Randomness vs. Reasoning

In this particular reading Hofstadter mentions the compelling yet almost universal notion of intelligent backtracking on page one hundred fifteen of Fluid Concepts. This intelligent backtracking is described by Hofstadter as a standard strategy detailing how to fix a past problem in a given series of steps. One must look at prior decisions made, undo them and take a different path or go to the next set of problems and backtrack further. This intelligent backtracking can be seen as an almost altered perception or perceptual regrouping of a current problem and can help the solver in discovering the solution through detection of errors. Hofstadter then explains the choice to determine a different path to the solution, which can either be randomly chosen or by deductive reasoning. Choosing randomness in finding a solution would lead to a trial and error method; one would hypothesize, and take a considerable amount of time. However, Hofstadter takes a different approach to the random method and describes that to reason and speculate at the predicted outcome would take more time than randomly selecting a choice and plowing full speed ahead to see if it works or not. Jumbo the word program that Hofstadter creates, exploits a random method of choice making rather than a reason based one. With this random choice method all possibilities and pathways are open to explore which is quite the opposite of normal computer programs with closed guidelines and parameters that are pre defined. Hofstadter details that a program with a simple control structure allows the system to complete certain tasks a complex control structure program would get bogged down in. As mentioned in class certain systems, like prolog, are better at solving particular problems than others, and are conversely more exhaustive at solving various problems than other types of systems.

The random choice versus deductive reasoning pertaining to the intelligent backtracking of the Jumbo program Hofstadter details was at first perplexing to me. I thought logically that deductive reasoning would be much quicker in this instance than simply selecting random paths; therefore one would not waste time on obviously wrong means. However, I did not take into consideration the full breadth of the process intelligent backtracking. To take a step back in a problem process and then guesstimate where possible other solutions will lead you indeed takes more time than selecting a random path and going with it. For a computer program the time and amount of code to actually check possible solutions before selecting one would be extremely lengthy and time consuming. When I thought deductive reasoning would be a faster process I was thinking more about how we humans use reasoning and quickly, I did not initially think in terms of computational length or how a computer program would go about doing the same thing. From my perspective it is as if Hofstadter took an unneeded element of hypothetical reasoning out of his Jumbo program to make it more intelligent, quicker, versatile, and more plastic. In conclusion I can see where Hofstadter’s notion of randomness over reason can actually lead to a quicker and less exhaustive solution in some cases.

Jumbo Jungle

Hofstadter details the workings of his Jumbo program in chapter two of Fluid Concepts. The purpose of this program is to model the instant mental processes of assembly and transformation. Jumbo is a builder program which constructs English pseudo words from a given set of letters using pre defined rules. Hofstadter emphasizes that Jumbo builds words and does not extract or compare English words with a pre loaded dictionary file. A simple dictionary comparison would not exhibit any intelligence or creativity, only quality assurance. Hofstadter is instead trying to emulate the spontaneous and unconscious composition of coherent wholes derived from scattered parts, a sort of creative construction and regrouping of letters into words. I personally like the analogy of visual art with the construction of words. A painter starts with a defined palette of colors and although the painter most likely has a mental picture or pre determined aspect he/she wishes to construct, the painter does not know exactly what the picture will look like or the subtle nuances and artistic expression it will have. Also one must consider that the painter knows which colors go best with certain others and which will mix to make a more defined and powerful picture. Much like the painter, the Jumbo program starts with a pre determined ‘picture’ or set of rules which govern its letter combinations and then constructs words from a palette of letters, the English alphabet. The program itself has no prediction of its output but will stay within the parameters it is given. Jumbo will have a sense of which letters fit with one another or are commonly grouped together, but one would expect for some errors in arrangement of multiple letter segments that might occur. However, Hofstadter explains that Jumbo will compute many possible letter groupings in parallel and seek out the groupings that are more probable and likely than the others. Each successful grouping of letters triggers another test for grouping those letters with another set and so on, until the most likely combination is reached. Hofstadter emphasizes that there must exists multiple stages of groupings with different parameters. Bonding, combining two neighboring elements together that can still be viewed as separate is different than Hofstadter’s notion of glomming. Glomming is a set of suitable bonded items that creates a higher level structure through its relationships, representing the parts as a whole and reducing further break up of its separate parts. This is just the basic workings of Hofstadter’s sophisticated Jumbo program.

When reading about the different levels of groupings such as bonds and gloms, it occurred to me that this process very closely emulates what humans actually do when constructing words. For example, when I see the mixed up letters ‘reeht’ I first pick out the bonding group of ‘he’. Then further structure it into the glom of ‘the’ and further still group all the given letters into ‘there’. When I grouped the ‘the’ I knew I had to be on the right path because ‘the’ is a word and well known word fragment and could not break the contain letters up again. I wonder how much prediction has to do with this aspect of word construction and if it is common to get multiple words with increasing input size. Such as the case as giving Jumbo ten letters to work with instead of five and receiving multiple different full word outputs.

Malleable Mental Objects

Hofstadter writes some interesting descriptions about working memory and virtual memory in this reading. To solve a problem one needs to extract information from long term memory and use it actively in their short term working memory. The steps in between are unknown and most likely complicated even though in our brains it can take mere seconds for them to be completed. This gap or unknown process between long term and working memory is what Hofstadter tries to pinpoint and explain on page ninety of Fluid Concepts. He gives a near perfect analogy for working or virtual memory, comparing it to a moving ball on a video game. The ball itself is not physical or stationary; instead it is an abstract object that is constructed of moving pixels and exhibits a type of predetermined behavior. Although the pixels make up the visual object it is completely different than a computer screen pixel or group of pixels, it floats on such pixel hardware in an ever changing state. Hofstadter details that this level distinction between virtual objects and their component hardware is similar to the distinction between working memory or mental objects and its physical origins. Working memory and mental objects are extremely fluid, malleable, and ever changing. One usually does not store such objects or concepts in long term memory and perhaps the ability to quickly alter these objects is linked to its rapidly fading nature in our memory.

Hofstadter’s visual analogy of a moving ball on a video game screen, such as pong, made this whole concept of the communication and distinct levels of mental objects and working memory ‘click’ in my mind. Even though working memory is linked to long term memory and physical aspects of the brain it is on a whole different level than both. Working memory is usually ever changing and can be altered extremely quickly and drastically within humans. I also believe that because of this ability to quickly alter these mental objects in working memory it becomes more difficult to store them in long term memory. I wonder how this concept would equate to machines, being that they have the ability to store working memory computations and objects in physical state memory if prompted to do so. Would that mean if humans ever had a mechanical memory module could we store most or all our working memory concepts and objects quickly and in permanent memory banks which we could later access anytime.

Hofstadter's Creative Wordsmithery

Hofstadter mentions on page eighty six of Fluid Concepts, that it is his firm belief that pattern perception, extrapolation and generalization are core elements of creativity. Furthermore, “one can only understand such cognitive processes only by modeling them in the most carefully designed and restricted microdomains” (Hofstadter, p.86). I would certainly agree with the first assertion, from what I have already read in this book there is no doubt in my mind that perceptual regrouping is a staple of creativity. Concerning generalization, the ability to associate patterns and extract analogies, I would have to agree with Hofstadter that it is another crux of creativity, and would go further and say it is a staple of foresight, prediction, and higher intelligence as well. As for the second assertion, I personally have no experience or knowledge in creating modeled intelligent processes in a carefully designed microdomain, but I am sure to find out by reading the rest of the book. I would imagine that one would undoubtedly run into multiple problems and hurdles trying to model creativity, it seems logical that the more confined the parameters the easier it could be. However, the pure essence of creativity is to be free of restrictions and parameters, it will be insightful indeed to see Hofstadter’s method of modeling a program to have the aspect of creativity. One can surely create a program to look like it is creative or random, but nonetheless a program executes given instructions and formulas, even if there is natural variables and extremely complicated computations. So can a program, computer, or A.I. truly be random or creative, since it can only do what it is instructed to do, I am sure Hofstadter will address his view on this later in the book.
Initially I had reservations about this book after viewing the first few pages and realizing that there was a great deal of math involved. However, after completing the first chapter there is much more than mathematical patterns discussed. Hofstadter’s literary canvas of the first chapter paints all sorts of mind blowing concepts, such as perceptual regrouping, conceptual spheres, and variations on themes. I am actually looking forward to reading the rest of the text, which is extremely rare for me personally. The ending to this chapter is quite a tease and sets up the rest of the book. With Hofstadter laying the initial framework of his definitions of intelligence and creativity in the first chapter he baits the reader to explore more of his book, with the sentence, “This article of faith (his definitions of intelligence and creativity) has guided me and my research group over the past decade and a half, and the remainder of this book is dedicated to conveying the results of those investigations.” (Hofstadter, p.86) Indeed another parry from the wordsmith and literary artist that is Douglas Hofstadter.

Hofstadter, Douglas. Fluid Concepts And Creative Analogies. 1995. Basic Books. New York, NY.

Adaptable Fluid Intelligence

On page fifty eight of Fluid Concepts, by Douglas Hofstadter there is a substantial point made about the process of problem solving. One must organize perceptually the individual elements that are recognizable first, and then step by step move towards other familiar patterns. Hofstadter then shows the reader a direct representation of this concept in his mountain sequence of numbers. This distinct organization of his mountain chain sequence number pattern into a visually relative grouping of plateaus, up runs and down runs is quite helpful in understanding the full concept. Personally, I learn a great deal through visual methods and this optical extrapolation which Hofstadter constructs further cements his idea of the power of perceptual regrouping. Hofstadter then mentions the concept of perceptual glue, or the grouping of like patterns through a common element visible throughout individual segments. Again re-solidifying the conceptual importance of perceptual regrouping, Hofstadter makes a clear point that pattern recognition and fluid reassembling is a vital aspect to intelligence. Another important concept expressed in this book pertaining to perception, is the aspect that we humans usually first recognize the most aesthetic pattern. Hofstadter then eloquently defines mathematics as the art of choosing the most elegant generalization to an abstract pattern. I certainly have never heard mathematics explained so surreptitiously, but it makes logical sense. Mathematicians are not mainly interested in how a problem is solved, but in what they can accomplish and create with such a solution. The ability to alter and sculpt a previous contribution into a greater and more powerful concept is what most mathematicians seem to be interested in. Again, making the unmistakable assertion that the power to reorganize ideas and adapt ones knowledge to emerging problems is a vital part of intelligence.
As I read more and more of this text I realize that Hofstadter is quite the wordsmith, and such phrases as bubble up, plateaus, fluidifying, perceptual glue, and variabilizations add an undeniable active quality to his book. These choice words make the concepts and numbers almost fly of the page and land directly in the mind. One receives a very live and vivid association of such concepts conveyed through this particularly active and colorful language.

Perceptual Intelligence

On page thirty five of Fluid Concepts, by Douglas Hofstadter, the author mentions his desire to program intelligence, not knowledge. The distinction made is a very important one, what does intelligence and knowledge mean to you? I have read many different definitions of intelligence and Hofstadter’s is one of the more succinct explanations. Hofstadter comments that intelligence must have a powerful, general, and abstract knowledge based core, but I believe it must go further than that. Many people also agree that intelligence must contain an element of prediction and foresight, again something is still lacking here. I believe strongly that intelligence must include an element of adaptability, as well. Hofstadter makes a valid reference to this by stating that throughout history younger individuals with an incredibly small knowledge base have made amazing insights into complex fields. Usually, younger brains have greater ease to adapt, form new neural networks and to view abstractions in a completely new way. This makes me ponder another factor of intelligence, perception and imagination. Does one’s ability to transform their perception and increase their imagination affect their intelligence? Hofstadter mentions the element of esthetic driven perception aiding him in the triangle between squares problem, but disabling him to see Gosper’s approach to the continued fraction of e. Perception is a very powerful window into one’s mind and thought process, but when utilized, focused perception can be a double edged sword. Individuals past experiences and perceptual grouping biases can disable them in some ways and aid them in others. It seems to me that keeping an open mind and refreshing your point of view is in fact an undeniable quality of intelligence. A good example to support this would be the recent workings and solutions to particular cryptology math problems I competed. At first glance I was able to solve about four of the ten problems present, usually by cancelling out the most noticeable numbers. However, later when I tried the same strategy on the remaining six problems I came up with no solutions. When I perceptually regrouped the numbers and approached the problems in a different way I was able to find many of the solutions. This happens to most people when they are stumped on a problem and then approach it the next day and find the solution almost immediately. Our ability to adapt differently and perceive problems from many points of view is an essential key to our intelligence.

Universal Mathgod

Is pattern recognition a form of intelligence? In short yes, the first pages of Fluid Concepts, by Douglas Hofstadter details his attempts at creating a pattern seeking, intelligent, computer program. Furthermore is there a link between all patterns in the universe? I found it refreshing and insightful to have a little background information about Hofstadter’s prior studies and academic exploits detailed in the prologue. It’s always good to have a description of how someone thinks or learned to think, due to their academic experience and interaction with like minds. Hofstadter begins his investigation into intelligence by developing a program that finds a pattern in a given set of numbers. The pattern he starts with is triangular numbers and squares. His description of triangular numbers got me thinking about one of my favorite movies ‘Pi’ and the golden ratio. Something about pattern recognition in numbers makes me reflect on the idea that there exists a master mathematical formula, most likely very complex for today’s standards, which links all things in the universe. I like to think of it as a grand all encompassing unified theory. A mathematical formula that can predict any number sequence, thought pattern, or physical action from the combination of chemicals, interaction of life forms, or any such objects in the universe. Wishful thinking on my part I know, but we humans, at least most I have talked to, find comfort in the belief that there is an explanation for everything, and that everything is connected. Hofstadter’s concept and mention of what he calls ‘Mathgod’ could be viewed as such a unified concept or governing rule that gives relation and order to all mathematical models. My thought is that there exists a universal ‘Mathgod’ which encircles all aspects of the universe, not just math. I was invigorated to see Hofstadter’s mention of perceptual regrouping, or the ability to view, categorize, and work with patterns in multiple ways dependent on how one perceives them. I strongly agree with him and believe this is a vital tool in creative and cognitive thinking. The adaptive principle behind evolution could also be related to this ability of perceptual regrouping. This reading certainly raised a lot of questions in my mind, such as; does the ability and variety of perceptual regrouping affect intelligence? Would humans be as intelligent as we are today if we had a limited imagination and severe constrictions on our abstract thoughts? Would the confinement or lack of our past experiences, which directly affect perception, cause us to think drastically different then our present ways? This line of questioning reintroduces a little chaos and an uncontrollable aspect into my thoughts about an all encompassing universal ‘Mathgod’.