Lynn Andrea Stein, "All is Foreknown, But Free Will Is Given” - God and Computers: Minds, Machines, and Metaphysics (A.I. Lab Lecture Series)
FOERST: Yeah. Welcome all to the seventh lecture in the fall series God and Computers: Minds, Machines, and Metaphysics. We are right now in the second part of the series. The first part dealt with what was called the human factor. What is intelligence? What is cognition? And stuff like that.
In the second part, now, we have several case studies where people present their own point of view how they as scientists deal with existential issues within and outside of their research. We had first Federico Girosi from a Christian perspective. Last week there was Francisco Varela from a Buddhist perspective. Today we have Lynn from a Jewish perspective. And next week, we will hear Bijoy Misra from a Hindu perspective.
And then the last two sections deal with, can we rebuild it? And then we will have Ray Kurzweil on spiritual machines and Rosa Picard on building machines which can deny their maker. So in that sense, we are right in the middle today.
And just an announcement, Thanksgiving, we don't have a lecture, of course, one day before Thanksgiving, because I don't expect anyone would come. But if you still want to do something with God and Computers this week, we have on Monday our discussion group at Harvard Divinity School run by Harvey Cox and me. So if you're interested, either write me email. My email address is email@example.com.
Or just come to the Harvard Divinity School, 45 Francis Avenue in the refectory, which is the dining hall sort of stuff. We meet at 12 o'clock. It's in this brochure unfortunately at 1 o'clock, but it's at 12 o'clock. If you're interested in the whole project, I have brochures again, because last week I didn't have them. So pick up a brochure if you're interested in what we are doing.
And now I would very much like to welcome Lynn, Lynn Andrea Stein, who is right now Associate Professor of Electrical Engineering and Computer Science and member of the AI Lab and the Laboratory of Computer Science here at MIT. Lynn has received her PhD from Brown in 1990, and has since then been at MIT. And she worked on a variety of topics.
Beside other projects, she worked on questions of cognitive science and robotics, common sense reasoning, software agents, and human-computer interactions. She has also spoken several times on questions on gender issues for, how is it to be a woman in computer science, and especially at MIT? And her specific interest is [? a question ?] on pedagogy.
She received, beside other awards, like for instance the National Science Foundation Young Investigator award, the Ruth and Joel Spira Teaching Award in 1995. And right now, just won a fellowship of the Bunting Institute at Harvard, where she will continue--
FOERST: Radcliffe. Oh, sorry. Isn't that the same?
FOERST: All right. Where she will continue this research in summer. I met Lynn in 1993 when she was co-teaching a course called Embodiment and Condition together with Rodney Brooks. And despite our different backgrounds and different opinions on a lot of things, we have been since then friends, and often have been involved in very lively debates about the nature of human cognition, the relationship of science and religion, and many more topics.
And in the center of all these discussions stood for her not necessarily a search for a truth, but the attempt to reconcile different approaches to life. And these discussions were also based on the willingness to engage in an open-ended and non-judgmental dialogue. And Lynn is, in my experience, one of the very few people in the lab who makes time to engage a lot in those issues, and I'm very happy that you're here today to share your thoughts with us. Welcome.
STEIN: Hi. I have just a few overheads, and so I'd like it if most of the time we could have the lights be on. That way, I could actually see you as well as having you see me. But for those of you who didn't receive the tremendous publicity that there's been, the title of my talk is All as foreknown, but free will is given.
As Anne mentioned, this talk is very much a case study. That is, I want to tell you about myself and what my perspectives on religion and science are. Sorry. They warned me to stand on this side of the projector.
And I will not, for the most part, be telling you about my work. One thing that is true, both of my work on the whole and my approach to religion is that I believe that stories are really at the center of everything. And so for today, I'd like to tell you the story of my religious perspective and the story to some extent of how I'm affected by that as a scientist, and how I reconcile being a religious person and being a scientist.
Let me start with the title of the talk, because I wrote it thinking one thing, and many read it thinking another. And I found it interesting, and both I hope to do justice to in my talk. When I wrote the title of the talk, or rather, when I choose the title, because it is, after all, a very old quotation, I chose it because of its apparently paradoxical nature, and I find myself, as a religious person and a scientist, enmeshed in such a paradox. And I want to talk to you about my view of paradox, because it affects both my view of religion and my view of reconciling that with my professional life.
But many people told me that they were coming to hear me speak on free will. And so let me tell you that I will touch briefly on the idea of free will. And in fact, I'd like to both begin and end with the paradox. But for the most part, the talk will not be about free will. Those of you who really want to know the details of my belief on free will can corner me after that talk.
So let me begin with free will, because it is the paradox in the title, and point out things both that I knew before and that arose after I chose this as a title. To me, the title is inherently paradoxical in the sense that if all is indeed foreknown, how can it be possible that we have free will? That is, if all is determined, how can we be choosing what we do?
But Anne pointed out to me that this was not originally seen as a paradox. And in fact, if you look at it from a purely religious perspective, it's not clear that there's a paradox here.
So if you take foreknowledge to be independent of how we choose what we do, then there isn't necessarily a paradox at the heart of this statement. It's only when you add in the idea of determinism, which draws largely from the scientific revolution, the idea that if everything is determined, then there can be no choice that this statement becomes a paradox. And so this statement is paradoxical precisely because we choose to apply something of the scientific worldview.
And my interpretation, my reconciliation of this statement is in part to accept the scientific perspective and in part to live outside the scientific perspective. So those are the themes that will run through my talk, the idea of being within the scientific perspective, but at the same time, being outside the scientific perspective.
And the theme of the talk is paradox, and science here is a search for truth. And I want to discuss to what extent that search for truth is a sensible or desirable enterprise.
So let me tell you now about the very first paradox I ever encountered. So the talk is divided into three portions. The first deals with liar paradoxes, a phrase I'll explain to those of you who are not familiar to it. We'll deal essentially with three different phases of paradox.
So the very first paradox that I ever encountered, at least that I ever remembered encountering, something I learned when I must have been about six or eight, some perverse relative told me that every rule has an exception. This seemed OK for a little while, and then I realized that most of the rules I knew had exceptions, so it seemed like a true statement.
Then I realized that so many of the rules I knew had exceptions that it might be that this rule was, in fact, its own exception. And then problem struck. Because after all, if this statement is the sole exception to the rule, every rule has an exception, then it cannot be that it's true, nor can it be that it's false.
So if we assume that every rule has an exception, then there must be an exception to this rule. But if this rule is the exception to the statement, every rule has an exception, then every rule has an exception, and this rule has no exception.
This was my first experience with statements that could not be either true or false. And as you stare at it, the statement flickers back and forth, and you can look at it from either side, but you can't really reconcile the two perspectives.
So here's a visual analog, just for fun. This is a famous figure, which, if you look at the black is a picture of a vase or a cup. But if you look at the white, it's a picture of two faces. And you can see either picture, but you really can't see both at once. And neither account fully describes this picture.
So there's something there that's not true and that's not false. that's not black and that's not white. And that is, in fact, the nature of paradox. And it's not our inability to see beyond it that makes it so. It is true of these statements and these pictures.
There's a name for this particular form of paradox, the every rule has an exception. It's called a liar paradox. And the classical liar paradox is a minor variant on this. This is actually a little closer to a Godel sentence.
But in part of my career, I actually studied some of the formal aspects of paradox, and the statement this sentence is false is as close as I can come in English to the formal logical paradoxes. that I looked at. So this statement cannot be true, nor can it be false. If it were true, then it would be false. And if it were false, then it would be true.
And this statement, or one very much like it, is at the heart of the incompleteness proof for first-order logic. That proof says that no logic can prove-- no logical theory can prove everything which is true in it. That is, there are things which can be true that cannot be proved in logics of a certain power.
And some people have taken that to mean that computers can never be intelligent, because there are things that logics-- and computers are essentially logical machines-- cannot do. Others have taken that as a statement about language. There's something wrong with a logical form of language such that it can't capture what this sentence is about.
Let me tell you about two logical attempts to grapple with this problem, which I learned about from a technical perspective, and which I think are unsatisfying from what one might call a theological or religious perspective. The first is a statement or an argument that this particular sentence is operating at multiple levels, and the reason that this sentence is paradoxical has to do with the levels at which the sentence is operating.
So by saying this sentence is false, that's referring to sort of ground truth flaws. Might call it false subzero. And that statement, because it's a statement at level 0. Is judged true or false at level 1. So this statement might be true at level 1, but false at level 0.
The problem is that if you say that, then you can construct a statement about level 1 and only judge that at level 2, and so on and so on until you get into infinite regress. And although I believe that there's something infinite about the world, I also believe that's not a satisfying resolution. To say the problem is true or false, just exist at so many levels. I mean, they do. Fine. But ultimately for any level, I can tell you a statement that won't be true or false at that level. So there must be something more.
A third alternative or another alternative is to say, the statement isn't true and it isn't false. It is, in fact, something other. And there are multivalued logics which allow for truth values, which are neither true nor false. And then this statement is assigned that other value.
And that gets a little closer to me. That is, I think there's something more than true or false. But in three-valued logics, you can also construct paradoxes. And again, escaping by saying, there's something else, but it is qualitatively the same as these statements that are problematic. It's simply a little different. We'll add a subscript or we'll add an extra truth value.
That seems to me not to get at the heart of what the paradox is about. Instead, I think the reason paradox exists is that truth and falsity are an inadequate dimension against which to judge certain things, and paradoxes are statements that bring home that idea.
Certainly, there are a lot of things in our lives that are neither true nor false. There are things which are true in degrees. There are things which are true in type or [? when ?] [? used ?] qualitatively.
So there are things which are true approximately. My height is 5' 6" or 5' 7", or those are maybe sort of true. I love my husband. Well, that's true, but truth somehow is inadequate to express the particular way I feel about him.
And so in some ways, like the all is foreknown and free will is determined, we're led to paradox in these statements because we look at things through the scientist's eyes. Because we say, true or false ought to be adequate measure for this statement.
But instead, I think-- and I think both as a scientist and as a religious person-- that there is more than truth and falsity. And truth and falsity are notions that we as scientists use to approximate some of those other things. And sometimes they're very powerful notions. But at other times they fall short, and we need to recognize when they fall short.
This idea also implies that there are questions that science can't answer. So I'd like to turn now to paradox is a finite approximation, and some of why science may not be able to answer.
A paradox I learned a little later in my life-- I think I was in high school at the time-- is the paradox that if you take nine tenths and nine hundredths and 90 hundredths, if you take 0.9 and you repeat it an infinite number of times, that is the same as 1. This was a very disturbing paradox for me. Every exception has a rule-- every rule has an exception it was not nearly so disturbing to me. This one really, really upset me.
I remember being at summer camp and lying on a hill, staring up at a starry sky-- and this is such a trite image. I hate to tell you. But lying there, staring up at the stars and thinking, how can this be true? And I guess this shows that I'm an ultimate MIT nerd, because for me, this was a major existential crisis.
But it really, really disturbed me. And let me put up another version of the paradox that I don't like quite as much, but that--
AUDIENCE: Why is that a paradox?
STEIN: Let me tell you Zeno's paradox, which is a variant on this, and then I'll come back to this one. OK? Gerry Sussman yells at me all the time that that was not a paradox, but to me it is. It's as disturbing as any paradox I know.
So this is the mathematical statement of Zeno's paradox. Zeno's paradox is if I want to get from here to there, and in the first instant I go halfway, and in the next instant, I go half of the remaining distance, and then the next instant, I go half of the distance left, and so on, I will never reach my goal. And mathematically, that's the infinite sum of 1 over 2 to the n, which you'll also tell me is not a paradox, that this infinite sum should be 1.
But when you say it in lay language, it sure sounds like it's going to take an infinite amount of time to cross a finite distance, and that's disturbing. I know it's because we're mathematically naive and unsophisticated.
But I think that the heart of both of these paradoxes is the idea-- I'm going to put this one up, because I like it better-- is the paradox of finite approximation.
So if indeed I could somehow encompass the infinity of this number, then I would indeed have reached 1. If I could encompass the infinity of time it would take me to cross halfway from here to there, and so on and so on, I would have reached my goal. But I am a finite being, and I cannot encompass that infinity.
Now I know a mathematical trick to let me pretend that I am. But when I sit down to think about it, I can think of 0.9, or 0.99, or 0.999. But at any time, I can only understand a finite number of those nines. I can only imagine a finite number of steps to reach my goal. And so there is going in me a limit to how far I can go, in spite of the fact that I can think in an objective but nonintuitive way about the infinity of things required to get to some place.
And what I came up with lying on the hillside, staring up at the stars, was a realization that what is in here is a attempt to capture that infinity in a way that was very reminiscent to me of a theological difficulty. In Judaism, we believe that the messiah has not yet come. And in essentially all movements of Judaism, there is a strong belief, wish, desire, that someday the messiah, the mashiach, should come.
Different movements within Judaism have different versions of this goal, this ideal, different imaginings of what it would be like. But in all, there is this yearning for the day that the messiah comes. And on certain holidays, we talk about the coming of the messiah. And this is something that from my youngest days was held up to me as a thing towards which one should aspire.
Now it's also problematic, because if the messiah comes, the world ain't going to be like it is. And although there are some things about the world I'm not very comfortable with, there are some other things that I like.
So even when I was young, I saw this as a problematic notion. And yet, my religion teaches me this is what I should wish for, what I should aspire to. And yet again, there's a story, a midrash-- in Judaism, there are a lot of stories-- there's a story that the messiah will come if every Jew observed Shabbat, one Sabbath. If every Jew observes, then the messiah will come. And yet, get two Jews in a room, you have three opinions. This is not about to happen.
When will the messiah come? Well the messiah to me-- OK, it's a naive, nerd-like notion. The messiah to me is like 0.9 repeating. At any time, we can't be there. We're finite. Our view of the world is finite. I think, scientifically, that the world is finite.
So I will never see the coming of the messiah. I may dream for it, wish for it, but it can't be accessible to me. Nor will my children see it, nor their children, nor any finite number of generations. And yet somehow, in the potential infinity of tomorrows is the coming of the messiah.
So very nerd-like, I told you, but this is me as case study. I feel like I'm under lab glass. On This to me is paradoxical because I can't encompass this infinity. And yet, I know that this is true.
So if this is true, if I'm finite but I live in an infinite world, how do I reconcile being a scientist and being a religious person? And how is it that I put together the fact, the idea that to me, there is something that is more than true and false, and yet as a scientist, I speak in the language of truth and falsity?
Well, there are a lot of things in the world, and some of them are very mysterious. I guess the place to start is to recognize that there are things not only that I don't know, but that I will never know, that I can't know, and yet that must be sought for.
And science is in many ways like adding digits to 0.9 repeating. Science is trying to get a better approximation on the world we know, with the understanding that I won't see 1, and my students won't see 1, and their students won't see 1. And in fact, surprisingly enough, the more you know, the more you know there is to know and you don't know.
And I don't think that's coincidence at all. I think that is, in fact, the nature of the world. There's always further to go. There's always more to do. And that's true from a religious perspective, and that's also true from a scientific perspective.
And accepting that both inspires me, because there's always someplace else to go, and intimidates me, gives me awe in the original sense of the word. I am struck with awe at the magnitude of the task before us. There's a saying, which I learned first as a song. And if I sang any better than Paul, I would sing it for you.
It's not incumbent upon you to finish the work, but neither are you free from attempting it, from trying. And that's a fundamental message of this idea of truth as being the inaccessible infinite. Or maybe truth is the wrong word. But I think that scientific truth is like that as well.
I think that when we build our tower of levels of truth values, we can continue to approximate the truth and falsity of any finite liar paradox, but there will always be a paradox yet remaining. There's always a higher level of the paradox. And the goal of complete understanding is always just outside our grasp.
So to return to the paradox at the beginning of my talk, how is it that I reconcile determinism and free will? Well, for me as a scientist, and in particular in the field of artificial intelligence, in order to engage in an attempt to create an intelligent artifact, I must be-- and indeed am as a professional-- deeply committed to the idea that there is nothing in me that cannot be understood.
But I'm deeply committed to that in the sense that I am deeply committed to 0.9 repeating being 1. If I had infinite time, if I had infinite resources, I must accept that everything in me is physical has an answer. There are questions of measurement. There are questions of certain kinds of combinations that can't be known.
A paradox I chose not to talk about is Heisenberg's. But the idea is that all there is to me could in principle be known. And as a scientist, I am committed to that. As a religious person, I am deeply agnostic about the question of determinism. And in fact, I hope it's not true.
But as a scientist, I accept that perhaps it is knowable. I assume that enough of it is knowable to make my work in attempting to build intelligent creatures, agents, artifacts useful, worthwhile. And I hope that by adding digits to the infinitely repeating number, I'm assisting in the approximation of the truth that may or may not be reachable, just as the messiah may never come in any finite approximation.
So determinism for me is a working hypothesis, in spite of the fact that it doesn't make my everyday life very comfortable. And I reconcile myself with that in part. I don't know if this one copied well enough. That's really not a good copy.
I reconcile that in part by only looking at part of the picture, and I'm all too aware that I do this. After all, if you look at the man on the ladder, he's doing just fine. He's going to climb up onto that balcony. Or if you look at these steps, they lead up to this other balcony. And it's only when you step back far enough to see the hole that you realize that there may be some disturbing inconsistencies here.
Have you seen it? It is, in fact, physically impossible for the building to be so constructed. There's a perspective shift when you go between the first and second levels. But those are perspective shifts that we all make all the time. And sometimes when we're pushed, we even know we make them.
Maybe free will is a post-hoc rationalization of the choices we already made. I actually happen to think that that applies to consciousness. Our conscious thought is a post-hoc rationalization of the things our brain and body did for us, and that particular insight involves some of my work with robots.
If that's the way the world is, it's got these weird inconsistencies in it, it's got these unknowable things, these things we can't ever quite reach, the things that fall between true and false, and we can retain our bearings just by looking at a part of the picture at once, there's something a bit disconcerting about that. And it would be nice sometimes to step back and see the whole thing and be able to accept the whole picture without having this uneasy flitting back and forth, changing of perspectives.
To me, this comes to the question of, what is God? What is that which is not human, bound by the world, physical? And as I said, I am not merely as a scientist a determinist, but a strong materialist even in my nonscientific views. I believe that I am built out of atoms and not eternal immortal soul. I don't accept that there is something inside my body or supervenient on it that is divine. And yet, I believe that there is a God.
I'd like to try to explain to you what I believe God is. And I have to tell you, this is a deeply embarrassing thing for a practicing scientist to get up and do, particularly in front of one's colleagues.
There are certain experiences that are so profound, so deep, so moving, so all-encompassing that I cannot say I had those experiences. I simply was those experiences. Looking back, I can reflect on them. I know I was a part and not the whole of the experience. And yet, during those instants, I was the experience. That night on the starry hill as a teenager was one of them. Childbirth was three of them.
There was a moment in the middle of my wedding ceremony that was one of them. I have very few memories of the actual wedding ceremony, because it was an experience I was so deeply inside that I was the experience. But I'm not going to tell you about some of the other experiences that have been like that.
I've been privileged to have had many experiences like that, though they are instants, points in a huge space of my life. But in those experiences, I came as close as I think it is possible to come to that which is divine. True and false were immaterial notions in those instants. There was no finite approximation to the experience. I was the experience. There was no me separate from the world. It was simply a state of being
perhaps the best description I've heard of this by a theologian is Buber's Thou, though I hate that way of phrasing it. But there is a thing which is so intense that it is overwhelming, and it is not something beyond the physical. If anything, it is more deeply physical. In childbirth, it was so because the pain was so intense and overwhelming that there was no conscious me. I simply was the experience.
I think that is very close to what God is. God is the infinite that makes the finite approximations possible. It is that towards which we strive. It is the coming of the messiah. It is some of what exists between true and false or outside of them. And that notion of God, a naive scientist's notion of God for the theologians in the audience, is to me the thing that is divinity.
Someone asked me in part of a group of religious people, how do you deal with the question of how could God allow the Shoah, the Holocaust? And it was interesting to go around the room and hear different people's answers. But I have to tell you that for me, frankly, that question is a type mismatch. It's one of the few things I can say to scientists in the audience that the theologians hopefully will have to struggle with a little and can't quite look down on me for.
OK. So what is a type mismatch? There are things that you can do with certain kinds of things and not with others, right? It makes sense to talk about whether it's a nice car, a big car, a red car. It doesn't really make sense to talk about whether it's a thoughtful car, a moral car, a valiant car. Those are type mismatches. They are questions that are nonsensical to ask about the artifact.
To me, to ask how God could have allowed the Shoah, how God could have allowed the Holocaust, is a nonsensical question. Given the notion of God I have just described to you, God is not a thing, period, full stop, but God is not anything such that it makes sense for God to have intervened or not intervened, to have permitted or not permitted. That isn't what religion, religiosity, the divine is to me.
So to me, God is that towards which we strive. It is the infinite towards which we are making finite approximations. It is that which lies between and outside true and false.
And there is, again, a Jewish notion. Whether these religious beliefs can be attributed to my Jewish upbringing, I can't say. But certainly culturally, I am a very Jewish person. And there is a notion in Judaism of tikkun olam, completing the world. That is the labor it is incumbent upon us to try.
Why am I a scientist? In the hope and the aspiration that I can help rebuild the world, help to make it complete. But in the full knowledge and understanding that for the world to be complete is beyond any finite approximation, is outside true and false, requires something that science alone does not empower me to achieve, and that no property of my finite mortality can ever get me to.
I just wanted to close with some very, very, very feeble attempts at scientific mysticism. There are some things that look perfectly plausible, and when you look deeper, turn out to be pretty deeply implausible, and this is one of them. And there are other things that just seem like they ought to be impossible, but are common parts of our everyday world. Thank you.
FOERST: We have wonderful time for questions. Do you want to answer them? Or do you want to--
STEIN: Oh, I'll-- [INAUDIBLE].
FOERST: Yeah. That's fine.
STEIN: OK. Sure.
AUDIENCE: I was thinking about Hegel's idea of thesis antithesis. [INAUDIBLE] and antithesis becomes the new thesis, and then there's another antithesis, and [INAUDIBLE].
STEIN: I think that's another example of the impossibility of ever arriving-- the question was a pointer to Hegel's notion of thesis, antithesis, and then synthesis, but synthesis becoming the new thesis. I don't know if people in the back can hear.
But I think that that's another wonderful example, and there are many, of approximating and then moving on. And maybe even completing, and yet somehow not completing. Always leaving a next step. And I know of very few things that can ever truly be called complete. Oh. Right there.
AUDIENCE: So then I'll be honest. I think you pulled a fast one on us, and here's why. You use a computing analogy. I put a lot of faith in something rather fragile. I have years' worth of documents in email that I've consigned to Windows NT.
And you you are the type theorist who comes along. When I ask you the big question in my life-- when will it crash? How will it crash? You tell me, it's type inconsistent. I can't answer that question. It doesn't exist.
And what troubles me is that you've taken what I think are very real dilemmas like the determinism dilemma-- which is not a linguistic dilemma. It's a very mundane and practical one. It's basically, if I am a clock, how can I be blamed for failing a class or not tidying up my bedroom, right? I just ticked away and obeyed my instructions.
And what you seem to have done is to have converted these very real dilemmas into linguistic ones. And it's my impression that the paradoxes you showed, the reason we're comfortable with them is because we somehow can come to terms with them as not being real. They're just linguistic constructs, right?
The notion of abstraction mathematically isn't real-- sorry-- infinity. It's just a mathematical abstraction. And so the fact that the sum of an infinite number of things is finite doesn't bother us because we never face it in real life. But determinism and free will aren't like that.
STEIN: Oh, see, I would say exactly the opposite. I believe very passionately in the reality of infinity. And what was the-- there was an example just before the infinite that you used? After Microsoft, after NT.
AUDIENCE: The clock. I was talking about the clock that can't be blamed.
STEIN: After that. Of the importance of these questions, I think that these questions are tremendously significant. They are tremendously important. And it's not that because their language, they don't bother me. I believe the fundamental truth reality of paradox.
And it really-- it's not that I can brush aside the liar sentence by saying, well, it's just a construct of language. The language gives us the ability to see something that is real, that is almost physical, but is visceral.
And to me, it's not that these things are simply our linguistic misunderstanding. It's that language is giving us insight into the fact that the world is deeply paradoxical. It's deeply, deeply inconsistent. I mean, that's so. And physics gives us the illusion that it's consistent.
So I guess I don't want to brush aside the question of determinism simply because I'm a clock. I mean, maybe a clock can be held responsible. Maybe by reducing things to logical terms we're claiming distinctions that don't really exist, because these things are true. They are real. They are physical.
But I also should say that I'm not trying to proselytize. I have a very bizarre theology, and I don't think you should adopt it if it doesn't work for you. I'm just putting myself under the microscope for you to examine it and laugh.
Though I'm deeply serious about it. You had a question.
AUDIENCE: Related to that, I'm curious why determinism is primarily only a cognitive term rather than also a volitional term. So the paradox is only by adding free will in the second half. But determinism, it seems to me, ought to be volitional.
STEIN: Hmm. So I guess the--
AUDIENCE: Simply to know is how to do.
STEIN: No. To know is certainly not to do. But--
AUDIENCE: So what is deterministic about it then, if I can know all that's deterministic?
STEIN: If I know which slit the photon went through, if I know whether Heisenberg's cat is dead or alive, then if I know and I am right in that knowing, then it's more than just knowledge. It's a fact about the world.
And I guess you could still argue, and I guess I may be arguing that there is more than facts about the world. But to know is not to act, but to know and know rightly is to constrain possibility. And to act is either to open possibility or to foreclose it.
AUDIENCE: And so if I know all about my body in principle-- and I fully agree with that from a materialist perspective-- does that make me determined beyond my-- beyond any other agency that I can explain just within this autonomous, known self?
STEIN: It depends whether I know what is or also how I will change, how it will change. And in all is foreknown, I take i to be not just a knowledge of what is at any instant, but that infinite knowing of now and future evolution. What are the rules that govern the system, to use a very mechanistic term?
But I agree that the paradox comes about in part because of this reduction to the material. Not because I believe there is a realm other than the material, but because we're used to thinking in terms of a material as constraining.
AUDIENCE: And that's sort of an unfortunate bias, in some way.
STEIN: There's a body of mysticism, which is coming into much vogue now called Kabbalah. It's Jewish mysticism. And I aspire someday to study it, but it is forbidden to study the Kabbalah before you're 40.
AUDIENCE: I loved the fact that you're giving a technical definition [INAUDIBLE], so I'm going to try to impress you on that. I thought that what you were getting at with these infinities was that the divine is closer to infinity, something you can never get to. But then when you describe God, your experience of God, my technical way of stating that, I would say that you weren't aware of the the meta. The meta makes you aware of your consciousness, or being in meta makes you aware of something in the ground level.
But you were expressing experiences in which the meta went away, and you were just strictly at ground level. That's the way I would characterize it. You may differ with that. But if that's the case, then I don't understand how that could be the definition of God, given that you were building up to it as this infinity thing, this abstraction of infinity.
STEIN: Well, first of all, I hope I didn't say I was defining God, because I don't know that I can. I was attempting to describe. But second, I think that your idea of the meta is a very evocative one.
For most of my life, not only am I having experiences, but I'm watching myself have these experiences, and I'm watching myself watching myself have these experiences. And I don't usually operate on all of those different levels. And yet any time I want, I have access to all of those levels.
And what happens in those moments where I am the experience is exactly a collapse of that infinite regression, or a potentially infinite regression. There is only the experience. There is no me outside the experience to be watching. And so that if me outside the experience watching is the incomplete fraction, in some ways, then being the experience is exactly that kind of collapse into the infinite.
But I also think I said that that was as close to experiencing the divine as I could come, and I don't know if it is possible to experience the divine. I only know that for me, those moments have been transcendent.
AUDIENCE: Lynn, does laser coherence capture some of your thought? I believe it's--
STEIN: I don't know enough about laser coherence to answer that question.
AUDIENCE: That all your states are in-- come together rather than being distinct.
STEIN: Perhaps. I just don't know enough about the technical end of the subject to know whether I feel it does justice to the metaphor. And these are, after all, only metaphors. Paul?
AUDIENCE: I thought your use of a paradox in order to point out things that were very beyond reason or beyond logic was very interesting. [INAUDIBLE] it [? seems to me ?] [? personally ?] a type error [INAUDIBLE] that you accused other people of doing. As a scientist, I should think you would probably not want to make statements about things that are not observant.
And what you're talking about, when you take a 0.99999, pretty soon you get to a point where there is no conceivable way that you will ever observe the difference between that. There's a continuity involved in mathematics between that 0.999 and a 1, and the error is actually measurable and very small. You are trying-- at some point, your measurement is impossible to distinguish those two, and therefore, they become, from a scientific point of view, the same concept, the same construct, and you should not worry about whether one's infinitely different than the other.
It seems to me that your other examples also fail to-- you're attempting to get a discrete interpretation of what is basically a continuous situation. The liar's paradox, the simplest form of which is I lie-- that's the simplest form of that paradox-- has an exact analogy in logic where you take an inverter and connect the output to the input.
And that's the question, well, does 0 equal 1, or does 1 equal 0? And we all know as engineers that that's a type error in the sense that you've taken the digital abstraction and you have violated it. And naturally, something outside of the digital action's going to happen, so the thing sits there and oscillates or does some other thing.
I don't know why these paradoxes that you have can't have similar interpretations. You just admit that the statement, this sentence is false, is an approximation to something vastly more complex. And depending on what you think of as an approximation to, the resolution of the paradox would differ in those ways.
And so it seems to me that by choosing a paradox as your mechanism for getting at God, you are violating your own rule as a scientist to avoid things which are unmeasurable. And therefore, you've placed God in a role of things that are unmeasurable in some [INAUDIBLE] sense.
STEIN: Well, certainly I think God is unmeasurable. But there are so many things I want to say to that. To begin with, while I'm bearing my soul, scientist really isn't the phrase I'd like. I have aspirations to be an applied philosopher, although I hear that term has been co-opted by the medical ethicists.
But I in fact am deeply concerned not just with the physical, but with the metaphysical. And I think that given that, it's easier to understand why your measurement error isn't, for me, a satisfactory resolution. I could always build a better measuring device. I might never-- for any measuring device, there would be an unmeasurable small error, but there would always be a better measuring device.
AUDIENCE: Not when you've used all the atoms in the universe.
STEIN: Not yet, when we've used all the atoms in the universe. Maybe we can-- I mean, maybe we can use them more efficiently. Maybe we can engineer smaller devices. Science is in part about what isn't yet possible, but will be someday. And so maybe not. Maybe there will be something that is so small as to be immaterial. And yet as a philosopher, I'll know it's there.
And the sun will probably explode first, and so this whole conversation, this whole line of argument is moot. But still, I'm concerned with what is so as much as with what is measurable.
As to the logical paradoxes like the liar sentence, in English, we can talk about its being a finite approximation to something much more complex, but I can state the Godel sentence, and I can't look at that as a finite approximation to something more complex. It is outside the notion of provable in the case of the Godel sentence. I can state things.
And in a former life, I lived in a world of logic, and I do see that the logical analogs of these paradoxes is deeply problematic in what they say about truth and falsity. And if you believe logic to be attempting to approximate those notions, or really attempting to get a handle on those notions, there is something beyond.
And that seems to me to be true of the world, but that's something I say on faith, and I can't prove to you scientifically. There are a lot of other things, but let me give some other people chances to ask questions.
AUDIENCE: As an AI researcher, though, when we talk about these various paradoxes and [INAUDIBLE]. The question is, though, is when we [INAUDIBLE] a complete system [INAUDIBLE] AI, [INAUDIBLE] system, we build that system, and at that point, we have continual knowledge, as a researcher [INAUDIBLE] that we're talking about, and that we can go in and [INAUDIBLE] at any point and then we can look [? to see if ?] the system, however complex it might be.
At that point, there becomes this question of-- and I don't mean this in the creation sense, but in the infinite sense, you know, well, did we just become God in the sense that we have infinite knowledge in respect to the system? Or since this system doesn't have this infinite expanse, is it really alive or intelligent?
STEIN: Spoken like a man who's never had trouble programming his VCR. As someone who quite often has trouble getting my audio-visual equipment to work, only to discover that it's not plugged in, I don't assume that I have complete knowledge of the system. Whether or not it's infinite knowledge depends on what you want to define as finite and infinite, and what dimensions you want to take.
I question your premise to begin with, that having built the system, we therefore have complete knowledge of it. But even should I accept that question, I think that there is more that is needed in order to address the questions of whether it could be alive, whether it could be conscious, et cetera.
So simply the fact that I've created something certainly doesn't bear on whether it could be alive or not alive. There's very little that went on in the creation of my children that didn't directly and viscerally involve me, and yet they are certainly alive. And there are other things I create in s different fashion that are certainly not alive. Big question outside the scope of this talk.
AUDIENCE: I was going to say that the illustration of the Escher drawing, talking about your paradoxical nature, I wouldn't say that's a paradox so much as it's sort of an interesting circumstance or [INAUDIBLE] when we project a three-dimensional object onto a two-dimensional representation. You couldn't create a three-dimensional sculpture, say, that had those same properties that the picture seems to have. So yeah, the two-dimensional representation, it comes up with this quirks, but that doesn't mean that our three-dimensionality is flawed because we can draw this picture. That means the two-dimensionality is not the end-all as far as capturing that.
And I guess I would make kind of a really large-- lead by analogy and say that human, like, language or human understanding as a whole is only going to be an approximation to the nature of the world. The idea that all the computing power we have available can't predict what's going to happen in a cubic inch of water or something.
And you know, it's just a mathematical or kind of a logical fact that you can't know everything about every atom or every particle in the universe, because you need a whole, like, shadow thing to hold all that information. And so it's a different kind of dimensionality collapse. Our understanding of things naturally has to be an approximation, or we can't be those particles, or we can't be the AstroTurf or a planet or something.
STEIN: Language and visual [INAUDIBLE] as well are all finite approximations and inadequate, in general, approximations of the entirety of that which they attempt to represent.
AUDIENCE: [INAUDIBLE] we know that's always going to happen. But then to around and say, oh, like, there's always going to be this gap, but I choose at this very high level-- like, the difference-- the split between two-dimensionality and three-dimensionality, I'm not going to call that God. But the split between my cognition and the sheer physicality, you know, of material things, I'm going to call that God.
STEIN: That which is beyond all approximations that we have. Beyond the approximation the physical world is to something, beyond the approximation our cognition is to something. But you're right. It's perhaps arbitrary to point a finger and say, there is God. But all I can do is represent.
FOERST: Yeah. We have to finish, unfortunately, because I don't want my speakers to be overwhelmed by more than 20 minutes' questions and grilling.
Thanks, you all, so much for coming, and I hope to see you next week.