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Do you really think that the best way to encourage critical thinking when you're older, is to avoid doing it when you're younger?

Just to be crystal clear, the series of posts explaining why I think Science and my religion are compatible don't exist yet. What I linked to is a series of posts explaining what I think Science is. I wanted to pin that down first before asking what is, or is not, compatible with it. Besides, how Science works is interesting in its own right.

Although I do believe in an afterlife, I do not believe that the mechanism for this is that the soul is immaterial. My "soul" is a pattern of information in my neurons, which is eventually going to be downloaded to new hardware.

It's true I was raised Christian, but I went through a period of doubt and reflection around the time I was in the 6th grade. I decided then that there was enough evidence specifically for the Resurrection of Jesus to believe in it. It's not a question of whether there are good explanations for religion in general, it's that this partiular sequence of events seems to me highly implausible from a naturalistic perspective.

You could say that my upbringing makes me biased, although that's a catch-22 because there's no course of conduct which can change how I was raised.

I don't think it's just because I was raised Christian---my best friend from college, who was Jewish, very reluctantly agreed with me that the evidence is good, and converted despite the risk that he would be disowned by his father. All I can say is that I decided the evidence was good enough, even taking into account any biases of my own that I can detect. Like always, you just do the best you can.

I understand the pull of the idea that there's a discord (though obviously not a strict logical contradiction) between laws of nature that work so well almost all the time, and exceptional events like miracles. But partly as a result of my experience in physics, I don't think this is as much of a problem as it appears at first glance. But I'm going to be talking about this very thing later on my blog though, so I won't discuss it here and now.

The lack of any valid arguments that they are incompatible?

But if you want a much more detailed answer, I'm going to be discussing just this question in the next few weeks on my blog. The posts which already exist are trying to define exactly what Science is, in order to lay the groundwork for this.

On the contrary, I want to take seriously all the reasonable arguments on both sides. The fact that I have an opinion about where the evidence as a whole leads does not prima facie make me impossible to argue with. Do you think it's pointless to argue with anyone who has a strong opinion about anything? Or do you think religion is a special case?

As for why I think Christianity is better than other religions, it's mainly because I believe that the Christian miracle claims are supported by better historical evidence than the miracle claims of other religions. Obviously in order to demonstrate this one would have to get into the nitty-gritty historical data, which I don't want to do here. But surely you can at least imagine a hypothetical set of historical data for which I'd be right. I think you have to actually think about each religion on a case-by-case basis, and not assume in advance they are all the same.

Why not just compartmentalize Science and Religion? Because I actually believe them both, as facts about the real world, so of course they can't live in totally watertight compartments. There may be situations in which I'm thinking more about one than the other, but that doesn't change the fact that there's only one world and that everything has to fit consistently together. What would you do if someone asked you: Why not just compartmentalize physics and economics? I'm having a hard time making sense of this question.

In other words, I agree with rationalism in its claim that we ought to apply Reason responsibly to everything, even Religon. I just disagree about what follows when you do that...

Taking logs of a dimensionful quantity is possible, if you know what you're doing. (In math, we make up our own rules: no one is allowed to tell us what we can and cannot do. Whether or not it's useful is another question.) Here's the real scoop:

In physics, we only really and truly care about dimensionless quantities. These are the quantities which do not change when we change the system of units, i.e. they are "invariant". Anything which is not invariant is a purely arbitrary human convention, which doesn't really tell me anything about the world. For example, if I want to know if I fit through a door, I'm only interested in the ratio between my height and the height of the door. I don't really care about how the door compares to some standard meter somewhere, except as an intermediate step in some calculation.

Nevertheless, for practical purposes it is convenient to also consider quantities which transform in a particularly simple way under a change of units systems. Borrowing some terminology from general relativity, we can say that a quantity X is "covariant" if it transforms like X --> (unit1 / unit2 )^p X when we change from unit1 to unit2. Here p is a real number which indicates the dimension of the unit. These things aren't invariant under a change of units, so we don't care about them in a fundamental way. But they're extremely useful nevertheless, because you can construct invariant quantities out of covariant ones by multiplying or dividing them in such a way that the units cancel out. (In the concrete example above, this allows us to measure the door and me separately, and wait until later to combine the results.)

Once you're willing to accept numbers which depend on arbitrary human convention, nothing prevents you from taking logs or sines or whatever of these quantities (in the naive way, by just punching the number sans units into your calculator). What you end up with is a number which depends in a particularly complicated way on your system of units. Conceptually, that's not really any worse. But remember, we only care if we can find a way to construct invariant quantities out of them. Practically speaking, our exprience as physicists is that quantities like this are rarely useful.

But there may be exceptions. And logs aren't really that bad, since as Kindly points out, you can still extract invariant quantities by adding them together. As a working physicist I've done calculations where it was useful to think about logs of dimensionful quantities (keywords: "entanglement entropy", "conformal field theory"). Sines are a lot worse since they aren't even monotonic functions: I can't imagine any application where taking the sine of a dimensionful quantity would be useful.