Er, Does Not Compute. Algorithms, Consciousness, and the Human Mind (An Emergent Reaction to Roger Penrose's The Emperor's New Mind)

This paper reflects the research and thoughts of a student at the time the paper was written for a course at Bryn Mawr College. Like other materials on Serendip, it is not intended to be "authoritative" but rather to help others further develop their own explorations. Web links were active as of the time the paper was posted but are not updated.

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Er, Does Not Compute. Algorithms, Consciousness, and the Human Mind (An Emergent Reaction to Roger Penrose's The Emperor's New Mind)

Laura Kasakoff

When I was in elementary school I hated doing my homework. (Some things never change.) Instead of just focusing on finishing my work, I would daydream about a computer that would do all of my homework for me. When I told my parents about my computer idea, my mother said it would just be easier to do my homework than create such a computer, and my father said it would be dishonest since the computer's completion of my assignments would not be my own work. However, this did not put an end to my fantasies of homework evasion. My dream changed to one of a computer that would work just like my brain. If asked to write a paper on the symbolism of birds in Arthur Miller's "The Crucible", it would write the paper exactly how I would if I took the time to author the paper myself. Would it really be dishonest to hand in work done by a computer that would produce precisely the quality of work that I would create myself?

I hoped that by reading Roger Penrose's "The Emperor's New Mind", I might gain insight as to how the human mind could be emulated by a computer. Surely a great mathematician like Penrose would show how a computer algorithm could function like a brain (and give new life to my childhood musings). I had not realized that Penrose actually believes that there is more to consciousness and human mathematical intuition than could ever be computed through an algorithmic process. While he does appreciate the eternal, ethereal nature of mathematics, it his respect for the human brain's ability to comprehend innate mathematical concepts that leads Penrose to the conclusion that the brain cannot be reduced to a computational procedure.

Penrose denies what is known as strong artificial intelligence which is the belief that we could program any computer to have intelligence with the correct algorithm. That is to say, our mental activity is a step by step execution of some complex algorithm. Philosophically, Penrose tries to discredit strong AI with the example of Searle's Chinese room. We are asked to imagine ourselves in a room where we can have no contact with the outside world, and we are given a story written in Chinese along with a yes-or-no question to answer pertaining to the story. We are also given a (presumably long) set of instructions, an algorithm, in English. Assuming that we can't speak Chinese, we will be acting like Schank's computer program answering yes-or-no questions which test for understanding of a story. After we complete the English instructions we will arrive at the correct answer, but would we really want to say that we had any understanding of the Chinese story originally presented to us?

Penrose hopes that Searle's hypothetical Chinese room will convince us that an algorithm alone cannot equal the understanding of human intuition. Penrose is angry that even Searle and others have been conditioned by computer people to concede that everything, including the human brain, is a digital computer. Penrose is attacking the school of thought proposed by Wolfram and his "digital determinism" by claiming that, despite popular belief, not "everything is a digital computer" (23). Also, Penrose does not understand how proponents of strong artificial intelligence can be happy with themselves since they end up subscribing to a very extreme form of dualism, the belief that separate from the body and the material brain, there exists a mind that has no physical component. Penrose points out that "[t]he mind-stuff of strong AI is the logical structure of an algorithm" (21). This is not the side of the mind-body debate that most strong AI supporters would want to champion.

Penrose insists that algorithmic processes can't be the only components that lead to human consciousness of the mind because there are incomputable numbers, non-recursive mathematical problems that humans but no computer can solve, and no complete strictly formulaic mathematical system. He describes how Turing machines cannot solve the halting problem by introducing an incomputable number. He presents Goedel's theorem to us to show how any attempt to formalize mathematics will have a statement that is not provable. Therefore, no matter what lens you use to examine the universe (mathematical or otherwise) an object exists for which there is nothing that can be done to calculate it. Nevertheless, I believe it is possible that emergent computer programs that try to model complex phenomena through simple rules, rather than increasingly complex mathematical equations may give rise to artificial intelligence and mathematical intuition in computers.

Penrose's inspiration for his belief that the brain is not computable stems from his work with tilings of the plane. Questions concerning plane tilings consider whether a set of tiles covers the plane periodically, that is, the polygonal tiles will repeat a given tiling pattern. There are many shaped tiles that can tile a plane "periodically" or "non-periodically", but the interesting question that Penrose and other mathematicians worked on was whether or not there existed a finite set of shapes that could tile the plane only non-periodically. Penrose was able to find a set of just two tiles that only tile the plane non-periodically. This is an example of a non-recursive problem that cannot be solved algorithmically by any computer. Therefore, since the brain can solve problems a computer can't, the brain cannot be emulated by a computer program.

Penrose says, "It is important to realize that algorithms do not, in themselves, decide mathematical truth. The validity of an algorithm must always be established by external means." Even if this is the case, couldn't we program a computer which possessed the consciousness to decide mathematical truths? After all, isn't our mathematical intuition an emergent system that develops from observation and practice? Penrose hopes that there really is a fundamental difference between our physical embodiments and the physical matter of a computer. Perhaps through a study of how environments affect agent, we can learn how the physiological components of our brain lead to certain thought processes, and then I do not see why with further understanding we should not be able to program these processes.

Of course Penrose spends a lot of time trying to define mathematical truth. I got the impression that Penrose sees mathematical truth as an emergent phenomenon itself. He says "We are driven to the conclusion that the algorithm that mathematicians actually use to decide mathematical truth is so complicated or obscure that its very validity can never be known to us...[But] mathematical truth is not a horrendously complicated dogma whose validity is beyond our comprehension. It is something built up from such simple and obvious ingredients..." (418). Penrose believes that humans are more fit than computers to comprehend these simple steps behind mathematical truth, but I believe with a deeper understanding of why we grasp mathematical concepts the way we do (perhaps through emergent modeling), we will be able to share this understanding with computers, too.

In fact, it seems that maybe Penrose himself has come to a contradiction because of his consideration of emergent phenomena. As an example of the emergent nature of mathematics Penrose describes how the Mandelbrot set emerges from a simple set of rules, but it produces such a beautiful pattern in the complex plane that Mandelbrot thought the computer he was working on had made a mistake when he saw it for the first time. He did not believe that such a natural beauty could be inherent in such a simple mathematical set of rules. If Penrose believes in the inherent god-given nature of mathematics, I think he should consider that the human brain could come from a set of simple rules as well. Of course the rule set might not be as easy as the one to generate Mandelbrot's set, but examples like Mandelbrot's set shows us that although the human brain is both miraculously beautiful and complex, the rules governing it need not be. Why does he think the most complex phenomena are so far from being computable? It is those things we can't easily grasp, paradoxical tricks that elude human intuition that create incomputable messes. The brain and the algorithm behind it might just be the next of God's mathematical jewels waiting to be uncovered.

I believe Penrose takes too great a leap from saying that some things are not computable to saying that the brain is one of these things. Why should something as familiar as our human brain be one such incomputable thing? We have seen in emergent phenomena like the Conway's Game of Life and Langton's Ant that completely deterministic systems are not necessarily predictable. So perhaps our actions themselves are all predetermined by the mathematical equation of our brain. Our sense of free will could stem from the fact that the algorithm is so complex that while our future is destined to be a certain way we cannot predict the outcome of our lives. After all, our brains are but a network of neurons out of which emerges our consciousness. Non-recursive mathematical problems that can only be solved non-algorithmically by the human mind, such as the Penrose tilings, are Penrose's main justification for his conclusion, but I hope that it will be possible through emergent modeling of the brain for a computer to show mathematical intuition even for non-algorithmic problems.

In the prologue of "The Emperor's New Mind", we meet a young boy in a futuristic society who is about ask an omnipotent computer a question at its grand "turning-on" ceremony. In the epilogue we discover the boy has asked the computer how it feels and the audience at the ceremony laughs. I think it is funny that Penrose should use such a story to try and convey the uniqueness of consciousness and "feeling" to human beings (or at least living creatures with some capacity to verbalize). I find the question "How do you feel?" to be one of the most annoying questions because it is nearly impossible to answer. At any given moment one feels so much more than what can be conveyed through the standard {sad, happy, tired...} responses. Perhaps the most intelligent computers in the world are unable to answer how they feel, but in all honestly can humans truly give a complete survey of their respective internal states? Perhaps the experience of emotions is itself an emergent phenomenon where the interaction of neurons and biochemical reactions and (Penrose's dear friend) quantum physics conflate to produce our emotional consciousness and self-awareness. If this is the case it makes sense that through computer modeling and animal robotics and other more emergent approaches to artificial intelligence, maybe one day the computer version of my brain will write this paper for me! [an error occurred while processing this directive]