I came from a different tradition of thinking, via Hugh Everett and Karl Popper, in their different ways. Both of them insisted that scientific theories are about what is really there and why observations come about, not just predicting what the observations are. Therefore, I couldn’t be satisfied with just an operational version of quantum mechanics.
I had to embrace the Everett, or many-universes, interpretation of quantum mechanics from the present point of view. The key thing about that is that it’s a realistic theory, as the philosophers say. That is, it’s a theory that purports to describe what really happens rather than just our experiences of what happens. Once you think of quantum theory that way, it’s only a very small step to realizing, first of all, that computation is the quantum theory of computation, which was my earlier work, and then that the quantum theory of computation is not sufficient to provide the foundation for the whole of physics. So, what’s the rest? Well, the rest is constructor theory.
What’s needed in constructor theory is to express it in terms that can be integrated with the rest of physics, formulas, equations, because only then can it make contact with other scientific theories. The principles of constructor theory then constrain the laws of other theories, which I call subsidiary theories now. The constructor theory is the deepest theory, and everything else is subsidiary to it. It constrains them, and that, then, leads to contact with experiment.
The key thing to do, apart from guessing what the actual laws are, is to find a way of expressing them. The first item on the agenda, then, is to set up a constructor-theoretic algebra, which is an algebra in which you can do two things. One is to express any other scientific theory in terms of what transformations can or cannot be performed. The analog in the prevailing formulation of physics would be something like differential equations, but in constructor theory it will be an algebra. And then to use that algebra also to express the laws of constructor theory, which won’t be expressed in terms of subsidiary theories. They will just make assertions about subsidiary theories.
Chiara Marletto, who’s a student I’m working with, and I are working on that algebra. It’s a conceptual jolt to think in terms of it rather than in the terms that have been traditional in physics for the last few decades. We try and think what it means, find contradictions between different strands of thought about what it means, realize that the algebra and the expressions that we write in the algebra don’t quite make sense, change the algebra, see what that means and so on. It’s a process of doing math, doing algebra, by working out things, interleaved with trying to understand what those things mean.
This rather mirrors how the pioneers of quantum theory developed their theory, too. In fact one of the formulations of quantum theory—namely, matrix mechanics, as invented by Heisenberg and others—isn’t based on the differential-equation paradigm but is more algebraic, and it, in fact, is another thing that can be seen as a precursor of constructor theory. We haven’t yet succeeded in making a viable algebra, but even with the rudimentary form of it we have now, we’ve got some remarkable results—this was mainly done by Chiara—which have almost magically provided a deeper foundation for information theory than was possible within physics before.
Like all fundamental theories, it’s difficult to predict what effect they will have, precisely because they’re going to change things at a fundamental level. But there’s one big thing I’m pretty sure the constructor-theoretic way of looking at physics has to offer our worldview in terms of everyday life—and that is optimism. “Optimism,” in my terminology, doesn’t mean expecting that things will turn out well all the time. It’s this very specific thing that I think captures the historical, philosophical trend of what optimism has meant if you remove the nonsense. Namely, the optimistic view is not that problems will not occur but that all problems and all evils are caused by lack of knowledge. And the converse of that is that all evils are soluble, given the right knowledge. And knowledge can be found by the methods of conjecture, criticism, and so on, which we know is the way of creating knowledge.
Although this sounds like a statement at a very human level, because it’s about knowledge and evils and being able to do things, and so on, it’s directly linked with constructor theory at the most fundamental level, because of the fundamental dichotomy in constructor theory, which claims that the whole of science is to be formulated in terms of the difference between transformations that are possible and those that are impossible and there isn’t a third possibility. That’s the thing. The whole thing doesn’t work if there’s a third possibility.
If a task, a transformation, is impossible, then constructor theory says it must be because there’s some law of physics that makes it impossible. Conversely, if there isn’t a law of physics that makes it impossible, then it’s possible. There’s no third possibility. What does “possible” mean? In the overwhelming majority of cases, though some things are possible because they happen spontaneously, things that are possible are possible because the right knowledge embodied in the right physical object would make them happen. Since the dichotomy is between that which is forbidden by the laws of physics and that which is possible with the right knowledge, and there isn’t any other possibility, this tells us that all evils are due to lack of knowledge.
This is counterintuitive. It’s contrary to conventional wisdom, and it’s contrary to our intuitive, or at least culturally intuitive, way of looking at the world. I find myself grasping for a third possibility. Isn’t there something that we can’t do even though there’s no actual law of physics that says we won’t be able to do it? Well, no, there can’t be. This is built into constructor theory. There’s no way of getting around it, and I think once you’ve seen that it’s at the foundations of physics, it becomes more and more natural. It becomes more and more sort of obvious, in the sense of “It’s weird but what else could it be?”
It’s rather like the intuitive shift that comes from realizing that people in Australia really are upside-down compared with us, and they really are down there through the Earth. One can know this intellectually, but to actually think in those terms takes an effort. It’s something that we all learn at some point to accept intellectually if we’re rational. But then to incorporate that into our worldview changes us. It changes us, for instance, because whole swaths of supernatural thinking are made impossible by truly realizing that the people in Australia are upside-down. And, similarly, whole swaths of irrational thinking are made impossible by realizing that, in the sense I’ve just described, there is no third possibility between being able to do it if we have the right knowledge and its being forbidden by the laws of physics.
The stereotype of how new ideas get into fundamental science is: First, somebody has the idea. Everyone thinks he’s crazy, and eventually he’s vindicated. I don’t think it happens like that very often. There are cases where it does, but much more often—and this is my own experience, when I’ve had new ideas—it’s not that people say, “You’re crazy; that can’t be true.” They say, “Yes, that’s nice, well done,” and then they go off and ignore it. And then, eventually, people say, “Oh, well, maybe it leads to this,” or “maybe it leads to that,” and “Maybe it’s worth working on. Maybe it’s fruitful,” and then eventually they work more on it.
This has happened in several of the things that I’ve done, and this is what I would expect to happen with constructor theory. I haven’t had anyone tell me that this is crazy and it can’t be right, but I’m certainly in the stage of most people, or most physicists, saying, “Well, that’s nice. That’s interesting. Well done,” and then going away and ignoring it.
No one else is actually working on it at the moment. Several of our colleagues have expressed something between curiosity and substantial interest, which may well go up as soon as we have results. At the moment, there’s no publication. I’ve submitted a philosophical paper, which hasn’t even been published yet. When that comes out, it’ll get a wider readership. People will understand what i
t’s about, but while in philosophy you can write a paper that just has hopes in it, or interpretations of things, in physics you need results. When we have our first few papers that have results, I think that an exponential process of people working on it will begin—if it’s true. Of course, it might be that some of these results are of the form “it can’t be true,” in which case it will end up as an interesting footnote to the history of physics.
I had to write the philosophical paper first because there’s quite a lot of philosophical foundation to constructor theory, and to put that into a physics paper would have simply made it too long and, to physicists, too boring. So I had to write something that we can refer to. It’s the philosophical paper first, and then the next thing was going to be constructor-theory algebra, which is the language and formalism and showing how both old laws and new constructor-theoretic laws can be expressed. But now it’s likely that the first paper on constructor theory will be constructor-theoretic information theory, because it’s yielded unexpectedly good results there.
We’re talking about the foundations of physics here, so the question is whether the theory is consistent, whether it’s fruitful, whether it leads to new discoveries. These foundational theories are of interest to people who like foundational theories, but their usefulness comes in their fruitfulness later.
Quantum theory is, again, a very good example. Almost nobody was actually interested in quantum theory except a few people who work on the foundations of quantum theory. But now several decades after its discovery, everybody who works on microchips, or everyone who works on information or cryptography, and so on, has to use quantum mechanics; and everybody who wants to understand their position in the universe—what we are—has to take a view of what quantum theory tells us about what we are.
For example, you have to take a view about whether it’s really true that we exist in vast numbers of parallel copies, some of them slightly different, some of them the same, as I think quantum mechanics inevitably leads to—or not. But there’s no rational way of not taking a position on that issue. Although apart from the issue of optimism, which is an unexpectedly direct connection to the everyday level, we can’t tell at the moment what constructor theory will tell us about ourselves and our position in the universe, and what every reasonable person should know, until we work out what the theory says—which we can’t do until we work it out properly within the context of theoretical physics.
I’m interested, basically, in anything that’s fundamental. It’s not confined to fundamental physics, but for me that’s what it all revolves around. In the case of constructor theory, how this is going to develop totally depends on what the theory turns out to say, and even more fundamentally whether it turns out to be true. If it turns out to be false that one cannot build a foundation to physics in the constructor-theoretic way, that will be extremely interesting, because that will mean that whole lines of argument that seemed to make it inevitable that we need a constructor theory are actually wrong, and whole lines of unification that seem to connect different fields don’t connect them, and yet therefore they must be connected in some other way, because the truth of the world has to be connected.
If it turns out to be wrong, the chances are it will be found to be wrong long before it’s falsified. This, again, is the typical way of scientific theories. What gets the headlines is if you do an experiment and you predict a certain particle and it doesn’t appear and then you’re proved wrong. But actually the overwhelming majority of scientific theories are proved wrong long before they ever get tested. They’re proved wrong by being internally inconsistent or being inconsistent with other theories that we believe to be true, or most often they’re proved wrong by not doing the job of explanation they were designed to do. So if you have a theory that’s supposed to, for example, explain the second law of thermodynamics and why there is irreversibility when the fundamental laws of physics are reversible, and then you find by analyzing this theory that it doesn’t actually do that, then you don’t have to bother to test it, because it doesn’t address the problem it was designed to address. If constructor theory turns out to be false, I think it’s overwhelmingly likely that it will be by that method—that it just doesn’t do this unification job, or foundational job, that it was designed to do.
Then we would have to learn the lesson of how it turned out to be wrong. Turning out to be wrong is not a disgrace. It’s not like in politics, where if you lose the election then you’ve lost. In science, if your idea that looked right turns out to be wrong, you’ve learned something.
One of the central philosophical motivations for why I do fundamental physics is that I’m interested in what the world is like—that is, not just the world of our observations, what we see, but the invisible world, the invisible processes and objects that bring about the visible. Because the visible is only the tiny, superficial, and parochial sheen on top of the real reality, and the amazing thing about the world and our place in it is that we can discover the real reality.
We can discover what’s at the center of stars even though we’ve never been there. We can find out that those cold, tiny objects in the sky that we call stars are actually million-kilometer, white, hot, gaseous spheres. They don’t look like that. They look like cold dots, but we know different. We know that the invisible reality is there giving rise to our visible perceptions.
That science has to be about that has been for many decades a minority and unpopular view among philosophers and, to a great extent, regrettably even among scientists. They have taken the view that science, just because it’s characterized by experimental tests, has to be only about experimental tests, but that’s a trap. If that were so, it would mean that science is only about humans, and not even everything about humans but about human experience only. It’s solipsism. It’s purporting to have a rigorous, objective worldview that only observations count, but ending up by its own inexorable logic as saying that only human experience is real, which is solipsism.
I think it’s important to regard science not as an enterprise for the purpose of making predictions but as an enterprise for the purpose of discovering what the world is really like, what is really there, how it behaves and why. Which is tested by observation. But it’s absolutely amazing that the tiny little parochial and weak and error-prone access that we have to observations is capable of testing theories and knowledge of the whole of reality, which has tremendous reach far beyond our experience. And yet we know about it. That’s the amazing thing about science. That’s the aspect of science that I want to pursue.
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A Theory of Roughness
Benoit Mandelbrot (1924–2010)
Mathematician, Yale University; author, The Fractal Geometry of Nature, d. October 14, 2010
INTRODUCTION by John Brockman
During the 1980s, Benoit Mandelbrot accepted my invitation to give a talk before The Reality Club. The evening was the toughest ticket in the ten-year history of live Reality Club events during that decade; it seemed like every artist in New York had heard about it and wanted to attend. It was an exciting, magical evening. I stayed in touch with Mandelbrot and shared an occasional meal with him every few years, always interested in what he had to say.
He didn’t make it easy. While his ideas were complicated but understandable, his French accent could make comprehension more difficult. His death in 2010 was a blow to anyone who values individuals who dedicate their lives to a scientific observation of the natural world. While the inclusion of this conversation in a book about the universe might seem tangential to some readers, it is in part a tribute to him and to his tireless capacity for what our efforts to understand the universe require: Reinvention.
Mandelbrot is best known as the founder of fractal geometry, which impacts mathematics, diverse sciences, and arts. Here he continues to push the envelope, with his theory of roughness. “There is a joke that your hammer will always find nails to hit,” he says. “I find that perfectly acceptable. The hammer
I crafted is the first effective tool for all kinds of roughness and nobody will deny that there is at least some roughness everywhere.”
A Theory of Roughness
There is a saying that every nice piece of work needs the right person in the right place at the right time. For much of my life, however, there was no place where the things I wanted to investigate were of interest to anyone. So I spent much of my life as an outsider, moving from field to field, and back again, according to circumstances. Now that I near eighty, write my memoirs, and look back, I realize with wistful pleasure that on many occasions I was ten, twenty, forty, even fifty years ahead of my time. Until a few years ago, the topics in my PhD were unfashionable, but they are very popular today.
My ambition was not to create a new field, but I would have welcomed a permanent group of people having interests close to mine and therefore breaking the disastrous tendency toward increasingly well-defined fields. Unfortunately, I failed on this essential point, very badly. Order doesn’t come by itself. In my youth I was a student at Caltech while molecular biology was being created by Max Delbrück, so I saw what it means to create a new field. But my work did not give rise to anything like that. One reason is my personality—I don’t seek power and do not run around. A second is circumstances—I was in an industrial laboratory, because academia found me unsuitable. Besides, creating close organized links between activities which otherwise are very separate might have been beyond any single person’s ability.
The Universe_Leading Scientists Explore the Origin, Mysteries, and Future of the Cosmos Page 35