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Posts tagged as “Intelligence”

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

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.

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.

What is “Understanding”?

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When I was growing up - or at least when I was a young graduate student in a Schankian research lab - we were all focused on understanding: what did it mean, scientifically speaking, for a person to understand something, and could that be recreated on a computer? We all sort of knew it was what we'd call nowadays an ill-posed problem, but we had a good operational definition, or at least an operational counterexample: if a computer read a story and could not answer the questions that a typical human being could answer about that story, it didn't understand it at all. But there are at least two ways to define a word. What I'll call a practical definition is what a semanticist might call the denotation of a word: a narrow definition, one which you might find in a dictionary, which clearly specifies the meaning of the concept, like a bachelor being an unmarried man. What I'll call a philosophical definition, the connotations of a word, are the vast web of meanings around the core concept, the source of the fine sense of unrightness that one gets from describing Pope Francis as a bachelor, the nuances of meaning embedded in words that Socrates spent his time pulling out of people, before they went and killed him for being annoying. It's those connotations of "understanding" that made all us Schankians very leery of saying our computer programs fully "understood" anything, even as we were pursuing computer understanding as our primary research goal. I care a lot about understanding, deep understanding, because, frankly, I cannot effectively do my job of teaching robots to learn if I do not deeply understand robots, learning, computers, the machinery surrounding them, and the problem I want to solve; when I do not understand all of these things, I stumble in the dark, I make mistakes, and end up sad. And it's pursuing a deeper understanding about deep learning where I got a deeper insight into deep understanding. I was "deep reading" the Deep Learning book (a practice in which I read, or re-read, a book I've read, working out all the equations in advance before reading the derivations), in particular section 5.8.1 on Principal Components Analysis, and the authors made the same comment I'd just seen in the Hands-On Machine Learning book: "the mean of the samples must be zero prior to applying PCA." Wait, what? Why? I mean, thank you for telling me, I'll be sure to do that, but, like ... why? I didn't follow up on that question right away, because the authors also tossed off an offhand comment like, "XX is the unbiased sample covariance matrix associated with a sample x" and I'm like, what the hell, where did that come from? I had recently read the section on variance and covariance but had no idea why this would be associated with the transpose of the design matrix X multiplied by X itself. (In case you're new to machine learning, if x stands for an example input to a problem, say a list of the pixels of an image represented as a column of numbers, then the design matrix X is all the examples you have, but each example listed as a row. Perfectly not confusing? Great!) So, since I didn't understand why Var[x] = XX, I set out to prove it myself. (Carpenters say, measure twice, cut once, but they'd better have a heck of a lot of measuring and cutting under their belts - moreso, they'd better know when to cut and measure before they start working on your back porch, or you and they will have a bad time. Same with trying to teach robots to learn: it's more than just practice; if you don't know why something works, it will come back to bite you, sooner or later, so, dig in until you get it). And I quickly found that the "covariance matrix of a variable x" was a thing, and quickly started to intuit that the matrix multiplication would produce it. This is what I'd call surface level understanding: going forward from the definitions to obvious conclusions. I knew the definition of matrix multiplication, and I'd just re-read the definition of covariance matrices, so I could see these would fit together. But as I dug into the problem, it struck me: true understanding is more than just going forward from what you know: "The brain does much more than just recollect; it inter-compares, it synthesizes, it analyzes, it generates abstractions" - thank you, Carl Sagan. But this kind of understanding is a vast, ill-posed problem - meaning, a problem without a unique and unambiguous solution. But as I was continuing to dig through the problem, reading through the sections I'd just read on "sample estimators," I had a revelation. (Another aside: "sample estimators" use the data you have to predict data you don't, like estimating the height of males in North America from a random sample of guys across the country; "unbiased estimators" may be wrong but their errors are grouped around the true value). The formula for the unbiased sample estimator for the variance actually doesn't look quite the matrix transpose - but it depends on the unbiased estimator of sample mean. Suddenly, I felt that I understood why PCA data had to have a mean of 0. Not driving forward from known facts and connecting their inevitable conclusions, but driving backwards from known facts to hypothesize a connection which I could explore and see. I even briefly wrote a draft of the ideas behind this essay - then set out to prove what I thought I'd seen. Setting the mean of the samples to zero made the sample mean drop out of sample variance - and then the matrix multiplication formula dropped out. Then I knew I understood why PCA data had to have a mean of 0 - or how to rework PCA to deal with data which had a nonzero mean. This I'd call deep understanding: reasoning backwards from what we know to provide reasons for why things are the way they are. A recent book on science I read said that some regularities, like the length of the day, may be predictive, but other regularities, like the tides, cry out for explanation. And once you understand Newton's laws of motion and gravitation, the mystery of the tides is readily solved - the answer falls out of inertia, angular momentum, and gravitational gradients. With apologies to Larry Niven, of course a species that understands gravity will be able to predict tides. The brain does do more than just remember and predict to guide our next actions: it builds structures that help us understand the world on a deeper level, teasing out rules and regularities that help us not just plan, but strategize. Detective Benoit Blanc from the movie Knives Out claimed to "anticipate the terminus of gravity's rainbow" to help him solve crimes; realizing how gravity makes projectiles arc, using that to understand why the trajectory must be the observed parabola, and strolling to the target. So I'd argue that true understanding is not just forward-deriving inferences from known rules, but also backward-deriving causes that can explain behavior. And this means computing the inverse of whatever forward prediction matrix you have, which is a more difficult and challenging problem, because that matrix may have a well-defined inverse. So true understanding is indeed a deep and interesting problem! But, even if we teach our computers to understand this way ... I suspect that this won't exhaust what we need to understand about understanding. For example: the dictionary definitions I've looked up don't mention it, but the idea of seeking a root cause seems embedded in the word "under - standing" itself ... which makes me suspect that the other half of the word, standing, itself might hint at the stability, the reliability of the inferences we need to be able to make to truly understand anything. I don't think we've reached that level of understanding of understanding yet. -the Centaur Pictured: Me working on a problem in a bookstore. Probably not this one.

Never Give Up

centaur 0

So, 2019. What a mess. More on that later; as for me, I've had neither the time nor even the capability to blog for a while. But one thing I've noticed is, at least for me, the point at which I want to give up is usually just prior to the point where I could have my big breakthrough.

For example: Scrivener.

I had just about given up on Scrivener, an otherwise great program for writers that helps with organizing notes, writing screenplays, and even for comic book scripts. But I'd become used to Google Docs and its keyboard shortcuts for hierarchical bulleted lists, not entirely different from my prior life using hierarchical notebook programs like GoldenSection Notes. But Scrivener's keyboard shortcuts were all different, and the menus didn't seem to support what I needed, so I had started trying alternatives. Then I gave on more shot at going through the manual, which had earlier got me nothing.At first this looked like a lost cause: Scrivener depended on Mac OS X's text widgets, which themselves implement a nonstandard text interface (fanboys, shut up, sit down: you're overruled. case in point: Home and End. I rest my case), and worse, depend on the OS even for the keyboard shortcuts, which require the exact menu item. But the menu item for list bullets actually was literally a bullet, which normally isn't a text character in most programs; you can't access it. But as it turns out, in Scrivener, you can. I was able to insert a bullet, find the bullet character, and even create a keyboard shortcut for it. And it did what it was supposed to!

Soon I found the other items I needed to fill out the interface that I'd come to know and love in Google Docs for increasing/decreasing the list bullet indention on the fly while organizing a list:

Eventually I was able to recreate the whole interface and was so happy I wrote a list describing it in the middle of the deep learning Scrivener notebook that I had been working on when I hit the snag that made me go down this rabbit hole (namely, wanting to create a bullet list):

Writing this paragraph itself required figuring out how to insert symbols for control characters in Mac OS X, but whatever: a solution was possible, even ready to be found, just when I was ready to give up.

I found the same thing with so many things recently: stuck photo uploads on Google Photos, configuration problems on various publishing programs, even solving an issue with the math for a paper submission at work.

I suspect this is everywhere. It's a known thing in mathematics that when you feel close to a solution you may be far from it; I often find myself that the solution is to be found just after the point you want to give up.

I've written about a related phenomenon called this "working a little bit harder than you want to" but this is slightly different: it's the idea that your judgment that you've exhausted your options is just that, a judgment.

It may be true.

Try looking just a bit harder for that answer.

-the Centaur

Pictured: a photo of the Greenville airport over Christmas, which finally uploaded today when I went back through the archives of Google Photos on my phone and manually stopped a stuck upload from December 19th.

Robots in Montreal

centaur 1
A cool hotel in old Montreal.

"Robots in Montreal," eh? Sounds like the title of a Steven Moffat Doctor Who episode. But it's really ICRA 2019 - the IEEE Conference on Robotics and Automation, and, yes, there are quite a few robots!

Boston Dynamics quadruped robot with arm and another quadruped.

My team presented our work on evolutionary learning of rewards for deep reinforcement learning, AutoRL, on Monday. In an hour or so, I'll be giving a keynote on "Systematizing Robot Navigation with AutoRL":

Keynote: Dr. Anthony Francis
Systematizing Robot Navigation with AutoRL: Evolving Better Policies with Better Evaluation

Abstract: Rigorous scientific evaluation of robot control methods helps the field progress towards better solutions, but deploying methods on robots requires its own kind of rigor. A systematic approach to deployment can do more than just make robots safer, more reliable, and more debuggable; with appropriate machine learning support, it can also improve robot control algorithms themselves. In this talk, we describe our evolutionary reward learning framework AutoRL and our evaluation framework for navigation tasks, and show how improving evaluation of navigation systems can measurably improve the performance of both our evolutionary learner and the navigation policies that it produces. We hope that this starts a conversation about how robotic deployment and scientific advancement can become better mutually reinforcing partners.

Bio: Dr. Anthony G. Francis, Jr. is a Senior Software Engineer at Google Brain Robotics specializing in reinforcement learning for robot navigation. Previously, he worked on emotional long-term memory for robot pets at Georgia Tech's PEPE robot pet project, on models of human memory for information retrieval at Enkia Corporation, and on large-scale metadata search and 3D object visualization at Google. He earned his B.S. (1991), M.S. (1996) and Ph.D. (2000) in Computer Science from Georgia Tech, along with a Certificate in Cognitive Science (1999). He and his colleagues won the ICRA 2018 Best Paper Award for Service Robotics for their paper "PRM-RL: Long-range Robotic Navigation Tasks by Combining Reinforcement Learning and Sampling-based Planning". He's the author of over a dozen peer-reviewed publications and is an inventor on over a half-dozen patents. He's published over a dozen short stories and four novels, including the EPIC eBook Award-winning Frost Moon; his popular writing on robotics includes articles in the books Star Trek Psychology and Westworld Psychology. as well as a Google AI blog article titled Maybe your computer just needs a hug. He lives in San Jose with his wife and cats, but his heart will always belong in Atlanta. You can find out more about his writing at his website.

Looks like I'm on in 15 minutes! Wish me luck.

-the Centaur

 

Information Hygiene

centaur 0

Our world is big. Big, and complicated, filled with many more things than any one person can know. We rely on each other to find out things beyond our individual capacities and to share them so we can succeed as a species: there's water over the next hill, hard red berries are poisonous, and the man in the trading village called Honest Sam is not to be trusted.

To survive, we must constantly take information, just as we must eat to live. But just like eating, consuming information indiscriminately can make us sick. Even when we eat good food, we must clean our teeth and got to the bathroom - and bad food should be avoided. In the same way, we have to digest information to make it useful, we need to discard information that's no longer relevant, and we need to avoid misinformation so we don't pick up false beliefs. We need habits of information hygiene.

Whenever you listen to someone, you absorb some of their thought process and make it your own. You can't help it: that the purpose of language, and that's what understanding someone means. The downside is your brain is a mess of different overlapping modules all working together, and not all of them can distinguish between what's logically true and false. This means learning about the beliefs of someone you violently disagree with can make you start to believe in them, even if you consciously think they're wrong. One acquaintance I knew started studying a religion with the intent of exposing it. He thought it was a cult, and his opinion about that never changed. But at one point, he found himself starting to believe what he read, even though, then and now, he found their beliefs logically ridiculous.

This doesn't mean we need to shut out information from people we disagree with - but it does mean we can't uncritically accept information from people we agree with. You are the easiest person for yourself to fool: we have a cognitive flaw called confirmation bias which makes us more willing to accept information that confirms our prior beliefs rather than ones that deny it. Another flaw called cognitive dissonance makes us want to actively resolve conflicts between our beliefs and new information, leading to a rush of relief when they are reconciled; combined with confirmation bias, people's beliefs can actually be strengthened by contradictory information.

So, as an exercise in information hygiene for those involved in one of those charged political conversations that dominate our modern landscape, try this. Take one piece of information that you've gotten from a trusted source, and ask yourself: how might this be wrong? Take one piece of information from an untrusted source, and ask yourself, how might this be right? Then take it one step further: research those chinks in your armor, or those sparks of light in your opponent's darkness, and see if you can find evidence pro or con. Try to keep an open mind: no-one's asking you to actually change your mind, just to see if you can tell whether the situation is actually as black and white as you thought.

-the Centaur

Pictured: the book pile, containing some books I'm reading to answer a skeptical friend's questions, and other books for my own interest.