“Ideas came with explosive immediacy, like an instant birth. Human thought is like a monstrous pendulum; it keeps swinging from one extreme to the other.”
--Eugene Field
“Mistakes are at the very base of human thought, feeding the structure like root nodules. If we were not provided with the knack of being wrong, we could never get anything useful done.”
--Lewis Thomas
Defays continued his discussion on Numbo and how it functions and raises some interesting points. He reviewed how Numbo relates to human thought, which is something that I have rarely seen stated in learning about specific computer programs. He made some claims, most of which I agree with wholeheartedly, about how Numbo resembles human performance.
He stated that, "Ideas are not systematically explored, and in fact are often abandoned before having been fully examined"(pp.150). This is true not just to solving math problems but to nearly every aspect of human life. It seems ideas in all fields are subject, such as, but not limited to, social & economic reform, music & movie reviews, and even something so simple as deciding what to have for dinner. Humans just aren't always systematic and often give up on ideas before considering them fully, two characteristics which I often consider flaws.
Defays continued with, "The combinations created are not always strongly goal-driven, so that unmotivated-appearing avenues are occasionally embarked upon"(pp.150). This relation to human thought processes seemed so apparently obvious to me. The first thing that came to mind was, 'Numbo daydreams too?' and as silly as that sounds, the analogy made sense to me and helped clarify how the temperature and the urgency systems in Numbo operated. It also made me consider that not all 'unmotivated-appearing avenues' are irrelevant and sometimes Numbo's and our wandering avenues can lead to solutions.
A third observation Defays made was that, "Solutions are often found that involve the chaining of several arithmetical operations in a seemingly logical way"(pp.151). While I didn't have many vivid analogies at hand when reading this, I couldn't deny its truth. In his detailing of Numbo's processing, Defays has shown this and I know humans do it too. Not just in math, of course, humans come to solutions of problems by way of linking different thoughts together, such as by using analogies. For example: analogy to better clarify a misunderstanding.
Although I do agree with these three similarities, I do not agree with his fourth, "Obvious solutions are found at once"(pp.150). Which is kind of funny because neither does he. He states earlier, on the same page, that due to the randomness of Numbo, "...it is sometimes possible to miss an obvious solution." And this argument, I believe, could have made a better comparison because occasionally humans do miss an obvious solution to a problem.
Overall, I give much credit to Defays' work on the Numbo system, I found it to be extremely interesting. I also greatly appreciate his discussion on how the program is similar and different to human thought. In the computer science courses I've taken for my cognitive science major it is not often discussed how the programs we use and write mirror, or don't mirror, human thought.
Something Like That
“And therefore education at the University mostly worked by the age-old method of putting a lot of young people in the vicinity of a lot of books and hoping that something would pass from one to the other, while the actual young people put themselves in the vicinity of inns and taverns for exactly the same reason.”
--Terry Pratchett
Daniel Defays' Numbo system is interesting but not quite as interesting, to me, as his rationalizing of why it operates the way it does. He claims that humans effortlessly use three types of knowledge to solve mathematical problems such as "rote small-number arithmetic (e.g., 6+1=7), ...knowledge of approximate sizes of numbers(e.g., multiplying 20 by 6 should bring us into the vicinity of 114), ...[and] procedural arithmetical knowledge (e.g., we can multiply 6 by 19)" (pp.135).
The third one mentioned somewhat surprised me because when doing math problems, such as crypto problems, I overlook that procedural knowledge I'm using because it is so basic. The second knowledge he mentions however, excited me in a nerdy way because it was something that I do often, not just in mathematics. "Just tell me how to get to NYC, we'll see if we can't find the hotel from there," is not an uncommon way to think about a problem for humans but I had never really considered it as a way to program a computer. This is just one way in which computer science has helped clarify my own ways of thinking. It amazes me how these simple thought patterns that humans use every day can turn into a year long programming project for a Belgian mathematician/psychologist.
Although Numbo is a wonderful work of art, it understandably still lacks many features which a human has when solving problems. One such feature is not having all learned processes always readily available to utilize when confronted with a problem. Another, which Defays specifically tried to correct, was that of association resulting in blindly-spreading activation leading to "uncontrolled, chaotic behaviors of the network"(pp.138). I'm not saying humans don't have some degree of control over their mind running through associations but instead that perhaps in some program, it should be embraced to better mimic humans. This happens all the time in humans, people losing focus or wandering off on some tangent. For example a typical student might be faced with a crypto problem, "Well, you can multiply 5 and 5, which is 25, which is like a quarter, four quarters in a dollar, that's equal to 100, I wonder how many licks does it really take to get to the center of a tootsie-pop, what was I doing?" Although something like this in a program would most likely never serve a purpose, other than to demonstrate association, I'm just saying that something error-like in a program doesn't always have to be rejected, especially when attempting to mimic human thought.
--Terry Pratchett
Daniel Defays' Numbo system is interesting but not quite as interesting, to me, as his rationalizing of why it operates the way it does. He claims that humans effortlessly use three types of knowledge to solve mathematical problems such as "rote small-number arithmetic (e.g., 6+1=7), ...knowledge of approximate sizes of numbers(e.g., multiplying 20 by 6 should bring us into the vicinity of 114), ...[and] procedural arithmetical knowledge (e.g., we can multiply 6 by 19)" (pp.135).
The third one mentioned somewhat surprised me because when doing math problems, such as crypto problems, I overlook that procedural knowledge I'm using because it is so basic. The second knowledge he mentions however, excited me in a nerdy way because it was something that I do often, not just in mathematics. "Just tell me how to get to NYC, we'll see if we can't find the hotel from there," is not an uncommon way to think about a problem for humans but I had never really considered it as a way to program a computer. This is just one way in which computer science has helped clarify my own ways of thinking. It amazes me how these simple thought patterns that humans use every day can turn into a year long programming project for a Belgian mathematician/psychologist.
Although Numbo is a wonderful work of art, it understandably still lacks many features which a human has when solving problems. One such feature is not having all learned processes always readily available to utilize when confronted with a problem. Another, which Defays specifically tried to correct, was that of association resulting in blindly-spreading activation leading to "uncontrolled, chaotic behaviors of the network"(pp.138). I'm not saying humans don't have some degree of control over their mind running through associations but instead that perhaps in some program, it should be embraced to better mimic humans. This happens all the time in humans, people losing focus or wandering off on some tangent. For example a typical student might be faced with a crypto problem, "Well, you can multiply 5 and 5, which is 25, which is like a quarter, four quarters in a dollar, that's equal to 100, I wonder how many licks does it really take to get to the center of a tootsie-pop, what was I doing?" Although something like this in a program would most likely never serve a purpose, other than to demonstrate association, I'm just saying that something error-like in a program doesn't always have to be rejected, especially when attempting to mimic human thought.
Intelligence: A Chance Occurrence?
“To dare every day to be irreverent and bold. To dare to preserve the randomness of mind which in children produces strange and wonderful new thoughts and forms. To continually scramble the familiar and bring the old into new juxtaposition.”
-- Gordon Webber
-- Eric Hoffer
Hofstadter talks about the intricacies of Jumbo and how it is a self-driven system, in that it has a flow of operation which is determined by factors of varying urgency and random numbers. He also claims that because of the great deal of randomness in his system that it may appear less 'intelligent' than it actually is. He does defend Jumbo by explaining that much of what we do is also random. Such things as deciding where to sit in a room, what to have for lunch, or what to wear on any given day (this is the case, at least, for most of the guys I know) have many weighted factors that may help you decide but these decisions can also be heavy with randomness. It is not in most people's best interest to take the time to rationalize out what their most viable option is for every decision they make. Just because we may not always be aware or willing to admit that many of our decisions are randomly driven, does not detract from our intelligence and could be an argument through simile for possible machine intelligence in Jumbo, or AI programs with randomness.
I enjoy that his defense of an intelligence that Jumbo may have is followed by a description of its epiphenomenal intelligence. He states that its intelligence, if any, was not intentional from its creators and emerged from the way in which the "small program-fragments interct with each other." I believe that our intelligence arises the same way, which could further link human and machine intelligence. I'm an advocate against "thinkodynamics", as Hofstadter puts it, or "laws governing thoughts at their own level." I am a staunch believer that our intelligence and our consciousness, if they differ, arose from largely random interactions between seperate parts, or functionings, of our brain, which themselves arose from more basic interactions among neurons.
So I do not believe that randomness in a system must deny that system of intelligence but perhaps that any system that is truly intelligent does have randomness in it. I believe that Hofstadter's views on entropy in machine and human systems and their relation to possible intelligence are ones that should be more widely considered by students and other computer scientists.
Wait, Where Was The Starting Line?
"The highest activities of consciousness have their origins in physical occurences of the brain just as the loveliest melodies are not too sublime to be expressed by notes."
-- William Somerset Maugham
"We must, however, acknowledge, as it seems to me, that man with all his noble qualities... still bears in his bodily frame the indelible stamp of his lowly origin."
-- Charles Darwin
On page 97 of Hofstadter's book, he mentions Herbert Simon, a cognitive scientist who claims "...that everything of interest in cognition takes place above the 100-millisecond level, which he characterizes as the time it takes for you to recognize your mother...". Simon is obviously in opposition to the idea of studying the smaller fractions of seconds that make up thought. According to Hofstadter on page 98, he claims that Simon is "...allowing one to totally sidestep or ignore all biological substrates of thought." This idea makes me immediately oppose or question Simon, in all of his views on thought, whether I believe he has any/many good arguments.
I consider myself a researcher who stresses a great deal on origins, from the universe itself to a single thought. Simon's arguments may get to the heart of what is currently able to be studied, such as macro thought processes (like identifying your mother), but I utterly disagree with his belief that the fractions of a second occurrences between neurons are not significant enough to consider. He equates the billions of neurons involved in thinking to the number of electrodes in a diode.
I believe that many cognitive scientists, as well as many physicists, would argue that those billions of neurons, or electrodes, respectively, are exactly what need to be studied in greater detail. To cast off some string of connections so easily seems reckless and unconcerned about the actual building blocks which make thinking possible. I believe that better technology and more research is all we need to change Simon's mind, as well as other like-minded scientists. It matters not which area of thought processing you study, it all comes back to the interaction between individual neurons that makes a difference.
No matter which field you're in: from philosophy, to geometry, to political science, to psychology, to neurology; breaking down your area of study to its original building blocks can and will offer great insight into your topic of interest.
-- William Somerset Maugham
"We must, however, acknowledge, as it seems to me, that man with all his noble qualities... still bears in his bodily frame the indelible stamp of his lowly origin."
-- Charles Darwin
On page 97 of Hofstadter's book, he mentions Herbert Simon, a cognitive scientist who claims "...that everything of interest in cognition takes place above the 100-millisecond level, which he characterizes as the time it takes for you to recognize your mother...". Simon is obviously in opposition to the idea of studying the smaller fractions of seconds that make up thought. According to Hofstadter on page 98, he claims that Simon is "...allowing one to totally sidestep or ignore all biological substrates of thought." This idea makes me immediately oppose or question Simon, in all of his views on thought, whether I believe he has any/many good arguments.
I consider myself a researcher who stresses a great deal on origins, from the universe itself to a single thought. Simon's arguments may get to the heart of what is currently able to be studied, such as macro thought processes (like identifying your mother), but I utterly disagree with his belief that the fractions of a second occurrences between neurons are not significant enough to consider. He equates the billions of neurons involved in thinking to the number of electrodes in a diode.
I believe that many cognitive scientists, as well as many physicists, would argue that those billions of neurons, or electrodes, respectively, are exactly what need to be studied in greater detail. To cast off some string of connections so easily seems reckless and unconcerned about the actual building blocks which make thinking possible. I believe that better technology and more research is all we need to change Simon's mind, as well as other like-minded scientists. It matters not which area of thought processing you study, it all comes back to the interaction between individual neurons that makes a difference.
No matter which field you're in: from philosophy, to geometry, to political science, to psychology, to neurology; breaking down your area of study to its original building blocks can and will offer great insight into your topic of interest.
MANGARAS. ANAGRAMS. SAGMARAN.
Hofstadter's chapter "The Unconscious Juggling of Mental Objects" intrigued me greatly. This chapter brought to the forefront a great mystery of human language ad thought for me. He discusses doing word problems commonly known as Jumbles, in daily newspapers. These problems are a collection of letters that when arranged in a proper way, spell out a word. These problems are typically referred to as anagrams and raise a great question within cognitive science.
Hofstadter believes that this mental activity of arranging letters in an anagram does not simply take place in the working memory of the letters given or the long-term memory of words known, but instead it takes place as an interaction between them.
I completely understand where Hofstadter is coming from with this argument and I've experienced it not so much in the newspaper's Jumble but in the game known as Boggle. In the game you compete against other players who are trying to figure out as many letter combinations that form words within a given 4x4 random letter grid.
"But how could semi-existent or nascent tokens come to participate in the juggling process, alongside fully-made tokens, on the one hand, and long-term memory types, on the other?" Hofstadter makes this argument when referring to the interaction between working memory (WM) and long term memory (LTM). This system involved many levels, including
I believe that the speed and capacity at which your WM operates, the common 7 +/- 2 chunks of information, involving amounts of data that are processed rapidly can affect how adept one is at solving anagrams. However, as Hofstadter also points out, it is not merely the short term memory that has an impact on an individual's ability to solve such problems but its interaction with the LTM. This is because the long term memory stores the alphabet of letters the person must refer to, as well as that persons vocabulary, along with heuristic rules on how to form words, such as consonant and vowel placement, among other rules.
Hofstadter believes that this mental activity of arranging letters in an anagram does not simply take place in the working memory of the letters given or the long-term memory of words known, but instead it takes place as an interaction between them.
I completely understand where Hofstadter is coming from with this argument and I've experienced it not so much in the newspaper's Jumble but in the game known as Boggle. In the game you compete against other players who are trying to figure out as many letter combinations that form words within a given 4x4 random letter grid.
"But how could semi-existent or nascent tokens come to participate in the juggling process, alongside fully-made tokens, on the one hand, and long-term memory types, on the other?" Hofstadter makes this argument when referring to the interaction between working memory (WM) and long term memory (LTM). This system involved many levels, including
I believe that the speed and capacity at which your WM operates, the common 7 +/- 2 chunks of information, involving amounts of data that are processed rapidly can affect how adept one is at solving anagrams. However, as Hofstadter also points out, it is not merely the short term memory that has an impact on an individual's ability to solve such problems but its interaction with the LTM. This is because the long term memory stores the alphabet of letters the person must refer to, as well as that persons vocabulary, along with heuristic rules on how to form words, such as consonant and vowel placement, among other rules.
Don't You Forget About Me
One page 75 of Hofstadter's book, he stimulates his readers thoughts about the common "me-too" phenomenon. The content in this section of the book coupled with Hofstadter's unique, down-to-earth writing style made for a refreshing read away from his pages and pages of mathematical sequences, no matter how enjoyable they may be. I was not expecting this topic to be mentioned in this book and it has reignited my desire to read it.The following conversation exemplifies the "me-too" phenomenon:
Melissa: "I love you, honey."
Brian: "Me too."
This of course can lead to some lighthearted argument but it is commonly understood that Brian, in this case, is requiting his love for Melissa and is not stating that he also loves him. Hofstadter truly intrigued me when he stated that "These little throwaway remarks... are completely unremarkable - yet for that reason they are most remarkable..." Although this topic may be a common one and overlooked by many researchers, I feel it is one of great importance to deeply understand. Outward generalizations such as this phenomenon can and do occur unconsciously and automatically but I believe it goes beyond that for many.
This topic in particular grabbed my attention because it is one I find myself constantly analyzing and often trying to make jokes about. When I bring up question regarding what a person's intentions were when they say "me too" or something in the same regard, they can sometimes become fumbled and don't understand what I'm really inquiring after. I've found myself in the same situation and it can be difficult to grasp how another person didn't understand the true meaning of your remark, even if you had swapped substructures from one level to another, added new components to the conversation, or even replaced a concept with a closely related one. These concepts were only a few given by Hofstadter in a list of abilities that humans possess to create and understand generalizations.
Although the "me-too" phenomenon is utterly fascinating in its commonplace complexity in our lives, I believe that all other common marvels of language and thought should be studied more in depth to gain a better understanding of the day-to-day workings of our minds and how complicated we really are.
Vague Analogies Are Like This Other Thing
"All perception of truth is the detection of an analogy."
"One good analogy is worth three hours discussion."
--James McCay
On page 63 of Hofstadter's book, he makes some bold claims about what intelligence is. Although he does not lay out the details exactly, he does go on to say he knows that, "analogy-making lies at the heart of of pattern perception and extrapolation." He continues with, "pattern-finding is the core of intelligence" and therefore, "analogy-making lies at the heart of intelligence."
His conclusions about intelligence amuse me. Although he may be making a very good point, it is still interesting that what he claims are central to intelligence are the topics he's most interested in and, as it seems to me so far, appears to excel at. However, I do agree that pattern-finding and analogy-making can be an important factors when determining intelligence. Perhaps because of that, it is also intriguing to me that he states these simple ideas haven't been studied much and that analogy-making is often referred to as "a specialized, isolated 'tool'."
After doing some research into the topic of the importance of analogy-making, I wasn't exactly overwhelmed by a wave of books and scholarly articles. Also, many of the articles I did peruse referenced Hofstadter in some way. I found quite a bit on analogy and natural language, although I was expecting to find significantly more. It was also surprising to find that many of the links I did uncover involved a look into cognitive science.
Hofstadter's arguments make terrific sense to me and after reading it, it seemed so obvious. Analogy is using what you've already learned in some context and applying it to another. This just seems so apparent! Maximize your learning by applying it wherever you can, then learn something new from that experience to apply elsewhere in the future and so on. This concept is astounding in its simplicity and shocking that it isn't being more widely studied.
Here is an informative and straightforward powerpoint article detailing four analogy-making systems, including Hofstadter and Mitchell's Copycat program:
http://web.cecs.pdx.edu/~mm/ArtificialIntelligenceFall2008/Slides11-12-2008.pdf
Here is a short article discussing some interesting points of analogy:
http://www.u-bourgogne.fr/LEAD/people/french/analogy.tics.pdf
--Henry David Thoreau
"One good analogy is worth three hours discussion."
--James McCay
On page 63 of Hofstadter's book, he makes some bold claims about what intelligence is. Although he does not lay out the details exactly, he does go on to say he knows that, "analogy-making lies at the heart of of pattern perception and extrapolation." He continues with, "pattern-finding is the core of intelligence" and therefore, "analogy-making lies at the heart of intelligence."
His conclusions about intelligence amuse me. Although he may be making a very good point, it is still interesting that what he claims are central to intelligence are the topics he's most interested in and, as it seems to me so far, appears to excel at. However, I do agree that pattern-finding and analogy-making can be an important factors when determining intelligence. Perhaps because of that, it is also intriguing to me that he states these simple ideas haven't been studied much and that analogy-making is often referred to as "a specialized, isolated 'tool'."
After doing some research into the topic of the importance of analogy-making, I wasn't exactly overwhelmed by a wave of books and scholarly articles. Also, many of the articles I did peruse referenced Hofstadter in some way. I found quite a bit on analogy and natural language, although I was expecting to find significantly more. It was also surprising to find that many of the links I did uncover involved a look into cognitive science.
Hofstadter's arguments make terrific sense to me and after reading it, it seemed so obvious. Analogy is using what you've already learned in some context and applying it to another. This just seems so apparent! Maximize your learning by applying it wherever you can, then learn something new from that experience to apply elsewhere in the future and so on. This concept is astounding in its simplicity and shocking that it isn't being more widely studied.
Here is an informative and straightforward powerpoint article detailing four analogy-making systems, including Hofstadter and Mitchell's Copycat program:
http://web.cecs.pdx.edu/~mm/ArtificialIntelligenceFall2008/Slides11-12-2008.pdf
Here is a short article discussing some interesting points of analogy:
http://www.u-bourgogne.fr/LEAD/people/french/analogy.tics.pdf
Getting Back To Basics
Hofstadter points out that researcher's goals can have major gulfs between them. Even though some research projects may seem to be related, they can have extremely different focuses and methodology. He distinguishes between two types of researchers: those who are interested in results and those who are interested in the essence of abstract qualia. By the way the section is written, it seems Hofstadter places himself in the latter category.
Although both types of research are needed and can benefit science in important ways, I believe it is more advantageous toward understanding the mind to look into the more abstract concepts, such as intelligence and creativity, as Hofstadter mentions. It is not only important to study the basic components of the mind in regards to mathematical sequencing and musical composition (which may be somewhat redundant) but it can also benefit every other research project related to human endeavor. By further understanding how humans can create unique ideas or artifacts and how they can manipulate stored or incoming information in such a way as to denote intelligence, however you define it, we can gain great insight into countless other fields and topics.
As Hofstadter writes, big, flashy complicated systems that can solve complex problems can be enormously beneficial to society but it is pertinent to fully grasp the how and why of that system, in terms of its most basic elements. Just as it is important to figure out the segmentation and unification of data in numerical sequencing problems, it is important to understand the basis for human thought patterns to better discover what the mind truly is and how it operates.
Although both types of research are needed and can benefit science in important ways, I believe it is more advantageous toward understanding the mind to look into the more abstract concepts, such as intelligence and creativity, as Hofstadter mentions. It is not only important to study the basic components of the mind in regards to mathematical sequencing and musical composition (which may be somewhat redundant) but it can also benefit every other research project related to human endeavor. By further understanding how humans can create unique ideas or artifacts and how they can manipulate stored or incoming information in such a way as to denote intelligence, however you define it, we can gain great insight into countless other fields and topics.
As Hofstadter writes, big, flashy complicated systems that can solve complex problems can be enormously beneficial to society but it is pertinent to fully grasp the how and why of that system, in terms of its most basic elements. Just as it is important to figure out the segmentation and unification of data in numerical sequencing problems, it is important to understand the basis for human thought patterns to better discover what the mind truly is and how it operates.
An Ocean of Neurons
It is evidently clear to readers of Douglas Hofstadter's work, especially in Fluid Concepts and Creative Analogies that he is a man of extreme passion for his work and has a liveliness about him that is quite refreshing.
With that said, his prologue of the above-mentioned book is quite informative. Although I related a great deal to his first chapter, the image he provides in the prologue of "flickering clusters" as an analogy to mental processes is extremely thought provoking. Perhaps I did not pay as much attention in chemistry class as Hofstadter did but his way of thinking about the mind makes perfect sense. As many scholars may refer to the mind as a stream of consciousness, he takes a look at what is making up that stream.
Many believe the mind to be a single unit operating for specific goals or even a compartmentalized structure with all parts working in unison. Hofstadter has supplied me with a new view of the mind: a jumble of parts that seem to play well together but may, at its base, be a beautifully chaotic mess. Looking at the beauty and consistency of the ocean, one might be inclined to suggest some purpose for it; some goal it is there to obtain. The same can be said for the beauty of human thought. It can appear to have some higher purpose like that ocean while both are made up of small parts, whether they are hydrogen and oxygen atoms or neurons, which can be chaotically interacting with each other.
Do these interactions take away any higher purpose or goal that the ocean or mind may have? I'm inclined to say of course not. Just because science can figure out how something works at the most basic level, that does not remove any mystery or allure but instead, should only add to it.
The Fluid Analogies Research Group (FARG) was a fantastic idea and I believe that Hofstadter and his colleagues have done a great deal for the field of cognitive science and science as a whole. By having these visual analogies they can attract a lot of attention to their research and the field because they are both interest grabbing and informative.
With that said, his prologue of the above-mentioned book is quite informative. Although I related a great deal to his first chapter, the image he provides in the prologue of "flickering clusters" as an analogy to mental processes is extremely thought provoking. Perhaps I did not pay as much attention in chemistry class as Hofstadter did but his way of thinking about the mind makes perfect sense. As many scholars may refer to the mind as a stream of consciousness, he takes a look at what is making up that stream.
Many believe the mind to be a single unit operating for specific goals or even a compartmentalized structure with all parts working in unison. Hofstadter has supplied me with a new view of the mind: a jumble of parts that seem to play well together but may, at its base, be a beautifully chaotic mess. Looking at the beauty and consistency of the ocean, one might be inclined to suggest some purpose for it; some goal it is there to obtain. The same can be said for the beauty of human thought. It can appear to have some higher purpose like that ocean while both are made up of small parts, whether they are hydrogen and oxygen atoms or neurons, which can be chaotically interacting with each other.
Do these interactions take away any higher purpose or goal that the ocean or mind may have? I'm inclined to say of course not. Just because science can figure out how something works at the most basic level, that does not remove any mystery or allure but instead, should only add to it.
The Fluid Analogies Research Group (FARG) was a fantastic idea and I believe that Hofstadter and his colleagues have done a great deal for the field of cognitive science and science as a whole. By having these visual analogies they can attract a lot of attention to their research and the field because they are both interest grabbing and informative.
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