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Symmetry provides a Turing-type test for 3D vision Zygmunt Pizlo Psychology, Purdue Will robots be smarter than we are? • Soon? • Ever? Can robots even hope to be smarter than we are? • If we want to answer this question, we must first find a way to determine whether robots actually have minds, and if they do, what’s in them? • Note that a robot CANNOT produce what looks like smart behaviors if it has no mind. – Having mind means, at the very least, that one keeps and uses a representation (a model) of the external environment and events. – There isn’t time to explain this now, so just take my word for it. Can robots have a mind and be intelligent? • This is one of the oldest questions in Artificial Intelligence. It started with Alan Turing: – (see the recent movie “The imitation game”) • Turing (1950) proposed a simple test to determine whether computers can think, and show signs of having intelligence: – do this by simply “talking” with a person or a computer via email and see whether you can tell the difference between talking with the person and with the machine. How good is Turing’s test? • Searle (1980), a Philosopher of Mind, criticized Turing’s test in his “Chinese room” argument in which: – having a set of rules that allow one to produce responses in Chinese to questions in Chinese, in itself, does not imply understanding what is being said. – there is also no reason to believe, or to claim, that a Googletype translator understands what is being said. • Searle went even further when he said that computers and robots will never be intelligent, as we humans are, because contemporary computers are made of transistors (physical), not neurons (biological) stuff. • I will return to Searle’s claim that there can be no intelligence in a robot made from physical stuff after examining Searle’s observation that it is impossible to be sure of what is actually in someone’s mind simply by observing his behavior. – Take four examples. Color perception We can verify experimentally whether an observer (human or robot) can tell different colors apart. So, we can know that both observers have different “percepts” when presented with red and green, but we will probably never know what either observer actually sees when she/it looks at red or green. Detecting a Lie • When I tell you which of two works of art I like more, you cannot easily, if at all, determine whether I am telling the truth. Weissman Gradus Observing Thinking During Problem Solving • A student is presented with a difficult problem, say, construct a triangle given its perimeter, the angle at one vertex and the length of the altitude drawn from this vertex. – This student does nothing for quite a while. Was she thinking about this problem or about the failing grade she is surely going to earn? • Note that neither “Deep Blue” nor “Watson”, two recent successes of AI, can even begin trying to solve this problem. Now, let’s consider an example where it is not only possible, but actually easy to uncover the state of somebody’s mind. Any observer looking at an animal, like this cat, says that he sees a symmetrical animal. We know that he perceives symmetry because we can demonstrate experimentally that he can tell when two halves of an object are the same or different. So, we can know that symmetry is in his mind when he looks at a symmetrical object. Symmetry connects physical, biological and mental events • The cat is actually symmetrical, so symmetry exists both in the biological world (the animal’s body) and in the mental world (the observer’s percept). • If we want to extend this argument to robots, which are made of physical stuff, we must show that symmetry exists in the physical world, as well: – Remember Searle’s argument that robots will never be like us because their CPU (the robot’s brain) is made of transistors, not neurons, like our brain. Symmetry does exist in the physical world. • Atoms and compounds are symmetrical: – Take carbon, C, the basis of organic chemistry, Astronomy • Stars and planets are symmetrical, too. Crystals are characterized by their symmetries Snowflakes have multiple symmetries – they are ice crystals Forces – Earth’s gravity is symmetrical Electric fields are symmetrical Plants are symmetrical, too. Thepotter_2006 And so are animals Butterfly Hunter Actually, almost all animals are symmetrical. I only know of one that is not, the fiddler crab. Your brain is symmetrical – you have two similar hemispheres Your DNA is symmetrical, too. Symmetry is ubiquitous. We find it everywhere we look! For the record: • the concept of symmetry is much more general than I illustrated up to now, but • what I showed you should be sufficient to support the rest of my story. Symmetry provides building blocks: • for physical, biological and mental phenomena. • So, symmetry does not belong exclusively to any of these worlds. • Symmetry can be considered the “neutral stuff”, in the terminology used by Baruch Spinoza, Gustav Theodor Fechner, William James, and Bertrand Russell. • Whether we observe physical, biological or mental (cognitive) symmetry simply depends on the observational tools we choose to use: – Perceiving a cat, vs. describing its body, vs. describing the carbon compounds in the individual cells. Sadly, Searle ignored the concept of symmetry entirely • and so did everyone else in the fields called Philosophy of Mind, Artificial Intelligence, as well as in popular science. • Transistors are very different physically than neurons, but symmetry resides in both. • Furthermore, symmetry makes it possible to compare a computer’s CPU and a human’s mind in a meaningful way. • In fact, symmetry is the essential feature of both. All of the remaining features are probably unimportant or superficial, at best. But there is even more… • I will now take two important additional steps in making my comparison of physical stuff (robots) and human beings. Physics is based on 3 Fundamental Principles. • Symmetry – just discussed. • A Least-action Principle. • Conservation Laws. • All three can, and should, be applied to the analysis of cognitive phenomena because this gives us a more complete understanding of what we mean by intelligence. Examples of Conservation Laws in Physics • Conservation of: – Energy – Momentum – Angular momentum –… – There are many conservations in physics. – I will illustrate only two. Conservation of momentum • https://www.youtube.com/watch?v=4IYDb6K5UF8 • Collision is a transformation. – Things are different after and before the transformation: – Speeds change and directions of motion change, too. • But some things (here momentum) are “conserved”. Conservation of angular momentum • Pirouette • A pirouette is a transformation. – Things change during the pirouette – Angular velocity – Distances of the body parts from the axis of rotation • But angular momentum is conserved. Can we talk about conservations in 3D vision? 3D percept from a single 2D image The world is 3D, the retinal image is 2D, and the percept is 3D. The 3D shapes of objects are conserved. 3D vision as a conservation • An observer looks at a 3D object: – There is a transformation of the physical object into the object’s representation in the observer’s mind. • First, the 3D shape is transformed into 2D retinal image by the rules of optics. • Second, the observer’s visual system infers the 3D shape from the 2D retinal image. – The observer knows that’s there… • If the perceived (inferred) 3D shape is identical to the geometrical shape of an object, then we can talk about conservation of shape. What is the nature of this inference? • Can a robot infer something? • If it can, is this inference human-like? We need the third Fundamental Principle of Physics, the least action principle to answer this question: • In perception and cognition, it is called the simplicity principle. • In Philosophy of Science, it is called Occam’s razor, and • In Information Theory it is called a Minimum Description Length principle. Ames's chair • Demo: http://shapebook.psych.purdue.edu/1.3/ • The 3D geometrical configuration we call a chair is the simplest interpretation (here by simplest we mean symmetrical). • It turns out that this simplicity principle leads to veridical percepts, which are conservations. Shape veridicality • Veridicality means that we see things the way they are “out there.” • Demos: http://shapebook.psych.purdue.edu/1.2/ • You see these shapes veridically and so does our robot. • In both cases, shape veridicality is produced by the least action principle, called simplicity. The Simplicity principle works the same way in all other aspects of 3D vision, including the perception of 3D scenes. The simplicity principle in 3D vision is completely analogous to the least action principle in Physics • Two examples: – Optics. – Electricity Fermat’s Principle • Light “chooses” a trajectory that minimizes time of travel. Kirchhoff's Laws for circuits • Current divides itself in such a way so that the total amount of heat generated in resistors is minimal. The least action principle is the link • between symmetries in nature and conservations. • It turns out that every conservation in Physics is a consequence of applying the least action principle to the symmetry of a natural phenomenon (Nöther’s, 1918, theorem). • Examples: • Time symmetry – conservation of energy. • Space symmetry – conservation of momentum. 3D vision in a nutshell • A simplicity (least action) principle is applied to the image of… • symmetrical objects, resulting in… • veridical 3D vision (the conservation of 3D shape) • Recall the 3 fundamental principles of Physics: – A least-action principle is applied to… – the symmetry of a phenomenon, resulting in – a conservation law. Can this approach be extended beyond 3D vision? • Almost certainly. – Language, problem solving, data mining… • There is always enough structure and regularity in these cognitive functions to allow symmetries (invariances) to be defined. • Once symmetries exist, the next challenge is to define a simplicity principle to allow something meaningful to be inferred. • This will lead to conservations that provide the key to understanding how the mind is related to the outside world and to other minds. Summary • Nöther (1918) showed that without a least-action principle there would be no conservations in Physics. • Wigner (1960), a Nobel prize winner in Physics, pointed out that without symmetries there would be no Laws of Nature. • I am suggesting that without all of these three principles, namely, symmetry, least action and conservations, there would be no human mind as we know it, and no intelligence. – We wouldn't be able to understand the environment and each other. What does this mean for the intelligence of robots? • If a robot does not use these 3 principles, it cannot be smart. • If the robot uses these principles, we will understand the robot’s mind. • Our natural sciences do not offer any magical 4th principle that would allow a robot to be smarter than we are. – So, a “singularity”, defined as super-intelligent robots, that is, robots too smart for us to comprehend them, is not likely to happen. – If it does happen, it is not likely to be an elaboration of currently existing AI systems. Conclusion • The important issue is not whether superintelligent robots are possible, that is, the issue addressed in this lecture series. • The really important issue is that the 3 fundamental principles now used to establish the merit of the hard sciences, namely, symmetry, least-action and conservations, provide a formalism that can be used both to explain the human mind and to develop an artificial mind as good, or perhaps even better than ours.