Tag: math

Is marriage a created thing like math, or like music?

“I believe in Christianity as I believe that the sun has risen: not only because I see it, but because by it I see everything else.” — C.S Lewis

math-music

We should stop speaking to our world as though the definition of marriage is a truth they should know like mathematical laws and start speaking as though it is a good and beautiful thing like music.

That C.S Lewis quote up the top of this post is profound. My Christianity actually shapes both the way I see and understand math and the way I see and understand music, because it shapes the way I see and understand everything. But how I see and use math and how a non-Christian sees and uses math is relatively similar; how I see music and how I use it is much more closely aligned to my faith. I sing in church, I do not do math in church (no matter how boring the sermon). There’s something different about the truth math contains and conveys and the truth music contains and conveys, and the way our faith or religious framework shapes the way we see and use them. No matter what we believe.

Christians who love natural law or revelation (and rightly) believe that creation points to God had much less to argue with when people held that nature and reason were good guides to truth. The problem is that everyone thinks nature points to their God; idolatry in its basest form is turning something from nature into God and understanding the rest of nature through the grid that creates. Just as C.S Lewis said he saw the world through the lens of his Christianity; secular Aussies do the same with their ‘religion’ or their sense of what the good human life looks like. Our worship frames how we see nature and created things like marriage. Secular worship (which expresses itself in diverse human cultures and sub-cultures built on common objects that people love like music, a sports team, an activity, or a shared sense of what a ‘good life is’) doesn’t present much of a challenge to how we see math; math doesn’t really challenge anyone’s view of the good or flourishing human life… but what we worship does shape the way we see other created things (objects and human relationships or realities) like marriage.

So here’s a question. Is marriage like math — an objectively true created thing that describes how the world works in a way that can be universally understood, or like music — a good created thing that cultures produce and enjoy subjectively based on their values? Should we expect everyone to think the same as us about marriage; is it an objectively knowable created thing, like math, or is it like music?

 

There are certain natural or created laws that from our finite and limited ability to observe how stuff works, seem universal. These laws — things we believe we’ve proven —are observations about nature; objective statements about how things are. We can express them as axioms or equations. These are universal.

2+2=4

When it comes to marriage many observers of nature who hold a belief that nature reveals something of God want to suggest a similar equation:

Marriage = 1 man + 1 woman

Often the natural argument here is that:

1 man + 1 woman + sex = a potential child.

That is natural. It is a biological equation; it seems axiomatic for those who think about the world like created things are like math not music. The only way we can change that is by artificially intervening with what is natural. That’s also long been the argument for defining marriage the way human cultures have defined it. It seems a natural fit for this objective truth. But it’s not necessarily axiomatic that marriage means that relationship; that is what is contested at the moment in our world. Because there is an alternative equation, more in the realm of music, where:

Marriage = 1 person + 1 person + love

Love is clearly a subjective thing, and much music is written trying to evoke and express that feeling. And this isn’t so much a question of how marriage should ultimately be viewed; but how it is in societies where people worship more than one god or different created things. It might have been enough to argue for marriage as though it is like math in the world operating in the age of reason — the enlightenment era when nature and our ability to know things about nature, and we viewed the world through that grid; but now we’re in the age of feelings, and arguments from reason are largely starting to sound like nonsense to people when it comes to how we should live or what should become cultural axioms and definitions.

 

So do people see marriage as being like math or music?

The position we come to on whether marriage is a universal truth or law that people will definitively see in the same universal way regardless of what they choose to worship (like math), or a thing we shape meaning for in our cultures (like music), will shape how we speak about marriage in our world. Do we speak of it like math, or like music?

Lots of Christian arguments I read in favour of the secular state defining marriage the way God defines it are built on the basis that it is a universal created good; a moral law written into the fabric of our humanity, much like math is written into the fabric of the cosmos.

But I don’t think it’s that simple, I think it is more like music: an imaginative shared act of creation where we act in concert with God’s design in a way that reflects who we are and what we believe about the world we live in.

We all — everyone, not just Christians — approach marriage as a ‘created’ thing; a part of nature, and we all approach created things through the ever-changing grid created by our worship. When we worship in such a way that we, or our cultures, become creators of meaning, and we create that meaning as we interact with created things. So modern secular Aussies believe we can even redefine the nature or purpose of created things (like marriage, or family, or human life) to fit our view of how the world works, or how we work best in the world. That’s why the definition of marriage is now contested; our culture keeps changing its common objects of worship and so re-ordering our loves and re-examining the way we interact with ‘nature’…

Mathematical truths operate at the objective level. We argue for them using proofs and logic and reason. The aim of discussions about these laws is to ‘prove’ something using a way of viewing and understanding the world that all people who know about math seem to share. The implications from our proving of things are clear axiomatic description of nature; the way things are. Natural law (for the ‘enlightened’ rationalist). Natural revelation (for the Christian).

Math is a pure way to get to the heart of how stuff works. To do math we employ logic and reason to describe the relationships underpinning everything in the cosmos; from the relationship between atoms to the relationship between planets. We can, using numbers, express, model, and predict the way these parts of creation will interact. Math describes the world. It has been described by some as the language of God; and there is something about the intricate order and design of the cosmos that it reveals; and its unchanging nature too; that says something about the nature and character of God… But not everyone sees math in these ways, and you don’t have to in order to believe true things about math or about the way different bodies interact in the world.

What we do with math, or the truths about the universe we extrapolate from math will vary based on what we worship, we may choose to worship math itself (or our own logic and reason), because of its explanatory power, and a very strange form of unnatural worship may even convince us that 2+2=5. But mathematical truths are natural and we can establish them, and see them in operation across human cultures towards good ends like commerce, agriculture and engineering. We harness math, but we don’t make it. It originates in nature itself and in the nature of God.

Music, at its heart, is the application of mathematical principles to sound. It is the ordering of mathematical truths to create beauty and is, by the nature of our different ears and cultural practices a subjective thing that has the potential to mean (and so reveal) different things to different people in a profoundly different way to math. Unless we’re recording the sounds of nature — like birdsongs or running a record needle over the cross section of a tree so that its rings form some sort of melody — music is something that we create in and for a culture. Music will still reveal what we worship — and human cultures across time and space testify to its place in forming us as people and representing how we view the world through the lens of our worship. It is totally ‘natural’ but in a way that works in harmony with who we are and what we worship, not in a way that directly demonstrates who God is via ‘nature’… Its origins are both divine and human. I’m fairly sure God is a musician who sings and makes beautiful noises (because of the birdsong and the picture of the throne room and what we’re called to do with music as his worshippers), but not all music points to God and not all musicians are expressing divine truth as they play — beyond the sounds themselves that arise as a product of cause and effect; when you bang stuff together, according to the laws of math, noise happens and travels through different mediums depending on what they are (physics is just math really). It is a natural phenomena but taken and shaped, subjectively, by people based on what we worship. You can’t really reasonably argue that Bach is better than Kanye, no matter how reasonable your argument is. You make that decision based on a values system you bring to the data; their music.

Problems with seeing marriage as math (a natural law)

One of the problems I observe in the way the western church, and its leaders, argue for our vision of a good natural human life is that we argue about issues that are like music as though they are like math; and expect reason and logic to win the day. This is perhaps truest in the arguments the leaders of the institutional churches in Australia are mounting in favour of the secular government maintaining a traditional definition of marriage. The problem with natural law arguments is that once an enlightened and liberated individual knows something is a ‘natural law’ they still feel totally free to break it; it’s not an argument that convinces anyone anymore once they’ve decided that real goodness lies apart from nature.

We modern Christians are so profoundly indebted to the enlightenment and the ‘age of reason’ and the natural theology tradition championed by Aquinas and his followers, and so excited about the way natural and special revelation sing in harmony to those of us attuned to hear both, that we treat moral arguments on issues that we see as derived from creation or nature as though they are mathematical truths for us to prove. An example of this way of thinking of marriage would be to insist on the axiomatic equation for marriage described above (1 man + 1 woman) and to point out that almost all cultures everywhere have recognised that as truth. The modern secular response is ‘so what’? And we don’t answer that objection by simply restating the proof, we need to demonstrate the proof in action the way music gives life to mathematical proofs.

We Christians want to keep riding the enlightenment pony in a post-enlightenment world. We settle for mounting reasonable arguments (that are reasonable and logical and tightly line up with ‘nature’); but these arguments are implausible because the good life now is much more about music than math. Our sense of what is good is much more derived from our ‘worship,’ our different stories of the good life, and our feelings than it is from some sort of natural law that we can simply choose to walk away from. Math might be true, as true as music… but it feels cold and emotionless. It takes a certain sort of rare soul to find math beautiful in the same way we find music beautiful. You might make avant-garde music celebrating obscure mathematical equations composed by algorithms rather than humans, but that is a particular taste that not everyone will share, and because it ignores the experiential nature of music; it won’t seem beautiful to anyone who doesn’t get the math.

We’re so used to operating in a culture where the ‘music’ sounded enough like ours that we could see its goodness. We’re like a bunch of Beatniks surrounded by Beatles tribute bands, that we didn’t really feel the need to keep pointing people to the Beatles, but now we live in the age of One Direction and Autotune and Pitbull and Kanye and Bieber… suddenly the music our world is making sounds very different and it’s like we’ve turned back to the math underpinning music to point out why the people around us have got music wrong.

Even though the Beatles are objectively and subjectively better and more beautiful than Bieber (and Bach is better than the Beatles), arguing for that with a bunch of numbers won’t shift anyone, you probably can’t actually argue someone out of their love for Bieber at all (and by analogy, I’m not sure you can argue someone out of or into a particular view of marriage without inviting them to first change the lens they use to see the world).

Math makes us understand music better — there’s a reason a lot of musicians do musical theory; which ends up being a bit about math. The answer for those who like Bieber rather than the Beatles, or Bach, isn’t pure math; it’s not to outlaw all other forms of music, it’s to make better music. Perhaps we also need to realise that part of the reason people like bad music and don’t see math as important — or rather the reason people are walking away from a ‘natural law’ in favour of what appears to be a position built entirely on feelings and personal preference, is that after we walked away from God’s design he gives us the consequences of that decision; which is to believe that bad stuff is good and math only important for making stuff we can use to do stuff we want to do.

Marriage is actually like music

There’s actually a bunch of objectively real and true things underpinning the making of music. How sound works; how our ears work; the physics involved with making, and recording, noises. But it also involves humans and human creativity. And that’s true in marriage too. God might have created and defined a fundamental relationship called marriage, but marriage is always experienced as a living breathing thing involving humans and human creativity. It’s always experienced subjectively, which is part of why how marriage works changes from culture to culture even if the fundamental axiom of what marriage is largely does not and has not. Marriage as God created it is music, not math.

Marriage is a good thing God made — but like music it’s a thing created when people take up a good thing design from God and approach it with love and imagination and the desire to make something beautiful (again, why Bach is better than Bieber); and ideally it’s something that reflects the relational, loving, life-giving, sacrificial nature of God (which is perhaps why the Bible speaks of our marriages as both a reflection of the ‘us’ who make men and women as people who bear the image of God, and as a reflection of the relationship between Jesus and the church, and about our oneness with God secured by our union with Christ as the ultimate marriage that our lives as Christians should anticipate).

Marriage and how we do it and speak about it in our world — a world full of knock-off Gods with cheap knock-off versions of marriage — is an opportunity for us to make something beautiful that glorifies God. To make a joyful and compelling noise that says something to the people around us about what is good for them and to call them to something better.  Talking about marriage in our public square is not just something we can reduce to a simple ‘natural’ or ‘reasonable’ equation. Even if 2+2=4; the world is convincing itself that 5 feels like a better answer. Understanding math or the created goodness of marriage will help our marriages be better and more beautifully musical; but that doesn’t mean we should speak to the world as though marriage is math when they don’t and can’t see it the way we do because their paradigm for approaching nature is different.

The reality is that just as knowing math helps make better music; knowing that there’s a created reality to marriage helps us make better marriages; but also, people don’t really want to hear about the math underpinning the music they’re listening to, they want to experience the beauty of the music, we show the goodness of our view of marriage by having and promoting beautiful marriages within our communities, and by helping other people have more beautiful marriages when they ask. We need both the objective truth that marriage between one man and one woman is created by the real God for a good purpose, and the subjective reality that we’re able to make something beautiful in our marriages using our imaginations.

But we also need to be empathetic listeners who try to understand why people make music that looks very different to the kind we like, and the kind we know is good, because that music reflects who they are. People are going to like different music, and make different music, and when we listen to that ‘music’ carefully — when we pay attention to how people speak of the created thing they call marriage (or what they want to call marriage) — we should pretty quickly be able to see that natural (math-like) arguments aren’t going to convince anyone who doesn’t first share our assumptions about the world and the place of reason. We talk like we’re talking about math while they’re talking like they’re talking about music; and it’s actually ok to talk about feelings and what beauty and the ‘good life’ looks like.

Listening to others in our world, and also knowing the deep truth math expresses (and even marriage as math in as much as the axiom is actually an expression of how God designed things) allows us to make music that resonates with people and with creation, and so might actually change the way the people around us see the world; the real way to change how they see the world is via Jesus and the ‘new eyes’ the Spirit brings; eyes that help us see the world through ‘by our Christianity’ in the C.S Lewis way… but when it comes to marriage and how to see truth about a created thing, repeating axioms isn’t going to cut it. We need symphonies that are remarkably more compelling than Bieber or whatever mass produced music people are pumping into their ears to hypnotise themselves to the truth of whatever view of the world is hot today; not cold laws. 

The way to prove that God’s vision for marriage is better isn’t to walk up to a bunch of people listening to music to shout numbers at them, it’s to play better music. It isn’t to insist on a natural proof, but to sing a supernaturally more beautiful song and then point to the amazing and intricate natural order behind the beauty, and the real relationship that marriage testifies to.

“For this reason a man will leave his father and mother and be united to his wife, and the two will become one flesh.”  This is a profound mystery—but I am talking about Christ and the church.” — Ephesians 5:31-32

Angry Birds Plush Toys, not actual size

TechCrunch has a scoop (not uncommon for the leading blog about goings on on the Internet). Everybody’s favourite iPhone game characters, the Angry Birds, are becoming tangible. Check out this range of plush toys headed your way (TechCrunch has photos of all of them).

Now, I can tell you that these birds aren’t actual size because somebody smart at
Wired/a> conducted some mathematical modelling on the game to determine its physics, and as a result, calculated that the red bird is five metres tall.

They worked out that there’s no air resistance in the angry birds world, and thus, gravity is the only force working on the bird (which moves at 2.46 angry birds per second in the horizontal direction).

“The only force acting on the bird (if the bird is not moving too fast) would be the gravitational force from the Earth. This is where I see lots of intro-student mistakes. They tend to want to put some force in the horizontal direction because the bird is moving that way. DON’T do that. That is what Aristotle would have you believe, but you don’t want to be in his club. There is no horizontal force in this case – no air resistance.

Check out the maths at Wired to see how the calculation of the bird’s height (actually 4.9m) was made.

The fastest path between four points: Math and Baseball

No, I’m not exploring my creative side by doing one of those drawings where you get those little coloured plastic cogs, and a pen, and swirl them around a page. That diagram is the result of careful mathematical study of the geometry of baseball, it represents the fastest path around all four bases – useful only if you hit a deep ball that doesn’t go over the fence and you want to run home – it’ll shave milliseconds off your time.

If you are running to first, or between first and second (or second and third, or third and home), which I believe in baseball parlance is a single (what would I know, I’m from Australia, we play cricket) the straight line is no doubt still the best bet. This circuitous route shaves about 25% off the time taken for the run – because turning sharp angles slows runners down substantially.

Some quotes from the story:

The issue is that turns slow runners down. The tighter the turn, the greater the slowdown, so while the straight-line path between the bases is the shortest, its sharp corners make it one of the slowest. Rounding the corner is faster, making the path a bit longer in favor of an efficient turn. And indeed, baseball players typically do this: They run straight along the baseline at the beginning and then, if they think they’ve hit a double or more, they bow out to make a “banana curve.”

But this can’t possibly be the quickest route, observes Davide Carozza, a math teacher at St. Albans School in Washington, D.C., who studied the problem while was an undergraduate at Williams College in Williamstown, Mass. It’d be faster, he reasons, to veer right from the beginning, running directly from the batter’s box to the widest portion of the curve. Of course, a runner is best off running straight toward first base until he’s certain he’s hit more than a single. But Carozza noticed that even when the ball heads straight for a pocket between fielders, making a double almost certain, runners almost never curve out right away.”

One of Carozza’s colleagues, Stewart Johnson, optimised the path by computer (coming up with that diagram).

“The result was surprisingly close to a circle, both in its shape and its speed: It swung nearly as wide and was only 6 percent faster than Carozza’s circle. On this path, a runner would start running 25 degrees to the right of the baseline — toward the dugout rather than toward first base — and then swing wide around second and third base before running nearly straight to home. Johnson also computed the best path for a double, and it swings nearly as wide, venturing 14 feet from the baseline.”