GEB is a series of rooms, locks, and keys, and the first of these keys is the concept of a strange loop. Discussing the central musical idea of the work, the “Canon per Tonos” of J. S. Bach's Musical Offerings, Douglas Hofstadter writes,
What makes this canon different from any other [is that] it is so constructed that [its] ending ties smoothly onto the beginning. . . . These successive modulations lead the ear to increasingly remote provinces of tonality, so that after several of them, one would expect to be hopelessly far away from the starting key. And yet . . . the original key of C minor [is eventually] restored.
This mobius strip of a thing, traveling further and further from a point only to arrive there again, Hofstadter calls a strange loop. It is a phenomenon that “occurs whenever, by moving upwards (or downwards) through the levels of some hierarchical system [a tangled hierarchy], we unexpectedly find ourselves right back where we started.”
Strange loops occur in different ways. Hofstadter finds them in the work of M. C. Escher in, for example, “Ascending and Descending” or “Waterfall.” But implicit in all of them, he says, whether they encompass a dozen steps or only one, is the concept of infinity. “What else is a loop,” he writes, “but a way of representing an endless process in a finite way.” The representation of strange loops through modulation of musical keys or in the optical illusion of a waterfall existing on two and three dimensions at once is paradoxical—the conflict between finite and infinite. It smells like a higher mathematics and is, as he continues, a kind of translation of the Epimenides paradox or liar paradox, namely “All Cretans are liars,” when Epimenides himself was from Crete. Epimenides gives us a linguistic paradox. A self-referential statement of language which is neither true nor false. What is it?
Hofstadter goes on quite a while discussion twentieth century mathematician Kurt Gödel's discovery of a strange loop at the heart of mathematics. His description is hard to feel, being read today at the end of a continuum that begins with special relativity, quantum mechanics, and the literary term. Nevertheless “Gödel showed,” he says, “that provability is a weaker notion than truth, no matter what axiomatic system is involved.” If I understand him correctly, he is saying that Gödel discovered at the base and heart of mathematics itself that disorder is the beginning even if order is the end: that language shouldn't make sense, but does. That Escher shouldn't be able to draw his waterfall, but there it is. That Bach can write a canon without end, a canon that cannot be written by formula, a canon whose every note makes sense only as it is nested in a network of contexts and relationships, that “there is something deeper” than “mere fugality.” He scrawls a question mark across Euclid's planes and then asks how it can be done.
So what is Hofstadter after? Why paint a picture of the mystery of meaning arriving from an infinite variety of tangled disorder? Hofstadter is after one mystery: the mystery of intelligence. Where does intelligence come from? And can it arise from systems of logic when such systems exist only as they bracket acceptable possibilities—a bracketing unavailable to real intelligence. Life, the context of human intelligence, is not a bracketed thing. Life is messy and random—infinitely so. There are rules, and then there are rules about rules, and then there are rules for constructing new rules, and so on and so forth. “Sometimes the complexity of our minds seems so overwhelming that one feels that there can be no solution to the problem of understanding intelligence.” And, lest it be missed, Hofstadter is a materialist . . . a materialist face to face with the question of the meaning of life and the challenge of transcendence—which, for him, is not an option. He's painted himself into a metaphysical corner, how shall he escape?
J. S. Bach; intelligence; meaning; Kurt Gödel
Showing posts with label complexity. Show all posts
Showing posts with label complexity. Show all posts
Friday, February 19, 2010
Thursday, June 19, 2008
three scientists
Science, too, stumbles toward religion. The horizon of human imagination and aspiration is just too large and too curious to submit to the narrow confines of a method, measure, rule.
So far I have pointed out the misunderstandings and mischaracterizations that have largely shaped the attitude of religion as it addresses science. Now I would like to survey three voices that come from the other direction; science addressing religion—well, not properly religion, more like faith or ethics. Two of these come from interviews broadcast in 2008 on American Public Media’s radio program “Speaking of Faith.”
The first is "Mathematics, Purpose, and Truth" with author Janna Levin, assistant professor of astrophysics at Columbia University and author of A Madman Dreams of Turing Machines, among other books.
The second is "Science and Hope" with Templeton Prize winner Dr. George Ellis, professor of applied mathematics at the University of Cape Town and a Quaker.
The third is an interview between host Dr. Moira Gunn and biologist and author Stewart Kauffman broadcast 6 June, 2008, on the podcast IT Conversations. The context of their discussion is Kauffman's book Reinventing the Sacred, but the subject is really emergence.
The Conversations
The conversation with Janna Levin centers largely around the following points. (1) Truth goes beyond what mathematics can demonstrate; Kurt Gödel’s incompleteness theorem. (2) How do we know what is real, when our perception is a point along a phenomenological continuum? We don't see the quantum. Our intuition is based on the neurons that have evolved in this world for our purposes. There are no true things that are unambiguously true, save things like 1+1=2. The rest of it is always something we approach without arriving, glimpsing truth out of the corner of the eye. “Every judgment is by its form one-sided and, to that extent, false” (Hegel). (3) How is it that mathematics not only exists, but we can perceive and understand it? (4) Time, determinism, and freedom [16:00], including the existence of free will. I especially like her reminder that we have come through radical changes in worldview since, say, pre-Copernican societies [33:15]. Same for her commitment that existential meaning must be based on truth. Levin is a reductionist, seeing, for example, many of our behaviors as an outgrowth of animal instincts encoded through evolutionary processes. At the same time, she is uncomfortable with this, only too glad to argue for free will in a world of lawful inevitability and subconscious instinct.
George Ellis is a cosmologist and an activist. And in his experience there exists what he calls “deep ethics,”an ethics emerging from the mathematical fabric of the universe. It is there, and no one knows why. As Ellis says, “We haven't got a clue in what way mathematics is embedded there, but it is there in some platonic space waiting to be discovered. We actually haven't got a clue how the laws of physics are embedded in the universe. We know they're there. We know they're effective. We don't know how they are embedded.” This deep ethic emerges whether one wants it to or not. And it is kenotic in nature: it is selfless, it is humble, it serves others. The proof of its existence is “self-authenticating. There is actually no other way of saying it. It is just something you either see or you don't see. There is no proof. It's something you recognize or you don't recognize.”
Ellis says that science has limits. “Science sees nothing about aesthetics or meaning or metaphysics.” Of course, this language evokes the God of the gaps problem. Ellis says, “It’s not the God of the gaps, it’s the God of the boundaries.”
The point about this is that there are boundaries to what science can handle, boundaries science cannot cross. (Not will not [which is the god of the gaps] but cannot.) And one of these important boundaries is ethics. So let's go back to the ethics. There's a whole lot of people out there trying to say, 'Well, ethics is understood by science through sociobiology.' There's another lot of social scientists saying ethics is understood through sociology and psychology and anthropology, and so on. And they are just profoundly mistaken when they say that, for a whole host of reasons. And perhaps we don't want to get technical about this, but the simple way to see how mistaken they are is to ask the following question to a scientist who says 'Look, science can comprehend ethics.' We can use science as a basis for ethics. 'So fine,' we say. 'Tell us what science says we should do in Iraq today.' Then you get this deafening silence because science is totally unable to say anything about that. The reason is there are no experiments in science to do with what is good and what is bad. There are no scientific units for good and bad. There's no experiment. It's just outside the scope of science, not only now, but forever, never ever will be within the bound of science.
And as for the origin of the universe:
My colleagues are producing theories of what they call creation of the universe out of nothing. But when you probe them, you find they're not producing theories of the creation of the universe out of nothing. They are assuming a huge machinery of quantum field theory and fields and particles and interactions, which generates the universe, not the creation of the universe out of nothing.
And, yet, it had to come from somewhere. “In the end, we run into a metaphysical blank, whether you pursue it scientifically or religiously, and you simply have to give up in wonder and awe and say, ‘I don't know the answer, and it's just marvelous the way things are.’”
Biologist and author Stewart Kauffman studies self-organizing systems, pursuing a cosmological position called emergence, which is growing in scientific popularity. What has to be overcome, Kauffman says, is reductionism, of which he outlines three features: (1) Everything that happens is describeable by natural laws. This means that the universe is (2) fundamentally deterministic. Like a computer, once you know the relevant information, then you can predict everything. And finally (3) reductionism is analytic. It says that knowledge is the product of reducing things to their elemental parts. Reductionism has been very successful, it is true, but not without ethical and existential costs. For the reductionist, the universe is made up of unrelated happenings from which no meaning can be abstracted; bare juxtaposition without explanation or narrative.
For this and other reasons, the adequacy of reducationism is being questioned by some within the scientific community. In its place is a platform called "emergence," which asks questions about the nature of the universe from the perspective of pure and infinite complexity. The result: a universe which cannot be completely explained, now or ever, by the fundamental laws of physics. Two nobel laureates in physics are notable enthusiasts: Phil Anderson, who wrote an article in Science in 1972 entitled "More is Different," and Robert Laughlin, whose latest book is entitled, A Different Universe. Like Anderson and Laufman, Kauffman believes that emergence is not only real and demonstrable, but it is a better platform than reductionism for doing science.
Reductionism doesn't work, he says, because complex things cannot be deduced. Reality is so unplottably chaotic, so infinitely complex, that trying to say "this comes from that" is a fool's errand. You can't simulate the development of complex things. In biology, for example, a physicists cannot explain the coming into existence of the heart. Emergence allows for cause and effect, but it throws its boundaries much larger to encompass the unexplainably complex.
This is the basis for Kauffman's critique of darwinian preadaptation. He asks, "Do you think you could say beforehand all the possible darwinian preadaptations of all the organisms now, or just for humans? Can we know all the adjacent possibles?" The answer is, of course, no. "There just isn't a mathematical framework to even try and do this. How would we know we plotted all the adjacent possibles?" Predictability is impossible. There are just too many variables. The future is just too odd.
So, then, Kauffman outlines four implications from emergence.
1. We cannot do what Newton said we should do. We can't specify the laws and then calculate what is going to happen, because we can't know all the adjacent possibles.
2. We can't make probability statements. We don't know all the adjacent possibles, and so we can't plot a sample that would allow us to come up with a probability statement. Nobel laureate Marie Gilmont says that a law is a compact description of the regularities of a process, but can we really do this? The evolution of the biosphere is beyond prediction and beyond the reach of natural law. What we're left with in the biosphere and up through economics is ceaseless creativity. You don't need a creator for this. Every advance through an adjacent possible reshapes the next adjacent possible. The entire matrix of adjacent possibles changes with every step in a way that cannot be predicted.
3. Reason is an insufficient guide for living our life. We have to reunite narrative, allegory, intuition, emotion, and reason. We have to rethink and understand our integrated humanity, throwing aside the split between the two cultures: science and the arts. Science is no longer the only way to get to the truth. History, art, law--lots of things tell us the truth now, not just the scientific method. We need more than just reductionism to help explain things. We live our lives forward, in the face of mystery, not knowing what is going to happen. What does it mean to be fully human in such a world? Kauffman goes on to talk about religion. He takes to task his reductionist friends, such as Richard Dawkins--Enlightenment atheists. What if you take "god" out of the equation and leave creativity, poses Kauffman, hypostasizing creativity. We have lived with creativity and have invented gods to explain it. Indeed, how many gods have we worshipped in human history? God is our most powerful symbol, but it is rife with abuse. "We can choose to use the word "God" if we want to," he says. But it isn't necessary. Instead, we can use "god," not to mean a creator, but to refer to the creativity that itself characterizes and shapes the universe.
4. We need a global ethic. We are connected to everything, emerging along with the rest of the universe. We are caught up in the natural creativity of the universe: which means, to use a religious word, we are all sacred. We need a shared ethic, a global ethic, an ethic that includes all of life and the planet. The secular West is reduced to fairness for friends, love of family, democracy, and free markets, but this is not a global ethic. We are reduced to consumers. We are commoditized. We need an ethic that will help guide the hetero- or homogeneous civilization that is developing. We need to be reconciled to nature. The notion that nature is there to be used by man, the whole purpose of knowledge from a Baconian view, needs to be thrown off. Instead, we need to embrace nature. So can we use this sense of god, and find meaning in it to orient our lives today? Kauffman thinks we can, and that it is as good as any other model of god, and perhaps better, since there is no theodicy issue.
Grammar
So what to do with the above three examples? I hope they serve to show that not only theologians, but scientists are struggling to make sense of the no man's land that exists between too-tidy reductionism and the Wild West of pure fideism. There seems to be a complete lack of any grammatical rules for passing between one side or the other, any schema that allows statements made by one side to be properly heard and evaluated on the other. No one seems to be able to define what governing power a scientific theory should have in the development of doctrine and vise versa (though things have gone unidirectional for a good while.) Can you just equate the big bang, with all its supporting mathematics etc., and Genesis 1.1? (As, for example, William Lane Craig tries to do in this debate with Peter Atkins.) What happens when they turn the Hadron Collider on early next year in Switzerland and discover the whole brane thing is correct and that the big bang is just a temporal phenomenon in a much larger and more complicated universe? Theology risks too much when it latches such and such a doctrine to today's scientific post--but, for all that, it can't just ignore it. And, if the above three physicists say anything about science, it says that scientists, too, cannot avoid the ethical and, yes, religious implications of their work.
Janna Levin; George Ellis; cosmology; religion and science; ethics; Stuart Kauffman; emergence; complexity; evolution; philosophy of science; probability; freedom; kenosis
So far I have pointed out the misunderstandings and mischaracterizations that have largely shaped the attitude of religion as it addresses science. Now I would like to survey three voices that come from the other direction; science addressing religion—well, not properly religion, more like faith or ethics. Two of these come from interviews broadcast in 2008 on American Public Media’s radio program “Speaking of Faith.”
The first is "Mathematics, Purpose, and Truth" with author Janna Levin, assistant professor of astrophysics at Columbia University and author of A Madman Dreams of Turing Machines, among other books.
The second is "Science and Hope" with Templeton Prize winner Dr. George Ellis, professor of applied mathematics at the University of Cape Town and a Quaker.
The third is an interview between host Dr. Moira Gunn and biologist and author Stewart Kauffman broadcast 6 June, 2008, on the podcast IT Conversations. The context of their discussion is Kauffman's book Reinventing the Sacred, but the subject is really emergence.
The conversation with Janna Levin centers largely around the following points. (1) Truth goes beyond what mathematics can demonstrate; Kurt Gödel’s incompleteness theorem. (2) How do we know what is real, when our perception is a point along a phenomenological continuum? We don't see the quantum. Our intuition is based on the neurons that have evolved in this world for our purposes. There are no true things that are unambiguously true, save things like 1+1=2. The rest of it is always something we approach without arriving, glimpsing truth out of the corner of the eye. “Every judgment is by its form one-sided and, to that extent, false” (Hegel). (3) How is it that mathematics not only exists, but we can perceive and understand it? (4) Time, determinism, and freedom [16:00], including the existence of free will. I especially like her reminder that we have come through radical changes in worldview since, say, pre-Copernican societies [33:15]. Same for her commitment that existential meaning must be based on truth. Levin is a reductionist, seeing, for example, many of our behaviors as an outgrowth of animal instincts encoded through evolutionary processes. At the same time, she is uncomfortable with this, only too glad to argue for free will in a world of lawful inevitability and subconscious instinct.
George Ellis is a cosmologist and an activist. And in his experience there exists what he calls “deep ethics,”an ethics emerging from the mathematical fabric of the universe. It is there, and no one knows why. As Ellis says, “We haven't got a clue in what way mathematics is embedded there, but it is there in some platonic space waiting to be discovered. We actually haven't got a clue how the laws of physics are embedded in the universe. We know they're there. We know they're effective. We don't know how they are embedded.” This deep ethic emerges whether one wants it to or not. And it is kenotic in nature: it is selfless, it is humble, it serves others. The proof of its existence is “self-authenticating. There is actually no other way of saying it. It is just something you either see or you don't see. There is no proof. It's something you recognize or you don't recognize.”
Ellis says that science has limits. “Science sees nothing about aesthetics or meaning or metaphysics.” Of course, this language evokes the God of the gaps problem. Ellis says, “It’s not the God of the gaps, it’s the God of the boundaries.”
The point about this is that there are boundaries to what science can handle, boundaries science cannot cross. (Not will not [which is the god of the gaps] but cannot.) And one of these important boundaries is ethics. So let's go back to the ethics. There's a whole lot of people out there trying to say, 'Well, ethics is understood by science through sociobiology.' There's another lot of social scientists saying ethics is understood through sociology and psychology and anthropology, and so on. And they are just profoundly mistaken when they say that, for a whole host of reasons. And perhaps we don't want to get technical about this, but the simple way to see how mistaken they are is to ask the following question to a scientist who says 'Look, science can comprehend ethics.' We can use science as a basis for ethics. 'So fine,' we say. 'Tell us what science says we should do in Iraq today.' Then you get this deafening silence because science is totally unable to say anything about that. The reason is there are no experiments in science to do with what is good and what is bad. There are no scientific units for good and bad. There's no experiment. It's just outside the scope of science, not only now, but forever, never ever will be within the bound of science.
And as for the origin of the universe:
My colleagues are producing theories of what they call creation of the universe out of nothing. But when you probe them, you find they're not producing theories of the creation of the universe out of nothing. They are assuming a huge machinery of quantum field theory and fields and particles and interactions, which generates the universe, not the creation of the universe out of nothing.
And, yet, it had to come from somewhere. “In the end, we run into a metaphysical blank, whether you pursue it scientifically or religiously, and you simply have to give up in wonder and awe and say, ‘I don't know the answer, and it's just marvelous the way things are.’”
Biologist and author Stewart Kauffman studies self-organizing systems, pursuing a cosmological position called emergence, which is growing in scientific popularity. What has to be overcome, Kauffman says, is reductionism, of which he outlines three features: (1) Everything that happens is describeable by natural laws. This means that the universe is (2) fundamentally deterministic. Like a computer, once you know the relevant information, then you can predict everything. And finally (3) reductionism is analytic. It says that knowledge is the product of reducing things to their elemental parts. Reductionism has been very successful, it is true, but not without ethical and existential costs. For the reductionist, the universe is made up of unrelated happenings from which no meaning can be abstracted; bare juxtaposition without explanation or narrative.
For this and other reasons, the adequacy of reducationism is being questioned by some within the scientific community. In its place is a platform called "emergence," which asks questions about the nature of the universe from the perspective of pure and infinite complexity. The result: a universe which cannot be completely explained, now or ever, by the fundamental laws of physics. Two nobel laureates in physics are notable enthusiasts: Phil Anderson, who wrote an article in Science in 1972 entitled "More is Different," and Robert Laughlin, whose latest book is entitled, A Different Universe. Like Anderson and Laufman, Kauffman believes that emergence is not only real and demonstrable, but it is a better platform than reductionism for doing science.
Reductionism doesn't work, he says, because complex things cannot be deduced. Reality is so unplottably chaotic, so infinitely complex, that trying to say "this comes from that" is a fool's errand. You can't simulate the development of complex things. In biology, for example, a physicists cannot explain the coming into existence of the heart. Emergence allows for cause and effect, but it throws its boundaries much larger to encompass the unexplainably complex.
This is the basis for Kauffman's critique of darwinian preadaptation. He asks, "Do you think you could say beforehand all the possible darwinian preadaptations of all the organisms now, or just for humans? Can we know all the adjacent possibles?" The answer is, of course, no. "There just isn't a mathematical framework to even try and do this. How would we know we plotted all the adjacent possibles?" Predictability is impossible. There are just too many variables. The future is just too odd.
So, then, Kauffman outlines four implications from emergence.
1. We cannot do what Newton said we should do. We can't specify the laws and then calculate what is going to happen, because we can't know all the adjacent possibles.
2. We can't make probability statements. We don't know all the adjacent possibles, and so we can't plot a sample that would allow us to come up with a probability statement. Nobel laureate Marie Gilmont says that a law is a compact description of the regularities of a process, but can we really do this? The evolution of the biosphere is beyond prediction and beyond the reach of natural law. What we're left with in the biosphere and up through economics is ceaseless creativity. You don't need a creator for this. Every advance through an adjacent possible reshapes the next adjacent possible. The entire matrix of adjacent possibles changes with every step in a way that cannot be predicted.
3. Reason is an insufficient guide for living our life. We have to reunite narrative, allegory, intuition, emotion, and reason. We have to rethink and understand our integrated humanity, throwing aside the split between the two cultures: science and the arts. Science is no longer the only way to get to the truth. History, art, law--lots of things tell us the truth now, not just the scientific method. We need more than just reductionism to help explain things. We live our lives forward, in the face of mystery, not knowing what is going to happen. What does it mean to be fully human in such a world? Kauffman goes on to talk about religion. He takes to task his reductionist friends, such as Richard Dawkins--Enlightenment atheists. What if you take "god" out of the equation and leave creativity, poses Kauffman, hypostasizing creativity. We have lived with creativity and have invented gods to explain it. Indeed, how many gods have we worshipped in human history? God is our most powerful symbol, but it is rife with abuse. "We can choose to use the word "God" if we want to," he says. But it isn't necessary. Instead, we can use "god," not to mean a creator, but to refer to the creativity that itself characterizes and shapes the universe.
4. We need a global ethic. We are connected to everything, emerging along with the rest of the universe. We are caught up in the natural creativity of the universe: which means, to use a religious word, we are all sacred. We need a shared ethic, a global ethic, an ethic that includes all of life and the planet. The secular West is reduced to fairness for friends, love of family, democracy, and free markets, but this is not a global ethic. We are reduced to consumers. We are commoditized. We need an ethic that will help guide the hetero- or homogeneous civilization that is developing. We need to be reconciled to nature. The notion that nature is there to be used by man, the whole purpose of knowledge from a Baconian view, needs to be thrown off. Instead, we need to embrace nature. So can we use this sense of god, and find meaning in it to orient our lives today? Kauffman thinks we can, and that it is as good as any other model of god, and perhaps better, since there is no theodicy issue.
So what to do with the above three examples? I hope they serve to show that not only theologians, but scientists are struggling to make sense of the no man's land that exists between too-tidy reductionism and the Wild West of pure fideism. There seems to be a complete lack of any grammatical rules for passing between one side or the other, any schema that allows statements made by one side to be properly heard and evaluated on the other. No one seems to be able to define what governing power a scientific theory should have in the development of doctrine and vise versa (though things have gone unidirectional for a good while.) Can you just equate the big bang, with all its supporting mathematics etc., and Genesis 1.1? (As, for example, William Lane Craig tries to do in this debate with Peter Atkins.) What happens when they turn the Hadron Collider on early next year in Switzerland and discover the whole brane thing is correct and that the big bang is just a temporal phenomenon in a much larger and more complicated universe? Theology risks too much when it latches such and such a doctrine to today's scientific post--but, for all that, it can't just ignore it. And, if the above three physicists say anything about science, it says that scientists, too, cannot avoid the ethical and, yes, religious implications of their work.
Janna Levin; George Ellis; cosmology; religion and science; ethics; Stuart Kauffman; emergence; complexity; evolution; philosophy of science; probability; freedom; kenosis
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