back to top
I) LIFE
6) Key Out 100 Plants In A Local Park
2) collect insects and watch their behavior in a terrarium
4.5) 270 Skills That a Honeybee Has
VI) COMPUTERS
8)from logic gates to computer
61.2) write simple computer programs in machine code:
61.3) program conway life, mandelbrot, and lorenz in lego bot
9) show them well programmed lego bots
I) SO BACK TO CRITTERS FOR HELP
16) watch videos of animal development
II) CELLULAR LIFE
22) watch single cell pond creatures [hr]
27) molec video inner life of cell [10min] more?
25) grow oscillatoria in water and glass jar.
III) WHAT IS THE MOLECULAR WORLD?
73.2) brownian motion: .
73.3) monomolecular lipid layer:
72.2) show how many ways an ethanol molecule can respond
31.2) Distributed Brownian Motion Machinery: Clathrin Coated Pits
44) Play With A Candle Flame
IV) DISSIPATIVE STRUCTURES: FLOW OF ENERGY THROUGH SYSTEMS CREATES PATTERNED DYNAMISM
64.2) chaotic waterwheel, thermostat and heater, door buzzer [hr]
33) show steam engine (with governer?)
34) Then Benard convection
42) BZ reaction :
44) play with a flame: [hr]
V) MATHEMATICAL DYNAMICAL SYSTEMS: EASY LABORATORY, ALL YOU NEED IS PENCIL, PAPER, COMPUTER
48) John Horton Conway's game of life
53) and rule 30, 110
56) 3n+1:
57) e/o fibo system:
58)logistic equation to mandelbrot set:
60) lorenz attractor:
VII) EVEN AT EQUILIBRIUM: PHYSICAL AND CHEMICAL PATTERN FORMATION
74) show periodic chart with samples of diff elements
76) phases of sulfur:
75) and breath on a window pane: ditto for water molecules
70) mineral exhibit 2000 minerals for free
VIII) IT ALL COMES FROM MATH
87) enumeration of finite graphs:
81) classification of finite simple groups:
IX) PUTTING IT ALL BACK TOGETHER: EVOLUTIONARY BIOLOGY
96) Tierra
X) THE FINAL FRONTIER: CAN WE UNDERSTAND HOW GEOCHEMISTRY CAN BECOME LIFE?
98) Ecosystem Of Reproducing Candle Wicks?
99) Self Sustaining Ecosystem Of Reproducing Chemical Robots?
100) Chemical Origin Of Life
XI) MIND?
XII) SUPERORGANISMS
Monday, May 18, 2009
Complexity Lab Manual Introduction version8
back to top
I) LIFE
If the question is, can life be simply a property of chemistry, then lets start off by exploring how complex life is. Lets go out there into a field or a park or woods or roadside and look at the plants. There are different kinds! I challenge you: can you find me 100 different kinds in an hour?
We can! In order to keep track we will tape some representative samples of each to pages in our plant press and in order to tell whether one is different from another, we will have to look closely. The leaves are arranged on the stems differently. some leaves have teeth or lobes. some are hairy, some smooth, some waxy.
Some of the plants are flowering, some have 4 petals, some 5, some 6.. some just a whole lot. some have 2 stamens, some have 3 or 5 or 10. there is every which way combinations. some have hairs below the flowers. some of the hairs (look REALLY closely with a hand lens) have sticky blobs on the tips!
Some of the plants are in seed, the seeds also have details, some have bumps, some have stems attached to them, some have hairs attached to the stems, some of the hairs (hand lenses again) are barbed... (6) Key Out 100 Plants In A Local Park
So far, we've found and described over 2 million different kinds of living plants, animals and microorganisms on this planet Earth. We can distinguish SO MUCH variety because there are SO many details in each organism to see. As far in as we look, with hand lens, with microscope, there are more and more details.
How does life become so detailed?
Surely one of the most interesting details is how animals behave. Lets go find some insects and keep them in a terrarium and play with them and let them eat and hop, fly around and watch how complex their behaviors are (lab2). You can do an ant colony, or a grasshopper or watch an observation beehive.
Don't be afraid to spend months or years watching and taking notes! Scientists have done this. For instance as of 1980, we've found 260 different behaviors in honeybees alone! In our own lives too, we have complex and subtle behaviors, but we don't usually give it much thought.
(4.5) List of 260 Skills That a Honeybee Has
To bring these observations to stark light, lets ask the question this way: what if i wanted to make a little robot that could mimic a honeybee with all those 260 amazing behaviors that a honeybee is capable of?
II) COMPUTERS
In the last 60 years, since WWII, we've begun to attempt mimicking life, by building computers to do computations that we are good at. We've even expanded to writing programs for things that no animal can do. We've even begun to build robots to physically mimic the capabilities of animals.
The levels of organization, complexity needed to do this is immense. Lets start off by looking at a digital electronics manual and notice how we can build a logic gate out of a few transistors, from 2 to 10 of them. Logic gates can do things like turn on only if two of its inputs are on (AND gate), or turn on only if its two inputs are different (XOR gate), or turn on if its input is off, and turn off if its input is on (NOT gate). Clever. We can build things out of these:
if we hook up a NOT gate to a piezoelectric crystal and capacitor so that the output of the NOT gate feeds back into its input with a delay. We get a logical inconsistency: if the gate through random static turns on, the signal is fed to its input and turns the gate off! This signal will feed back through and turn the gate back on and that...
It oscillates, the crystal helps it keep precise time, now we have a clock.
We can hook up more gates together and get a simple memory, if we signal it while it's input is on, it will remain on, if we signal it while its input is off, it will remain off.
now we can hook up a bunch of these together with more logic gates and put the clock input in and we can build a counter which in binary can count up to 8: 000, 001, 010, 011, 100, 101, 110, 111, 000, each digit feeds back to the input of the next digit with some xor gates to make that digit flip...
On and on it goes. we can build an addition circuit, a circuit that tells us whether binary number is bigger than another... the possibilities are endless.
we can put lots of memory bits together with decoders and make a long computer memory.
we can take our addition and comparison circuits and combine them with decoder circuits and the clock circuit to make a central processing unit for a computer
Notice the hierarchical levels. look at the pictures. a modern microprocessor CPU will have 1000s of circuits in it, millions of memory bits and gates...
(8) from logic gates to computer
The complexity doesn't stop there. Once we have our computer we can start programming it. Programming is easier than hooking circuits together and less technical so that we can build even more complexity.
Lets write a program in the machine code of our computer to sort a list of numbers. lets write a program to do a binary search for a number in the list and that tells us if it's there and how far along the list it is. we will explore a few of the basic building blocks of programs.
(61.2) write simple computer programs in machine code:
Now lets write longer programs. Notice that we will do it by 'chunking' them up into simpler processes which we've already written. This hierarchy is similar to the one we used to build up our computer from transistors. at each stage we have more complex parts to work with. (This process will become important if we want to discuss the origins of life from simple chemistry, simple atoms and molecules...)
(61.3) program John Horton Conway's game of life, Mandelbrot set, and Lorenz attractor
After you've gotten this taste, we will look at Lego Robots programmed to do complex tasks like chase each other, look for wall outlets to plug into or even play a game of soccer! Notice that the programs for these critters are THOUSANDS of lines long. They are made of HUNDREDS of smaller subroutines.
9) show them well programmed Lego bots
So can we program a Lego robot to even attempt to do what a honeybee can do? No. Well, at least we have some hints as to HOW COMPLEX a honeybee must be inside.
I) BACK TO LIVING CRITTERS
Scientists have dissected honeybees and have found that it IS complex inside. There are thousands of parts in there. WOW.
Imagine the process, the factories involved to build honeybee robots!
But honeybees aren't built in factories, they seem to develop from eggs, and when they hatch they get fed some pollen and presto, in 15 days a pristine complex honeybee. HOW? Well, we've managed to watch how animals develop, lets watch a video.
(16) watch videos of animal development
What did we learn from the video? The honeybee starts off as a cell. And then that cell splits into two, and then 4 and then 8 and then... 1024 of them. by now the cells are a little different than each other because that original cell was not simple, it had structures inside it. And now the cells start moving around and sensing each other and eating yolk and splitting some more, and soon they arrange themselves into more and more complicated structures, tissues, organs (more hierarchy) until we have a honeybee.
And even in adult animals, cells are still crawling around sensing things that are out of place and fixing things. Did you know that as you sit there and work on these labs, your neurons are sending out pseudopods all over your brain looking for new neurons to chat with? Is that how your personality grows and changes?
So we see that what makes us animals and plants marvelous is that we are colonies of living celled beings. And now the question: What are they?
II) CELLULAR LIFE
Well, lets watch some. Some animals are made entirely of a single cell only. When it reproduces and splits apart, the two cells don't stay joined to make an animal, but go off on their own separate ways.
There are lots of single celled critters in pond water, lets look (lab 22). These cells are small, calculate how small, calculate how many would fit inside a honeybee. Yet, they are complex. See how many of the insect behaviors or honeybee behaviors you can catch some of these little guys carrying out. Searching for food, exploring, eating, swimming from trouble, swimming from or towards light, finding a place to settle.
(22) watch single cell pond creatures
But the real complexity lies in the behavior inside: digesting, calculating, regulating water concentration, growing, finding mates, etc...
So how do cells work? what are they? The bigger ones seem to have fluids flowing inside, and parts too, can we watch with a higher magnification? It's difficult, but scientists HAVE taken them apart and looked, here's an animated video of SOME of what's going on inside (lab 27). Notice the video leaves out the most important part! All those crazy molecules are surrounded by and interacting with little water molecules and water molecules help give the whole cell it's structure and help bounce all the parts around into their right places.
27) molecular video "inner life of cell"
What REALLY is all that made of? How do cells get it all in there? Lets grow some algae in only distilled water in a glass jar and see what happens. (lab 25) It grows! what on earth does it make itself out of? water? air bubbles? glass? where does the green come from? where does all the machinery come from?
25) grow oscillatoria in water and glass jar
We are going to have to go in yet another level! molecules, chemistry!
We will watch for two things: where does the dynamism come from and where does the structures come from?
III) WHAT IS THE MOLECULAR WORLD?
When the question arises "how can life be JUST chemistry" I realize how little about chemistry the average person out of school knows. It is not JUST chemistry at all, but AMAZINGLY CHEMISTRY. Lets look. The first surprise is how MANY molecules there ARE in a single celled critter to make him work. Now we are beginning to observe physics without life in it, what can it do?
lets dump a few finely crushed paint flakes into water and boil it to kill all possible life in it and then watch under the microscope. What we will see after it all settles is that the tiny flakes are suspended in the water and are jiggling all around in crazy paths in what is called (after its discoverer) Brownian motion.
What's making them move? If we cool the water do they move less and as we heat the water do they move more (of course if we heat too much it will boil but that's another lab (34)) What we ultimately learn in physics is that heat is the motion of molecules and the paint fleck is jiggling around because many many tiny water molecules are banging into it. (lab 72.3)
Einstein showed how we can calculate the number of water molecules by observing this jiggling and Perrin did the observations and did the calculation: about 6X10^24 molecules in a cup of water! that's: 6,000,000, 000,000,000, 000,000,000!! 6million billion billion. too much to think about, so calculate how many would fit in one of the single celled critters you watched. do some division.
Still 10 billion billion in the largest cells! and a 100 billion in the smallest. you can try lab 18 to try to imagine a how much a billion is.
Another way to find out how small molecules are and how many there are is to spill a tiny drop of cooking oil onto a large bowl of still water. how small a drop do you need to cover the whole bowl? hard to do, might have to use a swimming pool indoors with no wind or waves. (lab 73.3)
from the Brownian motion experiment we realize also not only that there are so many molecules but that they are bouncing into each other 10^10 times a second so that's a lot of activity we get for free, before we even do any biology or chemistry or get energy flowing through things.
So what are molecules like? If we learn organic chemistry we find out that even a simple one like ethanol (alcohol) has complex behavior, it is like a little fuzzy sensing, calculating machine that can sense other molecules, distinguish between them and calculate how to interact with them in different temperatures, solvents, pH... Based on these calculations, It can absorb energy, connect with the other molecule, come apart, give off energy... (lab 72.2)
In fact we can watch a simulated movie of how these tiny machines can wiggle around each other with Brownian motion to come together and perform complex tasks. We can put a dozen different kinds of molecules together and they will be able to self assemble membranes into cages which catch food packets in cells and bring them inside. These are the Clathrin coated pits (31.2) Distributed Brownian Motion Machinery: Clathrin Coated Pits
Finally, if we get can tear a few electrons off of some molecules with intense heat and put them in oxygen, we can get a candle flame going. Play with it a little while and we will look at the complex set of reactions that are occurring. Even without life, we get a system of chemical reactions reminiscent of cellular metabolism! (lab 44)
IV) DISSIPATIVE STRUCTURES: FLOW OF ENERGY THROUGH SYSTEMS CREATES PATTERNED DYNAMISM
Now that we know that the molecular clay is is so different than what we think of us clay to be sculpted or blocks to be built with, that the molecular world is intensely detailed and fluid, we are ready to ask: what kind of things are living cells. for if they are not made of inert motionless bricks, not inert dumb clay already they are interesting.
Now the Brownian motion is completely random, complete chaos, trillions of molecules doing their own thing, not coordinated. Where does the coordination come from, the order? Energy flow! When energy flows through a system it causes work to be done, patterns to form out of chaos and stability to happen.
Lets start with an obvious kind of energy flow. lift a bucket of water off the ground to a height of 4 feet. That took work on your part, you burned food to do it, and now that bucket of water has potential energy in it. It can do work. We will build water wheel below it on a bicycle wheel and let falling water spin the wheel. that's the work it does and the pattern it creates. As long as there's still water in the bucket, the wheel will spin. (lab 64.2.1)
Another example is a thermostat. build a waterwheel out west, and instead of spinning a bicycle wheel, spin an electric generator and create electricity. let that electric energy flow through a heater and we get warm. but wait, TOO warm, it needs some control. Let's look at our thermostat.
We Put a bimetallic strip controlling a mercury switch in the path of the electric current. when the heat heats the two metals they bend differently and the strip expands, tilting the mercury which falls away from it's electric contact, and the current is cut.
now the heater is off and the room cools, the strip cools, and thus contracts and the mercury then tilts the other way falls into the contact and starts the heater again. This system will oscillate back and forth (hopefully in smaller and smaller oscillations) till it zeros in on the temperature we set it at by our initial tilt of the whole system.
This is an example of a system far from thermodynamic equilibrium. It has energy flowing through it. some energy is dissipated as heat even in the thermostat (useless heat). And it maintains itself in a state of order.
It does so by a process called negative feedback. MORE heat than required makes the circuit go off creating LESS heat. if we had hooked up the mercury ball the opposite way so that as it heats up it tilts further towards the contact or as it cools off it tilts away then the system would either get hotter and hotter... or colder and colder, that would be POSITIVE feedback, or runaway, instead of the system zeroing in on it's goal. (the goal we set for it) (lab 64.2.2)
Another system that works like this with negative feedback is a door buzzer. the same negative feedback controlling a switch turning it off is involved. this time we design it so that it achieves a steady state of oscillation and makes a sound. Many musical instruments work this way also. (lab 64.2.3)
One more interesting twist as these are really kind of boring repetitive behaviors. Back to our waterwheel. we will poke holes in the bottom of the cups of our waterwheels and see what happens. Interesting chaos! (lab 64.2.4)
(64.2) chaotic waterwheel, thermostat and heater, door buzzer
Back to heat flow. Almost all visible activity on Earth is due to heat flow. The sun is about 5700degrees (that's Celsius, in Fahrenheit it's about 10,000 degrees) hot at the surface (enough vaporize any substance) and that temperature causes it to glow white light at us. This light shines on the Earth and causes it to warm up. It is a common misconception that what enables life on earth to exist, to act, is that it is bathed in this sunlight. Our next lab will show that this misconception is GROSSLY untrue.
Lets take this mini steam engine and light a fire under it. There it goes pumping away! You might suppose that the heat of the fire is what makes it run. But if i were to put it in an oven so that the whole engine is at the temperature of the fire, you might think, more heat even better!
NO. it stops running. On further investigation you find that your engine has TWO pistons one in contact with the hot flame, the other in contact with the cool air outside. It is the alternation of expansion of one piston (in the flame) and compression of the other piston (in the cold) that makes the work happen. essentially heat energy is flowing from the flame to the cold air.
And the same on earth. the only reason your air is cooler than the sun is that the earth is not totally surrounded by suns! there is much cooler outer space surrounding most of the earth. (if the earth were surrounded completely by suns it would eventually become as hot as the sun and completely vaporize!)
And of course we could hook this rotating engine to all sorts of machines, even a loom, and make interesting patterns with it. This is the essence of far from equilibrium systems, which we also call dissipative systems (since they all dissipate heat), that energy must flow THROUGH them from a source of high potential energy to a sink of low potential energy. In between interesting stable pattern occurs.
(33) show steam engine
We can reduce this to the simplest system without machinery: Benard convection. We will set up a shallow petri dish of water (or some more appropriate fluid) and heat it from below. the water will begin to warm on the bottom and thus expand and become less dense and flow to the top higgledy piggledy. Of course that displaces the water at the top which must sink. Note that in order for any of this to happen there must again, be TWO temperatures, hot and cold.
As we keep increasing the temperature of the flame below you would expect the water to move more and more violently till it's a roiling boil. Correct... except for one thing! at a certain range of optimal temperatures you get the benard convection cells arranging themselves into a stable interesting hexagonal pattern. water in the centers rises and then flows out and falls at the edges. You can play with the cells, mess 'em up, they are stable.
(34) Then Benard convection
All the interesting weather patterns on earth are formed because of convection (and rotation of earth see labs 35-39)
Heat and electricity are not the only forms of energy flow, there is also chemical energy flow. energy is passed from molecule to molecule as they react and move around in their brownian motion. In this example, the Bellousov Zhazotinsky reaction (lab 42) we will see that as energy flows from the molecules of high energy potential ( ) to a set of simpler molecules at low potential ( ) an interesting visual pattern of cycles proceeds. Energy flow can produce ORDER!
(42) The Beloussov Zhabotinsky reaction
Now this begins to approach what is happening in life, at root, life is a system of oxidation reduction reactions similar to these that are organized into patterns by chemical energy flow. It is important to note that the souce of the patterns is NOT the DNA! without energy flow running complex chemical reactions to replicate and repair the DNA, the DNA itself will decay as do all things eventually at equilibrium.
We can even combine heat energy flow: convection, with chemical energy flow and we get a flame (lab 44). Note the diagram of the complex cycles of chemicall reactions that occur in even the simplest methane flame.
(44) play with a flame
And finally lets go back to our waterwheel and add in some funcky feedbacks. poke holes in the bottom of our cups mounted to the bicycle wheel. what happens? crazy chaos! (lab 64.2)
Now, these labs bring us to the essence of complexity lab. We start with simple systems with random motions and let something simple like energy flow throgh them and we get complex patterns. Is this really possible to go from the simple to the complex? Throughout much of human intellectual history the answer was NO! The universe for early people's begins most complex, most perfect from an eternal MIND and THEN slowly runs down to simpler and messier patterns.
Now this certainly seems to be the case in most ordinary situations, things run down. And it is correct that we even have the 2nd law of thermodynamics to formalize it: In a closed system (no energy coming in or out, no things coming in or out) all order eventually runs down to randomness. And that is in fact what happened with our engines and convections and BZ reactions. In the TOTAL system of fuel, cold air, and game in between, the system DID in fact eventually run down to less ordered state. instead of fuel vs cold air, we got ashes and carbon dioxide in luke warm air.
BUT.. for a PERIOD of time in a SUBsystem of that closed system (our engine or candle flame or the convecting fluids, or the patterns in the BZ reaction) which was open to energy flow from and to the larger system, became MORE ordered. That is possible under the 2nd law. While the whole system runs down, an open subsystem with energy flowing through it can become more ordered for a while. In fact the increase in order of the subsystem is OFFSET by a LARGER decrease in order in the larger system.
So here we begin to see examples of systems that can become more complex from simple beginnings. We see that even the evolution of complex beings from simpler beings does NOT contradict the 2nd law of thermodynamics that in the LONG run the entire system of sun, earth space will run down to less complex.
V) MATHEMATICAL DYNAMICAL SYSTEMS: EASY LABORATORY, ALL YOU NEED IS PENCIL, PAPER, COMPUTER
Now those were difficult processes to set up and analyse. The flame alone is still not completely analysed in terms of all the reactions involved, and we've certainly only begun understanding how cells work in all their detail. So next we go to paper and pencil (and computer) math games.
And again we will ask: if we start off with a simple set of rules and let them automatically follow each other, can we get something more complex than the simple set of rules? The ancients certainly had the ability to play many of the simple games we are about to explore, and surprisingly they did not. Perhaps their firm believe that complexity could not come from simplicity prejudiced them from even trying.
So lets dive into John Horton Conway's game of life, (lab 48), Stepen Wolframs rule 30 linear cellular automata (lab53), collatz's 3n+1 game (lab 56) , and my own even odd fibonaci game (57) and see what kind of glorious patterns can come out from simple pencil and paper calculations of simple rules.
(48) John Horton Conway's Game Of Life
(56) 3n+1: a simple number game with complex behavior
You will see that some of the rules create much order like 3n+1, others create extremely chaotic complexity like rule 30! and others create a subtle mix between some complexity and total chaos as in conway's life and my fibonacci game.
Another way to look at these games is to see them as simulations for the complex systems we played with above. In fact scientists are trying to gain insight into complex systems of chemical reactions like flames and life by simulating them with cellular automata.
Another kind of game that also can be used to simulate systems like the Benard convection and the Bz reaction are systems pleayed not with integers or discrete cells, but on the continuous real numbers. Get a load of what we can build from the simple iterated logistic equation (lab 58). Blow your mind from the Mandelbrot set created by simple iterations of a similar system (lab 58.2)
58) Iterated logistic equation to Mandelbrot set
Finally play with the lorenz attractor, best done with computer. It actually has similar properties to both Beneard convection and our crazy chaotic waterwheel. Do you see? (lab 60)
VII) EVEN AT EQUILIBRIUM: PHYSICAL AND CHEMICAL PATTERN FORMATION
So why is the Earth so interestiing, with it's rocks and minerals and weather and life? Well, we saw most of the mechanics that give us interesting weather, but where does all the DETAILS of life come from? those 100 different plants with all their parts. Those crazy complex molecular machines we saw inside living cells? The fact is that even without energy flow forming patterns, physics, chemistry, mathematics itself, still gives us complex patterns for free. No evolution required, no mind required.
Lets start out with a trip to a mineralogy exhibit at a museum (lab 70). these are all structures at equilibrium, they are not like the BZ reaction (though SOME of the formations you will see ARE the results of far from equilibrium processes that became frozen in as they developed). All this mineral diversity (there are more than 4000 different kinds) did NOT come from evolution, it comes from phsysics and chemistry! It comes from the capabilities of different kinds of atoms in the periodic chart (lab 74). Explore the radically different behaviors of protons, neutrons and electrons, just becase there are different nuumbers of them. Or different geometries, or different solutions to differential equations?
Again when we take water molecules and separate them into vapour in our breath and then we exhale and they drift about into clouds and come down as rain (a different state as vapour) and the raindrops take on a distinct shape because of intermolecular bonds)... or even more drastically when we breath on a cold window pain we get those cool complex jack frost patterns... How? (lab 75)
At this stage in our labs, we are getting close to the heart of the matter: Mathematics. before chemistry, before physics, there is math:
VIII) IT ALL COMES FROM MATH
Now, we've already seen crazy examples of order from simple mathematical rules, but those were kind of complicated since we had to keep iterating the system to build up the complexity, but what about just proposing a simple system of logical rules and see what must be true about a system that follows them?
The definition of a prime number is simple: any number who's only factors are itself and one is a prime number. 7=7*1 is prime, 12=6*2 or 3*4 is not. well lets list the prime numbers:
2 3 _ 5 _ 7 _ _ _ 11 _ 13 _ _ _ 17 _ 19 _
_ _23 _ _ _ _ _ 29 _31 _ _ _ _ _ 37 _ _ _
41 _ 43 _ _ _ 47 _ _ _ _ _ 53 _ _ _ _ _ 59_
Is there any pattern to them? The gaps are funny. Is it chaotic or is there a pattern? It seems chaotic, but not totally so... The number of primes less than N tends to N/ln(N) (lookup the "prime number theorem") and look there seem to be pairs 5;7, 11;13, 17;19, 29;31, 41;43... as far as we've looked these pairs happen, but no one can prove that they keep occuring...
Lets create some more exciting patterns out of simplicity, lets enumerate the finite graphs out of balls of clay and toothpics (lab 87)
the rules: a ball of clay at each end of the toothpick. all toothpicks same length, can't bend them, can't connect two toothpicks together at BOTH ends like O====O.
what happens? the shapes we get. we get loops, we get interlocked loops, we get 2 dimensions, we get 3 dimensions.... note that this doesn't require OUR MINDS to construct. this is pure math. If you don't believe it, i suppose we could build an experiment to shake these parts and sort the results by weight and get all these patterns.
This creativity of mathematics shows you where the creativity to make all those crazy states of matter and minerals from simply protons, neutrons and electrons comes from.
A more involved example of this type of interesting but not chaotic complexity coming from simple rules is the classification of all finite simple grouups.
(81) classification of finite simple groups
IX) PUTTING IT ALL BACK TOGETHER: EVOLUTIONARY BIOLOGY
...
I) LIFE
If the question is, can life be simply a property of chemistry, then lets start off by exploring how complex life is. Lets go out there into a field or a park or woods or roadside and look at the plants. There are different kinds! I challenge you: can you find me 100 different kinds in an hour?
We can! In order to keep track we will tape some representative samples of each to pages in our plant press and in order to tell whether one is different from another, we will have to look closely. The leaves are arranged on the stems differently. some leaves have teeth or lobes. some are hairy, some smooth, some waxy.
Some of the plants are flowering, some have 4 petals, some 5, some 6.. some just a whole lot. some have 2 stamens, some have 3 or 5 or 10. there is every which way combinations. some have hairs below the flowers. some of the hairs (look REALLY closely with a hand lens) have sticky blobs on the tips!
Some of the plants are in seed, the seeds also have details, some have bumps, some have stems attached to them, some have hairs attached to the stems, some of the hairs (hand lenses again) are barbed... (6) Key Out 100 Plants In A Local Park
So far, we've found and described over 2 million different kinds of living plants, animals and microorganisms on this planet Earth. We can distinguish SO MUCH variety because there are SO many details in each organism to see. As far in as we look, with hand lens, with microscope, there are more and more details.
How does life become so detailed?
Surely one of the most interesting details is how animals behave. Lets go find some insects and keep them in a terrarium and play with them and let them eat and hop, fly around and watch how complex their behaviors are (lab2). You can do an ant colony, or a grasshopper or watch an observation beehive.
Don't be afraid to spend months or years watching and taking notes! Scientists have done this. For instance as of 1980, we've found 260 different behaviors in honeybees alone! In our own lives too, we have complex and subtle behaviors, but we don't usually give it much thought.
(4.5) List of 260 Skills That a Honeybee Has
To bring these observations to stark light, lets ask the question this way: what if i wanted to make a little robot that could mimic a honeybee with all those 260 amazing behaviors that a honeybee is capable of?
II) COMPUTERS
In the last 60 years, since WWII, we've begun to attempt mimicking life, by building computers to do computations that we are good at. We've even expanded to writing programs for things that no animal can do. We've even begun to build robots to physically mimic the capabilities of animals.
The levels of organization, complexity needed to do this is immense. Lets start off by looking at a digital electronics manual and notice how we can build a logic gate out of a few transistors, from 2 to 10 of them. Logic gates can do things like turn on only if two of its inputs are on (AND gate), or turn on only if its two inputs are different (XOR gate), or turn on if its input is off, and turn off if its input is on (NOT gate). Clever. We can build things out of these:
if we hook up a NOT gate to a piezoelectric crystal and capacitor so that the output of the NOT gate feeds back into its input with a delay. We get a logical inconsistency: if the gate through random static turns on, the signal is fed to its input and turns the gate off! This signal will feed back through and turn the gate back on and that...
It oscillates, the crystal helps it keep precise time, now we have a clock.
We can hook up more gates together and get a simple memory, if we signal it while it's input is on, it will remain on, if we signal it while its input is off, it will remain off.
now we can hook up a bunch of these together with more logic gates and put the clock input in and we can build a counter which in binary can count up to 8: 000, 001, 010, 011, 100, 101, 110, 111, 000, each digit feeds back to the input of the next digit with some xor gates to make that digit flip...
On and on it goes. we can build an addition circuit, a circuit that tells us whether binary number is bigger than another... the possibilities are endless.
we can put lots of memory bits together with decoders and make a long computer memory.
we can take our addition and comparison circuits and combine them with decoder circuits and the clock circuit to make a central processing unit for a computer
Notice the hierarchical levels. look at the pictures. a modern microprocessor CPU will have 1000s of circuits in it, millions of memory bits and gates...
(8) from logic gates to computer
The complexity doesn't stop there. Once we have our computer we can start programming it. Programming is easier than hooking circuits together and less technical so that we can build even more complexity.
Lets write a program in the machine code of our computer to sort a list of numbers. lets write a program to do a binary search for a number in the list and that tells us if it's there and how far along the list it is. we will explore a few of the basic building blocks of programs.
(61.2) write simple computer programs in machine code:
Now lets write longer programs. Notice that we will do it by 'chunking' them up into simpler processes which we've already written. This hierarchy is similar to the one we used to build up our computer from transistors. at each stage we have more complex parts to work with. (This process will become important if we want to discuss the origins of life from simple chemistry, simple atoms and molecules...)
(61.3) program John Horton Conway's game of life, Mandelbrot set, and Lorenz attractor
After you've gotten this taste, we will look at Lego Robots programmed to do complex tasks like chase each other, look for wall outlets to plug into or even play a game of soccer! Notice that the programs for these critters are THOUSANDS of lines long. They are made of HUNDREDS of smaller subroutines.
9) show them well programmed Lego bots
So can we program a Lego robot to even attempt to do what a honeybee can do? No. Well, at least we have some hints as to HOW COMPLEX a honeybee must be inside.
I) BACK TO LIVING CRITTERS
Scientists have dissected honeybees and have found that it IS complex inside. There are thousands of parts in there. WOW.
Imagine the process, the factories involved to build honeybee robots!
But honeybees aren't built in factories, they seem to develop from eggs, and when they hatch they get fed some pollen and presto, in 15 days a pristine complex honeybee. HOW? Well, we've managed to watch how animals develop, lets watch a video.
(16) watch videos of animal development
What did we learn from the video? The honeybee starts off as a cell. And then that cell splits into two, and then 4 and then 8 and then... 1024 of them. by now the cells are a little different than each other because that original cell was not simple, it had structures inside it. And now the cells start moving around and sensing each other and eating yolk and splitting some more, and soon they arrange themselves into more and more complicated structures, tissues, organs (more hierarchy) until we have a honeybee.
And even in adult animals, cells are still crawling around sensing things that are out of place and fixing things. Did you know that as you sit there and work on these labs, your neurons are sending out pseudopods all over your brain looking for new neurons to chat with? Is that how your personality grows and changes?
So we see that what makes us animals and plants marvelous is that we are colonies of living celled beings. And now the question: What are they?
II) CELLULAR LIFE
Well, lets watch some. Some animals are made entirely of a single cell only. When it reproduces and splits apart, the two cells don't stay joined to make an animal, but go off on their own separate ways.
There are lots of single celled critters in pond water, lets look (lab 22). These cells are small, calculate how small, calculate how many would fit inside a honeybee. Yet, they are complex. See how many of the insect behaviors or honeybee behaviors you can catch some of these little guys carrying out. Searching for food, exploring, eating, swimming from trouble, swimming from or towards light, finding a place to settle.
(22) watch single cell pond creatures
But the real complexity lies in the behavior inside: digesting, calculating, regulating water concentration, growing, finding mates, etc...
So how do cells work? what are they? The bigger ones seem to have fluids flowing inside, and parts too, can we watch with a higher magnification? It's difficult, but scientists HAVE taken them apart and looked, here's an animated video of SOME of what's going on inside (lab 27). Notice the video leaves out the most important part! All those crazy molecules are surrounded by and interacting with little water molecules and water molecules help give the whole cell it's structure and help bounce all the parts around into their right places.
27) molecular video "inner life of cell"
What REALLY is all that made of? How do cells get it all in there? Lets grow some algae in only distilled water in a glass jar and see what happens. (lab 25) It grows! what on earth does it make itself out of? water? air bubbles? glass? where does the green come from? where does all the machinery come from?
25) grow oscillatoria in water and glass jar
We are going to have to go in yet another level! molecules, chemistry!
We will watch for two things: where does the dynamism come from and where does the structures come from?
III) WHAT IS THE MOLECULAR WORLD?
When the question arises "how can life be JUST chemistry" I realize how little about chemistry the average person out of school knows. It is not JUST chemistry at all, but AMAZINGLY CHEMISTRY. Lets look. The first surprise is how MANY molecules there ARE in a single celled critter to make him work. Now we are beginning to observe physics without life in it, what can it do?
lets dump a few finely crushed paint flakes into water and boil it to kill all possible life in it and then watch under the microscope. What we will see after it all settles is that the tiny flakes are suspended in the water and are jiggling all around in crazy paths in what is called (after its discoverer) Brownian motion.
What's making them move? If we cool the water do they move less and as we heat the water do they move more (of course if we heat too much it will boil but that's another lab (34)) What we ultimately learn in physics is that heat is the motion of molecules and the paint fleck is jiggling around because many many tiny water molecules are banging into it. (lab 72.3)
Einstein showed how we can calculate the number of water molecules by observing this jiggling and Perrin did the observations and did the calculation: about 6X10^24 molecules in a cup of water! that's: 6,000,000, 000,000,000, 000,000,000!! 6million billion billion. too much to think about, so calculate how many would fit in one of the single celled critters you watched. do some division.
Still 10 billion billion in the largest cells! and a 100 billion in the smallest. you can try lab 18 to try to imagine a how much a billion is.
Another way to find out how small molecules are and how many there are is to spill a tiny drop of cooking oil onto a large bowl of still water. how small a drop do you need to cover the whole bowl? hard to do, might have to use a swimming pool indoors with no wind or waves. (lab 73.3)
from the Brownian motion experiment we realize also not only that there are so many molecules but that they are bouncing into each other 10^10 times a second so that's a lot of activity we get for free, before we even do any biology or chemistry or get energy flowing through things.
So what are molecules like? If we learn organic chemistry we find out that even a simple one like ethanol (alcohol) has complex behavior, it is like a little fuzzy sensing, calculating machine that can sense other molecules, distinguish between them and calculate how to interact with them in different temperatures, solvents, pH... Based on these calculations, It can absorb energy, connect with the other molecule, come apart, give off energy... (lab 72.2)
In fact we can watch a simulated movie of how these tiny machines can wiggle around each other with Brownian motion to come together and perform complex tasks. We can put a dozen different kinds of molecules together and they will be able to self assemble membranes into cages which catch food packets in cells and bring them inside. These are the Clathrin coated pits (31.2) Distributed Brownian Motion Machinery: Clathrin Coated Pits
Finally, if we get can tear a few electrons off of some molecules with intense heat and put them in oxygen, we can get a candle flame going. Play with it a little while and we will look at the complex set of reactions that are occurring. Even without life, we get a system of chemical reactions reminiscent of cellular metabolism! (lab 44)
IV) DISSIPATIVE STRUCTURES: FLOW OF ENERGY THROUGH SYSTEMS CREATES PATTERNED DYNAMISM
Now that we know that the molecular clay is is so different than what we think of us clay to be sculpted or blocks to be built with, that the molecular world is intensely detailed and fluid, we are ready to ask: what kind of things are living cells. for if they are not made of inert motionless bricks, not inert dumb clay already they are interesting.
Now the Brownian motion is completely random, complete chaos, trillions of molecules doing their own thing, not coordinated. Where does the coordination come from, the order? Energy flow! When energy flows through a system it causes work to be done, patterns to form out of chaos and stability to happen.
Lets start with an obvious kind of energy flow. lift a bucket of water off the ground to a height of 4 feet. That took work on your part, you burned food to do it, and now that bucket of water has potential energy in it. It can do work. We will build water wheel below it on a bicycle wheel and let falling water spin the wheel. that's the work it does and the pattern it creates. As long as there's still water in the bucket, the wheel will spin. (lab 64.2.1)
Another example is a thermostat. build a waterwheel out west, and instead of spinning a bicycle wheel, spin an electric generator and create electricity. let that electric energy flow through a heater and we get warm. but wait, TOO warm, it needs some control. Let's look at our thermostat.
We Put a bimetallic strip controlling a mercury switch in the path of the electric current. when the heat heats the two metals they bend differently and the strip expands, tilting the mercury which falls away from it's electric contact, and the current is cut.
now the heater is off and the room cools, the strip cools, and thus contracts and the mercury then tilts the other way falls into the contact and starts the heater again. This system will oscillate back and forth (hopefully in smaller and smaller oscillations) till it zeros in on the temperature we set it at by our initial tilt of the whole system.
This is an example of a system far from thermodynamic equilibrium. It has energy flowing through it. some energy is dissipated as heat even in the thermostat (useless heat). And it maintains itself in a state of order.
It does so by a process called negative feedback. MORE heat than required makes the circuit go off creating LESS heat. if we had hooked up the mercury ball the opposite way so that as it heats up it tilts further towards the contact or as it cools off it tilts away then the system would either get hotter and hotter... or colder and colder, that would be POSITIVE feedback, or runaway, instead of the system zeroing in on it's goal. (the goal we set for it) (lab 64.2.2)
Another system that works like this with negative feedback is a door buzzer. the same negative feedback controlling a switch turning it off is involved. this time we design it so that it achieves a steady state of oscillation and makes a sound. Many musical instruments work this way also. (lab 64.2.3)
One more interesting twist as these are really kind of boring repetitive behaviors. Back to our waterwheel. we will poke holes in the bottom of the cups of our waterwheels and see what happens. Interesting chaos! (lab 64.2.4)
(64.2) chaotic waterwheel, thermostat and heater, door buzzer
Back to heat flow. Almost all visible activity on Earth is due to heat flow. The sun is about 5700degrees (that's Celsius, in Fahrenheit it's about 10,000 degrees) hot at the surface (enough vaporize any substance) and that temperature causes it to glow white light at us. This light shines on the Earth and causes it to warm up. It is a common misconception that what enables life on earth to exist, to act, is that it is bathed in this sunlight. Our next lab will show that this misconception is GROSSLY untrue.
Lets take this mini steam engine and light a fire under it. There it goes pumping away! You might suppose that the heat of the fire is what makes it run. But if i were to put it in an oven so that the whole engine is at the temperature of the fire, you might think, more heat even better!
NO. it stops running. On further investigation you find that your engine has TWO pistons one in contact with the hot flame, the other in contact with the cool air outside. It is the alternation of expansion of one piston (in the flame) and compression of the other piston (in the cold) that makes the work happen. essentially heat energy is flowing from the flame to the cold air.
And the same on earth. the only reason your air is cooler than the sun is that the earth is not totally surrounded by suns! there is much cooler outer space surrounding most of the earth. (if the earth were surrounded completely by suns it would eventually become as hot as the sun and completely vaporize!)
And of course we could hook this rotating engine to all sorts of machines, even a loom, and make interesting patterns with it. This is the essence of far from equilibrium systems, which we also call dissipative systems (since they all dissipate heat), that energy must flow THROUGH them from a source of high potential energy to a sink of low potential energy. In between interesting stable pattern occurs.
(33) show steam engine
We can reduce this to the simplest system without machinery: Benard convection. We will set up a shallow petri dish of water (or some more appropriate fluid) and heat it from below. the water will begin to warm on the bottom and thus expand and become less dense and flow to the top higgledy piggledy. Of course that displaces the water at the top which must sink. Note that in order for any of this to happen there must again, be TWO temperatures, hot and cold.
As we keep increasing the temperature of the flame below you would expect the water to move more and more violently till it's a roiling boil. Correct... except for one thing! at a certain range of optimal temperatures you get the benard convection cells arranging themselves into a stable interesting hexagonal pattern. water in the centers rises and then flows out and falls at the edges. You can play with the cells, mess 'em up, they are stable.
(34) Then Benard convection
All the interesting weather patterns on earth are formed because of convection (and rotation of earth see labs 35-39)
Heat and electricity are not the only forms of energy flow, there is also chemical energy flow. energy is passed from molecule to molecule as they react and move around in their brownian motion. In this example, the Bellousov Zhazotinsky reaction (lab 42) we will see that as energy flows from the molecules of high energy potential ( ) to a set of simpler molecules at low potential ( ) an interesting visual pattern of cycles proceeds. Energy flow can produce ORDER!
(42) The Beloussov Zhabotinsky reaction
Now this begins to approach what is happening in life, at root, life is a system of oxidation reduction reactions similar to these that are organized into patterns by chemical energy flow. It is important to note that the souce of the patterns is NOT the DNA! without energy flow running complex chemical reactions to replicate and repair the DNA, the DNA itself will decay as do all things eventually at equilibrium.
We can even combine heat energy flow: convection, with chemical energy flow and we get a flame (lab 44). Note the diagram of the complex cycles of chemicall reactions that occur in even the simplest methane flame.
(44) play with a flame
And finally lets go back to our waterwheel and add in some funcky feedbacks. poke holes in the bottom of our cups mounted to the bicycle wheel. what happens? crazy chaos! (lab 64.2)
Now, these labs bring us to the essence of complexity lab. We start with simple systems with random motions and let something simple like energy flow throgh them and we get complex patterns. Is this really possible to go from the simple to the complex? Throughout much of human intellectual history the answer was NO! The universe for early people's begins most complex, most perfect from an eternal MIND and THEN slowly runs down to simpler and messier patterns.
Now this certainly seems to be the case in most ordinary situations, things run down. And it is correct that we even have the 2nd law of thermodynamics to formalize it: In a closed system (no energy coming in or out, no things coming in or out) all order eventually runs down to randomness. And that is in fact what happened with our engines and convections and BZ reactions. In the TOTAL system of fuel, cold air, and game in between, the system DID in fact eventually run down to less ordered state. instead of fuel vs cold air, we got ashes and carbon dioxide in luke warm air.
BUT.. for a PERIOD of time in a SUBsystem of that closed system (our engine or candle flame or the convecting fluids, or the patterns in the BZ reaction) which was open to energy flow from and to the larger system, became MORE ordered. That is possible under the 2nd law. While the whole system runs down, an open subsystem with energy flowing through it can become more ordered for a while. In fact the increase in order of the subsystem is OFFSET by a LARGER decrease in order in the larger system.
So here we begin to see examples of systems that can become more complex from simple beginnings. We see that even the evolution of complex beings from simpler beings does NOT contradict the 2nd law of thermodynamics that in the LONG run the entire system of sun, earth space will run down to less complex.
V) MATHEMATICAL DYNAMICAL SYSTEMS: EASY LABORATORY, ALL YOU NEED IS PENCIL, PAPER, COMPUTER
Now those were difficult processes to set up and analyse. The flame alone is still not completely analysed in terms of all the reactions involved, and we've certainly only begun understanding how cells work in all their detail. So next we go to paper and pencil (and computer) math games.
And again we will ask: if we start off with a simple set of rules and let them automatically follow each other, can we get something more complex than the simple set of rules? The ancients certainly had the ability to play many of the simple games we are about to explore, and surprisingly they did not. Perhaps their firm believe that complexity could not come from simplicity prejudiced them from even trying.
So lets dive into John Horton Conway's game of life, (lab 48), Stepen Wolframs rule 30 linear cellular automata (lab53), collatz's 3n+1 game (lab 56) , and my own even odd fibonaci game (57) and see what kind of glorious patterns can come out from simple pencil and paper calculations of simple rules.
(48) John Horton Conway's Game Of Life
(56) 3n+1: a simple number game with complex behavior
You will see that some of the rules create much order like 3n+1, others create extremely chaotic complexity like rule 30! and others create a subtle mix between some complexity and total chaos as in conway's life and my fibonacci game.
Another way to look at these games is to see them as simulations for the complex systems we played with above. In fact scientists are trying to gain insight into complex systems of chemical reactions like flames and life by simulating them with cellular automata.
Another kind of game that also can be used to simulate systems like the Benard convection and the Bz reaction are systems pleayed not with integers or discrete cells, but on the continuous real numbers. Get a load of what we can build from the simple iterated logistic equation (lab 58). Blow your mind from the Mandelbrot set created by simple iterations of a similar system (lab 58.2)
58) Iterated logistic equation to Mandelbrot set
Finally play with the lorenz attractor, best done with computer. It actually has similar properties to both Beneard convection and our crazy chaotic waterwheel. Do you see? (lab 60)
VII) EVEN AT EQUILIBRIUM: PHYSICAL AND CHEMICAL PATTERN FORMATION
So why is the Earth so interestiing, with it's rocks and minerals and weather and life? Well, we saw most of the mechanics that give us interesting weather, but where does all the DETAILS of life come from? those 100 different plants with all their parts. Those crazy complex molecular machines we saw inside living cells? The fact is that even without energy flow forming patterns, physics, chemistry, mathematics itself, still gives us complex patterns for free. No evolution required, no mind required.
Lets start out with a trip to a mineralogy exhibit at a museum (lab 70). these are all structures at equilibrium, they are not like the BZ reaction (though SOME of the formations you will see ARE the results of far from equilibrium processes that became frozen in as they developed). All this mineral diversity (there are more than 4000 different kinds) did NOT come from evolution, it comes from phsysics and chemistry! It comes from the capabilities of different kinds of atoms in the periodic chart (lab 74). Explore the radically different behaviors of protons, neutrons and electrons, just becase there are different nuumbers of them. Or different geometries, or different solutions to differential equations?
Again when we take water molecules and separate them into vapour in our breath and then we exhale and they drift about into clouds and come down as rain (a different state as vapour) and the raindrops take on a distinct shape because of intermolecular bonds)... or even more drastically when we breath on a cold window pain we get those cool complex jack frost patterns... How? (lab 75)
At this stage in our labs, we are getting close to the heart of the matter: Mathematics. before chemistry, before physics, there is math:
VIII) IT ALL COMES FROM MATH
Now, we've already seen crazy examples of order from simple mathematical rules, but those were kind of complicated since we had to keep iterating the system to build up the complexity, but what about just proposing a simple system of logical rules and see what must be true about a system that follows them?
The definition of a prime number is simple: any number who's only factors are itself and one is a prime number. 7=7*1 is prime, 12=6*2 or 3*4 is not. well lets list the prime numbers:
2 3 _ 5 _ 7 _ _ _ 11 _ 13 _ _ _ 17 _ 19 _
_ _23 _ _ _ _ _ 29 _31 _ _ _ _ _ 37 _ _ _
41 _ 43 _ _ _ 47 _ _ _ _ _ 53 _ _ _ _ _ 59_
Is there any pattern to them? The gaps are funny. Is it chaotic or is there a pattern? It seems chaotic, but not totally so... The number of primes less than N tends to N/ln(N) (lookup the "prime number theorem") and look there seem to be pairs 5;7, 11;13, 17;19, 29;31, 41;43... as far as we've looked these pairs happen, but no one can prove that they keep occuring...
Lets create some more exciting patterns out of simplicity, lets enumerate the finite graphs out of balls of clay and toothpics (lab 87)
the rules: a ball of clay at each end of the toothpick. all toothpicks same length, can't bend them, can't connect two toothpicks together at BOTH ends like O====O.
what happens? the shapes we get. we get loops, we get interlocked loops, we get 2 dimensions, we get 3 dimensions.... note that this doesn't require OUR MINDS to construct. this is pure math. If you don't believe it, i suppose we could build an experiment to shake these parts and sort the results by weight and get all these patterns.
This creativity of mathematics shows you where the creativity to make all those crazy states of matter and minerals from simply protons, neutrons and electrons comes from.
A more involved example of this type of interesting but not chaotic complexity coming from simple rules is the classification of all finite simple grouups.
(81) classification of finite simple groups
IX) PUTTING IT ALL BACK TOGETHER: EVOLUTIONARY BIOLOGY
...
Monday, May 11, 2009
3n+1: A Simple Number Game With Complex Behavior
3n+1
Here is a dirt simple game that requires only 4th grade arithmetic, yet leads to a hard puzzle.
Pick a number, say 5. It's odd, so let's multiply it by 3 and add one. We get 16. That one is even so we will divide by 2. We get 8. It's even again so divide by 2. We get 4. Then we get 2. Then we get 1. Oh, that's an odd number, so multiply by 3 and add one. We get 4. Then we get 2. Hey wait a minute, we just did that! so this little game ends up looping around! Ok, let's try starting with another number.
Remember the rules:
If the number you get is even, divide it by 2.
If the number you get is odd, multiply it by 3 and then add one.
How about 7? what happens?
It ends up in that 4,2,1, loop again, right?
This is called a mathematical dynamical system. you have a set of rules that you repeatedly operate on a given number with. The sequence of numbers you get is called an orbit. the loop 4,2,1 is called a closed orbit.
Try some more numbers, and see where they end up. Try 19. Hmm... that one is interesting, but it still ends up in our closed 4,2,1 orbit.
Do they all? Did you try 27? Oops, you will need a calculator! Even with a calculator It's too much work. Let's write a computer program to do it for us.
def iterate[n]
if int(n/2)=n/2 then 'if the integer portion of n/2 =n/2 then there is no remainder, so even
n=n/2
else
n=3*n+1
endif
return
simple program:
input n
while n<>1
iterate[n]
print n
wend
print "we've reached the loop"
program to calculate an orbit for each n:
for start_n = 1 to largest_n
print start_n; print ": ";
n=start_n
while n<>1
iterate[n]
print n; print ", ";
wend
print
next start_n
here's all the orbits for numbers less than 27:
1 4 2 1
2 / (i write a slash if we hit a number we've already tried)
3 10 5 16 8 4 2 1
4 /
5 /
6 3 /
7 22 11 34 17 52 26 13 40 20 10 /
Note here that if n is odd, 3n+1 is even so you always divide by 2 after 3n+1ing, however SOMETIMES you can divide by 2 TWICE, and as with 5, you can divide by 2 THREE times. So in general it's a little crazy. we can't tell on average how many times we mult by 3 vs divide by 2. So no trends.
8 /
9 28 14 7 /
10/
11/
12 even numbers are boring we already hit them all!
13 /
15 36 18 9 /
17 /
19 58 29 88 44 22 11/
21 64 32 16 8 /
(as an aside, is there an odd number n such that for each m, 3n+1=2^m? say 2^7.. so what is 2^m mod 3?
1 1
2 2
4 1
8 2
16 1
32 2
64 1
128 2
ah. half of them)
23 70 35 106 53 160 80 40 20 10 5 /
but note that 3*53+1 does =32*5, hmm..
25 76 38 19 /
Here is 27:
27 82 41 124 62 31 94 47 142 71 214 107 322
(odd, why ending in 1s and 7s? well, 3*1+1=4 and half 4 is either ending in 7 or 2 and half 2 ends in 1! 3*7+1 ends in 2 and half that ends in 1. how would the pattern break? half 2 is sometimes ending in 6! oh, so this IS odd!)
161 484 242 121 364 182 91 274 137 412 206
(see the pattern breaks finally)
103 310 155 466 233 700 350 175 526 263
(woah! whats going on here, this one is different than all the other's we've done so far, it keeps growing!)
790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1,
WOW! That's a complicated pattern for such a simple set of rules to produce. in fact we can do something curious here's the program i wrote to produce that list of numbers:
n=27
while n<>1
n=iterate(n)
print n;", ";
wend
wait
function iterate(n)
if int(n/2)=n/2 then
iterate=n/2
else
iterate=3*n+1
end if
end function
here's the entire orbit it produces
82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1,
the program produced a sequence of characters longer and more complicated than the sequence of characters in the original program. or is it more complicated? or is it random? These are difficult concepts to pin down. One of the major themes to this complexity lab is to ask what does it mean to ask whether a simple system can produce complex behavior. It is difficult to pin down what we mean by 'complex'.
Remember, ultimately we are motivated by the question "can a simple set of laws of chemistry and physics produce a complicated living organism from scratch?"
Here's orbits for more numbers:
29 88 44 22 11/
31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 (oh, 310 is in the orbit starting with 27, so we already know what happens)
33 100 50 25 /
35 /
etc... We need to keep a list of nums we've already found, so that we don't keep calculating orbits we've already spent time calculating!
we can write a program to do that too.
Now what is going on here? notice that most of the numbers lead to short sequences that end up in the repeating loop 4, 2, 1. But 27 goes wild. It looks like it never will settle into that loop, but it eventually does! Notice the seemingly chaotic nature of the alternation of odd even here. (and we will have to come up with a careful definition of what we mean by chaotic) very chancy.
Now if you want, you can try to delve into the nature of the numbers. All the factors of 2 and 3, are there any patterns going on? Can you estimate on average how often we multiply by 3 or divide by 2 and try to guess whether the sequence can grow without end? Or is there any rhyme or reason why we might not hit a number with a large power of 2 as a factor and that sends the sequence all the way back down to a small number again...
So now we have some questions.
Is there any order to this game or is it totally chaotic?
Is there any sequence that keeps growing forever and never settles down to 4,2,1?
Are there any other loops like 4,2,1 that a sequence might settle down to?
If all sequences settle down to 4,2,1 or some other loop, how far can they go before settling down?
If there are other loops how long can they be?
It is not hard to write a computer program to play this game and even keep track of all the old numbers and detect when you've reached a loop.
Guess what? After x years of study, mathematicians do not know the answers to ANY of these questions. Though we've calculated sequences out to the gazillions and SO FAR, they seem to all settle to 4,2,1, but no one knows how to prove that that ALWAYS happens.
Curious, eh?
There are more games like this in the complexity lab manual.
Here is a dirt simple game that requires only 4th grade arithmetic, yet leads to a hard puzzle.
Pick a number, say 5. It's odd, so let's multiply it by 3 and add one. We get 16. That one is even so we will divide by 2. We get 8. It's even again so divide by 2. We get 4. Then we get 2. Then we get 1. Oh, that's an odd number, so multiply by 3 and add one. We get 4. Then we get 2. Hey wait a minute, we just did that! so this little game ends up looping around! Ok, let's try starting with another number.
Remember the rules:
If the number you get is even, divide it by 2.
If the number you get is odd, multiply it by 3 and then add one.
How about 7? what happens?
It ends up in that 4,2,1, loop again, right?
This is called a mathematical dynamical system. you have a set of rules that you repeatedly operate on a given number with. The sequence of numbers you get is called an orbit. the loop 4,2,1 is called a closed orbit.
Try some more numbers, and see where they end up. Try 19. Hmm... that one is interesting, but it still ends up in our closed 4,2,1 orbit.
Do they all? Did you try 27? Oops, you will need a calculator! Even with a calculator It's too much work. Let's write a computer program to do it for us.
def iterate[n]
if int(n/2)=n/2 then 'if the integer portion of n/2 =n/2 then there is no remainder, so even
n=n/2
else
n=3*n+1
endif
return
simple program:
input n
while n<>1
iterate[n]
print n
wend
print "we've reached the loop"
program to calculate an orbit for each n:
for start_n = 1 to largest_n
print start_n; print ": ";
n=start_n
while n<>1
iterate[n]
print n; print ", ";
wend
next start_n
here's all the orbits for numbers less than 27:
1 4 2 1
2 / (i write a slash if we hit a number we've already tried)
3 10 5 16 8 4 2 1
4 /
5 /
6 3 /
7 22 11 34 17 52 26 13 40 20 10 /
Note here that if n is odd, 3n+1 is even so you always divide by 2 after 3n+1ing, however SOMETIMES you can divide by 2 TWICE, and as with 5, you can divide by 2 THREE times. So in general it's a little crazy. we can't tell on average how many times we mult by 3 vs divide by 2. So no trends.
8 /
9 28 14 7 /
10/
11/
12 even numbers are boring we already hit them all!
13 /
15 36 18 9 /
17 /
19 58 29 88 44 22 11/
21 64 32 16 8 /
(as an aside, is there an odd number n such that for each m, 3n+1=2^m? say 2^7.. so what is 2^m mod 3?
1 1
2 2
4 1
8 2
16 1
32 2
64 1
128 2
ah. half of them)
23 70 35 106 53 160 80 40 20 10 5 /
but note that 3*53+1 does =32*5, hmm..
25 76 38 19 /
Here is 27:
27 82 41 124 62 31 94 47 142 71 214 107 322
(odd, why ending in 1s and 7s? well, 3*1+1=4 and half 4 is either ending in 7 or 2 and half 2 ends in 1! 3*7+1 ends in 2 and half that ends in 1. how would the pattern break? half 2 is sometimes ending in 6! oh, so this IS odd!)
161 484 242 121 364 182 91 274 137 412 206
(see the pattern breaks finally)
103 310 155 466 233 700 350 175 526 263
(woah! whats going on here, this one is different than all the other's we've done so far, it keeps growing!)
790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1,
WOW! That's a complicated pattern for such a simple set of rules to produce. in fact we can do something curious here's the program i wrote to produce that list of numbers:
n=27
while n<>1
n=iterate(n)
print n;", ";
wend
wait
function iterate(n)
if int(n/2)=n/2 then
iterate=n/2
else
iterate=3*n+1
end if
end function
here's the entire orbit it produces
82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1,
the program produced a sequence of characters longer and more complicated than the sequence of characters in the original program. or is it more complicated? or is it random? These are difficult concepts to pin down. One of the major themes to this complexity lab is to ask what does it mean to ask whether a simple system can produce complex behavior. It is difficult to pin down what we mean by 'complex'.
Remember, ultimately we are motivated by the question "can a simple set of laws of chemistry and physics produce a complicated living organism from scratch?"
Here's orbits for more numbers:
29 88 44 22 11/
31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 (oh, 310 is in the orbit starting with 27, so we already know what happens)
33 100 50 25 /
35 /
etc... We need to keep a list of nums we've already found, so that we don't keep calculating orbits we've already spent time calculating!
we can write a program to do that too.
Now what is going on here? notice that most of the numbers lead to short sequences that end up in the repeating loop 4, 2, 1. But 27 goes wild. It looks like it never will settle into that loop, but it eventually does! Notice the seemingly chaotic nature of the alternation of odd even here. (and we will have to come up with a careful definition of what we mean by chaotic) very chancy.
Now if you want, you can try to delve into the nature of the numbers. All the factors of 2 and 3, are there any patterns going on? Can you estimate on average how often we multiply by 3 or divide by 2 and try to guess whether the sequence can grow without end? Or is there any rhyme or reason why we might not hit a number with a large power of 2 as a factor and that sends the sequence all the way back down to a small number again...
So now we have some questions.
Is there any order to this game or is it totally chaotic?
Is there any sequence that keeps growing forever and never settles down to 4,2,1?
Are there any other loops like 4,2,1 that a sequence might settle down to?
If all sequences settle down to 4,2,1 or some other loop, how far can they go before settling down?
If there are other loops how long can they be?
It is not hard to write a computer program to play this game and even keep track of all the old numbers and detect when you've reached a loop.
Guess what? After x years of study, mathematicians do not know the answers to ANY of these questions. Though we've calculated sequences out to the gazillions and SO FAR, they seem to all settle to 4,2,1, but no one knows how to prove that that ALWAYS happens.
Curious, eh?
There are more games like this in the complexity lab manual.
57) The Iterated Logistic Map and The Mandelbrot Set: An Intro To Mathematical Dynamical Systems
An Integer Dynamical System With A Curious Array Of Orbits
fn+1= (fn+fn-1)/2 if even odd else (fn+fn-1)/4 if even even or odd odd
58) Iterates Of The Unimodal Map: Intro To Concepts In Mathematical Dynamical Systems
Xnew=mXold(1-Xold) and Mandelbrot set stability, sensitive dependence on initial conditions, repellors, periodic orbits, chaos, phase space, bifurcations
Pick a number, say 3. double it, 6. double it again 12, well you see where that goes.
pick a fraction like 1/2, double it, 1, double it again, 2, double it again, 4
what if we square numbers: 2, 4, 16, 256 grows wildly
how about start with 1/2? 1/4, 1/16, 1/256... that one keeps shrinking forever, but at least it's not unbounded. in fact it approaches a particular number: 0.
what if i decide to multiply a number by -2? start with 3, we get -6, 18, -54, 162, that one bounces back and forth wildly
what if i decide to multiply by -1/2? start with 2, -1, -1/2, 1/4, -1/8, 1/16... that one swings back and forth but the swings are smaller and smaller and that one zeros in on 0.
what if i decide to multiply by -1? 2, -2, 2, -2.. huh, this one keeps oscillating back and forth between two values.
god it would take days to write this! can i make an anthology instead? or at least pilfer a chapter from Devaney and rewrite it to emphasize my own points?
find a system with period four i.e. multiply i
then look at exp(2pi/3) for period 3.
now follow mx(1-x), look at fixed, periodic, attractor, repellor, bifurcation,
structural stability
sensitive dependence on initial condition
wandering orbit
infinite many orbits
chaos
whole bifurcation cascade
cantor dust
then look at z^2+c
the space of bifurcations on c
Mandelbrot set.
what were the concepts from Liu: singularity theory? structural stability, genericity? ...
fn+1= (fn+fn-1)/2 if even odd else (fn+fn-1)/4 if even even or odd odd
58) Iterates Of The Unimodal Map: Intro To Concepts In Mathematical Dynamical Systems
Xnew=mXold(1-Xold) and Mandelbrot set stability, sensitive dependence on initial conditions, repellors, periodic orbits, chaos, phase space, bifurcations
Pick a number, say 3. double it, 6. double it again 12, well you see where that goes.
pick a fraction like 1/2, double it, 1, double it again, 2, double it again, 4
what if we square numbers: 2, 4, 16, 256 grows wildly
how about start with 1/2? 1/4, 1/16, 1/256... that one keeps shrinking forever, but at least it's not unbounded. in fact it approaches a particular number: 0.
what if i decide to multiply a number by -2? start with 3, we get -6, 18, -54, 162, that one bounces back and forth wildly
what if i decide to multiply by -1/2? start with 2, -1, -1/2, 1/4, -1/8, 1/16... that one swings back and forth but the swings are smaller and smaller and that one zeros in on 0.
what if i decide to multiply by -1? 2, -2, 2, -2.. huh, this one keeps oscillating back and forth between two values.
god it would take days to write this! can i make an anthology instead? or at least pilfer a chapter from Devaney and rewrite it to emphasize my own points?
find a system with period four i.e. multiply i
then look at exp(2pi/3) for period 3.
now follow mx(1-x), look at fixed, periodic, attractor, repellor, bifurcation,
structural stability
sensitive dependence on initial condition
wandering orbit
infinite many orbits
chaos
whole bifurcation cascade
cantor dust
then look at z^2+c
the space of bifurcations on c
Mandelbrot set.
what were the concepts from Liu: singularity theory? structural stability, genericity? ...
A Selection Of Representative Labs With Commentary
CHAPTER 1
LIFE
How varied and detailed is life on Earth?
6) Key Out 100 Plants In A Local Park [6WKS] [or a two session blitz just to collect 100 different plants and press them]
By learning to key out and LOOK at organisms hard enough to distinguish their varieties, we learn two things:
there is a bewildering variety
organisms are incredibly DETAILED. As close as we look at them as much as we magnify and look inward, we find levels and levels of complex details. How does it happen?
And how complex is their behavior?
2) collect insects and watch their behavior in a terrarium
after much observation you can find out:
4.5) List of 270 Skills That a Honeybee Has
Can we get a handle on it from computer science? In the past 60 years we have learned to build some complexity ourselves. Follow the levels of complexity as we build up from transistors a computer with elaborate software.
CHAPTER 6
COMPUTERS
It's not so easy to see how animals work, maybe we can at least try to make some robots that act as complex and see from scratch how it might work?
8) from logic gates to computer [1/2 hr?] show them, or make some simple circuits in digi-lab.
61.2) write simple computer programs in machine code: binary search, sort, rule 30 etc... [hr]
61.3) program John Horton Conway's game of life, Mandelbrot set, and Lorenz attractor in basic or something or maybe the lego bot language
[hr?] show them?
Researchers in the field of Artificial Intelligence are now asking themselves, what it would take to build an animal, to build clever behaviors from the bottom up. We are trying to check our understanding of intelligence by building complex things and seeing if they can ACT intelligently.
9) show them well programmed lego bots ( (intro to another whole workshop) and listings of 1000 lined programs [1/2hr]
But we still Can't do it! Our robots are clunky and stupid in comparison with a honeybee!
CHAPTER 1
SO BACK TO CRITTERS FOR HELP
16) watch videos of animal development
This is an amazing process. And it works because animals are colonies of living cells, all talking with each other, feeling each other out and reproducing and sending their kids to the right places. We build machines from the outside in factories, but animals and plants are built from within by cells. What are cells?
CHAPTER 2
CELLULAR LIFE
Some critters are a single cell all in one, lets watch some:
22) watch single cell pond creatures [hr]
Take some time to watch the intricate behaviors of living single celled organisms. Already at this level, there is so much capability. The capabilities that make life so rich are not concentrated at the top, the most centralized level, but are distributed throughout every size scale! Even at the cellular level, and below...
So what kind of 'things' are cells?
27) molecular video "inner life of cell" [10min] more?
cells are hierarchical structures of organelles, macromolecular assemblies, macromolecules, small molecules. The properties of cells are also due to the most common molecule in them: water.
They are whirlwinds of swirling interacting molecules. The structure and organization goes in several more levels deep, as complex as a whole giant city.
and finally the most common machinery: proteins. they can self assemble into complex structures like undulipodia, they can change shape, travel along tracks, act as a complex logic elements in processing information, respond to EM radiation
25) grow oscillatoria in water and glass jar. watch it move. then at second to last session, weigh it, dry it, last session, burn it, weigh the ash
[10min sessions a few times]
PART 2
PHYSICS AND MATH
So how do cells do it? Well, no need to go to biology for the complexity of cells, the capabilities of cells. Physics, chemistry, and mathematics already gives us this. We are slowly whittling away at the divide between chemistry and life!
Physics and math gives us:
1) Patterns at far from equilibrium: energy flow through systems creates ordered dynamism
2) But even at equilibrium, rest, pattern comes ultimately from mathematics
3) And the clay that physics and math get to sculpt into organisms?
molecules!
CHAPTER 3
WHAT IS THE MOLECULAR WORLD?
So what is the molecular world like that it gives life it's subtle creative qualities? What are we 'made of'
Well, how many molecules are there in a cell?
73.2) Brownian motion: hints at the existence of many tiny molecules, constantly in motion due to heat, and hints at how small they are, how many in a drop of water.
73.3) monomolecular lipid layer: another clue to how big molecules are. Then we sketch out how the number of molecules in a glass of water can be calculated from experiments like these
[hr]
Atoms, molecules are not building BLOCKS, they are little machines, not clunky, but fuzzy, sensitive to their environment and each other, reactive, each atom is a complex of electron orbitals which are solutions to wave equations... molecules are flexible, constantly wiggling, not alive, but... can't describe what they are in common every day terms.
any labs we can do to show how molecules interact? orgo reactions, soap/oil/water, collisions? orientations? chirality..
72.2) show how many ways an ethanol molecule can respond to its chemical environment?
At the molecular level you already have a kind of trial and error mechanism for fitting together puzzles. one of the roots of our intelligence. molecules are always moving, wiggling, interacting with each other 10^10 times a second! molecules in a warm universe with energy flow are not like a jumble of cold automobile parts just sitting there, molecules can self assemble!
Show diagrams/video of how simple molecular interactions cooperate to form complex structures and processes:
31.2) Distributed Brownian Motion Machinery: Clathrin Coated Pits
molecules pass energy to each other in reactions, store energy in bonds, thus networks of their reactions can be ordered by energy flowing through systems of molecules.
molecules react with EM radiation. vision comes for free at the lowest level
44) Play With A Candle Flame
CHAPTER 4
DISSIPATIVE STRUCTURES: FLOW OF ENERGY THROUGH SYSTEMS CREATES PATTERNED DYNAMISM
If molecules aren't simple building blocks, then organisms are not 'things' at all, 'phenomena' would be a better adjective, or, to be less academic; 'dances'? What kind of phenomena are living cells? they are chemical systems animated by energy flow.
Our usual experience is that things wear out after a while and run down. You may have heard of the second law of thermodynamics which says "all closed systems (nothing coming in or out) run down and become less, not more ordered. If this is so, then how can life oppose this 'universal' tendency? Well, life is not a closed system!
One process that helps is positive and negative feedback. Lets explore some machines and simple processes that can do this.
64.2) chaotic waterwheel, thermostat and heater, door buzzer [hr]
In our next labs
33) show steam engine (with governor?) can i show that it needs hot and cold?
34) Then Benard convection
[hr]
We show the basic system animated by energy flow: Benard convection: We start off with wood (or some kind of fuel, highly ordered in any case) and air (unusual, out of equilibrium with all its oxygen..) and light the wood into flame. It is important that the flame is much hotter than the air above It.
The flame will heat from below a pan of shallow water. As the bigger closed system of wood and air and water run down to ashes and luke-warm carbon dioxide and water, for a while, a wondrous thing happens. Our pan of water (not closed, open to heat flowing through it) becomes ordered into an hexagonal array of gyrating convection cells.
We call these subsystems FAR from thermodynamic equilibrium systems or Dissipative Systems (they dissipate heat).
And what makes CELLS swirl? this time it is the flow of chemical energy. High energy bonds come in (sugars) and again low energy bonds come out in the form of carbon dioxide. In the meanwhile the cells swirl with activity. here are some simpler examples.
Can life even arise spontaneously from chemistry?
42) The Beloussov Zhabotinsky reaction : a simple far from equilibrium chemical system that you can watch forming periodic spatial patterns
Put convection and chemical reaction cycles together and you get:
44) play with a flame: [hr]
They are more complex than you think! And they contain complex networks of chemical reactions reminiscent of the metabolic chart!
CHAPTER 5
MATHEMATICAL DYNAMICAL SYSTEMS: EASY LABORATORY, ALL YOU NEED IS PENCIL, PAPER, COMPUTER
But living creatures are more complicated then these. Can chemistry really result in the complexity we found in living cells? Where do all those different patterns and structures come from? MATH! Mathematics gives us so much pattern for free. Simple rules repeated over and over again between many identical simple units can create surprising unpredictable patterns.
48) John Horton Conway's Game Of Life: a simple system of simple rules wherein there are patterns of many classes of behaviors, and simple patterns can develop into surprisingly complex ones. we can even make a finite pattern that results in an endlessly interesting one
53) One dimensional cellular automata rules 30 and 110 even dirt simpler set of rules that produces an endless stream of creativity
[1/2hr] [1/2 hr]
56) 3n+1: a simple number game with complex behavior we have yet to fully understand
57) e/o Fibonacci system: another one with much more complex behavior. these only involve addition and division.
58) Iterated logistic equation to Mandelbrot set: simple math rules give the most complex geometric structure we've ever imagined
60) Lorenz attractor: a simple dynamic system that results in a curious subtly behaving system with a sprinkling of unpredictability. By the way, it is very similar in behavior to the chaotic waterwheel.
[hr]
CHAPTER 7
EVEN AT EQUILIBRIUM: PHYSICAL AND CHEMICAL PATTERN FORMATION
Even without the dynamical systems set into motion by energy flow, the laws of physics are fecund: We find pattern formation even at equilibrium.
The wonder is, why isn't the universe a seamless haze of psychedelic chaos? Why isn't it just a bland grey blob of continuous matter? Why isn't the universe simply one huge neutron or quark or is THERE anything at the bottom? Somehow the physics and math give us all these phase transitions, clumpings for free.
74) show periodic chart with samples of diff elements: gas, liquid, metal, graphite, sulfur, semiconductor..
76) phases of sulfur: even with one kind of atom, depending on temperature, we get wildly different behaviors
75) and breath on a window pane: ditto for water molecules, how do they 'calculate' the beautiful patterns of 'jack frost' on window panes?
[1/2 hr]
70) mineral exhibit a dozen elements, a dozen transition metals and 2000+ combinations all for free.[1/2 hr? depends where]
CHAPTER 8
IT ALL COMES FROM MATH
At root, why is this universe so full of patterns? MATH!
From mathematics alone, we get surprising complexity but not total chaos from the simplest static logical rules
And why do we have this interesting periodic chart of elements, each with their potent particular properties? Physics and math again! Propose a simple set of rules and let them play out and you often find that you get a set of discrete entities which follow them that is interestingly diverse but not infinitely chaotic! This is the core of pattern formation in our universe. It's built in at the very basic logical structure of it.
87) enumeration of finite graphs: keep adding one more edge to a graph and you discover radical new behaviors. clues to things like how we get the behaviors in the periodic chart of elements?[1/2 hr]
81) classification of finite simple groups: example of simple static rules giving surprisingly diverse but only a tiny bit of chaotic pattern [1/2hr]
PART 3
THE BIG QUESTIONS: EVOLUTION, ORIGINS OF LIFE, AND MIND
CHAPTER 9
PUTTING IT ALL BACK TOGETHER: EVOLUTIONARY BIOLOGY
Then we put it all back together again and tackle the most fascinating subject: what is it that brings us all those wonderful critters we found outside at the beginning of our exploration? Evolutionary biology.
96) Tierra a system of programs that can reproduce, evolve, and form ecosystems [hr]
CHAPTERS FOR FURTHER STUDY:
CHAPTER 10
THE FINAL FRONTIER: CAN WE UNDERSTAND HOW GEOCHEMISTRY CAN BECOME LIFE?
The final frontier: is life SOLELY a consequence of chemistry and mathematics? If you perform labs in this topic, you are at the forefront of the scientific adventure.
CHAPTER 11?
MIND
Bar, why do you leave off discussing mind and consciousness? because I'm not greedy? but the labs watching behavior of single cells, the computer science topics, 260 skills of honeybees, building AI programs to simulate critters is the start.
CHAPTER 12?
SUPERORGANISMS
And finally we come back to the ants! This is the most recent hierarchical level of complex behavior to evolve on earth. not only critters with minds who can explore and learn about and manipulate their world, but some organisms come together and build highly cohesive societies:
Ants, honeybees, wasps, termites, naked mole rats, wolves and... humans.
LIFE
How varied and detailed is life on Earth?
6) Key Out 100 Plants In A Local Park [6WKS] [or a two session blitz just to collect 100 different plants and press them]
By learning to key out and LOOK at organisms hard enough to distinguish their varieties, we learn two things:
there is a bewildering variety
organisms are incredibly DETAILED. As close as we look at them as much as we magnify and look inward, we find levels and levels of complex details. How does it happen?
And how complex is their behavior?
2) collect insects and watch their behavior in a terrarium
after much observation you can find out:
4.5) List of 270 Skills That a Honeybee Has
Can we get a handle on it from computer science? In the past 60 years we have learned to build some complexity ourselves. Follow the levels of complexity as we build up from transistors a computer with elaborate software.
CHAPTER 6
COMPUTERS
It's not so easy to see how animals work, maybe we can at least try to make some robots that act as complex and see from scratch how it might work?
8) from logic gates to computer [1/2 hr?] show them, or make some simple circuits in digi-lab.
61.2) write simple computer programs in machine code: binary search, sort, rule 30 etc... [hr]
61.3) program John Horton Conway's game of life, Mandelbrot set, and Lorenz attractor in basic or something or maybe the lego bot language
[hr?] show them?
Researchers in the field of Artificial Intelligence are now asking themselves, what it would take to build an animal, to build clever behaviors from the bottom up. We are trying to check our understanding of intelligence by building complex things and seeing if they can ACT intelligently.
9) show them well programmed lego bots ( (intro to another whole workshop) and listings of 1000 lined programs [1/2hr]
But we still Can't do it! Our robots are clunky and stupid in comparison with a honeybee!
CHAPTER 1
SO BACK TO CRITTERS FOR HELP
16) watch videos of animal development
This is an amazing process. And it works because animals are colonies of living cells, all talking with each other, feeling each other out and reproducing and sending their kids to the right places. We build machines from the outside in factories, but animals and plants are built from within by cells. What are cells?
CHAPTER 2
CELLULAR LIFE
Some critters are a single cell all in one, lets watch some:
22) watch single cell pond creatures [hr]
Take some time to watch the intricate behaviors of living single celled organisms. Already at this level, there is so much capability. The capabilities that make life so rich are not concentrated at the top, the most centralized level, but are distributed throughout every size scale! Even at the cellular level, and below...
So what kind of 'things' are cells?
27) molecular video "inner life of cell" [10min] more?
cells are hierarchical structures of organelles, macromolecular assemblies, macromolecules, small molecules. The properties of cells are also due to the most common molecule in them: water.
They are whirlwinds of swirling interacting molecules. The structure and organization goes in several more levels deep, as complex as a whole giant city.
and finally the most common machinery: proteins. they can self assemble into complex structures like undulipodia, they can change shape, travel along tracks, act as a complex logic elements in processing information, respond to EM radiation
25) grow oscillatoria in water and glass jar. watch it move. then at second to last session, weigh it, dry it, last session, burn it, weigh the ash
[10min sessions a few times]
PART 2
PHYSICS AND MATH
So how do cells do it? Well, no need to go to biology for the complexity of cells, the capabilities of cells. Physics, chemistry, and mathematics already gives us this. We are slowly whittling away at the divide between chemistry and life!
Physics and math gives us:
1) Patterns at far from equilibrium: energy flow through systems creates ordered dynamism
2) But even at equilibrium, rest, pattern comes ultimately from mathematics
3) And the clay that physics and math get to sculpt into organisms?
molecules!
CHAPTER 3
WHAT IS THE MOLECULAR WORLD?
So what is the molecular world like that it gives life it's subtle creative qualities? What are we 'made of'
Well, how many molecules are there in a cell?
73.2) Brownian motion: hints at the existence of many tiny molecules, constantly in motion due to heat, and hints at how small they are, how many in a drop of water.
73.3) monomolecular lipid layer: another clue to how big molecules are. Then we sketch out how the number of molecules in a glass of water can be calculated from experiments like these
[hr]
Atoms, molecules are not building BLOCKS, they are little machines, not clunky, but fuzzy, sensitive to their environment and each other, reactive, each atom is a complex of electron orbitals which are solutions to wave equations... molecules are flexible, constantly wiggling, not alive, but... can't describe what they are in common every day terms.
any labs we can do to show how molecules interact? orgo reactions, soap/oil/water, collisions? orientations? chirality..
72.2) show how many ways an ethanol molecule can respond to its chemical environment?
At the molecular level you already have a kind of trial and error mechanism for fitting together puzzles. one of the roots of our intelligence. molecules are always moving, wiggling, interacting with each other 10^10 times a second! molecules in a warm universe with energy flow are not like a jumble of cold automobile parts just sitting there, molecules can self assemble!
Show diagrams/video of how simple molecular interactions cooperate to form complex structures and processes:
31.2) Distributed Brownian Motion Machinery: Clathrin Coated Pits
molecules pass energy to each other in reactions, store energy in bonds, thus networks of their reactions can be ordered by energy flowing through systems of molecules.
molecules react with EM radiation. vision comes for free at the lowest level
44) Play With A Candle Flame
CHAPTER 4
DISSIPATIVE STRUCTURES: FLOW OF ENERGY THROUGH SYSTEMS CREATES PATTERNED DYNAMISM
If molecules aren't simple building blocks, then organisms are not 'things' at all, 'phenomena' would be a better adjective, or, to be less academic; 'dances'? What kind of phenomena are living cells? they are chemical systems animated by energy flow.
Our usual experience is that things wear out after a while and run down. You may have heard of the second law of thermodynamics which says "all closed systems (nothing coming in or out) run down and become less, not more ordered. If this is so, then how can life oppose this 'universal' tendency? Well, life is not a closed system!
One process that helps is positive and negative feedback. Lets explore some machines and simple processes that can do this.
64.2) chaotic waterwheel, thermostat and heater, door buzzer [hr]
In our next labs
33) show steam engine (with governor?) can i show that it needs hot and cold?
34) Then Benard convection
[hr]
We show the basic system animated by energy flow: Benard convection: We start off with wood (or some kind of fuel, highly ordered in any case) and air (unusual, out of equilibrium with all its oxygen..) and light the wood into flame. It is important that the flame is much hotter than the air above It.
The flame will heat from below a pan of shallow water. As the bigger closed system of wood and air and water run down to ashes and luke-warm carbon dioxide and water, for a while, a wondrous thing happens. Our pan of water (not closed, open to heat flowing through it) becomes ordered into an hexagonal array of gyrating convection cells.
We call these subsystems FAR from thermodynamic equilibrium systems or Dissipative Systems (they dissipate heat).
And what makes CELLS swirl? this time it is the flow of chemical energy. High energy bonds come in (sugars) and again low energy bonds come out in the form of carbon dioxide. In the meanwhile the cells swirl with activity. here are some simpler examples.
Can life even arise spontaneously from chemistry?
42) The Beloussov Zhabotinsky reaction : a simple far from equilibrium chemical system that you can watch forming periodic spatial patterns
Put convection and chemical reaction cycles together and you get:
44) play with a flame: [hr]
They are more complex than you think! And they contain complex networks of chemical reactions reminiscent of the metabolic chart!
CHAPTER 5
MATHEMATICAL DYNAMICAL SYSTEMS: EASY LABORATORY, ALL YOU NEED IS PENCIL, PAPER, COMPUTER
But living creatures are more complicated then these. Can chemistry really result in the complexity we found in living cells? Where do all those different patterns and structures come from? MATH! Mathematics gives us so much pattern for free. Simple rules repeated over and over again between many identical simple units can create surprising unpredictable patterns.
48) John Horton Conway's Game Of Life: a simple system of simple rules wherein there are patterns of many classes of behaviors, and simple patterns can develop into surprisingly complex ones. we can even make a finite pattern that results in an endlessly interesting one
53) One dimensional cellular automata rules 30 and 110 even dirt simpler set of rules that produces an endless stream of creativity
[1/2hr] [1/2 hr]
56) 3n+1: a simple number game with complex behavior we have yet to fully understand
57) e/o Fibonacci system: another one with much more complex behavior. these only involve addition and division.
58) Iterated logistic equation to Mandelbrot set: simple math rules give the most complex geometric structure we've ever imagined
60) Lorenz attractor: a simple dynamic system that results in a curious subtly behaving system with a sprinkling of unpredictability. By the way, it is very similar in behavior to the chaotic waterwheel.
[hr]
CHAPTER 7
EVEN AT EQUILIBRIUM: PHYSICAL AND CHEMICAL PATTERN FORMATION
Even without the dynamical systems set into motion by energy flow, the laws of physics are fecund: We find pattern formation even at equilibrium.
The wonder is, why isn't the universe a seamless haze of psychedelic chaos? Why isn't it just a bland grey blob of continuous matter? Why isn't the universe simply one huge neutron or quark or is THERE anything at the bottom? Somehow the physics and math give us all these phase transitions, clumpings for free.
74) show periodic chart with samples of diff elements: gas, liquid, metal, graphite, sulfur, semiconductor..
76) phases of sulfur: even with one kind of atom, depending on temperature, we get wildly different behaviors
75) and breath on a window pane: ditto for water molecules, how do they 'calculate' the beautiful patterns of 'jack frost' on window panes?
[1/2 hr]
70) mineral exhibit a dozen elements, a dozen transition metals and 2000+ combinations all for free.[1/2 hr? depends where]
CHAPTER 8
IT ALL COMES FROM MATH
At root, why is this universe so full of patterns? MATH!
From mathematics alone, we get surprising complexity but not total chaos from the simplest static logical rules
And why do we have this interesting periodic chart of elements, each with their potent particular properties? Physics and math again! Propose a simple set of rules and let them play out and you often find that you get a set of discrete entities which follow them that is interestingly diverse but not infinitely chaotic! This is the core of pattern formation in our universe. It's built in at the very basic logical structure of it.
87) enumeration of finite graphs: keep adding one more edge to a graph and you discover radical new behaviors. clues to things like how we get the behaviors in the periodic chart of elements?[1/2 hr]
81) classification of finite simple groups: example of simple static rules giving surprisingly diverse but only a tiny bit of chaotic pattern [1/2hr]
PART 3
THE BIG QUESTIONS: EVOLUTION, ORIGINS OF LIFE, AND MIND
CHAPTER 9
PUTTING IT ALL BACK TOGETHER: EVOLUTIONARY BIOLOGY
Then we put it all back together again and tackle the most fascinating subject: what is it that brings us all those wonderful critters we found outside at the beginning of our exploration? Evolutionary biology.
96) Tierra a system of programs that can reproduce, evolve, and form ecosystems [hr]
CHAPTERS FOR FURTHER STUDY:
CHAPTER 10
THE FINAL FRONTIER: CAN WE UNDERSTAND HOW GEOCHEMISTRY CAN BECOME LIFE?
The final frontier: is life SOLELY a consequence of chemistry and mathematics? If you perform labs in this topic, you are at the forefront of the scientific adventure.
CHAPTER 11?
MIND
Bar, why do you leave off discussing mind and consciousness? because I'm not greedy? but the labs watching behavior of single cells, the computer science topics, 260 skills of honeybees, building AI programs to simulate critters is the start.
CHAPTER 12?
SUPERORGANISMS
And finally we come back to the ants! This is the most recent hierarchical level of complex behavior to evolve on earth. not only critters with minds who can explore and learn about and manipulate their world, but some organisms come together and build highly cohesive societies:
Ants, honeybees, wasps, termites, naked mole rats, wolves and... humans.
Saturday, May 9, 2009
44) Play With A Candle Flame
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Materials
candle, matches, bunsen burner, chart of reactions, white cards to catch soot, high temp cooking thermometer, a container to keep out random air currents?
are there differences between the two flames? do flames have boundaries? how stable are they? map out the temperatures, how do they spread? what are those blobs that sometimes form on the wick?
look at the chart of reactions in a flame, there are dozens of reactions!
Materials
candle, matches, bunsen burner, chart of reactions, white cards to catch soot, high temp cooking thermometer, a container to keep out random air currents?
are there differences between the two flames? do flames have boundaries? how stable are they? map out the temperatures, how do they spread? what are those blobs that sometimes form on the wick?
look at the chart of reactions in a flame, there are dozens of reactions!
42) Belousov-Zhabotinski Reaction
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Materials: this needs some interesting chemicals: bromous acid, malate, a cerium salt...
Method:
can be done in a petri dish. how long before it runs down.
Discussion
which molecule supplies the energy and what's left? what's the path of energy flow here?
Materials: this needs some interesting chemicals: bromous acid, malate, a cerium salt...
Method:
can be done in a petri dish. how long before it runs down.
Discussion
which molecule supplies the energy and what's left? what's the path of energy flow here?
33) Build A Steam Engine
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How does a steam engine work, how hard is it to make one? Or at least show a small working sterling engine? How does it work? can we fit a governer onto it? Can we show that it needs a source of hot AND cold?
How does a steam engine work, how hard is it to make one? Or at least show a small working sterling engine? How does it work? can we fit a governer onto it? Can we show that it needs a source of hot AND cold?
64.2) Chaotic Waterwheel, Thermostat and Heater, Door Buzzer.
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Materials: well oiled bicycle wheel, tape, plastic cups, awl, 20" or so plastic pan, wood to mount bicycle wheel and bucket, small bucket, water
either build this or have it already built.
64.3) Thermostat and Heater
Materials: will a simple house thermostat work under power from a large battery and can i run a small heater off of that also? styrofoam insulated box? wires, nuts and bolts, thermometer (respond as fast as thermocouple?)
Method:
setup a thermostat in a styrofoam box and hook it up to some kind of small heater with a fan to warm the box. keep the thermostat open. hook them all up to a battery. watch how the mechanism works and reason it out.
64.4) Door Buzzer
Materials: large battery, thick paper, thin wire, nail, odds and ends hardware..
Method: wrap paper into a tube to fit nail into. wrap the wire around it 100 times or whatever. make a circuit out of the wire, the nail and a peice of metal the nail must contact. get it set up so it buzzes. What can you do to change to rate of buzzing? number of windings? weight of nail? a spring pulling opposite? or use gravity.
Discussion: discuss the kinds of feedbacks involved.
Materials: well oiled bicycle wheel, tape, plastic cups, awl, 20" or so plastic pan, wood to mount bicycle wheel and bucket, small bucket, water
either build this or have it already built.
64.3) Thermostat and Heater
Materials: will a simple house thermostat work under power from a large battery and can i run a small heater off of that also? styrofoam insulated box? wires, nuts and bolts, thermometer (respond as fast as thermocouple?)
Method:
setup a thermostat in a styrofoam box and hook it up to some kind of small heater with a fan to warm the box. keep the thermostat open. hook them all up to a battery. watch how the mechanism works and reason it out.
64.4) Door Buzzer
Materials: large battery, thick paper, thin wire, nail, odds and ends hardware..
Method: wrap paper into a tube to fit nail into. wrap the wire around it 100 times or whatever. make a circuit out of the wire, the nail and a peice of metal the nail must contact. get it set up so it buzzes. What can you do to change to rate of buzzing? number of windings? weight of nail? a spring pulling opposite? or use gravity.
Discussion: discuss the kinds of feedbacks involved.
9) Can We Build Ant Robots?
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Materials:
Lego robots? and printouts of some 1000 line sourcecodes.
get some kits with activators, sensors, logic blocks. try hooking 'em up to get simple robots to move around and follow lights etc.. how many parts do we need?
get some simple robots working show some more complex ones. you need LOTS MORE logic blocks and sensors to make interesting robots! just HOW MANY?
i must learn this
use the lego robots, just show 'em in action and show 1000 lines of code!
Materials:
Lego robots? and printouts of some 1000 line sourcecodes.
get some kits with activators, sensors, logic blocks. try hooking 'em up to get simple robots to move around and follow lights etc.. how many parts do we need?
get some simple robots working show some more complex ones. you need LOTS MORE logic blocks and sensors to make interesting robots! just HOW MANY?
i must learn this
use the lego robots, just show 'em in action and show 1000 lines of code!
61.3) Program More Elaborate Math Games
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Do these in basic or, again, the lego robot language. We should try Conway Life, iterates of logistic map, and a program to draw the mandelbrot set, and show the lorenz attractor.
Do these in basic or, again, the lego robot language. We should try Conway Life, iterates of logistic map, and a program to draw the mandelbrot set, and show the lorenz attractor.
61.2) Simple Machine Language Programs
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Materials:
preferably the same programming environment as the lego robots or maybe use something like the Tierra machine code!
Get a programming book again and pick a few simple ones; binary search, sorting, and of course we will program up the one dimensional cellular automata; rule 30!
ALTERNATE VERSION FOR SCIENCE CENTERS:
10) write machine code? hmmm simplest. show 4 bit processor has few basic instructions, inc, dec, set=0, dec and loop, so they can make simple programs on a screen of some kind... but what's gonna happen here? it takes some period of learning of motivation to figure out how to make a program. what do you want them to be able to accomplish?
ultimately program legobots but i don't want it to be abstract, i want them to see that it's all based on these basic mechanical components. the legobot programing environment was a mystical make believe geometric representation on a computer screen. i don't want that! that's magic!
so can you make a simple legobot that's controlled by the code for that simple machine? 4 bit instruction code, 15 instructions with the 16th code signaling for an extended instruction set.
ok, make it 8bit 4 bit code 4 bit register code, 16 registers
inc reg
dec reg
set=0 reg
if not zero reg branch loc
brach loc
shift right reg
shift left reg
if flag branch loc
M[addr]=reg
reg=M[addr]
M[reg]=A
A=M[reg]
Halt
add
sub
i suppose i should have stack implementation
subroutine call and return
load program counter etc..
extended instructions (2 4bit nibbles)
X fwd steps
Xrot (rotate clockwise 22.5deg) or from 0 to 360-22.5deg (16 options)
Xwrite
Xread
Xload imm reg
extended instruction:
(can add other sensors and actions later)
show the actual circuitry of the robot, the 4 bit processor
bar, you are dreaming. how will you test this all out to see how feasible it is? and again... how will kids write the programs?
so you see the blow up 4bit processor circuit on the wall.
then you have the legobot with hex display or something and button for load, read, reset etc.. like my 1802 board. and lights and things insiode the clear case to simulate these signals going to the 4bit processor. the clock rate is like a pulse every 2seconds so they can see all the steps... or again, you can turn a dial to slow down the pulse rate or speed it up... hmmm
hell you can make the bot big enough (good, robust) to have a keyboard with a button for each command, labeled, inc, dec, loop, back, rotate... and then a shift key to use those same keys for the hex numbers. of course you have on the wall the diagram for the circuit that polls the keyboard! well it's a simple circuit, keypress signals a register with input etc.. 16 line to 4 bit decoder...
then describe CPU architecture: memory, registers, program counter, execution, transfers, how arithmetic operations work and effect flags, how branch instructions chagne program counter, describe hex notation, describe 0-1=255, etc..
so then what? so they start making programs:
move 5
rotate
move 5
rotate
move 5
rotate
move 5
that makes a square that's easy enough to suggest to a kid.
show some programs that the kid can watch and then he modifies them...
the concept of looping...
loop 2
loop 1
move 5
test for bump
until 1
rotate
until 2
bar that's a sophisticated concept! do you think you can really get kids at a science center to begin to play with this stuff? i don't think science museum is the right environment for sitting down and experimenting and thinking.
i don't know. what if you just show the programs and see how they loop, proceed while watching the bot, and then you can modify the programs?
then you can watch on the wall a diagram (watch the bouncing ball...) run through a complicated program while watching the bot go at it...
Further lessons:
give examples of use of each instruction.
describe register pointers
write simple turtle programs to make shapes
describe branches for if then
then introduce loops
adding list of numbers
searching list of numbers
then you can show langton ant
describe subroutines
should get my old forth book for outline of what to teach, do i got my 68000 book? i've got the 1802 manual and a programming lesson based on it!
We can program langton's ant:
' not sure how i'm implementing read and write to the floor!
' reg B=0
' reg C=1
'
load imm B, 0
load imm C, 1
[3]
read to A
if A zero branch [1] ' if land on a 1
write B 'write blank
rot 12 ' rot counter clockwise
fwd 1
branch [2]
[1] ' if land on a 0
write C ' write 1
rot 4 ' rot clockwise
fwd 1
[2]
brach [3]
Materials:
preferably the same programming environment as the lego robots or maybe use something like the Tierra machine code!
Get a programming book again and pick a few simple ones; binary search, sorting, and of course we will program up the one dimensional cellular automata; rule 30!
ALTERNATE VERSION FOR SCIENCE CENTERS:
10) write machine code? hmmm simplest. show 4 bit processor has few basic instructions, inc, dec, set=0, dec and loop, so they can make simple programs on a screen of some kind... but what's gonna happen here? it takes some period of learning of motivation to figure out how to make a program. what do you want them to be able to accomplish?
ultimately program legobots but i don't want it to be abstract, i want them to see that it's all based on these basic mechanical components. the legobot programing environment was a mystical make believe geometric representation on a computer screen. i don't want that! that's magic!
so can you make a simple legobot that's controlled by the code for that simple machine? 4 bit instruction code, 15 instructions with the 16th code signaling for an extended instruction set.
ok, make it 8bit 4 bit code 4 bit register code, 16 registers
inc reg
dec reg
set=0 reg
if not zero reg branch loc
brach loc
shift right reg
shift left reg
if flag branch loc
M[addr]=reg
reg=M[addr]
M[reg]=A
A=M[reg]
Halt
add
sub
i suppose i should have stack implementation
subroutine call and return
load program counter etc..
extended instructions (2 4bit nibbles)
X fwd steps
Xrot (rotate clockwise 22.5deg) or from 0 to 360-22.5deg (16 options)
Xwrite
Xread
Xload imm reg
extended instruction:
(can add other sensors and actions later)
show the actual circuitry of the robot, the 4 bit processor
bar, you are dreaming. how will you test this all out to see how feasible it is? and again... how will kids write the programs?
so you see the blow up 4bit processor circuit on the wall.
then you have the legobot with hex display or something and button for load, read, reset etc.. like my 1802 board. and lights and things insiode the clear case to simulate these signals going to the 4bit processor. the clock rate is like a pulse every 2seconds so they can see all the steps... or again, you can turn a dial to slow down the pulse rate or speed it up... hmmm
hell you can make the bot big enough (good, robust) to have a keyboard with a button for each command, labeled, inc, dec, loop, back, rotate... and then a shift key to use those same keys for the hex numbers. of course you have on the wall the diagram for the circuit that polls the keyboard! well it's a simple circuit, keypress signals a register with input etc.. 16 line to 4 bit decoder...
then describe CPU architecture: memory, registers, program counter, execution, transfers, how arithmetic operations work and effect flags, how branch instructions chagne program counter, describe hex notation, describe 0-1=255, etc..
so then what? so they start making programs:
move 5
rotate
move 5
rotate
move 5
rotate
move 5
that makes a square that's easy enough to suggest to a kid.
show some programs that the kid can watch and then he modifies them...
the concept of looping...
loop 2
loop 1
move 5
test for bump
until 1
rotate
until 2
bar that's a sophisticated concept! do you think you can really get kids at a science center to begin to play with this stuff? i don't think science museum is the right environment for sitting down and experimenting and thinking.
i don't know. what if you just show the programs and see how they loop, proceed while watching the bot, and then you can modify the programs?
then you can watch on the wall a diagram (watch the bouncing ball...) run through a complicated program while watching the bot go at it...
Further lessons:
give examples of use of each instruction.
describe register pointers
write simple turtle programs to make shapes
describe branches for if then
then introduce loops
adding list of numbers
searching list of numbers
then you can show langton ant
describe subroutines
should get my old forth book for outline of what to teach, do i got my 68000 book? i've got the 1802 manual and a programming lesson based on it!
We can program langton's ant:
' not sure how i'm implementing read and write to the floor!
' reg B=0
' reg C=1
'
load imm B, 0
load imm C, 1
[3]
read to A
if A zero branch [1] ' if land on a 1
write B 'write blank
rot 12 ' rot counter clockwise
fwd 1
branch [2]
[1] ' if land on a 0
write C ' write 1
rot 4 ' rot clockwise
fwd 1
[2]
brach [3]
27) Microstructure Of Cells
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go in deeper: how many parts? look at freeze etch electron micrographs! organelles, shot through with internal fibers, membranes, tracks along which proteins can move things along. sensors on the outside. mitochondria protein factories. 1000 different enzymes. it's chemistry! YIKES. how much?
this is a whole course, how much to teach?
show Biovisions "inner life of cell" animation of cell. are there any more? will need computer and way to get it onto big screen, unless only 6 or 7 kids, computer screen is fine.
go in deeper: how many parts? look at freeze etch electron micrographs! organelles, shot through with internal fibers, membranes, tracks along which proteins can move things along. sensors on the outside. mitochondria protein factories. 1000 different enzymes. it's chemistry! YIKES. how much?
this is a whole course, how much to teach?
show Biovisions "inner life of cell" animation of cell. are there any more? will need computer and way to get it onto big screen, unless only 6 or 7 kids, computer screen is fine.
A Selection Of Representative Labs With Commentary
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CHAPTER 1
LIFE
How varied and detailed is life on Earth?
6) Key Out 100 Plants In A Local Park [6WKS] [or a two session blitz just to collect 100 different plants and press them]
By learning to key out and LOOK at organisms hard enough to distinguish their varieties, we learn two things:
there is a bewildering variety
organisms are incredibly DETAILED. As close as we look at them as much as we magnify and look inward, we find levels and levels of complex details. How does it happen?
And how complex is their behavior?
2) collect insects and watch their behavior in a terrarium
after much observation you can find out:
4.5) List of 270 Skills That a Honeybee Has
Can we get a handle on it from computer science? In the past 60 years we have learned to build some complexity ourselves. Follow the levels of complexity as we build up from transistors a computer with elaborate software.
CHAPTER 6
COMPUTERS
It's not so easy to see how animals work, maybe we can at least try to make some robots that act as complex and see from scratch how it might work?
8) from logic gates to computer [1/2 hr?] show them, or make some simple circuits in digi-lab.
61.2) write simple computer programs in machine code: binary search, sort, rule 30 etc... [hr]
61.3) program John Horton Conway's game of life, Mandelbrot set, and Lorenz attractor in basic or something or maybe the lego bot language
[hr?] show them?
Researchers in the field of Artificial Intelligence are now asking themselves, what it would take to build an animal, to build clever behaviors from the bottom up. We are trying to check our understanding of intelligence by building complex things and seeing if they can ACT intelligently.
9) show them well programmed lego bots ( (intro to another whole workshop) and listings of 1000 lined programs [1/2hr]
But we still Can't do it! Our robots are clunky and stupid in comparison with a honeybee!
CHAPTER 1
SO BACK TO CRITTERS FOR HELP
16) watch videos of animal development
This is an amazing process. And it works because animals are colonies of living cells, all talking with each other, feeling each other out and reproducing and sending their kids to the right places. We build machines from the outside in factories, but animals and plants are built from within by cells. What are cells?
CHAPTER 2
CELLULAR LIFE
Some critters are a single cell all in one, lets watch some:
22) watch single cell pond creatures [hr]
Take some time to watch the intricate behaviors of living single celled organisms. Already at this level, there is so much capability. The capabilities that make life so rich are not concentrated at the top, the most centralized level, but are distributed throughout every size scale! Even at the cellular level, and below...
So what kind of 'things' are cells?
27) molecular video "inner life of cell" [10min] more?
cells are hierarchical structures of organelles, macromolecular assemblies, macromolecules, small molecules. The properties of cells are also due to the most common molecule in them: water.
They are whirlwinds of swirling interacting molecules. The structure and organization goes in several more levels deep, as complex as a whole giant city.
and finally the most common machinery: proteins. they can self assemble into complex structures like undulipodia, they can change shape, travel along tracks, act as a complex logic elements in processing information, respond to EM radiation
25) grow oscillatoria in water and glass jar. watch it move. then at second to last session, weigh it, dry it, last session, burn it, weigh the ash
[10min sessions a few times]
PART 2
PHYSICS AND MATH
So how do cells do it? Well, no need to go to biology for the complexity of cells, the capabilities of cells. Physics, chemistry, and mathematics already gives us this. We are slowly whittling away at the divide between chemistry and life!
Physics and math gives us:
1) Patterns at far from equilibrium: energy flow through systems creates ordered dynamism
2) But even at equilibrium, rest, pattern comes ultimately from mathematics
3) And the clay that physics and math get to sculpt into organisms?
molecules!
CHAPTER 3
WHAT IS THE MOLECULAR WORLD?
So what is the molecular world like that it gives life it's subtle creative qualities? What are we 'made of'
Well, how many molecules are there in a cell?
73.2) Brownian motion: hints at the existence of many tiny molecules, constantly in motion due to heat, and hints at how small they are, how many in a drop of water.
73.3) monomolecular lipid layer: another clue to how big molecules are. Then we sketch out how the number of molecules in a glass of water can be calculated from experiments like these
[hr]
Atoms, molecules are not building BLOCKS, they are little machines, not clunky, but fuzzy, sensitive to their environment and each other, reactive, each atom is a complex of electron orbitals which are solutions to wave equations... molecules are flexible, constantly wiggling, not alive, but... can't describe what they are in common every day terms.
any labs we can do to show how molecules interact? orgo reactions, soap/oil/water, collisions? orientations? chirality..
72.2) show how many ways an ethanol molecule can respond to its chemical environment?
At the molecular level you already have a kind of trial and error mechanism for fitting together puzzles. one of the roots of our intelligence. molecules are always moving, wiggling, interacting with each other 10^10 times a second! molecules in a warm universe with energy flow are not like a jumble of cold automobile parts just sitting there, molecules can self assemble!
Show diagrams/video of how simple molecular interactions cooperate to form complex structures and processes:
31.2) Distributed Brownian Motion Machinery: Clathrin Coated Pits
molecules pass energy to each other in reactions, store energy in bonds, thus networks of their reactions can be ordered by energy flowing through systems of molecules.
molecules react with EM radiation. vision comes for free at the lowest level
44) Play With A Candle Flame
CHAPTER 4
DISSIPATIVE STRUCTURES: FLOW OF ENERGY THROUGH SYSTEMS CREATES PATTERNED DYNAMISM
If molecules aren't simple building blocks, then organisms are not 'things' at all, 'phenomena' would be a better adjective, or, to be less academic; 'dances'? What kind of phenomena are living cells? they are chemical systems animated by energy flow.
Our usual experience is that things wear out after a while and run down. You may have heard of the second law of thermodynamics which says "all closed systems (nothing coming in or out) run down and become less, not more ordered. If this is so, then how can life oppose this 'universal' tendency? Well, life is not a closed system!
One process that helps is positive and negative feedback. Lets explore some machines and simple processes that can do this.
64.2) chaotic waterwheel, thermostat and heater, door buzzer [hr]
In our next labs
33) show steam engine (with governor?) can i show that it needs hot and cold?
34) Then Benard convection
[hr]
We show the basic system animated by energy flow: Benard convection: We start off with wood (or some kind of fuel, highly ordered in any case) and air (unusual, out of equilibrium with all its oxygen..) and light the wood into flame. It is important that the flame is much hotter than the air above It.
The flame will heat from below a pan of shallow water. As the bigger closed system of wood and air and water run down to ashes and luke-warm carbon dioxide and water, for a while, a wondrous thing happens. Our pan of water (not closed, open to heat flowing through it) becomes ordered into an hexagonal array of gyrating convection cells.
We call these subsystems FAR from thermodynamic equilibrium systems or Dissipative Systems (they dissipate heat).
And what makes CELLS swirl? this time it is the flow of chemical energy. High energy bonds come in (sugars) and again low energy bonds come out in the form of carbon dioxide. In the meanwhile the cells swirl with activity. here are some simpler examples.
Can life even arise spontaneously from chemistry?
42) The Beloussov Zhabotinsky reaction : a simple far from equilibrium chemical system that you can watch forming periodic spatial patterns
Put convection and chemical reaction cycles together and you get:
44) play with a flame: [hr]
They are more complex than you think! And they contain complex networks of chemical reactions reminiscent of the metabolic chart!
CHAPTER 5
MATHEMATICAL DYNAMICAL SYSTEMS: EASY LABORATORY, ALL YOU NEED IS PENCIL, PAPER, COMPUTER
But living creatures are more complicated then these. Can chemistry really result in the complexity we found in living cells? Where do all those different patterns and structures come from? MATH! Mathematics gives us so much pattern for free. Simple rules repeated over and over again between many identical simple units can create surprising unpredictable patterns.
48) John Horton Conway's Game Of Life: a simple system of simple rules wherein there are patterns of many classes of behaviors, and simple patterns can develop into surprisingly complex ones. we can even make a finite pattern that results in an endlessly interesting one
53) One dimensional cellular automata rules 30 and 110 even dirt simpler set of rules that produces an endless stream of creativity
[1/2hr] [1/2 hr]
56) 3n+1: a simple number game with complex behavior we have yet to fully understand
57) e/o Fibonacci system: another one with much more complex behavior. these only involve addition and division.
58) Iterated logistic equation to Mandelbrot set: simple math rules give the most complex geometric structure we've ever imagined
60) Lorenz attractor: a simple dynamic system that results in a curious subtly behaving system with a sprinkling of unpredictability. By the way, it is very similar in behavior to the chaotic waterwheel.
[hr]
CHAPTER 7
EVEN AT EQUILIBRIUM: PHYSICAL AND CHEMICAL PATTERN FORMATION
Even without the dynamical systems set into motion by energy flow, the laws of physics are fecund: We find pattern formation even at equilibrium.
The wonder is, why isn't the universe a seamless haze of psychedelic chaos? Why isn't it just a bland grey blob of continuous matter? Why isn't the universe simply one huge neutron or quark or is THERE anything at the bottom? Somehow the physics and math give us all these phase transitions, clumpings for free.
74) show periodic chart with samples of diff elements: gas, liquid, metal, graphite, sulfur, semiconductor..
76) phases of sulfur: even with one kind of atom, depending on temperature, we get wildly different behaviors
75) and breath on a window pane: ditto for water molecules, how do they 'calculate' the beautiful patterns of 'jack frost' on window panes?
[1/2 hr]
70) mineral exhibit a dozen elements, a dozen transition metals and 2000+ combinations all for free.[1/2 hr? depends where]
CHAPTER 8
IT ALL COMES FROM MATH
At root, why is this universe so full of patterns? MATH!
From mathematics alone, we get surprising complexity but not total chaos from the simplest static logical rules
And why do we have this interesting periodic chart of elements, each with their potent particular properties? Physics and math again! Propose a simple set of rules and let them play out and you often find that you get a set of discrete entities which follow them that is interestingly diverse but not infinitely chaotic! This is the core of pattern formation in our universe. It's built in at the very basic logical structure of it.
87) enumeration of finite graphs: keep adding one more edge to a graph and you discover radical new behaviors. clues to things like how we get the behaviors in the periodic chart of elements?[1/2 hr]
81) classification of finite simple groups: example of simple static rules giving surprisingly diverse but only a tiny bit of chaotic pattern [1/2hr]
PART 3
THE BIG QUESTIONS: EVOLUTION, ORIGINS OF LIFE, AND MIND
CHAPTER 9
PUTTING IT ALL BACK TOGETHER: EVOLUTIONARY BIOLOGY
Then we put it all back together again and tackle the most fascinating subject: what is it that brings us all those wonderful critters we found outside at the beginning of our exploration? Evolutionary biology.
96) Tierra a system of programs that can reproduce, evolve, and form ecosystems [hr]
CHAPTERS FOR FURTHER STUDY:
CHAPTER 10
THE FINAL FRONTIER: CAN WE UNDERSTAND HOW GEOCHEMISTRY CAN BECOME LIFE?
The final frontier: is life SOLELY a consequence of chemistry and mathematics? If you perform labs in this topic, you are at the forefront of the scientific adventure.
CHAPTER 11?
MIND
Bar, why do you leave off discussing mind and consciousness? because I'm not greedy? but the labs watching behavior of single cells, the computer science topics, 260 skills of honeybees, building AI programs to simulate critters is the start.
CHAPTER 12?
SUPERORGANISMS
And finally we come back to the ants! This is the most recent hierarchical level of complex behavior to evolve on earth. not only critters with minds who can explore and learn about and manipulate their world, but some organisms come together and build highly cohesive societies:
Ants, honeybees, wasps, termites, naked mole rats, wolves and... humans.
CHAPTER 1
LIFE
How varied and detailed is life on Earth?
6) Key Out 100 Plants In A Local Park [6WKS] [or a two session blitz just to collect 100 different plants and press them]
By learning to key out and LOOK at organisms hard enough to distinguish their varieties, we learn two things:
there is a bewildering variety
organisms are incredibly DETAILED. As close as we look at them as much as we magnify and look inward, we find levels and levels of complex details. How does it happen?
And how complex is their behavior?
2) collect insects and watch their behavior in a terrarium
after much observation you can find out:
4.5) List of 270 Skills That a Honeybee Has
Can we get a handle on it from computer science? In the past 60 years we have learned to build some complexity ourselves. Follow the levels of complexity as we build up from transistors a computer with elaborate software.
CHAPTER 6
COMPUTERS
It's not so easy to see how animals work, maybe we can at least try to make some robots that act as complex and see from scratch how it might work?
8) from logic gates to computer [1/2 hr?] show them, or make some simple circuits in digi-lab.
61.2) write simple computer programs in machine code: binary search, sort, rule 30 etc... [hr]
61.3) program John Horton Conway's game of life, Mandelbrot set, and Lorenz attractor in basic or something or maybe the lego bot language
[hr?] show them?
Researchers in the field of Artificial Intelligence are now asking themselves, what it would take to build an animal, to build clever behaviors from the bottom up. We are trying to check our understanding of intelligence by building complex things and seeing if they can ACT intelligently.
9) show them well programmed lego bots ( (intro to another whole workshop) and listings of 1000 lined programs [1/2hr]
But we still Can't do it! Our robots are clunky and stupid in comparison with a honeybee!
CHAPTER 1
SO BACK TO CRITTERS FOR HELP
16) watch videos of animal development
This is an amazing process. And it works because animals are colonies of living cells, all talking with each other, feeling each other out and reproducing and sending their kids to the right places. We build machines from the outside in factories, but animals and plants are built from within by cells. What are cells?
CHAPTER 2
CELLULAR LIFE
Some critters are a single cell all in one, lets watch some:
22) watch single cell pond creatures [hr]
Take some time to watch the intricate behaviors of living single celled organisms. Already at this level, there is so much capability. The capabilities that make life so rich are not concentrated at the top, the most centralized level, but are distributed throughout every size scale! Even at the cellular level, and below...
So what kind of 'things' are cells?
27) molecular video "inner life of cell" [10min] more?
cells are hierarchical structures of organelles, macromolecular assemblies, macromolecules, small molecules. The properties of cells are also due to the most common molecule in them: water.
They are whirlwinds of swirling interacting molecules. The structure and organization goes in several more levels deep, as complex as a whole giant city.
and finally the most common machinery: proteins. they can self assemble into complex structures like undulipodia, they can change shape, travel along tracks, act as a complex logic elements in processing information, respond to EM radiation
25) grow oscillatoria in water and glass jar. watch it move. then at second to last session, weigh it, dry it, last session, burn it, weigh the ash
[10min sessions a few times]
PART 2
PHYSICS AND MATH
So how do cells do it? Well, no need to go to biology for the complexity of cells, the capabilities of cells. Physics, chemistry, and mathematics already gives us this. We are slowly whittling away at the divide between chemistry and life!
Physics and math gives us:
1) Patterns at far from equilibrium: energy flow through systems creates ordered dynamism
2) But even at equilibrium, rest, pattern comes ultimately from mathematics
3) And the clay that physics and math get to sculpt into organisms?
molecules!
CHAPTER 3
WHAT IS THE MOLECULAR WORLD?
So what is the molecular world like that it gives life it's subtle creative qualities? What are we 'made of'
Well, how many molecules are there in a cell?
73.2) Brownian motion: hints at the existence of many tiny molecules, constantly in motion due to heat, and hints at how small they are, how many in a drop of water.
73.3) monomolecular lipid layer: another clue to how big molecules are. Then we sketch out how the number of molecules in a glass of water can be calculated from experiments like these
[hr]
Atoms, molecules are not building BLOCKS, they are little machines, not clunky, but fuzzy, sensitive to their environment and each other, reactive, each atom is a complex of electron orbitals which are solutions to wave equations... molecules are flexible, constantly wiggling, not alive, but... can't describe what they are in common every day terms.
any labs we can do to show how molecules interact? orgo reactions, soap/oil/water, collisions? orientations? chirality..
72.2) show how many ways an ethanol molecule can respond to its chemical environment?
At the molecular level you already have a kind of trial and error mechanism for fitting together puzzles. one of the roots of our intelligence. molecules are always moving, wiggling, interacting with each other 10^10 times a second! molecules in a warm universe with energy flow are not like a jumble of cold automobile parts just sitting there, molecules can self assemble!
Show diagrams/video of how simple molecular interactions cooperate to form complex structures and processes:
31.2) Distributed Brownian Motion Machinery: Clathrin Coated Pits
molecules pass energy to each other in reactions, store energy in bonds, thus networks of their reactions can be ordered by energy flowing through systems of molecules.
molecules react with EM radiation. vision comes for free at the lowest level
44) Play With A Candle Flame
CHAPTER 4
DISSIPATIVE STRUCTURES: FLOW OF ENERGY THROUGH SYSTEMS CREATES PATTERNED DYNAMISM
If molecules aren't simple building blocks, then organisms are not 'things' at all, 'phenomena' would be a better adjective, or, to be less academic; 'dances'? What kind of phenomena are living cells? they are chemical systems animated by energy flow.
Our usual experience is that things wear out after a while and run down. You may have heard of the second law of thermodynamics which says "all closed systems (nothing coming in or out) run down and become less, not more ordered. If this is so, then how can life oppose this 'universal' tendency? Well, life is not a closed system!
One process that helps is positive and negative feedback. Lets explore some machines and simple processes that can do this.
64.2) chaotic waterwheel, thermostat and heater, door buzzer [hr]
In our next labs
33) show steam engine (with governor?) can i show that it needs hot and cold?
34) Then Benard convection
[hr]
We show the basic system animated by energy flow: Benard convection: We start off with wood (or some kind of fuel, highly ordered in any case) and air (unusual, out of equilibrium with all its oxygen..) and light the wood into flame. It is important that the flame is much hotter than the air above It.
The flame will heat from below a pan of shallow water. As the bigger closed system of wood and air and water run down to ashes and luke-warm carbon dioxide and water, for a while, a wondrous thing happens. Our pan of water (not closed, open to heat flowing through it) becomes ordered into an hexagonal array of gyrating convection cells.
We call these subsystems FAR from thermodynamic equilibrium systems or Dissipative Systems (they dissipate heat).
And what makes CELLS swirl? this time it is the flow of chemical energy. High energy bonds come in (sugars) and again low energy bonds come out in the form of carbon dioxide. In the meanwhile the cells swirl with activity. here are some simpler examples.
Can life even arise spontaneously from chemistry?
42) The Beloussov Zhabotinsky reaction : a simple far from equilibrium chemical system that you can watch forming periodic spatial patterns
Put convection and chemical reaction cycles together and you get:
44) play with a flame: [hr]
They are more complex than you think! And they contain complex networks of chemical reactions reminiscent of the metabolic chart!
CHAPTER 5
MATHEMATICAL DYNAMICAL SYSTEMS: EASY LABORATORY, ALL YOU NEED IS PENCIL, PAPER, COMPUTER
But living creatures are more complicated then these. Can chemistry really result in the complexity we found in living cells? Where do all those different patterns and structures come from? MATH! Mathematics gives us so much pattern for free. Simple rules repeated over and over again between many identical simple units can create surprising unpredictable patterns.
48) John Horton Conway's Game Of Life: a simple system of simple rules wherein there are patterns of many classes of behaviors, and simple patterns can develop into surprisingly complex ones. we can even make a finite pattern that results in an endlessly interesting one
53) One dimensional cellular automata rules 30 and 110 even dirt simpler set of rules that produces an endless stream of creativity
[1/2hr] [1/2 hr]
56) 3n+1: a simple number game with complex behavior we have yet to fully understand
57) e/o Fibonacci system: another one with much more complex behavior. these only involve addition and division.
58) Iterated logistic equation to Mandelbrot set: simple math rules give the most complex geometric structure we've ever imagined
60) Lorenz attractor: a simple dynamic system that results in a curious subtly behaving system with a sprinkling of unpredictability. By the way, it is very similar in behavior to the chaotic waterwheel.
[hr]
CHAPTER 7
EVEN AT EQUILIBRIUM: PHYSICAL AND CHEMICAL PATTERN FORMATION
Even without the dynamical systems set into motion by energy flow, the laws of physics are fecund: We find pattern formation even at equilibrium.
The wonder is, why isn't the universe a seamless haze of psychedelic chaos? Why isn't it just a bland grey blob of continuous matter? Why isn't the universe simply one huge neutron or quark or is THERE anything at the bottom? Somehow the physics and math give us all these phase transitions, clumpings for free.
74) show periodic chart with samples of diff elements: gas, liquid, metal, graphite, sulfur, semiconductor..
76) phases of sulfur: even with one kind of atom, depending on temperature, we get wildly different behaviors
75) and breath on a window pane: ditto for water molecules, how do they 'calculate' the beautiful patterns of 'jack frost' on window panes?
[1/2 hr]
70) mineral exhibit a dozen elements, a dozen transition metals and 2000+ combinations all for free.[1/2 hr? depends where]
CHAPTER 8
IT ALL COMES FROM MATH
At root, why is this universe so full of patterns? MATH!
From mathematics alone, we get surprising complexity but not total chaos from the simplest static logical rules
And why do we have this interesting periodic chart of elements, each with their potent particular properties? Physics and math again! Propose a simple set of rules and let them play out and you often find that you get a set of discrete entities which follow them that is interestingly diverse but not infinitely chaotic! This is the core of pattern formation in our universe. It's built in at the very basic logical structure of it.
87) enumeration of finite graphs: keep adding one more edge to a graph and you discover radical new behaviors. clues to things like how we get the behaviors in the periodic chart of elements?[1/2 hr]
81) classification of finite simple groups: example of simple static rules giving surprisingly diverse but only a tiny bit of chaotic pattern [1/2hr]
PART 3
THE BIG QUESTIONS: EVOLUTION, ORIGINS OF LIFE, AND MIND
CHAPTER 9
PUTTING IT ALL BACK TOGETHER: EVOLUTIONARY BIOLOGY
Then we put it all back together again and tackle the most fascinating subject: what is it that brings us all those wonderful critters we found outside at the beginning of our exploration? Evolutionary biology.
96) Tierra a system of programs that can reproduce, evolve, and form ecosystems [hr]
CHAPTERS FOR FURTHER STUDY:
CHAPTER 10
THE FINAL FRONTIER: CAN WE UNDERSTAND HOW GEOCHEMISTRY CAN BECOME LIFE?
The final frontier: is life SOLELY a consequence of chemistry and mathematics? If you perform labs in this topic, you are at the forefront of the scientific adventure.
CHAPTER 11?
MIND
Bar, why do you leave off discussing mind and consciousness? because I'm not greedy? but the labs watching behavior of single cells, the computer science topics, 260 skills of honeybees, building AI programs to simulate critters is the start.
CHAPTER 12?
SUPERORGANISMS
And finally we come back to the ants! This is the most recent hierarchical level of complex behavior to evolve on earth. not only critters with minds who can explore and learn about and manipulate their world, but some organisms come together and build highly cohesive societies:
Ants, honeybees, wasps, termites, naked mole rats, wolves and... humans.
Friday, April 24, 2009
95) Word Mutation Game
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start with one word, and let it reproduce and mutate and interact to form sentences, eventually stories...
dog:
bog cog fog hog jog log dig dug dong do doc doe doo dot doge dogs
use a computer program with spell-check dictionary
combinations:
dog jog. hog jog. bog log. dog dig. hog dig. dog dug. hog dug. dog dong. hog dong. dig bog. dug bog. doc dong. doe dig. dog doo. hog doo. doc jog. doge dong. dog dig log. dog dug log. do dog dig. dig dog doo. do dogs dig. do dogs dig log.
now keep only the words that can interact in sentences:
dog bog hog jog log dig dug dong do doc doe doo doge
mutate them:
hag hug ho hob hoe hoo hop hot how hoy hogs
ajog jo job joe jot joy jogs
blog clog flog slog long lo lob lol lop lot low logs etc...
more combinations:
hog hag. dog hug. dog hop. do dog hop. how do dog hop. how do dogs dig logs. do dogs hug hot docs. how long do dogs dig. do long logs clog bogs. etc....
now if you introduce some geography to all these sentences so that they only join with neighbors. the words themselves are reproduced out of sentences...
now of course the ecological possibilities are fixed from MY understanding of language and imagination. in real biological evolution, you got some fixed ecology given by geology, physics, chemistry, geometry... but the new critters themselves also create new ecological possibilities.
well, in my system the evolution of the words "how" and "do" did the same thing.
I'll never evolve the word "doggy" because "dogg" cant evolve. but now if I allow mutations in SENTENCES, in particular insertions and deletions, I could get: "dog go", and if I allow rare double mutations, a deletion and a mutation can give me "doggy".
here is a toy biology that I thoroughly understand and can play with to get insight into all the quirky details that are possible in this biological evolution game.
Bar, you can make this a game people play! MUCH more interesting than scrabble!
start with one word, and let it reproduce and mutate and interact to form sentences, eventually stories...
dog:
bog cog fog hog jog log dig dug dong do doc doe doo dot doge dogs
use a computer program with spell-check dictionary
combinations:
dog jog. hog jog. bog log. dog dig. hog dig. dog dug. hog dug. dog dong. hog dong. dig bog. dug bog. doc dong. doe dig. dog doo. hog doo. doc jog. doge dong. dog dig log. dog dug log. do dog dig. dig dog doo. do dogs dig. do dogs dig log.
now keep only the words that can interact in sentences:
dog bog hog jog log dig dug dong do doc doe doo doge
mutate them:
hag hug ho hob hoe hoo hop hot how hoy hogs
ajog jo job joe jot joy jogs
blog clog flog slog long lo lob lol lop lot low logs etc...
more combinations:
hog hag. dog hug. dog hop. do dog hop. how do dog hop. how do dogs dig logs. do dogs hug hot docs. how long do dogs dig. do long logs clog bogs. etc....
now if you introduce some geography to all these sentences so that they only join with neighbors. the words themselves are reproduced out of sentences...
now of course the ecological possibilities are fixed from MY understanding of language and imagination. in real biological evolution, you got some fixed ecology given by geology, physics, chemistry, geometry... but the new critters themselves also create new ecological possibilities.
well, in my system the evolution of the words "how" and "do" did the same thing.
I'll never evolve the word "doggy" because "dogg" cant evolve. but now if I allow mutations in SENTENCES, in particular insertions and deletions, I could get: "dog go", and if I allow rare double mutations, a deletion and a mutation can give me "doggy".
here is a toy biology that I thoroughly understand and can play with to get insight into all the quirky details that are possible in this biological evolution game.
Bar, you can make this a game people play! MUCH more interesting than scrabble!
Thursday, April 23, 2009
47) Simplest Organic Redox Cycle
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Harold J. Morowitz mentions a simple system of redox cycles of CO2 +H2O yielding formaldehyde and O2 and back again catalyzed by Fe2+/3+ under sunlight/shade, can we do that lab? how would we detect it's working? I suppose the BZ reaction is already more complex and it has a visual indicator!
If I have a vat of water (with CO2 dissolved in it ) over some catalyst, such as Fe++ ions, spread on the bottom, and I let high energy light (like ultraviolet) strike the catalyst on one side and leave the other side in the dark, we get something like Benard convection. On the lit side we get CO2 + H2O yielding higher energy molecules: CH2O + O2, these will diffuse to the dark side and oxidize back to CO2 and H2O, and as the catalyst on the light side use up all the CO2 there, the CO2 from the dark side will diffuse back to the light side, forming a cycle. This is theoretical, I haven't done it, or seen a physical description of it. The BZ reaction, however, under similar non equilibrium conditions does produce spiral wave patterns. These patterns from above might look stationary but they are made out of migrating molecules, so they are a different sort than patterns in crystals and snowflakes.
Notice that we need a hot side AND a cold side. If i we shone the UV light on the whole vat of water, and insulated the vat so that no heat was able to escape, the molecules would just build up more and more complicated gunk as the temperature rose, and then as the temperature rises even higher they would eventually come apart until the whole setup would be as hot as the UV source and it would consist of a random plasma of atomic ions. NO PATTERN, gotta have the hot and cold.
can I do a reaction like this?
Harold J. Morowitz mentions a simple system of redox cycles of CO2 +H2O yielding formaldehyde and O2 and back again catalyzed by Fe2+/3+ under sunlight/shade, can we do that lab? how would we detect it's working? I suppose the BZ reaction is already more complex and it has a visual indicator!
If I have a vat of water (with CO2 dissolved in it ) over some catalyst, such as Fe++ ions, spread on the bottom, and I let high energy light (like ultraviolet) strike the catalyst on one side and leave the other side in the dark, we get something like Benard convection. On the lit side we get CO2 + H2O yielding higher energy molecules: CH2O + O2, these will diffuse to the dark side and oxidize back to CO2 and H2O, and as the catalyst on the light side use up all the CO2 there, the CO2 from the dark side will diffuse back to the light side, forming a cycle. This is theoretical, I haven't done it, or seen a physical description of it. The BZ reaction, however, under similar non equilibrium conditions does produce spiral wave patterns. These patterns from above might look stationary but they are made out of migrating molecules, so they are a different sort than patterns in crystals and snowflakes.
Notice that we need a hot side AND a cold side. If i we shone the UV light on the whole vat of water, and insulated the vat so that no heat was able to escape, the molecules would just build up more and more complicated gunk as the temperature rose, and then as the temperature rises even higher they would eventually come apart until the whole setup would be as hot as the UV source and it would consist of a random plasma of atomic ions. NO PATTERN, gotta have the hot and cold.
can I do a reaction like this?
From Convection On Spinning Surfaces To Complex Weather Patterns On Earth and Jupiter
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35) Taylor Cuette Vortices Between Two Spinning Surfaces
The next spin we can introduce to the story IS spinning. If you put a rotating cylinder inside another rotating cylinder and fill the space between them with fluid a similar thing happens. As you increase the relative speeds various discrete numbers of fluid rolls form:
Pictures here:
http://www.intothecool.com/physics.php
36) Combine Convection With A Spinning Earth And We Get Our Atmospheric Circulation Patterns
When you combine convection on the surface of the Earth under sunlight with the fact that the Earth spins (Coriolis effect) the convection breaks up into a curious pattern of cells which dominate world weather patterns.
37) Storm Cells
Add the complication of the fact that when you cool moist air it breaks up into DISCRETE tiny droplets of water or ice, which then fall... you get distinct creatures which can last for many days called storm cells, hurricanes and tiny tornadoes.
Pictures of diagrams of storm cells
http://australiasevereweather.com/photography/photos/2003/0330de29.jpg?
http://hurricanetrackinfo.com/hurricane%20tracking%202.jpg
http://www.qc.ec.gc.ca/meteo/images/Fig_13-10.jpg
http://www.britannica.com/thunderstorms_tornadoes/ocliwea114a4.html
38) Vortex Streets
Lab with fluids or smoke to show the formation of discrete vortices in turbulent fluid flow!
39) Weather On Jupiter
Increase the speed of rotation of our spinning sphere and the weather goes wild: Jupiter
Pictures of discrete cells on Jupiter.
http://www.jpl.nasa.gov/images/jupiter/jupiter-v1_640x542.jpg
http://www.gearthblog.com/images/images2006/jupiter.jpg
The great red spot of Jupiter is one of many storm cells. Some last for years, the red spot has so far lasted a couple hundred years at least. (actually I'm combobulating three kinds of structures here: the Taylor vortices, the Benard cells, the complex thing a terrestrial storm cell is, and turbulence vortices. (hah! are there distinct types here? do they all blend? ) ) not 100% sure which the red spot is, or maybe a combination.. Already there is much complication before we even get to biological evolution!
35) Taylor Cuette Vortices Between Two Spinning Surfaces
The next spin we can introduce to the story IS spinning. If you put a rotating cylinder inside another rotating cylinder and fill the space between them with fluid a similar thing happens. As you increase the relative speeds various discrete numbers of fluid rolls form:
Pictures here:
http://www.intothecool.com/physics.php
36) Combine Convection With A Spinning Earth And We Get Our Atmospheric Circulation Patterns
When you combine convection on the surface of the Earth under sunlight with the fact that the Earth spins (Coriolis effect) the convection breaks up into a curious pattern of cells which dominate world weather patterns.
37) Storm Cells
Add the complication of the fact that when you cool moist air it breaks up into DISCRETE tiny droplets of water or ice, which then fall... you get distinct creatures which can last for many days called storm cells, hurricanes and tiny tornadoes.
Pictures of diagrams of storm cells
http://australiasevereweather.com/photography/photos/2003/0330de29.jpg?
http://hurricanetrackinfo.com/hurricane%20tracking%202.jpg
http://www.qc.ec.gc.ca/meteo/images/Fig_13-10.jpg
http://www.britannica.com/thunderstorms_tornadoes/ocliwea114a4.html
38) Vortex Streets
Lab with fluids or smoke to show the formation of discrete vortices in turbulent fluid flow!
39) Weather On Jupiter
Increase the speed of rotation of our spinning sphere and the weather goes wild: Jupiter
Pictures of discrete cells on Jupiter.
http://www.jpl.nasa.gov/images/jupiter/jupiter-v1_640x542.jpg
http://www.gearthblog.com/images/images2006/jupiter.jpg
The great red spot of Jupiter is one of many storm cells. Some last for years, the red spot has so far lasted a couple hundred years at least. (actually I'm combobulating three kinds of structures here: the Taylor vortices, the Benard cells, the complex thing a terrestrial storm cell is, and turbulence vortices. (hah! are there distinct types here? do they all blend? ) ) not 100% sure which the red spot is, or maybe a combination.. Already there is much complication before we even get to biological evolution!
34) Benard Convection
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back to best labs summary contents
Materials: shallow petri dish, some fluid either water with sparkles in it? or a higher viscosity fluid? some way to heat it from below uniformly. A way to heat it from above also, perhaps blow dryer. thermometer, maybe curious lighting techniques?
Method: watch water heat up, heat quickly to boil, seems to be chaos. Now heat more slowly and find temperature at which convection cells form. may have to experiment with depth of water. Now take temperature of bottom surface and air above water. now try the experiment again but this time heating both the bottom and heating the air above, do we get convection cells?
Discussion
If you heat a shallow layer of water in a pan, at a low temperature you get random motions in the water molecules as they carry the heat (molecular motion) from the high temperature bottom of the pan to the low temperature surface of the water. On a macro scale what you begin to see is that the layer of water directly above the pan expands (gets warmer) and thus less dense than the layer above it and rises. This rising layer breaks up into blobs randomly. Of course if blobs are rising, blobs of water at the top must sink because they are more dense (cooler). Already the fact that these homogenous layers break up into blobs is curious math. In fact, i'm not sure we fully understand it (lookup studies of water droplets and splashes, very complex!). The breaking up of the top layer into blobs as they descend, i think is mediated in a complex way by the surface tension of the water at the top. (surface tension is the stuff that makes water creep up the edges of a container of water a millimeter or so, called the meniscus.)
As you raise the temperature of the bottom of the pan relative to the top of the water you get more random motion. at a certain temperature difference, though, these rising and falling blobs eventually arrange themselves (surprise!) into a fairly neat hexagonal array of convection cells. Warm water rises in the center of each cell and falls at the edges. This is called Benard convection (named after the first to study them, Claude Bernard). As we increase the temperature difference even more, eventually the motion becomes random again and the water begins to boil.
Two surprising things about this phenomenon are the pattern and the phase transitions. The pattern is relatively neat, most cells are the same size and mostly the same hexagonal shape. The phase transitions are like the ones we couldn't predict for water, at different stages in heating we get a different distinct story. For water it was ice, water, vapor. For sulfur, it is orthorhombic sulfur, yellow liquid, red viscous liquid, and various stages of vapor. For our shallow pan of water, it is: random conductive heating, Benard convection, roiling boil. Actually as the temperature gets hotter and hotter, the boiling goes through a few more qualitative changes.
This also happens in the extremely thin layer of atmosphere on earth. It is the beginning of weather patterns.
back to best labs summary contents
Materials: shallow petri dish, some fluid either water with sparkles in it? or a higher viscosity fluid? some way to heat it from below uniformly. A way to heat it from above also, perhaps blow dryer. thermometer, maybe curious lighting techniques?
Method: watch water heat up, heat quickly to boil, seems to be chaos. Now heat more slowly and find temperature at which convection cells form. may have to experiment with depth of water. Now take temperature of bottom surface and air above water. now try the experiment again but this time heating both the bottom and heating the air above, do we get convection cells?
Discussion
If you heat a shallow layer of water in a pan, at a low temperature you get random motions in the water molecules as they carry the heat (molecular motion) from the high temperature bottom of the pan to the low temperature surface of the water. On a macro scale what you begin to see is that the layer of water directly above the pan expands (gets warmer) and thus less dense than the layer above it and rises. This rising layer breaks up into blobs randomly. Of course if blobs are rising, blobs of water at the top must sink because they are more dense (cooler). Already the fact that these homogenous layers break up into blobs is curious math. In fact, i'm not sure we fully understand it (lookup studies of water droplets and splashes, very complex!). The breaking up of the top layer into blobs as they descend, i think is mediated in a complex way by the surface tension of the water at the top. (surface tension is the stuff that makes water creep up the edges of a container of water a millimeter or so, called the meniscus.)
As you raise the temperature of the bottom of the pan relative to the top of the water you get more random motion. at a certain temperature difference, though, these rising and falling blobs eventually arrange themselves (surprise!) into a fairly neat hexagonal array of convection cells. Warm water rises in the center of each cell and falls at the edges. This is called Benard convection (named after the first to study them, Claude Bernard). As we increase the temperature difference even more, eventually the motion becomes random again and the water begins to boil.
Two surprising things about this phenomenon are the pattern and the phase transitions. The pattern is relatively neat, most cells are the same size and mostly the same hexagonal shape. The phase transitions are like the ones we couldn't predict for water, at different stages in heating we get a different distinct story. For water it was ice, water, vapor. For sulfur, it is orthorhombic sulfur, yellow liquid, red viscous liquid, and various stages of vapor. For our shallow pan of water, it is: random conductive heating, Benard convection, roiling boil. Actually as the temperature gets hotter and hotter, the boiling goes through a few more qualitative changes.
This also happens in the extremely thin layer of atmosphere on earth. It is the beginning of weather patterns.
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