People are always surprised to find out I'm a religious man, partly because I don't behave in the way that they expect "religious people" to behave, but mostly because I'm an extremely rigorous scientist. It's the latter that I want to discuss here.
Occam's Razor Is Almost Always Wrong
You've probably heard a variation of the dictum of the Earl of Ockham, something like "The simplest explanation that fits the facts is probably the case." The simplest explanation of how we get energy from food is that chemical bonds in food are broken in a linear sequence of steps and the energy of these bonds is absorbed by the body. In a first biochemistry course, you discover the simple chain of events has a circle in it called the Krebs Cycle, which is certainly not the most direct route. The next course will tell you "what you learned before is close to the truth, but here's what really happens." In fact, every biochemistry course adds more complications to accommodate more facts. And that's the point I want o make: because you never have all the facts, whatever explanation you have is a useful simplification, but it is not real; it is an analogy.
Particles, Waves and a Probabilistic Cat
I am always stunned that some aspects of quantum theory are taught in high schools and that people then speak of the dual nature of electrons as particles and waves or of Schrödinger's cat, as if they understand them. I took several courses in quantum chemistry and statistical mechanics in college and didn't really understand it until several years later. Generally, people get a take-away message - usually incorrect - and, though what they've ben taught makes no sense, feel "people who understand these things and are a lot smarter than me say it's so, so it's true." This is making science into a thing of faith, a religion.
For the record, an electron is not both a particle and a wave, nor is it a particle that moves in a wave, nor a particle with wave-like characteristics. An electron is neither a particle nor a wave; in fact, we don't know what it is, but we have observations of how it behaves in various circumstances. Some of these behaviors we can describe with math developed to describe particles, others require math developed to describe waves, even though these exclude each other and particles are never waves. We have analogies that help us understand electrons, but the analogies contradict each other. It's like the story of the blind men and the elephant [one feels a leg and says it's a tree, another the tail and says it's a rope, another a tusk and says it's a spear]
The most important feature of quantum mechanics for my purposes here is Heisenberg's uncertainty principle. We know the world through our senses, which require bouncing a particle or a wave off a thing to see it. This action to sense it changes the object's energy, so it is no longer exactly the thing you were trying to sense. On the atomic level, you can know where an electron is, or where it's going, but not both. No matter what you do, there is something you cannot know.
Why the world has things that cannot be known leads from physical chemistry to more abstract math.
It Doesn't Add Up
Physics does not describe the world, except through analogy. When the analogy breaks down, different math gets employed. Zeno's paradox that motion is impossible because, for an arrow to reach its target, it must first go half the distance, but before that happens it must o 1/4th the way, and so on in an infinite number of steps, was "solved" by the invention of calculus by Newton and Leibnitz. The paradox still exists, we just have math that can accept an infinite number of steps now.
Similarly, Euclidean geometry works great for describing the arc of a tossed ball, so that's what we use. It doesn't work, however, in the relativistic world described by Einstein, so Riemann's geometry, where parallel lines intersect and infinitely long lines circle back on themselves, is used.
Attempts to combine quantum mechanics and gravity have led to the use of string theory, which is so flexible that it can describe almost anything. Its drawbacks are math so complicated that few can follow it (I can't) and the necessity of ten perhaps even 26) spatial dimensions.
There is, however, a problem with numbers themselves, which you may have sensed as early as you were told that you can't divide by zero. Kurt Gödel proved, mathematically, that any system complicated enough to include the set of integers is internally inconsistent and contradicts itself.
As long as you try to use math and physics to describe the world, you are automatically wrong.
The logical next step is recursive
Let's say you abandon math and try to explain the world logically. Even if you use Bertrand Russell's symbolic logic, there is always that nagging something which cannot be known. The simplest version of this is this version of the Liar's Paradox: "This sentence is false." Logically, if you say that it's true, it's false and if you say it's false, it's true. The important point is: it has no truth value until you assign it one, just as Schrödinger's cat is neither dead nor alive, but has only probabilities of being alive or dead until you look at it. Your interaction with it changes it, just as bouncing particles or waves off objects does.
Metaphysics, free will and other unprovable things that don't matter
1) What if you were only a brain in a vat and everything you think you experience were merely electrical signals being fed into that brain? The world would be exactly the same. Because we experience the world through our senses, which require bouncing particles or waves off of things to be converted into electrical neural pulses, it is exactly the same. Our brains are encased in a skull where there is no light, yet we believe the electrical signals from our optic nerves are sight - it is a matter of faith and of choice. You could choose to believe you are only a brain in a vat, but it is a difficult and unrewarding choice (I've tried it).
2) What if the universe were created 5 minutes ago? Imagine everything came into being at the same time, with all of its characteristics, including you with all of your (imagined) memories. The world would be exactly the same. There is no way to prove that this is not the case and you could choose to believe the world is only 5 minutes old, but again, it's an unfruitful choice. Though I choose to believe the universe was created some 15 billion years ago (or is it 13.5?), it is a matter of faith as much as for fundamentalist Christians who believe Bishop Usher's date of 4004 BC.
3) What if you didn't have free will, but everything you did were predetermined and fated to happen? Again, nothing would change. At first, it would seem that choosing to believe in determinism removes one from responsibility for one's actions, so that any "immoral" act is permissible (I'm not going to get into ethics, though I could - for me it ends in existentialism, situational ethics and moral relativism), but you have to behave the same way whatever you believe. The randomness inherent in quantum mechanics seems at first to decide in the favor of free will, but deeper investigation returns one to a matter of choice that makes no difference.
Faith in science
Why should it be that there are things we cannot know, inherent contradictions in our math and logic and fundamental philosophical questions that cannot be decided? The standard response is: we do not know now, but science will explain it in the future. This is a statement of faith in science as a religion, which I find abhorrent.
The question of God
The final undecidable problem of philosophy is the existence of God and I say that, like the other questions, it does not matter what you choose to believe. It is impossible to either disprove the existence of God or prove the existence of God (a friend of mine, a pastor, was incensed when I picked out a flaw in every "proof" of God's existence collected in "Does God Exist?" by Hans Küng, saying "I think he knows more about this than you do." That there is necessarily a flaw is in fact what allows me to have faith).
If you choose to believe in God, you can believe in God's creating the universe in such a way that His existence cannot be proven, but must be a matter of faith. All the other un-fillable holes in knowledge I've described then become analogous, making for a harmonious whole that I find comforting.
Religion, whichever flavor you choose, is all about metaphor and analogy. Just as physics is not truth, but a useful analogy to the truth, religions are filled with stories whose truth (or falsehood) is immaterial, except in the usefulness to one's own existence. Christianity speaks to me through its influence through art, in the literature, paintings and music of my culture. Do I believe in the Lutheran "Book of Concord's" statement that each part of the Holy Trinity is distinct, yet each contains the entirety of the others? Rarely about as often as I entertain the idea that the world was created 5 minutes ago.
Then again, it does not matter. I believe what I choose to believe because that choice exists.
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