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Posts tagged as “Jesus and Godel”

What is Lent?

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Lent

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.