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Posts tagged as “Jesus and Godel”

What is Lent?

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Twenty-Twenty, man! A year that sucked, followed by a year that sounds like "Twenty-Twenty Won" (and don't get me started on the third act of the trilogy, "Twenty-Twenty Too" ... not even the Sharknado team could have come up with the plots of the Twenty-Twenty franchise).

As we're recovering from last year - recovering from January of THIS year - the normal rhythms of life have been quietly reasserting themselves. Elections are followed by inaugurations. Winter weather will soon be followed by spring plantings. And Ash Wednesday will soon be followed by Easter.

"Two thousand twenty-one" in our calendar marks two millennia, give or take, since the birth of Jesus, the founder of Christianity, the world's largest religion. Today, "Ash Wednesday" in the Christian calendar marks the beginning of Lent, the solemn observance of Jesus's Crucifixion.

You can follow the links to find out what Lent and Ash Wednesday and Christianity and the Crucifixion mean to other people. But what I want to tell you about what they mean to me. Lent has always been a time for me to reconnect with my own faith, and each year I do that a slightly different way.

Lent celebrates Jesus's Resurrection, when He turned death into new life - and turned failure as a regional preacher into success at creating a world-spanning church. Prior to His death, Jesus went into the wilderness and was tempted for 40 days, which Christians emulate by giving things up for Lent.

Well, the pandemic has knocked a loop for most of the things that I normally give up for Lent: giving up meat (I'm mostly eating vegan), giving up alcohol (I try to avoid drinking at home), giving up soda (long story). While I've been blessed to not be starving this pandemic, it's still been a time of deprivation.

That got me thinking. I once heard someone suggest, "Give up Something Bad for Lent!" (as opposed to the normal giving up something good). Well, what about flipping it on its head entirely? What about, rather than giving up something bad for Lent, why not take on something good for Lent?

Normally I try not to talk about what I've given up for Lent - on the principle Jesus puts forth in Matthew 6:5 that praying for show is its own reward - that is, no reward at all. But again, flipping it on its head entirely, if I've taken on something good for Lent, why not take on something to share with everyone?

So, like my Drawing Every Day series, for the next forty days, I'm going to blog about what Lent means to me. And the key meaning of Lent, for me, is reconnection - dare I say, Resurrection? Christianity is supposed to be a "catholic" religion - catholic, meaning "universal," a religion for everyone.

The universality of Christianity means that it's for everyone. Everyone has free will. Everyone can screw up. Everyone can feel a loss of connection to God. And Jesus's role was to light the way - taking on our screwups in His death, and washing them away in His Resurrection.

SO, in the coming weeks, I hope to show you what I'm trying to connect back to every Lent. For some of you, this will be bread and butter; for others, this will be alien. Regardless, I hope I'm going to be able to leave you with an understanding of why every year I walk the path of Lent towards the Resurrection.

-the Centaur

What is Christianity?

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rough sketch of jesus

tl;dr: Christianity is following Jesus.

I know, I know, that seems obvious: His name is on the tin. Jesus Christ - Christianity, right? But it's surprising to me sometimes how non-obvious that is, or how often people who claim to be Christians don't seem to be putting that first.

I grew up in the South. I've seen fundamentalists claim to be Bible-worshipping Christians; what about Jesus-following Christians? I've seen Baptists challenge each other about following doctrine - what about following Jesus? I've seen Catholics rant about following Church dogma - how about following Jesus?

Now, a fundamentalist might tell you that you need to turn to the Bible to know Jesus, and I've had Baptists tell me there's only one true interpretation of the Bible which determines the correct doctrines, which sounds very Catholic in its curation of official doctrines collated as dogma.

But in the violent arguments that sometimes follow, the participants rarely seem to come back to the name Jesus. They'll argue that you must read your Bible, or that belief in evolution makes you an atheist, or that breaking from church teachings cuts you off from grace and makes you an apostate.

Where is Jesus in all that? He's not.

Even in church board meetings, when we're worrying about our tight budgets, supporting our ministries, and our fellowships with other churches, I frequently find that the discussion rarely comes back to Jesus. Even though drawing people to Christ is in our mission statement, we get bogged down with details.

When it's my turn to speak, I bring up Jesus's name in a way that's relevant, and let the Spirit guide me through the rest. Think of it as a high-powered version of What Would Jesus Do, but instead leading to questions like, "If this budget exists to draw people to Jesus, how would He want us to use it?"

Which leads to the question, what does following Jesus mean?

That's a big question, but first off, Jesus says "Be not afraid!" Actually, he says that quite a bit, more than a dozen times in the New Testament. He also says, "Repent!" over a dozen times - meaning, change your mind to change the way you live, breaking your commitment to the things you're doing wrong.

Change is scary, because we're often surprisingly committed to the things that we're doing that are wrong. We find it hard to give them up, which is one reason why Lent is important - it asks us to give things up temporarily, to help us build up the muscles we need to quit things forever.

So following Jesus involves fearless repentance. But what is wrong, and how should we turn to the right, and how do we manage the scary thought that the things we're doing may be things we should abandon? Well, to me, the reason Christianity is named after Jesus is that He's the answer to all three questions.

Jesus Christ isn't the typical "first name - last name" combination familiar to modern Western audiences. The "Jesus" part is His actual name, but in that's actually a twice-removed transliteration to English through Greek of the original Hebrew "Yeshua", which roughly means "God saves".

The "Christ" part is a title - which is why sometimes you hear of the man referred to as "Jesus, son of Joseph from Nazareth" as "Christ Jesus". Christ originally meant "the anointed one", but in Christian theology it came to mean the "messiah", or Savior.

So Jesus Christ means God saves, twice over. But what does that mean? Jesus saves who from what?

Well, He saves us from the consequences of our bad choices. In Christian theology, our sins merit punishment, but Jesus's death on the cross was a sacrifice which blots all that out - so there's no need to be trapped in sin for fear that you won't be forgiven: repentance comes at no cost, thanks to Jesus.

That manages the fear, but what are we doing wrong? Jesus said the two greatest commandments are loving the one God and loving your neighbor as yourself. In practice, I think this means putting nothing above doing the right thing, and making sure we treat others as we wish to be treated.

Jesus says all religious laws are ultimately derived from these foundations. This gets tricky in practice, because there are many rules written down in the Bible and put forth by churches and passed into law by the hands of man, and its hard to follow them all. In fact, sometimes they don't even seem to be just.

That's where Jesus comes in again. Over and over in the New Testament, people ask questions of Jesus about how different rules and laws conflict. Again and again, He responds not by picking one rule over the other, but by asking the question of what principles are at stake, and what outcome is good?

That's how Jesus outwitted the challengers who asked whether it was legal to heal someone on the Sabbath: "Which is lawful on the Sabbath, to do good or to do evil, to save life or destroy it?" Again and again, Jesus asks basic questions like these, using an almost scientific mindset applied to ethics.

In fairness to my Christian brethren, I got to this understanding by reading the Bible to find out who Jesus was, by debating doctrine with my Baptist friends, by learning Catholic dogma, and by ultimately coming to my own conclusions in the Episcopal tradition, combining scripture, tradition and reason together.

But I think these principles are universal. Whether you're a Christian or not, you can look honestly at what you're doing, decide whether it's right or wrong, and put aside the wrong in favor of the right. You shouldn't be afraid to do so, because choosing to do the right thing is its own reward.

There always is a better way, and you're always free to choose it.

To me, that's following Jesus, and is the bedrock principle of Christianity. Of course, there's more: Christians believe in Jesus as a divine member of the Trinity, one God in three Persons. But I don't think the principles of Christianity are true because Jesus said them; I think He said them because they're true.

-the Centaur

Jesus and Gödel

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kurt godel

Yesterday I claimed that Christianity was following Jesus - looking at him as a role model for thinking, judging, and doing, stepping away from rules and towards principles, choosing good outcomes over bad ones and treating others like we wanted to be treated, and ultimately emulating what Jesus would do.

But it's an entirely fair question to ask, why do we need a role model to follow? Why not have a set of rules that guide our behavior, or develop good principles to live by? Well, it turns out it's impossible - not hard, but literally mathematically impossible - to have perfect rules, and principles do not guide actions. So a role model is the best tool we have to help us build the cognitive skill of doing the right thing.

Let's back up a bit. I want to talk about what rules are, and how they differ from principles and models.

In the jargon of my field, artificial intelligence, rules are if-then statements: if this, then do that. They map a range of propositions to a domain of outcomes, which might be actions, new propositions, or edits to our thoughts. There's a lot of evidence that the lower levels of operation of our minds is rule-like.

Principles, in contrast, are descriptions of situations. They don't prescribe what to do; they evaluate what has been done. The venerable artificial intelligence technique of generate-and-test - throw stuff on the wall to see what sticks - depends on "principles" to evaluate whether the outcomes are good.

Models are neither if-then rules nor principles. Models predict the evolution of a situation. Every time you play a computer game, a model predicts how the world will react to your actions. Every time you think to yourself, "I know what my friend would say in response to this", you're using a model.

Rules, of a sort, may underly our thinking, and some of our most important moral precepts are encoded in rules, like the Ten Commandments. But rules are fundamentally limited. No matter how attached you are to any given set of rules, eventually, those rules can fail you, and you can't know when.

The iron laws behind these fatal flaws are Gödel's incompleteness theorems. Back in the 1930's, Kurt Gödel showed any set of rules sophisticated enough to handle basic math would either fail to find things that were true, or would make mistakes - and, worse, could never prove that they were consistent.

Like so many seemingly abstract mathematical concepts, this has practical real-world implications. If you're dealing with anything at all complicated, and try to solve your problems with a set of rules, either those rules will fail to find the right answers, or will give the wrong answers, and you can't tell which.

That's why principles are better than rules: they make no pretensions of being a complete set of if-then rules that can handle all of arithmetic and their own job besides. They evaluate propositions, rather than generating them, they're not vulnerable to the incompleteness result in the same way.

How does this affect the moral teachings of religion? Well, think of it this way: God gave us the Ten Commandments (and much more) in the Old Testament, but these if-then rules needed to be elaborated and refined into a complete system. This was a cottage industry by the time Jesus came on the scene.

Breaking with the rule-based tradition, Jesus gave us principles, such as "love thy neighbor as thyself" and "forgive as you wish to be forgiven" which can be used to evaluate our actions. Sometimes, some thought is required to apply them, as in the case of "Is it lawful to do good or evil on the Sabbath?"

This is where principles fail: they don't generate actions, they merely evaluate them. Some other process needs to generate those actions. It could be a formal set of rules, but then we're back at square Gödel. It could be a random number generator, but an infinite set of monkeys will take forever to cross the street.

This is why Jesus's function as a role model - and the stories about Him in the Bible - are so important to Christianity. Humans generate mental models of other humans all the time. Once you've seen enough examples of someone's behavior, you can predict what they will do, and act and react accordingly.

The stories the Bible tells about Jesus facing moral questions, ethical challenges, physical suffering, and even temptation help us build a model of what Jesus would do. A good model of Jesus is more powerful than any rule and more useful than any principle: it is generative, easy to follow, and always applicable.

Even if you're not a Christian, this model of ethics can help you. No set of rules can be complete and consistent, or even fully checkable: rules lawyering is a dead end. Ethical growth requires moving beyond easy rules to broader principles which can be used to evaluate the outcomes of your choices.

But principles are not a guide to action. That's where role models come in: in a kind of imitation-based learning, they can help guide us by example until we've developed the cognitive skills to make good decisions automatically. Finding role models that you trust can help you grow, and not just morally.

Good role models can help you decide what to do in any situation. Not every question is relevant to the situations Jesus faced in ancient Galilee! For example, when faced with a conundrum, I sometimes ask three questions: "What would Jesus do? What would Richard Feynman do? What would Ayn Rand do?"

These role models seem far apart - Ayn Rand, in particular, tried to put herself on the opposite pole from Jesus. But each brings unique mental thought processes to the table - "Is this doing good or evil?" "You are the easiest person for yourself to fool" and "You cannot fake reality in any way whatsoever."

Jesus helps me focus on what choices are right. Feynman helps me challenge my assumptions and provides methods to test them. Rand is benevolent, but demands that we be honest about reality. If two or three of these role models agree on a course of action, it's probably a good choice.

Jesus was a real person in a distant part of history. We can only reach an understanding of who Jesus is and what He would do by reading the primary source materials about him - the Bible - and by analyses that help put these stories in context, like religious teachings, church tradition, and the use of reason.

But that can help us ask what Jesus would do. Learning the rules are important, and graduating beyond them to understand principles is even more important. But at the end of the day, we want to do the right thing, by following the lead of the man who asks, "Love thy neighbor as thyself."

-the Centaur

Pictured: Kurt Gödel, of course.

Free Will and the Halting Problem

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turing headshot

Lent is when Christians choose to give things up or to take things on to reflect upon the death of Jesus. For Lent, I took on this self-referential series about Lent, arguing Christianity is following Jesus, and that following role models are better than following rules because all sets of rules are ultimately incompete.

But how can we choose to follow Jesus? To many Christians, the answer is simple: "free will." At one Passion play (where I played Jesus, thanks to my long hair), the author put it this way: "You are always choose, because no-one can take your will away. You know that, don't you?"

Christians are highly attached to the idea of free will. However, I know a fair number of atheists and agnostics who seem attached to the idea of free will being a myth. I always find this bit of pseudoscence a bit surprising coming from scientifically minded folk, so it's worth asking the question.

Do we have free will, or not?

Well, it depends on what kind of free will we're talking about. Philosopher Daniel Dennett argues at book length that there are many definitions of "free will", only some varieties of which are worth having. I'm not going to use Dennett's breakdown of free will; I'll use mine, based on discussions with people who care.

The first kind of "free will" is undetermined will: the idea that "I", as consciousness or spirit, can make things happen, outside the control of physical law. Well, fine, if you want to believe that: the science of quantum mechanics allows that, since all observable events have unresolvable randomness.

But the science of quantum mechanics also suggests we could never prove that idea scientifically. To see why, look at entanglement: particles that are observed here are connected to particles over there. Say, if momentum is conserved, and two particles fly apart, if one goes left, the other must go right.

But each observed event is random. You can't predict one from the other; you can only extract it from the record by observing both particles and comparing the results. So if your soul is directing your body's choices, we could only tell by recording all the particles of your body and soul and comparing them.

Good luck with that.

The second kind of "free will" is instantaneous will: the idea that "I", at any instant of time, could have chosen to do something differently. It's unlikely we have this kind of free will. First, according to Einstein, simultaneity has no meaning for physically separated events - like the two hemispheres of your brain.

But, more importantly, the idea of an instant is just that - an idea. Humans are extended over time and space; the brain is fourteen hundred cubic centimeters of goo, making decisions over timescales ranging from a millisecond (a neuron fires) to a second and a half (something novel enters consciousness.)

But, even if you accept that we are physically and temporally extended beings, you may still cling to - or reject - an idea of free will: sovereign will, the idea that our decisions, while happening in our brains and bodies, are nevertheless our own. The evidence is fairly good that we have this kind of free will.

Our brains are physically isolated by our skulls and the blood-brain barrier. While we have reflexes, human decision making happens in the neocortex, which is largely decoupled from direct external responses. Even techniques like persuasion and hypnosis at best have weak, indirect effects.

But breaking our decision-making process down this way sometimes drives people away. It makes religious people cling to the hope of undetermined will; it makes scientific people erroneously think that we don't have free will at all, because our actions are not "ours", but are made by physical processes.

But arguing that "because my decisions are made by physical processes, therefore my decisions are not actually mine" requires the delicate dance of identifying yourself with those processes before the comma, then rejecting them afterwards. Either those decision making processes are part of you, or they are not.

If they're not, please go join the religious folks over in the circle marked "undetermined will."

If they are, then arguing that your decisions are not yours because they're made by ... um, the decision making part of you ... is a muddle of contradictions: a mix of equivocation (changing the meaning of terms) and a category error (mistaking your decision making as something separate from yourself).

But people committed to the non-existence of free will sometimes double down, claiming that even if we accept those decision making processes as part of us, our decisions are somehow not "ours" or not "free" because the outcome of our decision making process is still determined by physical laws.

To someone working on Markov decision processes - decision machines - this seems barely coherent.

The foundation of this idea is sometimes called Laplace's demon - the idea that a creature with perfect knowledge of all physical laws and particles and forces would be able to predict the entire history of the universe - and your decisions, so therefore, they're not your decisions, just the outcome of laws.

Too bad this is impossible. Not practically impossible - literally, mathematically impossible.

To see why, we need to understand the Halting Problem - the seemingly simple question of whether we can build a program to tell if any given computer program will halt given any particular input. As basic as this question sounds, Alan Turing proved in the 1930's that this is mathematically impossible.

The reason is simple: if you could build an analysis program which could solve this problem, you could feed itself to itself - wrapped in a loop that went forever if the original analysis program halts, and halts if it ran forever. No matter what answer it produces, it leads to a contradiction. The program won't work.

This idea seems abstract, but its implications are deep. It applies to not just computer programs, but to a broad class of physical systems in a broad class of universes. And it has corollaries, the most important being: you cannot predict what any arbitrary given algorithm will do without letting the algorithm do it.

If you could, you could use it to predict whether a program would halt, and therefore, you could solve the Halting Problem. That's why Laplace's Demon, as nice a thought experiment as it is, is slain by Turing's Machine. To predict what you would actually do, part of the demon would have to be identical to you.

Nothing else in the universe - nothing else in a broad class of universes - can predict your decisions. Your decisions are made in your own head, not anyone else's, and even though they may be determined by physical processes, the physical processes that determine them are you. Only you can do you.

So, you have sovereign will. Use it wisely.

-the Centaur

Pictured: Alan Turing, of course.

Sunday is a Day of Rest

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sunday is a day of rest

So I had originally planned on doing a full post each day of Lent, but to make things easier on myself, I decided it was better to respect the Sabbath and treat Sunday as a day of rest.

The Sabbath is a distinctive religious observance as it is about us as much as it is about God.

While we need the grace we get from, say, the Eucharist, the purpose of going to Mass is to worship. But Sunday isn't just about setting aside a day of rest to contemplate God: it's about setting aside a day of rest for ourselves - at least one day out of the week that we can recharge. It's great if we can focus that on God, and that's why the Hebrews had such strict rules about what you could do on Sunday, rules that continue today in the Jewish community and in our former Blue Laws.

But God knows that we need rest and recuperation. The job of living never stops, and it's good for us to take out at least one day to recharge - if we don't make time for it, we can work ourselves to death. As Jesus said, "The Sabbath was made for man, not man for the Sabbath."

One of the ways I respect Sunday is to avoid shopping unless it's a necessity. Another is to attend Mass (in the before times) or to watch online worship (in these days of the zombie apocalypse). But I'm not altogether good about respecting it, either religiously or personally. And rather than working to 4am again, I instead decided, let's respect the Sabbath, and just share a link of what I'm reading.

Gifts of God for the People of God is a devotional book about the Episcopal Mass by Reverend Furman Buchanan, the priest of St. Peter's, my East Coast church (and where I and my wife were married).

In this book, Buchanan breaks down the parts of the Holy Eucharist and shares explanations of their structure, theological function, and deeper meaning. It's a personal book, in which Buchanan shares experiences from his own life; but it's also good for study groups, with each chapter ending in a series of questions and challenges. My West Coast church, Saint Stephen's in-the-Field, has used it successfully in a Lenten study course, which inspired me to finish this book (which I had already started) for Lent.

I recommend this book. The Holy Eucharist is deeply meaningful to me and I was gratified when I left Catholicism to find a surrogate communion which understands this form of worship as well, if not better.

The former priest of Saint Stephen's, Reverend Ken Wratten, once claimed "Jesus says we can take our Sabbath whenever we want to," pointing out even though he celebrated Holy Eucharist on Sundays, it and Saturday were working days for him, so he took Monday as his actual Sabbath. I wouldn't go quite as far as "whenever we want to" (though there's a lot of evidence backing up Father Ken's claim, including the decision in Acts of the Apostles of the Jerusalem Council that Gentiles don't have to follow the law of Moses) but I would encourage you to take a day of rest in your week whenever you can.

-the Centaur

P.S. Forgive my horrible color scheme on the graphic, I wanted to whip something up quickly in Illustrator and it started fighting me, so I didn't get to do the pass I'd normally do of trying out a variety of schemes in color-scheme-picking-programs to compensate for my color blindness.

The Soul is the Form of the Body

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aquinas headshot

If you've ever gone to a funeral, watched a televangelist, or been buttonholed by a street preacher, you've probably heard Christianity is all about saving one's immortal soul - by believing in Jesus, accepting the Bible's true teaching on a social taboo, or going to the preacher's church of choice.

(Only the first of these actually works, by the way).

But what the heck is a soul? Most religious people seem convinced that we've got one, some ineffable spiritual thing that isn't destroyed when you die but lives on in the afterlife.  Many scientifically minded people have trouble believing in spirits and want to wash their hands of this whole soul idea.

Strangely enough, modern Christian theology doesn't rely too much on the idea of the soul. God exists, of course, and Jesus died for our sins, sending the Holy Spirit to aid us; as for what to do with that information, theology focuses less on what we are and more on what we should believe and do.

If you really dig into it, Christian theology gets almost existential, focusing on us as living beings, present here on the Earth, making decisions and taking consequences. Surprisingly, when we die, our souls don't go to heaven: instead, you're just dead, waiting for the Resurrection and the Final Judgement.

(About that, be not afraid: Jesus, Prince of Peace, is the Judge at the Final Judgment).

This model of Christianity doesn't exclude the idea of the soul, but it isn't really needed: When we die, our decision making stops, defining our relationship to God, which is why it's important to get it right in this life; when it's time for the Resurrection, God has the knowledge and budget to put us back together.

That's right: according to the standard interpretation of the Bible as recorded in the Nicene creed, we're waiting in joyful hope for a bodily resurrection, not souls transported to a purely spiritual Heaven. So if there's no need for a soul in this picture, is there any room for it? What is the idea of the soul good for?

Well, quite a lot, as it turns out.

The theology I'm describing should be familiar to many Episcopals, but it's more properly Catholic, and more specifically, "Thomistic", teachings based on the writings of Saint Thomas Aquinas, a thirteenth-century friar who was recognized - both now and then - as one of the greatest Christian philosophers.

Aquinas was a brilliant man who attempted to reconcile Aristotle's philosophy with Church doctrine. The synthesis he produced was penetratingly brilliant, surprisingly deep, and, at least in part, is documented in books which are packed in boxes in my garage. So, at best, I'm going to riff on Thomas here.

Ultimately, that's for the best. Aquinas's writings predate the scientific revolution, using a scholastic style of argument which by its nature cannot be conclusive, and built on a foundation of topics about the world and human will which have been superseded by scientific findings on physics and psychology.

But the early date of Aquinas's writings affects his theology as well. For example (riffing as best I can without the reference book I want), Aquinas was convinced that the rational human soul necessarily had to be immaterial because it could represent abstract ideas, which are not physical objects.

But now we're good at representing abstract ideas in physical objects. In fact, the history of the past century and a half of mathematics, logic, computation and AI can be viewed as abstracting human thought processes and making them reliable enough to implement in physical machines.

Look, guys - I am not, for one minute, going to get cocky about how much we've actually cracked of the human intellect, much less the soul. Some areas, like cognitive skills acquisition, we've done quite well at; others, like consciousness, are yielding to insights; others, like emotion, are dauntingly intractable.

But it's no longer a logical necessity to posit an intangible basis for the soul, even if practically it turns out to be true. But digging even deeper into Aquinas's notion of a rational soul helps us understand what it is - and why the decisions we make in this life are so important, and even the importance of grace.

The idea of a "form" in Thomistic philosophy doesn't mean shape: riffing again, it means function. The form of a hammer is not its head and handle, but that it can hammer. This is very similar to the modern notion of functionalism in artificial intelligence - the idea that minds are defined by their computations.

Aquinas believed human beings were distinguished from animals by their rational souls, which were a combination of intellect and will. "Intellect" in this context might be described in artificial intelligence terms as supporting a generative knowledge level: the ability to represent essentially arbitrary concepts.

Will, in contrast, is selecting an ideal model of yourself and attempting to guide your actions to follow it. This is a more sophisticated form of decision making than typically used in artificial intelligence; one might describe it as a reinforcement learning agent guided by a self-generated normative model.

What this means, in practice, is that the idea of believing in Jesus and choosing to follow Him isn't simply a good idea: it corresponds directly to the basic functions of the rational soul - intellect, forming an idea of Jesus as a (divinely) good role model, and attempting to follow in His footsteps in our choice of actions.

But the idea of the rational soul being the form of the body isn't just its instantaneous function at one point in time. God exists out of time - and all our thoughts and choices throughout our lives are visible to Him. Our souls are the sum of all of these - making the soul the form of the body over our entire lives.

This means the history of our choices live in God's memory, whether it's helping someone across the street, failing to forgive an irritating relative, going to confession, or taking communion. Even sacraments like baptism that supposedly "leave an indelible spiritual character on the soul" fit in this model.

This model puts the following Jesus, trying to do good and avoid evil, and partaking in sacraments in perspective. God knows what we sincerely believe in our hearts, whether we live up to it or not, and is willing to cut us slack through the mechanisms of worship and grace that add to our permanent record.

Whether souls have a spiritual nature or not - whether they come from the Guf, are joined to our bodies in life, and hang out in Hades after death awaiting reunion at the Resurrection, or whether they simply don't - their character is affected by what we believe, what we do, and how we worship here and now.

And that's why it's important to follow Jesus on this Earth, no matter what happens in the afterlife.

-the Centaur

A Bayesian Account of Miracles

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bayes headshot

Christianity is a tall ask for many skeptically-minded people, especially if you come from the South, where a lot of folks express Christianity in terms of having a close personal relationship with a person claimed to be invisible, intangible and yet omnipresent, despite having been dead for 2000 years.

On the other hand, I grew up with a fair number of Christians who seem to have no skeptical bones at all, even at the slightest and most explainable of miracles, like my relative who went on a pilgrimage to the Virgin Mary apparitions at Conyers and came back "with their silver rosary having turned to gold."

Or, perhaps - not to be a Doubting Thomas - it was always of a yellowish hue.

Being a Christian isn't just a belief, it's a commitment. Being a Christian is hard, and we're not supposed to throw up stumbling blocks for other believers. So, when I encounter stories like these, which don't sound credible to me and which I don't need to support my faith, I often find myself biting my tongue.

But despite these stories not sounding credible, I do nevertheless admit that they're technically possible. In the words of one comedian, "The Virgin Mary has got the budget for it," and in a world where every observed particle event contains irreducible randomness, God has left Himself the room He needs.

But there's a long tradition in skeptical thought to discount rare events like alleged miracles, rooted in  Enlightenment philosopher David Hume's essay "Of Miracles". I almost wrote "scientific thought", but this idea is not at all scientific - it's actually an injection of one of philosophy's worst sins into science.

Philosophy! Who needs it? Well, as Ayn Rand once said: everyone. Philosophy asks the basic questions What is there? (ontology), How do we know it? (epistemology), and What should we do? (ethics). The best philosophy illuminates possibilities for thought and persuasively argues for action.

But philosophy, carving its way through the space of possible ideas, must necessarily operate through arguments, principally verbal arguments which can never conclusively convince. To get traction, we must move beyond argument to repeatable reasoning - mathematics - backed up by real-world evidence.

And that's precisely what was happening right as Hume was working on his essay "Of Miracles" in the 1740's: the laws of probability and chance were being worked out by Hume's contemporaries, some of whom he corresponded with, but he couldn't wait - or couldn't be bothered to learn - their real findings.

I'm not trying to be rude to Hume here, but making a specific point: Hume wrote about evidence, and people claim his arguments are based in rationality - but Hume's arguments are only qualitative, and the quantitative mathematics of probability being developed don't support his idea.

But they can reproduce his idea, and the ideas of the credible believer, in a much sounder framework.

In all fairness, it's best not to be too harsh with Hume, who wrote "Of Miracles" almost twenty years before Reverend Thomas Bayes' "An Essay toward solving a Problem in the Doctrine of Chances," the work which gave us Bayes' Theorem, which became the foundation of modern probability theory.

If the ground is wet, how likely is it that it rained? Intuitively, this depends on how likely it is that the rain would wet the ground, and how likely it is to rain in the first place, discounted by the chance the ground would be wet on its own, say from a sprinkler system.

In Greenville, South Carolina, it rains a lot, wetting the ground, which stays wet because it's humid, and sprinklers don't run all the time, so a wet lawn is a good sign of rain. Ask that question in Death Valley, with rare rain, dry air - and you're watering a lawn? Seriously? - and that calculus changes considerably.

Bayes' Theorem formalizes this intuition. It tells us the probability of an event given the evidence is determined by the likelihood of the evidence given the event, times the probability of the event, divided by the probability of the evidence happening all by its lonesome.

Since Bayes's time, probabilistic reasoning has been considerably refined. In the book Probability Theory: The Logic of Science, E. T. Jaynes, a twentieth-century physicist, shows probabilistic reasoning can explain cognitive "errors," political controversies, skeptical disbelief and credulous believers.

Jaynes's key idea is that for things like commonsense reasoning, political beliefs, and even interpreting miracles, we aren't combining evidence we've collected ourselves in a neat Bayesian framework: we're combining claims provided to us by others - and must now rate the trustworthiness of the claimer.

In our rosary case, the claimer drove down to Georgia to hear a woman speak at a farmhouse. I don't mean to throw up a stumbling block to something that's building up someone else's faith, but when the Bible speaks of a sign not being given to this generation, I feel like its speaking to us today.

But, whether you see the witness as credible or not, Jaynes points out we also weigh alternative explanations. This doesn't affect judging whether a wet lawn means we should bring an umbrella, but when judging a silver rosary turning to gold, there are so many alternatives: lies, delusions, mistakes.

Jaynes shows, with simple math, that when we're judging a claim of a rare event with many alternative explanations, our trust in the claimer that dominates the change in our probabilistic beliefs. If we trust the claimer, we're likely to believe the claim; if we distrust the claimer, we're likely to mistrust the claim.

What's worse, there's a feedback loop between the trust and belief: if we trust someone, and they claim something we come to believe is likely, our trust in them is reinforced; if we distrust someone, and they claim something we come to believe is not likely, our distrust of them is reinforced too.

It shouldn't take a scientist or a mathematician to realize that this pattern is a pathology. Regardless of what we choose to believe, the actual true state of the world is a matter of natural fact. It did or did not rain, regardless of whether the ground is wet; the rosary did or did not change, whether it looks gold.

Ideally, whether you believe in the claimer - your opinions about people - shouldn't affect what you believe about reality - the facts about the world. But of course, it does. This is the real problem with rare events, much less miracles: they're resistant to experiment, which is our normal way out of this dilemma.

Many skeptics argue we should completely exclude the possibility of the supernatural. That's not science, it's just atheism in a trench coat trying to sell you a bad idea. What is scientific, in the words of Newton, is excluding from our scientific hypotheses any causes not necessary or sufficient to explain phenomena.

A one-time event, such as my alleged phone call to my insurance agent today to talk about a policy for my new car, is strictly speaking not a subject for scientific explanation. To analyze the event, it must be in a class of phenomena open to experiments, such as cell phone calls made by me, or some such.

Otherwise, it's just a data point. An anecdote, an outlier. If you disbelieve me - if you check my cell phone records and argue it didn't happen - scientifically, that means nothing. Maybe I used someone else's phone because mine was out of charge. Maybe I misremembered a report of a very real event.

Your beliefs don't matter. I'll still get my insurance card in a couple of weeks.

So-called "supernatural" events, such as the alleged rosary transmutation, fall into this category. You can't experiment on them to resolve your personal bias, so you have to fall back on your trust for the claimer. But that trust is, in a sense, a personal judgment, not a scientific one.

Don't get me wrong: it's perfectly legitimate to exclude "supernatural" events from your scientific theories - I do, for example. We have to: following Newton, for science to work, we must first provide as few causes as possible, with as many far-reaching effects as possible, until experiment says otherwise.

But excluding rare events from our scientific view of the world forecloses the ability of observation to revise our theories. And excluding supernatural events from our broader view of the world is not a requirement of science, but a personal choice - a deliberate choice not to believe.

That may be right. That may be wrong. What happens, happens, and doesn't happen any other way. Whether that includes the possibility of rare events is a matter of natural fact, not personal choice; whether that includes the possibility of miracles is something you have to take on faith.

-the Centaur

Pictured: Allegedly, Thomas Bayes, though many have little faith in the claimants who say this is him.

The Bible as Primary Source

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Growing up in the Bible Belt meant that many of my friends didn't just believe that the Bible was divinely inspired, they believed it was literally true and argued - sometimes, strongly argued - that accepting the Bible as the infallible Word of God was absolutely necessary for salvation.

There's a great Christian word for that point of view: idolatry.

Biblical idolatry, to be specific: worshipping the Bible instead of Jesus. As I said when I started this series, Christianity is about following Jesus (faith), away from your old life (repentance), and towards the kingdom of heaven (goodness), in the hope of salvation (only accomplished by his sacrifice and grace).

Placing the Bible, a book - a collection of books, in three different languages, by dozens of authors, over centuries, collated by a completely different group of people - as the center of your religion is placing an thing - a divinely inspired thing, perhaps, but a thing - in place of Jesus God, and distorts Christianity.

Treating the Bible like a fax from God gets you so caught up in the buzzing of the machinery that you miss the message. People I respect get lost mining the minutiae of the Bible, combing through their  Interlinear Bibles to construct their own elaborate castles in the air in favor of simply following Jesus.

But how do you get to know Jesus if you don't know the Bible? You don't, full stop. Yes, you can - and should - read the Apostle's Creed, which summarizes what Christians have learned about Jesus, as approved by the descendants of his own apostles - who have evolved into our modern bishops.

But for us today - and even when the Apostle's Creed reached essentially its current form, 700 years after Jesus died - we must rely on the Bible to tell us who Jesus was. While the Church has traditions about Jesus not recorded in the Bible, even the Church itself doesn't consider these very reliable.

So we're stuck with the Bible to get to know Jesus - which is as it should be, scientifically (if you include history in the "sciences," writ large, which I do) because the New Testament of the Bible is the only extended primary source material we have about Jesus's life.

Before we drill into that, here's a question: Do you believe George Washington cut down a cherry tree?

If so, shame on your primary school history teachers, because it very likely didn't happen. The cherry tree myth was invented 7 years after George Washington's death - and almost 70 years after the alleged incident - by an early biographer, who didn't even include it until the book's fifth edition.

That doesn't mean it didn't happen - but if it had happened, it probably would have been mentioned in the writings of Washington or people who knew him. But the story was first told after everyone who could verify it was dead, by a biographer out to show Washington's success was due to his "Great Virtues."

Historians prefer not to use that kind of second-hand evidence (though, if all else is lacking, they'll grit their teeth and soldier on). They prefer to use primary sources - documents and diaries, art and artifacts, recordings and records that were directly created in the time of study, preferably by the people involved.

Put another way, if you want to know what George Washington thought, you need to look at what he actually said and did. Speculating about what he might have thought or did can be interesting, but unless that speculation can be tied back to actual documents about Washington ... you're just making it up.

In the same vein, students of the "historical Jesus" hunted for writings about Him by His contemporaries, and found only a handful: a few references in the historians Josephus and Tacitus written around AD 90 and AD 115, and just possibly some in the Talmud, collected around 200 from older oral traditions.

All these recount narratives that are brief and generally second- or third-hand. These primary sources let us know that Jesus existed. But if you want to know more about Jesus's life - whether you're a historian or a Christian or both - and you're looking for primary sources, the Bible is it.

We don't need to imagine that the Bible is an infallible fax from God in order to recognize we need to treat its words with utmost respect. If you wanted to learn what George Washington wrote in his diary, you wouldn't make a new diary entry up, now would you? The same is true of the Bible.

There are hundreds of manuscripts of the Old Testament and thousands of the New Testament, with many discrepancies; but this is where we start. I prefer the New Oxford Annotated Bible, others prefer the Interlinear; to help interpret them, I use histories like Ehrman's and Anglican and Catholic catechisms.

Jesus is God. Jesus lived as a human being. The Bible was written by human beings who were met and moved by Him, and was preserved by people who were following in His example of reading and sharing the Scriptures. We don't need to deify the Book; we need to look through it to the God behind it.

-the Centaur

Pictured: a primary source, in this case a 1st-century bust alleged to be Josephus, a historian born shortly after Jesus died, and who wrote about him while Jesus's contemporaries were still living. Whoa. Timing-wise, that'd be like ... like a picture of me in my 60's, if I had written a biography of JFK.

Black Holes and Divine Revelation

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Growing up with Superman comics, Hollywood movies and Greek mythology can give you a distorted idea of the spiritual world. Colorful heroes with flashy powers hurl villains into the Phantom Zone, and a plucky bard with a fancy lyres can sing his way into hell to rescue his bride, if only he doesn't look back.

This models the afterlife as a distant but reachable part of the natural world. The word "supernatural" gets tossed around without force, because there are rules for breaking the rules: like warp drive breaking the laws of motion or the cheat codes to the Matrix, you can hack your way into and out of the afterlife.

But spirituality is not magic, and prayers aren't spells. While I've argued "spirit" isn't strictly necessary for the practice of Christianity, most theologians would agree that the supernatural realm is a reflection of the grander reality of God and operates on His will - not a set of rules that could be manipulated by Man.

Even the idea of the "afterlife" isn't necessary. We're waiting in hope for bodily resurrection. We die, and stay dead, yet our essences live on in the mind of God, to be resurrected in a future world which outstrips even our boldest imaginations (though C. S. Lewis sure tried in The Great Divorce and The Last Battle).

Death, in this view, is a one-way trajectory. It isn't likely that people are going to and returning from the afterlife, no matter how many tunnels of light are reported by hypoxia patients, because the afterlife is not a quasi-physical realm to be hacked into, but a future physical state accompanied by spiritual perfection.

So if no-one's come back from Heaven to tell us about the afterlife, how do we know to seek it?

This is not trivial for someone who teaches robots to learn. In reinforcement learning, we model decision making as Markov decision processes, a mathematical formalism in which we choose actions in states to receive rewards, and use the rewards to estimate the values of those actions to make better choices.

But if no-one has returned from a visit to the state of the afterlife, how can we estimate the reward? One typical way around this dilemma is imitation learning: the trajectories of one agent can be used to inform another agent, granting it knowledge of the rewards in states that it cannot visit.

That agent might be human, or another, more skilled robot. You can imagine it as an army of robots with walkie-talkies trying to cross a minefield: as long as they keep radioing back what they've observed, the other robots can use that information to guide their own paths, continuing to improve.

But we're back to the same problem again: there's no radio in the afterlife, no cell service in Heaven.

One-way trajectories like this exist in physics: black holes. Forget the traversable black holes you see in movies from The Black Hole to Star Trek to Interstellar: a real black hole in general relativity is defined as a region of space where trajectories go in, but do not come back out; its boundary is the event horizon.

It's called the event horizon because no events beyond the horizon affect events outside the horizon. Other than the inexorable pull to suck more world-lines in, no information comes back from the black hole: no reward is recorded for the unvisited states of the Markov decision process.

Death appears to be a black hole, literally and figuratively. We die, remain dead, and are often put in a cold dark place in the ground, communicating nothing back to the world of the living, now on a trajectory beyond the event horizon, heading to that undiscovered country of Shakespeare and Star Trek.

In our robot minefield example, that might be a mine with a radio scrambler, cutting off signals before any other robots could be told not to follow that path. But what if there was someone with a radio who was watching that minefield from above, say a rescue helicopter, signaling down the path from above?

In a world where spirituality is a reflection of the grander reality of God, there's no magical hack which can give us the ability to communicate with the afterlife. But in a world where every observed particle event has irreducible randomness, God has plenty of room to turn around and contact us.

Like a faster-than-light radio which only works for the Old Ones, we can receive information from God if and only if He chooses to. The Old Testament records many stories of people hearing the voice of God - in dreams, in waking, in writing on the wall, in voices thundering from the heaven, in whispers.

You don't need to treat the Bible like a fax from God to imagine that the information it contains could be inconceivably precious, a deposit of revelation which could never be received from any amount of human experience. No wonder the Church preserved these books and guarded them so jealously.

But even this sells short the value that we get from God incarnating as Jesus.

Jesus Christ, a human being, provides a direct model of the behavior we should follow, informed by the knowledge of Jesus God, the portion of the Trinity most directly comprehensible by us. This is the best example we could have for imitation learning: a trace of the behavior of a divinely inspired teacher.

No amount of flying around the Earth will bring someone back from the dead; there may very well be "a secret chord that pleases the Lord," but you can't sing yourself into the afterlife. Fortunately, the afterlife has already sent an emissary, showing us the behavior we need to model to follow Him there.

-the Centaur

Pictured: Guess who.

Original Sin and Markov Decision Processes

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Original Sin is the idea that all humans are irretrievably flawed by one bad decision made by Adam in the Garden of Eden. One bite of that apple (well, it wasn't an apple, but nevermind), broke Creation in the Fall, corrupted everyone's souls from birth, leading to the requirement of baptism to liberate us.

But the Fall didn't happen. The universe is not broken, but is unimaginably old and vast. The evolution of humans on the earth is one story out of myriads. The cosmology of the early Hebrews recorded in Genesis is myth - myth in the Catholic sense, a story, not necessarily true, designed to teach a lesson.

What lessons does Genesis teach, then?

Well, first off, that God created the universe; that it is well designed for life; that humanity is an important part of that creation; and that humans are vulnerable to temptation. Forget the Fall: the story of the serpent shows that humans out of the box can make shortsighted decisions that go horribly wrong.

But what's the cause of this tendency to sin, if it isn't a result of one bad choice in the Fall? The answer is surprisingly deep: it's a fundamental flaw in the decision making process, a mathematical consequence of how we make decisions in a world where things change as a result of our choices.

Artificial intelligence researchers often model how we make choices using Markov decision processes - the idea that we can model the world as a sequence of states - I'm at my desk, or in the kitchen, without a soda - in which we can take actions - like getting a Coke Zero from the fridge - and get rewards.

Ah, refreshing.

Markov decision processes are a simplification of the real world. They assume time steps discretely, that states and actions are drawn from known sets, and the reward is a number. Most important is the Markov property: the idea that history doesn't matter: only the current state dictates the result of an action.

Despite these simplifications, Markov decision processes expose many of the challenges of learning to act in the world. Attempts to make MDP more realistic - assuming time is continuous, or states are only partially observable, or multidimensional rewards - only make the problem more challenging, not less.

Hm, I've finished that soda. It was refreshing. Time for another?

Good performance at MDPs is hard because we can only observe our current state: you can't be at two places or two times at once. The graph of states of an MDP is not a map of locations you can survey, but a set of possible moments in time which we may or may not reach as a result of our choices.

In an earlier essay, I described navigating this graph like trying to traverse a minefield, but it's worse, since there's no way to survey the landscape. The best you can do is to enumerate the possible actions in your current state and model what might happen, like waving a metal detector over the ground.

Should I get a Cherry Coke Zero, or a regular?

This kind of local decision making is sometimes called reactive, because we're just reacting to what's right in front of us, and it's also called greedy, because we're choosing the best actions out of the information available in the current state, despite what might come two or three steps later.

If you took the wrong path in a minefield, even if you don't get blown up, you might go down a bad path, forcing you to backtrack ... or wandering into the crosshairs of the badguys hiding in a nearby bunker. A sequence of locally good actions can lead us to a globally suboptimal outcome.

Excuse me for a moment. After drinking all those sodas, I need a bio break.

That's the problem of local decision making: if you exist in a just very slightly complicated world - say, one where the locally optimal action of having a cool fizzy soda can lead to a bad outcome three steps later like bathroom breaks and a sleepless night - then those local choices can lead you astray.

The most extreme example is a Christian one. Imagine you have two choices: a narrow barren road versus a lovely garden path. Medieval Christian writers loved to show that the primrose path led straight to the everlasting bonfire, whereas the straight and narrow led to Paradise.

Or, back to the Garden of Eden, where eating the apple gave immediate knowledge and long-term punishment, and not eating it would have kept them in good grace with God. This is a simple two-stage, two-choice Markov decision process, in which the locally optimal action leads to a worse reward.

The solution to this problem is to not use a locally greedy policy operating over the reward given by each action, but to instead model the long-term reward of sequences of actions over the entire space, and to develop a global decision policy which takes in account the true ultimate value of each action.

Global decision policies sometimes mean delaying gratification. To succeed at life, we often need to do the things which are difficult right now, like skipping dessert, in favor of getting more reward later, like seeing the numbers on your scale going back down to their pre-Covid numbers.

Global decision policies also resemble moral rules. Whether based on revelation from God, as discussed in an earlier essay, or based on the thinking of moral philosophers, or just the accumulated knowledge of a culture, our moral rules provide us a global decision policy that helps us avoid bad consequences.

The flaw in humanity which inspired Original Sin and is documented in the Book of Genesis is simply this: we're finite beings that exist in a single point in time and can't see the long-term outcome of our choices. To make good decisions, we must develop global policies which go beyond what we see.

Or, for a Christian, we must trust God to give us moral standards to guide us towards the good.

-the Centaur

Pictured: Andrey Markov.

The Total Depravity of the No Free Lunch Theorem

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Many Christians believe that we can only do good by the grace of God. In its most extreme form, this theory of "total depravity" suggests that we are literally incapable of choosing the good, choosing to follow God, or to even believe in Him without His direct supernatural aid, offered as a free gift.

Total depravity is false, but it contains an important truth about why we need God's help not to screw up.

In artificial intelligence, we model smart things like people as "intelligent agents". An agent, broadly stated, is something that exists in a larger environment, observing situations, taking actions, and receiving rewards - a bit like the entities navigating through Markov decision processes last time.

But agents are a broader concept, not strictly tied to the Markov property: anything that makes decisions about actions in a larger environment can be an agent. The line between agent and environment can be clear, as with humans contained within our skins; or it might be fuzzy, like a control system for a factory.

While the idea of "intelligence" is fuzzy, one of the things that makes an agent smart is rational behavior - making the right choices. Another thing that makes an agent smart is learning - improving your behavior in the future based on the experiences that you've had in the past.

The field I work in, deep reinforcement learning, focuses on building learning agents that improve their rationality based on their experiences, generally within a partially-observable Markov decision process in which it's reasonably clear what counts as rational, even if the agent can't clearly see the whole world.

This "partial observability" is one real-world limitation that virtually all agents in Creation share. Robot sensors have a limited range, the factory controller doesn't have a sensor on all its circuits, and we can't see behind our own heads (hey, there's a creepy man standing behind you right now - don't look!)

Partial observability means we need to make the best decisions we can based on the information that is available to us. We look both ways at a crosswalk to try to reduce our uncertainty, waiting if a car is coming, and we call out "corner" in a restaurant kitchen to try to reduce the uncertainty of others.

Obviously, if you don't know which door holds the lady or the tiger, it's hard to pick. But even if an agent had perfect knowledge of the current state of the world around it - not that current state is well-defined in general relativity / quantum mechanics, but nevermind - making perfectly correct decisions is impossible.

Well, not necessarily impossible: a perfectly omniscient agent could make perfectly optimal decisions, because it would know the true value of each action, not just its immediate reward. But without that kind of revelation of information from the future, we can only learn from our past experiences.

And that's where the no free lunch theorem comes in: there is no guaranteed way to learn correctly.

Imagine a simple decision problem: to turn left or right on a forking path in a garden. (Perhaps only one of those directions leads to the "straight and narrow" - sorry, this is a Lenten series, gotta bring that in somewheres). At each fork in the road, there are two more potential paths than there were before.

A path that forks at each stage is like that problem where you double the number of pennies you give someone each day for a whole month. It starts with small change - first day a penny; the second, two, the third, four, and so on - but last day of the month, you're shelling out ten million bucks - a billion pennies.

In this garden of forking paths, there are a billion possible destinations. But in the mind of an agent trying to learn what to do, the problem is even harder: there are also a billion intermediate steps, and at each point, the agent must make a decision, with two possible choices.

If you perfect knowledge and tried to write down a guidebook, it would have a billion entries, with a recommended decision at each point. But if you don't have perfect knowledge, if you're a learning agent, then your best option is to go into the garden and fill out that guidebook yourself.

This is almost inconceivably hard. If you imagine a library with every possible guidebook, one in which each book differed from every other by at least one decision out of those billions, then there are two to the power of a billion possible books - that's a number with roughly three hundred million digits.

The only way to fill out the guidebook correctly is to visit all billion possible paths. If you can't do that, then at some point, you're going to need to guess the entries for the parts of the garden that you haven't visited. And then it gets tricky, because there are two to the power of a billion possible gardens.

If you're in a garden where the straight and narrow can be approximated by alternating left and right to stay near the middle, you might guess that outer entries of the table should turn inward, the far left turning right, and the far right turning left. But for all you know, more reward can be found further out.

The no free lunch theorem says that there is no principled way to fill in parts of the book you haven't seen. At best, you can assume that parts of the garden you've seen are similar to the ones you haven't, but if you could be in literally any possible garden, then those assumptions will inevitably fail.

What does this all mean for free will versus total depravity?

Well, first off, if you are an intelligent agent, then you can sample actions from your action space. The actions you can take aren't good or evil, they're decisions in your brain and actions of your body. Some of those actions can, by chance, be good ones; God has not so ordered the world to exclude the good.

And if you do good works and see that they are good, why, then, you could learn to do them again. There's nothing preventing this; again, God has not so ordered the world to exclude the good. But there's no guarantee that you're going to learn the right lessons, and there lies the problem.

In deep reinforcement learning, we see this problem writ large. I teach robots the size of people how to navigate buildings meant for people, and while you think that would be simple, we often observe robot control policies that have completed thousands of successful runs suddenly run straight into a wall.

Deep learning systems do not generalize the way human beings would. While a human that learns to drive without hitting things in their hometown will often be able to transfer this skill when they go off for college, a robot moving to a new environment may expose strange "pathologies" in its behavior.

This is the meaning of "my thoughts are not your thoughts, neither are your ways my ways" in Scripture: even if a human being honestly chooses to believe in God, sincerely tries to do good, and accidentally gets it right, there is no guarantee that what they've learned from that experience will transfer.

In fact, it's more likely to not transfer. Sins of pride, self-righteousness, scrupulousness, and intolerance lead us astray as much as temptations to indulge in things that are "lawful but not expedient". We can turn to Scripture, to church Tradition, or to our own Reason to try to improve, but we'll likely screw up.

This is why God's grace is so important. God is actively and spiritually trying to help us come to believe, know and love him, and hopes that this love will prompt us to do the right thing, bringing the Kingdom of Heaven into being here on this Earth.

But across a broad spectrum of possible universes, it's mathematically impossible for us to always get it right even if we're trying really hard - literally the only way that we could actually be consistently good is to have perfectly omniscient knowledge of the entire future of the Universe - to actually be God.

We can't be God. The position is taken. We don't know what He knows, and we are going to screw it up. Fortunately He's ordered the universe so it's possible to get it right, He's sent his Son as an example of how to get it right, and His Spirit acts in the world to give us the grace we need to actually get it right.

-the Centaur

Pictured: David Wolpert, who discovered one of the depressingly many No Free Lunch theorems.

Make Holy the Lord’s Day

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To make sure my Sabbath remains a Sabbath, and since responsible people are still working remotely because of the pandemic, in lieu of writing an essay, I'll use that time to watch recorded services from Saint Stephen's in-the-Field instead (note these were filmed at our sister parish St. John the Divine).

If you haven't "gone to Mass" today, I encourage you to take a devotional.

Stay safe, seek rest, and God bless.

-the Centaur

Pictured: a graphic. Wow, Illustrator is ... so unnecessarily hard to use, and the Illustrator community seems filled with a small contingent of strangely unhelpful people who can't seem to realize there are other drawing programs out there and legitimate reasons to question why Illustrator does Illustrator.

Pascal’s Wager and Purchasing Parsley

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Hang out with philosophers or theologians long enough, you're likely to run into "Pascal's Wager": the Blaise Pascal's idea that you should believe in God, because if He exists, betting on Him wins you everything and betting against Him loses you everything, whereas if He doesn't, you lose nothing.

Right off the bat, we can see this original version of the wager is an intellectually dishonest argument: you don't "lose nothing" if you choose to believe that God exists and He doesn't. At best, you're being credulous; at worst, if you're being cynical about your belief, you're sacrificing your intellectual integrity.

Pascal backs off from all or nothing a bit as he's trying to dig himself out of the hole, claiming that he's comparing infinite gains of eternity in heaven against finite losses you can experience here on Earth. Some may have sincere trouble in believing, but he argues they should try to convince themselves.

Now, let's be fair to Pascal here: if you read his original text, he wasn't actually trying to convince atheists to believe per se, but instead, trying to show that the world is too uncertain for logical proofs of the existence of God, but we're probably better off acting like God exists, in case it moves us to faith.

Unfortunately, Pascal died before he could fully explain himself: the wager appears to be the introduction of a book on the value of faith that he never finished. But, like a philosophical zombie, the argument has continued its life, hollowed out from its original intent, eating brains in every new generation.

Let's slay this zombie, shall we?

Pascal's wager first appears to be an exercise in game theory: a mathematical formalism for analyzing the best choices in games. In this case, you are playing a game against the Cosmos. Your move is to believe, or not, and the Cosmos's "move" is whether God exists, or not.

[Now, the theologically savvy among you might feel like pointing out that God created Creation, and is not a part of it - which is why I used Carl Sagan's more inclusive formulation of the Cosmos as "all that is, was, and ever shall be," and I'm going to run you off with a broom if you argue about what "is" means].

This leads to a simple table: your choice of belief times the existence of God. If He is, and you choose to believe: payout plus infinity; choose not to believe: payout minus infinity. If He is not, whether you choose to believe or not, the payout is zero, or at least finite. Pick the cell with the highest value.

The emotional force of this argument is strong - for the believer - for, in decision theory, we should weigh the probability of one cell against the other, and intuitively, unless we judge the possibility of God to be literally zero, the infinite payout of the God-exists column dominates finite payouts of God-doesn't.

Mathematically, that's, um, specious at best - it looks true, but it's not a valid decision-theoretic argument. First off, Pascal put infinity in the God column specifically to outweigh any possible finite payout, but technically, we can't multiply infinite quantities by finite quantities this way.

Now, when it comes down to the question of whether infinities are actually real, or just a bad metaphor that leads people astray, I'm firmly ready to go to infinity - and beyond! But, technically mathematically, most of the time "infinity" is just a stand in for "this process can go on indefinitely without a limit."

As soon as you admit that the payout of Heaven might be finite for the purposes of modeling, then the probability assigned to the "God exists" column can be set so low that the "God doesn't" column becomes attractive. But that gets us no further than Pascal and his strict (zero-probability) unbelievers.

To me, the key flaw in Pascal's wager is what physicist E. T. Jaynes called the "mind projection fallacy": assuming that the constructs you're using in your mental models exist in reality. That's how Pascal can even put the wager to someone in the first place: he sets up the board and says "you must wager".

But the gameboard Pascal sets up doesn't exist in reality, and there's no reason for someone else to model the problem the same way. A student of religion might add columns for different views of God: Jesus who saves, Zeus who's a jerk, the Great Electron, which doesn't judge, but just is, whoa whoa.

Equally well, a student of epistemology might add many columns for belief: strict disbelief, partial belief, certain belief; an evangelical might add columns for "the hope so's" and "the know so's". Even the probabilities of columns are up for grabs. We've got a matrix of confusing possibilities.

This flaw in the wager, like the flaws in much science and folk psychology about belief, is that we do not reason about facts provided by others according to the models in the other's head: we reason about the claims that others make about facts, which we internalize based on own beliefs - and trust of the other.

Even in the simplest form, moment you start counting the columns of the wager as beliefs, the infinities disappear: there's only a claim of infinite goods in heaven, and a claim of infinite punishment in hell - and a claim that the alternative yields you only finite rewards.

And those claims are mixed in with everything else we know. As a mathematical exercise, the self-contained four-cell version of the wager has a maximum payout in the "believe in a God who exists" cell; as something that corresponds to reality, the cells of the wager start to leak.

Mathematics is an abstraction of reality - an act of creative human imagination to create repeatable forms of reasoning. I'm on the side that there is an actual reality behind this repeatability of mathematics, or it would not work; but applying mathematics to any particular problem must leave out certain details.

This is leads to the law of leaky abstractions: the notion that, no matter how good the abstraction, sooner or later it is going to fail to model the world. Forget game theory, decision matrices, and probabilities: even something as simple as the mathematical concept of number can break down.

One of the reasons I haven't published my tabbouleh recipe is that it's hard to quantify the ingredients - two bunches of parsley, four bunches of scallions, six tomatoes, two cups of fine bulgur, the juice of a lemon, etc - but since tomatoes are of different sizes, that "six" is a messy number.

But at least tomatoes come in integral quantities. Parsley comes in bunches, which are not just of different sizes; they're composed of individual stems, picked from different plants, which have different degrees of growth, freshness and wilt. Parsley needs to be cleaned and picked to use in tabbouleh.

Sometimes, you need to buy three bunches of parsley in order to end up with two. That's the law of leaky abstractions for you: you have to purchase parsley in integral units of bunches, but the bunches themselves don't correspond to the quantities that you can actually use in your recipe.

Picking beliefs for use in our minds is far more complicated than assembling a heritage Lebanese salad. There are thousands of potential facts affecting any given problem, more intertwined than the branching leaves of those leafy greens; but like them, some are fresh and edible, others black and wilted.

This was the actual point of Pascal's argument, the one he hoped to expound on his unfinished book. But the wager, because it's a mathematical abstraction - because it's repeatable reasoning - has lived on, a zombie argument which purports to give a rational reason why you should believe in God.

Ultimately, we need to carefully winnow through information that we get from others before incorporating it into our beliefs; there is no royal road to convincing anyone of anything, much less God. As for belief in God, many Christians think that must ultimately come not from reason, but from grace.

Fortunately, God gives that gift of belief for free, if we want it.

-the Centaur

Pictured: Blaise Pascal.

Apologize for Christianity? Why, Never!

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lewis headshot

Christianity has all sorts of weird words: Primum Mobile, Eucharist, Paraclete; there are other words which are used in weird ways, like adoration, adoption ... and apologetics. "Christian apologists" doesn't refer to people who are apologizing for Christianity: it refers to theologians trying to defend it.

As I hinted at last time, in a worldview where belief in God rests on faith as a free gift of grace from God, Christian apologetics are both indispensable and unnecessary, essential and impossible. Christians are called on to spread the Gospel, with the knowledge that no rational argument can ever convince.

That hasn't stopped people from trying, though. The greatest Christian apologist of the past two hundred years, full stop, is C. S. Lewis, author of not just the Narnia series but also great apologetic works like The Screwtape Letters, The Great Divorce and The Abolition of Man.

And so, while Lewis's works have moved me greatly, I often find his works have holes in their hearts. The brilliant G. K. Chesterton, author of In Defense of Sanity, is even worse; his favorite trick is to turn common ideas into paradoxes to make a point - frequently at the cost of intellectual honesty.

I've heard it said that Chesterton argued that all great things contain paradoxes, because at the heart of everything is the paradox of the cross: a tool of condemnation turned into salvation, death turned into life, failure, humiliation and defeat turned into success, glory and victory.

And this is perfectly good Christian theology - and consistent with Godel's incompleteness theorem that we discussed earlier. Most Christian religions assert that at the heart of the faith are mysteries that cannot be fully understood, just like Godel showed that all systems of thought have ultimate limits.

But it's unsatisfying for a rationalist, even a Christian one, for it means that many Christians - even as they are sincerely trying to do their best to spread the Gospel the best way that they know how - are at the same time committing to statements that are at best foolish and at worst lies.

And if you are tempted to retort that it's good to be foolish in the name of the Lord, like David with his tamborine, I want to be super crystal clear that I don't mean the good, faithful kind of foolishness, but a performative, "bad faith" foolishness in which people pretend things are other than what they are.

You've met the type. The street preacher with the specious comeback; the televangelist who carefully edits his stories to play his position. The new "friend" who, when they find out you are a Christian, asks "Why don't you come to my church?" with the words "instead of yours" hanging in the air.

For a Catholic growing up in the south, in Greenville, South Carolina, hometown of Bob Jones University, this was particularly irksome. As a child, I was buttonholed by street preachers across the street from BJU, who'd pester me on subsequent weeks on whether I'd read the pamphlets they shoved on me.

If these people find out you believe in evolution, whoo boy, the volume gets turned up to eleven. I aaalmost ended up going into evolutionary biology as my field, and I can't tell you how many bad arguments I've heard about why evolution won't work. No, not bad arguments - meaningless.

But it wasn't just evolution. Many of the arguments which were forced upon me were purely theological. One argument really stuck with me - a true Chesterton style paradox, what at first appears to be a nearly meaningless argument which nevertheless captures an important truth about Christianity.

Call this "argument" the Cross over the Chasm. The idea is that in the beginning, God and Man were united, but Adam's sin caused the Fall, creating a chasm that cannot be bridged. Man can try to cross the chasm with good works, but fails; God can try to cross it with grace, but grace doesn't reach either.

But that's where the Cross comes in. While the arm of good works can't reach, and the arm of grace can't reach; but you can write Jesus vertically between them, and turn those two arms and the word Jesus into a cross that bridges the gap. Jesus's sacrifice on the cross bridges the gap between god and Man.

Now, what's bad about this Cross over the Chasm episode?

By itself, nothing, but in the moment, what happened was this: a friend found out that I was Catholic, and decided to "show" me the true role of Jesus in religion - except of course, in the mind of people like him, he doesn't have a religion, but a close personal relationship with Jesus Christ.

Never mind that this "argument" doesn't actually "show" anything - at best, it's a mnemonic for a few bits of theology which are perfectly consistent with Catholic doctrine. (Many people in the Bible belt who are upset about what Catholics supposedly believe don't realize there are fewer differences than they think).

But the real problem is that people who act like my friend did there are both implicitly rejecting the faith of fellow Christians - and lying about their own faith. Religion is the word we use for someone whose close personal relationship with an invisible person is a vital part of their worldview. Denying that is a lie.

And denying the faith of a fellow Christian is attacking that faith. I also have a personal relationship with Jesus Christ - which, in humility, I'd never describe as close, because it's never as I'd like, a relationship I'm always trying to improve, with the help of His grace; but I do believe and I choose to follow Him.

That's super hard, and we don't need to throw stumbling blocks up for other believers. For a Christian, other Christians should not be our theological enemies. And so, while I don't believe in buttonholing Christians to get them to convert to other branches of Christianity, I think it's good to ask:

What was good about the Cross over the Chasm episode?

Well, first off, it's a really clear mnemonic for really important theology. It's a great little story which clearly shares important truths about Christianity: humanity and God are separated, but reaching for each other in works and Grace, and Jesus - and His sacrifice - is the mediator that makes union possible.

It's not at all a logical argument, but the story has stuck with me for years. Had my friend come up to me, enthused, about this new metaphor, rather than presenting it as one more argument against my faith (!) even though it didn't contradict my faith (!!) it could have acted as a bulwark, not a stumbling block.

More importantly, at least my friend was trying to share the Gospel. Once a woman told a televangelist she didn't like how he was spreading the Gospel. He asked how she was spreading it. She replied that she wasn't spreading it. His response: "Well, I like how I'm doing it better than how you're not doing it."

I'm acutely aware that many people don't want to be proselytized, and that's their prerogative, of course - I know from experience I don't enjoy it myself. I far prefer the Episcopal "Tea with the vicar OR DEATH!" "Oh? Well, tea please" to any amount of street preaching or personal buttonholing.

But, if you are interested in the Christian faith, know that ultimately, rational argument will fail.

A paradox - a mystery - lies at the center of the faith: "Christ has died, Christ is risen, Christ will come again." While I'm  comfortable with this idea, sometimes it takes a Chesterton paradox - or a sketched diagram of a cross - to break through the rational so that the free gift of grace will start working.

-the Centaur

Pictured: C. S. Lewis.

Ayn Rand and the Catholic Religion

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At first glance, Jesus Christ and Ayn Rand seem as far apart as possible. Jesus founded the world's largest religion; Ayn Rand founded Objectivism, a prominent atheistic philosophy. Jesus sacrificed His life for our sins; Ayn Rand is the self-described "arch-apostle of selfishness."

But one thing Objectivism and Christianity have in common is the importance of every person. To Ayn Rand, each individual human being is an independent entity whose rights are derived from their status as a rational human being - and the foundation of morals is respect for the rights of those individuals.

Morals have a parallel foundation in Christianity. Each human is a rational animal - a being with intellect and will, one who can come to believe in Jesus and choose to follow them. Whether those beings choose to do that or not, the foundation of ethics is treating those individuals as an end in and of themselves.

That's the meaning of the word "catholic" in "one holy, catholic and apostolic church" in the Nicene Creed and the name of the "Roman Catholic Church": catholic, meaning universal, meaning, embracing all believers, open to all. Christianity isn't for a specific group: it's for everyone.

There are obvious differences between Objectivism and Christianity. Objectivism is based on the evidence of existence; Christianity is based on a foundation of faith. Objectivism rejects the idea of an agent as an explanation for existence; Christianity places the agent God as the logical ground of being.

In Objectivism, the individual is sovereign; in Christianity, God is sovereign. In Objectivism, pursuing your own values is the ultimate end goal of your actions; in Christianity, pursuing your own will over God's is a sin, and is one of the biggest stumbling blocks we need to overcome.

The biggest difference, of course, is their attitudes towards altruism: Objectivism rejects self-sacrifice as evil, whereas Christianity places it as its highest good, founded as it is on the greatest self-sacrifice of all, the Son of God's death on the Cross to blot out the sins of all mankind.

But this last difference is less of a difference than it first appears. Objectivists are not altruistic, but they are benevolent: trying to make the world better for human beings. Christians should focus on the Kingdom of God rather than the world - but to do so, we must love our neighbors as ourselves.

This Great Commandment, this fundamental respect for others as equals to ourselves, is all too easily forgotten in Christianity when we fall prey to one of Christianity's greatest sins: self-righteousness. Jesus told his disciples to shake the dust off their sandals and move on if people rejected the Gospel.

Three and a half centuries after Jesus, Saint Augustine was recommending religious persecution for people who refused to convert to Christianity; eleven hundred years after, that had devolved into the Inquisition; fifteen hundred years after, it perhaps hit its nadir in the witch trials.

God is more than capable of giving every human being the experiences they need to choose whether or not to believe in Him. He's got the budget for it. And while He wants us to witness to good news about Jesus to help them believe, He doesn't need us to do that - and doesn't want us to do it by force.

Forcing others to conform to our beliefs is precisely the opposite of casting the dust off our sandals. Forcing others to conform to our beliefs is precisely the opposite of turning the other cheek. In those circumstances, that's when I turn to the Great Commandment - but sometimes, I need a little help.

That's where the clarity of Objectivism comes in. Saying "love thy neighbor as yourself" is poetic, but open to a lot of interpretation about what that "love" really means. If we instead ask the very specific question: Am I treating the other human being in this transaction as a unit? we can get somewhere.

Each person is a rational being, an independent agent, an end in and of themselves. Ethics consists of making decisions which are good for those people, not for abstract concepts or groups - which is where Augustine went wrong, by putting "pastoral" concerns over letting individuals make their own decisions.

The temptation in dealing with the other - the jerk, the liar, the thief, the guy who leaves his shopping cart catty-cornered blocking off two parking spaces - is to demonize them, to see them as evil. But this is a kind of fundamental attribution error - blaming behavior on people's nature, rather than circumstances.

Some people fail to put the shopping cart back because they're oblivious; others don't care; and yes, there are people who do it because they're deliberately trying to be jerks. The action is the same - whether it's an asshole trying to tick people off, or a harried mother whose baby's diaper has exploded.

There is real evil in the world - but it rests in the actions, not the people. People, in and of themselves, are not evil. They may do evil - they may have committed sins - but in the end, they are people, individual human beings, worthy of respect - concrete units, not instances of abstract groups or concepts.

Remembering that people are people, worthy of respect as people, is paradoxically hardest when the person's beliefs are different. You want to go after the jerk in the parking lot. But you also get outraged at the political opponent, or the person whose philosophy or religion are different. They're so wrong!

Yet they're still people. And so, when the question arises, I ask myself: am I thinking of this person as a member of a class - as an asshole, or a political opponent, or a religious one - or as a concrete unit, as a rational being who has the same right to their own life that I do - and the same right to make choices?

Once I accept that person as a person, my values say I should love them as myself - and love, to me, is taking on other's goals over your own. This isn't quite the self-sacrificial cartoon version of altruism that Ayn Rand criticized, as I have many other values which I will not and should not compromise.

But Christian values come first. Ayn Rand helps me to remember that people are not abstract characters in my internal mental drama, but real, concrete, existing human beings - and once I remember that, Jesus Christ can help guide me to treat that person as my neighbor, and to love them as myself.

-the Centaur

Pictured: Ayn Rand. I had a trouble capturing her rotation, as this essay set her spinning in her grave.

You Can’t Prove Anything With the Bible

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james sketch

While Christianity means following Jesus, the starting point for that journey today is the Bible - whether you're a fundamentalist who takes the Bible as literal truth, or a Catholic who views it through the lens of dogma and tradition, or a rational theist like myself who treats the Bible as primary source material.

But one thing you can't do with the Bible - even if you're a fundamentalist and thinks it's literally true, or a Catholic who believes in the richness of orthodox doctrine, and especially not a rational theist - is actually prove anything with it, not without breaking the meaning of "proof".

Perhaps I'm oversensitive about this point. In colloquial language, proof can just mean evidence offered to reach a conclusion: you can offer your driver's license as a proof of your identity, gather facts to prove innocence or guilt, offer those proofs as trial to help a jury reach a conclusion.

But that's not the way that people used the word "proof" to argue about the Bible when I was growing up, nor is it the way that I've seen people use the word around me to argue for their beliefs. Those people use the word proof like this: "You should believe X, same as me, and I can prove it with the Bible!"

The most egregious example I heard was a Catholic priest at Christmas mass give an enormous list of Catholic doctrine - mostly, political doctrines - which they then followed by the extraordinary statement that all of these things logically followed from the Resurrection of Jesus Christ.

But the theology of the Catholic Church - four hundred pages of catechism in my 1983 copy, near nine hundred in the 1994 edition, thirteen hundred pages in McBrien's Catholicism, or 1500 pages in the latest edition of Denzinger - do not logically follow from the hundred thousand words of the Gospels and Acts.

You can take the Gospels on faith. You can take the Bible to be mythical truth, like the Catholic Church does, or to be literal truth, like fundamentalists do. And, guided by grace, you can build a theology on it. But you cannot use it as a foundation for logical argument, for the text requires interpretation.

The Bible consists of around seventy books with a wide variety of content - myths, histories, stories, songs, proverbs, parables, essays, biographies, letters, and prophecies. These texts are not written with sufficient precision for them to serve as axioms for logical argument - nor were they meant to.

The reason is simple to understand: axioms for logical argument must be atomic, with meanings that are completely self-contained to serve as bases for logical deductions; but the meaning of any particular passage of the Bible must be taken in their textual, historical and religious context.

This isn't an argument for relativism or for radical textual analysis, but the simple point that even the shortest sentence in the Bible, "Jesus wept," has a meaning which can only understood by reading the story in the text that surrounds it - and every act of reading is an act of creative imagination.

Researchers in artificial intelligence have discovered that reading even the simplest possible stories generally requires inventing novel concepts that don't yet exist in the mind of the reader. Each reader must recreate within themselves knowledge contained in the stories, knowledge they don't yet have.

And they recreate that information based on what they already do know, and so will idiosyncratically create their own unique interpretations of the concepts of the story. Perhaps this is why different Christian groups I encounter seem to read the Bible in such different ways.

Now, most groups of Christians I know are convinced that there is one true way to read the Scriptures. One friend once claimed that there was "only one true interpretation" - despite coming from a tradition that claimed each Christian was responsible for their own interpretation of the Bible. And yet ...

Catholics complain Protestants ignore the plain words of Scripture in which Jesus gives spiritual authority to Peter and his descendants - which is the source of the authority of the Pope over the Church - or the words that indicate that the bread and wine of the Eucharist become the literal body and blood of Jesus.

Protestants complain Catholics read into the plain words of the Scripture things that are not there - interpreting the metaphorical language of the Last Supper to be literal - or read out things that are there - like ignoring the existence of Jesus's brothers and sisters to preserve the doctrine of the ever-virgin Mary.

You might be able to build a theology on such a foundation. And, if guided by grace, you might even be able to build a true theology on such a foundation. And that theology itself might contain logical arguments. But those arguments rest on your interpretations of the Bible, not the Bible itself.

Actual logical arguments require a funny kind of paradox in their application. Mathematics is repeatable reasoning, an act of creative imagination that builds tools which enables one person to build an argument which another person can reproduce precisely. But this repeatability comes at a terrible cost.

Logical arguments need axioms which are unambiguous within the context of their formal language - even though they are not precisely defined in the real world. And the conclusions you draw from those axioms are true only within the context of that language, even if they have a broad scope of application.

Points and lines in Euclidean geometry have a precise meaning in relationship to each other, but are "undefined terms" with respect to reality, only qualitatively described. This enables us to use the proofs of Euclidean geometry for a vast variety of practical applications, even though ideal "points" do not exist.

And even though Euclidean geometry doesn't describe the real world at all. Space is actually curved - not a barrier for mathematical analysis, though it is more complicated - and intermixed with time; but the more precise details of the Einsteinian space-time continuum don't show up at normal human scales.

But it does show a deeper truth: if an argument is rigorous enough to be logically true, that truth is restricted to the formal realm, and may not correspond to reality; if an argument is grounded in reality, its truth is contingent upon evidence which can be overturned, and cannot have the force of a formal proof.

In the early days after Jesus's ascension, Peter thought he had it all worked out, following both Jesus and Jewish law. But God spoke to him in a dream, making Peter realize that the old rules weren't appropriate for new believers, leading to a decision to no longer require all of them.

We build elaborate theological structures on top of our interpretations of the Bible. But insofar as they're based on the Bible, they're not proofs; and insofar as they are proofs, they're not guaranteed to apply to the Bible. We need to be humble about what we can prove, to leave room for the Spirit to work on us.

-the Centaur

Pictured: King James. Yeah, that King James, commissioner of the King James Bible.

Truth and Holiness

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darwin headshot

Back in the day, I had both a "Jesus fish" and a "Darwin fish" on the back of my car (as I recall, it was an Isuzu Rodeo, a nice car but nowhere near as reliable as my beloved Nissan Pathfinder or my seemingly unkillable Toyota Prius). I also had a "Cthulhu fish" fridge magnet which I had as a joke.

But I wouldn't have put a Cthulhu bumper sticker on my car, because the school of fish on that bumper were not a joke (though I admit I enjoyed the smidge of irony) but instead represented a sincere advertisement of my beliefs - and while it's a fun story, Cthulhu doesn't cut that mustard.

You're reading a Lenten series, so I hope it's apparent that I'm a Christian; during this series, I mentioned that once I thought of becoming an evolutionary biologist. To some Christians, these things seem hard to fit together, as many Christians are dead set on sticking to the cosmology of the Hebrews.

But the stories told in Genesis are wrong, at least as cosmology, geology, biology or history. The meaning behind the misleading Catholic term "myth" for some stories in the Bible is that stories are inspired by God and teach important truths, even if they aren't precisely accurate histories.

Despite some people's attempts to treat the Bible as a fax from God, our understanding of God has progressed since the books of the Bible were written by their authors, collated by early Christians, and ultimately approved by the early Catholic Church.

For example, the Trinity - the notion that the one (1) God manifests in three distinct "persons", Father, Son and Holy Ghost - doesn't appear directly in the Bible; we developed that understanding over time. But it's the most important Christian doctrine. You can't understand Jesus as the Son of God without it.

On the other hand, other ideas we have discarded. Even within the Bible, we see debates between sincere believers, such as the rejection of Jewish dietary rules for Gentiles in Acts of the Apostles. Doctrines like the divine right of kings and the proper treatment of slaves have been abandoned.

Now, science is familiar with this process. Some scientific ideas were bad from the get-go. The Earth was never at the center of the universe, matter isn't composed of four elements, and the motion of projectiles can't be explained by an "impulse" that slowly runs out: these ideas were never right.

Other ideas - like the Earth being round, matter being made of atoms, or light being made of waves or particles - started off right. Now, Earth isn't perfectly round, and atoms aren't perfectly indivisible, and tiny things are weirdly both waves and particles - but these ideas were on the right track from the beginning.

There's very little that science can "prove" to be true. All science is based on observation, generalization and experiment, and new experiments could show nuances that could force us to throw out our ideas - the technical term for this is "defeasible" reasoning - likely outcomes which might be true.

This is a natural outcome of the probabilistic reasoning that underlies most of our formal reasoning apparatus (and might even explain some of the inner guts of cognition as well): unless something is absolutely certain, conclusions founded on it can't be absolutely certain.

The best you can hope for, as far as proofs go, is to develop theorems of broad applicability. Physicists argue from symmetries, which enable vast regions of deduction from very few premises. Computer scientists use the theory of computation, which applies to a broad category of possible universes.

But, between our observations, our generalizations, our experiments, our theories, and our theorems, science has come up with a few things we can count on - the Earth is round, matter is made of atoms, and at the speed and scale experienced by humans, the Newtonian approximation to mechanics.

Science doesn't have definitive truths, but it is an engine for seeking it - for expanding the regions we think are probable and discarding the ideas which contradict experiment or each other. "The sole test of any idea open to observation is experiment" is the best tool we have for reaching truth - in any area.

That's why I put the Darwin fish with its cute little feet on my car: to represent the search for truth. But science is not enough. Science, by itself, is amoral: it can tell us what exists in the world, but it can't tell us what to do with it. That's where ethics, morals, religion and spirituality come in.

You can go far without invoking the supernatural. Philosophers argue that you can't go from an "is" to an "ought" - to argue from what exists to what to do about it - but this isn't quite true. Ayn Rand points out ethics are judgments about what's good for human beings, so we're not free to pick any ethics we like.

But as we discussed earlier, no individual human being experiences enough to make accurate ethical judgments on their own - nor are we guaranteed that our society has experienced enough to make our ethics accurate either. And if there really is an afterlife or a spiritual realm, experience won't cut it.

If there is a God, then we rely on Him to inform us about the spiritual dimension of the universe which either exist in the afterlife we haven't yet reached or are part of the cosmic nature of the universe which we don't have the stature to grasp. And this information - this Revelation - is therefore special.

This is the reason early Jews and Christians wrote down their experiences, and the reason the early Church collated it and preserved it. It's the reason fundamentalists treat the Bible as literally true, and the reason I treat the Bible as primary source material.

Ethics come from the spiritual dimension of the universe, and are ultimately holy. What we should do is determined by what is - and who - is behind it. Choosing the right action isn't just a good idea: it's seeking holiness - it's choosing to follow God. And that's why the Jesus fish was on my bumper.

I say "truth and holiness" - with the truth first - because truth must come first. I don't believe in Jesus because I think He's holy; I think He's holy because I believe the stories about him are true. And while parts of the Bible that are myth, to me the Gospels (and Acts) are my primary source about Jesus.

But once you understand the truth, you need to decide what to do about it. And like the cosmology of the Bible was modified by on our current understanding, there are principles in the Bible that have needed refinement as we learn more about the world. But it's important to start there, every time.

Truth, and holiness: first find out what's true, then try to do the right thing, treating the good as sacred.

-the Centaur

Pictured: Chuck D.

Suitcase Words and Sloppy Theology

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hofstadter headshot

If you're a working scientist - if you work day-to-day in domains not well understood enough to engineer solutions from known principles, if collecting data, generating theories, formulating hypotheses, and testing them are your bread and butter - then religious arguments often seem pretty crappy.

It's not that scientists can't make terrible mental gaffes, of course - they're human, like everyone else. But there's a certain mental discipline necessary for doing real science well which surpasses even the rigor expected in the philosophical and rationalist communities. We just don't know as much as we like.

And while some theology, regardless of whether you buy the premises, is based on solid argument - even though he lacked modern tools of valid argumentation, Aquinas is no slouch - vast swathes of religious thinking is based on a particular kind of garbage: reasoning from analogy.

Again, don't get me wrong: analogical reasoning is indispensable. Cognitive scientist Douglas Hofstadter built his career by demonstrating the power of analogy in thought. At one talk, his host said something like, "We'll join you at coffee hour after we drop Doug's books off at my office slash study."

Hofstadter whirled, smiled, and said, "At your office slash study. Beautiful." Beautiful, because his host had illustrated precisely what Hofstadter had shown in his talk: that we use analogy constantly in our day to day reasoning, case in point: an office slash study is a place used for work and to store books.

Everyone knew what he meant, and that's the beauty of the analogy. But just because we understand his off-the-cuff comment doesn't mean it's a meaningful foundation for a science of "office slash studies" - it was a convenience category, useful for calling something out, not for drawing firm conclusions.

Unfortunately, Christian "apologetics" leans heavily on analogies. In God in the Dock, C. S. Lewis said that Islam is the greatest of the Christian heresies, and all that's best in Judaism survives in Christianity. Well, that's cute, and it may even make you think, but it's bunk if you know the histories of the religions.

All too often, Christians use analogies about Jesus, their faith, and the world to argue for one point or the other - but then go beyond it to act as if those analogies were real. This is how Augustine got in the trap of arguing for forced conversions for "pastoral" reasons, forgetting about the real people being abused.

One such analogy is behind the idea that "food dulls the soul." This is a relatively obscure theological point, I admit - as J. K. Rowling might say, we're pretty deep in wand lore here - but it illuminates both the positive value of this kind of reasoning and the pitfalls inherent in this kind of imprecise reasoning.

"Food dulls the soul" is a concept - from Lewis or Miller, elaborated by a local priest - that if you find yourself backsliding into a sin you thought you'd conquered, check your diet over the last twenty-four hours: it's likely that you had a big, hearty - dare I say gluttonous - meal which softened you up.

The general idea is that the Devil assails a poorly defended point - it's easy to accidentally overeat - before attempting deeper corruption. The proposed theological mechanism is that "food dulls the soul" - focusing you on your body, detaching you from your spiritual connection, making it easier to sin.

I've observed this. The overall phenomenon is real. The explanation even has a grain of truith in it. But as stated, the explanation is garbage. True-sounding garbage: the precise phrase would be specious bullshit, statements that sound true but which are simply made up to suit the author's purpose.

For the soul is the form of the body. At very the least, it's an eternal Einsteinian record of every event that ever happened to you in the mind of God, and at the most, it's an eternal, indestructible spiritual essence under the total control of the Supreme Being of the Universe.

The soul is the form of the body. You can't separate it from the body. You can't be born without it, or sell it to the Devil, or cut it away with a subtle knife. If you hop in the transporter, or get transported to the grid, your soul will go with you, no matter how convoluted the episode. Commander Data would have one.

And so: you can't "dull" the soul. That would be like wearing out the number five: it's not even wrong, it's incoherent. And yet, something rings quite true about this idea - to the point that I recognized the immediately. What gives, then? This is a problem well known to artificial intelligence researchers:

"Soul" is a suitcase word.

In The Emotion Machine, Marvin Minsky defines "suitcase words" as words with a whole cluster of meanings we carry around like a suitcase. My favorite is "consciousness," which packs in attention (I was conscious of the noise) to wakefulness (I lost consciousness) to sensation (conscious experience).

When that priest discussed "food dulling the soul," he was engaged in a bit of sloppy theology to convey a subtle idea. The soul should be reserved for the theological soul - which has a precise definition to keep us out of trouble - but it's a stand-in for our intellects, our hearts, our spirits, our state of grace.

The theological soul itself can't be dulled, but we humans as rational animals can get in a very animal state, where we are focused on this world to the exclusion of the next. Our rationality become reactive; our spiritual senses can get dulled; our actions are in touch with our bodies, not our spirits.

Whether the Devil literally exists or not, whether we are tempted by spiritual forces of evil or whether we're simply vulnerable to engaging in locally greedy policies rather than appropriately delaying gratification to gather greater reward, we can get in a mode where we're self-satisfied.

And when we do - when we overfeed our bellies, or underfeed our spirits - that's when we are vulnerable to falling into deeper problems. Like the "office slash study" where Hofstadter's books got dropped off, "food dulls the soul" is an analogy, a stand-in for a whole cluster of related ideas.

Much of Christian apologetics and spiritual advice falls into this category. Specious bullshit is too unkind for this kind of analogical reasoning when it is used in its proper fashion: as a roadmap. This kind of theology is technically untrue, but may be useful, guiding us in the general direction of the good.

Feynman once said "the sole test of any idea is experiment". But is it? Astronomers might disagree. Even though telescopes put on space probes are called "experiments", they aren't: they are instruments for gathering observations. Astronomy is an (almost) purely observational science.

But even though it isn't strictly true as stated, Feynman's maxim is nevertheless useful - a bright, clearly visible sign that can guide us away from deadend a priori thought-mazes and towards evidence-grounded a posteriori theories which are falsifiable.

The same can be said of many theological maxims. Food may not technically dull the soul, but it can get you into trouble. Islam isn't a Christian heresy and Judaism isn't contained within Christianity, but the faiths do exist in a relationship which is fruitful for Christian thinkers to seriously consider.

But, while they may be useful, these maxims aren't literally true. So be careful with the theology you encounter. It may be a useful crutch for your thinking, but don't swallow it whole or try to build castles atop of it. At best it will leave a bad taste in your mouth, at worst buried in a pile of sand.

That last bit isn't true either, but hopefully you get something out of what I mean.

-the Centaur

Pictured: Douglas Hofstadter.

Raise Your Oxen on the Sabbath Day

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raise your oxen

Keeping with the Sunday theme of a day of rest, let's keep this short. Jesus once said:

And answered them, saying, Which of you shall have an ass or an ox fallen into a pit, and will not straightway pull him out on the sabbath day? [Luke 14:5]

To help me observe the Sabbath, I attend Mass, perhaps read a section of a religious book, and try to avoid shopping (or even to have groceries / packages arrive on Sunday, if I can).

But sometimes errands gotta err. And Jesus points out that the Sabbath was made for us:

And he said unto them, The sabbath was made for man, and not man for the sabbath. [Mark 2:27]

And so one way to take your day of rest is to deal with the things which are like your oxen in the well - those things in a metaphorical pit which will keep getting worse unless you make them better.

-the Centaur

Coveting is the Least of Your Worries

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watson headshot

Coveting is distinctive among the Ten Commandments in that it is a thought crime. For those not familiar with the Ten Commandments, they're a set of guidelines from God in Exodus and Deuteronomy in the Bible. How the guidelines break into "ten" is up for debate, but the rough outline, loosely interpreted, is:

  1. God is the Lord of everything.
  2. Don't have any other Gods.
  3. Don't misuse God's name.
  4. Keep the Sabbath holy.
  5. Honor your parents.
  6. Don't murder people.
  7. Don't commit adultery.
  8. Don't steal things.
  9. Don't lie in court.
  10. Don't covet your neighbor's stuff.

The first command is a statement of God's authority; the second through the ninth are involve some kind of action - making an idol, cursing a blue streak, shopping on Sunday, dressing up like a bat, killing Bruce Wayne's parents, making off with the Lost Ark, telling Tom Cruise he can't handle the truth.

But coveting is different. You don't have to physically do anything, like take your neighbor's nice new car: you just need to think about it. Jesus goes even further in Matthew 5:27-28, suggesting that if you look at a woman with lust, you've committed adultery with her in your heart.

Seems harsh, but I've heard priests speculate that God's reasoning behind these challenging passages is that coveting is really bad for you. It's not just that coveting your neighbor's house, spouse or possessions is a gateway to theft or adultery, it's that it puts your brain in a bad state.

Coveting is "yearning to possess something": possessions themselves are things which can possess us if we are not careful. But there's nothing wrong with wanting something per se: you can want a soda if you're thirsty, a better car if you're in the rat race, the four walls of your freedom if you're a monk.

But coveting someone else's possessions - not wanting a house to keep up with the Joneses, but wanting your neighbor Jones's specific house - is the problem. Coveting the possessions of others puts us in mental conflict with the people around us, which can lead to real conflict.

So even though it seems innocuous, coveting is a pitfall which is important enough that God wanted to warn us about it. But in a way, that makes coveting a very obvious pitfall. Unfortunately, coveting is just one of the ways that our human brains can go wrong with regards to our view of the people around us.

One of the modern "technologies" that humans have developed for maintaining the health of our minds is cognitive behavior therapy, a collection of experimentally tested cognitive and behavioral psychology techniques, designed to improve our well-being by detecting and correcting bad thought patterns.

These "cognitive distortions" can be self-destructive - thoughts like "I'm not good enough" - but they can just as easily be self-serving - "Everything would work out if they'd just listen to me." These self-serving narratives have the advantage of making us feel good about ourselves - but they don't better ourselves.

When we interact with other people, a healthy mental response keeps things in perspective. Someone speaks over you in a meeting, which happened to me a lot today; but you recognize that there are simple explanations involving no bad intent (as it turns out, my internet was flaky, and my voice kept cutting out).

But when cognitive distortions kick in, simple events like that can get overgeneralized ("This always happens to me"), magnified ("They didn't hear me at all"), can swamp out positives (like forgetting the good stuff) and can lead to catastrophizing ("Everything is going to hell in a handbasket").

These distortions aren't accurate, but they enhance the intensity of the events, worsening our stress levels - but, paradoxically, making it feel a relief when the events are over, giving us a bit of a dopamine hit for surviving the encounter, leading to the distortions growing stronger and stronger.

Cognitive distortions can turn into internal narratives, which can turn a momentary event into a years-long obsession. On one volunteer project, our group leader took offense when the previous leader tried to boss me around. I'd barely remember this, if our group leader didn't bring it up every time we talk.

Loving your neighbor as yourself is hard. But Jesus also says in Matthew 5:44 that you should love your enemies and pray for those who persecute you. Jesus clearly meant this to be directed at real enemies, people who've harmed us, but it applies with equal force to people who we just think have harmed us.

Loving your enemies is really hard if those enemies exist only in your own mind, because your cognitive distortions will twist anything that they do into something that is evil - like in politics, where partisans disbelieve anything the opposition leader says, even if he's reading the time off of an atomic clock.

But learning not to covet is like ... training wheels for eliminating cognitive distortions. It's good and healthy to want a sandwich if you're hungry. It's not so healthy to want someone else's sandwich. Perhaps that won't motivate you to take it. But you might think they got the better deal.

Even in something as petty as who gets the best slice of the cake, we can build tiny slights up into a tower of resentments. Techniques such as "one cuts, the other chooses" may be game-theory optimal, but we are rarely in situations where these techniques can always be applied.

So the solution starts with us. Don't covet your sister's slice of the cake. Don't resent your coworker's "DAYYMNN" sportscar. (No, really, it is VERY jawdroppingly nice). Don't covet your neighbor's spouse. Learn to distinguish between wanting to improve your situation, and envying the situations of others.

Building the cognitive tools we need to avoid self-serving narratives is hard, because each person's mind and situation are unique. Fortunately, we can start with something easier, something both easy to detect and easy to fix, by following the tenth of the Ten Commandments: do not covet your neighbor's stuff.

-the Centaur

Pictured: John Watson, founder of behaviorism.