Religious freedom

June 30, 2015

One of the reasons I’m returning to blogging is the Supreme Court’s recent decision to legalize gay marriage across the nation.

The most common objection raised by religious conservatives (other than that the Supreme Court had no jurisdiction over this issue) is that gay marriage represents a blow to the religious freedom of conservative Christians.

This claim is obviously not true when it comes to positive expressions of religious freedom, namely the activities that Christians choose to perform. Gay marriage does not prevent Christians from worshiping, conducting bible studies, getting married, and so on.

Rather, the complaint lies with negative expressions of religious freedom, such as refusing to perform certain actions. For example, some Christian business owners feel that it is an expression of religious freedom to refuse service to gay customers. A much cited example involves a gay couple asking a Christian-run bakery to make them a wedding cake. Should the owners of the bakery be allowed to refuse such a request?

The same issue arises in the case of businesses required to provide birth control to their employees. If the business owners have religious objections to birth control, should they still be required to provide it?

Slippery slope arguments are not always particularly powerful, but there seems to be a case for one here. If we were all allowed to refuse certain services to people based on our personal distaste for these services, what would society look like? I suspect it would be a very difficult place to do business. Not only would it be more difficult to find business that provided a particular service, but there would be widespread discrimination.

Indeed, if service could be refused based on the religious convictions of the business owner, surely other sorts of objections should also be allowed? Shouldn’t white supremacists be allowed to refuse service to blacks? Shouldn’t Democrats be allowed to refuse service to Republicans, and vice versa? Where would this sort of thing stop?

I think the only way to avoid this quagmire is to set a very simple rule: if you are going to offer a service, offer it to whoever requests it. Otherwise, don’t offer the service at all.

This is, in fact, what some conservative Christians are doing. There is a county in Alabama (if memory serves) that has stopped issuing marriage licences, be they for heterosexual or homosexual couples. This makes a sort of sense – at least it is not discriminatory. Unfortunately, the problem is that local government is supposed to provide services like the issuing of marriage licences, so if it ceases providing these services, it’s not doing its job. But this would certainly be a reasonable solution for private businesses.

Unfortunately it is not a viable solution in the case of birth control and other examples of services the government requires private businesses to provide. In these cases, the business is not free to make its own decisions, but must follow the law. The US government has come up with a solution: provide the services to the business’s employees directly, so that the business owners are relieved of that responsibility. This seems pretty fair to me.

To sum up, I think a greater distinction needs to be made between positive expressions of religious freedom (e.g., worship) and negative expressions of religious freedom (e.g., refusal to provide a service). I don’t think the latter deserves the same degree of protection as the former.

Back on the Horse

June 27, 2015

Hi Readers!

After a prolonged absence, I’m considering a return to blogging.

The last few weeks have been very rough for me: I am going through a divorce.

Luckily, it is about as amicable as can be expected, and my soon-to-be-exwife and I have worked through most of the details without lawyers.

Given that I have moved to a new place, and have a little more freedom than before, it occurred to me that a return to blogging would be fun. So, here I am.

Watch this space.

The wishes of the dying

December 27, 2013

Hello reader!

My first semester as a high school teacher is just about over, and I find myself with a little space to think about ethics again. The question currently on my mind concerns the wishes of the dead. Specifically, why fulfill the wishes of those who have died, given that they are no longer present, and therefore unaware of what’s happening?

In short, can a consequentialist ethical system, such as my own consensual utilitarianism, defend the fulfillment of dead people’s wishes?

I think it can. First, I hold that the fulfillment of a dead person’s wishes can only influence those who are still alive. There is no compelling evidence for the afterlife. On the contrary, the biological evidence suggests that when people die, they don’t go anywhere, they simply die.

Therefore, in order for the granting of a dead person’s wishes to be morally compelling, these wishes must stand to benefit those who are still alive. This is often the case. Indeed, one of the most common forms in which people make requests concerning their death is through a legal will, which specifies how a person’s estate is to be distributed among family and friends. It is obvious that this distribution of goods is likely to benefit the recipients, making it morally compelling to carry it out.

(Exceptions may, of course, occur. If the consequences of a person’s will cause more harm than good, then the case for carrying it out is greatly diminished.)

But there is an argument for granting a dead person’s wishes even when there are no material goods to be given. This occurs any time a dying person deliberately formulates her requests to benefit others. For instance, someone might ask that his busy wife take a few days off work each year to visit one of their favorite vacation spots. Or someone might ask that his good friend occasionally visit the coffee shop they spent so much time in, in order to remember and celebrate their friendship. In any of these cases, consensual utilitarianism (and indeed, any consequentialist ethical system), would recommend that the dying person’s wishes be carried out.

But what about situations in which the wishes do not bring any benefit to the living? Should they still be respected? And if so, why? For instance, what if a dying person asks that his plot of undeveloped land not be sold or used, even though the relatives who will become owners of the land live far away and will essentially never see it?

It is very difficult to make a case that such a wish should be respected. There is one possible defense, though, and this is similar to the general defense against behaviors like lying. While it may occasionally be morally permissible to lie, lying in general should be avoided because it breaks down the foundation of trust upon which all other moral decision making is built. In a similar fashion, there is a systemic argument in favor of obeying dead people’s wishes. If such wishes were routinely denied, people would not be quite as happy, especially near death, because they would not trust their family and friends to do as they asked. In this case, the argument involves the happiness of the people who die, rather than those who live on.

This argument is not a particularly strong one, though. If a person’s final wishes really do involve harm, or merely prevent good from being done, then it may be more morally compelling to disobey these wishes for the sake of concrete good that will come from doing so, rather than obeying them out of a more abstract concern for the well-being of future wish-makers.

The big lesson from all of this, I think, is that we should not make selfish wishes. If, instead, we formulate our wishes to benefit the living, then we are giving a lasting gift, namely the opportunity to increase the well being of our family and friends after we are gone.

If, however, we formulate wishes that have a selfish purpose (to ensure that no one forgets us, perhaps, or to ensure that something we owned is not given away), then we are not leaving the world in a better state after our death, and it is hard to argue that such wishes should be respected.

The end of the line

June 25, 2013

It’s been some time since I last posted, so you’ve probably realized that either I’m busy or have lost interest.

It’s actually a bit of both.

First, I’m in the rather stressful process of moving house, and of bringing my planetary science job to a close as I go about changing careers.

But more important, I’ve lost interest in arguing against religion. The roots of religious doctrine lie in the ancient, ignorant past, when almost everyone was superstitious by today’s standards, and almost no one understood the importance of accounting for the cognitive biases that affect us all.

This is not to say that religion fails to do good things in today’s society. Religion does a lot of good. But its supernatural claims are so obviously the result of pre-scientific ignorance. So obviously, indeed, that I no longer feel compelled to point it out.

Furthermore, despite the tone of the preceding paragraphs, I’m no longer comfortable making an ongoing project of tearing down other people’s beliefs. If people want to believe ridiculous things, they’re welcome to do so, and I have better things to do than point such ridiculousness out to them, at least in a regular forum such as this one.

And so it seems that Coming of Age is coming to an end.

I’m considering starting a completely new blog on philosophy and ethics, but I have to take serious stock of the time I have for it, and whether I have anything substantial to say.

In the meantime, this blog will stay online even though it will become largely inactive. I encourage you to delve into the various essays I’ve written over the years, if you haven’t already done so.

Thanks so much for reading.

How vanishing points work (Part 3)

May 31, 2013

In the second part of this series, we discovered that any set of parallel lines has a single vanishing point.

Let’s see what happens when there are two non-parallel lines in our field of view. Imagine standing at the corner of a field where two boundary fences meet:


It’s already pretty clear that these two fences, which sit at right angles to each other, are going to have different vanishing points, so I’ve marked them in as red and green “x”s. As always, we can locate the vanishing points using the rule laid out in the first post. We simply have to draw lines through the center of the eye that lie parallel to each fence. Here’s the bird’s eye view for the first fence:


I’ve left out the individual light rays from each fence post, to reduce clutter. But I have followed the required rule: I’ve drawn a ray from the center of the eye that lies parallel to the first fence. The vanishing point is marked with a red “x”.

If I do the same for the second fence, I get:


Bringing the two diagrams together, we have:


And indeed, there are two vanishing points, one for each fence. Note that the red vanishing point lies to the left of the center of gaze, while the green vanishing point lies to the right of the center of gaze, just as we observe in the first figure in this post.

We can now add a new rule:

Each distinct set of parallel lines has its own vanishing point.

In my experience with drawing things like buildings, I’ve used exactly two vanishing points. This makes sense because building’s floor plans are traditionally made up of a bunch of rectangles stuck together, and a bunch of rectangles are composed of only two sets of parallel lines. Each set has its own vanishing point.

Consider the following pair of drawings as examples. The drawing on the left is an outline of a building’s floor plan, and the sketch on the right is a 3-D rendering of that plan using two vanishing points:


A real 3-D building also has vertical lines, not just horizontal ones. So technically this third set of parallel lines (all the uprights in the right-hand sketch above) should have their own vanishing point, making the sketch look something like this:


The reason we don’t see such extreme perspective in real-life is that the vanishing points are usually much farther apart on our field of view. In the above sketch, they’re pretty close together, yielding a sort of fish-eye lens look.

Things get even more complicated when we have rectangles that are at different angles to each other. Each rectangle now needs its own pair of vanishing points (ignoring the uprights for now). So, the following two simple rectangular buildings require a total of four vanishing points:


I’ve labeled each vanishing point according to the block it belongs to. If we wanted to, we could add the extra vanishing point needed for the uprights, but I think the point has been made – it can get complicated!

And that wraps up this series. I hope to have more science-related posts published soon, but summer time is kicking in and the outdoors are beckoning!

How vanishing points work (Part 2)

May 30, 2013

In the first part of this series, we came up with a rule for finding the location on the retina that corresponds to the vanishing point of a straight line in our field of view.

What if we have more than one straight line – will we need more than one vanishing point?

It depends!

Let’s consider two special cases. First, we’ll look at two parallel lines in our field of view. Imagine being back on our country road, and this time there is a fence on each side of the road:


The eye’s view of two parallel fences, as one might see on either side of a road. Should they both have the same vanishing point?

If we consider a single horizontal wire from each fence, we will have two lines that, in the real world, are parallel. The question is, do they have the same vanishing point? Well, let’s follow our rule on how to get the vanishing point from a line. We’ll apply it first to fence 1, then to fence 2.

First, fence 1:


In the above figure, I’ve drawn a line through the center of the eye that is parallel to fence 1. It hits the edge of the eye at the red “x”. But this is exactly where the vanishing point was for the fence we looked at in the first post. In fact, if we put the light ray drawings for the two fences together, we get:


The two fences have the same vanishing point. This gives us a second rule for vanishing points:

Any set of parallel lines has a single vanishing point.

(You might have noticed that I implicitly assumed this rule to be true when I showed the very first picture of the fence along the country road. The three horizontal wires in the fence, which are all parallel to one another, were assumed to have the same vanishing point. I didn’t have to make this assumption. I could have drawn the fence with only a single wire, and the result would have been the same. It just wouldn’t have looked much like a real fence!)

Here’s where I’d like to mention the direction that the eye is looking in. Notice, in the above figure, that the person is looking a little to the right of center (thick grey arrow). This means that the vanishing point of the two fences lies a little to the left of the center of her gaze. Looking back to the first image in this post, you’ll see that this is indeed the case. The vanishing point of the two fences is to the left of the figure’s center.

If the person were to move her eyes so that she was gazing in a different direction, the only thing we would have to change in the light ray diagram is the position of the thick gray arrow. For example, let’s say she looks sharply to the left. The light ray diagram now looks like this:


The only thing that’s changed is the direction of the thick grey arrow. But this now means that the vanishing point lies to the right of the center of gaze. To the viewer, then, the scene now looks something like this:


Now the vanishing point is to the right of the viewer’s field of view. It’s quite remarkable how much the scene changes due to the simple act of looking in a different direction. But I guess that’s really the point of looking in a different direction in the first place – to change the scene!

In the next post I’ll look at what happens when we have two perpendicular lines in our field of view.

How vanishing points work (Part 1)

May 29, 2013

This is another sciency post, following on from my discussion of parallel sun rays.

If you’ve ever attempted realistic perspective drawings, you’ve undoubtedly come across the issue of vanishing points – the point toward which a set of parallel lines appears to converge. How many vanishing points should there be? And why do they even exist in the first place? Read on for some answers!

The first thing I’d like to demonstrate is that what we see as an apparent convergence of parallel lines is an artifact of the (almost) spherical shape of our eyeballs.

To start, let’s imagine we’re standing by the side of a country road looking at a fence receding into the distance, represented by this idealized sketch:


The eye’s view of a fence receding into the distance. The red “x” on the left indicates the vanishing point.

I’ve labeled the fence posts so that we can see how they map onto the eye’s retina. I’ve also indicated the vanishing point with a red “x”. This is the point at which the three horizontal wires in the fence appear to converge.

Let’s consider a bird’s eye view of both the fence and the eyeball of the person looking at it. I’m going to draw the eyeball REALLY big so that we can see what the light rays are doing inside it. I’m also going to leave out the details like the lens, the cornea, and all the other bits and pieces of the optical system. All I’m going to show is a simple sphere that focuses light through a point at the sphere’s center, like this:


View from above. Light rays from the fence posts enter a simplified (and over-sized) eye and strike the retina at the back. The eye is looking in the direction indicated by the thick grey arrow.

The first thing to note in this picture is the set of fence posts from the first figure, as seen from above. A light ray (black line) leads from each fence post to a large circle representing the eye. Each light ray passes through the center of the circle and strikes the back of the eye – the retina, where I’ve repeated its original label.

The other thing I’ve included in this figure is the direction the eye is looking in. This is indicated by the thick grey arrow. For the most part, this direction won’t be important, but I’m including it for completeness (and it will come in handy a little later).

Notice that when moving from fence post A to G, the position of the post’s images on the retina get closer and closer together. This is why the fence posts appear to get closer and closer together in the perspective view (first figure), even though they are equally spaced in the real world.

There’s something annoying about the above figure, though: the image on the retina is backwards, which makes it a little harder to interpret. We don’t have this difficulty in real vision because our brain makes the necessary transformation to a normal, unreversed image. What I’m going to do, then, is make things simpler by looking at where the light rays strike the front of the eyeball, since this will give us an image that’s the right way around, and it will make the figures a little simpler, without affecting the basic physics.

So, here is the simplified version of the above figure:


As before, the positions of the fence posts on the eye get closer and closer together as the fence posts get farther and farther away.

What happens if we add more fence posts even farther away? Will the images of these fence posts converge to a single point on the eyeball? Yes, indeed, they will. Consider the following picture, where I’ve added just one extra fence post that’s a lot farther away than the original set:


Notice how the light ray from fence post H is almost parallel to the fence itself. And indeed, if we were to place yet another fence post an infinite distance away, the light ray from that post would, in fact, be parallel to the fence. Which means that the vanishing point for the fence is located directly up from the center of the eye, as indicated by a red “x” in the following picture:


This gives us a nifty rule for finding the vanishing point for any straight line in our field of view:

To find the vanishing point of any straight line, draw a second line that:

1. starts from the center of the eye and

2. is parallel to the first line. 

The vanishing point is where this new line crosses the retina.

Note how the vanishing point is drawn on the eye. This is because the vanishing point is an artifact of the eye’s optics. There is no vanishing point in the real world.

In the second part of this series, I’ll look at what happens when we have more than one line in our field of view. How many vanishing points will we need?