You don’t suck at math (Part 1)
I want you to imagine that you’ve decided to play softball for your company’s softball team. Your coach, a guy from the accounting department, is a former math teacher, and has taken it upon himself train all of you. You spend an hour or so each day training. These training sessions take place inside one of those company meeting rooms. For the first 40 minutes, you listen to him talk about the different baseball games that he has been to; he draws various diagrams on the whiteboard, explaining in detail the dimensions of each ballpark. Then, for the final 20 minutes–in order to give you a more hands on experience–you watch some tapes of the most important moments in baseball history: Babe Ruth’s famous “called shot,” Bucky Dent’s home run in Fenway park during the division tie breaker, and the victory celebration of the 2004 world series, won by the Boston Red Sox.
Your teacher, who stresses the importance of some personal softball experience in learning the game, also assigns homework each week. Here is your first assignment: go home and make a video tape of yourself swinging the bat. Make sure the video is in focus, and that your whole body is in the frame. Take ten swings left handed, and ten swings right handed. Similar exercises are assigned throughout following weeks. Then your first game of the year comes along. Your team loses 23 to 0. The rest of the season doesn’t go very well either; you lose the first 10 games of the season. After a while, you manage to win a close one, and then a few more after that. But, for the most part, the season is a disappointment. You walk away from the experience believing that you and your teammates just aren’t the sort of people who can be good at softball. You don’t sign up for the team the next year.
This story, as unrealistic as it is, is not so different than the experience people go through when they are “taught” mathematics in school. In short, they are presented with a series of activities that superficially feature the subject matter, but in reality are absolutely unlike doing activity that generated that subject matter, and also quite unlike any secondary activity that allows one to really appreciate that subject matter. Watching baseball, and even mimicking the basic moves that baseball players do, is nothing like playing baseball–it won’t make you good at what they do. Similarly, watching someone drone on about the quadratic equation, or about the cosine and sine functions, or anti-derivatives, won’t make you good at math. Neither, really, will rote memorization of formulas or repeating procedures for doing problems (this may, however, at least get you to where you can pass the test). To get good at math, actual math, you have to sit and think, and explore, and even see things for yourself. Fortunately, this is easier, and more fun.
Many people tell me that they gave up on math when they could no longer follow what was going on in their math class. Well, I’m going to let you in on a secret: I almost never know what is going on in my math class. Granted, my classes are probably harder than the ones you were taking, but the difference isn’t so great as you might imagine. I don’t think I’ve ever been to a math lecture that I followed the entire way through. Losing track of what is going on in a math class is the norm. A good percentage of the time, it isn’t even your fault that you lose track of what is going on. Often, it is the fault of the lecturer. At some point along the way he may do something that actually makes it impossible for you to follow the rest of the lecture–for example, introducing a notation that you aren’t familiar with, and not explaining it. Or he could be assuming knowledge of a concept that he never taught. The lecturer isn’t necessarily being negligent in all of this. It’s just that explaining mathematics is actually quite difficult–you have to bring people to where you are, without knowing exactly what is missing. Knowing what information to supply so that your audience can see what you see can be even more difficult than the doing of mathematics itself. The format of a daily lecture, in which the students frantically write down everything that the lecturer is writing, while simultaneously attempting to follow the logic of what he is saying, simply doesn’t lend itself well to actual comprehension.
The sort of brain that is good at following a math lecture, in fact, may not be at all the sort of brain that is good at actually grasping mathematical structure. It is true that some brains are better than others at doing math, but I seriously doubt you’ve ever received reliable information on whether or not you’ve got one of the better ones in this regard. Think about this: there was a time when most people were illiterate, when reading and writing was reserved for the scholars. Now virtually everyone can read. This is because we, as a society, have figured out how to really teach reading, how to facilitate a person’s learning of what is actually quite an involved mental task. But I don’t think we’ve accomplished this with math yet.
A person said to me recently that she isn’t good at math because she just isn’t a right brain sort of person. I’ve heard similar comments in the past. My response is that you don’t do math with the right side of your brain, you do it with your whole brain! I’m sorry, my friend, but you’ve been duped by a false dichotomy. The logical and analytical are not opposed to the creative and fanciful (let alone separated neatly into distinct compartments in your physical brain. The things we believe these days!)–your mind is an organic whole, and I doubt any part of it is completely inactive in anything you do. If you are an artsy or creative type, that is probably going to help you do math, believe it or not. Does your mind have a tendency to go off on tangents? Can you not stay focused on what the teacher is saying? Good! This means that your brain is actually doing something. Don’t fight it! Quit paying attention, and pay attention to the thoughts that you are having (OK, sorry, now I’m sounding like Morpheus from The Matrix).
The main thing that makes math seem difficult is when someone is seeing something that you aren’t, but this isn’t communicated. They have a picture in your head, that you don’t see. Or there is an idea, or a whole train of thought, that is simply missing, and that makes everything seem arbitrary and complicated. Everything is difficult when you don’t know what it really is. For example, I bet you’ve heard of the quadratic formula. You may even remember part of it! You may even know that it’s used to “solve” quadratic equations. At some point in your math education, I bet you were presented with this monster:
What you are seeing is the result of moderately long process of reasoning that is not presented to you when you are given the formula. It’s easy to think that, since the result looks complicated, the process itself must have been so, and that it’s something you could never have come up with. But actually, it is merely the result of many steps that are, in themselves, straightforward. These steps constitute a perfectly logical and natural series of thoughts, a series of thoughts that maybe aren’t so different from the sorts of thoughts that you would start to have in your math class. You (or I) might not be able to come up with the quadratic formula on your own, but you can at least get a good idea of how someone did. In my next post, I’m going to give you a down to earth explanation of where this comes from, and how and why a person would come upon it naturally, and I’m going to try to get you to see it in the way that I see it. This, I hope, will give you an idea of how people think about mathematics. Moreover, I hope I can convey the idea that, when we see where these things come from, and see the kind of thinking that caused them, everything becomes a lot more interesting. The quadratic formula can actually be seen as a simple example of the sort of mathematics I study–Algebraic Geometry. I’m hoping, also, that I can (if it seems interesting enough), build up from there a more general description of what Algebraic Geometry is. We’ll have to see how far I get with that, though.
More than Math
What I call materialism is the belief that the material world is all that exists, that everything else is somehow derivative of a base level reality that is somehow “material.” The most common sort of materialism, scientific materialism, adds to this the belief that science is the most suitable technique for coming to know the truth about this baseline reality. Some people associate this view with rational thinking itself, with a sort of wise willingness to look beyond mere appearances and see things as they really are.
Against this view, I ask that the reader would try to join me in a sort of shift of perspective. We are all aware of the distinction between perception and reality, between the familiar world (clouds, trees, etc) and the world that we imagine is somehow beneath that, the world that is somehow objective and concrete, and is considered as the more fundamental cause of our perceptions itself. Nowadays we tend to think that science is what is best able to study that “baseline reality”: we tend to identify that baseline reality with something like atoms, particles, waves, quantum states, or whatever. Now, whether such a world–a baseline reality that is the cause of all of our subjective experience–exists in general, I am not quite sure, nor even am I sure exactly if this is a meaningful question to ask. But what I want you to try to do now is try to imagine that the world described by science in particular, whatever it is, is not actually as the world “as it really is,” or even a “best approximation” of that world. Instead, I’d like you to try to imagine that the content of science is even more deeply psychological than the familiar world, that it is even further removed than the familiar world is from whatever baseline reality might actually exist. That is, try to think of science itself as the end result of a very psychological process indeed: one of applying a deeply abstract and mentally generated structure (namely, mathematics) to the world that we find ourselves experiencing.
Now, this point of view is actually quite natural, once a person gets used to it. In some sense at least, this has to be what science really is, though I don’t think this is all that it is. Now, from this new point of view, it is actually quite a remarkable fact that science works at all. That is, it is remarkable that all of these particular abstract mental structures, things we came up with in our mind, do seem to find a correspondence to the reality that we perceive. Some would say that this fact alone refutes the perspective shift that I have endorsed, and is evidence for the truth of something more like scientific materialism. And I actually think this is somewhat correct; science is obviously much more than just a mental construct. But I think it also indicates that we, at least today, do not think deeply enough about the very question of why science works. I believe that our popular ways of thinking about the world do not actually have a satisfactory answer to that question. Further, I believe that it is mainly in answering this question that materialism has gone horribly awry. Or, from another point of view, materialism is caused by a gravely mistaken answer to this question. What I believe is the mistake, and the whole hubris of materialism, is to suppose that a sufficient explanation for the effectiveness of science is simply that some sort of mathematically describable structure is itself a final explanation for what is really there, is a sufficient explanation for reality itself.
Why does mathematics hold such an extraordinary ontological status? I see no good reason that it should. Thus, I wish to make the following proposition: what if we were to give to “natural language” (a terminology that actually already belies a materialist bias) the same ontological weight as we currently give to mathematics? To put it in less philosophical language, what if popcorn and lakes were as fundamentally real as pi and the integers? After all, undoubtedly they are, to most people.


This would, I believe, mean that a great many things would become real to us again! Suppose–imagine–that we simply took it for granted that thought and language are somehow fundamental, that their very existence and association with the world is basic, axiomatic. I think, then, that we would think of the appearances as being predictable when we describe them in the manner that science does precisely because the “thought patterns” being put to use–the ideas and language of mathematics–have a rigid, precise, and predictable structure. Rather than idolizing it, lifting it up as the proper foundation of all other truth, we could simply say that mathematics is the language that we can use to talk in a very unique and useful and beautiful way about the world. And we could say that art, for example, is another such way. Or poetry. The representations of the poet are no good for making the sorts of predictions that science makes, but that is not the point. It is not their nature to do so. The point is that they are just as real; it is only a philosophical bias to say otherwise. From our new perspective, we can then truly say, with philosophical rigor rather than simply mystical vagueness, that an artist knows something about a cat, or a tree, or a mountain range, that a scientist does not (and vice versa). Even if we were to exhaust what mathematics can say about reality, there would still be something very definite left–indeed a great deal left.
What is “lettucetomato?”
Whenever I order a deli sandwich, I like to have lettuce on it. Lettuce always makes a sandwich better (unless it is old, nearly rotten lettuce, and even then the effect is somewhat neutral). It is crisp, and adds a fresh, crunchy texture to it. I do not, however, feel the same way about tomato. In fact, I think tomato destroys a sandwich. That’s right, I said it: tomato destroys a sandwich. It is slimy, and it completely dominates the taste and texture of the sandwich. Thus I always order my sandwiches with lettuce, but no tomato.
You are probably thinking by now: where is he going with this? Well, I’ll tell you. My preference for lettuce without tomato causes all sorts of problems for NYC deli counter sandwich makers. This is because these two vegetables are virtually inseparable in their minds. In fact, I think that most of them are under the impression that lettuce and tomato are a single object, known simply as “lettucetomato.” Here is a typical interaction:
Me: I’d like a roast beef sandwich on a roll.
Deli guy: What kind of cheese?
Me: Swiss cheese.
Deli guy: Lettucetomato?
Me: Just lettuce, no tomato.
Deli guy: (skeptical or puzzled look)
Me: Can I have mayonnaise also? And maybe some pickles?
If the deli guy is less of the questioning type, i.e. one of the ones who simply listens to you list the ingredients, the interaction will go more like this:
Me: Could I have a roast beef sandwich on a roll?
Deli guy: What do you want on it?
Me: I’d like swiss cheese, mayonnaise, lettuce, and–
Deli guy: (somewhat eagerly) tomato?
Me: No, no tomato. Just lettuce.
Deli guy: (confused, almost hurt, expression)
It is as if he can’t resist completing the (imagined) compound word. I hope I’m not stereotyping here, but I think that perhaps this is especially true for the Hispanic deli guys. Something about the two words maybe rolls together really nicely for their natural way of speaking. Perhaps they think of the word “lettuce” as practically being a prefix to the word “tomato,” so that if they say the former without saying the latter, it just feels incomplete.
Now really, in spite of whatever linguistic justification there may be for this practice, I must still protest. In truth, these vegetables couldn’t be more different, and the effects they have on a sandwich are diametrically opposed. Lettuce is green, tomato is red. Lettuce, as I said, is crispy and crunchy. It has, on its own, practically no flavor, but has a fresh feel to it, and its texture compliments a sandwich very well. It adds a crunchiness to things, but doesn’t take over or adversely affect any of the main components of the sandwich. Tomato, on the other hand, is soft, slimy, and has a very distinct flavor. When mixed in a bite with any cold cut, it tends to become a distraction. It also tends to soak and thus ruin the bread of the sandwich.
I honestly don’t know why anyone ever gets tomato on a sandwich, but I suppose I won’t protest this too much. People have their tastes. But I say that the fact that tomato has become so deeply associated with lettuce in the sandwich ordering procedure is utterly unacceptable, and must be challenged. I hope you will join me in this venture. I have some preliminary ideas. The first is to modify the above dialog in the following manner:
Me: Could I have a roast beef sandwich on a roll?
Deli guy: What do you want on it?
Me: I’d like swiss cheese, mayonnaise, and some lettuce-but-please-don’t-destroy-my-sandwich-with-tomato.
Deli guy: Excuse me?
I haven’t really thought of where to go from here, but I’m sure the reader can improvise some creative interactions that will also gently get the point across that lettuce is, in fact, its own vegetable, and ought to be treated as such. This technique, however, can only be used if the deli guy lets you list your own ingredients. For the more inquisitive deli guys, I suggest the following:
Me: I’d like a roast beef sandwich on a roll.
Deli guy: What kind of cheese?
Me: Swiss cheese.
Deli guy: Lettucetomato?
Me: What is “lettucetomato?”
Deli guy: Uh…lettuce and tomato, do you want them?
Me: Do I have to have both?
Deli guy: (Pause)
Me: I’d rather have neither if I can only have both.
And then go from there. I am open to other suggestions.
Changing the way we think about healthcare
My last post drew a lot of comments, and a lot of interesting debate about healthcare. This seems to have died down now, but I still feel a certain lack of closure. I feel like, in the midst of all the political debate, the most important considerations, in regards to this particular issue, have not even really been addressed. Though the original post was about much more, all of our debate centered around the best way of financing healthcare. This was all basically working under the assumption that healthcare is something to be bought, that it has a price on it. Even the liberals, who argue on moral grounds that the government should pay for our healthcare, fall victim to this to this way of thinking. Liberals are certainly right in saying that healthcare is our collective responsibility, and that we all should chip in for it. The problem with their view is simply that they don’t go far enough with what that means–they simply conclude that, because of this, the government should “pay for” healthcare for everyone. Now, even if the economics of this happen to work out better than the current scenario, I think we will still have many issues. I think that the intrinsic problem to all of this is that we, as a society, are thinking of healthcare as a commodity, as something which can be bought at the right price. I believe that as long as we are looking at it like this, there will be problems. The liberal solution and the conservative solution share the defect that both are far too focused on the economic side of the problem–I believe that this economic emphasis is itself at the root of the problem.
In the comments of my post, I found myself defending a conservative take on healthcare, on the grounds that the liberal solution would cause more problems than it would solve. I did this because I wanted to address the whole issue from the “practical” angle that I had said the question ought to reduce to, once it was recognized that both sides agree on the moral imperative of improving healthcare. When it comes to practical questions, I tend to lean conservative. But really, I had all along a simpler ground on which to criticize the liberal solution, and the conservative solution along with it. A basic theme of my original post was that collective evils–that is, wide scale social problems, like the lack of healthcare–tend to be the cumulative result of many individual evils. One thing that I believe contributes to the problems we have with healthcare is a flawed way of thinking about it that most of us, liberal or conservative, succumb to. The truth is, neither the liberal solution nor the conservative one really address this problem.
Healthcare in the Kingdom of God
And he arose and left the synagogue and entered Simon’s house. Now Simon’s mother-in-law was ill with a high fever, and they appealed to him on her behalf. And he stood over her and rebuked the fever, and it left her, and immediately she rose and began to serve them.
Now when the sun was setting, all those who had any who were sick with various diseases brought them to him, and he laid his hands on every one of them and healed them. And demons also came out of many, crying, “You are the Son of God!” But he rebuked them and would not allow them to speak, because they knew that he was the Christ.
And when it was day, he departed and went into a desolate place. And the people sought him and came to him, and would have kept him from leaving them, but he said to them, “I must preach the good news of the kingdom of God to the other towns as well; for I was sent for this purpose.” And he was preaching in the synagogues of Judea. (Luke 4.38-44)
Then the angel showed me the river of the water of life, bright as crystal, flowing from the throne of God and of the Lamb through the middle of the street of the city; also, on either side of the river, the tree of life with its twelve kinds of fruit, yielding its fruit each month. The leaves of the tree were for the healing of the nations. (Revelation 22.1-2)
Healthcare, from the standpoint of the coming kingdom of God, is fundamentally about free healing, about something freely given. The healing of individuals, and the restoration of the health of the world, is a part of the Gospel, the good news of Jesus Christ. If we are to emulate the attitude Jesus had towards healing, we are to give it simply because people need it, and not because of anything we will get out of it. We must do it simply out of a love of our neighbor, because we are to view their health as being as important as our own.
As things stand now, however, the life saving drug that a person needs still comes at a price. A doctor will provide care, but this is because he knows beforehand that the insurance company has agreed (directly or indirectly) to pay him. And under a government health insurance plan, it would be no different: the doctor would provide care, but this is because he knows that the government will pay him. It doesn’t take place exactly like this–at least hospitals are, after all, legally required to treat someone, regardless of whether or not they can pay. And there are many doctors who routinely sacrifice their own benefit in order to go against these financial conventions and provide help to people who need it. But it is certainly true that a major interest of many of the people who get into the medical field is money. This is something that needs to be changed.
There are some things that only a trained professional can do, and of course he ought to be compensated for his contribution to society. So I am certainly not saying that we should stop paying doctors! But what I am saying is that we need a collective improvement in how all of us think about the health of our neighbors. I think we have to reach a point in which everyone, doctor or not, accepts in his heart that the health of those around us is actually all of our responsibility. We must realize that improving it means, ultimately, changing the way that we all relate to each other. This is not easy. It means much more than a sacrifice of tax dollars. It means sacrificing our time, our energy, even our deepest aspirations, to be with those who are sick, to really care for them. This isn’t to say that many people don’t do this already. It is just to say that when we, as a society, become better at this, better healthcare will follow naturally. There is no reason why we cannot improve both our own collective medical knowledge and our own willingness to help each other to such a degree that the broken healthcare system we have now would cease to exist as we know it.
I cannot tell you what this looks like; I can only say that when I look at the way things are right now, everywhere I see systemic violations of the basic principle of unconditional love, and thus I see room for improvement. I know there are people who have thought about this a lot more than me. One that I stumbled across is Patch Adams, who was made famous through the movie that was made about him. The following article, written by him, contains many insights, and I would encourage everyone to read it:
The Role of Government
The other day, a couple of friends and I were talking about healthcare, and one of them expressed surprise at the fact that I am often so resistant to the idea of the government involving itself in certain sorts of things. She thought that this contradicted the fact that I, in other instances, have been quite adamant about the idea that some things are wrong, and should be forbidden by law simply because of this fact, and not based on any foreseen calculations of what the consequences of legislation against them would be. In other words, I believe that sometimes it is a moral imperative for the government to act, to do something, in the interest of justice, regardless of the potential negative consequences. The example of this that I think she had in mind is my stance on abortion. Another good example of such a situation–a situation far less controversial now than abortion–is the issue of slavery in the 19th century. Basically everyone now agrees that it was the right thing, the moral thing, for the government to abolish slavery, regardless of the potential consequences. Now, for my friend, the basic right of every citizen to healthcare is example of a similar sort of moral imperative. Her basic question was this: why do I support a sort of universal government intervention in one such case, but not necessarily in another? Why do I apparently believe that the state should guarantee an unborn child the right to live, but not the right of every citizen to receive medical treatment?
To begin to answer this I think we should first notice that, in fact, the government is neither able to guarantee the life of every unborn child, nor is it able to guarantee every citizen medical care. Many abortions will still take place if abortion is made illegal. And if we add a federal option to the health care system, this will not mean that no one will ever be deprived of appropriate health care. Both of these problems–abortions and lack of health care–are caused by much more than simply how the government has chosen to involve itself in these matters. Secondly, let me make it clear that I absolutely believe that every person deserves adequate health care. To be able to help someone live, and to decide not to, is clearly immoral. I believe this in the same way that I believe every person deserves to be fed, or to have clothing and shelter. When we–any of us–are able to provide things to people, and instead look the other way, we are committing evil. With this out of the way, I would like to try to explain why I would support government intervention in some situations, but not in others. Basically, my answer has to do with the kind of government intervention that would take place. But, to understand this, I think I must first explore some interesting theoretical questions about the nature of goodness and justice in society.
Global and local principles
Goodness, though intuitively perceived by everyone, is hard to define, and thus perhaps ought to be taken in this discussion as basic and undefined. But what is justice? Most people would probably agree that the concept of justice refers to a good or right ordering of things on some level. And there are really only two levels with which I wish to concern myself in my attempt to understand justice: there is the local level and a global level. What does each mean? Well, let’s start with the local level. Locally, justice has to do with a right relationship between individuals: when human beings relate to each other properly (i.e. “goodly,” whatever that means), we might call that justice. But actually, justice is usually spoken of more often in reference to it’s negation: injustice. That is, justice is usually talked about in the context of a breach of good relationships: for example, when people break the law, we talk about bringing them to justice, giving them a punishment appropriate to their crime.
It is, incidentally, an interesting and important question as to why, how, or whether people should be punished for crimes. Many have asked what justification there actually is for doing this. And attempting to answer this question, I believe, leads to a consideration of the global aspects of justice. In particular, one justification for punishing people for crimes is the following: when a person commits a crime, we might think of him as having disrupted a sort of “universal balance.” He has sinned against an absolute law, and thus disrupted something fundamental and universal. Then his punishment is meant to, in some way or another, restore the balance. Now, most societies throughout history have believed in some sort of moral reality. That is, they have believed in some sort of real “moral fabric” to the universe: when people commit wrong, they are affecting this. The eastern idea of karma is a good example of this. Many people today, on the other hand, tend to believe that laws and punishments are really only a means to an end: for example, laws are meant to deter people from committing crimes, and thus bring about a more peaceful or ideal society.
So here we have two different “global” components that come into play when thinking about justice: a sort of “moral fabric” notion on the one hand, and the notion of a good or well functioning society on the other. Many disagreements in ethics have to do with these different conceptions of justice on a global scale.
Global justice and God
I believe that these two different conceptions of justice on a global scale actually come together under a Christian understanding of justice. Christianity teaches that a good and wise and powerful God created the world we live in to be absolutely good, but that we, his creatures, have turned against this plan. In some sense at least, the injustice that we see in the world is ultimately our own doing–all of us our responsible. And actually, Christianity believes in non-human spiritual entities, and believes that the bad ones (demons–i.e. angels that have turned against God) are also at fault in some way too. But, whether through demons or through human beings, injustice originates on the individual level, in all of us, and this adds up, on the collective level, to the world not functioning in the way that God would have it. In this sense, Christian ethics is “consequentialist”–that is, concerned with the overall goodness and flourishing of society.
On the other hand, in the Christian understanding of things, there exists a real moral fabric in the sense that God, and only God, knows what each of us have done, and how it has affected the whole. He also knows how our decisions affect our relationship with him, he who is the author and standard of what is good, beautiful, and true. He cares about this, and will hold each of us accountable for it in the end. In Christian theology (at least in the west–I know the eastern Church thinks of things a bit differently), our sense of guilt is actually more than just a feeling: it is a reality that has to do with how we stand before the good God who created us. So our intuitive notion of a universal moral fabric ultimately goes back to our relationship with our Creator.
Now, God has a plan to fix things through his own grace and mercy, brought into our world through the suffering love of Jesus. Much could be said about this, of course, but for our purposes it is enough to know two things. First we must know that the plan is is taking place right now, and so what we do matters in terms of that plan–that is, in terms of God bringing about a right ordering of things. Secondly, we must know that God’s global plan begins on an individual level, and proceeds from the inside out. Christianity teaches that “the kingdom of God is like a mustard seed”–that true healing tends to come from the inside out, and often in unexpected ways, through the work of God himself. One of Christ’s most basic teachings was that a focus religious ritual and external appearances–what he called “the righteousness of the scribes and pharisees”–will never bring about true change to our hearts.
This principle, I believe, is also true on the level of societies. Think, for the moment, of humanity as being a vast web of personal interactions. These take place every day–some seem inconsequential, others of great import. A man buys a hot dog, and chats with the vendor. A woman decides to forgive her husband. A teenager decides to join a gang. A teacher says some encouraging words to a child. A couple decides to get married. Now, whatever broader social structures exist in society, this is what society actually looks like close up. And it is here, I think, that the most important battle between good and evil is fought, and the overall health of society is determined. Thus I believe that changes in the large social organizing principles of our society will never bring about any real improvement if the individuals that inhabit that social structure are still just as broken. Conversely, genuine moral improvement within individuals will lead to a better social structure naturally. But it is God–either through design or through his own continued presence and influence in the world–who will knit this all together on a global scale. And this brings us to:
Government intervention
In our increasingly secular society, I believe that liberals and conservatives both look to some sort of impersonal but universal structure to fill the role of God in the above regard. For liberals, that structure tends to be government. For conservatives, it tends to be the free market. Let me say that I don’t trust the free market to fix things any more than I trust the government to do so. Believing that any of these organized products of fallen humanity will ever bring about the peace and justice that only God can bring is a recipe for frustration and despair. Most systemic evil we encounter is a result of moral evil on the individual level. A greedy choice here, a decision to look the other way there–it all adds up to people who can be helped not receiving help. Things are not so complicated, after all. What is really needed in our society is not a a massive reform bill, or a more consistent embrace of free market principles, but better, more loving decisions made by individuals.
According to Christianity, no human entity–no person, committee, or government–is even remotely capable of bringing about the overall sort of justice that God will eventually realize in the new creation, when he finally puts the world to rights. Part of this is due to our own brokenness: any plans we come up with to put things right will ultimately be affected by our own tendencies towards evil. But, more than this, understanding how to correctly order things is not our job, it is not a task our finite minds are capable of, even in their ideal state. It is beyond us. And even if we could imagine it, we do not have the power to enact it. A total right ordering of things is accomplished by God; we can participate in it by being obedient to him, but only he knows how to bring it about. But the great thing is that, as human beings, we can contribute to the overall right ordering of things, by obeying Jesus’ great commandment to love him, and thus love our neighbor as ourselves. If you aren’t a Christian, you may have a bit of a problem with the former, but you can still try the latter.
Now, one cannot conclude a priori that doing so will never entail support for government intervention of the sort called for by president Obama’s health care plan. But we must recognize the limitations and potential dangers of such things, where they exist. For me, the real area of disagreement between myself and my friend, in this case, is obviously not what is right or wrong. We both agree that it is wrong for people to be deprived of healthcare. The disagreement stems from what each of us thinks the government is, and what the government should actually be doing. I see the basic power of the state, in terms of bringing about real social healing–that is, the repairing of social relationships that would facilitate the availability of healthcare to everyone, not the literal healing provided by healthcare itself!–to be fairly limited. As I said before, a Christian ethic believes that social healing ultimately comes from the inside out. It is brought to individuals by the Spirit of Christ within them, and to society by the actions of individuals, guided by that Spirit. Government, of course, cannot provide this. It can only administer things from the outside in.
I believe the government can most positively contribute to good by forbidding certain clear individual acts of evil: murder, rape, theft, etc. Thus I always support “government intervention” in situations where justice is most clearly able to be brought about by their controlling influence, and even then I am wary of potential problems: how do we know what those situations are? What is an appropriate punishment? How do we avoid corruption and abuse of power? In spite of these difficulties, the government is fairly capable of enacting laws that forbid certain grave evils on this individual level. It is capable of setting and enforcing important universal commands on the behavior of individuals–do not kill, do not steal, etc. Certainly, no government is perfect at this, and there are still many problems. But we all seem to agree that it is the right thing for the state to pursue justice in this way, that it is preferable to the alternative of anarchy.
“The reformer is always right about what is wrong. He is generally wrong about what is right.” --GK Chesterton
Much of the systemic evil in our society, however, is more complex than simple “law breaking.” For example, consider gentrification and the related lack affordable housing. This is caused by many factors, and there may be some actual lawbreaking involved. But it is not easy, overall, to say who exactly is at fault or how they should be dealt with–landlords, tenants, real estate brokers, etc. I don’t mean by this that nobody is at fault, but rather that too many people are at fault in different ways for us to really be able to adequately assign blame. Many individual decisions add up a complex, collective evil. I would say that the rising cost of healthcare, and the lack of coverage for many individuals, is a similar problem. For this reason, I think we have to consider such issues differently when we ask ourselves whether or not there is a moral imperative for government intervention. It may be that we can isolate some basic evil that is being committed on an individual level, which is causing the problem, and agree as a society that this sort of thing should be forbidden. Sometimes, even in what seem like complex social issues, this may happen–I don’t rule this out. But I don’t think this is the sort of thing we are talking about when we consider the healthcare plan advocated by president Obama. Here we are talking about a complex and specific social plan enacted by the government. The question of supporting it becomes a practical one more than a moral one. This is true even though there is a moral imperative to try to deal with the social problem. In other words, it is society’s moral duty to try to deal with the social problem, but government is not necessarily the appropriate entity to act, at least not in the way that Obama has envisioned them acting. It may be, but determining this is may be a practical question rather than a moral imperative. And it may be a very difficult question, and one for which the burden of proof is on him, to show that it will result in a greater good. I admire the fact that he has actually tried to do this (and I also acknowledge that I really ought to research the issue more), but still I remain somewhat skeptical.
Things That are Real
I present to you one of the finest moments in the history of cinema:
In the scene, this printer is condemned for being the frustrating piece of technology that it is, and the characters in Office Space are pouring their wrath out on what is, for them, a symbol of their entire futile existence as office workers. The audience easily identifies with them, sharing in their anger towards the printer and the inhuman system that it symbolizes. In this scene and others, Office Space does a good job of expressing a basic frustration that people these days have with the sort of artificial way of life many of us are thrust into, and how such a lifestyle goes against our basic humanity. We human beings have an instinctive ability to decide what things in this world truly matter, and what things don’t. We can see that being confined to an office cubical for eight hours a day can be a soul-crushing waste of time–I say “can be” because I’m sure there are exceptions to this, where the work being done is itself rewarding somehow, and I don’t mean to trash anyone’s vocation. But we can easily see how so many aspects of our modern life go against our basic humanity. We know that these things are artificial. And we know that other things, things like friendship, family, love, art, and truth, are real somehow. Or, at least, if anything proved to be real, it would have to be those things. What I believe deserves more consideration is the question of how and why we are able to make the necessary distinction in order to make such judgments. That is, where does this distinction come from?
The real and its enemies
I propose that some things in life are actually real, whereas some are unreal, and that people can tell the difference, though far from perfectly. I will not be using the ordinary meanings of these words here. That is to say, I will not be using the most immediate senses of the word “real” that it has acquired in contemporary usage. The distinction I wish to make has nothing directly to do with what actually exists–some “real” things are not realized in our world, at least to the degree that they ought to be, whereas some “unreal” things exist in abundance. Nor does the distinction have anything fundamental to do with the human process of manufacturing, effort, or planning. For example, many things are very intricately planned, like a ballet or a symphony, yet will fall on the side of “the real.” Other things have no clear human design, but nevertheless fall on the side of “the unreal”–for example, the HIV virus is not man made (unless you buy the conspiracy theories), but it is quite unreal.
Perhaps some more examples are in order. I hope none of these seem either too sentimental or too morbid; neither is my intent. A family gathering held each year, for thanksgiving, is real. It is real when people gather together and share memories, tell jokes, and think of each other fondly. It is unreal, however, when they let old grudges or gossip skew their perception of one another, when they hold false expectations of each other and judge each other. A couple of glasses of beer, and a few good laughs, shared between old friends, are real. Severe drunkenness, and an angry shouting match, resulting in the destruction of a friendship, is unreal. Marriage is real; pornography is unreal. The smile of a baby is real; cancer in a baby is unreal. Life is real, death is unreal. Real things are intrinsically good; they are part of reality as it should be. Unreal things are intrinsically bad, and are an unwanted intrusion on a good world. Our world, the world we all know, seems to be a synthesis of real and unreal components.
Now, it is my view that we live in a society that craves realness, but lacks the ability find it consistently, that lets unrealness flourish, all too often. Much of this is a matter of confusion. Since our world is a mixture of the real and the unreal, often we create false associations between the two, and so we seek realness in the wrong places. For example, one might seek love and acceptance, which are real, through the pursuit of fame and power, which are unreal. We usually don’t know how to get the real without also getting some of the unreal mixed in. We are, may I say, like sheep without a shepherd.
Jesus: champion of the real
Of all the charges that can be made against Christianity, perhaps the most troubling for me is the simple charge of irrelevance. This is not simply the charge that it doesn’t matter, but further that it couldn’t matter; that is, not simply the charge that it is untrue, but the charge that, if it were true, it wouldn’t be worth much. This is the charge that my most basic conviction really has nothing to say about life, the real life that people live, and that it is even opposed to the flourishing of such life. It is, in the terms of the above, the charge that Christianity is “unreal.” And I think that many people honestly believe this, and won’t give a consideration to Jesus Christ precisely for the reason that they don’t think he has anything to say to them, that he doesn’t speak to their most fundamental reality. They think that, if he really were who the Christians say he is, this would not be good news at all. On the contrary, this would probably mean that the universe is essentially artless and boring.
I understand this sentiment well. I confess that I feel it myself sometimes. After all, who does not get the sense, when confronted with, say, a certain type of street evangelist (those guys who hand out little slips of paper telling you to believe in Jesus or go to hell), that this person is out of touch with life, ordinary life? His slip of paper must appear as an invitation to become like him. And who would want to be like that guy? I don’t usually doubt the sincerity of his motives, but I fear that it is hard for another person to look at such a thing and believe that what stands behind it is of any real value. More generally, much of popular preaching presents, as Dallas Willard says, a Jesus who is “barely conscious.” Often, Christianity doesn’t present a Jesus who we could imagine is actually interested in the things that we clearly perceive as mattering.
So I understand the sentiment. I understand it, but I believe that it is, as a fundamental objection to Christianity, untrue. Seen properly, God is actually the author of the real (whereas Satan, perhaps, is the author of the unreal). As such, God is supremely concerned about the real moments of our ordinary life–more concerned than you or I. One proof of this is simply the central belief of Christianity that God became a man, and experienced these moments, all for our sake. Christians have called this the incarnation. Think, for a moment, about what it means for our everyday life, for the things that all human beings do and go through–that the creator of the universe poured himself into a person! Now, Jesus spent most of his years on this world doing nothing particularly memorable, from a historical standpoint. The New Testament mentions only one public incident between his infancy and his last years. He wasn’t famous during this time. We aren’t told much of what he did then, but I imagine he must have lived a pretty ordinary life. Only those closest to him saw much of it, of course, but I think this is part of the point. In this part of his life, Jesus identifies with the ordinary experience of every man (and woman). The God-man, the one man who ever lived a perfect life, only really made a scene at the end (it was, of course, of prime importance that Jesus eventually did make a scene, since through making it he became our redemption). And that is part of the point: a perfect life, in God’s sight, isn’t all heroic deeds and public attention. Part of the point of the incarnation was to solidify the permanent meaning and basic reality of ordinary human experience. All that is good in human life, Jesus made his own, God’s own. And if we are to believe that Christ’s righteousness–his basic goodness as a human being–becomes our own, then at least part of the reason that our redemption takes place at all has to do with the basic, unrecorded, ordinary life of Jesus. And you see the corollary right? It’s the eternal significance, for each of us, of the real moments of our ordinary, everyday lives.
Eternal significance
In particular, I’m thinking about the eternal significance of how we think and act, including what things we choose to value, and the perspectives we adopt towards life itself. Not believing in any sort of eternal weight to how we go about life is, perhaps, the central tragedy of our age. Even though all people have the ability to intuitively judge what is significant, to know what is real, so many of them are ultimately nihilists–so many people today don’t believe that life will ever really amount to anything, that it all turns to dust in the end. People want to make life count, but they don’t believe that there is anything it could really count towards. This rejection of meaning, in fact, is embraced so strongly by some that it, in spite of itself, practically amounts to a conviction. So people say, sometimes with a hint of irony, “life may be pointless, but at least I…” But if life is pointless, there is no “at least.” The phrase “at least” implies a context in which things are meaningful. One could say, “we lost all our money, but at least we still have each other” or “the Yankees didn’t make the playoffs, but at least their prospects are good for next season.” But to say “at least” without specifying greater context of things in which a comparison could take place simply doesn’t make any sense.
The truth is, our lives are not arbitrary; on the contrary everything fits together in a grand story that will all come together in the end. So life is not a game, and if we live like it is, we are building on a foundation that will crumble. People today are so wonderful, yet so tragic. People are wonderful because God made them that way. People are tragic because they don’t know what and who they really are; they don’t know that they are unique creations of God, and they don’t know that their actions and their lives actual matter, actually count, forever. Not just for the future, nor just for the sake of some vague notion of “having lived a good life” or even “having made a difference.” What you do matters forever; what you say to people matters forever.
I know some brilliant and fun people who are agnostics and atheists. Sometimes, around them, I feel like I am witnessing a great drama in which the participants are dangerously unaware of the real consequences of their most basic decisions and habits of speech and thought. I think to myself: these people do not believe in God, and would barely give consideration to the story I believe in, and yet the truths it speaks of are so obviously present in their lives. In their beauty, I want to cry out to them: is it really so hard to believe that you were created in the image of God, a God who loves you and pursues you? And in their folly, I also want to cry out to them: don’t submit to unreality, don’t trade the real for an illusion! Is it so hard to believe that your cynicism is a spiritual poison that first stings, and then numbs, and then kills the life of your soul? Or that when you mock, or when you gossip, you are doing permanent damage to yourself and others, that you are participating in a plot to rid you of your very humanity? I admit, this often can be hard to believe, and quite hard to remember. I would do well, as I write this, to realize how much my warning applies to myself. I’m not sure God loves me. And I poison myself with cynicism, and I mock and I gossip. Further, I’m too proud to really believe this, as I write it–I’m just doing the standard Christian move of deliberately admitting I’m as much of a sinner as anyone. But it is true, nevertheless.
Our decisions, good and bad, affect our relationship with the most basic reality that there is. This is the basic reality that is, to some degree, perceptible to everyone, that is behind the scenes of all of our interactions in this life, that is rarely spoken of directly but is, in the end, what really counts. It is the reality that God cares about, and it is not a secret. But it is, often, hard for us to see; many things in the world work against our seeing it, and on our own we drift away from it. But there is one who always perceives this reality, and who can and will always show it to us, who will cut through the dark fog of evil that blinds us, one who knows what is really important and is eager to share it:
To the Jews who had believed him, Jesus said, “If you hold to my teaching, you are really my disciples. Then you will know the truth, and the truth will set you free.” (John 8.31-32)
I said before that it is wrong to think that Jesus doesn’t care about the things that people intuitively know are significant and real, that he does actually care about these things. I want to make the point stronger now: I think it would be correct to say that Jesus only cares about the things that matter. And if a person decides to try to care about the things that Jesus cares about, he will quickly begin to see more clearly what is really real, what matters to the reality that God always has in mind. If Jesus sees something as unimportant or needless, or worse–like empty religious ritual, or self-righteousness, or selfish accumulation of honor and wealth–then you can bet it is not actually worth anything in the end. If Jesus seems to care about something–like praying for your enemies, or feeding the hungry, or celebrating, or being welcoming to children–you can bet that it matters. So Jesus can show us what life is really about; he is the one we can trust to deliver us what is real.
FAQ’s about my doctorate in mathematics
People often ask me a standard series of questions about “what I do.” I don’t know where these questions came from, but their occurrence, and even their order, is fairly predictable. I have collected them, along with my standard responses, followed by commentary, here. Caution: if you read this, asking these questions to me in a future conversation may be rendered redundant, and thus you may find yourself short on ammunition if we find ourselves in a one on one conversation. This can be awkward.
Question 1: What do you do?
Standard response: I am in graduate school. I’m getting a PhD in mathematics.
Remarks: I have fine tuned this one quite a bit over the years. if I simply say “I am in graduate school” I am immediately met with the obvious question “cool, what are you studying?” If I leave out the PhD part, I often get the question: “are you getting your masters?” to which I reply, “no, PhD.” This usually provokes some sort of awed response, “oh wow, that must be intense.” The person then often follows this with a remark about their lack of ability in math. Or, the person simply assumes I am getting a masters, which creates an awkward moment on question 5 (see below).
Question 2: A. How long do you have left? OR B. When are you going to be finished?
Standard response: I don’t know exactly. I’m hoping less than a year. I could be finished soon, or it could take me a while. It all depends on how tough my problem turns out to be–it could take another month to solve, or several years. There’s no way to tell.
Remarks: I’ll confess, I despise this question. To draw an analogy, this is bit like asking someone, immediately after they tell you their job description, “Oh that’s cool. When are you going to get a promotion?” Would you find that annoying? It makes me feel like being in graduate school is an introduction, a prelude to my real life, which will begin after I get my degree. This is often despairing, because I don’t know when I will have my degree. I don’t want to think about it like this; as far as I’m concerned, what I’m doing now is what I do. I don’t have to keep doing it, though I don’t really have much else going on for me right now. When I graduate, I’ll either do more of the same as a professor somewhere, or I’ll move on to something else. The main difference between being a graduate student and being a professor is, well, about fifty thousand dollars.
Question 3: What are you going to do when you graduate?
Standard response: Well, if I stay in academia, then probably I will teach at a university somewhere, and do research. The balance between the two depends on the appointment itself–some schools are more concerned with teaching, whereas some are more research oriented. But I may do something else entirely.
Remarks: This response is a pretty honest assessment of my situation; it basically contains all the answers I’ve given to this question over the years, which have varied depending on my state of mind in regards to getting my degree. There have been times when I’ve felt like this definitely isn’t my calling in life, and I’ve strongly considered quitting–these moments are all captured by the “I may do something else entirely” response.
Follow up to question 3: You said you might do something else entirely. What would you do instead?
Response I’d like to give: What will I do if I give up on mathematics? I don’t know. Maybe I’ll go to grad school for something else; maybe I’ll become a journalist; maybe I’ll move to Africa; maybe I’ll become a monk. Maybe I’ll just find something that pays the bills, and stay in that the rest of my life. I don’t know who decided that life is something you are supposed to have a plan for…they’ve been drilling that lie into our heads since kindergarten, and I’ve had enough of it.
Response I usually give: Uh…uh….uh.
Question 4: What do you have to do to get a PhD in math? Do you have to come up with a new equation or something?
Standard response: No, actually math isn’t really mainly about equations. It’s more like…[as I try to come up with an analogy, people often interject with their own suggestion, to which I either try to twist around enough to apply it, or frankly explain that it isn't really like whatever they suggested]…looking for patterns or trying to solve a puzzle! Have you heard of prime numbers? Yeah, well suppose you noticed that there seem to be an endless supply of them, and wanted to show this. This is true, but how can one prove it? Mathematicians try to come up with true statements, and then prove them–or disprove them if they turn out to be false. Or we try to show something, and then make the correct statement afterwords.
Remarks: The last remark often provokes a puzzled expression. I suppose they are wondering how you can show something without first knowing what it is you are trying to show. Since I haven’t really done any original mathematics yet myself, I’m not quite sure how this goes yet either. But perhaps it is helpful to think of it like a process of exploration, after which one gives a tidy account what was discovered.
I actually like, however, the answer a student friend of mine gives to this question better: “we just make shit up.”
Question 5: How long have you been doing this?
Standard response: [Varies, depending on when the question was asked.]
Remarks: The answer to this question can be quite shocking if the person has been assuming that I am merely getting a masters degree. Please never ask a PhD student this question.
Question 6: Do you like it?
Standard response: Sometimes I like it, sometimes I hate it. It depends on my mood and prospects, at the moment.
Remarks: This question, like “how are you doing,” is one that is hard to give a sincere answer to. Giving the truth on this is painful…I usually feel like I’m lying when I answer this question.
Question 7: So when do classes start back up?
Standard response: Classes? Start?
Remarks: Although PhD programs in mathematics are, ostensibly, organized around taking classes, and this follows the standard two-semester yearly fall/spring cycle, I usually do not think of things in these terms at all. It’s more about focusing on getting the thesis done.
Question 8: So, like, do you see numbers everywhere?
Standard response: (awkward grin)
Remarks: (none)
Book Review: The Blind Watchmaker (Creation and Evolution, Part 3)
I enjoyed this book more than I thought I would, though I did think the earlier chapters were much more interesting than the later ones. Dawkins is a talented and vivid writer. Like most good science writers, he is especially good at finding analogies that give a clear picture of a complicated idea. He gave me a better understanding of how biologists understand evolution.
Let me begin with a note on the word “evolution” itself. As I noted in my first post, a certain amount of equivocation goes on in regards to this word. Sometimes it is used to describe the process by which living things have changed into other living things, and to the descent of all life from a common ancestor through a gradual and long process. Sometimes it refers to this, but also includes within it the notion that the main guiding force in this process has been natural selection. This latter definition was the one I gave in my first post, though now I’m thinking it would be better to give this the label of “Darwinism.” This is how I will be using the words from now on. I’m not sure if Dawkins himself commits any equivocation linguistically in the book–it usually seems like he uses the word “evolution” in the more general sense. But I think he is guilty of allowing the conflation to shape his own thinking about the matter, viewing the evidence for evolution in the general sense to serve as evidence for Darwinism. This, I think, is a consequence of his materialism. More on this later.
So let us turn to the book itself. The Blind Watchmaker is basically a defense of Darwinism, particularly against any form of creationism. I found the third and fourth chapters of this book, in particular, to be quite interesting. I think they provide the intellectual backbone for the way of thinking about evolution that is characteristic of Dawkins himself, and that shapes the rest of the book. In the third chapter, Dawkins describes a computer simulation that he invented. He views this simulation as a sort of (very) simplified model of evolution, giving the reader a more accessible picture of how it might have taken place. Dawkins describes how he wrote a computer program that would draw a “tree”: on the first “generation” it would draw a single vertical line segment. On the second generation, it would add to the upper tip of this line two new line segments, set at an angle to each other, on the third generation it would add two new segments to each of these, and so on. Thus after a number of generations, a complex tree is drawn. Now, Dawkins built into his program nine “genes”: these were parameters that influenced how the program would draw the tree. The parameters would influence the angle between the line segments, the length of the new line segments, and the number of successive steps branching that will occur when the program was run. For example, giving a positive value to gene number 5 would increase the angle between branches. This is all meant to be analogous to how a biological organism’s genes determine it’s development from the embryo onward.
By changing these parameters, Dawkins is able to create a myriad of complex and varying trees. Dawkins then introduces the notion of a “child” to a particular tree. This is simply another tree with almost the same genes as the “parent” tree. Dawkins wrote another program that would randomly introduce minor changes–”mutations”–to the genes of a particular tree, and then draw the resulting tree. Using this program, Dawkins is able to “evolve” a variety of different trees. He does this by running the program to create various different “children” of a given tree, and then selecting one of those based on his aesthetic preference. He then repeats the process. In doing so, he is able to push the appearance of the tree in a direction of his choosing–he is even able to make, to his own surprise, trees that bear a striking resemblance to insects.
In the fourth chapter, Dawkins argues that the simplified model described in the third chapter is analogous to what goes on in the reproduction of biological life. The main difference is that biological life is a lot more complicated: there are thousands of genes, rather than just nine. Dawkins pictures all of the different possible permutations of these genes as a sort of “genetic space”–each permutation represents a point in this space. And, since genes largely determine the development of the organism, a particular point in genetic space basically represents a particular organism. Now, this space is many dimensional–it has as many dimensions as there are genes, so we can’t really picture it. But the spacial analogy is still quite helpful, from a intuitive standpoint: we can think of organisms that have similar genes as being “close” in genetic space. Genetic space is incomprehensibly vast but, in in each instance of reproduction, a minor move may be made within this genetic space. Dawkins argues that, in order for us to believe that it is plausible for complex biological systems (for example, the eye) to evolve, we must realize that while the two different states in question (an organism with no eye vs. as organism with fully functional eyes) are very far apart in genetic space, it is in principle possible to travel from one state to the other via minor changes in the gene sequence. There is nothing deep to this claim–it is simply a consequence of the fact that an organism’s gene sequence, contained in its DNA, is a concrete and definite string of data (A’s and T’s and C’s and G’s, as my biology teacher used to say) that can and does experience minor modifications (mutations) when the organism reproduces and passes it on to its progeny (this is ignoring, for purposes of simplicity, the additional variation that occurs as a result sexual reproduction). We must, if we are to accept Darwinism, also believe that each required step (for a given path between the two states) could provide a survival advantage to the new organism.
Dawkins goes on to defend the idea that all of this is possible–that such a process of natural selection could introduce the variation and complexity that we see in life today, and that even the origin of biological life itself, while unlikely, could be accounted for by natural selection operating on self-replicating entities that came about by chance in a vast universe. He gives convincing refutations of common objections regarding the fruitfulness of natural selection in producing certain types of complexity. Moreover, to Dawkins, Darwinism is really the only good way to explain the situation we find ourselves in. Hence near the end of the book, he makes this astonishing remark:
The theory of evolution by cumulative natural selection is the only theory that is in principle capable of explaining the existence of organized complexity. Even if the evidence did not favour it, it would still be the best theory available! In fact the evidence does favour it. But that is another story. (p. 317)
Reading this quote in isolation might lead one to believe that Dawkins is forgetting about the idea of a designer. In fact, Dawkins has already dismissed this possibility as superfluous: Dawkins argues that, to posit God as an explanation for the organized complexity of life, one is positing something that is already so complex that it must itself require an explanation more incredible than what we were trying to explain in the first place. Thus one accomplishes nothing in positing a designer. I will quote him in full here:
If we want to postulate a deity capable of engineering all the organized complexity in the world, either instantaneously or by guiding evolution, that deity must already have been vastly complex in the first place. The creationist, whether a naive Bible-thumper or an educated bishop, simply postulates an already existing being of prodigious intelligence intelligence and complexity. If we are going to allow ourselves the luxury of postulating organized complexity without offering an explanation, we might as well make a job of it and simply postulate the existence of life as we know it! (p. 316)
This is an ingenious variation of the “who made God” argument, but I think it is fundamentally flawed, at least as an argument against the existence of God. I think Dawkins is ignoring the fact that there are important metaphysical differences between God and the material world. What are those differences? Essentially, they boil down to the fact that is God is infinite and personal, whereas the material universe is finite and impersonal. Because God is infinite and personal, it doesn’t really make sense to talk about “how complex” he is. Complexity is an idea we can only apply to finite and (in principle) comprehensible systems, things that are by their nature describable. I believe that it simply does not make sense to look at such a God in terms of the categories of complexity that Dawkins has set up in his study of biological life. Anything that could be understood in those categories would not be God. I think that the reason God is conceived of in this way by Dawkins is because his materialism is so strong that he actually imagines God, if he did exist, would be pretty much like how he sees the universe–an “object” of some sort, which we could study.
But God is, rather, a being with a will, consciousness, and creativity–that is what I mean when I say that he is personal. These attributes are fundamental to who he is. They are metaphysically irreducible, so to speak. If we are to say that God is the cause of the design in the universe, we mean that he employed these faculties (and perhaps others) to create it. Life in the universe is ultimately derivative of his activity, as an autonomous agent, somehow. Even Dawkins would probably admit that such a being would be capable of creating life as we know it, by any number of means. But the deeper question of whether such a God exists hinges on much more than the question of how life came into being. It is more of a philosophical question than a scientific one (but to materialists like Dawkins, the only real questions are scientific in nature).
If we are using God simply as an explanation for the origin of life, then I agree with Dawkins that he would be a superfluous hypothesis. Thus Dawkins’ argument actually turns out, at best, to be not so much an argument against the existence of God, but rather an argument against the inference of the existence of God based on the existence of organized complexity. Perhaps he only means it as such. And actually I think Dawkins is right with this, that we shouldn’t “infer” a creator from the design apparent in nature, as the intelligent design theorists often say we should. But neither should we dismiss the involvement of a creator simply because we’ve discovered a mechanism (natural selection) that can create the appearance of design. This, I think, is where Dawkins goes fundamentally wrong in his own thinking: having dismissed the need to posit God as the explanation for every particular appearance of design, he totally dismisses the possibility of God’s involvement in the process of bringing about that appearance. This is an understandable move for an atheist, but I wish he would realize that it is his atheism that is what is driving the conclusion.
In the book Dawkins does make, I think, a strong case for the conclusion that all of life is ultimately related by a common ancestor. The fossil record and the study of genetics seem to indicate this, as Dawkins describes in detail. There may be, within a theistic paradigm at least, another explanation for this data, but I have never heard one that I have found convincing. I remain open to one, but right now I consider the arguments provided by Dawkins in this regard to be quite persuasive. Thus I think that the problem with materialist evolution turns out to be, not it’s view of the history of life, in terms of common ancestry, but rather it’s preoccupation with natural selection as the shaping factor. This does not seem to me to be warranted by the evidence. I stress the fact, however, that I am saying this from within a theist paradigm already. The most plausible view from this position, to me, seems to be one where much of biological life did come into being gradually, but where God was intimately involved in the whole process. Obviously there are a myriad of ways in which this could have happened. Dawkins, in his dismissal of divine involvement, gives very little space or credit to any sort of suggestion. He lumps all such theories together, and portrays each as a sort of lame concession, something that the most sensible theologians have adopted now because the previous consensus, instantaneous creation, has been refuted by the evidence. This is not even historically accurate–even Augustine (who lived more than a thousand years before Darwin), I’ve been told, had a sort of theory of evolution.
But I think that the reason that such a view–a “God guided evolution”–now seems like a lame concession to Dawkins, and to many others, is the affect that our tendencies toward materialism have had on our intuitive understanding of how God interacts with the world. In short, one with a bent towards materialism will inevitably view the activity of God himself as a series of interventions in what is essentially a mechanical universe. Thus God guided evolution can come to seem like a sort of haphazard and convoluted series of miraculous interventions. And I think that this sort of thing is rightly seen as an unnecessary hypothesis, and unworthy of any wise designer.
But this is not how the God described in the bible, the Creator God first worshiped by the Jews, interacts with his creation. The God of the bible is always intimately involved in his creation–he forms it, nurtures it, and sustains it. The bible suggests that life itself cannot go on without the constant activity of God. We cannot reduce the whole of God’s activity in the world to a sort “interference.” As Dawkins himself points out, we don’t even really understand exactly why or how an embryo develops into a fully formed animal. I don’t think it is unreasonable to believe, from a Christian standpoint, that “the Lord, the giver of life” is specially involved in this sort of thing. In the same way, God must have overseen, shaped, and nurtured the development of life on earth, from its beginnings until now, and onward. Thus I think that it should be stressed that theories of divine involvement in the development of life on earth need not reduce to the idea that God committed a series of interventions. Nor, I think, must it then reduce to the idea that God “set things up so that evolution would happen.” No doubt this is true to some extent in any such theory, but I think that this idea, taken to it’s extreme, boarders on Deism and concedes way more to the mechanism of natural selection than is warranted in a theistic paradigm.
Anyway, we should be grateful to Dawkins for his concise summary and defense of materialist evolution–he has show us what is possible from this viewpoint. But we should not, of course, be as quick as he is to dismiss God’s involvement in the history of life on earth. As I come to the close of this post, I’d like to make a note on where I’ll be going with all of this. In my next post on this subject, I would like to begin to consider things from a more biblical perspective. I will begin to consider the question of how we ought to integrate the bible into our understanding of the history of life on earth. The next book I will be reading, in this regard, is Lost World of Genesis One: Ancient Cosmology and the Origins Debate, by John Walton. One other thing I would still like to consider is, in addition to the involvement of God in the history of life, the possible involvement of angels as well–particularly “bad angels” (demons). I think that a consideration of their possible activity might shed light on how God is related to some of the more violent, and thus seemingly evil, aspects of evolution. Though I know of some who have considered this possibility (I think CS Lewis does so in The Problem of Pain; I don’t know if Walton does in his book), I feel like there is much potential here that ought to be explored.
Creation and Evolution, Part 2: materialism and science
In my last post on this subject, I gave definitions for some of the important ideas that I think I will be invoking a lot. This material can be found here.
In this post, I would like to first draw attention to what I consider to be a fundamental error made in popular thinking today in regards to the relationship between science and naturalism or materialism. See the previous post for the distinction between naturalism and materialism. I will mostly be using the word “materialism” for now, because I think the word better brings to mind the idea that is ingrained in the public consciousness. The error has to do with the perceived relationship between materialism and science. It is the the following: materialism is thought to be a conclusion of science, when it is actually a premise. So what do I mean by this? I mean that people today tend to think that materialism is established by science, when actually materialism is just an operating principle of scientific inquiry. People think that science proves that the world is a blind, impersonal, mechanism that goes on of its own accord. But actually this is what science assumes before it does anything else.
In all fairness, this isn’t quite accurate. The above sentence in bold is somewhat oversimplified. I actually don’t want to suggest (as some might) that one must be a materialist to do science, that one must deny the existence of anything besides nature to even begin to try to describe nature using mathematics and the scientific method. I only mean to say that, to do an experiment, and to search for the patterns and laws that explain the behavior of physical reality, one must first assume that the part of reality under consideration at the moment can be so explained. And this requires at least the assumption that the part of reality under examination operates according to fixed laws, that it’s behavior can be predicted in a describable way. And this requires, among other things, that the portion of reality under consideration is not being interfered with by a supernatural agent.
Now, the assumption of science–that patterns in reality can be discerned by observation and experimentation–has proved fruitful. It has lead to many amazing pieces of technology, and has literally transformed our world. One of the basic reasons the science has “caught on,” I believe, is because it works. It is certainly a huge philosophical leap, however, to conclude that, because science works in this fashion, a large scale materialism of the entirety of all that exists, throughout all time, is true. It is a huge leap to believe that, because we can model the patterns that exist within nature with mathematics, all that exists is an impersonal nature, governed by mathematical laws.
Perhaps the reader wonders if it is, indeed, such a leap. I would like to offer an analogy. This analogy will appeal, in particular, to anyone who has studied the area of mathematics known as topology. Suppose you are a tiny creature confined to the surface of a very large sphere–say, a sphere with a radius of about 4,000 miles (I know of one sphere with approximately such a radius…). You have a single tool: a pair of scissors. You begin cutting out pieces of the ground that you are walking on. Every piece that you cut out, no matter how big, appears to be, well, quite flat. Not totally flat–their are some irregularities, but you can smooth them out. You might, therefore, be tempted to conclude that you are stand on a basically flat surface, with some bumps, rather than a sphere. But you would be wrong (One interesting thing about this example, for those who understand the topology, is that this isn’t simply a matter of scale–the sphere really is an intrinsically “different object” than any of the flatten-able pieces that you can cut out of it, even the very large ones). So, to explain the analogy, cutting out a piece of the surface and flattening it is analogous to observing a part of reality and discovering the patterns that are there–this is what we do when we do science. We can apply this “local materialism” to whatever aspects of reality we study. But it is a genuine leap to move to a “global materialism.”
Now, I believe that this error itself forms part of the basis, for the secular world, for a rejection of the supernatural, and thus in particular of Christian revelation. It also plays into an entire mythology about the history of science in relation to religion, in which the ancient and superstitious and supernatural explanations for phenomena offered by the religions of our ancestors have now been overturned by scientific explanations. I will not go into detail about this here; perhaps I will do so in a future post. For now I refer the reader to this excellent article on the subject, from a slightly different angle. For the Christian world, on the other hand, the error forms the basis for an irrational fear of science. It thus causes many to adhere to a confused epistemology, in which the results of secular science are “trusted” in varying degrees, depending in large part on how conservative one is theologically. This, of course, is an irrational standard.
Now, if one gets into the academic side of things, including academic debates about creation and evolution, he will certainly find an awareness of this basic fact that materialism, under the guise of naturalism, functions as a premise in scientific study. Sometimes this is called “methodological naturalism” and is distinguished from “philosophical naturalism.” But I do not think you will find a real awareness of all of the different ramifications of acknowledging this, some of which I will try to get to in in this series. Thus I think the error is not simply “popular level”; I think it still functions strongly in the thinking of scholars and scientists and theologians who participate in this debate. I think that if people would really let an awareness of this error seep into their bones, to really accept and come to appreciate how fundamental it is and how it pervades the different worldviews that many of us subscribe to (and causes confusion within our own worldviews), and the very way we think about what science is doing, and how it progresses, then we might clear up a lot of our confusion.
In particular, I think we need to come to an appreciation of how the materialist assumption, though justified even for a non-materialist in one scientific setting, may not be justified in another setting, even if a scientific one. There may be settings in which the materialist assumption will do us no good, and may even be terribly misleading. This might be the case in the creation vs. evolution debate. I’d like to offer another analogy that I hope illustrates this.
Suppose a crime has taken place, let’s say a robbery. The police are called to investigate a robbery which took place in the middle of the night. Now, let us consider two possible scenarios. In the first, the robbery took place while no one was home, and the crime scene has not been touched since it happened. In this case, the police perhaps have a lot to work with. Anyone who has watched television police shows knows that often quite a lot of what happened during a crime can be deduced from the physical evidence left at the crime scene. The modern use of finger prints and DNA can establish with near certainty that a person was at the crime scene. And even without these means, often the more basic physical evidence left behind can be used to reconstruct a convincing narrative of what probably happened. It’s not hard to imagine how such evidence (signs of forced entry, footprints, mess left by the robbers, etc) could be used to deduce, for example, that the robbers entered through the back door, rummaged through some drawers in the kitchen, moved on the the bedroom, etc. Even if they got some of the details wrong, they’d have a pretty good idea of what happened.
Now let us change the scenario. Suppose the robbers entered in the middle of the night while people were home, but no one woke up. In the morning, upon realizing they had been robbed, the victims called the police. Then, deciding they have little hope of retrieving their possessions, they decide to clean up a bit in preparation for a party that they had been planning on having that night. Suppose further that the police, being especially busy, were unable to come and investigate the crime scene until the next day, after this party had taken place. The party, of course, leaves the house a total mess. What do you think the police will conclude when they arrive? If they have any sense, they will decide that the crime scene is basically worthless now. So many things have happened in between, so many people have been in and out, so many objects have been moved, misplaced, broken, etc. Whatever evidence there was for the original crime has probably been forever lost in a sea of other alterations to the environment.
Now I’d like the reader to consider a third possibility. Suppose the police, in the scenario just described, investigated the crime scene as if it were untouched since the event of the robbery. Never-mind why they would do such a thing, or that to do so they would have to completely ignore the testimony of the victims. What would they conclude? Well, who knows what sort of bizarre scenarios they might concoct in order to describe what happened! Maybe we were dealing with a large and particularly messy group of thieves. Or perhaps the thieves themselves invited their friends over for a party…I leave it to the imagination of the reader to come up with other scenarios. But, depending on the state of scene, some of these scenarios might even seem plausible. This is an important point.
If it’s not clear already, in the analogy just given, the police investigation of the crime scene is analogous to the use of the scientific method to investigate the history of life on this earth. The “crime” is whatever took place before recorded history. The first scenario is analogous to the situation in which materialism is true, and so science is perhaps able to reconstruct a plausible history of life on earth. The second scenario is analogous to what would happen if materialism is false, and the evidence of the past has been influenced by the activity of supernatural agents–the supernatural agents are the people who thew the party, and those who attended the party. When I further imagined that the investigation proceeded as if the crime scene had remained untouched, this is akin to investigating the history of the earth under the materialist hypothesis when, in fact, materialism is false, and that evidence is “tainted” by the activity of supernatural agents. Thus I want the reader to have clear in his head that our initial philosophical assumptions will affect how we read the evidence, and that if these philosophical assumptions prove false, we are in danger of misreading the evidence.
Another point I would like the reader to get clear in his head is that evolution by natural selection is meant, by its strongest proponents, to be a description of the actual history of life on earth, which is a very concrete thing: cells, and plants, and flesh and blood creatures, all living and dying, changing, thriving, and going extinct. This whole gigantic history is what is being proposed and described. It may be admitted that we don’t have the whole picture yet, but it is always claimed by evolutionists that we basically know the sort of thing that happened to bring about life as we now know it–we know the basic outline of the story. When evolution is argued for, however, it is usually done so on the basis of it being a good scientific model the describes the evidence that we have before us. “No other theory” it is said, “can account for the data in the way that evolution does.” I think that this is intrinsically problematic. It is one thing to say a theory accounts for the data better than any other theory–it is quite another to say that that theory is true. This, I think, is especially the case when we are talking about history, unrepeatable history for which there is not, for the most part, any record. We should consider more carefully the relationship between a scientific model and truth. How do we relate one to the other?
Philosophically, this is not an easy question. Furthermore, the answer may be different depending on what kind of “science” we are doing. In the sciences of physics and chemistry, we are dealing mostly with observation of phenomena in the present. We look at events that are concrete and repeatable–the motion of a tennis ball as it glides through the air, the orbit of Venus, the oscillation of a spring. We then try to find a general “law” that describes in general the behavior of a wide class of phenomena at the same time. For example, Newton’s laws of motion can be used to describe, using simple calculus (calculus is simple, trust me!), all of the three above events.
Now, even in the case of basic physics, there arise philosophical issues when we consider the relationship between the phenomena, the world around us we observe, and the model we use to explain them. But, whatever we conclude about these philosophical issues, all will probably agree that there is some deep connection between the model and the reality. I want to argue that the history of life on this earth may not be like this. For one, it happened only once. Also, the vast majority of it has not been observed. So even for the materialist, this makes things quite different. We don’t know beforehand how much of what actually happened can be gleaned from what we see now. Thus I sometimes wonder if the people who talk about evolution, who write books about how it could have happened (such as The Blind Watchmaker, which I’ll be reviewing soon), actually think very much about whether what they are saying is true. Sometimes it seems like they are more concerned with saying “this could have happened this way” than they are with being sure they know what actually happened, or at least with concluding that we don’t know what actually happened. Not thinking about this distinction enough causes them, I believe, to overstep the bounds of what is genuinely known; to present clear speculation as near fact, merely on the grounds that it is the only plausible scientific model.
Ultimately, I think that the religious and the non-religious must come to terms with the fact that they are simply operating under different premises. All too often, people of all sorts, materialist or not, seem to make the leap: evolution by natural selection has been show to be plausible total explanation for the state of life on earth today, therefore evolution by natural selection gives us the true history of life on earth. The materialist can be somewhat forgiven for this–having hit upon the only plausible solution to his problem of how life came to be, he is right to adopt it. But those of us whose worldview allows for more possibilities should not make the inference so immediately, if we should even make it at all. It could, in fact, turn out that the best answer a non-materialist can ever give to the question of the origin of life is, at least in some sense, one of considerable more uncertainty than the materialist one. This should not be taken as a weakness of that position, anymore than it is a weakness of the position of the cop who, having realized that the crime scene was altered, concluded that the true details of the crime were now inaccessible to his investigation. That is, skepticism about the details of the origin of life might be a simple consequence of what we believe about the sorts of things that go on in a universe where beings with free will exist and influence things.
Let me speak now from a non-materialist perspective–in fact, let me speak from a Christian perspective. I am not, by all of this, saying that we will be unable to conclude anything about the origin and history of life, though we may be able to conclude considerably less than we thought we could. Neither will we have to reject wholesale what secular science says about origins–we just have to always keep in mind what their assumptions are, and take their work for what it’s worth, in recognition of that. Thus we should not, as the creationists and intelligent design proponents are prone to, fight evolution, try to show that it is false or heavily problematic. But neither should we accept it practically wholesale and then try to reconcile it with our own scripture and theology, as some of the theistic evolutionists do. Rather, we should recognize it for what it is: the theory of origins that comes about when one assumes materialism throughout all space and time. Only when we see it clearly as that can we begin, from the standpoint of Christian truth, to put it in its proper context, to glean what we can from it, assimilate it and put it within our own paradigm, making whatever adjustments are necessary. This, of course, will not be easy, and I am not claiming to have the answers as to what we will ultimately conclude. I’m only arguing that we need to begin in the right way. And I believe that some are already making such progress, and I hope in the future books that I read on this project to learn about it.
The HAC Basketball Diaries, Volume 1
My old high school JV basketball coach just showed up on facebook. Boy does that bring back memories! For those of you that didn’t know me in high school, you might be thinking to yourself: Phil played basketball? Yes, indeed, I did play basketball. Despite being 5 ft 4, and despite being, at the time, somewhat “hefty,” I indeed played on the junior varsity basketball team.
How is this possible, you might ask? Simple: my tiny private school required that you play a sport. There were also no cuts in any of the sports whatsoever, so I was guaranteed to make the team. As a result of this policy, the JV team (which actually combined players from two different school, Harley and Allendale Columbia) had, I think, close to 25 players. This was a pretty ridiculous spectacle, especially at away games. They would always have to bring out extra chairs for us. We played in the absolute worst division, division “double D” or something like that. We’d have to drive hours to get to some of our games–those teams were usually in some small town where the local high school sports were actually a big deal. All of the teams we played absolutely hated us: we were the “rich kids” (never mind that I wasn’t rich) from the private school out of town, and we certainly didn’t take things seriously enough. We were an undignified squadron, with our bloated 25 man roster and our bad attitudes. Our team didn’t even have cheerleaders; at home games, the other team would bring their cheerleaders to our court, along with half of the town, so it was basically like a home game for them.
I should mention something which should come as no surprise at this point: we were absolutely terrible at basketball. We had some talented players, but we were basically hopeless…no one expected us to ever win. We’d go into games and literally get blown out by 50 points. Sometimes our score was in the single digits well into the second half. This, by the way, generated considerable playing time for myself. Though I was, by nature, a career bench warmer, often the game was effectively over before the second half even started. The second and third tier players would get their time in the third quarter, and sometimes I’d get to play for nearly the entire fourth quarter.
My career statistics included 0 points, several rebounds, 1 assist (I remember this one because I threw the ball to a guy who was wide open, and got complimented by his father for it afterwords), several fouls, and 1 delay of game warning. Near the end of my “career,” I took on a sort of mascot status, and it became a great hope among both the JV and varsity players that I would score before my time was up. To this end, whenever I found myself in a game (which was becoming a less and less frequent occurrence), there would be a huge push to get me the ball. Whenever I had the ball, I would be expected to shoot. The varsity coach was not pleased with this whole ordeal. In what might have been my last game, I took one particularly ill-advised heave from near half court, which, if I remember correctly, glanced off the side of the backboard. In the locker room afterwords, I remember him confronting me: “Do you think you’re funny, Phil Williams?” I suppose he thought my stunts were making a mockery of the game–this was true, I admit. In my defense, however, I’d like to point out that my very presence on the team had been making a mockery of the game for the last two years, and no one had really complained about it until quite recently.
I remember that there were only a couple of teams in the league that we actually felt we had a shot of beating. One was this tiny Christian school–their team only had five players, and so they played the same five players entire game. In spite of this, we managed to lose to them. There was another game where the team we were playing seemed to be missing just as many shots as us. I think the game was basically tied going into half-time. At that point it began to dawn on me that we were matched up with a team that was nearly as bad as ourselves. Our coach, coach Stevens, then had a simple half-time message for us: “They suck. They suck! We can beat them.” This was true–nevertheless, we lost that game as well. Coach Stevens certainly did have some great locker room speeches in some of those games. After one particularly pathetic performance, he opened with the lines, “Lackadaisical is one way to describe that effort. Piss poor is another.”
The closest we ever came to a win in any of the games that I was actually present at was a home game. I’m not sure what the team that we were playing was…it might have been that school that only played five players. Anyway, we managed to play a close game the whole way through, and found ourselves up by 2 points, with almost no time left. The other team had the ball. We were due for a win, provided we simply let them inbound the ball, and nothing miraculous happened. That’s basically what happened–the ball was passed in, and time quickly expired without them managing to score. I remember the feeling of shock and excitement that came over me–we actually won a game! I didn’t think this was possible. The whole team rushed off the bench, and we were yelling and cheering at mid-court.
It was then that the news was broken to us: the game isn’t over. What? Why not? There was a foul, before the inbounds pass. The refs called a foul on our best player, a late call regarding something that supposedly took place before the ball was even on the court. I certainly didn’t see a foul; the guy they called it on (whom, by the way, I’ve just been texting about this game), has always insisted that there was no foul. Nevertheless, the refs called it. This gave the other team two free throws, which they (to their credit) managed to make, sending the game into overtime. We lost in overtime.
In my two years of basketball, the team went 0 and 20 the first year, and 2 and 18 the second year. And I managed to miss the only two games that we actually won! Looking back on it, perhaps I was something of a curse on that team; or, more charitably, perhaps I was simply the embodied image of our hopelessness. In spite of this sad status, I have many fond memories of my basketball years.