Monday, October 28, 2013

Thermodynamics and Theories of Atonement

I don't know if it has always been this way, but I suspect it has. Many people want a simple idea that will explain everything, even when the idea that really explains everything doesn't exist, yet.

People are really good at seeing patterns. We evolved that way, and it serves us well. We look for patterns to explain the world that is happening around us. I mean, it is more than just nice to know where our next meal is coming from, or what people and places are safe. What seems to me one very natural result of all this pattern seeking is the desire to find one pattern that will explain everything. It's not only physicists who want a Theory Of Everything (TOE)--a single theory that unifies all of physics from the quantum mechanical to the cosmic. Theologians have sought for theories of everything for at least several centuries. I'm neither a historian nor philosopher (beyond the aspiration to be a Knower Of Everything--sometimes referred to by less flattering names), but Aristotle's First Great Cause appealed to my triple great grandfather, Orson Pratt, as a reasonable view of God and everything, and I'm pretty sure, even from my piecemeal philosophical education, that he was not the first to attempt such an all-encompassing formulation of existence. The maybe 10 people who have followed all my musings over the last couple of years already know that I'm on my own quest to make such a formulation for myself. Right now, though, I want to explain why I don't think we should be bothered by attempts at TOEs that don't quite make it. To this end I have two stories, one about the laws of thermodynamics (an area where I am somewhat expert), and the other about theories of atonement. If you were looking for an essay that explains Atonement using Thermodynamics, I'm sorry to disappoint you.

The Power of Thermodynamics

Some days you have moments that remind you you really have learned something in all your years of study. My Biochemistry students do a lot of teaching themselves. I don't leave them alone without guidance, but I help them work exercises through which they build their own understanding of Biochemistry. This often means working through simple models that don't capture every nuance of reality. When my students noticed one of these simplifications (without being aware that was what they had done) and asked about it, I began to explain that what they had learned was a good first approximation. "A good what?!" I wanted to say, don't you understand English? Parse the words. Approximation = not real but trying to be. First = there is something coming after. Good = reality is functionally approximated in many instances. I was much more politic in my response. This was a good student, and I appreciate his frank feedback, hard work, and honesty about what he knows and is learning. Since then the phrase has become a favorite joke with him, and he uses it whenever he can--fortunately, correctly.

The laws of thermodynamics are not first approximations, and I would feel comfortable saying that they go beyond good. But it turns out that the laws of thermodynamics are really hard to apply rigorously to real situations. We can measure temperature changes and other energy changes really well for everyday things, and even for some very big things and some microscopic things. But when you get down to measuring energy of individual molecules, it gets really tricky. You see, temperature is an average. The cool breeze blowing by your face on a lovely summer evening is really a huge number of molecules running into, and past, you at a whole lot of different speeds. Some barely bump into you. Many hit you at the average wind speed. Some hit you moving a whole lot faster. We can measure the energy of the wind, but what is the energy in one air molecule in that wind? Measuring that becomes a problem long before you get to quantum mechanical considerations and the Heisenberg uncertainty principle. These exact laws of thermodynamics that tell us exactly how energy moves around among things in the observable universe turn out to be very difficult to understand when you examine small numbers of molecules--say fewer than 100.

Now that I've set that up, what do Biochemists do? Below is a picture of regulation of the lac Operon. The details don't really matter, but I'll explain a bit of what is going on. There is a piece of DNA (a gene) that codes for proteins (X, Y, and Z) that help bacteria digest lactose (the sugar in milk). Making these proteins takes energy, so the bacterium regulates it in a rather complex fashion.
Click on the image for higher resolution and source information

Now for the relevant part of the picture. How many DNA molecules are shown? How many of each of the other kinds of molecules are shown? Do any of them exceed the 100 molecule lower limit? Of course, the answer is no. This makes a lot of sense. Reactions don't actually take place between 100 lac Operon genes and 100 RNA polymerase molecules. They take place one molecule at a time. One DNA strand reacts with one RNA polymerase molecule. It happens an astounding number of times per second (billions and trillions are small numbers when we are talking about numbers of chemical reactions going on over a period of time), but each reaction is just one or two or three molecules interacting in a particular time and place.

So how do we relate macroscopic, exact, thermodynamic numbers to microscopic, highly random events? There are many different kinds of answers to this, but I will give two fairly general ones: 1. really well when we can measure the average of large numbers of reactions. 2. lots of different, approximate ways when we are looking at things on a molecular scale. We fail to apply the laws of thermodynamics precisely to lots of real situations we are interested in, so we have developed a whole bunch of different ways to approximate reality. Currently, if a computer program wants to calculate exactly what is going on in a chemical reaction, right down to the last detail, it must limit the system to tens, or at most thousands, of atoms. A single protein can have thousands of atoms, and that is without calculating any of the water molecules around it. So programs leave out most or all of the water and treat it as a flat background instead of like the individual molecules it really is. But there are even more molecules that need to be considered. What about things like salts, sugars, amino acids, and other small molecules that are floating around in the cell but aren't directly involved in reacting with the protein? What about neighboring proteins, or DNA, or membranes that bump into the protein we are interested in? Most computer programs for calculating what goes on in cells make lots of approximations. There is no way around it. The only practical way to avoid lots of approximations is to just measure the real cell, but if that's what we're going to do, why try to calculate it at all? We want to understand and simplify things so that we can make predictions and develop technologies on human timescales. We don't want to test every chemical in the world, plus all the chemicals we can synthesize, for usefulness as a high blood-pressure drug. We want to just figure out a few of the best candidates. So we make approximations. Pretty much any approximation you find in the scientific literature works for a number of real cases. Somebody found the approximation useful. In that sense, the approximation is good and true. It reflects a significant part of the reality of some biochemical process.

Does it bother anybody that lots of these approximations only work for special cases, and not necessarily very well for very many of those? If I'm anybody, then yes. In fact, many fields have a small number of practitioners that spend inordinate amounts of time worrying about just such problems. If you mean does it bother many people by percentage of the earth's population? No. It doesn't even bother most practicing Biochemists. You see, they've found that they can do their work--often really well--without even being aware of these problems. Ask most Biochemists, and they won't even know what you are talking about if you bring up thermodynamics of small systems. If you ask about statistical mechanics, they will probably have heard of it, but either never had to take a course in it, or may have actively avoided studying it. If you talk to most Physical Chemists who are doing computations of biological processes, they will be able to identify many of the approximations they are making, but will likely be only vaguely aware of some relevant biochemical complexities. Lots of their computations are informative despite this limitation. Maybe it will surprise you, but laws of nature seem to work just fine even if we don't understand them.

Theories of Atonement

I've already admitted to not being a theologian. In fact, I'm taking most of my theology from a podcast on Mormon Matters and a brief perusal of links to articles on the accompanying blog post. Over the centuries, various explanations have been put forth of how the Atonement works and why the sacrifice of Christ was necessary. Many of them appear in Mormonism in the metaphors and stories we use to help each other understand and benefit from the Atonement. Some of these ideas include explanations like:

When we sin we give Satan power over us, and Christ had to buy us back. There are cosmic demands of justice that not even God can ignore, so Christ had to suffer and die for us. Jesus's example was so great and powerful that people before and since have been made whole through its influence on their lives. Jesus's sacrifice gave him complete empathy for all of our pains and sins because he suffered them all.

I haven't fleshed out a single one of these theories anywhere near enough to give you a full sense of their strengths, or their weaknesses. I decided not to after reading some of the wonderful explanations and syntheses found in links on the Mormon Matters blog--you really ought to read some if you are at all interested. The articles are wonderful, and often moving. What I will say is that most of the authors, even with their preferred theories, don't claim to have written the final word on the Atonement. None of them have a Theory of Everything for the Atonement. None of them claim to have synthesized all of the revelations about the Atonement into one coherent model. Some of the theories do better than others, and I like some theories better than others. But what does this philosophical mess mean? Does it mean that none of the theories are right? Does it mean that the Atonement isn't a real thing, or that Jesus wasn't divine, or that His suffering and death weren't really necessary for the Atonement?

Let me take you back to Thermodynamics. If I'm being honest, every one of the several theories of Atonement has worked for somebody. Even the ones I think are morally bankrupt. Each one approximates some aspect of the Atonement correctly. Does it bother me that some of these theories only work to explain some special cases of repentance or salvation? That some don't explain how certain evils are overcome, or why Jesus had to suffer for me? Yes. But lots of people experience the power of the Atonement, anyway. In fact, some of them truly are Saints, living lives of goodness beyond what most of us manage. They do really good work without understanding the best theories of Atonement, and maybe without even knowing the theories exist. Some people spend a lot of time looking for that theory of everything. I'm inclined to admire them. I want to know it all. But somehow, the Atonement works just fine, even if I don't understand it.

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