Monday, April 04, 2011
Gödel, Escher, Bach….and ?
The above named book is one that I had on my low priority reading list for a long time. I remember it made a big splash when it was published and, according to the cover of the 20th anniversary edition that I purchased at a closeout sale, it was awarded a Pulitzer Prize. Having read it, I am rather underwhelmed. The book is very witty and creatively written. But I have a hard time finding a strong purpose. It strikes me as a book that wannabe intellectuals would read and expect anyone that pretends to know anything to read. I found considerable weaknesses in the book from my background.
Dr. Hofstadter was attempting to intellectually bare his soul, so to speak, and as a result some of the incoherence cannot be avoided. I think he was attempting to show that thinking, as he understands it from his studies of Artificial Intelligence, is very tangled within itself and that one must step outside any one level of thinking to describe it. The problem he faces is that in human thinking one does that with the same processes that are being examined. This is where Gödel comes in with his proof that no system can prove its own self-consistency. Hofstadter spends much of the book trying to create a sort of intuitive understanding of this theorem using various computer languages that he creates and number theory systems. Along the way he attempts to illustrate the concepts with very entertaining and creative sketches between imaginary characters, Tortoise, Achilles, Crab, Sloth, himself, Alan Turing, and Charles Babbage. He is successful to a great degree, but I am left with a feeling at the end of , “So what?”
I think the real purpose is to present his ideas of Artificial Intelligence, where it is and where he thinks it is going. This is where I have the most disagreement with him. The greatest deficiency that I see in his discussion is that he apparently has little understanding of how human brains are constructed and operate, and seems to consider them simply larger rat brains. This is a problem I have with Daniel Dennett as well.
The most notable difference operationally between human and rat brains is that a rats experience seems to be distributed and averaged over the entire cortex, whereas human brains can access specific memories. The anatomical equivalent of the rat brain cortex is buried deep beneath the surface of a human brain as a structure called the archecortex and forms part of what is referred to as the limbic system. This portion of the human brain appears to behave similarly to the rat brain in that it responds in a general rather than specific way to events and stimuli.
One of my first objections is that intelligence is never defined, nor is an attempt made other than intelligence is what human brains have. There was a rather sardonic note that whatever computers are made to do that resembles functions of the human mind it is not accepted as intelligence. And perhaps that is quite accurate. Computers perform their computational tasks deterministically. One of the characteristics of human intelligence is that it does not appear to be deterministic.
One of the recurring themes throughout the book is one of hierarchies and levels of hierarchies. This seems to work sufficiently well for simple things, but when it comes to describing human thinking it becomes extremely strained with levels within levels. The massive interconnectedness of human brains, when treated hierarchically, becomes unwieldy. Hofstadter also seems to find it quite difficult to account for human thinking to think about itself. This is one of the apparent thrusts of Gödel’s theorem, that formal systems cannot describe themselves.
Hofstadter is trying to compare computers to minds and mind function to algorithms. I think he is doomed without a proper grounding. Brains and nerves are not binary in the same way computers are binary. The connectivity in a computer is sparse compared to the simplest of brains. Nerves fire on the basis of summation, up to a threshold, nothing happens, after the threshold only a single amplitude response occurs. More inputs than enough to trigger a response have no additional effect. The human brain is probably mathematically chaotic, and no AI machine would ever be allowed to be, nor do I think it can be constructed. It is in the non-algorithmic tasks that human brains excel, and I have grave doubts that any machine that is not essentially a human brain in structure can ever do the same.
One suggestion that I would make is to create an operational definition of intelligence—intelligence is what is measured by intelligence tests. To the degree that a computer program can pass an intelligence test, it is intelligent. That is the same standard we use for humans. Of course the one major discrepancy is that humans use the same skill sets in everyday tasks that a computer does not or else cannot do.
The other suggestion I would make is to approach it all from the standpoint of networks. Every nerve cell in the brain is connected to hundreds to thousands of other nerves, and to and from all areas. One can roughly delineate four major levels of the brain, the brainstem which is reflexive and determinate in nature, the midbrain, which has a degree of networking and integration of inputs and outputs, the limbic system, and the cortex. Each of these parts has a high degree of interconnectivity within its area, and also to higher and lower areas. Higher areas also can feed back to the lower ones, in some cases partially controlling responses, e.g. holding one’s breath, or holding back tears. (Or possibly overriding the response rather than directly inhibiting it.) My own observation of the way my brain works and misfires is that it would be best considered as a massive relational database, where most things were indexed hundreds or thousands of ways, and the ultimate unit of data is extremely small, e.g. smaller than a single letter in a word. I know from the way malapropisms and spoonerisms are created and the way I sometimes have momentary aphasia, that words are built up a letter at a time, and the letters may be built up in turn. It would appear hierarchical, but I think it actually happens in a massively parallel manner. Anyone who has dealt with neural networks has seen the phenomena occur even in simple networks. What appears to be hierarchical functioning is simply networks of networks, and the apparent distance down the hierarchy is actually the functional distance in the number of links required to reach or assemble the appropriate network. The implication of all this, and it is not new with me, is that intelligence is in the connectivity of the brain.
From my viewpoint, we will never truly create an intelligent mechanical device. We will, just as we do with robots, create computational equipment that can do certain skills much better than humans. We already do that, and we will continue to do so, creating more and more complex manipulations. From my own observations, part of human thinking depends absolutely on physical experience. Physical experience provides primary referents for many ideas. That kind of experience cannot be given to computers, and therefore they will not be able to do things that depend on such experience.
Unlike the science fiction writers of fifty years ago, I am not threatened by computers. Part of it is possibly the contempt of familiarity, since I make my living with them. But I think it is grounded in a full appreciation of the differences between computational machinery and programs and human brains. The differences are just too great.
Dr. Hofstadter was attempting to intellectually bare his soul, so to speak, and as a result some of the incoherence cannot be avoided. I think he was attempting to show that thinking, as he understands it from his studies of Artificial Intelligence, is very tangled within itself and that one must step outside any one level of thinking to describe it. The problem he faces is that in human thinking one does that with the same processes that are being examined. This is where Gödel comes in with his proof that no system can prove its own self-consistency. Hofstadter spends much of the book trying to create a sort of intuitive understanding of this theorem using various computer languages that he creates and number theory systems. Along the way he attempts to illustrate the concepts with very entertaining and creative sketches between imaginary characters, Tortoise, Achilles, Crab, Sloth, himself, Alan Turing, and Charles Babbage. He is successful to a great degree, but I am left with a feeling at the end of , “So what?”
I think the real purpose is to present his ideas of Artificial Intelligence, where it is and where he thinks it is going. This is where I have the most disagreement with him. The greatest deficiency that I see in his discussion is that he apparently has little understanding of how human brains are constructed and operate, and seems to consider them simply larger rat brains. This is a problem I have with Daniel Dennett as well.
The most notable difference operationally between human and rat brains is that a rats experience seems to be distributed and averaged over the entire cortex, whereas human brains can access specific memories. The anatomical equivalent of the rat brain cortex is buried deep beneath the surface of a human brain as a structure called the archecortex and forms part of what is referred to as the limbic system. This portion of the human brain appears to behave similarly to the rat brain in that it responds in a general rather than specific way to events and stimuli.
One of my first objections is that intelligence is never defined, nor is an attempt made other than intelligence is what human brains have. There was a rather sardonic note that whatever computers are made to do that resembles functions of the human mind it is not accepted as intelligence. And perhaps that is quite accurate. Computers perform their computational tasks deterministically. One of the characteristics of human intelligence is that it does not appear to be deterministic.
One of the recurring themes throughout the book is one of hierarchies and levels of hierarchies. This seems to work sufficiently well for simple things, but when it comes to describing human thinking it becomes extremely strained with levels within levels. The massive interconnectedness of human brains, when treated hierarchically, becomes unwieldy. Hofstadter also seems to find it quite difficult to account for human thinking to think about itself. This is one of the apparent thrusts of Gödel’s theorem, that formal systems cannot describe themselves.
Hofstadter is trying to compare computers to minds and mind function to algorithms. I think he is doomed without a proper grounding. Brains and nerves are not binary in the same way computers are binary. The connectivity in a computer is sparse compared to the simplest of brains. Nerves fire on the basis of summation, up to a threshold, nothing happens, after the threshold only a single amplitude response occurs. More inputs than enough to trigger a response have no additional effect. The human brain is probably mathematically chaotic, and no AI machine would ever be allowed to be, nor do I think it can be constructed. It is in the non-algorithmic tasks that human brains excel, and I have grave doubts that any machine that is not essentially a human brain in structure can ever do the same.
One suggestion that I would make is to create an operational definition of intelligence—intelligence is what is measured by intelligence tests. To the degree that a computer program can pass an intelligence test, it is intelligent. That is the same standard we use for humans. Of course the one major discrepancy is that humans use the same skill sets in everyday tasks that a computer does not or else cannot do.
The other suggestion I would make is to approach it all from the standpoint of networks. Every nerve cell in the brain is connected to hundreds to thousands of other nerves, and to and from all areas. One can roughly delineate four major levels of the brain, the brainstem which is reflexive and determinate in nature, the midbrain, which has a degree of networking and integration of inputs and outputs, the limbic system, and the cortex. Each of these parts has a high degree of interconnectivity within its area, and also to higher and lower areas. Higher areas also can feed back to the lower ones, in some cases partially controlling responses, e.g. holding one’s breath, or holding back tears. (Or possibly overriding the response rather than directly inhibiting it.) My own observation of the way my brain works and misfires is that it would be best considered as a massive relational database, where most things were indexed hundreds or thousands of ways, and the ultimate unit of data is extremely small, e.g. smaller than a single letter in a word. I know from the way malapropisms and spoonerisms are created and the way I sometimes have momentary aphasia, that words are built up a letter at a time, and the letters may be built up in turn. It would appear hierarchical, but I think it actually happens in a massively parallel manner. Anyone who has dealt with neural networks has seen the phenomena occur even in simple networks. What appears to be hierarchical functioning is simply networks of networks, and the apparent distance down the hierarchy is actually the functional distance in the number of links required to reach or assemble the appropriate network. The implication of all this, and it is not new with me, is that intelligence is in the connectivity of the brain.
From my viewpoint, we will never truly create an intelligent mechanical device. We will, just as we do with robots, create computational equipment that can do certain skills much better than humans. We already do that, and we will continue to do so, creating more and more complex manipulations. From my own observations, part of human thinking depends absolutely on physical experience. Physical experience provides primary referents for many ideas. That kind of experience cannot be given to computers, and therefore they will not be able to do things that depend on such experience.
Unlike the science fiction writers of fifty years ago, I am not threatened by computers. Part of it is possibly the contempt of familiarity, since I make my living with them. But I think it is grounded in a full appreciation of the differences between computational machinery and programs and human brains. The differences are just too great.
// posted by Bill @ 6:28 PM 
