I have to state a caveat before I begin. These are not necessarily the top ten, they are the ten that have influenced me in a way that is easily identifiable. It's entirely possible that there are people who have influenced me more than people on this list, but in ways I can't identify or remember as well. Numbers 2-10 are listed roughly chronologically, and I have grouped together people who have influenced me in similar ways.
1: Jesus Christ.
There is a lot I could say here, but the most important thing is that nothing that matters in my life would ever last if it wasn't for what Jesus Christ did. I don't know how something that happened 2,000 years ago can be such a powerful and direct strength to me, but I know that it is. I know that my character and my greatest desires are directly attributable to the power that comes from Christ's atonement.
2. My dad.
Throughout my teenage years, my dad never stopped letting me know the kind of potential he knew I had. He never stopped letting me know that I was capable of more than I was doing. He cared about my success. My response was somewhat of a delayed reaction, but because of his example, I've gained a desire to reach my highest potential. Thanks, dad. I love you.
3. Oliver Sacks.
Oliver Sacks basically gave birth to my love of neuroscience. For those who haven't seen the movie Awakenings, it's about his work with a group of patients suffering from a Parkinson's-like neurological disorder in which they are unresponsive to almost anything. Sacks figures out how to treat their condition, and remarkably many of them "wake up" and are able to live normal lives for a while. Unfortunately, the medication used to treat their condition eventually wears off, and they become unresponsive once again. Oliver Sacks told stories that opened my eyes to how truly amazing the brain is, and it made me hungry to learn more.
4. Carl Sagan.
Carl Sagan makes science an art. His description of the wonder of modern science and the discoveries we've made borders on poetry. Often, science is viewed as an extremely left-brained, analytical, and objective pursuit of life, which it frequently is. But Sagan paints a picture of the beauty and awe inherent in the way the world and the universe and life work. I love science, and I'm going to spend the rest of my life doing it, but anytime it gets too black-and-white, Sagan brings the color flowing back in for me.
5, 6, and 7: Lawrence E. Corbridge, King Benjamin, and James Watson.
These three people set into motion an extended experience that was really what made my LDS mission, and much of my life since then, meaningful for the best reasons. I've summarized this experience in a previous post, but I'll elaborate a little more here. Lawrence E. Corbridge gave a talk/speech entitled "The Fourth Missionary" that explained the difference between doing the right thing because you're supposed to and doing the right thing because you want to. As a missionary, I had mainly the former attitude at the time I read this talk, but I wanted to do the work out of desire. Corbridge's talk inspired me that such a change was possible, and convinced me that it was something I needed to look for.
I began searching the scriptures for stories of people whose hearts were changed to have desires to do good. The best example I found was in the book of Mosiah in the Book of Mormon, when an ancient American king teaches his people about experiencing a change of heart by the power of the Holy Ghost. I read his sermon multiple times over the period of a couple months, and James Watson, my missionary companion at the time, was my mentor and example through it all (largely without meaning to be, I'm sure). Nothing happened abruptly, but I know that because these things helped me open myself to the influence of the spirit of God, He changed my heart and helped me have a desire to do good. I owe more to that than almost anything.
8. Don R. Clarke.
In many Christian denominations, services include the observance of the sacrament, also called the Lord's supper. It is reminiscent of the last supper of Jesus Christ and His apostles, in which Christ gives bread and wine to remind His followers, then and now, of His crucifixion, suffering, and sacrifice for all of us. In the Church of Jesus Christ of Latter-Day Saints, the sacrament is observed each week during Sunday services, and for those like me who have grown up in the church, it's easy to lose appreciation for the ordinance. Elder Clarke helped to bring life back into this experience for me. He gave me specific ideas of what I could do to make the sacrament meaningful each week, ideas that are summarized here. As I apply his suggestions consistently, the effect has been gradual, but the sacrament has become a source of great spiritual power and strength in my life. It keeps me safe from falling into old habits and helps me keep moving forward. Near the end of my mission, I wanted to make sure there was a way to keep all of the incredibly valuable character developments I experience. Because of Elder Clarke, observing the sacrament helps me to avoid losing any progress I've made. Week after week, year after year, this has become a life-preserving spiritual resource for me.
9 and 10: Eliezer Yudkowsky and Douglas Hofstadter.
I'd be surprised if anyone reading this knows who Eliezer Yudkowsky is. Not only would that require my level of geekiness, it would also require my specific kind of geekiness, and given the readership of this blog, that's simply too improbable. Let me sum up. Eliezer Yudkowsky is the author of an online Harry Potter fanfic called "Harry Potter and the Methods of Rationality" (and yes, I can hear the laughter from here). The Harry in this story is an incredibly intelligent young boy whose intellectual acuity is far beyond those of his peers, much like Ender Wiggin of Ender's Game fame. Like Ender, Harry has a highly developed ability to read people, is extremely creative, and can make intelligent decisions rapidly. Harry makes multiple references to Douglas Hofstadter, including his award-winning book "Godel, Escher, Bach", much of which I have read. Harry uses principles of decision theory, science, mathematics, and probability, as well as his inherent skills, to get himself into and out of a variety of intense and difficult situations.
The story, while its plot is highly engaging, is in many ways a front for Yudkowsky to promote the idea of applied rationality. I could spend a whole post talking about applied rationality, and probably will, but this post is dedicated to how it's influenced me. I consider myself an intellectual by nature, and rationality has made me at least twice as much as I was before. I spend a great deal of in-between time thinking about rationality, intellectual acuity, and how I can multiply my opportunities simply by being smart about the way I make decisions. And I have to admit it's kind of a stimulant for me. I definitely think about it more often than I should, and I definitely use it to compare myself to other people far more than I should. Ways to conscientiously make yourself smarter are inherently addicting, especially for a left-brained person like me. Practicing rationality has taken several of my unique traits and multiplied them, and it's starting to throw things off balance in a way I can't really describe yet. In my current habitat of academia, this imbalance is largely working to my favor, but I need to take some time and consider how it's affecting other necessary areas of my life. Other areas that I'm going to want to take part in someday, even if not right now.
Metamorphose
Showing posts with label godel escher bach. Show all posts
Showing posts with label godel escher bach. Show all posts
Tuesday, April 1, 2014
Thursday, January 2, 2014
Capturing meaning with isomorphisms
One of the main themes of Godel, Escher, Bach (GEB) is the process of transmitting meaning through different forms. This is one of the reasons formal systems were created; to structurally organize interpreted meaning into a usable form. Mathematics itself can be thought of as a huge collection of formal systems, some of which are meant to express abstract principles (pure mathematics), and some that are tools that assist us with making calculations of real-world situations (applied mathematics). Hofstadter includes a formal system of his own making that operates the same way as addition, though he uses different symbols.
The existence of isomorphisms is necessary to the creation of a formal system, or at least one that is meant to have an interpretation or application in the real world. Hofstadter defines isomorphisms as information-preserving transformations. I like to think of them as almost a sort of transportation device that moves information from one form to another.
Isomorphisms are almost constantly present in our lives without our conscious realization of them. All of our five senses can be thought of as isomorphisms. The eyes receive the input of visible light, then transduce the electromagnetic radiation into neural signals to be sent to the brain. The ears transform vibrations in the air into our experience of sound. The nose and tongue use different mechanisms to receive the properties and configuration of various chemicals, then preserve that information in the form of a neural network of signals. And sensory receptors throughout our bodies receive pressure and heat stimuli, which they use to communicate to the brain what is happening in the outside world.
Beyond that, we use isomorphisms as tools to accomplish innumerable tasks. As you read these words, the cognitive networks in your brain are converting the otherwise meaningless figures known as letters into the experience of understanding concepts real and abstract. You may be listening to a CD, whose microscopic convoluted substructure is being read by an audio player and transformed into the sonic vibrations of a speaker unit, which in turn is being translated by the brain into the physical and emotional perception of music. And ever since the day you were conceived, an army of RNA polymerase and ribosomes has grown and multiplied and worked tirelessly to translate DNA into RNA and then into protein to build the complete, complex, complicated biological organism that houses your consciousness (since the part of you that matters wasn't made by any simple nucleic acid or enzyme). Isomorphisms are inescapable.
The above picture, Liberation by artist M.C. Escher, illustrates a transformation of one form to another. The title suggests that it's meant to be viewed from bottom to top, as if the birds above are being freed from their restrictive form below. But what if we made a slight alteration to this work? If we renamed it Capture, would it be interpreted differently? From freedom to bondage?
Capture is exactly what much of modern applied science has done and will do until everything is known. The natural phenomena that became interpreted as Newton's laws of motion, Le Chatelier's principle of dynamic equilibrium, the laws of thermodynamics, the central dogma of molecular biology, Kepler's conjectures of planetary motion, Kubler-Ross's five stages of grief, the Darwinian perspective of evolution, and thousands more were all "captured" to some extent from their free position in the universe to the human's world of pen and paper. But how well were they captured? How much information was accurately preserved? Looking back at Escher's Liberation, how far down can you go before the birds aren't really birds anymore?
In reality, the workings of the universe are so much bigger than any theorem, conjecture, or law that we try to use for capture. It's going to be a long time before we understand everything; much less express or use that knowledge intelligently. Few isomorphisms are perfect. Information is almost always lost in translation. But even if the birds are more beautiful than the triangular prisons we hold them in, the snares allow us to use the rigidity of form while retaining our appreciation for the unlimited.
The existence of isomorphisms is necessary to the creation of a formal system, or at least one that is meant to have an interpretation or application in the real world. Hofstadter defines isomorphisms as information-preserving transformations. I like to think of them as almost a sort of transportation device that moves information from one form to another.
Isomorphisms are almost constantly present in our lives without our conscious realization of them. All of our five senses can be thought of as isomorphisms. The eyes receive the input of visible light, then transduce the electromagnetic radiation into neural signals to be sent to the brain. The ears transform vibrations in the air into our experience of sound. The nose and tongue use different mechanisms to receive the properties and configuration of various chemicals, then preserve that information in the form of a neural network of signals. And sensory receptors throughout our bodies receive pressure and heat stimuli, which they use to communicate to the brain what is happening in the outside world.
Beyond that, we use isomorphisms as tools to accomplish innumerable tasks. As you read these words, the cognitive networks in your brain are converting the otherwise meaningless figures known as letters into the experience of understanding concepts real and abstract. You may be listening to a CD, whose microscopic convoluted substructure is being read by an audio player and transformed into the sonic vibrations of a speaker unit, which in turn is being translated by the brain into the physical and emotional perception of music. And ever since the day you were conceived, an army of RNA polymerase and ribosomes has grown and multiplied and worked tirelessly to translate DNA into RNA and then into protein to build the complete, complex, complicated biological organism that houses your consciousness (since the part of you that matters wasn't made by any simple nucleic acid or enzyme). Isomorphisms are inescapable.
The above picture, Liberation by artist M.C. Escher, illustrates a transformation of one form to another. The title suggests that it's meant to be viewed from bottom to top, as if the birds above are being freed from their restrictive form below. But what if we made a slight alteration to this work? If we renamed it Capture, would it be interpreted differently? From freedom to bondage?
Capture is exactly what much of modern applied science has done and will do until everything is known. The natural phenomena that became interpreted as Newton's laws of motion, Le Chatelier's principle of dynamic equilibrium, the laws of thermodynamics, the central dogma of molecular biology, Kepler's conjectures of planetary motion, Kubler-Ross's five stages of grief, the Darwinian perspective of evolution, and thousands more were all "captured" to some extent from their free position in the universe to the human's world of pen and paper. But how well were they captured? How much information was accurately preserved? Looking back at Escher's Liberation, how far down can you go before the birds aren't really birds anymore?
In reality, the workings of the universe are so much bigger than any theorem, conjecture, or law that we try to use for capture. It's going to be a long time before we understand everything; much less express or use that knowledge intelligently. Few isomorphisms are perfect. Information is almost always lost in translation. But even if the birds are more beautiful than the triangular prisons we hold them in, the snares allow us to use the rigidity of form while retaining our appreciation for the unlimited.
Tuesday, December 31, 2013
Formal systems
I'm afraid that, at least for these first few posts, it's going to sound a lot like a summary of a chapter of Godel, Escher, Bach (GEB). Hopefully my essay isn't like that.
Hofstadter begins the book with a puzzle of his own invention, which I will reproduce here. The MU-puzzle includes three and only three letters: M, I, and U. Groups of these three letters are referred to in the system as "strings" (which include MIU, IMMUMMU, MIUIUIUIU, and such). The puzzle consists of beginning with a given string, MI, and trying to produce the string "MU" within the limits of the following rules:
1. If the string's last letter is "I", you can add a "U" to the end.
2. You can produce a new string by duplicating everything after the "M". For example, MI can become MII, MUIUI can become MUIUIUIUI, MUU can become MUUUU, etc.
3. You can replace "III" with a "U" at any point in the string if you wish.
4. If you have a "UU" anywhere in the string, you can delete it (the "UU", not the string).
If you're a total nerd like I am, you might actually find some enjoyment in trying to produce the string "MU". I didn't, but Hofstadter explains in GEB that he doesn't mean for the puzzle to be solved (although he says the solution is later in the book). Solving the puzzle itself gives you experience with some of the workings of formal systems.
Hofstadter refers to given strings like "MI" as axioms, statements that you must assume to begin with since they cannot be proven. Strings produced from the axiom are called theorems, since they are provable on the basis of the axiom and the given rules.
The reason that formal systems are such a frequently-used tool of GEB is because humans and computers treat them so differently. I played with the MU-puzzle for maybe five to ten minutes before giving up. I don't know if there really is an answer, or if the author will present some "cheater" solution later in the book. But if it is truly impossible to produce "MU", a computer would continue attempting the theorem indefinitely, whereas a human would, eventually, give up.
In Hofstadter's words, jumping out of the system is a skill that seems almost wholly unique to humans. Humans "jump out of the system" by giving up on a task, postponing a task, trying to change the rules, etc. And jumping out of the system isn't always bad; in fact, exiting a system is many times an intelligent move. Computers inherently have a problem with exiting systems because staying in the system is usually what they are programmed to do.
Hofstadter then uses the three letters of the MIU-system to describe three different ways to approach a task or a system:
-Mechanical mode (M-mode), in which the task is carried out systematically much like a computer would do,
-Intelligent mode (I-mode), in which the subject learns how to use the rules and creates new ways of solving the task, much like a human would do, and
-Un-mode (U-mode), which Hofstadter doesn't describe at this point, but I assume involves jumping out of the system or changing the rules, thereby altering the internal system you began with.
Bored yet?
Hofstadter begins the book with a puzzle of his own invention, which I will reproduce here. The MU-puzzle includes three and only three letters: M, I, and U. Groups of these three letters are referred to in the system as "strings" (which include MIU, IMMUMMU, MIUIUIUIU, and such). The puzzle consists of beginning with a given string, MI, and trying to produce the string "MU" within the limits of the following rules:
1. If the string's last letter is "I", you can add a "U" to the end.
2. You can produce a new string by duplicating everything after the "M". For example, MI can become MII, MUIUI can become MUIUIUIUI, MUU can become MUUUU, etc.
3. You can replace "III" with a "U" at any point in the string if you wish.
4. If you have a "UU" anywhere in the string, you can delete it (the "UU", not the string).
If you're a total nerd like I am, you might actually find some enjoyment in trying to produce the string "MU". I didn't, but Hofstadter explains in GEB that he doesn't mean for the puzzle to be solved (although he says the solution is later in the book). Solving the puzzle itself gives you experience with some of the workings of formal systems.
Hofstadter refers to given strings like "MI" as axioms, statements that you must assume to begin with since they cannot be proven. Strings produced from the axiom are called theorems, since they are provable on the basis of the axiom and the given rules.
The reason that formal systems are such a frequently-used tool of GEB is because humans and computers treat them so differently. I played with the MU-puzzle for maybe five to ten minutes before giving up. I don't know if there really is an answer, or if the author will present some "cheater" solution later in the book. But if it is truly impossible to produce "MU", a computer would continue attempting the theorem indefinitely, whereas a human would, eventually, give up.
In Hofstadter's words, jumping out of the system is a skill that seems almost wholly unique to humans. Humans "jump out of the system" by giving up on a task, postponing a task, trying to change the rules, etc. And jumping out of the system isn't always bad; in fact, exiting a system is many times an intelligent move. Computers inherently have a problem with exiting systems because staying in the system is usually what they are programmed to do.
Hofstadter then uses the three letters of the MIU-system to describe three different ways to approach a task or a system:
-Mechanical mode (M-mode), in which the task is carried out systematically much like a computer would do,
-Intelligent mode (I-mode), in which the subject learns how to use the rules and creates new ways of solving the task, much like a human would do, and
-Un-mode (U-mode), which Hofstadter doesn't describe at this point, but I assume involves jumping out of the system or changing the rules, thereby altering the internal system you began with.
Bored yet?
Saturday, December 28, 2013
Godel, Escher, Bach
Well, I'm back. I decided to resurrect this blog because of something I'm starting to work on in college. I'm involved in the honors program at my school, and part of the program is completing what's called a great questions essay. I'm mainly using this blog right now to have a place to gather and organize my thoughts. I want to have a better idea of exactly how I want to approach this, and writing about it helps. I don't think much of this will appeal to a wide range of people, and I don't know how much I expect it to be read. Frankly, I think a lot of people will find it boring. However, it would be helpful for me to have this as a sounding board where others could give me ideas or opinions I can use, but I guess we'll see how well that pans out.
The essay I'm going to write will be based largely on a few themes from the book "Godel, Escher, Bach" by Douglas Hofstader. I was introduced to this work while reading a spinoff of Harry Potter called "Harry Potter and the Methods of Rationality". And yes, it is at least as geeky as the title implies. I like it because I'm a science nerd and so is the pseudo-Harry in the story. Anyway, the story references "Godel, Escher, Bach" (hereafter referred to as GEB) several times. Some time after starting to read this, I was looking at some things I could do to complete other requirements of the honors program, and reading GEB was one of them. I thought I would give it a try.
It's a tough book. It's tough no matter who you are. One distinguishing feature of GEB is just how familiar the author is with many academic disciplines. His main background, as evident from the book, is mathematics, computer science, physics, and philosophy; but he is also quite adeptly acquainted with life sciences, music, literature, art, and even Zen. I especially enjoy how much effort Hofstadter puts in to "dumbing down" the subject at first just enough for me to understand it. It makes it an interesting read for me because it's a challenge, as if the author is daring me to intellectually keep up and try to understand what he's explaining. What impressed me the most is how smoothly he incorporates all these areas of study to describe one of the overarching themes of the book: consciousness. He often explores this through the question: "Can a machine be programmed to think, act, or operate the way humans do?"
This is the great question I plan to address in my essay. Because GEB covers this topic so thoroughly, most of my posts here are going to be a sort of commentary about principles Hofstadter discusses in the book. However, I may later depart from those more often, since I plan in my essay to address the theological perspective of the issue, which Hofstadter never touches. To those reading this post, I would recommend trying to read a couple posts if you're interested, and if you're still bored after that, give up. I don't want to waste anyone's time with this blog if what I discuss isn't what you're interested in. But if it does appeal to you, it would be helpful to have additional feedback. So here goes.
The essay I'm going to write will be based largely on a few themes from the book "Godel, Escher, Bach" by Douglas Hofstader. I was introduced to this work while reading a spinoff of Harry Potter called "Harry Potter and the Methods of Rationality". And yes, it is at least as geeky as the title implies. I like it because I'm a science nerd and so is the pseudo-Harry in the story. Anyway, the story references "Godel, Escher, Bach" (hereafter referred to as GEB) several times. Some time after starting to read this, I was looking at some things I could do to complete other requirements of the honors program, and reading GEB was one of them. I thought I would give it a try.
It's a tough book. It's tough no matter who you are. One distinguishing feature of GEB is just how familiar the author is with many academic disciplines. His main background, as evident from the book, is mathematics, computer science, physics, and philosophy; but he is also quite adeptly acquainted with life sciences, music, literature, art, and even Zen. I especially enjoy how much effort Hofstadter puts in to "dumbing down" the subject at first just enough for me to understand it. It makes it an interesting read for me because it's a challenge, as if the author is daring me to intellectually keep up and try to understand what he's explaining. What impressed me the most is how smoothly he incorporates all these areas of study to describe one of the overarching themes of the book: consciousness. He often explores this through the question: "Can a machine be programmed to think, act, or operate the way humans do?"
This is the great question I plan to address in my essay. Because GEB covers this topic so thoroughly, most of my posts here are going to be a sort of commentary about principles Hofstadter discusses in the book. However, I may later depart from those more often, since I plan in my essay to address the theological perspective of the issue, which Hofstadter never touches. To those reading this post, I would recommend trying to read a couple posts if you're interested, and if you're still bored after that, give up. I don't want to waste anyone's time with this blog if what I discuss isn't what you're interested in. But if it does appeal to you, it would be helpful to have additional feedback. So here goes.
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