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Posts tagged as “Intelligence”

The Embodied AI Workshop is Tomorrow, Sunday, June 20th!

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embodied AI workshop

What happens when deep learning hits the real world? Find out at the Embodied AI Workshop this Sunday, June 20th! We’ll have 8 speakers, 3 live Q&A sessions with questions on Slack, and 10 embodied AI challenges. Our speakers will include:

  • Motivation for Embodied AI Research
    • Hyowon Gweon, Stanford
  • Embodied Navigation
    • Peter Anderson, Google
    • Aleksandra Faust, Google
  • Robotics
    • Anca Dragan, UC Berkeley
    • Chelsea Finn, Stanford / Google
    • Akshara Rai, Facebook AI Research
  • Sim-2-Real Transfer
    • Sanja Fidler, University of Toronto, NVIDIA
      Konstantinos Bousmalis, Google

You can find us if you’re signed up to #cvpr2021, through our webpage embodied-ai.org or at the livestream on YouTube.

Come check it out!

-the Centaur

The Embodied AI Workshop at CVPR 2021

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embodied AI workshop

Hail, fellow adventurers: to prove I do something more than just draw and write, I'd like to send out a reminder of the Second Embodied AI Workshop at the CVPR 2021 computer vision conference. In the last ten years, artificial intelligence has made great advances in recognizing objects, understanding the basics of speech and language, and recommending things to people. But interacting with the real world presents harder problems: noisy sensors, unreliable actuators, incomplete models of our robots, building good simulators, learning over sequences of decisions, transferring what we've learned in simulation to real robots, or learning on the robots themselves.

interactive vs social navigation

The Embodied AI Workshop brings together many researchers and organizations interested in these problems, and also hosts nine challenges which test point, object, interactive and social navigation, as well as object manipulation, vision, language, auditory perception, mapping, and more. These challenges enable researchers to test their approaches on standardized benchmarks, so the community can more easily compare what we're doing. I'm most involved as an advisor to the Stanford / Google iGibson Interactive / Social Navigation Challenge, which forces robots to maneuver around people and clutter to solve navigation problems. You can read more about the iGibson Challenge at their website or on the Google AI Blog.

the iGibson social navigation environment

Most importantly, the Embodied AI Workshop has a call for papers, with a deadline of TODAY.

Call for Papers

We invite high-quality 2-page extended abstracts in relevant areas, such as:

  •  Simulation Environments
  •  Visual Navigation
  •  Rearrangement
  •  Embodied Question Answering
  •  Simulation-to-Real Transfer
  •  Embodied Vision & Language

Accepted papers will be presented as posters. These papers will be made publicly available in a non-archival format, allowing future submission to archival journals or conferences.

The submission deadline is May 14th (Anywhere on Earth). Papers should be no longer than 2 pages (excluding references) and styled in the CVPR format. Paper submissions are now open.

I assume anyone submitting to this already has their paper well underway, but this is your reminder to git'r done.

-the Centaur

Wrong, Wrong, Wrong

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chipman, pruitt, bolton

tl;dr: Opponents of things should never be appointed to oversee them.

So President Biden has nominated David Chipman to lead the ATF - and he was wrong to do so.

It's not that Chipman isn't qualified to lead the ATF - he's a 25-year ATF veteran. It's that Chipman is explicitly disqualified to lead an agency that oversees firearms - because he's a gun control advocate. It's not that he can't be trusted to make good decisions: he can be trusted to make bad ones.

Previous presidents have made the same mistake. To lead the EPA, Donald Trump nominated Scott Pruitt, a noted environmental skeptic who had sued the EPA. To serve as ambassador to the UN, George Bush nominated John Bolton, a noted United Nations skeptic who said that it does not really exist.

Political cards on the table: I voted for Joe Biden, and I'm happy with him. And while I'm a gun rights proponent - if the Second Amendment didn't exist, we'd need to invent it - I recognize both the need for and constitutional legitimacy of gun legislation, which shouldn't be set in stone as our society evolves.

But intellectual and moral integrity demands that if I call an opponent out for their misbehavior, that I also call out allies for the same behavior. Calling out misbehavior only on one side is worse than hypocritical: it undermines trust in the political system, and encourages further distorted value judgments.

And humans are great at distorting value judgments when emotions are involved. From the most basic arguments all the way up to the most complex adjudication of fact and law, our moods and emotions affect whether we judge something to be true or false.

In a way, we should expect this: researchers like Antonio Damasio have shown that rational decision making breaks down in people whose emotions are impaired, because the value judgments provided by our emotions are necessary for making mental decisions.

But a functioning emotional system can also lead us astray: emotions can impair our judgments. Studies show we're more likely to screw up simple if-then syllogisms if they're emotionally charged. Even judges, trained to be impartial, are more likely to make mistakes with legal arguments on "hot" political topics.

Heightened emotion distorts perceptions, leads us to attribute our feelings to arbitrary targets we come across, and reduces self-control - precisely what you don't want to have in someone who needs to make impartial decisions about something, and precisely what you do have in the person of a political activist.

Now, I'm not questioning Chipman or Bolton's integrity (Pruitt's lack of integrity is well documented, down to his sound-proof booth), or Chipman or Bolton or Pruitt's patriotism, or their expertise. But all three of them are interested enough in the areas they later oversaw to have gone into them as opponents.

In our public life, there is politics, and there is civics, and the two should not mix. Politics literally means deciding how to allocate scarce resources, and it is right and expected for us to dive in rough and tumble to ask for what we want - a participatory political system grants moral authority to a government.

But government's purpose is to bring the use of force under rational control, and more broadly, to allocate resources correctly when policy has been made. Inevitably, decisions will need to be made on matters of fact at an agency - and a political partisan can be trusted to screw them up even if they're trying not to.

When a partisan appoints a opponent of something to oversee it, the person that they've appointed will, very likely, whether they want to or not, "lean their hand on the till" to make things come out for their own partisan ends - meaning they will, sooner or later, fail in their civic duty to make an honest decision.

If you're passionate about something, you might feel that it's all right to put a partisan in charge of it,  because then you'll get what you want. But that's evil, on two grounds - first of all, because you are subverting the political process to get a result through the back door that you can't through the front.

But more importantly, impartial decisions will need to be made - and by putting a partisan in charge, you're explicitly hoping for them to make a wrong decision to help implement your political desires. Tyrants, bigots and the corrupt throughout history have employed the same tactic. Stop doing it.

Regardless of our political desires, we need to step back and decouple our understanding of people into (at least) two parts: their politics, and their competence. If their political orientation isn't a direct conflict of interest for to the matter at hand, their basic competence is the primary qualification for doing the job.

I was happy when Trump picked Bolton as National Security Advisor: whether I agree with their politics or not, Bolton had the experience to do the job and the attitude towards the job to do it right. Bush should never have appointed Bolton to the UN: even when he made the right decisions, we couldn't trust them.

I might not have agreed with Scott Pruitt politically, but as a lawyer and state Senator, he was well qualified to be Attorney General of Oklahoma. It was morally wrong for Donald Trump to appoint a climate change denier to lead the EPA, and, predictably, that led to Pruitt lying about climate issues.

I thank David Chipman for his service at the ATF, and would approve of his nomination to another agency. But the moment that he joined a political movement against guns, he disqualified himself from overseeing gun law enforcement, and if confirmed, he will inevitably make some serious mistakes.

-the Centaur

Pictured: Chipman, Pruitt, Bolton

Pascal’s Wager and Purchasing Parsley

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pascal headshot

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.

The Total Depravity of the No Free Lunch Theorem

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wolpert headshot

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.

 

Original Sin and Markov Decision Processes

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markov headshot

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.

Black Holes and Divine Revelation

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einstein headshot

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.

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 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

Day 057

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Turing Drawing

Alan Turing, rendered over my own roughs using several layers of tracing paper. I started with the below rough, in which I tried to pay careful attention to the layout of the face - note the use of the 'third eye' for spacing and curved contour lines - and the relationship of the body, the shoulders and so on.

Turing Rough 1

I then corrected that into the following drawing, trying to correct the position and angles of the eyes and mouth - since I knew from previous drawings that I tended to straighten things that were angled, I looked for those flaws and attempted to correct them. (Still screwed up the hair and some proportions).

Turing Rough 2

This was close enough for me to get started on the rendering. In the end, I like how it came out, even though I flattened the curves of the hair and slightly squeezed the face and pointed the eyes slightly wrong, as you can see if you compare it to the following image from this New Yorker article:

Turing Photo

-the Centaur