully hard question to answer. But whatever our position, we should try to make sure it’s based on fact and not preference or discomfort.

Issue 2: Accomodationism vs Confrontationalism

This is an old debate in the atheist movement, so perhaps I’m behind the times, but I remember when it was The Thing To Talk About, back in 2010 or so. The question was: how nice should atheists be to religious believers? Should we mock their beliefs? Argue against them stridently? Be charitable? Not argue at all? Try instead to build bridges? Now, this ended up being even more complicated than I’ve laid out here, because people were actually asking totally different questions from each other. Some people claimed that it was simply the moral choice to argue fiercely against religion, no matter what the consequences. Some people distinguished between criticizing people and criticizing belief. Some people argued that either mocking and stridency or gentleness and charity were empirically more likely to convince religious believers. We had consequentialism, deontology and personal preference all jumbled up and split roughly into two opposing camps. It was a mess. And even on the empirical stuff, we don’t really know what convinces people to change their minds in the long term, especially on big issues like religion.

This makes this issue ripe for being primarily motivated by emotion rather than reason. In this case, I think the motivating emotion is distaste. People who like criticizing religion harshly find it completely distasteful, yes, icky, when they read people saying that it doesn’t matter if theistic claims aren’t true, it only matters what theists do, or saying that we should overlook our differences in order to engage in interfaith work. And I think that people who don’t like confrontation, who personally prefer to avoid it, who are uncomfortable at the metaphorical holiday dinner tables, find it extremely distasteful to watch the PZ Myerses of the world lambast and tear apart religious commenters or bloggers, pulling no punches. It’s gross to them. It’s just too much.

And I respect people’s personal preferences. Certainly people should choose for themselves what type of argument to engage in (though if we find that one approach is strikingly more effective than another, perhaps we might have some oblgation to subsume our discomfort for the good of atheist activism (if convincing religious people they’re wrong is to you a worthwhile goal)). But distaste is not a good argument. If we’re criticizing the argument styles of others (and I do it all the time), we should make sure it’s coming from a place of reason and evidence, just like everything else.

Conclusion

By no means do I think everyone engaging in these discussions is irrational, or has no good arguments. But I think anyone arguing on these issues should be examining their arguments with extra scrutiny, so as not to fall into the trap of constructing arguments ad hoc to fit their preconceived emotional stance.

What do you all think? Am I completely wrong? Are these not the motivating emotions at all? I’d love to hear in comments!

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[Blogathon] Maaaaaaaaath

Have I scared you yet? Talking about math seems like one of the easiest ways to terrify people, make them feel stupid, and cause them actual pain. I think that’s a shame, because math is AWESOME. I’m going to try to convince you of that in the next few hundred words.

What is math?

Math is the study of patterns and logic. Any repeating pattern or system analyzed rigorously and logically can be math. The coastline of Britain? Sure! The spread of diseases? Absolutely! What the relationship between the number of sides of a shape where all sides are the same length and the area of the shape? Definitely.

Since any pattern or system is up for grabs, math is incredibly creative. You get to just pick whatever rules or approach or framework you think might yield useful or interesting results and see where they lead you. Let’s say you were interested in triangles. You could take the points of the triangles as coordinates (like (2,5) and (3,4) and stuff) and do all kinds of calculations to see what the area was. OR, you could not care at all where the points are and just take lengths of sides. OR, you could not bother with calculations or algebra at all and do the whole thing geometrically. You can even prove things with gifs!

Ok, why are you getting so excited right now?

Because that makes math AWESOME. Anything can be explored. Look, pick some rules you’ve decided to follow. See where they lead. BOOM, you’re in an entire world of your own making. Those rules are axioms. Seeing where they lead, logically, means you prove things with them, sometimes you call those conclusions theorems. And now you have a totally new mathematical world. It might as well be writing fiction or LARPing.

You think I’m kidding, but I’m not. There are 5 axioms called the Euclidean axioms. They are as follows.

  1. A straight line can be drawn between any two points
  2. A finite line can be extended infinitely in both directions
  3. A circle can be drawn with any center and any radius
  4. All right angles are equal to each other
  5. Given a line and a point not on the line, only one line can be drawn through the point parallel to the line.

You can have all kinds of fun with just these. Take a piece of paper and see if you can convince yourself, even informally, that these seem to be true. Use crayons, markers, pencil, whatever.

Now throw them all out. Fuck ‘em. We’re going to start our own mathematics with blackjack and hookers. What if instead of a straight line being the shortest distance between two points, a semicircle is. Seriously. You just invented geometry on a convex (curving inward, like the inside of a beachball) plane. It’s called hyperbolic geometry.

It looks like this.

And this.

And people freaking crochet hyperbolic curves.

You could have done basically the same thing by saying, ok, I learned in like 7th grade that all triangles have 180 degrees. Well, what if they don’t? A triangle is a shape with three sides, right? What if I want more than 180 degrees? Well, you can have whatever you want. In math, the only rule is that you have to follow your own rules. What those are, you get to decide. So draw a triangle with more than 180 degrees. Ok, it’s hard, I grant you. It seems like it would have to have more than three sides. What are we missing? What assumptions are we making? Oh! That the sides have to be straight! What if they curved out! Like a triangle you blew air into?

Congratulations, you just invented elliptical geometry. It’s the geometry that explains why planes fly like the curved line instead of the straight one:

Because the earth is curved, not flat, so the geometry changes. And triangles, just like you wanted, have more than 180 degrees.

Then Why Does Math Feel So Awful to Learn?

There are a few reasons why people hate math. For one, no one teaches math as something fun and creative. They teach it as something boring and rote, where the rules are set up beforehand and totally unchanging. To get fun math, you have to go to youtube to see people like Vi Hart make math the beautiful thing it is.

Second, because math is so abstract, it can be hard to visualize, and it makes it feel mysterious, even after you understand the problem. Like in biology, once you understand why evolution works, you get it. You know how it works. Sometimes, I’ll prove something for a class, and I’ll know it’s right, and that everything follows logically, and still not really know what I just did. For instance, visualize a line for me. That’s one dimension. What’s the two dimensional form of that? Right, a square. And three dimensions? A cube, great. And next? That question is the intellectual equivalent of moving both index fingers together in front of someone’s face, asking them to follow the fingers with their eyes, and then suddenly moving them in different directions. You just don’t know what happened to you. (For readers of Flatland, there’s a reason the sphere gets very upset when asked if there are more than three dimensions)

That shape, by the way, is called a tesseract, and it looks like the picture below in three dimensions, even thought it’s a four dimensional thing. But what does the next one look like? At some point, visualizations run out and logic and proof must take over.

Thirdly, math has a language, and it’s not an easy one to learn. There are all the symbols, for one: numbers, logical operators, less than, more than, exponent, subscript, and on and on until you think you’ll drown in them. And then there are the rules for how they fit together. This implies that. Why again? Oh yes, because this. And that makes sense because? Oh, right. But eventually, if you follow math far enough, you develop a deep respect for mathematical notation, its minimalism, its utility, and you begin to deeply distrust anyone who says, “Math would be fun, but why are there so many symbols?” (Though of course, there’s tons of math to be done without them. You get to make the rules, remember?). But you also get to criticize notation, decide that some is better than others, and take sides on Newtonian vs Leibnizian differential notation.

Proofs Without Words

But because it is in some sense, a language, I wish it was taught like one. I wish that young children read proofs without fully understanding them, just as we are encouraged to read texts in Spanish without looking up every single word. I wish we contented ourselves with the gist of the proof, the point, so that we learned to prioritize the meaning over the form, just as we may not be able to word-for-word translations of our French teacher’s request, but we know it’s time to sit down.

What’s the Point of Math? And of this blog post?

Well, math is beautiful. And fun. And creative. And the point of this blog post was to convince you of that. But if pure practicality is important to you, know that if you set up the rules properly, in that they reflect the way the universe works, then you’re going to get empirically verifiable predictions from the logical conclusions of the rules. That’s how physicists knew there had to be a Higgs Boson long before we could even in principle find one. That’s how we started building bridges.

Math can describe with incredible accuracy how the world works. But it can do so much else besides. It is a powerful discipline, and it deserves our respect. For some of us, it has commanded our reverence.

(If you’re still not convinced math is awesome, I really encourage you to check out Vi Hart’s videos and these math gifs)

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