Gemsbok in the Carl Akely Hall of African Mammals
(photo by Chris Randolph, thanks for reminding me of this!)
and now for some rembrandt:
Saturday, January 28, 2012
Rembrandt at the American Museum Of Natural History
Gemsbok in the Carl Akely Hall of African Mammals
(photo by Chris Randolph, thanks for reminding me of this!)
and now for some rembrandt:
Sunday, January 8, 2012
How to Think About a Worm Evolving Into a Bird
that's quite a stretch, yes... i mean where do all the parts come from right? looks like the worm is some kind of simple clay and some artist with an imagination has to sculpt the bird parts out of the worm-clay
that's a reasonable idea. given that we come from a culture of artists and craftsmen and not the modern biology class.
So the first step is to describe what kind of 'clay' we've discovered a worm is. If we want to know how a worm can change into a bird, first of all, do you have any idea how a bird egg turns into a bird? that would be a start. I mean, how do you think birds get sculpted all around us everyday? If I told you, you'd be more amazed than your disbelief that a worm could turn into one.
so for a worm to evolve into a bird of course we mean that a worm gives birth to a bird, or of course that a worm gives birth to a slightly different worm that gives birth to a slightly different one, and eventually worms are hatching with nubby legs and eye spots, and eventually heart and lungs, and feathers and wings... Seems incredible, eh? but really what you want to start with is how does a bird give birth to a bird? It lays an egg and the egg turns into a bird. lets start there! How does it happen?
[and then you may have some vague notion that a bird is so different than a worm, that it has so many more complex parts and behaviors that for this to happen the number of minute changes necessary is astronomical and couldn't happen in a 1000 years or a million years. But that's just the point, you just have a VAGUE notion. do you really know how to think about just HOW MANY changes are necessary? and is it some kind of continuous sculpting or is there a discrete number of changes at all? ARE animals made up of discrete parts that CAN be changed one part at a time?]
of course in the egg that you eat, before it is fertilized, there is no bird structure. WHERE DOES THE BIRD STRUCTURE COME FROM, that's your whole question. where does the structure come from and then prior to that, where does the design for the structure come from, i mean it's pretty clear that there is some clever designs in a bird.
[bar, i think the common notion of design is that a person designs something at least with an intention in mind, even thought the process may be an evolution by trial and error of ideas in mind. so we need another word? while the parts of the bird mostly work well, they werent put together in the bird with any intention. after i intentionally design a mechanism who's parts work well together, how would i describe the product? can't think of a word at the moment.]
ok, well, how does the bird come about? what is a bird? A bird, like every other big animal and plant is a gigantic society of cooperating single celled amoebas that start off from a single amoeba that colonizes the food in the egg. The egg is the shore of a lush tropical island and a single livinig amoeba organism detaches from the society of amoebas that is the mother bird and washes up on that shore of a tropical island and starts eating.
you've heard that you are made up of cells, all animals are. what are they? They are tiny individual organsisms. perhaps you've watched some pond water under a microscope and watched amoebas and stentors and parameciums swimming around in there... These are real critters not so much more different than the animals that we are familiar with. They swim about, they can smell, feel vibrations (hear) some can see light and dark, even react to moving edges of shadows... they have the same desires as we do, hunger, fleeing from harm, cold, hot, having to pee, wanting to find mates... they have capacity for memory and the ability to explore and try things out and learn from mistakes. they can eat and transform their food into internal organs and grow and eventually reproduce, some with mating and some just by splitting in half.
they also exhibit variation in their children just as our children are not identical to us or each other.
How do they do it? what's inside THEM? another hierarchical level of smaller cells? no, what's inside cells, what ultimately makes life alive is another whole level of giganticism different than ours. Just as each of us or a bird is huge beyond a cell's belief, made of a trillion of them, each cell is a stupendous squaredance of molecular assemblies. there is business inside cells, processes, patterns, decision making loops, trial and error processes of creativity, on a stupendous scale. a living cell is a squaredance of molecules, as many molecules as there are bricks in all of new york city.
wander around in that city and walk by all the buildings and cars and people... and imagine that all the buildings are made of bricks, and that each brick is a kind of simple squrimy crawly robot that can interact with the other bricks and make simple mechanical decisions around each other as if it had a simple computer program subroutine written inside it with some if statements...
now wander around that city and imagine all those bricks crawling around each other and forming patterns and building that city from the bottom up, a dynamic city that can grow it's own parts, take them apart and rebuild, redesign depending on its needs, ultimately able to reproduce itself and send forth a whole new city.
So that's a single living cell. With all that dynamism and bustling of moving, interacting, decision making parts, these living cells can respond to each other with creative subtlety and morph each other into different shaped cells and come together and create huge complex structures.
I think the main problem in imagining how an egg can turn into an adult animal or how an animal can evolve into another kind of animal is that we really don't have a good sense for just how complex even the begining egg already is. how responsive to circumstances and how able to explore and create... The complexity inside is just not something we have much experience with. We certainly aint taught agbout it in school.
So, the chicken egg is a yolky shore on which this single complex cell washes up. what can it do? Bear in mind throughout this description how the bird is not going to be sculpted from the outside by a few clumsy hands, but that it is going to be built, grown from the inside by dozens, thousands, MILLIONS, B I L L I O N S of these critters crawling around each other and growing more of each other.
Is there anything we are familiar with to which we can compare it? I'm not sure!
Now that we know there are enough tiny construction workers INSIDE that growing bird embryo, lets show where all the detailed features come about. Let's imagine a crew of construction workers about to build a wing. The first thing they do is lay out a ground plan and arrange themselves into different crews. One group agrees to work on bones, another group agrees to work on blood vesels, another on muscles, nerves, feathers... so some of the workers lay themselvces out in a
[ok, so i can lookup some of the developmental processes and describe them, how the cells crawl around, how they signal each other and decide based on who they are surrounded by and what signals they recieve they change thir professions from building inside of bone to outside of bone, from laying down skin to building feather shafts and then these split up into some building shafts and some building feather vanes etc...
...
Fine, so now i've described to you that theres a society of tiny construction workers building the bird on that shore of yolk out of themselves. But how do they KNOW how to do it? where does the blueprint come from? Ah, that comes to the heart of our understanding of the digital changes generation after generation whereby a worm can givce rise to a bird.
Inside each living cell is an identical library of blueprints and bulletin boards. This library of course is the DNA that makes up our genes. Each blueprint has a bulletin board attached to it, by which ...
Ok, just as the cells are construction workers in the growing embryo, inside the cells are the proteins (the molecular robots of which there are as many as there are bricks in nyc) which are the construction workers that build and maintain the growing cell. Just like cells, these robots can tear down and build new robots, they can interact with each other, they can come together to make larger structures, they can process information, making basic level decisions based on signals supplied by the concentrations of small molecules and by contacting other robots.
Some of these protein robots build dynamic scaffolding that shapes the cells. Some of them act as sense organs on the surface of cells. The sense organs can detect neighboring cells, which kind they are and they can also sense signal molecules that are sent from afar by other cells. Others act as connectors that enable certain cells to attach to each other. Other proteins act as information processing units, like simple logic gates in our computers or simple subroutines in complex computer programs. All these robots come together to control the way cells behave and respond to their environment.
Now inside that initial cell that detaches from the mother cell-society and lands on the yolk is the DNA library for making proteins. It contains blueprints for about 10,000 different kinds of proteins. I think that might correspond to how many different kinds of parts and professions of people that a large city might contain, continuiing the analogy of a cell being as complex as a bustling city.
But at any one time, the cell is only building a few thousand kinds out of that repetoir of 10,000. And this particular selection out of the possible 10,000 is what makes one cell act differently than another cell that is building a different set of protein robots.
An important thing to mention about these prootein robots is how they 'decide' which robots to tear down, and which neww kinds to build. well, attached to each robot blueprint is a bulletin board that specifies when and whether and how much that blueprint is to be read and used too construct another robot. The existing protein-robots act together and integrate the signals coming from outside the cell (what other cells surround it and what signals from far away cells are being recieved) with the current goings on inside the cell and and depending on what's going on, will attach themselvces in various combinations to each bulletin board. So, depending on the state of the cell and the state of its surroundings only certain proteins are being produced, and in certain amounts, and this process can even specify where in teh cell the proteins will go.
These processes will even result in different sensory proteins being placed on the surface of the cell and different signal molecules being sent out of the cell, so that the cell can communicate with other cells what THEY ought to be doing.
Now we are getting close to how the form of the bird comes about! Where does the feather come from? What kind of design process is this? Is there a blueprint in there with the shape of a feather on it? Alas, no! It's way crazier than THAT! It's at this point we have to take a side road and talk about how complex pattern appears in this universe from very simple rules that are spread out across the system as opposed to being 'crafted' by 'craftsmen' with an overarching central plan in mind.
>>>>HERE IS WHY I CAN'T WRITE COMPLEXITY LAB MANUAL YET. I NEED TO DISCOVER MORE (IN A GRAD PROGRAM) DISS'PATEEV! (actually, we might know enough detail about how the genetic ciruits specify forms in embryos now. so maybe i gotta learn that. but I think i need a nonmolecular/cellular analogy to help people without years of molec bio to understand!
>>>the key thiing to explain is how simple local rules on a grid, or possessed by 100s of simple agents can come together cooperatively into complex geometric shapes. So lets find a simple rule that will produce an intresteing complex shape and then ask: how do you suppose we can specify the rules for a robot to draw this shape, or perhaps a 100 robots to swarm around and draw it. ok, which example should i use? langton's blob and highway? it's a weird shape, too messy to use as an example. now one of those worm dragons would be cool. ok. how about something from conway life? does any simple seed bloom into a pattern that someone would find fascinating but easy to grasp? r pentomino makes a mess. can a random seed in evoloop grow into an evoloop? (90 rules!)
what's a simple way to specify the construction of a rough sketch of the mandelbrot set?
COOPERATIVE/DISTRIBUTED PATTERN FORMATION
Where does pattern come from? snowflakes, frost on window panes, hurricanes, [damm, i can't think of any other intersting natural patterns other than living critters? hmm... why the gap? thats a problem. the patterns in living critters come from a combination of molecular scale interactions and large scale properties of materials like surface tension and like the fibonacci spirals in plants coming from patterns of strain on the surface of the apical meristem. hmm... so of course we don't see many molecular scale patterns because we are too big, unless they anneal for long periods of time and form large crystals? well there are feathery patterns of percolation, weird patterns in goethite.. there are some cloud patterns, there is the large scale weather pattern on earth as a whole, and the crazier looking one on jupiter and saturn. the patterns of ice formation on europa, BZ if anyone bothered to look... bar, this is nothing like a BIRD WING! hmm...
why do i have to move to mathematical games for that kiind of complexity? the worm games, langton's ant, r-pentomino in conway life, mandelbrot set... and ARE there examples of nonliving molecular scale pattern formation as complicated as those mathematical ones? How to even hunt for them?
THIS IS THE KEY GOAL OF COMPLEXITY LAB MANUAL AND FURTHER RESEARCH ON MY PART, TO BRIDGE THAT GAP.
well, onward. lets start with static: snowflakes. Actually, we aren't terribly sure how snowflake patterns form. We do understand that water molecules have shape, and have a certain geometry to the way their ends electromagnetically attract each other. and how much the molecules can bend when attached to each other in large grops. We know what amounts of energy are iinvolved in breakiing and forming those bonds. we can more or less understand how water will form hexagonal symmetry. we know how the subtle conditiions in clouds with their moisture contentt and temperatures and relative humidities will allow water molecules to bond to the surface of the growing snowflake and then come off again or affect how other water molecules bond. how the curvature of the surface affects whether and where and how easily more molecules will bond.
and then given these parameters, they specify a set of feedback loops in certain geometries which result in the shapes of snowflakes.
Math is involved. let me givce you some examples of how a set of rules of feedbacks in geometry will give you complicated shapes.
1) fractal triangle: suppose we start with an equilateral triangle
>>>>>bar, this is WAY TOO LONG A DIVERSION!
...
BACK TO EMBRYOLOGY
so lets look at a simple set of feedback loops in a geometrical context made out of a small set of protein robots and their blueprints. now i gotta describe hoxology that produces turings stripes leading to segment formation in embryos. then how these systems can 'count' which segment they are on and initiate bud formation. how other systems will expand buds, patterns of apoptosis in the bud that can lay out patterns of bones... the fractal complexity of feathers? well at least there's some work on pattern formation in butterfly wings.
if we don't belive it we can show BZ, snowflakes and ... see those are nice but the digital nature of the genes i think is what can give us more interesting pattern than snowflakes and the ability of biologicall systems to form quick feedbacks to narrow responses to form more discrete boundaries than BZ?
God, i need to learn more. but there are plenty of math systems like langton's ant, and those worms with simple rules that create dragon shapes... rule 110 creates complex structures. gotta find more examples. come on you got sayama's evo loops with like 90 rules with 9 states in each cell. but living cells have 10,000 rules with god knows how many states. oh.
can we rebuild the langton self rep loop rules to form the loop from ONE cell? That would be way cool. it would basically be embrygenisis. construct it stage by stage:
1) 1:00000000-->2
2) 0:00010000-->2
3) 2:00020000-->3
4) 0:00030000-->2
5) 0:00000023-->4 etc... would take weeks of hard work to do, maybe sayama could help.
well, that's complexity lab manual. I have't studied hoxology in detail, but i've got ennough math to intuit that diffequs on continuous gradients can create spike bifurcations. I Don't know exactly how the 90 rules for selfrep loop work, but i've worked enough examples that i'm sure if i look into it i'll see how those rules can produce structure and that i can probably make rules that produce more sturcture. or for that matter the simplest random rules like 110 and langtons ant already givee curious structure.
Now this is no longer an essay about how a worm can evolve into a bird. but hell, who says the answer to that question is going to come simply? What's the simplest i can boil this down to explain at least the direction and how complicated it would really be? hmmm
I think one of my problems is that I DON'T UNDERSTAND IN DETAIL say, the genetic circuits in segment formation, give rise to the turing mechanism of segment formation. that's the point of complexity lab to write this book without the vague handwaving found in all the other books. (do i really have detail notes on capra's book?)
...
that's a reasonable idea. given that we come from a culture of artists and craftsmen and not the modern biology class.
So the first step is to describe what kind of 'clay' we've discovered a worm is. If we want to know how a worm can change into a bird, first of all, do you have any idea how a bird egg turns into a bird? that would be a start. I mean, how do you think birds get sculpted all around us everyday? If I told you, you'd be more amazed than your disbelief that a worm could turn into one.
so for a worm to evolve into a bird of course we mean that a worm gives birth to a bird, or of course that a worm gives birth to a slightly different worm that gives birth to a slightly different one, and eventually worms are hatching with nubby legs and eye spots, and eventually heart and lungs, and feathers and wings... Seems incredible, eh? but really what you want to start with is how does a bird give birth to a bird? It lays an egg and the egg turns into a bird. lets start there! How does it happen?
[and then you may have some vague notion that a bird is so different than a worm, that it has so many more complex parts and behaviors that for this to happen the number of minute changes necessary is astronomical and couldn't happen in a 1000 years or a million years. But that's just the point, you just have a VAGUE notion. do you really know how to think about just HOW MANY changes are necessary? and is it some kind of continuous sculpting or is there a discrete number of changes at all? ARE animals made up of discrete parts that CAN be changed one part at a time?]
of course in the egg that you eat, before it is fertilized, there is no bird structure. WHERE DOES THE BIRD STRUCTURE COME FROM, that's your whole question. where does the structure come from and then prior to that, where does the design for the structure come from, i mean it's pretty clear that there is some clever designs in a bird.
[bar, i think the common notion of design is that a person designs something at least with an intention in mind, even thought the process may be an evolution by trial and error of ideas in mind. so we need another word? while the parts of the bird mostly work well, they werent put together in the bird with any intention. after i intentionally design a mechanism who's parts work well together, how would i describe the product? can't think of a word at the moment.]
ok, well, how does the bird come about? what is a bird? A bird, like every other big animal and plant is a gigantic society of cooperating single celled amoebas that start off from a single amoeba that colonizes the food in the egg. The egg is the shore of a lush tropical island and a single livinig amoeba organism detaches from the society of amoebas that is the mother bird and washes up on that shore of a tropical island and starts eating.
you've heard that you are made up of cells, all animals are. what are they? They are tiny individual organsisms. perhaps you've watched some pond water under a microscope and watched amoebas and stentors and parameciums swimming around in there... These are real critters not so much more different than the animals that we are familiar with. They swim about, they can smell, feel vibrations (hear) some can see light and dark, even react to moving edges of shadows... they have the same desires as we do, hunger, fleeing from harm, cold, hot, having to pee, wanting to find mates... they have capacity for memory and the ability to explore and try things out and learn from mistakes. they can eat and transform their food into internal organs and grow and eventually reproduce, some with mating and some just by splitting in half.
they also exhibit variation in their children just as our children are not identical to us or each other.
How do they do it? what's inside THEM? another hierarchical level of smaller cells? no, what's inside cells, what ultimately makes life alive is another whole level of giganticism different than ours. Just as each of us or a bird is huge beyond a cell's belief, made of a trillion of them, each cell is a stupendous squaredance of molecular assemblies. there is business inside cells, processes, patterns, decision making loops, trial and error processes of creativity, on a stupendous scale. a living cell is a squaredance of molecules, as many molecules as there are bricks in all of new york city.
wander around in that city and walk by all the buildings and cars and people... and imagine that all the buildings are made of bricks, and that each brick is a kind of simple squrimy crawly robot that can interact with the other bricks and make simple mechanical decisions around each other as if it had a simple computer program subroutine written inside it with some if statements...
now wander around that city and imagine all those bricks crawling around each other and forming patterns and building that city from the bottom up, a dynamic city that can grow it's own parts, take them apart and rebuild, redesign depending on its needs, ultimately able to reproduce itself and send forth a whole new city.
So that's a single living cell. With all that dynamism and bustling of moving, interacting, decision making parts, these living cells can respond to each other with creative subtlety and morph each other into different shaped cells and come together and create huge complex structures.
I think the main problem in imagining how an egg can turn into an adult animal or how an animal can evolve into another kind of animal is that we really don't have a good sense for just how complex even the begining egg already is. how responsive to circumstances and how able to explore and create... The complexity inside is just not something we have much experience with. We certainly aint taught agbout it in school.
So, the chicken egg is a yolky shore on which this single complex cell washes up. what can it do? Bear in mind throughout this description how the bird is not going to be sculpted from the outside by a few clumsy hands, but that it is going to be built, grown from the inside by dozens, thousands, MILLIONS, B I L L I O N S of these critters crawling around each other and growing more of each other.
Is there anything we are familiar with to which we can compare it? I'm not sure!
Now that we know there are enough tiny construction workers INSIDE that growing bird embryo, lets show where all the detailed features come about. Let's imagine a crew of construction workers about to build a wing. The first thing they do is lay out a ground plan and arrange themselves into different crews. One group agrees to work on bones, another group agrees to work on blood vesels, another on muscles, nerves, feathers... so some of the workers lay themselvces out in a
[ok, so i can lookup some of the developmental processes and describe them, how the cells crawl around, how they signal each other and decide based on who they are surrounded by and what signals they recieve they change thir professions from building inside of bone to outside of bone, from laying down skin to building feather shafts and then these split up into some building shafts and some building feather vanes etc...
...
Fine, so now i've described to you that theres a society of tiny construction workers building the bird on that shore of yolk out of themselves. But how do they KNOW how to do it? where does the blueprint come from? Ah, that comes to the heart of our understanding of the digital changes generation after generation whereby a worm can givce rise to a bird.
Inside each living cell is an identical library of blueprints and bulletin boards. This library of course is the DNA that makes up our genes. Each blueprint has a bulletin board attached to it, by which ...
Ok, just as the cells are construction workers in the growing embryo, inside the cells are the proteins (the molecular robots of which there are as many as there are bricks in nyc) which are the construction workers that build and maintain the growing cell. Just like cells, these robots can tear down and build new robots, they can interact with each other, they can come together to make larger structures, they can process information, making basic level decisions based on signals supplied by the concentrations of small molecules and by contacting other robots.
Some of these protein robots build dynamic scaffolding that shapes the cells. Some of them act as sense organs on the surface of cells. The sense organs can detect neighboring cells, which kind they are and they can also sense signal molecules that are sent from afar by other cells. Others act as connectors that enable certain cells to attach to each other. Other proteins act as information processing units, like simple logic gates in our computers or simple subroutines in complex computer programs. All these robots come together to control the way cells behave and respond to their environment.
Now inside that initial cell that detaches from the mother cell-society and lands on the yolk is the DNA library for making proteins. It contains blueprints for about 10,000 different kinds of proteins. I think that might correspond to how many different kinds of parts and professions of people that a large city might contain, continuiing the analogy of a cell being as complex as a bustling city.
But at any one time, the cell is only building a few thousand kinds out of that repetoir of 10,000. And this particular selection out of the possible 10,000 is what makes one cell act differently than another cell that is building a different set of protein robots.
An important thing to mention about these prootein robots is how they 'decide' which robots to tear down, and which neww kinds to build. well, attached to each robot blueprint is a bulletin board that specifies when and whether and how much that blueprint is to be read and used too construct another robot. The existing protein-robots act together and integrate the signals coming from outside the cell (what other cells surround it and what signals from far away cells are being recieved) with the current goings on inside the cell and and depending on what's going on, will attach themselvces in various combinations to each bulletin board. So, depending on the state of the cell and the state of its surroundings only certain proteins are being produced, and in certain amounts, and this process can even specify where in teh cell the proteins will go.
These processes will even result in different sensory proteins being placed on the surface of the cell and different signal molecules being sent out of the cell, so that the cell can communicate with other cells what THEY ought to be doing.
Now we are getting close to how the form of the bird comes about! Where does the feather come from? What kind of design process is this? Is there a blueprint in there with the shape of a feather on it? Alas, no! It's way crazier than THAT! It's at this point we have to take a side road and talk about how complex pattern appears in this universe from very simple rules that are spread out across the system as opposed to being 'crafted' by 'craftsmen' with an overarching central plan in mind.
>>>>HERE IS WHY I CAN'T WRITE COMPLEXITY LAB MANUAL YET. I NEED TO DISCOVER MORE (IN A GRAD PROGRAM) DISS'PATEEV! (actually, we might know enough detail about how the genetic ciruits specify forms in embryos now. so maybe i gotta learn that. but I think i need a nonmolecular/cellular analogy to help people without years of molec bio to understand!
>>>the key thiing to explain is how simple local rules on a grid, or possessed by 100s of simple agents can come together cooperatively into complex geometric shapes. So lets find a simple rule that will produce an intresteing complex shape and then ask: how do you suppose we can specify the rules for a robot to draw this shape, or perhaps a 100 robots to swarm around and draw it. ok, which example should i use? langton's blob and highway? it's a weird shape, too messy to use as an example. now one of those worm dragons would be cool. ok. how about something from conway life? does any simple seed bloom into a pattern that someone would find fascinating but easy to grasp? r pentomino makes a mess. can a random seed in evoloop grow into an evoloop? (90 rules!)
what's a simple way to specify the construction of a rough sketch of the mandelbrot set?
COOPERATIVE/DISTRIBUTED PATTERN FORMATION
Where does pattern come from? snowflakes, frost on window panes, hurricanes, [damm, i can't think of any other intersting natural patterns other than living critters? hmm... why the gap? thats a problem. the patterns in living critters come from a combination of molecular scale interactions and large scale properties of materials like surface tension and like the fibonacci spirals in plants coming from patterns of strain on the surface of the apical meristem. hmm... so of course we don't see many molecular scale patterns because we are too big, unless they anneal for long periods of time and form large crystals? well there are feathery patterns of percolation, weird patterns in goethite.. there are some cloud patterns, there is the large scale weather pattern on earth as a whole, and the crazier looking one on jupiter and saturn. the patterns of ice formation on europa, BZ if anyone bothered to look... bar, this is nothing like a BIRD WING! hmm...
why do i have to move to mathematical games for that kiind of complexity? the worm games, langton's ant, r-pentomino in conway life, mandelbrot set... and ARE there examples of nonliving molecular scale pattern formation as complicated as those mathematical ones? How to even hunt for them?
THIS IS THE KEY GOAL OF COMPLEXITY LAB MANUAL AND FURTHER RESEARCH ON MY PART, TO BRIDGE THAT GAP.
well, onward. lets start with static: snowflakes. Actually, we aren't terribly sure how snowflake patterns form. We do understand that water molecules have shape, and have a certain geometry to the way their ends electromagnetically attract each other. and how much the molecules can bend when attached to each other in large grops. We know what amounts of energy are iinvolved in breakiing and forming those bonds. we can more or less understand how water will form hexagonal symmetry. we know how the subtle conditiions in clouds with their moisture contentt and temperatures and relative humidities will allow water molecules to bond to the surface of the growing snowflake and then come off again or affect how other water molecules bond. how the curvature of the surface affects whether and where and how easily more molecules will bond.
and then given these parameters, they specify a set of feedback loops in certain geometries which result in the shapes of snowflakes.
Math is involved. let me givce you some examples of how a set of rules of feedbacks in geometry will give you complicated shapes.
1) fractal triangle: suppose we start with an equilateral triangle
>>>>>bar, this is WAY TOO LONG A DIVERSION!
...
BACK TO EMBRYOLOGY
so lets look at a simple set of feedback loops in a geometrical context made out of a small set of protein robots and their blueprints. now i gotta describe hoxology that produces turings stripes leading to segment formation in embryos. then how these systems can 'count' which segment they are on and initiate bud formation. how other systems will expand buds, patterns of apoptosis in the bud that can lay out patterns of bones... the fractal complexity of feathers? well at least there's some work on pattern formation in butterfly wings.
if we don't belive it we can show BZ, snowflakes and ... see those are nice but the digital nature of the genes i think is what can give us more interesting pattern than snowflakes and the ability of biologicall systems to form quick feedbacks to narrow responses to form more discrete boundaries than BZ?
God, i need to learn more. but there are plenty of math systems like langton's ant, and those worms with simple rules that create dragon shapes... rule 110 creates complex structures. gotta find more examples. come on you got sayama's evo loops with like 90 rules with 9 states in each cell. but living cells have 10,000 rules with god knows how many states. oh.
can we rebuild the langton self rep loop rules to form the loop from ONE cell? That would be way cool. it would basically be embrygenisis. construct it stage by stage:
1) 1:00000000-->2
2) 0:00010000-->2
3) 2:00020000-->3
4) 0:00030000-->2
5) 0:00000023-->4 etc... would take weeks of hard work to do, maybe sayama could help.
well, that's complexity lab manual. I have't studied hoxology in detail, but i've got ennough math to intuit that diffequs on continuous gradients can create spike bifurcations. I Don't know exactly how the 90 rules for selfrep loop work, but i've worked enough examples that i'm sure if i look into it i'll see how those rules can produce structure and that i can probably make rules that produce more sturcture. or for that matter the simplest random rules like 110 and langtons ant already givee curious structure.
Now this is no longer an essay about how a worm can evolve into a bird. but hell, who says the answer to that question is going to come simply? What's the simplest i can boil this down to explain at least the direction and how complicated it would really be? hmmm
I think one of my problems is that I DON'T UNDERSTAND IN DETAIL say, the genetic circuits in segment formation, give rise to the turing mechanism of segment formation. that's the point of complexity lab to write this book without the vague handwaving found in all the other books. (do i really have detail notes on capra's book?)
...
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