When 1 + 1 Doesn't Equal 2

My bike Shadowfax. He's so fast he's blurry.

     I used to go for bike rides along the Willamette River in Eugene at night. When I was in college and wanted to clear my head, get some exercise or mull over a math proof (really), I'd hop on Shadowfax and do the loop. Sometimes at 2:00 or 3:00am if I was up.
     One time I stopped at one of my favorite spots - one of the bridges over the river. I was looking at the moon/street light hitting the water and two guys rode up and stopped to chat. They may have been homeless, they may have been drunk, and they may have been on drugs - sometimes it's hard to tell. One of them asked what I do. I told him I was a math major at the U of O. He scoffed. Mathematicians. Let me tell you about mathematicians. One plus one does not equal two, one plus one equals one plus one and two equals two. He went on in this line of reasoning for a while, talking about all kinds of related topics. He honestly seemed like one of those bums who has all the answers to the questions no one is asking.
     Shadowfax and I rode on, and I didn't give it much thought until later. Until now, really. I've talked about how equality means that one side is the same as the other, (or that each side of an equation is the exact same as the other). 2x + 3 = 5 when x = 1 and 1 + 1 = 2.
     Equality only exists in the abstract, though. 1 + 1 = 2 only if you are dealing with a concept, like "numbers" or "apples." By that I mean, if I were to take a literal, tangible apple and then put another apple right next to it, those two apples are not the exact same. They weigh different and look different and one of them has more worms. No two apples are exactly the same. 1 + 1 does not equal 2, because I don't have two of the exact same thing.
     But If I think of those two apples as the generic, abstract label of "apple," then I go from having one apple to two apples when I add them up. I can "add" the two apples because I can label them as "the same," and this abstract label lets me deal with equality. Does this make any sense? One plus one does not equal two, unless the two things are completely identical. One plus one equals one plus one, when the two things are not identical.
     What does this mean? It means that in the real, tangible world, equality doesn't exist. No two things are exactly the same out here.
     Well, what does that mean. Equality from a social perspective means that all people are given the same opportunity, regardless of gender, race, religion, etc. Is that even possible? No, it's not, because no two people, cultures, backgrounds or beliefs are the same. Equality can't happen in the real world. Maybe that notion is obvious, I don't know. But it's undeniably true.
     So should we even pursue social equality? There will always be rich and poor, healthy and sick, feeble and strong. Can we really grant Equal Opportunity to people applying for jobs, when one guy comes from a wealthier family than the other? To truly grant equal opportunity we'd need to make everyone go to the same school and come from the same family and be born at the same time. That sounds stupid.

Cara had a photo idea and ran with it.

     When I think about the ideals of social equality, from the vantage point that equality doesn't remotely exist in the real world, I start to think it's misguided. Equality: treat all people the same. No! We don't treat men and women the same, nor should we. I don't have breasts to feed my son. Cara doesn't have muscles to move heavy things (and I mean, like, really really big muscles like mine). Men and women are so clearly not equal that trying to treat them the exact same is absurd. (And for the record, there's little doubt that women are better than men, in my opinion. As a whole, the only thing that they aren't capable of doing as well as men are feats of physical strength and agility, which isn't such a big deal in today's society (we're not running from sabretooth tigers anymore. Yes I am putting parentheses within parentheses.), and they can bear and nurture children. Of course I am going to hold a door open for them!).
     This is all very easy for me to say. I am a white, straight, middle-class, educated, attractive, charming, physically imposing Christian male. Some of those attributes are by choice, some are by chance, some are by birth, and some are fabrications, but the point is I am not a person who is historically oppressed in the United States. It's easy for me to say things like "we don't need to try to treat people equal when they are not equal," because it doesn't tend to impact me negatively. But I recognize that those in power view "not equal" as "inferior" and begin to exploit. I get that, and I think things like Affirmative Action and Equal Opportunity hiring are wonderful things (although I think affirmative action should move towards being based more on socio-economic standing and less reliant on race, but that's for another time). So let me go back a step.

     Equality doesn't exist in the real world, only in the abstract. Fine. But if I am going to apply my purely mathematical logic to the real world, I need to apply it to my abstract world as well. Equality only exists in the abstract, but I still use it. I still write and solve equations as if 2x + 3 equaled 5. In my perfect, ideal, non-real world, equality is real and it is useful. Is it such a stretch to think that the abstract concepts of equality in the real world aren't useless either? Math breaks down when you apply it to physics. It turns into a model of the world and not an absolute law, mostly because we can't ever know everything and have all the necessary data. In the same way, equality breaks down in society, it becomes a goal we should strive for. We can't ever have a perfect society, but we can strive for it in the same way we strive for cleaner energy or faster transportation. Really, as a Christian I am called to be perfect, knowing full well that I never will be. I am called to strive for it, just like as a society we should strive for equality.

     People and groups and individuals and genders are not equal. That is a wonderful, necessary thing. If they were truly all the same, the world would be a simpler, more boring-er, less accomplished place. We shouldn't treat everyone the same, that's a disservice to all of our tremendous differences. We should treat everyone with the same respect and the same regard (at least as far as it is truly deserved), but we shouldn't treat them the same. 1 + 1 doesn't equal 2, thank God.

     (One last, tangentially related indulgence: This is why I love math. I like to take things that it teaches me, logic it has instilled in my brain, and see how it applies to other things. This application tends to shed new light on things for me, things that other people have probably had figured out for a long time. I don't expect other people to do this with mathematics, but I think they should do it with whatever they know and love. And I don't expect my students to need to be able to solve quadratic equations in life, but damn it I wish they were all equipped to at least analyze their world with cold, hard logic. That's all math is, logic applied to a specific, well defined system. A system where 1 + 1 = 2 and that idea leads to a lot of other ideas. How can I convince a 14-year-old with an iphone that this is worth caring about? I don't know. Thanks for reading.)