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**take N nodes that can be on or off. hook 'em together into a network with various logical gates coming into each one with an average of k inputs from the others. look at the ensemble of all such possible systems.**

ORGANISMS

1) Collect Ant Colonies

Materials:

pocket knife, spade, zip lock baggies, 15ml vials, pooter, magnifying lens, white collecting pan, white sheet or pillow case...

you can find ants anywhere! begin by getting on the ground and looking. you can also find them crawling over rocks, stone walls and tree trunks. where can you find ant colonies? under logs, under stones, under leaves in the forest, sometimes in between the leaves, in acorns, in the roots with the grass. inside rotting logs and branches.

if you find the pale white eggs and larva, you've got a jackpot. collect a bunch and a bunch of the ants with them. if you want to dig further you can look for the queen. then you will have a self perpetuating colony.

there are many approaches. if you think the whole colony is inside an acorn or a twig or a branch, collect the whole thing and put it in a plastic baggy, or container. you can then observe it. if you want to be sure there's a queen in there you've got to bust it open on a big white surface and see who runs out.

even if you collect several dozen workers with a mess of larvae and eggs, you will have PLENTY to observe.

2) Observe Ant Behavior

materials:

15mm vials. paper and tape to make covers for the vials, small piece of sponge, honey, egg, peanut butter... water dropper, more elaborate ant colony housing from texts

keeping your ants happy can become quite a bit of animal husbandry, but fairly simple procedures will yield good results. ants are pretty hardy. mostly make sure they don't DRY OUT, at the same time make sure they don't get moist so that mold grows. give 'em air once in a while. feed them a tiny bit every few days. cover them to keep 'em dark at night. don't let them get too cold. don't let them overheat in the sun or anything.

you can take the paper wrappers off their vials and watch them for a while with a hand lens and take notes. watching during feeding is interesting. see how they react to different foods. you can even feed them live fruit flies, maybe disable them by cooling them off and clipping their wings.

you should be able to observe activities like these:

dig, take care of larvae, take care of queen, move things around find water, sugar, attack fruit flies, lay trails, greet each other, feed each other, eat stuff, bring stuff to larvae, settle down at night, clean each other, clean antennas...

observing a few days a week for two or three weeks should give you plenty of opportunities to see stuff. try to list the activities. try to break 'em up into discrete actions of parts of ants as if you were going to build a robot ant and you need to program in each action. can you find maybe 40 activities? 100s of actions?

3) Cooperative Organization In Social Insect Colonies

Is there a simple setup that I can show cooperative organization: a bunch of ants build a complex structure out of goofy small movements? the queen is NOT in charge.

4) How a Honeybee Colony Decides On a New Nest.

5) Key Out Ants Under Dissection Scope.

ants have LOTS of parts! 14+21+6*6+2*14 +2*9 =100 external parts! wait! plus dozens of hairs, hundreds on the antennae, sensor pits? fine pits and reticulations on the exoskeleton...

The Key to ants of Illinois will work. can add some details from Holldobler and Wilson's key.

6) Key Out 100 Plants In A Local Park

Materials: identification key to flowering plants, trees, winter twigs. a picture identification guide is also useful. jewelers loupe type lens, tweezers, dissecting needle, plant press, notebook, pen and pencil.

the first step in this Endeavour is to learn to see in detail, and learn to use the keys, learn the technique, learn to master the terms for the different features of plants. the best way to do this is to go out with someone and have 'em teach you first hand about 50 different plants that are easy for you to recognize. once you got these down THEN try to key THEM out with the keys, to learn how the keys work and get used to taking the flowers apart and use the hand lens. if you get lost in the key you can always look ahead to the plant you know it is and work through the key backwards.

use the key in conjunction with the picture book too.

discussion: try to key out a few species in the same genus if you can find them. grasses, asters, cinquefoils, goldenrods are good tricky ones to try.

one thing you learn from this experience is just HOW MUCH detail there is in each critter available to use in telling them apart.

7) Insect Diversity

or... collect a bucket of 500 different insects, really see diversity! Point out that there are between 3 to 10 times as many kinds of insects as there are plants in the world.

8) From Transistors To Computers

To begin learning about building complex critters out of parts, lets explore the complex machines already around us.

how do computers work? how do they decode the keyboard and get letter shapes on the screen? how fast? go through the levels of complexity from the digital gates made out of transistors up to digital circuits made of 10s 100s thousands of gates

start with that old Signetics catalog I had when I was a kid. notice how a half a dozen transistors fit together to make a seamlessly working logic gate, already sophisticated behavior. then see how to fit some gates together to make a flip flop, a decoder, a multiplexer, a timer.

go through exercises and fit 'em together to get jobs done.

now watch how to fit those chips together to make arithmetic units, circuits to display numbers on displays.

now see how to fit 'em all together to make a microprocessor, the central processor unit, the ram, the keyboard decoder.

9) Can We Build Ant Robots?

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

10) Program Ant Simulations

So how many logic blocks? We need A LOT, we can't build a robot out of these big clunky parts, the only way we know how to do it today is to use a microprocessor chip and write complicated programs on it. So to program our ant robots remember how many different activities, how many distinct actions we found our ants did as they went about their daily activities? we must write dozens of subroutines to control each action. Then we have to write complicated programs to coordinate those actions and help our ant robots decide when to perform them!

show 'em some sophisticated programs, bot programs.

11) Self Sustaining Ecosystem Of Reproducing Robots?

Well, so far we weren't very successful at making full blown ant robots, certainly not ones a few millimeters long! but lets imagine that we WERE successful at it. Now lets try to create a whole world of ant robots that can keep growing and giving birth to new colonies.

What would they need? They would have to find food! what would the food be like? they would need energy in the form of electricity. where would that come from? i guess we could make some plant like robots to collect solar energy and devise some way for the ants to collect it.

Next thing is that the ant robots and plant robots would wear out eventually so they will have to reproduce. So our ecosystem has to have a bunch of parts scattered about. and the ants would have to know how to build more ants out of themselves out of the parts. ants don't usually eat their own dead colony members so we will have to create scavenger robots that go around collecting dead ants and taking them apart and using their parts to build new scavenger robots. then the ants can go collect the scavengers and take THEM apart and make new ants out of them. The plants too would have to be able to use some of the parts to make new plants.

Next thing to notice is that in our collection outings we found that there were dozens of kinds of ants, HUNDREDS of kinds of plants and insects, not to mention all the worms, birds, mites... and we haven't even looked at the microscopic creatures yet... the point is that each kind of robot will have different parts and we know that in nature the creatures can eat each other and refashion the old parts into new kinds. So:

imagine what kind of sophisticated robots we would have to build that can reshape parts! they would need welders, cutters, sanders, chemical laboratories, they would need to construct new parts from scratch from the soil and rocks because eventually all the PARTS would start wearing out... How could we construct an ENTIRE working ecosystem of all these miniature factories and THEIR parts...

Ok, it's time to see how real creatures on Earth manage this!

12) Ant Anatomy: Dissect Insects

So how ARE ants built? Dissect one under a scope and projector. maybe not an ant! this would be amazing. it's really complicated in there. Also have slides of finer dissections and photomicrographs. each of those joints has its own muscles, fibers everywhere, nerves, sensors... trachea, stinger and acid gland, nerves, sensors, each antenna joint filled with hairs and sensors. learn to count an array of hairs, parts of compound eye facets. find the brain.

see if you can get an ant to move EACH joint, doing some activity.

13) Ant Brains: Photomicrographs

Any vital stains to see how many neurons? get photo micrographs. 100X100X100 of them? and the connections between!

14) Dissect An Automobile, Ants Are MORE Complicated!

It is difficult to discover just how all the parts of an insect actually make that insect work, and in fact scientists have not yet come to a full understanding. but we DO know how cars work. so lets look inside a car and see how all the subsystems come together to make a car and see how each system works how they are put together, how many parts it takes. how many DIFFERENT kinds of materials it takes.

Also note that cars don't have brains! WE act as their brains, so they don't come anywhere CLOSE to the sophistication of a bug!

15) How Are Automobiles Built?

Now the question is: how are automobiles made? They certainly don't make each other, like animals do! Let's visit (virtually?) an automobile factory. Well that's quite a production, but the auto factory doesn't make all the parts, it doesn't chew up 'plant machines' and produces the parts from scratch! other factories do that!

remember we tried to imagine a working ecosystem of robots that could build each other from existing parts. This is our chance to explore how the ecosystem of machines works in the real world. so the next step is to track down the path of each car part and find out what industry it takes to produce it and what parts, materials each of those use, and ... how many different kinds of industrial facilities are required. don't forget all the factories to make the parts of the factories.

Again remember that none of these factories have brains, it's all being coordinated by PEOPLE.

In order to go back to our attempt to make the robot ecology, remember that we've got to add brains/programs to each of our robot factories...

16) So How ARE Ants Built?

Well, do ants go about collecting worn out parts and building each other out of them? remember we found lots of subtle parts inside our insects! not even sure what makes a DISCRETE part in an insect, and how are they put together? we didn't find nuts and bolts!

Ants don't do it this way AT ALL. we know how ants do it. Ants come from EGGS. We can find some ant eggs and dissect them under a microscope. We would NOT find any parts! but if we wait a few days or weeks, and dissected that egg we would see parts! WERE on earth did they come from? then of course we wait longer and the egg turns into a grub. doesn't look like an ant at all, but it does have parts. at this point the other ants feed the grub. but they don't feed it ant parts! they feed it nectar, and chewed up insects. are there parts in the chewed up insects? sort of, but mangled...

very mysterious.

let's try to take a closer look: show stop motion photos of development: cells! A developing ant is a little confusing, so perhaps start off with C. elegans or some such so we can see the distinct cells. what we find is that it all seems to be made of CELLS. the cells are the basic reproducing building blocks, and they move around and respond to each other. They create each other and lay down systems of fibers and pull each other around into shapes and induce each other into becoming different cell types and communicate with each other...

All the while the cells are SOMEHOW absorbing food from the yolk of the egg to make all themselves and the fibers... but there are NO cells in the yolk, no parts that we can see! How do they do it? what kind of mysterious creatures are these cells? Maybe they are the ultimate robots that we must learn to build?

17) Watching Flower Or Mushroom Development

Any way to watch? grow mushrooms? dissect flower heads in various stages and use vital stain!

18) Back To Brains. How To Imagine 20Billion Neurons.

start out with 3 blocks of tofu. begin by slicing one into 10 slices. now turn it and make 10 slices again so you got 100 slivers, now turn it sideways and 10 more slices and you got 1000 little cubes. spread them out, make 'em into groups, patterns... get to know a thousand.

if you want a permanent collection of a 1000 blocks, can you do it with a block of wood and a jigsaw? would need fine grain wood, and start out with maybe a 6X6" block of wood? cutting the last few planes would be hard, use a 6X6X12" block and only slice off half of it. now clamp the slices together and make the cross cuts... the slivers will fly around... maybe a 12X12" piece? now how to clamp the 100 slivers to make the last 10 cuts? how to clamp them? maybe it can be done carefully? the last few cuts will have to be done piecemeal?

this brings to mind a puzzle: could you get a gel, make it into a block, inject some dye into it to make patterns, let the gel harden and then cut it into 1000 blocks? then can you put it back together?

a more biological way to make a thousand: fold a piece of paper, fold it again, fold it again... after 5 or 6 folds its too hard to do. that only gets you to 32 or 64 layers.

lets cut instead: nah by the time you get to the 64 stage you got to cut each stack separately... so you still end up making zillions of cuts...

what about a long string? if we want to end up with 1024 1cm pieces, then we'll need 1000cm or 10meters or 30 feet of string ok. get two people unroll it and pull it out, fold it and cut. keep folding and cutting after 5 cuts you got a bundle of 32 strings 1foot long, ok measure it and cut them in half. now 64strings 6" long, that's starting to get difficult! after two more cuts it'll be 256 strings about an inch and a half long that might not be too hard, 512 tiny 2cm pieces? that'll take some care... ok, start out with 64feet of string! this might work! now if you tie die the original roll of string all blotchy different colors, by the time you got it all cut up into a writing mass of 1024 different 2cm strings, they will be all different colors, it might look interesting. and a more permanent collection than the blocks of tofu.

but you can see that if you could get a hold of some living cells and let THEM do the cutting on their own, you can have the process automated by reproducing automata! that would be nice to watch!

maybe one way to find this is to look at trees outside. find one with a branch that has branched 10 times, once each year: 2, then 4 then 8... if over those 10 years none of the branches has died, then at the ends of the branch, there should be 1024 tips! this can give some idea...

back to the blocks of tofu, remember we only got to 1000!

so cut up the other 2 blocks the same way. now go outside and find a really big building on a street corner. begin with the first block of tofu. start lining up the little blocks along one wall of the building from the corner, it'll take about 15 feet to line up all 1000. picturing it? now go back to the corner and line up the next 1000 along the other side of the building.

now the hard part. back to the corner and stack up the little blocks of the third 1000 UP from the tip of the corner. That goes UP 15feet. see them?

now IMAGINE. fill in one side of the building with a million each little tofu blocks. that is a thousand rows high of a thousand tofus long. do you see the face of the building filled with a grid of a 1000X1000 little tofu blocks? Now fill in the other side. now more imagine: imagine the whole 15foot cube of building as filled solid with 1000 of those grids. 1 billion blocks of tofu! now 20 such buildings in the neighborhood.

perhaps an art project can be tried. if you can find such a corner and paint it smooth white. if you can get a couple thousand tiles 1X1cm. then you can mark off, or tile off the thousand on each bottom, mark off the thousand up the corner, and BEGIN to mark the grids at the bottom corner and put in the tiles, make 'em different colors. every few weeks people could add more tiles when they get a chance? how much could we get done to help us imagine a billion?

anyway once you spend some time with imagining these 20 buildings of billion neurons each, you can next imagine bringing over a TRUCKLOAD of thread, and start connecting the neurons to each other across the buildings. remember many neurons are connected to THOUSANDS of others! again to imagine a dendrite splitting up into a thousand branches, so go back and find your tree branch with the 10 branchings.... that's what your dendrite will look like, and 1000 other tofu blocklets will send threads to it...

19) What Is A 20Billion Neuron Brain Capable Of?

Later we will watch single celled critters called ciliates. We will realize how complicated they are: structurally and behaviorally. Neurons are about as complicated as ciliates! One of the purposes of this whole set of labs is to gain intuitions of what 20billion such creatures can create when they are all connected to each other.

20 How Complex Is Language?

Try this activity. find a good dictionary and pick a page at random. count how many of the words you know the meaning of. If a word has more than one meaning and you know both meanings count them both. this is somewhat subjective, and it's a little tricky to decide how many distinct meanings to choose for a word (and THAT is interesting, the question is: is language discrete or continuous?), but let's see what happens. anyway, write down the total and pick another page at random. do the same thing. write that total down. pick 30 pages at random this way. now take the average of all your totals. now multiply this average number of words you know per page by how many pages in the dictionary. that's how many distinct words/meanings you know. how many did you get? mine came to about 90,000.

21) How Many Connections Between Words?

Here's another experiment: imagine writing them all down on a giant piece of paper. now start joining words that are related. what kind of tangled web would you get? how MANY connections do you think there would be? what does that number mean?

how about this: pick any two words at random, say sun and horizon. can you think of how they go together? how about arm-chair and cucumber? i can't. anyway how many pairs of those 20,000 words you know are there? (20,000X20,000) how many of them can you figure out a connection for?

now try it for three words at random: pig, roof, zombie: nah. book, stable, star, almost. cucumber watermelon sizzle yeah I can think of one for that. how many possible connections here? (some fraction of 20,000^3 )

what are we measuring here? can you make up an infinite number of sentences? probably. but some of us can make more than others! so what are we measuring?

LIVING CELLS

22) Look At Pond Water.

So, we found out that what makes living creatures interesting, what builds them, what makes brains complicated, are CELLS. It's time to find out what kind of creatures these are! In fact cells are to a certain extent, independent organisms. Let's watch some. Some cells make up a whole animal all by themselves. here are some free living cells. watch Stentor, watch rotifers =1000 cells. watch euglena, a small cell. they can do as many things as ants can!! almost. cells are free living amazing beings.

make a list of activities that cells can do. also 40 or 50 different activities... What ARE these critters. So our next task is to imagine if we can build MICROSCOPIC robots that can do what these free living cells can do, that can do what the cells inside plants and animals can do to come together and make large critters.

and how will our robots reproduce? these cells don't seem to have parts! We need to look deeper. We will need a bigger microscope!

be careful to explore the range of magnifications, convenient hand lens to complex microscope.

23) Watch Stentor

Record behavior!

24) Watch Euglena, Bacteria

Record behavior and compare.

25) What Are The Building Blocks For Cells?

Lets grow some Oscillatoria. We'll collect some Oscillatoria from a pond. watch it. pretty sophisticated algae! the strands can slide against each other and arrange themselves into sheets to catch the sun! of course they reproduce. notice that there are two different kinds of cells in the strands.

Here are some electron micrographs: pretty complicated inside.

now we'll grow them from scratch. We'll boil a jar to kill all the critters in it wash it out. Next we'll filter some water out, to get all the critters and gunk and parts out of it. boil it to kill any other critters we missed. look at it under a microscope. can't find anything in there? ok, we'll put it in the jar, put in a few strands of Oscillatoria, leave some air, and put it in the sun.

what happens? IT GROWS! what on earth is it building all those parts out of? where does the GREEN come from? It's time for our next level of discovery: CHEMISTRY!

Maybe there is lots of stuff still in the water! we can try to distill the water and use that. does it grow as well?

we can try to grow it in a plastic vial instead of glass, does it grow as well in that?

after we grow a bunch of Oscillatoria, we can dry it out, then burn it. turns into smoke. what's THAT? here, try burning some wood, how does THAT turn to smoke, and moisture, and ash. Just what IS stuff that it can go through these TRANSFORMATIONS? We have to imagine a whole new level of parts and how they are put together. It certainly is looking like living creatures take each other apart and can even use water, glass and air into VERY SMALL parts to make themselves! what are these parts?

26) Paper Chromatography

Lets grind up a plant and try to separate it into parts using paper chromatography.

27) Microstructure Of Cells

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?

28) Metabolic Wall Chart!

29) Which Has More Moving Parts: A Bacteria Or New York City?

For people in a big city like New York. sit across from a large apartment building in the city. start counting how many bricks it takes to get from the left side of one window to the next. count how many windows across the building there are. multiply to find how many bricks are all the way across the building. lets say the building is square and lets be generous and pretend the building is entirely filled with bricks. so if we take this number, say it is 250, lets multiply it by itself to get how many bricks there are laid flat in one layer all the way through the building. now count how many bricks from the bottom of one window to the bottom of the next window. multiply that by how many floors. that's how many layers of bricks there would be if the building were entirely filled with bricks. multiply this number of layers by the number of bricks in a layer. that's A LOT of bricks!

Now how many buildings are there in that block? you can multiply again. walk up the street or avenue and count. maybe 4X10? so multiply that by how many bricks per building!

Now how many blocks in your city? multiply again! how many streets long by how many streets wide is it? you may need to get a full sized map and count, approximate! for NYC, I figured 200 streets from the bottom to the top times 10 avenues wide gives me 2000 blocks in Manhattan then I multiply by 5 for all 5 boroughs of my city.

so how many bricks do you get? you may want to use scientific notation to write it down.

here's the fun part. imagine ALL those bricks in your minds eye. now, how many molecules are there swirling around in an E. coli bacteria? how do we count that? from our chemistry section we learned that one mole of molecules contains 6X10^23 molecules. Let's start with how large a bacteria is. from our microscope explorations we figured it was about one micron X micron X 3microns long. that's 3cubic micrometers. lets convert to cubic cm! multiply by 1cubic mm per 10^3x10^3x10^3 micrometers =10^-9 mm^3 x 1cubic cm per 10x10x10 mm = 10^-12cm^3 x 1mol/18cubic cm H2O *5/100= 5x10x 6x10^23 molecules/mol =

[now the question is: do i just suggest the methods or do i also show the worked out answers:

there are more atoms in the simplest bacteria than there are bricks in NYC. there are more enzymes huffing and puffing doing their work and taking part in construction projects in that bacteria than there people in NYC (8million) there are more ribosomes in that bacteria than there are buildings in NYC churning out new enzymes every second.

a bacteria is busier place than all of NYC!

there is a mole of atoms in my finger approximately:

10,000,000,000,000,000,000,000 of them. think of each group of three zeros as another level of complexity. the reality of Avogadro's number is that it takes that many levels of complexity to grow my finger (and the rest of me) and repair my finger when it is cut, and to maintain it and make it act.

Avogadro's number is a wild part of our knowledge of reality that has NOT yet entered popular consciousness.

let's see, E. coli: let's say 3cubic micrometer. so 6*10^23 molecules/18cm^3 H2O is

10^23 molecules/3cm^3

10^23 /3cm^3

10^23/3000 mm^3

10^20/3mm^3

10^20/3*10^9 micron^3

10^11molecules/micron^3

that's 100billion.

now a million ribosomes*60proteins*1000 aminos*10H2O= that's 60billion right there. must be a high estimate.

if a protein is 12,000 H2O's into 10^11 that could be 10 million proteins/enzymes

10bricks laid across a window, 20 high that's 200 * 10 *10 windows that's 20,000 *100 deep that's 2million bricks per building if it were solid. times 5 * 10 buildings per block is 100million *200 *10 blocks per Manhattan is 200billion * 5 boroughs that's 1000 billion. oops more bricks than molecules. but if you don't imagine buildings to be solid.. well anyway the numbers are comparable

30) Visualize All The Detail In One E. Coli

Can we make a wall sized chart of all the cityfull of details in an E. coli? or what would it take to build a barn sized model with moving parts that we can play with?

31) Distributed Brownian Motion Machinery: Clathrin Coated Pits

Learn the particular kind of Brownian motion machinery that cells exploit to explore possibilities and make patterns and solve problems. show the mechanism of clathrin coated pits that cells use to ingest food packets.

some forms of endocytosis in cells is done as follows: receptor molecules randomly swim around on the cell membrane. when one bumps into the thing it's supposed to sense outside of the cell, it attaches, and rearranges it's butt sticking into the cell. clathrin molecules swim around just beneath the cell membrane inside. when one bumps into an activated receptor's butt it holds on with it's center while it holds out its 3 arms which are arranged symmetrically and bent INTO the membrane a little bit. well eventually another receptor swims by and bumps into the thing that's got to be brought into the cell, it activates and another clathrin attaches. the clathrins hold each other's arms. each molecule only "knows" about its neighbors. as more of this happens, aided by Brownian motion of all molecules involved, a cage is formed around a piece of cell membrane enclosing the stuff to be brought in and eventually pinches off. very clever. look:

Receptor-mediated endocytosis by clathrin-coated vesicles

By Dr Tony Jackson *

A review of how research into the components of the clathrin coat has provided insights into the operation of these molecular machines

http://www.abcam.com/index.html?pageconfig=resource&rid=10236&pid=14

mechanism of forming clathrin coated vesicles:

http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=1225879&blobtype=pdf

The clathrin machine is not like a computer program at all. the processing is totally distributed. furthermore I suspect we could isolate the molecules involved and get them to work without the whole live cell shebang. have to probably supply the proteins ready phosphorylated though.

why not call it a machine? what's your definition of a machine? something with gears, pulleys and integrated circuits? I think of machines as things you can understand by seeing how the separate parts interact.

32) The DNA Is NOT The Brain!

The whole cell is like this, rampantly parallel. The DNA is not a miniature dictator, ruling the cell, just as the queen bee does not rule the hive. It's a bulletin board that all the proteins use for keeping track of things, no one is in charge.

PHYSICAL/CHEMICAL DYNAMICAL SYSTEMS FAR FROM EQUILIBRIUM: difference in temperature leads to disorder in the total system by way of energy flow which however can lead to INCREASE in order in a subsystem

33) Build A Steam Engine

How does a steam engine work, how hard is it to make one?

34) Benard Convection

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.

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!

40) Dynamic Processes In Mineral Formation

Are there dynamic processes in mineral formation like convection? How did that piece of Goethite at the American Museum of Natural History form?

41) After 4.5Billion Years Of Mixing, The Earth Has NOT Blended To Homogeneity

Basic question though is why as the Earth churns round and round 4billion years doesn't everything blend into to homogenous grey clay? why are heterogeneities formed at every level?

42) Belousov-Zhabotinski Reaction

43) Deep Sea Manganese Nodules

Concentration of metals at the interface at the ocean bottom due to redox chemistry mediated by organisms

44) Play With A Candle Flame

45) Suns Have Complex Dynamic Organization

Suns are complicated self organizing critters with life cycles

47) Simplest Organic Redox Cycle

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?

MATHEMATICAL DYNAMICAL SYSTEMS:

CELLULAR AUTOMATA

48) John Horton Conway's Game Of Life: http://blackskimmer.blogspot.com/2007/07/john-horton-conways-game-of-life-here.html

49) Game of Go

50) Cellular Automata With NON Local Rules.

I want to relate this to how quantum mechanics gives us molecular orbitals like aromatic molecules.

51) Cellular Automata Robust Under Random Fluctuations

Find cell automata who's complex patterns are robust under random fluctuations. unlike Conway life, like chemistry

52) Cellular Automata With Random Input

53) Explore The Space Of 1 Dimensional Cellular Automata

54) Kauffman's NK Boolean Networks

ORGANISMS

1) Collect Ant Colonies

Materials:

pocket knife, spade, zip lock baggies, 15ml vials, pooter, magnifying lens, white collecting pan, white sheet or pillow case...

you can find ants anywhere! begin by getting on the ground and looking. you can also find them crawling over rocks, stone walls and tree trunks. where can you find ant colonies? under logs, under stones, under leaves in the forest, sometimes in between the leaves, in acorns, in the roots with the grass. inside rotting logs and branches.

if you find the pale white eggs and larva, you've got a jackpot. collect a bunch and a bunch of the ants with them. if you want to dig further you can look for the queen. then you will have a self perpetuating colony.

there are many approaches. if you think the whole colony is inside an acorn or a twig or a branch, collect the whole thing and put it in a plastic baggy, or container. you can then observe it. if you want to be sure there's a queen in there you've got to bust it open on a big white surface and see who runs out.

even if you collect several dozen workers with a mess of larvae and eggs, you will have PLENTY to observe.

2) Observe Ant Behavior

materials:

15mm vials. paper and tape to make covers for the vials, small piece of sponge, honey, egg, peanut butter... water dropper, more elaborate ant colony housing from texts

keeping your ants happy can become quite a bit of animal husbandry, but fairly simple procedures will yield good results. ants are pretty hardy. mostly make sure they don't DRY OUT, at the same time make sure they don't get moist so that mold grows. give 'em air once in a while. feed them a tiny bit every few days. cover them to keep 'em dark at night. don't let them get too cold. don't let them overheat in the sun or anything.

you can take the paper wrappers off their vials and watch them for a while with a hand lens and take notes. watching during feeding is interesting. see how they react to different foods. you can even feed them live fruit flies, maybe disable them by cooling them off and clipping their wings.

you should be able to observe activities like these:

dig, take care of larvae, take care of queen, move things around find water, sugar, attack fruit flies, lay trails, greet each other, feed each other, eat stuff, bring stuff to larvae, settle down at night, clean each other, clean antennas...

observing a few days a week for two or three weeks should give you plenty of opportunities to see stuff. try to list the activities. try to break 'em up into discrete actions of parts of ants as if you were going to build a robot ant and you need to program in each action. can you find maybe 40 activities? 100s of actions?

3) Cooperative Organization In Social Insect Colonies

Is there a simple setup that I can show cooperative organization: a bunch of ants build a complex structure out of goofy small movements? the queen is NOT in charge.

4) How a Honeybee Colony Decides On a New Nest.

5) Key Out Ants Under Dissection Scope.

ants have LOTS of parts! 14+21+6*6+2*14 +2*9 =100 external parts! wait! plus dozens of hairs, hundreds on the antennae, sensor pits? fine pits and reticulations on the exoskeleton...

The Key to ants of Illinois will work. can add some details from Holldobler and Wilson's key.

6) Key Out 100 Plants In A Local Park

Materials: identification key to flowering plants, trees, winter twigs. a picture identification guide is also useful. jewelers loupe type lens, tweezers, dissecting needle, plant press, notebook, pen and pencil.

the first step in this Endeavour is to learn to see in detail, and learn to use the keys, learn the technique, learn to master the terms for the different features of plants. the best way to do this is to go out with someone and have 'em teach you first hand about 50 different plants that are easy for you to recognize. once you got these down THEN try to key THEM out with the keys, to learn how the keys work and get used to taking the flowers apart and use the hand lens. if you get lost in the key you can always look ahead to the plant you know it is and work through the key backwards.

use the key in conjunction with the picture book too.

discussion: try to key out a few species in the same genus if you can find them. grasses, asters, cinquefoils, goldenrods are good tricky ones to try.

one thing you learn from this experience is just HOW MUCH detail there is in each critter available to use in telling them apart.

7) Insect Diversity

or... collect a bucket of 500 different insects, really see diversity! Point out that there are between 3 to 10 times as many kinds of insects as there are plants in the world.

8) From Transistors To Computers

To begin learning about building complex critters out of parts, lets explore the complex machines already around us.

how do computers work? how do they decode the keyboard and get letter shapes on the screen? how fast? go through the levels of complexity from the digital gates made out of transistors up to digital circuits made of 10s 100s thousands of gates

start with that old Signetics catalog I had when I was a kid. notice how a half a dozen transistors fit together to make a seamlessly working logic gate, already sophisticated behavior. then see how to fit some gates together to make a flip flop, a decoder, a multiplexer, a timer.

go through exercises and fit 'em together to get jobs done.

now watch how to fit those chips together to make arithmetic units, circuits to display numbers on displays.

now see how to fit 'em all together to make a microprocessor, the central processor unit, the ram, the keyboard decoder.

9) Can We Build Ant Robots?

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

10) Program Ant Simulations

So how many logic blocks? We need A LOT, we can't build a robot out of these big clunky parts, the only way we know how to do it today is to use a microprocessor chip and write complicated programs on it. So to program our ant robots remember how many different activities, how many distinct actions we found our ants did as they went about their daily activities? we must write dozens of subroutines to control each action. Then we have to write complicated programs to coordinate those actions and help our ant robots decide when to perform them!

show 'em some sophisticated programs, bot programs.

11) Self Sustaining Ecosystem Of Reproducing Robots?

Well, so far we weren't very successful at making full blown ant robots, certainly not ones a few millimeters long! but lets imagine that we WERE successful at it. Now lets try to create a whole world of ant robots that can keep growing and giving birth to new colonies.

What would they need? They would have to find food! what would the food be like? they would need energy in the form of electricity. where would that come from? i guess we could make some plant like robots to collect solar energy and devise some way for the ants to collect it.

Next thing is that the ant robots and plant robots would wear out eventually so they will have to reproduce. So our ecosystem has to have a bunch of parts scattered about. and the ants would have to know how to build more ants out of themselves out of the parts. ants don't usually eat their own dead colony members so we will have to create scavenger robots that go around collecting dead ants and taking them apart and using their parts to build new scavenger robots. then the ants can go collect the scavengers and take THEM apart and make new ants out of them. The plants too would have to be able to use some of the parts to make new plants.

Next thing to notice is that in our collection outings we found that there were dozens of kinds of ants, HUNDREDS of kinds of plants and insects, not to mention all the worms, birds, mites... and we haven't even looked at the microscopic creatures yet... the point is that each kind of robot will have different parts and we know that in nature the creatures can eat each other and refashion the old parts into new kinds. So:

imagine what kind of sophisticated robots we would have to build that can reshape parts! they would need welders, cutters, sanders, chemical laboratories, they would need to construct new parts from scratch from the soil and rocks because eventually all the PARTS would start wearing out... How could we construct an ENTIRE working ecosystem of all these miniature factories and THEIR parts...

Ok, it's time to see how real creatures on Earth manage this!

12) Ant Anatomy: Dissect Insects

So how ARE ants built? Dissect one under a scope and projector. maybe not an ant! this would be amazing. it's really complicated in there. Also have slides of finer dissections and photomicrographs. each of those joints has its own muscles, fibers everywhere, nerves, sensors... trachea, stinger and acid gland, nerves, sensors, each antenna joint filled with hairs and sensors. learn to count an array of hairs, parts of compound eye facets. find the brain.

see if you can get an ant to move EACH joint, doing some activity.

13) Ant Brains: Photomicrographs

Any vital stains to see how many neurons? get photo micrographs. 100X100X100 of them? and the connections between!

14) Dissect An Automobile, Ants Are MORE Complicated!

It is difficult to discover just how all the parts of an insect actually make that insect work, and in fact scientists have not yet come to a full understanding. but we DO know how cars work. so lets look inside a car and see how all the subsystems come together to make a car and see how each system works how they are put together, how many parts it takes. how many DIFFERENT kinds of materials it takes.

Also note that cars don't have brains! WE act as their brains, so they don't come anywhere CLOSE to the sophistication of a bug!

15) How Are Automobiles Built?

Now the question is: how are automobiles made? They certainly don't make each other, like animals do! Let's visit (virtually?) an automobile factory. Well that's quite a production, but the auto factory doesn't make all the parts, it doesn't chew up 'plant machines' and produces the parts from scratch! other factories do that!

remember we tried to imagine a working ecosystem of robots that could build each other from existing parts. This is our chance to explore how the ecosystem of machines works in the real world. so the next step is to track down the path of each car part and find out what industry it takes to produce it and what parts, materials each of those use, and ... how many different kinds of industrial facilities are required. don't forget all the factories to make the parts of the factories.

Again remember that none of these factories have brains, it's all being coordinated by PEOPLE.

In order to go back to our attempt to make the robot ecology, remember that we've got to add brains/programs to each of our robot factories...

16) So How ARE Ants Built?

Well, do ants go about collecting worn out parts and building each other out of them? remember we found lots of subtle parts inside our insects! not even sure what makes a DISCRETE part in an insect, and how are they put together? we didn't find nuts and bolts!

Ants don't do it this way AT ALL. we know how ants do it. Ants come from EGGS. We can find some ant eggs and dissect them under a microscope. We would NOT find any parts! but if we wait a few days or weeks, and dissected that egg we would see parts! WERE on earth did they come from? then of course we wait longer and the egg turns into a grub. doesn't look like an ant at all, but it does have parts. at this point the other ants feed the grub. but they don't feed it ant parts! they feed it nectar, and chewed up insects. are there parts in the chewed up insects? sort of, but mangled...

very mysterious.

let's try to take a closer look: show stop motion photos of development: cells! A developing ant is a little confusing, so perhaps start off with C. elegans or some such so we can see the distinct cells. what we find is that it all seems to be made of CELLS. the cells are the basic reproducing building blocks, and they move around and respond to each other. They create each other and lay down systems of fibers and pull each other around into shapes and induce each other into becoming different cell types and communicate with each other...

All the while the cells are SOMEHOW absorbing food from the yolk of the egg to make all themselves and the fibers... but there are NO cells in the yolk, no parts that we can see! How do they do it? what kind of mysterious creatures are these cells? Maybe they are the ultimate robots that we must learn to build?

17) Watching Flower Or Mushroom Development

Any way to watch? grow mushrooms? dissect flower heads in various stages and use vital stain!

18) Back To Brains. How To Imagine 20Billion Neurons.

start out with 3 blocks of tofu. begin by slicing one into 10 slices. now turn it and make 10 slices again so you got 100 slivers, now turn it sideways and 10 more slices and you got 1000 little cubes. spread them out, make 'em into groups, patterns... get to know a thousand.

if you want a permanent collection of a 1000 blocks, can you do it with a block of wood and a jigsaw? would need fine grain wood, and start out with maybe a 6X6" block of wood? cutting the last few planes would be hard, use a 6X6X12" block and only slice off half of it. now clamp the slices together and make the cross cuts... the slivers will fly around... maybe a 12X12" piece? now how to clamp the 100 slivers to make the last 10 cuts? how to clamp them? maybe it can be done carefully? the last few cuts will have to be done piecemeal?

this brings to mind a puzzle: could you get a gel, make it into a block, inject some dye into it to make patterns, let the gel harden and then cut it into 1000 blocks? then can you put it back together?

a more biological way to make a thousand: fold a piece of paper, fold it again, fold it again... after 5 or 6 folds its too hard to do. that only gets you to 32 or 64 layers.

lets cut instead: nah by the time you get to the 64 stage you got to cut each stack separately... so you still end up making zillions of cuts...

what about a long string? if we want to end up with 1024 1cm pieces, then we'll need 1000cm or 10meters or 30 feet of string ok. get two people unroll it and pull it out, fold it and cut. keep folding and cutting after 5 cuts you got a bundle of 32 strings 1foot long, ok measure it and cut them in half. now 64strings 6" long, that's starting to get difficult! after two more cuts it'll be 256 strings about an inch and a half long that might not be too hard, 512 tiny 2cm pieces? that'll take some care... ok, start out with 64feet of string! this might work! now if you tie die the original roll of string all blotchy different colors, by the time you got it all cut up into a writing mass of 1024 different 2cm strings, they will be all different colors, it might look interesting. and a more permanent collection than the blocks of tofu.

but you can see that if you could get a hold of some living cells and let THEM do the cutting on their own, you can have the process automated by reproducing automata! that would be nice to watch!

maybe one way to find this is to look at trees outside. find one with a branch that has branched 10 times, once each year: 2, then 4 then 8... if over those 10 years none of the branches has died, then at the ends of the branch, there should be 1024 tips! this can give some idea...

back to the blocks of tofu, remember we only got to 1000!

so cut up the other 2 blocks the same way. now go outside and find a really big building on a street corner. begin with the first block of tofu. start lining up the little blocks along one wall of the building from the corner, it'll take about 15 feet to line up all 1000. picturing it? now go back to the corner and line up the next 1000 along the other side of the building.

now the hard part. back to the corner and stack up the little blocks of the third 1000 UP from the tip of the corner. That goes UP 15feet. see them?

now IMAGINE. fill in one side of the building with a million each little tofu blocks. that is a thousand rows high of a thousand tofus long. do you see the face of the building filled with a grid of a 1000X1000 little tofu blocks? Now fill in the other side. now more imagine: imagine the whole 15foot cube of building as filled solid with 1000 of those grids. 1 billion blocks of tofu! now 20 such buildings in the neighborhood.

perhaps an art project can be tried. if you can find such a corner and paint it smooth white. if you can get a couple thousand tiles 1X1cm. then you can mark off, or tile off the thousand on each bottom, mark off the thousand up the corner, and BEGIN to mark the grids at the bottom corner and put in the tiles, make 'em different colors. every few weeks people could add more tiles when they get a chance? how much could we get done to help us imagine a billion?

anyway once you spend some time with imagining these 20 buildings of billion neurons each, you can next imagine bringing over a TRUCKLOAD of thread, and start connecting the neurons to each other across the buildings. remember many neurons are connected to THOUSANDS of others! again to imagine a dendrite splitting up into a thousand branches, so go back and find your tree branch with the 10 branchings.... that's what your dendrite will look like, and 1000 other tofu blocklets will send threads to it...

19) What Is A 20Billion Neuron Brain Capable Of?

Later we will watch single celled critters called ciliates. We will realize how complicated they are: structurally and behaviorally. Neurons are about as complicated as ciliates! One of the purposes of this whole set of labs is to gain intuitions of what 20billion such creatures can create when they are all connected to each other.

20 How Complex Is Language?

Try this activity. find a good dictionary and pick a page at random. count how many of the words you know the meaning of. If a word has more than one meaning and you know both meanings count them both. this is somewhat subjective, and it's a little tricky to decide how many distinct meanings to choose for a word (and THAT is interesting, the question is: is language discrete or continuous?), but let's see what happens. anyway, write down the total and pick another page at random. do the same thing. write that total down. pick 30 pages at random this way. now take the average of all your totals. now multiply this average number of words you know per page by how many pages in the dictionary. that's how many distinct words/meanings you know. how many did you get? mine came to about 90,000.

21) How Many Connections Between Words?

Here's another experiment: imagine writing them all down on a giant piece of paper. now start joining words that are related. what kind of tangled web would you get? how MANY connections do you think there would be? what does that number mean?

how about this: pick any two words at random, say sun and horizon. can you think of how they go together? how about arm-chair and cucumber? i can't. anyway how many pairs of those 20,000 words you know are there? (20,000X20,000) how many of them can you figure out a connection for?

now try it for three words at random: pig, roof, zombie: nah. book, stable, star, almost. cucumber watermelon sizzle yeah I can think of one for that. how many possible connections here? (some fraction of 20,000^3 )

what are we measuring here? can you make up an infinite number of sentences? probably. but some of us can make more than others! so what are we measuring?

LIVING CELLS

22) Look At Pond Water.

So, we found out that what makes living creatures interesting, what builds them, what makes brains complicated, are CELLS. It's time to find out what kind of creatures these are! In fact cells are to a certain extent, independent organisms. Let's watch some. Some cells make up a whole animal all by themselves. here are some free living cells. watch Stentor, watch rotifers =1000 cells. watch euglena, a small cell. they can do as many things as ants can!! almost. cells are free living amazing beings.

make a list of activities that cells can do. also 40 or 50 different activities... What ARE these critters. So our next task is to imagine if we can build MICROSCOPIC robots that can do what these free living cells can do, that can do what the cells inside plants and animals can do to come together and make large critters.

and how will our robots reproduce? these cells don't seem to have parts! We need to look deeper. We will need a bigger microscope!

be careful to explore the range of magnifications, convenient hand lens to complex microscope.

23) Watch Stentor

Record behavior!

24) Watch Euglena, Bacteria

Record behavior and compare.

25) What Are The Building Blocks For Cells?

Lets grow some Oscillatoria. We'll collect some Oscillatoria from a pond. watch it. pretty sophisticated algae! the strands can slide against each other and arrange themselves into sheets to catch the sun! of course they reproduce. notice that there are two different kinds of cells in the strands.

Here are some electron micrographs: pretty complicated inside.

now we'll grow them from scratch. We'll boil a jar to kill all the critters in it wash it out. Next we'll filter some water out, to get all the critters and gunk and parts out of it. boil it to kill any other critters we missed. look at it under a microscope. can't find anything in there? ok, we'll put it in the jar, put in a few strands of Oscillatoria, leave some air, and put it in the sun.

what happens? IT GROWS! what on earth is it building all those parts out of? where does the GREEN come from? It's time for our next level of discovery: CHEMISTRY!

Maybe there is lots of stuff still in the water! we can try to distill the water and use that. does it grow as well?

we can try to grow it in a plastic vial instead of glass, does it grow as well in that?

after we grow a bunch of Oscillatoria, we can dry it out, then burn it. turns into smoke. what's THAT? here, try burning some wood, how does THAT turn to smoke, and moisture, and ash. Just what IS stuff that it can go through these TRANSFORMATIONS? We have to imagine a whole new level of parts and how they are put together. It certainly is looking like living creatures take each other apart and can even use water, glass and air into VERY SMALL parts to make themselves! what are these parts?

26) Paper Chromatography

Lets grind up a plant and try to separate it into parts using paper chromatography.

27) Microstructure Of Cells

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?

28) Metabolic Wall Chart!

29) Which Has More Moving Parts: A Bacteria Or New York City?

For people in a big city like New York. sit across from a large apartment building in the city. start counting how many bricks it takes to get from the left side of one window to the next. count how many windows across the building there are. multiply to find how many bricks are all the way across the building. lets say the building is square and lets be generous and pretend the building is entirely filled with bricks. so if we take this number, say it is 250, lets multiply it by itself to get how many bricks there are laid flat in one layer all the way through the building. now count how many bricks from the bottom of one window to the bottom of the next window. multiply that by how many floors. that's how many layers of bricks there would be if the building were entirely filled with bricks. multiply this number of layers by the number of bricks in a layer. that's A LOT of bricks!

Now how many buildings are there in that block? you can multiply again. walk up the street or avenue and count. maybe 4X10? so multiply that by how many bricks per building!

Now how many blocks in your city? multiply again! how many streets long by how many streets wide is it? you may need to get a full sized map and count, approximate! for NYC, I figured 200 streets from the bottom to the top times 10 avenues wide gives me 2000 blocks in Manhattan then I multiply by 5 for all 5 boroughs of my city.

so how many bricks do you get? you may want to use scientific notation to write it down.

here's the fun part. imagine ALL those bricks in your minds eye. now, how many molecules are there swirling around in an E. coli bacteria? how do we count that? from our chemistry section we learned that one mole of molecules contains 6X10^23 molecules. Let's start with how large a bacteria is. from our microscope explorations we figured it was about one micron X micron X 3microns long. that's 3cubic micrometers. lets convert to cubic cm! multiply by 1cubic mm per 10^3x10^3x10^3 micrometers =10^-9 mm^3 x 1cubic cm per 10x10x10 mm = 10^-12cm^3 x 1mol/18cubic cm H2O *5/100= 5x10x 6x10^23 molecules/mol =

[now the question is: do i just suggest the methods or do i also show the worked out answers:

there are more atoms in the simplest bacteria than there are bricks in NYC. there are more enzymes huffing and puffing doing their work and taking part in construction projects in that bacteria than there people in NYC (8million) there are more ribosomes in that bacteria than there are buildings in NYC churning out new enzymes every second.

a bacteria is busier place than all of NYC!

there is a mole of atoms in my finger approximately:

10,000,000,000,000,000,000,000 of them. think of each group of three zeros as another level of complexity. the reality of Avogadro's number is that it takes that many levels of complexity to grow my finger (and the rest of me) and repair my finger when it is cut, and to maintain it and make it act.

Avogadro's number is a wild part of our knowledge of reality that has NOT yet entered popular consciousness.

let's see, E. coli: let's say 3cubic micrometer. so 6*10^23 molecules/18cm^3 H2O is

10^23 molecules/3cm^3

10^23 /3cm^3

10^23/3000 mm^3

10^20/3mm^3

10^20/3*10^9 micron^3

10^11molecules/micron^3

that's 100billion.

now a million ribosomes*60proteins*1000 aminos*10H2O= that's 60billion right there. must be a high estimate.

if a protein is 12,000 H2O's into 10^11 that could be 10 million proteins/enzymes

10bricks laid across a window, 20 high that's 200 * 10 *10 windows that's 20,000 *100 deep that's 2million bricks per building if it were solid. times 5 * 10 buildings per block is 100million *200 *10 blocks per Manhattan is 200billion * 5 boroughs that's 1000 billion. oops more bricks than molecules. but if you don't imagine buildings to be solid.. well anyway the numbers are comparable

30) Visualize All The Detail In One E. Coli

Can we make a wall sized chart of all the cityfull of details in an E. coli? or what would it take to build a barn sized model with moving parts that we can play with?

31) Distributed Brownian Motion Machinery: Clathrin Coated Pits

Learn the particular kind of Brownian motion machinery that cells exploit to explore possibilities and make patterns and solve problems. show the mechanism of clathrin coated pits that cells use to ingest food packets.

some forms of endocytosis in cells is done as follows: receptor molecules randomly swim around on the cell membrane. when one bumps into the thing it's supposed to sense outside of the cell, it attaches, and rearranges it's butt sticking into the cell. clathrin molecules swim around just beneath the cell membrane inside. when one bumps into an activated receptor's butt it holds on with it's center while it holds out its 3 arms which are arranged symmetrically and bent INTO the membrane a little bit. well eventually another receptor swims by and bumps into the thing that's got to be brought into the cell, it activates and another clathrin attaches. the clathrins hold each other's arms. each molecule only "knows" about its neighbors. as more of this happens, aided by Brownian motion of all molecules involved, a cage is formed around a piece of cell membrane enclosing the stuff to be brought in and eventually pinches off. very clever. look:

Receptor-mediated endocytosis by clathrin-coated vesicles

By Dr Tony Jackson *

A review of how research into the components of the clathrin coat has provided insights into the operation of these molecular machines

http://www.abcam.com/index.html?pageconfig=resource&rid=10236&pid=14

mechanism of forming clathrin coated vesicles:

http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=1225879&blobtype=pdf

The clathrin machine is not like a computer program at all. the processing is totally distributed. furthermore I suspect we could isolate the molecules involved and get them to work without the whole live cell shebang. have to probably supply the proteins ready phosphorylated though.

why not call it a machine? what's your definition of a machine? something with gears, pulleys and integrated circuits? I think of machines as things you can understand by seeing how the separate parts interact.

32) The DNA Is NOT The Brain!

The whole cell is like this, rampantly parallel. The DNA is not a miniature dictator, ruling the cell, just as the queen bee does not rule the hive. It's a bulletin board that all the proteins use for keeping track of things, no one is in charge.

PHYSICAL/CHEMICAL DYNAMICAL SYSTEMS FAR FROM EQUILIBRIUM: difference in temperature leads to disorder in the total system by way of energy flow which however can lead to INCREASE in order in a subsystem

33) Build A Steam Engine

How does a steam engine work, how hard is it to make one?

34) Benard Convection

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.

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!

40) Dynamic Processes In Mineral Formation

Are there dynamic processes in mineral formation like convection? How did that piece of Goethite at the American Museum of Natural History form?

41) After 4.5Billion Years Of Mixing, The Earth Has NOT Blended To Homogeneity

Basic question though is why as the Earth churns round and round 4billion years doesn't everything blend into to homogenous grey clay? why are heterogeneities formed at every level?

42) Belousov-Zhabotinski Reaction

43) Deep Sea Manganese Nodules

Concentration of metals at the interface at the ocean bottom due to redox chemistry mediated by organisms

44) Play With A Candle Flame

45) Suns Have Complex Dynamic Organization

Suns are complicated self organizing critters with life cycles

47) Simplest Organic Redox Cycle

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?

MATHEMATICAL DYNAMICAL SYSTEMS:

CELLULAR AUTOMATA

48) John Horton Conway's Game Of Life: http://blackskimmer.blogspot.com/2007/07/john-horton-conways-game-of-life-here.html

49) Game of Go

50) Cellular Automata With NON Local Rules.

I want to relate this to how quantum mechanics gives us molecular orbitals like aromatic molecules.

51) Cellular Automata Robust Under Random Fluctuations

Find cell automata who's complex patterns are robust under random fluctuations. unlike Conway life, like chemistry

52) Cellular Automata With Random Input

53) Explore The Space Of 1 Dimensional Cellular Automata

54) Kauffman's NK Boolean Networks

let each cycle synchronously, the nodes turning each other on and off. there ought to be 2^N possible states to such a system. Kaufmann found that when K is around 2 most of the systems end up falling into one of a MERE sqrt(N) possible attractive cycles! the systems do not explore anywhere NEAR the 2^N possible states.

Phase transitions occur in various behaviors of Boolean networks when average connectivity is increased continuously. This combines the results of cellular automata and zero one laws on random graphs. For certain values of K the system falls into a number of discrete behaviors.

what if I had Conway life but with increasing connectivity? so a random net with on average n connections, n goes from 0 to 8 to 20...? and the rules are like Conway life:

Conway life neighborhood is 8, with rules:

0 1 die

2 3 live

exactly 3 born

4 5 6 7 8 die

so with my random net average neighborhood is n, rules are:

<n/4 die

n/4<= c <=3n/8 live

exactly 3n/8 or 3n/8<= c <n/2 born

>=n/2 die

hmm.. what are the geometries for each n?

n=0: isolated cells

n=1: pairs of cells

n=2: two possible geometries: infinite line, many disconnected infinite lines, infinite circle, many circles of size n=3 on up.

n=3: infinite tree, isolated tetrahedra, infinite tree of triangles, random combinations of tree and triangles, infinite chain of double triangles, messy

n=4: infinite planar lattice, isolated octahedra, mind boggling how would you even begin to classify the possibilities for each n?

55) Coin Flipping And Random Walks

DYNAMICAL SYSTEMS

56) 3n+1 Game

57) 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? ...

59) 3 Body Problem In Newtonian Mechanics

Newton: two suns 6 differential equations, reduce to one in theta? gets you 5 clean classes of orbits: circles, ellipses, parabolas, hyperbolas, all 2 dimensional. in 1 dimension if one sun can go through the other, a straight line oscillating.

all simple periodic.

now add a third sun. all of a sudden it's more difficult. Newton couldn't solve it, he intuited chaos. the continental physicists didn't like chaos, fudged their work. finally Poincare was brave enough to tackle it: chaos!

so actually it IS a lab we can do? we can simulate it with iterations. but I thought iterations produce complicated dynamics where the original differential equations don't. now I'm confused. well, at least see if the iterations for two body produce chaos or periodic orbits.

60) Lorenz Attractor and Chaotic Waterwheel

we can run simulations of this one. and we can build the chaotic waterwheel!

61) Compare Various Combinations Of Discrete And Continuous In These Dynamical Systems

Now compare cellular automata, with time discrete dynamical systems with differential equation dynamical systems

EXAMPLES FROM COMPUTER SCIENCE AND CYBERNETICS

62) Positive Feedback

63) Binary Search

63.5) Examples Of Trial And Error Algorithms

64) Negative Regulatory Feedback

65) Compare Trial And Error With Direct Prediction

Compare trial and error programs with direct prediction. Build some bots with both man in the cab of the backhoe, and trial and error algorithms, compare the different styles. I'm thinking here of two different approaches to designing machines to do what clathrin coated pit mediated endocytosis does.

66) Data vs. Algorithm

67) Hierarchical vs. Distributed Control

68) Iteration vs. Recursion

68) Exploratory Play Algorithms

PATTERN FORMATION AT EQUILIBRIUM. PHYSICS/CHEMISTRY:

70) Collect And Learn About Rocks And Minerals

collect rocks and minerals learn about fracture, crystal shape, color, hardness, chemical tests. see a whole mineralogy collection.

71) Listen To The "How Rocks And Minerals Form" Exhibit At The American Museum of Natural History

http://www.uwgb.edu/dutchs/EarthSC202Notes/minerals.htm

Why don't the elements combine higgledy-piggledy like different colors of clay, mixing, mixing until it's all grey? Because the atoms are discrete and the quantum mechanics, the discrete charges, the mathematics again gives us only certain discrete combinations. Only half a dozen to a dozen ways nitrogen combines with oxygen. Iron ions come in +2 or +3 electrical charges and have a specific size. Ditto aluminum ions. Silicate networks come in a surprising but finite number of variations and they have negative electrical charges. These all get matched up into many hundreds of different discrete structures. These structures can even be modified by the environment in which they grow.

Yet, we don't know how to predict this from first principles of the properties of each element involved! For instance, If I give you a ton of silicon, a ton of oxygen, a few pounds of iron, calcium, potassium, sodium, magnesium and hydrogen. Predict the minerals in various ranges of temperature and pressure that we get as we cool the mix from a molten mass.

72) Molecules Have Shape

are there some labs I can do to show that molecules have shape?

73) 10 Million Billion Billion Molecules Of Water In A Glass

can i make labs to show how many molecules?

can we at least observe Brownian motion of a minute dead particle in distilled water? can we see that the path is bumpy? what would make the path bumpy? what are all the things the particle is bouncing AGAINST? if the water were infinitely smooth, would the path be bumpy? does it bounce more in hotter water? when we heat the water more, it becomes steam. what's that? we can compress steam, but we can't compress water.

74) Periodic Chart Of Elements

Look too, at the structure of the periodic chart. why do we get this particular mix of capabilities for free, rather than a haze of nucleons?

75) Phase Transitions In Water: Breath, Oceans, And Snowflakes

Given the shape of water molecules, their stickiness etc... predict what happens as I raise the temperature from zero degrees Fahrenheit to 300 degrees. Also predict what happens when I drop the temperature back down to zero on your window in winter, or what happens when a cloud of water molecules, rises in the air and goes down to zero degrees. What falls out?

76) Phase Transitions For Sulfur: Even Wilder!

The different arrangements that Sulfur atoms get themselves into is odd. Again, We don't know how to predict this from first principles.

77) We Couldn't Predict Buckyballs After 60 Years Of Quantum Chemistry

PATTERN FORMATION AT EQUILIBRIUM. MATH:

propose a set of rules and let them play out and you often find you get a set of discrete entities which follow them that is interestingly diverse but not infinitely chaotic!

78) Prime Numbers

Prime Numbers are simple to define: a whole number that has only itself and 1 as factors, i.e. 7=7X1 and 13=13X1 are prime but 12=2X6=3X4 is not.

So with that simple definition what do we get? The further out you go into bigger numbers the more factors there are to divide into them so the primes start dwindling: there are more primes between 2 and a 100 then between 1000 and 1100. Do they dwindle out all together? No. A simple proof shows us that there are a infinite number of them.

(I should give the proof huh?)

Is there any pattern to them? 2 3 _ 5 _ 7 _ _ _ 11 _ 13 _ _ _ 17 _ 19 _ _ _23 _ _ _ _ _ 29 _31 _ _ _ _ _ 37 _ _ _41 _ 43... The gaps are funny. Is it chaotic or is there a pattern?

One pattern is that some primes come in pairs! 11, 13; 17, 19; 41, 43. does THAT keep happening? Actually it's been 2500 years and no one has figured out a proof of it. With computers we've calculated that it keeps happening WAY WAY out there...

79) Fibonacci Numbers

80) 5 Platonic Solids

Given the simple laws of 3 dimensional geometry, how many REGULAR POLYHEDRA can we make, where each face is an identical regular polygon and each vertex where they meet is identical? I.e. a pyramid out of four equilateral triangles, or a cube out of 6 squares? The surprise is that we can only make FIVE such discrete figures: pyramid (tetrahedron), double pyramid (octahedron, 8 triangles) , cube, dodecahedron (12 pentagons) , and icosahedron (20 triangles). We get a curious dollop of discrete complexity but not an infinite amount of chaos.

http://www.cut-the-knot.org/do_you_know/polyhedra.shtml

(with simple proof of this fact!)

http://mathforum.org/sum95/math_and/poly/reg_polyhedra.html

81) Classification Of Finite Simple Groups

http://blackskimmer.blogspot.com/2007/03/classification-of-finite-simple-groups.html

82) Combinatorics

number of connection vs. number of nodes in a graph

83) Linear, Polynomial, Exponential, Factorial...

different functions linear, polynomial, exponential, factorial, 1/x

84) Exponential Growth

for instance make sure they know what happens when you keep doubling, as in the story of rice grains on a chess board.

85) Integer, Rational, Real

86) Analog vs. Digital

87) Enumerations Of Finite Graphs

88) Zero One Laws In Random Graphs

http://blackskimmer.blogspot.com/2007/03/zero-one-laws-in-random-graphs.html

89) Must Be Tons More Math

what other math do they need? Bar, you've got a LOT of math under your belt helping you put this all in perspective.

PUT IT BACK TOGETHER: EVOLUTION

90) Diversity And Disparity Of Life

explore the diversity to 100 phyla, 10,000s families 20million species. note they all have the same biochemical core!

now, don't forget that there are 8000 different species of ants! we found a dozen or so! what's that all about? and of course birds dogs cats squirrels fish Stentor worms on and on, they all can do these things! What's THAT all about? they designing each other? and plants, and Stentor and fungi and bacteria. how many? show a classification of 5 kingdoms of 100 different crazy phyla, with 10,000s of families, 20million species? wow!

and remember: we've found that they all seem to work on the same core of cellular machinery! they are all variations on a theme! what's THAT about?

91) There Are At Least 3 Styles Of Design

we can imagine at least 3 different kinds of design:

a) trial and error

b) the way we reason things out to work well, efficiently

c) solutions to max min problems mathematically?

92) Collect Fossils

93) Geology, Strata, Time

they seem to change from layer to layer and seem to respond to the shifting of continents.

94) Geochemical History

there's geochemical history too, which gives us hints of changing climate, evolution of basic microbial metabolisms...

95) Word Mutation Game

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!

96) Tierra, An Ecosystem Of Evolving, Reproducing Computer Programs

97) Theory Of Darwinian Evolution

THE FINAL FRONTIER. LIFE FROM CHEMISTRY?

98) Ecosystem Of Reproducing Candle Wicks?

As we imagined a self sustaining ecosystem of robots and parts, lets see if we can imagine an ecosystem of candle flames. i mean the wick is the catalyst to the complex dynamic structure of the candle flame, but the wick gets used up. can we imagine a wick that can also catalyze the reconstruction of more wick from the wax using the energy from the flame to drive it? cotton wicks are actually complex structures built by organisms. what's the simplest wick structure we can come up with chemically? then one that can catalyze it's own growth from the wax. would it need nitrogen or sulfur or... ok, so we give it a more complex growth medium! would it need a complex structure of catalysts? how would it recreate THEM?

could it reproduce? by breaking apart? by branching? float away on the molten wax? anchor itself on the edge of the molten wax/solid wax boundary?

99) Self Sustaining Ecosystem Of Reproducing Chemical Robots?

The final challenge is how can chemistry bump around and come up with the first earliest sophisticated creatures in the first place? remember our attempt at constructing a working ecosystem of robots, lets try to make one come together by constructing parts that bumble around and find each other.

First you realize how basic the blocks will have to be. we'd have to break up all the life processes into the most basic processes we can imaging and make a part that embodies that process, each of the parts must be responsive active though... now that we have explored some chemistry, and we've explored how complex patterns can form in simple cellular automata...

100) Chemical Origin Of Life

CHNOPS on mud under energy flow. I want to build more and more elaborate versions of Morowitz's example (#43) of redox cycles on surfaces which will develop boundaries and feed back into manipulating the geometry of the catalysts creating more and more complex organic chelates which manipulate the geometry of the catalysts even more until finally i get the simplest core of cellular metabolism

101 exercises.

now remember that each of these experiences will feed insight into the others, so mix them up in time? once they try building robots, writing programs, they should go back and watch ants to see them differently.

what they accomplish:

learn to write programs, see hierarchy of complexity

several math games: Conway life, primes, Tierra

be able to explain how Darwinian evolution works

how to see the hierarchy of transistors/switches that make up a computer

how it compares to network in brain

how to use microscope to see details of tiny critters, plant cells

watch the BEHAVIOR of the speck that Stentor is!

key out 100 different plants in central park with all their DETAILS

how to calculate

complexity lab in a box:

simple microscope with good lighting mechanism

electronics kit from transistors to chips to microprocessor with keyboard and simple 8X80 display with forth or basic

key to couple hundred common plants (which region? the basic weeds!)

key to 500 families of bugs

mineralogy book

fossil book

complexity lab manual

some spare ICs to take apart and look at under microscope

ALL THE CLASSES IT TOOK/TAKES TO LEARN THIS

Biology

Watch pond water

Botany

Zoology

Observations of ant colonies, collecting and keying out

Learn 500 spp plants

Cell Bio

Evolutionary theory

Digital Electronics

Microprocessors

Computer Programming

Data Structures/Algorithms

AI reasoning vs. trial and error, knowledge representation

Cellular Automata/Dynamical systems

Mathematical structures primes, Fibonacci numbers, groups

Auto Repair

Chemistry

Organic Chemistry

Mineralogy

Geology

Bateson's Mind and Nature

Phase transitions occur in various behaviors of Boolean networks when average connectivity is increased continuously. This combines the results of cellular automata and zero one laws on random graphs. For certain values of K the system falls into a number of discrete behaviors.

what if I had Conway life but with increasing connectivity? so a random net with on average n connections, n goes from 0 to 8 to 20...? and the rules are like Conway life:

Conway life neighborhood is 8, with rules:

0 1 die

2 3 live

exactly 3 born

4 5 6 7 8 die

so with my random net average neighborhood is n, rules are:

<n/4 die

n/4<= c <=3n/8 live

exactly 3n/8 or 3n/8<= c <n/2 born

>=n/2 die

hmm.. what are the geometries for each n?

n=0: isolated cells

n=1: pairs of cells

n=2: two possible geometries: infinite line, many disconnected infinite lines, infinite circle, many circles of size n=3 on up.

n=3: infinite tree, isolated tetrahedra, infinite tree of triangles, random combinations of tree and triangles, infinite chain of double triangles, messy

n=4: infinite planar lattice, isolated octahedra, mind boggling how would you even begin to classify the possibilities for each n?

55) Coin Flipping And Random Walks

DYNAMICAL SYSTEMS

56) 3n+1 Game

57) 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? ...

59) 3 Body Problem In Newtonian Mechanics

Newton: two suns 6 differential equations, reduce to one in theta? gets you 5 clean classes of orbits: circles, ellipses, parabolas, hyperbolas, all 2 dimensional. in 1 dimension if one sun can go through the other, a straight line oscillating.

all simple periodic.

now add a third sun. all of a sudden it's more difficult. Newton couldn't solve it, he intuited chaos. the continental physicists didn't like chaos, fudged their work. finally Poincare was brave enough to tackle it: chaos!

so actually it IS a lab we can do? we can simulate it with iterations. but I thought iterations produce complicated dynamics where the original differential equations don't. now I'm confused. well, at least see if the iterations for two body produce chaos or periodic orbits.

60) Lorenz Attractor and Chaotic Waterwheel

we can run simulations of this one. and we can build the chaotic waterwheel!

61) Compare Various Combinations Of Discrete And Continuous In These Dynamical Systems

Now compare cellular automata, with time discrete dynamical systems with differential equation dynamical systems

EXAMPLES FROM COMPUTER SCIENCE AND CYBERNETICS

62) Positive Feedback

63) Binary Search

63.5) Examples Of Trial And Error Algorithms

64) Negative Regulatory Feedback

65) Compare Trial And Error With Direct Prediction

Compare trial and error programs with direct prediction. Build some bots with both man in the cab of the backhoe, and trial and error algorithms, compare the different styles. I'm thinking here of two different approaches to designing machines to do what clathrin coated pit mediated endocytosis does.

66) Data vs. Algorithm

67) Hierarchical vs. Distributed Control

68) Iteration vs. Recursion

68) Exploratory Play Algorithms

PATTERN FORMATION AT EQUILIBRIUM. PHYSICS/CHEMISTRY:

70) Collect And Learn About Rocks And Minerals

collect rocks and minerals learn about fracture, crystal shape, color, hardness, chemical tests. see a whole mineralogy collection.

71) Listen To The "How Rocks And Minerals Form" Exhibit At The American Museum of Natural History

http://www.uwgb.edu/dutchs/EarthSC202Notes/minerals.htm

Why don't the elements combine higgledy-piggledy like different colors of clay, mixing, mixing until it's all grey? Because the atoms are discrete and the quantum mechanics, the discrete charges, the mathematics again gives us only certain discrete combinations. Only half a dozen to a dozen ways nitrogen combines with oxygen. Iron ions come in +2 or +3 electrical charges and have a specific size. Ditto aluminum ions. Silicate networks come in a surprising but finite number of variations and they have negative electrical charges. These all get matched up into many hundreds of different discrete structures. These structures can even be modified by the environment in which they grow.

Yet, we don't know how to predict this from first principles of the properties of each element involved! For instance, If I give you a ton of silicon, a ton of oxygen, a few pounds of iron, calcium, potassium, sodium, magnesium and hydrogen. Predict the minerals in various ranges of temperature and pressure that we get as we cool the mix from a molten mass.

72) Molecules Have Shape

are there some labs I can do to show that molecules have shape?

73) 10 Million Billion Billion Molecules Of Water In A Glass

can i make labs to show how many molecules?

can we at least observe Brownian motion of a minute dead particle in distilled water? can we see that the path is bumpy? what would make the path bumpy? what are all the things the particle is bouncing AGAINST? if the water were infinitely smooth, would the path be bumpy? does it bounce more in hotter water? when we heat the water more, it becomes steam. what's that? we can compress steam, but we can't compress water.

74) Periodic Chart Of Elements

Look too, at the structure of the periodic chart. why do we get this particular mix of capabilities for free, rather than a haze of nucleons?

H

Be B C N O F

Na Mg Al Si P S Cl

K Ca Ti Cr Mn Fe Co Ni Cu Zn As Se Br

Sr Mo Sn Sb I

Pb

75) Phase Transitions In Water: Breath, Oceans, And Snowflakes

Given the shape of water molecules, their stickiness etc... predict what happens as I raise the temperature from zero degrees Fahrenheit to 300 degrees. Also predict what happens when I drop the temperature back down to zero on your window in winter, or what happens when a cloud of water molecules, rises in the air and goes down to zero degrees. What falls out?

76) Phase Transitions For Sulfur: Even Wilder!

The different arrangements that Sulfur atoms get themselves into is odd. Again, We don't know how to predict this from first principles.

77) We Couldn't Predict Buckyballs After 60 Years Of Quantum Chemistry

PATTERN FORMATION AT EQUILIBRIUM. MATH:

propose a set of rules and let them play out and you often find you get a set of discrete entities which follow them that is interestingly diverse but not infinitely chaotic!

78) Prime Numbers

Prime Numbers are simple to define: a whole number that has only itself and 1 as factors, i.e. 7=7X1 and 13=13X1 are prime but 12=2X6=3X4 is not.

So with that simple definition what do we get? The further out you go into bigger numbers the more factors there are to divide into them so the primes start dwindling: there are more primes between 2 and a 100 then between 1000 and 1100. Do they dwindle out all together? No. A simple proof shows us that there are a infinite number of them.

(I should give the proof huh?)

Is there any pattern to them? 2 3 _ 5 _ 7 _ _ _ 11 _ 13 _ _ _ 17 _ 19 _ _ _23 _ _ _ _ _ 29 _31 _ _ _ _ _ 37 _ _ _41 _ 43... The gaps are funny. Is it chaotic or is there a pattern?

One pattern is that some primes come in pairs! 11, 13; 17, 19; 41, 43. does THAT keep happening? Actually it's been 2500 years and no one has figured out a proof of it. With computers we've calculated that it keeps happening WAY WAY out there...

79) Fibonacci Numbers

80) 5 Platonic Solids

Given the simple laws of 3 dimensional geometry, how many REGULAR POLYHEDRA can we make, where each face is an identical regular polygon and each vertex where they meet is identical? I.e. a pyramid out of four equilateral triangles, or a cube out of 6 squares? The surprise is that we can only make FIVE such discrete figures: pyramid (tetrahedron), double pyramid (octahedron, 8 triangles) , cube, dodecahedron (12 pentagons) , and icosahedron (20 triangles). We get a curious dollop of discrete complexity but not an infinite amount of chaos.

http://www.cut-the-knot.org/do_you_know/polyhedra.shtml

(with simple proof of this fact!)

http://mathforum.org/sum95/math_and/poly/reg_polyhedra.html

81) Classification Of Finite Simple Groups

http://blackskimmer.blogspot.com/2007/03/classification-of-finite-simple-groups.html

82) Combinatorics

number of connection vs. number of nodes in a graph

83) Linear, Polynomial, Exponential, Factorial...

different functions linear, polynomial, exponential, factorial, 1/x

84) Exponential Growth

for instance make sure they know what happens when you keep doubling, as in the story of rice grains on a chess board.

85) Integer, Rational, Real

86) Analog vs. Digital

87) Enumerations Of Finite Graphs

88) Zero One Laws In Random Graphs

http://blackskimmer.blogspot.com/2007/03/zero-one-laws-in-random-graphs.html

89) Must Be Tons More Math

what other math do they need? Bar, you've got a LOT of math under your belt helping you put this all in perspective.

PUT IT BACK TOGETHER: EVOLUTION

90) Diversity And Disparity Of Life

explore the diversity to 100 phyla, 10,000s families 20million species. note they all have the same biochemical core!

now, don't forget that there are 8000 different species of ants! we found a dozen or so! what's that all about? and of course birds dogs cats squirrels fish Stentor worms on and on, they all can do these things! What's THAT all about? they designing each other? and plants, and Stentor and fungi and bacteria. how many? show a classification of 5 kingdoms of 100 different crazy phyla, with 10,000s of families, 20million species? wow!

and remember: we've found that they all seem to work on the same core of cellular machinery! they are all variations on a theme! what's THAT about?

91) There Are At Least 3 Styles Of Design

we can imagine at least 3 different kinds of design:

a) trial and error

b) the way we reason things out to work well, efficiently

c) solutions to max min problems mathematically?

92) Collect Fossils

93) Geology, Strata, Time

they seem to change from layer to layer and seem to respond to the shifting of continents.

94) Geochemical History

there's geochemical history too, which gives us hints of changing climate, evolution of basic microbial metabolisms...

95) Word Mutation Game

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!

96) Tierra, An Ecosystem Of Evolving, Reproducing Computer Programs

97) Theory Of Darwinian Evolution

THE FINAL FRONTIER. LIFE FROM CHEMISTRY?

98) Ecosystem Of Reproducing Candle Wicks?

As we imagined a self sustaining ecosystem of robots and parts, lets see if we can imagine an ecosystem of candle flames. i mean the wick is the catalyst to the complex dynamic structure of the candle flame, but the wick gets used up. can we imagine a wick that can also catalyze the reconstruction of more wick from the wax using the energy from the flame to drive it? cotton wicks are actually complex structures built by organisms. what's the simplest wick structure we can come up with chemically? then one that can catalyze it's own growth from the wax. would it need nitrogen or sulfur or... ok, so we give it a more complex growth medium! would it need a complex structure of catalysts? how would it recreate THEM?

could it reproduce? by breaking apart? by branching? float away on the molten wax? anchor itself on the edge of the molten wax/solid wax boundary?

99) Self Sustaining Ecosystem Of Reproducing Chemical Robots?

The final challenge is how can chemistry bump around and come up with the first earliest sophisticated creatures in the first place? remember our attempt at constructing a working ecosystem of robots, lets try to make one come together by constructing parts that bumble around and find each other.

First you realize how basic the blocks will have to be. we'd have to break up all the life processes into the most basic processes we can imaging and make a part that embodies that process, each of the parts must be responsive active though... now that we have explored some chemistry, and we've explored how complex patterns can form in simple cellular automata...

100) Chemical Origin Of Life

CHNOPS on mud under energy flow. I want to build more and more elaborate versions of Morowitz's example (#43) of redox cycles on surfaces which will develop boundaries and feed back into manipulating the geometry of the catalysts creating more and more complex organic chelates which manipulate the geometry of the catalysts even more until finally i get the simplest core of cellular metabolism

101 exercises.

now remember that each of these experiences will feed insight into the others, so mix them up in time? once they try building robots, writing programs, they should go back and watch ants to see them differently.

what they accomplish:

learn to write programs, see hierarchy of complexity

several math games: Conway life, primes, Tierra

be able to explain how Darwinian evolution works

how to see the hierarchy of transistors/switches that make up a computer

how it compares to network in brain

how to use microscope to see details of tiny critters, plant cells

watch the BEHAVIOR of the speck that Stentor is!

key out 100 different plants in central park with all their DETAILS

how to calculate

complexity lab in a box:

simple microscope with good lighting mechanism

electronics kit from transistors to chips to microprocessor with keyboard and simple 8X80 display with forth or basic

key to couple hundred common plants (which region? the basic weeds!)

key to 500 families of bugs

mineralogy book

fossil book

complexity lab manual

some spare ICs to take apart and look at under microscope

ALL THE CLASSES IT TOOK/TAKES TO LEARN THIS

Biology

Watch pond water

Botany

Zoology

Observations of ant colonies, collecting and keying out

Learn 500 spp plants

Cell Bio

Evolutionary theory

Digital Electronics

Microprocessors

Computer Programming

Data Structures/Algorithms

AI reasoning vs. trial and error, knowledge representation

Cellular Automata/Dynamical systems

Mathematical structures primes, Fibonacci numbers, groups

Auto Repair

Chemistry

Organic Chemistry

Mineralogy

Geology

Bateson's Mind and Nature

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