Another Thursday Mull
Locked
 
|
Thoughts on what cellular automata have to tell us about development.
Dear Friamers, I fell across Wolfram in Steves Office and abducted it. At the risk of creating a GIANT windsucking all around FRIAMLAND, I have to admit I had never read or even SEEN the book. I had read a review which suggested that the first six pages were the best and I have read those pages and am having thoughts about why the book so excites people. It provides an instant model for the nature/nurture problem. So, for argument purposes, allow me to define a WS = a Wolfram Space, which is simply an R by C grid with one square blackened in the first row (1, n/2) and squares blackened in subsequent rows in accordance with some simple rule. Here is an eleven by x wolfram space where blackened squares are represented by xs. . oooooxooooo ooooxoxoooo oooxoxoxooo ooxoxoxoxoo oxoxoxoxoxo xoxoxoxoxox this is the ws which is given by the set of eight rules which may be summarized as a cell is black if either of its neighbors was black on the step before, and white if both its neighbors were white on the step before. The eight rules in this case are xxx xxo xox xoo oxx oxo oox ooo x x x x x o x o OK SO! (For those of you who love this stuff, God will reward you patience as you have watched me, a neophyte, make a dogs breakfast of it. Thank you from both of us.) Lets map a developmental space (DS) onto a WS as follows. Each Row will represent an instant in development of some trait with the first row representing the first cell division and the last row representing the form of the trait in the adult organism. Ok, so lets say the 6th row on a the above WS represents the final form of some pattern in an organism. We might think of xoxoxoxoxo as being alternating bands of a salamanders tail. Three ways of thinking about the nature/nurture problem can be represented as three ways of understanding the columns in this DS. GENETIC ATOMISM. Each column represents a series of gene products produced by a single gene. If asked why the adult has a particular pattern, the GENETIC ATOMIST will say because there is a geenfur each element in the pattern. GENETIC HOLISM Each Column represents the impact of a single genetic instruction dictating the pattern at that stage of development. Asked why the adult has a particular pattern the GENETIC HOLIST will answer, because there is a geenfur the pattern. THE DEVELOPMENTAL SYSTEMS THEORY (aka EVO-DEVO): Each column represents a location at that stage of development homologous with the location in the adult. (Dont hold me to this idea; its not the important part) Each of the eight RULES is a gene. Asked why the adult has a particular pattern, the DST theorist will say, because there are eight genes determining the relation between the state of affairs at each homologous location and the state of affairs at the same location in the next developmental stage. What I like about this metaphor is that it gives me a sense of why development is so.......MYSTERIOUS. It is mysterious for the same reasons that the patterns formed by cellular automata are mysterious. Quoting pp 39-40 from Wolfram, The pictures in the previous section plainly show that it takes only very simple rules to produce highly complex behavior. Yet a first this [conclusion] may seem almost impossible to believe. For it goes against some of the most basic intuition[s] about the way things normally work. For our everyday experience has led us to expect that an object that looks complicated must have been constructed in a complicated way. But such an assumption can be completely wrong. For the patterns we saw are in effect built according to very simple plans. Yet what emerges from these plans shows an immense level of complexity. How is may the contribution of the environment be represented in this metaphor. Recall that each row in a WS (=DS) represents a stage in development. According to DEVELOPMENTAL systems theorys approach to the nature/nurture problem, the form of the organism at each next stage of development is the result of the interaction of the organism (including its genes and gene products and the results of all previous environmental impacts) with the environment at the present stage of development. Thus we can understand the role of the environment to be to perturb the automatic progression of the stages in the DS by changing squares and thus toggling the organism into a new developmental pattern. For instance a single environmental event, the changing of the 6,2 location from o to x changes our salamander from a creature with a striped tail to one with a solid black tail. oooooxooooo ooooxXxoooo oooxxxxxooo ooxxxxxxxoo oxxxxxxxxxo xxxxxxxxxxx This example gives new life to what is meant by environment/gene interaction. Let us imagine for a moment two populations of salamanders, genetically identical, but whose environments differ ONLY in the presence or absence of the environmental factor that transforms the 2,6 location from o to x. Imagine further that tail pattern is connected to a specific mate recognition mechanism, such that striped salamanders will mate only with striped salamanders, etc. In such a system a SINGLE environmental impact could result in reproductive isolation and speciation. One implication of this idea is that if, as Wolfram repeatedly asserts, biological systems must work this way, then biological systems must be extraordinarily buffered against environmental variance. In fact, I would be on the look out for a class of cellular automata that are self repairing. I can year you all shouting at me HOORAY. THE OLD GUY GOT IT If so, thanks again for your patience. You will be rewarded in heaven. Unfortunately, I shall probably not be there it see the presentation. All the best, Nick Nicholas S. Thompson Professor of Psychology and Ethology Clark University [hidden email] http://home.earthlink.net/~nickthompson/ [hidden email] -------------- next part -------------- Dear Friamers, I fell across Wolfram in Steves Office and abducted it. At the risk of creating a GIANT windsucking all around FRIAMLAND, I have to admit I had never read or even SEEN the book. I had read a review which suggested that the first six pages were the best and I have read those pages and am having thoughts about why the book so excites people. It provides an instant model for the nature/nurture problem. So, for argument purposes, allow me to define a WS = a Wolfram Space, which is simply an R by C grid with one square blackened in the first row (1, n/2) and squares blackened in subsequent rows in accordance with some simple rule. Here is an eleven by x wolfram space where blackened squares are represented by xs. . oooooxooooo ooooxoxoooo oooxoxoxooo ooxoxoxoxoo oxoxoxoxoxo xoxoxoxoxox this is the ws which is given by the set of eight rules which may be summarized as a cell is black if either of its neighbors was black on the step before, and white if both its neighbors were white on the step before. The eight rules in this case are xxx xxo xox xoo oxx oxo oox ooo x x x x x o x o OK SO! (For those of you who love this stuff, God will reward you patience as you have watched me, a neophyte, make a dogs breakfast of it. Thank you from both of us.) Lets map a developmental space (DS) onto a WS as follows. Each Row will represent an instant in development of some trait with the first row representing the first cell division and the last row representing the form of the trait in the adult organism. Ok, so lets say the 6th row on a the above WS represents the final form of some pattern in an organism. We might think of xoxoxoxoxo as being alternating bands of a salamanders tail. Three ways of thinking about the nature/nurture problem can be represented as three ways of understanding the columns in this DS. GENETIC ATOMISM. Each column represents a series of gene products produced by a single gene. If asked why the adult has a particular pattern, the GENETIC ATOMIST will say because there is a geenfur each element in the pattern. GENETIC HOLISM Each Column represents the impact of a single genetic instruction dictating the pattern at that stage of development. Asked why the adult has a particular pattern the GENETIC HOLIST will answer, because there is a geenfur the pattern. THE DEVELOPMENTAL SYSTEMS THEORY (aka EVO-DEVO): Each column represents a location at that stage of development homologous with the location in the adult. (Dont hold me to this idea; its not the important part) Each of the eight RULES is a gene. Asked why the adult has a particular pattern, the DST theorist will say, because there are eight genes determining the relation between the state of affairs at each homologous location and the state of affairs at the same location in the next developmental stage. What I like about this metaphor is that it gives me a sense of why development is so . so . so ..MYSTERIOUS. It is mysterious for the same reasons that the patterns formed by cellular automata are mysterious. Quoting pp 39-40 from Wolfram, The pictures in the previous section plainly show that it takes only very simple rules to produce highly complex behavior. Yet a first this [conclusion] may seem almost impossible to believe. For it goes against some of the most basic intuition[s] about the way things normally work. ¶ For our everyday experience has led us to expect that an object that looks complicated must have been constructed in a complicated way. ¶ But such an assumption can be completely wrong. For the patterns we saw are in effect built according to very simple plans. Yet what emerges from these plans shows an immense level of complexity. How is may the contribution of the environment be represented in this metaphor. Recall that each row in a WS (=DS) represents a stage in development. According to DEVELOPMENTAL systems theorys approach to the nature/nurture problem, the form of the organism at each next stage of development is the result of the interaction of the organism (including its genes and gene products and the results of all previous environmental impacts) with the environment at the present stage of development. Thus we can understand the role of the environment to be to perturb the automatic progression of the stages in the DS by changing squares and thus toggling the organism into a new developmental pattern. For instance a single environmental event, the changing of the 6,2 location from o to x changes our salamander from a creature with a striped tail to one with a solid black tail. oooooxooooo ooooxXxoooo oooxxxxxooo ooxxxxxxxoo oxxxxxxxxxo xxxxxxxxxxx This example gives new life to what is meant by environment/gene interaction. Let us imagine for a moment two populations of salamanders, genetically identical, but whose environments differ ONLY in the presence or absence of the environmental factor that transforms the 2,6 location from o to x. Imagine further that tail pattern is connected to a specific mate recognition mechanism, such that striped salamanders will mate only with striped salamanders, etc. In such a system a SINGLE environmental impact could result in reproductive isolation and speciation. One implication of this idea is that if, as Wolfram repeatedly asserts, biological systems must work this way, then biological systems must be extraordinarily buffered against environmental variance. In fact, I would be on the look out for a class of cellular automata that are self repairing. I can year you all shouting at me HOORAY. THE OLD GUY GOT IT If so, thanks again for your patience. You will be rewarded in heaven. Unfortunately, I shall probably not be there it see the presentation. All the best, Nick |
«
Return to Friam
|
1 view|%1 views
| Free forum by Nabble | Edit this page |