One of the more important themes in this section of Hofstadter’s book is the theme of backtracking. I think that the idea of backtracking relates particularly well to the way that humans might solve a particular problem. For example a person driving from city A to city B, would start all the way back at city A if he or she gets lost along the way, he or she will back track to the most recent spot where they weren’t lost and from there proceed on to city B, this time hopefully on the right path.
However I do believe that there are times when starting from the beginning is the easier choice to make. I thought about this when Hofstadter was talking about unhappy gloms. Suppose, instead of gloms being composed of a grouping of letters that form words, the gloms are a grouping of words that form sentences. An author knows that the first sentence in any body of work is one of the most important sentences for that work. It is the sentence that hooks the reader to read further, so the author wants to get that first sentence right. During the editing process the author decides that the first sentence needs some work, now it could be that the gloms need to be rearranged or the order of the gloms needs to be changed. Or it could be that the first sentence is entirely removed and re-glommed to form a sentence that is much more effective.
I agree with Hofstadter in the context of Jumbo that the idea of backtracking may be the more intuitive approach to reform a word from gloms, and in fact may very well be the more intuitive approach to many problems solving situations. I do think that it is in the context of the problem to be solved whether or not backtracking or starting over is the easiest and best approach.
Wednesday, September 30, 2009
Wednesday, September 23, 2009
Bonds, Chains, And Gloms Oh My
What I found particularly interesting about Hofstadter’s brief explanation of Jumbo is the process that Jumbo goes through to form its possible word candidates for the “Jumble” puzzle. As Hofstadter explains it isn’t necessarily if the word formed is correct, but the process by which the word is formed. This suggests to me that Jumbo doesn’t actually solve the “Jumble” puzzle but tries to form words using the anagrams presented.
What really peaked my interest was the partial rule base that Hofstadter provided in this section. In this he states that his rule base wasn’t based on any kind of letter to letter frequency but only on priorities that he himself believes viable in his own process for forming words in the “Jumble”.
I believe that Hofstadter has thought deeply about his own process for forming words using anagrams. I however don’t know if that is exactly how I form words trying to solve anagrams. Maybe on some level, it is very similar to the process that I use. I will certainly have to think more about it to come to any kind of conclusion on the differences between his process and my own.
After reading this section it reminded me about something that I had seen on the internet a few years ago. Research at Cambridge had discovered that it doesn’t matter the order of the letters as long as the first and last letter of a word are correct, people would have a tendency to figure the word out with almost no effort. This is not the original article but here is a link to an example of this.
http://www.mylittleportal.com/mixed-letters-still-readable
What really peaked my interest was the partial rule base that Hofstadter provided in this section. In this he states that his rule base wasn’t based on any kind of letter to letter frequency but only on priorities that he himself believes viable in his own process for forming words in the “Jumble”.
I believe that Hofstadter has thought deeply about his own process for forming words using anagrams. I however don’t know if that is exactly how I form words trying to solve anagrams. Maybe on some level, it is very similar to the process that I use. I will certainly have to think more about it to come to any kind of conclusion on the differences between his process and my own.
After reading this section it reminded me about something that I had seen on the internet a few years ago. Research at Cambridge had discovered that it doesn’t matter the order of the letters as long as the first and last letter of a word are correct, people would have a tendency to figure the word out with almost no effort. This is not the original article but here is a link to an example of this.
http://www.mylittleportal.com/mixed-letters-still-readable
Sunday, September 20, 2009
That Word Game
With Hofstadter’s mention of the word puzzle game “Jumble” my eyebrows raised. My grandfather had introduced me to the daily “Jumble” when I was around fifteen years old. Since that time I have always had a fascination with word games. But I never really gave any thought about the process that I used in solving the puzzles that I played.
On thinking of my three favorite word games, “Jumble”, “Scrabble”, and “Boggle”, I wonder if my process for creating words in those games is the same for each or if there is major variation. I suppose that in particular with “Scrabble” I tend to separate the letter tiles into consonants and vowels, until a good word can be arranged. But in “Jumble” and “Boggle” I think that I try to chunk the letters more like Hofstadter suggested into words that are possible solutions.
I look forward to learning more about Jumbo and Hofstadter’s rational for solving anagrams. Over the course of Hofstadter’s conversation on anagrams I am going to make a conscious effort to compare his process in solving and my own. It will be interesting to learn where our processes are the same and where they differ.
Here are some links to the word games mentioned above.
Jumble: http://www.jumble.com
Boggle: http://en.wikipedia.org/wiki/Boggle
Scrabble: http://www.hasbro.com/scrabble/en_US
On thinking of my three favorite word games, “Jumble”, “Scrabble”, and “Boggle”, I wonder if my process for creating words in those games is the same for each or if there is major variation. I suppose that in particular with “Scrabble” I tend to separate the letter tiles into consonants and vowels, until a good word can be arranged. But in “Jumble” and “Boggle” I think that I try to chunk the letters more like Hofstadter suggested into words that are possible solutions.
I look forward to learning more about Jumbo and Hofstadter’s rational for solving anagrams. Over the course of Hofstadter’s conversation on anagrams I am going to make a conscious effort to compare his process in solving and my own. It will be interesting to learn where our processes are the same and where they differ.
Here are some links to the word games mentioned above.
Jumble: http://www.jumble.com
Boggle: http://en.wikipedia.org/wiki/Boggle
Scrabble: http://www.hasbro.com/scrabble/en_US
Wednesday, September 16, 2009
Spider Webs
Hofstadter talks about in pages 70 – 86 the concept of variations on themes. When Hofstadter began describing variations, I immediately thought ‘yep that seems right, variations are all around us’. But it wasn’t until I really started thinking about variations that I truly realized how encompassing the concept really is. Take for instance the theme of entertainment. Without being an expert on the field of entertainment even having a little knowledge about history one can see how the concept of entertainment has expanded and spider-webbed rapidly in the short existence of human kind.
This is not meant to be a thorough history of entertainment but only an example of how widespread variation is in the world. For instance story telling has been in part a form of entertainment since the earliest written records of man, this was in the beginning done orally possibly in front of the evening cook fires, later the theatre became big morphing oral story telling into a oral and visual way of telling a story as well as being able to tell the same story to large masses of people. But are there other ways to entertain large masses of people? Well what about athletics, the gladiatorial arena’s of ancient Rome for instance or maybe jousting in the kingdoms of medieval times. Certainly the cinema has had a large impact on entertainment, morphing the art of storytelling not only into a form of entertainment but also into a record of history, starting as silent films and eventually getting sound and voices (the talkies), and animation, recorded on a medium to be enjoyed again and again.
Entertainment grew from a few forms to many: Modern Cinema, music concerts covering most if not all genres, sporting events from young kids to the professionals, board games, card games, computer games. The list goes on. But entertainment is only one example and most definitely could be sub-divided into many more sub-concepts that are just as vastly spanning.
This is not meant to be a thorough history of entertainment but only an example of how widespread variation is in the world. For instance story telling has been in part a form of entertainment since the earliest written records of man, this was in the beginning done orally possibly in front of the evening cook fires, later the theatre became big morphing oral story telling into a oral and visual way of telling a story as well as being able to tell the same story to large masses of people. But are there other ways to entertain large masses of people? Well what about athletics, the gladiatorial arena’s of ancient Rome for instance or maybe jousting in the kingdoms of medieval times. Certainly the cinema has had a large impact on entertainment, morphing the art of storytelling not only into a form of entertainment but also into a record of history, starting as silent films and eventually getting sound and voices (the talkies), and animation, recorded on a medium to be enjoyed again and again.
Entertainment grew from a few forms to many: Modern Cinema, music concerts covering most if not all genres, sporting events from young kids to the professionals, board games, card games, computer games. The list goes on. But entertainment is only one example and most definitely could be sub-divided into many more sub-concepts that are just as vastly spanning.
Monday, September 14, 2009
Climb The Mountain Because It Is There.
In this newest section to be read Douglas Hofstadter discusses two ideas when approaching pattern finding in numbers. The first of his ideas is that pattern finding is not always an easy process. That is to say that given one problem over another problem, one may be easier to solve than the other. This idea also suggests the persistence and patience is needed in divining the solution to any given problem. This has bearing on all real world problems in general and is not necessarily only limited to pattern finding or mathematics. The most that I took away from this is that toil and hard work can yield fruits for success.
This idea has a certain cosmetic feel to his use of mountains, chains, and plateaus when trying to find the pattern in a sequence. But brings me further into the idea of persistence in problem solving in general. Mountains can literally be upraised sections of ground which are barren and rocky or forested and life renewing. Semiotically, mountains can be many things. A mountain range can be the border between two warring countries that forces peace, or the natural border of a city, state, or country. Or it can be in reference to the amount of work that someone may have to do. Consider for instance the phrase, “I have mountains of work to take care of before I can enjoy the weekend.” The ascension of the work being half of the number of task needed to reach the half way point, the apex, or the half the total time needed to complete all the tasks. Symbolically a mountain, when pertaining to problem solving may also represent one task that needs to be completed. Take for example a computer program that one may wish to write. The ascension of the mountain in this case might be the preliminary work needed in writing the code for the program, such as understanding the problem, theories on how to solve the problem, and etc. While the apex of the mountain, the peak, would be the actual coding of the program to be written, one could spend any amount of time climbing the mountain and viewing the world from the peak. Descending the mountain, I would say represents the debugging of the code and finally ending with a finished product. After climbing this mountain, pick-nicking at the peak, and descending back to the base, the next mountain is ready to be climbed.
This idea has a certain cosmetic feel to his use of mountains, chains, and plateaus when trying to find the pattern in a sequence. But brings me further into the idea of persistence in problem solving in general. Mountains can literally be upraised sections of ground which are barren and rocky or forested and life renewing. Semiotically, mountains can be many things. A mountain range can be the border between two warring countries that forces peace, or the natural border of a city, state, or country. Or it can be in reference to the amount of work that someone may have to do. Consider for instance the phrase, “I have mountains of work to take care of before I can enjoy the weekend.” The ascension of the work being half of the number of task needed to reach the half way point, the apex, or the half the total time needed to complete all the tasks. Symbolically a mountain, when pertaining to problem solving may also represent one task that needs to be completed. Take for example a computer program that one may wish to write. The ascension of the mountain in this case might be the preliminary work needed in writing the code for the program, such as understanding the problem, theories on how to solve the problem, and etc. While the apex of the mountain, the peak, would be the actual coding of the program to be written, one could spend any amount of time climbing the mountain and viewing the world from the peak. Descending the mountain, I would say represents the debugging of the code and finally ending with a finished product. After climbing this mountain, pick-nicking at the peak, and descending back to the base, the next mountain is ready to be climbed.
Tuesday, September 8, 2009
Work Small
After reading the next section in “Fluid Concepts and Creative Analogies” by Douglas Hofstadter, I immediately took notice of Hofstadter’s realization that when working the programming contest that he had proposed to his class, he took out the ability to work small. As a student in the computer science field, I immediately thought that working small is better. As Hofstadter informs, he finds it useful to work small and gradually grow into the bigger problem at hand when trying to find the patterns within the sequences. This also has bearing within the field of computer science. It immediately brought to mind the idea of ‘Divide and Conquer’.
In the ‘Divide and Conquer’ concept, you take an initially large problem, in this case a large sequence of numbers (or a large complicated computer program) and solve the problem by dividing it into parts and taking each separate part as a smaller problem to be solved. The smaller solved problems are then combined to recreate the initial large problem.
Using this concept will help largely with my Game Design class in which I am going to design a MUD with a labyrinth. Instead of designing the labyrinth as a whole, I will break the labyrinth down into the smaller problem of rooms, stringing a series of these rooms together to actually create the labyrinth. By working a large problem into a set of smaller problems I can get solution easier.
In the ‘Divide and Conquer’ concept, you take an initially large problem, in this case a large sequence of numbers (or a large complicated computer program) and solve the problem by dividing it into parts and taking each separate part as a smaller problem to be solved. The smaller solved problems are then combined to recreate the initial large problem.
Using this concept will help largely with my Game Design class in which I am going to design a MUD with a labyrinth. Instead of designing the labyrinth as a whole, I will break the labyrinth down into the smaller problem of rooms, stringing a series of these rooms together to actually create the labyrinth. By working a large problem into a set of smaller problems I can get solution easier.
Monday, September 7, 2009
Finding The Patterns In Sequences.
Hofstadter describes various ways to find the pattern in sequences (which in this case was mathematical). In working with the squares between triangles sequence, Hofstadter suggested in not so many words that it was easier to work small and gradually get larger volumes of data, but as a consequence it could be easy to come to the wrong conclusions. I especially thought that the ‘sniffing’ technique was particularly helpful and seems to be inclined more to humans over machines. That is that the ‘sniffing’ technique is what humans tend to do when searching for patterns with in a sequence.
The one area where I found suitable for machines that may not be so suitable for humans was the area of breadth-first over depth-first searching. Bread-first searching I think is more suited to human pattern finding in sequences as opposed to depth-first searching which is certainly suited to machine pattern finding. Breadth-first searching tends, at least in my opinion to be more intuitive to the way humans looks at various things, in general, due to our conditioning from birth, such as reading horizontally across a line of text, as opposed to reading vertically down a block of text.
The one area where I found suitable for machines that may not be so suitable for humans was the area of breadth-first over depth-first searching. Bread-first searching I think is more suited to human pattern finding in sequences as opposed to depth-first searching which is certainly suited to machine pattern finding. Breadth-first searching tends, at least in my opinion to be more intuitive to the way humans looks at various things, in general, due to our conditioning from birth, such as reading horizontally across a line of text, as opposed to reading vertically down a block of text.
Saturday, September 5, 2009
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