1) can't go out and collect ants or plants or insects so will have to have some kind of... could have a table of 100 laminated leaves and you get to mess around and see if they all look different! can you really tell? can you see enough detail if you use a handlense? through the lamination? can you really tell the diff between a few different grass blades? under 30times you can see the cell surfaces, rows of stomates.. really? pressed like that? got to be dried/pressed THEN laminated. under sanitary conditions? but the point of this exercise is too see the levels of detail, the trichomes, the cell patterns, stomate patterns... can you see that through lamination?
2) certainly have rows and rows of 1000s of insects. in individual cases so you can pick em up and see in detail the hairs and subtle... i mean to key out the ant genera i had to look at subtle details, shapes dammit
how does one take the time to do this at a science center?
how does one get the cumulative impact of all these lessons by randomly walking around a science center for an unpredictable amount of time? well, one of my dreams was to have a science center where kids would come back to time and time again over course of weeks after school and slowly put together story. bar, YOUR SIMPLIFIED version of 4 workshops was 4 periods of 6 weeks. that's like 48 hour meetiings. no one is going to spend THAT much time at a science center! MAYBE.. how many times did I visit the American Museum of Natural History the last time I lived in Manhattan? DOZENS! Complexity lab sums up A LIFETIME OF YOUR STUDY. how can you compact that into a few science center experiences?
ok, i'm not being realistic!
so at a science center what if different kids see their own mix of a FEW of the complexity lab things? would that still be of value?
come on make a list of labs that can be perused quickly at a science center:
1) for sure i can make a display of 30X30 insects=1000 that obviously look different lets see: 1cm each is 1ft by 1ft, hmm not much, some like butterflies and moths and dragonflies (and larvae?) will take up to 10X10cm so... say 20 10X10s + 40 5X5cms + 100 2X2s +2000 1X1s =2000 + 1000 + 400 + 2000 = 5400cm^2, 54X100 = 1 1/2 X 3 ft, nothing!
even 100 10X10 + 100 5X5 + 1000 2x2 + 5000 1X1=
10,000+2500+4000+5000 = 21,500 = 3X8ft that's nice, that's 6200 insects!, hell i can even have a 5X10 case with a swirl of a 100 tiny insects! so that's 10,000 different insects. you can include spiders and other land arthropods...
remember wanting a montage of 1000s of diff organisms? hell, you can have a diarama you can walk through: hanging plants above you, scatter tiny critters up front, blow ups of microscopic critters in spots, sea critters in one spot, progressively in the background larger fish and mammals, birds.. maybe you can pack in a million diff critters? 1million would be too much work to assemble! that's a 1000 people working on 1000 each. Too much? That's the work it takes to produce a FEW movies! Yeah but it won't net you 8$/person for 1000s of people? and gov grants are tight these days. well hell a sceicne center charges these days..
anyway 10s of 1000s is easy enough
2) then two different insects under 30 power or whatever to see detail
3) then slide of complexity of surface of plant leaf...
4) can still have table of leaves and keys lying about and the kids can try their hand at keying out a few leaves...
5) how many of those 260 honeybee behaviors can you see in a few minutes watching an observation hive? well you can at least have a list of 100 50 30 obvious behaviors basic to honeybee life and ask: how many can you spot?
6) insect munching on grass under lense?
7) what kind of animal can you have in a cage or tank that's really active and you can see lots of behaviors? i think the point is that an observation hive would show the most behaviors.
now bar, how much of the computer stuff can you learn in a few minutes?
8) well you can certainly have a bare computer chip a basic one, like an 8080 or something, see how tiny, then another under microscope see a hint at the complexity, then a wall sized blow up, then..
9) diagram of the various circuits, flip flops, multiplexers... how they work
how does someone look and realize how they work? animations of how the signals go though them.. you can even have a table where you put in a grid of cubes... a giant sized digiboard! with signal inputs with leds. you put a logic gate on a signal input and see the output, then you look at the diagrams and put the blocks together. have blocks with those numeric displays.. how do you match up the leads? a numeric display will have 7 inputs per digit. what's the geometry here? make it big enough so that it has 8 block faces: 3 blocks long, then you have to snake the other block outputs to them, need a way to cross wires, that's a block! a wire cross block.
bar that's insane! do you know how big the damm thing will have to be? how much can you do with a grid on a wall pannel? the blocks stick to it. make 'em.. i was thinking 2X2 inches to make it easy to handle. so a grid (it's gonna be little kids!) 6feet wide by 2feet tall is 36X12 blocks. is that enough to make ciruits? then chunk the circuits but then there is the problem of leads... nope! have blocks that represent various combinations of 4 wires at a time split 8wires into different directions: 8 input on one face and it's 4 blocks long and the 8 other faces are one lead out each.
it would take much too long to make a circuit on this!!
need a better idea. but bar it would be cool! kids would love it!
well? at least display of how to combine transistors to make two different gates
next level how to combine bunch of gates to make circuts clock, counter...
next level how to combine these to make central processor
animations showing how the signals work... could be a short movie like they have at these places.
[hell bar, think the whole complexity lab thing out as a video series like nova or...oh. nah.. it's got to be interactive!]
you can make the circuites show the signals going though at each step if you have the kid be the clock, he clocks it at his own pace to follow through, if he gets lost he resets it. he has switches he can flick up or down to set up the inputs...
10) write machine code? hmmm simplest. show 4 bit processor has few basic instructions, inc, dec, set=0, dec and loop, so they can make simple programs on a screen of some kind... but what's gonna happen here? it takes some period of learning of motivation to figure out how to make a program. what do you want them to be able to accomplish?
ultimately program legobots but i don't want it to be abstract, i want them to see that it's all based on these basic mechanical components. the legobot programing environment was a mystical make believe geometric representation on a computer screen. i don't want that! that's magic!
so can you make a simple legobot that's controled by the code for that simple machine?
inc
dec
dec and loop 2 4bit address = program has 256 steps! that's plenty
load register 4 bit or 8bit number
move forward one click or 4bit number clicks
rotate right or one of 16 compass directions
rotate left
beep
turn on light
turn off light
detect bump sensor
detect lighth sensor
branch if detect
..
show the actual circuitry of the robot, the 4 bit processor
bar, you are dreaming. how will you test this all out to see how feasible it is? and again... how will kids write the programs?
so you see the blow up 4bit processor circuit on the wall.
then you have the legobot with hex display or something and button for load, read, reset etc.. like my Cosmac 1802 board. and lights and things inside the clear case to simulate these signals going to the 4bit processor. the clock rate is like a pulse every 2seconds so they can see all the steps... or again, you can turn a dial to slow down the pulse rate or speed it up... hmmm
hell you can make the bot big enough (good, robust) to have a keyboard with a button for each command, labeled, inc, dec, loop, back, rotate... and then a shift key to use those same keys for the hex numbers. of course you have on the wall the diagram for the circuit that polls the keyboard! well it's a simple circuit, keypress signals a register with input etc.. 16 line to 4 bit decoder...
so then what? so they start making programs:
move 5
rotate
move 5
rotate
move 5
rotate
move 5
that makes a square that's easy enough to suggest to a kid.
show some programs that the kid can watch and then he modifies them...
the concept of looping...
loop 2
loop 1
move 5
test for bump
until 1
rotate
until 2
bar that's a sophisticated concept! do you think you can really get kids at a science center to begin to play with this stuff? i don't think science museum is the right environment for sitting down and experimenting and thinking.
i don't know. what if you just show the programs and see how they loop, proceed while watching the bot, and then you can modify the programs?
then you can watch on the wall a diagram (watch the bouncing ball...) run through a complicated program while watching the bot go at it...
don't know.
11) watch real sophisticated bots play soccer but at least you've seen their innards?
12) not gonna dissect an insect in a science museum! of course can have CLASSES at the museum! oh.
12) alongside the microchip display, a slide of a slice of a honeybee brain, under microscope... wow, big wallsize pic of complicated connections
13) model of a car with tough plastic parts and bolts? can take it apart put together (would be chaotic) then how to show that a blow up car sized ant has more parts? well there are the slides... car sized model insect with take apart parts... but, these parts will have the fine sculptre that the insect parts would have.. so at what level is the insect more complicated? hmmm well, it's got 6 legs for instance, show the joints, the tarsal segments, the mechanisms to make the joints, the springy muscles... would have to be able to split the leg open, the wires going throu to the various muscles for nerves, does the tracheal system go into the legs? it must, it goes into the wings, right? hell the veination for the wings alone.. that they are actually hollow fluid filled tubes (i forget, one for trachea one for hemolymph?) the sensors! connected to the nerve wires. ganglia in the legs? so bar how much more complex is a leg than a wheel assembly?
wheel: hub, cap, 6 bolts, innertube, tire, main bolt, i'm forgetting, break disk, complicated break clamp assembly, about 6 parts, the actual actuator mechanism, forget.. axle, ball joint, steering bars, joints, bolts...
leg: femur shell, hairs, tibia shell, hairs, joint, ligaments? muscle, joint to coxa, muscles, tracheal tubes, nerve wires, tarsal joint, each tarsal segment, hairs, tarsal pad, sensors, hairs,
how is it more parts? of course... where is the engine? each muscle moves under its own power.. the engines... are millions of them microscopic.. gar... how many tissue types does an insect have? 100? 50? how many does a modern car have? probably on the same order. and a car might have a 1000 parts including all the tubes and bolts and nuts.. can you show me 1000 parts in an insect? that would be hard.
the comparison between insect and car isn't at the level of organs and tissues... although the 100s of hairs on the insect is impressive or the complexity of the wing venation, or the ridges on the exoskeleton, the texture is more complex, the branching of the tracheal system is much more complex than a car's lube system.. air intake valve.. hmm that begins to hint at it.. that the insect has engines in each of its muscles... hmm... this is actally tricky to show. i don't know the answer. hell bar, you remember that book of honeybee anatomy! go find it at suny, it's GOT to be more complex than a car! i maen things are repeated by segments! a car has what, maybe 6 segments or something?
hell the mouthparts, the glands.. yeah but the carborator the fuel pump... yeah but each segment of the mouthparts has it's own muscles and nerves...
well this is a challange.
14) well anyway now show all the factories necessary to build a car, all the raw material extraction industries... there's the rub, that you can show, maybe as a movie.
now comes the fun part:
15) next to that, a video of how all those insect parts develop INSIDE a pupa! and all from the food the larvae ate.
16) now in terms of slides i can't show how real they are cause we aint gonna slice plants with razor blade and make slides at a science museum exhibit.. why not? why not have a demonstrator do it? make the slides on the spot for the kids to look at under the microscopes? well... if we do... then what can we show about plant development? the apical meristem, how each successive leaf has more cells... then the cells expand..
some kids will look in the microscopes but the demonstrator can also project her microscope onto a big screen
look bar, you want to make this a big deal like that bodies exhibit! god that was really macabre and weird, i don't believe it actually happened, i mean it's basically a snuff film eh?
18) ok 20billion interconnected neurons... ok, demonstrate some multiplication... so you can have already assembled 4" blocks of a 1000 little blocks (yeah but you have to assemble tons of them each time... well you could make 100s of blocks of jello each day... and have a demonstrator slice them... that's messy...
you could have some trays with tons of blocks piled up and color coded, so 1 gold block, 8 silver blocks to make the simplest cube and 27 white blocks and 125 blue blocks, and you can show how multiplication works and how volume and surface area interact and then 100 red blocks to make a 10X10 square and finally 1000 green blocks for 10X10X10 show pictures, at 1" each the cube aint even a cubic foot it wold take 5blocks per second thats 200seconds thats 4 minutes to assemble it, kids could do that
well you can at least have some partially taken apart on display and then you could have at one corner of the exhibit.. my corner wall with the little blocks laid out and you gotta imagine... 1000 inches is hmm 80 ft, have it outside?
so a wall sized micrograph had maybe a big cpu chip with a million transistors... but not so interconnected... then what about a model? make neurons tiny with lots of long dendrites... lots of space in between them.. a display of ( i mean the amnh used to have those incredibly cool glass models of radiolarians... that's what I was brought up on!) so can we construct a model.. with a 1000X1000X1000 neurons all hooked up together with really fine threads? would be a bitch to make, say 10million threads, impossible. can we find some critters that can grow it for us? OOOOHH...
now bar, you can digitally produce movies to show some of this! or even interactive program to display, to manipulate...
demonstrate binary exponential branching, fissioning how? Bar people make tv shows like this, remember that morrison guy, made a tv show with all those contraptions and experiments... he videod that chef pulliing the chinese dough out to a thousand noodles by doubling. you got that book? i think so somewhere...
you pick enough of these to fit in a few episodes and you find a producer... do people watch tv anymore?
dendritic growth? hmm... in a block of jello?
19) so then a video of animal development
20) ok pond water under microscopes watch single celled critters, make sure during all these you are showing how to calculate size, calculate number of cells per organ...
21) show algae growing in sealed containers. they'll have to imagine it happening
22) how long does paper chomotography take, not too long... can we do one like they did with the proteins from squashed cells, and split 'em up into a 100 different spots? discrete spots? that'd be way cool, a hint that something interesting is going on in there... that the critters are made of discrete parts, if we put plants in a blender or squeeze out some clear juices and... what? to get the proteins.. at least they would see the various steps get a hint at what's going on connect the dots, then you can show similar papers with 100 diff proteins separateed out...
if you had a sheet with some visible color spots and then spray some kind of indicator on it and see all the invisible spots show up...
what other molecular demonstrations? see that tv show idea is cool, you can edit splice, speed up time, set up in advance.. only have to do it once then everybody can watch over and over again... how to convince of brownian motion? how to convince them that the jiggling is dead? well you can show diffusion... which is slow.. i don't see how i can demonstrate molecules in an exhibit. But it's the most important thing to do!
23) i guess you could repeatedly demonstrate lipid monolayer..
24) molecles in cell: lots of video animations i guess,
a way to demonstrate organized activity from brownian motion? so we show the clathrin coated pit animation... how can we show that mechanical parts can do this? There was a video of this on youtube i think
now if you could program a whole bunch of interacting legobots with identical simple programs with random input and watch to see if emergent behavior.. video of termites consttructing tower? or weaver ants bending a leaf...
25) wall size metabolic chart with picture representations of each of the molecules
26) photogrtaphs and diagrams calculate how many bricks in the city the museum is in. then display of avogadros number, we are always measuring and calculating in these exhibits, display showing how to cut up cubes of cm^3 etc... to get at how many molecules inside a tiny cell... how DO we calculate how many ribosomes, how many proteins in a cell? weigh the batch of goop, how do you determine molec wieght of a single protein? then divide. you know, i don't know.
yeah? so supply the kids with clipboards and pencils and lots of paper... no, little 10 page notebooks on clipboards and the kids can be always calculatiing... drawing stuff... remember they encouraged that in the nature room at amnh..
27) ok a waterwheel is an easy exhibit, and have the kids pour the water back up to the top or use beebees if the water is too messy (can you make chaotic waterwheel with beebees? they'd get stuck in the holes..have it vibrating (simulates browninan motion!)) to show it takes work to make the thing run
gotta show them there is no MECHANISM behind it!
28) neg feedback show nice big sized thermostat working see the mechanism. make a mechanism with a fast acting thermostat and quick heating with a thermometer so the kids can blow on it or warm it with their hands (?) or someting and watch it try to maintain equilibrium. Let the kids put it together backwards so it goes into runaway positive feedback.
29) now chaotic waterwheel! show some complexity from a simple mechanism! (what's the siimplest mechanism that can act like langton's ant, though not takiing 10,000 steps! )
30) door buzzer solenoid thing, can you make one oscillate really slowly? that'd be cool. how do you show that chemical energy is being USED UP as these patterns are being formed? well what can we get it running on a zinc/coper strip lemonjuice cell? the zinc and copper are the fuel. can we get one going with a really thin zinc and copper strip and watch them get eaten away till they are all gone and the thing stops running? we can get alot of amps out of a voltaic pile, ah. how do you connect? lead to each layer or is it already in series...
31) beakman motor, that's a fun thing to do in an exhibit! have them shape the wire themsevles to get it to work.
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so rotary motion is easy to get, but what about something more complicated, interesting? well chaotic waterwheel is interesting... simple thermoacoustic engine running a loom mechanism where each of the mechanisms that lift each individual warp strand is identical and embodies rule 30 and ... can it be done?
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32) simplest thermoacoustic engine show it needs hot and cold, but you know bar... it's not so transparent how the damm thing works. better to show someting with cylinders where the air actually expands and contracts. hmmm... anyway can you make one that you can run on heat cool enough for kids to play with and they can see that you can't surround it totally with heat but need hot cold?
33) benard convection: how to show? hmm it appears to require rather exacting requirements? i don't think so but the cells are small. would have to use magnifier, it wouldn't really mean much to kids wold it? see this petrie dish of fluid, then you what? turn a dial? how show you are actually heating it? how much heat do i need, what source can i use, do i need enough heat to burn someone? again i want to show that if you heat top and bottom it doesn't work. in all of these i need to show the need for hot cold.
make one 2 inches by a few feet and have the kids control things to start heating it and see...
now i was going to say can i get convection going in a big container and put a paddlewheel in there belted to another gear on top and show that stuff is swirling, that it can do work? how do i show hot cold with that arrangement? what if i made a glass container closed at top with paddle wheel shaft coming out the top and i can heat or cool the top and bottom?
what can i do to get close to what jupiter looks like? something that produces vortex streets.. layer of oil on water produces colors depending on thickness.. if i get complicated patterns going on the water below them will it modulate the thickness enough to show patterns?
33.5) lava lamp is bascially sloppy benard convection and way cool. and it's big, and it's slow, and we should be able to show and convince that the top needs to be cooler than the bottom!
Saturday, May 1, 2010
Monday, May 18, 2009
List of Representative Labs
back to top
I) LIFE
6) Key Out 100 Plants In A Local Park
2) collect insects and watch their behavior in a terrarium
4.5) 270 Skills That a Honeybee Has
VI) COMPUTERS
8)from logic gates to computer
61.2) write simple computer programs in machine code:
61.3) program conway life, mandelbrot, and lorenz in lego bot
9) show them well programmed lego bots
I) SO BACK TO CRITTERS FOR HELP
16) watch videos of animal development
II) CELLULAR LIFE
22) watch single cell pond creatures [hr]
27) molec video inner life of cell [10min] more?
25) grow oscillatoria in water and glass jar.
III) WHAT IS THE MOLECULAR WORLD?
73.2) brownian motion: .
73.3) monomolecular lipid layer:
72.2) show how many ways an ethanol molecule can respond
31.2) Distributed Brownian Motion Machinery: Clathrin Coated Pits
44) Play With A Candle Flame
IV) DISSIPATIVE STRUCTURES: FLOW OF ENERGY THROUGH SYSTEMS CREATES PATTERNED DYNAMISM
64.2) chaotic waterwheel, thermostat and heater, door buzzer [hr]
33) show steam engine (with governer?)
34) Then Benard convection
42) BZ reaction :
44) play with a flame: [hr]
V) MATHEMATICAL DYNAMICAL SYSTEMS: EASY LABORATORY, ALL YOU NEED IS PENCIL, PAPER, COMPUTER
48) John Horton Conway's game of life
53) and rule 30, 110
56) 3n+1:
57) e/o fibo system:
58)logistic equation to mandelbrot set:
60) lorenz attractor:
VII) EVEN AT EQUILIBRIUM: PHYSICAL AND CHEMICAL PATTERN FORMATION
74) show periodic chart with samples of diff elements
76) phases of sulfur:
75) and breath on a window pane: ditto for water molecules
70) mineral exhibit 2000 minerals for free
VIII) IT ALL COMES FROM MATH
87) enumeration of finite graphs:
81) classification of finite simple groups:
IX) PUTTING IT ALL BACK TOGETHER: EVOLUTIONARY BIOLOGY
96) Tierra
X) THE FINAL FRONTIER: CAN WE UNDERSTAND HOW GEOCHEMISTRY CAN BECOME LIFE?
98) Ecosystem Of Reproducing Candle Wicks?
99) Self Sustaining Ecosystem Of Reproducing Chemical Robots?
100) Chemical Origin Of Life
XI) MIND?
XII) SUPERORGANISMS
I) LIFE
6) Key Out 100 Plants In A Local Park
2) collect insects and watch their behavior in a terrarium
4.5) 270 Skills That a Honeybee Has
VI) COMPUTERS
8)from logic gates to computer
61.2) write simple computer programs in machine code:
61.3) program conway life, mandelbrot, and lorenz in lego bot
9) show them well programmed lego bots
I) SO BACK TO CRITTERS FOR HELP
16) watch videos of animal development
II) CELLULAR LIFE
22) watch single cell pond creatures [hr]
27) molec video inner life of cell [10min] more?
25) grow oscillatoria in water and glass jar.
III) WHAT IS THE MOLECULAR WORLD?
73.2) brownian motion: .
73.3) monomolecular lipid layer:
72.2) show how many ways an ethanol molecule can respond
31.2) Distributed Brownian Motion Machinery: Clathrin Coated Pits
44) Play With A Candle Flame
IV) DISSIPATIVE STRUCTURES: FLOW OF ENERGY THROUGH SYSTEMS CREATES PATTERNED DYNAMISM
64.2) chaotic waterwheel, thermostat and heater, door buzzer [hr]
33) show steam engine (with governer?)
34) Then Benard convection
42) BZ reaction :
44) play with a flame: [hr]
V) MATHEMATICAL DYNAMICAL SYSTEMS: EASY LABORATORY, ALL YOU NEED IS PENCIL, PAPER, COMPUTER
48) John Horton Conway's game of life
53) and rule 30, 110
56) 3n+1:
57) e/o fibo system:
58)logistic equation to mandelbrot set:
60) lorenz attractor:
VII) EVEN AT EQUILIBRIUM: PHYSICAL AND CHEMICAL PATTERN FORMATION
74) show periodic chart with samples of diff elements
76) phases of sulfur:
75) and breath on a window pane: ditto for water molecules
70) mineral exhibit 2000 minerals for free
VIII) IT ALL COMES FROM MATH
87) enumeration of finite graphs:
81) classification of finite simple groups:
IX) PUTTING IT ALL BACK TOGETHER: EVOLUTIONARY BIOLOGY
96) Tierra
X) THE FINAL FRONTIER: CAN WE UNDERSTAND HOW GEOCHEMISTRY CAN BECOME LIFE?
98) Ecosystem Of Reproducing Candle Wicks?
99) Self Sustaining Ecosystem Of Reproducing Chemical Robots?
100) Chemical Origin Of Life
XI) MIND?
XII) SUPERORGANISMS
Complexity Lab Manual Introduction version8
back to top
I) LIFE
If the question is, can life be simply a property of chemistry, then lets start off by exploring how complex life is. Lets go out there into a field or a park or woods or roadside and look at the plants. There are different kinds! I challenge you: can you find me 100 different kinds in an hour?
We can! In order to keep track we will tape some representative samples of each to pages in our plant press and in order to tell whether one is different from another, we will have to look closely. The leaves are arranged on the stems differently. some leaves have teeth or lobes. some are hairy, some smooth, some waxy.
Some of the plants are flowering, some have 4 petals, some 5, some 6.. some just a whole lot. some have 2 stamens, some have 3 or 5 or 10. there is every which way combinations. some have hairs below the flowers. some of the hairs (look REALLY closely with a hand lens) have sticky blobs on the tips!
Some of the plants are in seed, the seeds also have details, some have bumps, some have stems attached to them, some have hairs attached to the stems, some of the hairs (hand lenses again) are barbed... (6) Key Out 100 Plants In A Local Park
So far, we've found and described over 2 million different kinds of living plants, animals and microorganisms on this planet Earth. We can distinguish SO MUCH variety because there are SO many details in each organism to see. As far in as we look, with hand lens, with microscope, there are more and more details.
How does life become so detailed?
Surely one of the most interesting details is how animals behave. Lets go find some insects and keep them in a terrarium and play with them and let them eat and hop, fly around and watch how complex their behaviors are (lab2). You can do an ant colony, or a grasshopper or watch an observation beehive.
Don't be afraid to spend months or years watching and taking notes! Scientists have done this. For instance as of 1980, we've found 260 different behaviors in honeybees alone! In our own lives too, we have complex and subtle behaviors, but we don't usually give it much thought.
(4.5) List of 260 Skills That a Honeybee Has
To bring these observations to stark light, lets ask the question this way: what if i wanted to make a little robot that could mimic a honeybee with all those 260 amazing behaviors that a honeybee is capable of?
II) COMPUTERS
In the last 60 years, since WWII, we've begun to attempt mimicking life, by building computers to do computations that we are good at. We've even expanded to writing programs for things that no animal can do. We've even begun to build robots to physically mimic the capabilities of animals.
The levels of organization, complexity needed to do this is immense. Lets start off by looking at a digital electronics manual and notice how we can build a logic gate out of a few transistors, from 2 to 10 of them. Logic gates can do things like turn on only if two of its inputs are on (AND gate), or turn on only if its two inputs are different (XOR gate), or turn on if its input is off, and turn off if its input is on (NOT gate). Clever. We can build things out of these:
if we hook up a NOT gate to a piezoelectric crystal and capacitor so that the output of the NOT gate feeds back into its input with a delay. We get a logical inconsistency: if the gate through random static turns on, the signal is fed to its input and turns the gate off! This signal will feed back through and turn the gate back on and that...
It oscillates, the crystal helps it keep precise time, now we have a clock.
We can hook up more gates together and get a simple memory, if we signal it while it's input is on, it will remain on, if we signal it while its input is off, it will remain off.
now we can hook up a bunch of these together with more logic gates and put the clock input in and we can build a counter which in binary can count up to 8: 000, 001, 010, 011, 100, 101, 110, 111, 000, each digit feeds back to the input of the next digit with some xor gates to make that digit flip...
On and on it goes. we can build an addition circuit, a circuit that tells us whether binary number is bigger than another... the possibilities are endless.
we can put lots of memory bits together with decoders and make a long computer memory.
we can take our addition and comparison circuits and combine them with decoder circuits and the clock circuit to make a central processing unit for a computer
Notice the hierarchical levels. look at the pictures. a modern microprocessor CPU will have 1000s of circuits in it, millions of memory bits and gates...
(8) from logic gates to computer
The complexity doesn't stop there. Once we have our computer we can start programming it. Programming is easier than hooking circuits together and less technical so that we can build even more complexity.
Lets write a program in the machine code of our computer to sort a list of numbers. lets write a program to do a binary search for a number in the list and that tells us if it's there and how far along the list it is. we will explore a few of the basic building blocks of programs.
(61.2) write simple computer programs in machine code:
Now lets write longer programs. Notice that we will do it by 'chunking' them up into simpler processes which we've already written. This hierarchy is similar to the one we used to build up our computer from transistors. at each stage we have more complex parts to work with. (This process will become important if we want to discuss the origins of life from simple chemistry, simple atoms and molecules...)
(61.3) program John Horton Conway's game of life, Mandelbrot set, and Lorenz attractor
After you've gotten this taste, we will look at Lego Robots programmed to do complex tasks like chase each other, look for wall outlets to plug into or even play a game of soccer! Notice that the programs for these critters are THOUSANDS of lines long. They are made of HUNDREDS of smaller subroutines.
9) show them well programmed Lego bots
So can we program a Lego robot to even attempt to do what a honeybee can do? No. Well, at least we have some hints as to HOW COMPLEX a honeybee must be inside.
I) BACK TO LIVING CRITTERS
Scientists have dissected honeybees and have found that it IS complex inside. There are thousands of parts in there. WOW.
Imagine the process, the factories involved to build honeybee robots!
But honeybees aren't built in factories, they seem to develop from eggs, and when they hatch they get fed some pollen and presto, in 15 days a pristine complex honeybee. HOW? Well, we've managed to watch how animals develop, lets watch a video.
(16) watch videos of animal development
What did we learn from the video? The honeybee starts off as a cell. And then that cell splits into two, and then 4 and then 8 and then... 1024 of them. by now the cells are a little different than each other because that original cell was not simple, it had structures inside it. And now the cells start moving around and sensing each other and eating yolk and splitting some more, and soon they arrange themselves into more and more complicated structures, tissues, organs (more hierarchy) until we have a honeybee.
And even in adult animals, cells are still crawling around sensing things that are out of place and fixing things. Did you know that as you sit there and work on these labs, your neurons are sending out pseudopods all over your brain looking for new neurons to chat with? Is that how your personality grows and changes?
So we see that what makes us animals and plants marvelous is that we are colonies of living celled beings. And now the question: What are they?
II) CELLULAR LIFE
Well, lets watch some. Some animals are made entirely of a single cell only. When it reproduces and splits apart, the two cells don't stay joined to make an animal, but go off on their own separate ways.
There are lots of single celled critters in pond water, lets look (lab 22). These cells are small, calculate how small, calculate how many would fit inside a honeybee. Yet, they are complex. See how many of the insect behaviors or honeybee behaviors you can catch some of these little guys carrying out. Searching for food, exploring, eating, swimming from trouble, swimming from or towards light, finding a place to settle.
(22) watch single cell pond creatures
But the real complexity lies in the behavior inside: digesting, calculating, regulating water concentration, growing, finding mates, etc...
So how do cells work? what are they? The bigger ones seem to have fluids flowing inside, and parts too, can we watch with a higher magnification? It's difficult, but scientists HAVE taken them apart and looked, here's an animated video of SOME of what's going on inside (lab 27). Notice the video leaves out the most important part! All those crazy molecules are surrounded by and interacting with little water molecules and water molecules help give the whole cell it's structure and help bounce all the parts around into their right places.
27) molecular video "inner life of cell"
What REALLY is all that made of? How do cells get it all in there? Lets grow some algae in only distilled water in a glass jar and see what happens. (lab 25) It grows! what on earth does it make itself out of? water? air bubbles? glass? where does the green come from? where does all the machinery come from?
25) grow oscillatoria in water and glass jar
We are going to have to go in yet another level! molecules, chemistry!
We will watch for two things: where does the dynamism come from and where does the structures come from?
III) WHAT IS THE MOLECULAR WORLD?
When the question arises "how can life be JUST chemistry" I realize how little about chemistry the average person out of school knows. It is not JUST chemistry at all, but AMAZINGLY CHEMISTRY. Lets look. The first surprise is how MANY molecules there ARE in a single celled critter to make him work. Now we are beginning to observe physics without life in it, what can it do?
lets dump a few finely crushed paint flakes into water and boil it to kill all possible life in it and then watch under the microscope. What we will see after it all settles is that the tiny flakes are suspended in the water and are jiggling all around in crazy paths in what is called (after its discoverer) Brownian motion.
What's making them move? If we cool the water do they move less and as we heat the water do they move more (of course if we heat too much it will boil but that's another lab (34)) What we ultimately learn in physics is that heat is the motion of molecules and the paint fleck is jiggling around because many many tiny water molecules are banging into it. (lab 72.3)
Einstein showed how we can calculate the number of water molecules by observing this jiggling and Perrin did the observations and did the calculation: about 6X10^24 molecules in a cup of water! that's: 6,000,000, 000,000,000, 000,000,000!! 6million billion billion. too much to think about, so calculate how many would fit in one of the single celled critters you watched. do some division.
Still 10 billion billion in the largest cells! and a 100 billion in the smallest. you can try lab 18 to try to imagine a how much a billion is.
Another way to find out how small molecules are and how many there are is to spill a tiny drop of cooking oil onto a large bowl of still water. how small a drop do you need to cover the whole bowl? hard to do, might have to use a swimming pool indoors with no wind or waves. (lab 73.3)
from the Brownian motion experiment we realize also not only that there are so many molecules but that they are bouncing into each other 10^10 times a second so that's a lot of activity we get for free, before we even do any biology or chemistry or get energy flowing through things.
So what are molecules like? If we learn organic chemistry we find out that even a simple one like ethanol (alcohol) has complex behavior, it is like a little fuzzy sensing, calculating machine that can sense other molecules, distinguish between them and calculate how to interact with them in different temperatures, solvents, pH... Based on these calculations, It can absorb energy, connect with the other molecule, come apart, give off energy... (lab 72.2)
In fact we can watch a simulated movie of how these tiny machines can wiggle around each other with Brownian motion to come together and perform complex tasks. We can put a dozen different kinds of molecules together and they will be able to self assemble membranes into cages which catch food packets in cells and bring them inside. These are the Clathrin coated pits (31.2) Distributed Brownian Motion Machinery: Clathrin Coated Pits
Finally, if we get can tear a few electrons off of some molecules with intense heat and put them in oxygen, we can get a candle flame going. Play with it a little while and we will look at the complex set of reactions that are occurring. Even without life, we get a system of chemical reactions reminiscent of cellular metabolism! (lab 44)
IV) DISSIPATIVE STRUCTURES: FLOW OF ENERGY THROUGH SYSTEMS CREATES PATTERNED DYNAMISM
Now that we know that the molecular clay is is so different than what we think of us clay to be sculpted or blocks to be built with, that the molecular world is intensely detailed and fluid, we are ready to ask: what kind of things are living cells. for if they are not made of inert motionless bricks, not inert dumb clay already they are interesting.
Now the Brownian motion is completely random, complete chaos, trillions of molecules doing their own thing, not coordinated. Where does the coordination come from, the order? Energy flow! When energy flows through a system it causes work to be done, patterns to form out of chaos and stability to happen.
Lets start with an obvious kind of energy flow. lift a bucket of water off the ground to a height of 4 feet. That took work on your part, you burned food to do it, and now that bucket of water has potential energy in it. It can do work. We will build water wheel below it on a bicycle wheel and let falling water spin the wheel. that's the work it does and the pattern it creates. As long as there's still water in the bucket, the wheel will spin. (lab 64.2.1)
Another example is a thermostat. build a waterwheel out west, and instead of spinning a bicycle wheel, spin an electric generator and create electricity. let that electric energy flow through a heater and we get warm. but wait, TOO warm, it needs some control. Let's look at our thermostat.
We Put a bimetallic strip controlling a mercury switch in the path of the electric current. when the heat heats the two metals they bend differently and the strip expands, tilting the mercury which falls away from it's electric contact, and the current is cut.
now the heater is off and the room cools, the strip cools, and thus contracts and the mercury then tilts the other way falls into the contact and starts the heater again. This system will oscillate back and forth (hopefully in smaller and smaller oscillations) till it zeros in on the temperature we set it at by our initial tilt of the whole system.
This is an example of a system far from thermodynamic equilibrium. It has energy flowing through it. some energy is dissipated as heat even in the thermostat (useless heat). And it maintains itself in a state of order.
It does so by a process called negative feedback. MORE heat than required makes the circuit go off creating LESS heat. if we had hooked up the mercury ball the opposite way so that as it heats up it tilts further towards the contact or as it cools off it tilts away then the system would either get hotter and hotter... or colder and colder, that would be POSITIVE feedback, or runaway, instead of the system zeroing in on it's goal. (the goal we set for it) (lab 64.2.2)
Another system that works like this with negative feedback is a door buzzer. the same negative feedback controlling a switch turning it off is involved. this time we design it so that it achieves a steady state of oscillation and makes a sound. Many musical instruments work this way also. (lab 64.2.3)
One more interesting twist as these are really kind of boring repetitive behaviors. Back to our waterwheel. we will poke holes in the bottom of the cups of our waterwheels and see what happens. Interesting chaos! (lab 64.2.4)
(64.2) chaotic waterwheel, thermostat and heater, door buzzer
Back to heat flow. Almost all visible activity on Earth is due to heat flow. The sun is about 5700degrees (that's Celsius, in Fahrenheit it's about 10,000 degrees) hot at the surface (enough vaporize any substance) and that temperature causes it to glow white light at us. This light shines on the Earth and causes it to warm up. It is a common misconception that what enables life on earth to exist, to act, is that it is bathed in this sunlight. Our next lab will show that this misconception is GROSSLY untrue.
Lets take this mini steam engine and light a fire under it. There it goes pumping away! You might suppose that the heat of the fire is what makes it run. But if i were to put it in an oven so that the whole engine is at the temperature of the fire, you might think, more heat even better!
NO. it stops running. On further investigation you find that your engine has TWO pistons one in contact with the hot flame, the other in contact with the cool air outside. It is the alternation of expansion of one piston (in the flame) and compression of the other piston (in the cold) that makes the work happen. essentially heat energy is flowing from the flame to the cold air.
And the same on earth. the only reason your air is cooler than the sun is that the earth is not totally surrounded by suns! there is much cooler outer space surrounding most of the earth. (if the earth were surrounded completely by suns it would eventually become as hot as the sun and completely vaporize!)
And of course we could hook this rotating engine to all sorts of machines, even a loom, and make interesting patterns with it. This is the essence of far from equilibrium systems, which we also call dissipative systems (since they all dissipate heat), that energy must flow THROUGH them from a source of high potential energy to a sink of low potential energy. In between interesting stable pattern occurs.
(33) show steam engine
We can reduce this to the simplest system without machinery: Benard convection. We will set up a shallow petri dish of water (or some more appropriate fluid) and heat it from below. the water will begin to warm on the bottom and thus expand and become less dense and flow to the top higgledy piggledy. Of course that displaces the water at the top which must sink. Note that in order for any of this to happen there must again, be TWO temperatures, hot and cold.
As we keep increasing the temperature of the flame below you would expect the water to move more and more violently till it's a roiling boil. Correct... except for one thing! at a certain range of optimal temperatures you get the benard convection cells arranging themselves into a stable interesting hexagonal pattern. water in the centers rises and then flows out and falls at the edges. You can play with the cells, mess 'em up, they are stable.
(34) Then Benard convection
All the interesting weather patterns on earth are formed because of convection (and rotation of earth see labs 35-39)
Heat and electricity are not the only forms of energy flow, there is also chemical energy flow. energy is passed from molecule to molecule as they react and move around in their brownian motion. In this example, the Bellousov Zhazotinsky reaction (lab 42) we will see that as energy flows from the molecules of high energy potential ( ) to a set of simpler molecules at low potential ( ) an interesting visual pattern of cycles proceeds. Energy flow can produce ORDER!
(42) The Beloussov Zhabotinsky reaction
Now this begins to approach what is happening in life, at root, life is a system of oxidation reduction reactions similar to these that are organized into patterns by chemical energy flow. It is important to note that the souce of the patterns is NOT the DNA! without energy flow running complex chemical reactions to replicate and repair the DNA, the DNA itself will decay as do all things eventually at equilibrium.
We can even combine heat energy flow: convection, with chemical energy flow and we get a flame (lab 44). Note the diagram of the complex cycles of chemicall reactions that occur in even the simplest methane flame.
(44) play with a flame
And finally lets go back to our waterwheel and add in some funcky feedbacks. poke holes in the bottom of our cups mounted to the bicycle wheel. what happens? crazy chaos! (lab 64.2)
Now, these labs bring us to the essence of complexity lab. We start with simple systems with random motions and let something simple like energy flow throgh them and we get complex patterns. Is this really possible to go from the simple to the complex? Throughout much of human intellectual history the answer was NO! The universe for early people's begins most complex, most perfect from an eternal MIND and THEN slowly runs down to simpler and messier patterns.
Now this certainly seems to be the case in most ordinary situations, things run down. And it is correct that we even have the 2nd law of thermodynamics to formalize it: In a closed system (no energy coming in or out, no things coming in or out) all order eventually runs down to randomness. And that is in fact what happened with our engines and convections and BZ reactions. In the TOTAL system of fuel, cold air, and game in between, the system DID in fact eventually run down to less ordered state. instead of fuel vs cold air, we got ashes and carbon dioxide in luke warm air.
BUT.. for a PERIOD of time in a SUBsystem of that closed system (our engine or candle flame or the convecting fluids, or the patterns in the BZ reaction) which was open to energy flow from and to the larger system, became MORE ordered. That is possible under the 2nd law. While the whole system runs down, an open subsystem with energy flowing through it can become more ordered for a while. In fact the increase in order of the subsystem is OFFSET by a LARGER decrease in order in the larger system.
So here we begin to see examples of systems that can become more complex from simple beginnings. We see that even the evolution of complex beings from simpler beings does NOT contradict the 2nd law of thermodynamics that in the LONG run the entire system of sun, earth space will run down to less complex.
V) MATHEMATICAL DYNAMICAL SYSTEMS: EASY LABORATORY, ALL YOU NEED IS PENCIL, PAPER, COMPUTER
Now those were difficult processes to set up and analyse. The flame alone is still not completely analysed in terms of all the reactions involved, and we've certainly only begun understanding how cells work in all their detail. So next we go to paper and pencil (and computer) math games.
And again we will ask: if we start off with a simple set of rules and let them automatically follow each other, can we get something more complex than the simple set of rules? The ancients certainly had the ability to play many of the simple games we are about to explore, and surprisingly they did not. Perhaps their firm believe that complexity could not come from simplicity prejudiced them from even trying.
So lets dive into John Horton Conway's game of life, (lab 48), Stepen Wolframs rule 30 linear cellular automata (lab53), collatz's 3n+1 game (lab 56) , and my own even odd fibonaci game (57) and see what kind of glorious patterns can come out from simple pencil and paper calculations of simple rules.
(48) John Horton Conway's Game Of Life
(56) 3n+1: a simple number game with complex behavior
You will see that some of the rules create much order like 3n+1, others create extremely chaotic complexity like rule 30! and others create a subtle mix between some complexity and total chaos as in conway's life and my fibonacci game.
Another way to look at these games is to see them as simulations for the complex systems we played with above. In fact scientists are trying to gain insight into complex systems of chemical reactions like flames and life by simulating them with cellular automata.
Another kind of game that also can be used to simulate systems like the Benard convection and the Bz reaction are systems pleayed not with integers or discrete cells, but on the continuous real numbers. Get a load of what we can build from the simple iterated logistic equation (lab 58). Blow your mind from the Mandelbrot set created by simple iterations of a similar system (lab 58.2)
58) Iterated logistic equation to Mandelbrot set
Finally play with the lorenz attractor, best done with computer. It actually has similar properties to both Beneard convection and our crazy chaotic waterwheel. Do you see? (lab 60)
VII) EVEN AT EQUILIBRIUM: PHYSICAL AND CHEMICAL PATTERN FORMATION
So why is the Earth so interestiing, with it's rocks and minerals and weather and life? Well, we saw most of the mechanics that give us interesting weather, but where does all the DETAILS of life come from? those 100 different plants with all their parts. Those crazy complex molecular machines we saw inside living cells? The fact is that even without energy flow forming patterns, physics, chemistry, mathematics itself, still gives us complex patterns for free. No evolution required, no mind required.
Lets start out with a trip to a mineralogy exhibit at a museum (lab 70). these are all structures at equilibrium, they are not like the BZ reaction (though SOME of the formations you will see ARE the results of far from equilibrium processes that became frozen in as they developed). All this mineral diversity (there are more than 4000 different kinds) did NOT come from evolution, it comes from phsysics and chemistry! It comes from the capabilities of different kinds of atoms in the periodic chart (lab 74). Explore the radically different behaviors of protons, neutrons and electrons, just becase there are different nuumbers of them. Or different geometries, or different solutions to differential equations?
Again when we take water molecules and separate them into vapour in our breath and then we exhale and they drift about into clouds and come down as rain (a different state as vapour) and the raindrops take on a distinct shape because of intermolecular bonds)... or even more drastically when we breath on a cold window pain we get those cool complex jack frost patterns... How? (lab 75)
At this stage in our labs, we are getting close to the heart of the matter: Mathematics. before chemistry, before physics, there is math:
VIII) IT ALL COMES FROM MATH
Now, we've already seen crazy examples of order from simple mathematical rules, but those were kind of complicated since we had to keep iterating the system to build up the complexity, but what about just proposing a simple system of logical rules and see what must be true about a system that follows them?
The definition of a prime number is simple: any number who's only factors are itself and one is a prime number. 7=7*1 is prime, 12=6*2 or 3*4 is not. well lets list the prime numbers:
2 3 _ 5 _ 7 _ _ _ 11 _ 13 _ _ _ 17 _ 19 _
_ _23 _ _ _ _ _ 29 _31 _ _ _ _ _ 37 _ _ _
41 _ 43 _ _ _ 47 _ _ _ _ _ 53 _ _ _ _ _ 59_
Is there any pattern to them? The gaps are funny. Is it chaotic or is there a pattern? It seems chaotic, but not totally so... The number of primes less than N tends to N/ln(N) (lookup the "prime number theorem") and look there seem to be pairs 5;7, 11;13, 17;19, 29;31, 41;43... as far as we've looked these pairs happen, but no one can prove that they keep occuring...
Lets create some more exciting patterns out of simplicity, lets enumerate the finite graphs out of balls of clay and toothpics (lab 87)
the rules: a ball of clay at each end of the toothpick. all toothpicks same length, can't bend them, can't connect two toothpicks together at BOTH ends like O====O.
what happens? the shapes we get. we get loops, we get interlocked loops, we get 2 dimensions, we get 3 dimensions.... note that this doesn't require OUR MINDS to construct. this is pure math. If you don't believe it, i suppose we could build an experiment to shake these parts and sort the results by weight and get all these patterns.
This creativity of mathematics shows you where the creativity to make all those crazy states of matter and minerals from simply protons, neutrons and electrons comes from.
A more involved example of this type of interesting but not chaotic complexity coming from simple rules is the classification of all finite simple grouups.
(81) classification of finite simple groups
IX) PUTTING IT ALL BACK TOGETHER: EVOLUTIONARY BIOLOGY
...
I) LIFE
If the question is, can life be simply a property of chemistry, then lets start off by exploring how complex life is. Lets go out there into a field or a park or woods or roadside and look at the plants. There are different kinds! I challenge you: can you find me 100 different kinds in an hour?
We can! In order to keep track we will tape some representative samples of each to pages in our plant press and in order to tell whether one is different from another, we will have to look closely. The leaves are arranged on the stems differently. some leaves have teeth or lobes. some are hairy, some smooth, some waxy.
Some of the plants are flowering, some have 4 petals, some 5, some 6.. some just a whole lot. some have 2 stamens, some have 3 or 5 or 10. there is every which way combinations. some have hairs below the flowers. some of the hairs (look REALLY closely with a hand lens) have sticky blobs on the tips!
Some of the plants are in seed, the seeds also have details, some have bumps, some have stems attached to them, some have hairs attached to the stems, some of the hairs (hand lenses again) are barbed... (6) Key Out 100 Plants In A Local Park
So far, we've found and described over 2 million different kinds of living plants, animals and microorganisms on this planet Earth. We can distinguish SO MUCH variety because there are SO many details in each organism to see. As far in as we look, with hand lens, with microscope, there are more and more details.
How does life become so detailed?
Surely one of the most interesting details is how animals behave. Lets go find some insects and keep them in a terrarium and play with them and let them eat and hop, fly around and watch how complex their behaviors are (lab2). You can do an ant colony, or a grasshopper or watch an observation beehive.
Don't be afraid to spend months or years watching and taking notes! Scientists have done this. For instance as of 1980, we've found 260 different behaviors in honeybees alone! In our own lives too, we have complex and subtle behaviors, but we don't usually give it much thought.
(4.5) List of 260 Skills That a Honeybee Has
To bring these observations to stark light, lets ask the question this way: what if i wanted to make a little robot that could mimic a honeybee with all those 260 amazing behaviors that a honeybee is capable of?
II) COMPUTERS
In the last 60 years, since WWII, we've begun to attempt mimicking life, by building computers to do computations that we are good at. We've even expanded to writing programs for things that no animal can do. We've even begun to build robots to physically mimic the capabilities of animals.
The levels of organization, complexity needed to do this is immense. Lets start off by looking at a digital electronics manual and notice how we can build a logic gate out of a few transistors, from 2 to 10 of them. Logic gates can do things like turn on only if two of its inputs are on (AND gate), or turn on only if its two inputs are different (XOR gate), or turn on if its input is off, and turn off if its input is on (NOT gate). Clever. We can build things out of these:
if we hook up a NOT gate to a piezoelectric crystal and capacitor so that the output of the NOT gate feeds back into its input with a delay. We get a logical inconsistency: if the gate through random static turns on, the signal is fed to its input and turns the gate off! This signal will feed back through and turn the gate back on and that...
It oscillates, the crystal helps it keep precise time, now we have a clock.
We can hook up more gates together and get a simple memory, if we signal it while it's input is on, it will remain on, if we signal it while its input is off, it will remain off.
now we can hook up a bunch of these together with more logic gates and put the clock input in and we can build a counter which in binary can count up to 8: 000, 001, 010, 011, 100, 101, 110, 111, 000, each digit feeds back to the input of the next digit with some xor gates to make that digit flip...
On and on it goes. we can build an addition circuit, a circuit that tells us whether binary number is bigger than another... the possibilities are endless.
we can put lots of memory bits together with decoders and make a long computer memory.
we can take our addition and comparison circuits and combine them with decoder circuits and the clock circuit to make a central processing unit for a computer
Notice the hierarchical levels. look at the pictures. a modern microprocessor CPU will have 1000s of circuits in it, millions of memory bits and gates...
(8) from logic gates to computer
The complexity doesn't stop there. Once we have our computer we can start programming it. Programming is easier than hooking circuits together and less technical so that we can build even more complexity.
Lets write a program in the machine code of our computer to sort a list of numbers. lets write a program to do a binary search for a number in the list and that tells us if it's there and how far along the list it is. we will explore a few of the basic building blocks of programs.
(61.2) write simple computer programs in machine code:
Now lets write longer programs. Notice that we will do it by 'chunking' them up into simpler processes which we've already written. This hierarchy is similar to the one we used to build up our computer from transistors. at each stage we have more complex parts to work with. (This process will become important if we want to discuss the origins of life from simple chemistry, simple atoms and molecules...)
(61.3) program John Horton Conway's game of life, Mandelbrot set, and Lorenz attractor
After you've gotten this taste, we will look at Lego Robots programmed to do complex tasks like chase each other, look for wall outlets to plug into or even play a game of soccer! Notice that the programs for these critters are THOUSANDS of lines long. They are made of HUNDREDS of smaller subroutines.
9) show them well programmed Lego bots
So can we program a Lego robot to even attempt to do what a honeybee can do? No. Well, at least we have some hints as to HOW COMPLEX a honeybee must be inside.
I) BACK TO LIVING CRITTERS
Scientists have dissected honeybees and have found that it IS complex inside. There are thousands of parts in there. WOW.
Imagine the process, the factories involved to build honeybee robots!
But honeybees aren't built in factories, they seem to develop from eggs, and when they hatch they get fed some pollen and presto, in 15 days a pristine complex honeybee. HOW? Well, we've managed to watch how animals develop, lets watch a video.
(16) watch videos of animal development
What did we learn from the video? The honeybee starts off as a cell. And then that cell splits into two, and then 4 and then 8 and then... 1024 of them. by now the cells are a little different than each other because that original cell was not simple, it had structures inside it. And now the cells start moving around and sensing each other and eating yolk and splitting some more, and soon they arrange themselves into more and more complicated structures, tissues, organs (more hierarchy) until we have a honeybee.
And even in adult animals, cells are still crawling around sensing things that are out of place and fixing things. Did you know that as you sit there and work on these labs, your neurons are sending out pseudopods all over your brain looking for new neurons to chat with? Is that how your personality grows and changes?
So we see that what makes us animals and plants marvelous is that we are colonies of living celled beings. And now the question: What are they?
II) CELLULAR LIFE
Well, lets watch some. Some animals are made entirely of a single cell only. When it reproduces and splits apart, the two cells don't stay joined to make an animal, but go off on their own separate ways.
There are lots of single celled critters in pond water, lets look (lab 22). These cells are small, calculate how small, calculate how many would fit inside a honeybee. Yet, they are complex. See how many of the insect behaviors or honeybee behaviors you can catch some of these little guys carrying out. Searching for food, exploring, eating, swimming from trouble, swimming from or towards light, finding a place to settle.
(22) watch single cell pond creatures
But the real complexity lies in the behavior inside: digesting, calculating, regulating water concentration, growing, finding mates, etc...
So how do cells work? what are they? The bigger ones seem to have fluids flowing inside, and parts too, can we watch with a higher magnification? It's difficult, but scientists HAVE taken them apart and looked, here's an animated video of SOME of what's going on inside (lab 27). Notice the video leaves out the most important part! All those crazy molecules are surrounded by and interacting with little water molecules and water molecules help give the whole cell it's structure and help bounce all the parts around into their right places.
27) molecular video "inner life of cell"
What REALLY is all that made of? How do cells get it all in there? Lets grow some algae in only distilled water in a glass jar and see what happens. (lab 25) It grows! what on earth does it make itself out of? water? air bubbles? glass? where does the green come from? where does all the machinery come from?
25) grow oscillatoria in water and glass jar
We are going to have to go in yet another level! molecules, chemistry!
We will watch for two things: where does the dynamism come from and where does the structures come from?
III) WHAT IS THE MOLECULAR WORLD?
When the question arises "how can life be JUST chemistry" I realize how little about chemistry the average person out of school knows. It is not JUST chemistry at all, but AMAZINGLY CHEMISTRY. Lets look. The first surprise is how MANY molecules there ARE in a single celled critter to make him work. Now we are beginning to observe physics without life in it, what can it do?
lets dump a few finely crushed paint flakes into water and boil it to kill all possible life in it and then watch under the microscope. What we will see after it all settles is that the tiny flakes are suspended in the water and are jiggling all around in crazy paths in what is called (after its discoverer) Brownian motion.
What's making them move? If we cool the water do they move less and as we heat the water do they move more (of course if we heat too much it will boil but that's another lab (34)) What we ultimately learn in physics is that heat is the motion of molecules and the paint fleck is jiggling around because many many tiny water molecules are banging into it. (lab 72.3)
Einstein showed how we can calculate the number of water molecules by observing this jiggling and Perrin did the observations and did the calculation: about 6X10^24 molecules in a cup of water! that's: 6,000,000, 000,000,000, 000,000,000!! 6million billion billion. too much to think about, so calculate how many would fit in one of the single celled critters you watched. do some division.
Still 10 billion billion in the largest cells! and a 100 billion in the smallest. you can try lab 18 to try to imagine a how much a billion is.
Another way to find out how small molecules are and how many there are is to spill a tiny drop of cooking oil onto a large bowl of still water. how small a drop do you need to cover the whole bowl? hard to do, might have to use a swimming pool indoors with no wind or waves. (lab 73.3)
from the Brownian motion experiment we realize also not only that there are so many molecules but that they are bouncing into each other 10^10 times a second so that's a lot of activity we get for free, before we even do any biology or chemistry or get energy flowing through things.
So what are molecules like? If we learn organic chemistry we find out that even a simple one like ethanol (alcohol) has complex behavior, it is like a little fuzzy sensing, calculating machine that can sense other molecules, distinguish between them and calculate how to interact with them in different temperatures, solvents, pH... Based on these calculations, It can absorb energy, connect with the other molecule, come apart, give off energy... (lab 72.2)
In fact we can watch a simulated movie of how these tiny machines can wiggle around each other with Brownian motion to come together and perform complex tasks. We can put a dozen different kinds of molecules together and they will be able to self assemble membranes into cages which catch food packets in cells and bring them inside. These are the Clathrin coated pits (31.2) Distributed Brownian Motion Machinery: Clathrin Coated Pits
Finally, if we get can tear a few electrons off of some molecules with intense heat and put them in oxygen, we can get a candle flame going. Play with it a little while and we will look at the complex set of reactions that are occurring. Even without life, we get a system of chemical reactions reminiscent of cellular metabolism! (lab 44)
IV) DISSIPATIVE STRUCTURES: FLOW OF ENERGY THROUGH SYSTEMS CREATES PATTERNED DYNAMISM
Now that we know that the molecular clay is is so different than what we think of us clay to be sculpted or blocks to be built with, that the molecular world is intensely detailed and fluid, we are ready to ask: what kind of things are living cells. for if they are not made of inert motionless bricks, not inert dumb clay already they are interesting.
Now the Brownian motion is completely random, complete chaos, trillions of molecules doing their own thing, not coordinated. Where does the coordination come from, the order? Energy flow! When energy flows through a system it causes work to be done, patterns to form out of chaos and stability to happen.
Lets start with an obvious kind of energy flow. lift a bucket of water off the ground to a height of 4 feet. That took work on your part, you burned food to do it, and now that bucket of water has potential energy in it. It can do work. We will build water wheel below it on a bicycle wheel and let falling water spin the wheel. that's the work it does and the pattern it creates. As long as there's still water in the bucket, the wheel will spin. (lab 64.2.1)
Another example is a thermostat. build a waterwheel out west, and instead of spinning a bicycle wheel, spin an electric generator and create electricity. let that electric energy flow through a heater and we get warm. but wait, TOO warm, it needs some control. Let's look at our thermostat.
We Put a bimetallic strip controlling a mercury switch in the path of the electric current. when the heat heats the two metals they bend differently and the strip expands, tilting the mercury which falls away from it's electric contact, and the current is cut.
now the heater is off and the room cools, the strip cools, and thus contracts and the mercury then tilts the other way falls into the contact and starts the heater again. This system will oscillate back and forth (hopefully in smaller and smaller oscillations) till it zeros in on the temperature we set it at by our initial tilt of the whole system.
This is an example of a system far from thermodynamic equilibrium. It has energy flowing through it. some energy is dissipated as heat even in the thermostat (useless heat). And it maintains itself in a state of order.
It does so by a process called negative feedback. MORE heat than required makes the circuit go off creating LESS heat. if we had hooked up the mercury ball the opposite way so that as it heats up it tilts further towards the contact or as it cools off it tilts away then the system would either get hotter and hotter... or colder and colder, that would be POSITIVE feedback, or runaway, instead of the system zeroing in on it's goal. (the goal we set for it) (lab 64.2.2)
Another system that works like this with negative feedback is a door buzzer. the same negative feedback controlling a switch turning it off is involved. this time we design it so that it achieves a steady state of oscillation and makes a sound. Many musical instruments work this way also. (lab 64.2.3)
One more interesting twist as these are really kind of boring repetitive behaviors. Back to our waterwheel. we will poke holes in the bottom of the cups of our waterwheels and see what happens. Interesting chaos! (lab 64.2.4)
(64.2) chaotic waterwheel, thermostat and heater, door buzzer
Back to heat flow. Almost all visible activity on Earth is due to heat flow. The sun is about 5700degrees (that's Celsius, in Fahrenheit it's about 10,000 degrees) hot at the surface (enough vaporize any substance) and that temperature causes it to glow white light at us. This light shines on the Earth and causes it to warm up. It is a common misconception that what enables life on earth to exist, to act, is that it is bathed in this sunlight. Our next lab will show that this misconception is GROSSLY untrue.
Lets take this mini steam engine and light a fire under it. There it goes pumping away! You might suppose that the heat of the fire is what makes it run. But if i were to put it in an oven so that the whole engine is at the temperature of the fire, you might think, more heat even better!
NO. it stops running. On further investigation you find that your engine has TWO pistons one in contact with the hot flame, the other in contact with the cool air outside. It is the alternation of expansion of one piston (in the flame) and compression of the other piston (in the cold) that makes the work happen. essentially heat energy is flowing from the flame to the cold air.
And the same on earth. the only reason your air is cooler than the sun is that the earth is not totally surrounded by suns! there is much cooler outer space surrounding most of the earth. (if the earth were surrounded completely by suns it would eventually become as hot as the sun and completely vaporize!)
And of course we could hook this rotating engine to all sorts of machines, even a loom, and make interesting patterns with it. This is the essence of far from equilibrium systems, which we also call dissipative systems (since they all dissipate heat), that energy must flow THROUGH them from a source of high potential energy to a sink of low potential energy. In between interesting stable pattern occurs.
(33) show steam engine
We can reduce this to the simplest system without machinery: Benard convection. We will set up a shallow petri dish of water (or some more appropriate fluid) and heat it from below. the water will begin to warm on the bottom and thus expand and become less dense and flow to the top higgledy piggledy. Of course that displaces the water at the top which must sink. Note that in order for any of this to happen there must again, be TWO temperatures, hot and cold.
As we keep increasing the temperature of the flame below you would expect the water to move more and more violently till it's a roiling boil. Correct... except for one thing! at a certain range of optimal temperatures you get the benard convection cells arranging themselves into a stable interesting hexagonal pattern. water in the centers rises and then flows out and falls at the edges. You can play with the cells, mess 'em up, they are stable.
(34) Then Benard convection
All the interesting weather patterns on earth are formed because of convection (and rotation of earth see labs 35-39)
Heat and electricity are not the only forms of energy flow, there is also chemical energy flow. energy is passed from molecule to molecule as they react and move around in their brownian motion. In this example, the Bellousov Zhazotinsky reaction (lab 42) we will see that as energy flows from the molecules of high energy potential ( ) to a set of simpler molecules at low potential ( ) an interesting visual pattern of cycles proceeds. Energy flow can produce ORDER!
(42) The Beloussov Zhabotinsky reaction
Now this begins to approach what is happening in life, at root, life is a system of oxidation reduction reactions similar to these that are organized into patterns by chemical energy flow. It is important to note that the souce of the patterns is NOT the DNA! without energy flow running complex chemical reactions to replicate and repair the DNA, the DNA itself will decay as do all things eventually at equilibrium.
We can even combine heat energy flow: convection, with chemical energy flow and we get a flame (lab 44). Note the diagram of the complex cycles of chemicall reactions that occur in even the simplest methane flame.
(44) play with a flame
And finally lets go back to our waterwheel and add in some funcky feedbacks. poke holes in the bottom of our cups mounted to the bicycle wheel. what happens? crazy chaos! (lab 64.2)
Now, these labs bring us to the essence of complexity lab. We start with simple systems with random motions and let something simple like energy flow throgh them and we get complex patterns. Is this really possible to go from the simple to the complex? Throughout much of human intellectual history the answer was NO! The universe for early people's begins most complex, most perfect from an eternal MIND and THEN slowly runs down to simpler and messier patterns.
Now this certainly seems to be the case in most ordinary situations, things run down. And it is correct that we even have the 2nd law of thermodynamics to formalize it: In a closed system (no energy coming in or out, no things coming in or out) all order eventually runs down to randomness. And that is in fact what happened with our engines and convections and BZ reactions. In the TOTAL system of fuel, cold air, and game in between, the system DID in fact eventually run down to less ordered state. instead of fuel vs cold air, we got ashes and carbon dioxide in luke warm air.
BUT.. for a PERIOD of time in a SUBsystem of that closed system (our engine or candle flame or the convecting fluids, or the patterns in the BZ reaction) which was open to energy flow from and to the larger system, became MORE ordered. That is possible under the 2nd law. While the whole system runs down, an open subsystem with energy flowing through it can become more ordered for a while. In fact the increase in order of the subsystem is OFFSET by a LARGER decrease in order in the larger system.
So here we begin to see examples of systems that can become more complex from simple beginnings. We see that even the evolution of complex beings from simpler beings does NOT contradict the 2nd law of thermodynamics that in the LONG run the entire system of sun, earth space will run down to less complex.
V) MATHEMATICAL DYNAMICAL SYSTEMS: EASY LABORATORY, ALL YOU NEED IS PENCIL, PAPER, COMPUTER
Now those were difficult processes to set up and analyse. The flame alone is still not completely analysed in terms of all the reactions involved, and we've certainly only begun understanding how cells work in all their detail. So next we go to paper and pencil (and computer) math games.
And again we will ask: if we start off with a simple set of rules and let them automatically follow each other, can we get something more complex than the simple set of rules? The ancients certainly had the ability to play many of the simple games we are about to explore, and surprisingly they did not. Perhaps their firm believe that complexity could not come from simplicity prejudiced them from even trying.
So lets dive into John Horton Conway's game of life, (lab 48), Stepen Wolframs rule 30 linear cellular automata (lab53), collatz's 3n+1 game (lab 56) , and my own even odd fibonaci game (57) and see what kind of glorious patterns can come out from simple pencil and paper calculations of simple rules.
(48) John Horton Conway's Game Of Life
(56) 3n+1: a simple number game with complex behavior
You will see that some of the rules create much order like 3n+1, others create extremely chaotic complexity like rule 30! and others create a subtle mix between some complexity and total chaos as in conway's life and my fibonacci game.
Another way to look at these games is to see them as simulations for the complex systems we played with above. In fact scientists are trying to gain insight into complex systems of chemical reactions like flames and life by simulating them with cellular automata.
Another kind of game that also can be used to simulate systems like the Benard convection and the Bz reaction are systems pleayed not with integers or discrete cells, but on the continuous real numbers. Get a load of what we can build from the simple iterated logistic equation (lab 58). Blow your mind from the Mandelbrot set created by simple iterations of a similar system (lab 58.2)
58) Iterated logistic equation to Mandelbrot set
Finally play with the lorenz attractor, best done with computer. It actually has similar properties to both Beneard convection and our crazy chaotic waterwheel. Do you see? (lab 60)
VII) EVEN AT EQUILIBRIUM: PHYSICAL AND CHEMICAL PATTERN FORMATION
So why is the Earth so interestiing, with it's rocks and minerals and weather and life? Well, we saw most of the mechanics that give us interesting weather, but where does all the DETAILS of life come from? those 100 different plants with all their parts. Those crazy complex molecular machines we saw inside living cells? The fact is that even without energy flow forming patterns, physics, chemistry, mathematics itself, still gives us complex patterns for free. No evolution required, no mind required.
Lets start out with a trip to a mineralogy exhibit at a museum (lab 70). these are all structures at equilibrium, they are not like the BZ reaction (though SOME of the formations you will see ARE the results of far from equilibrium processes that became frozen in as they developed). All this mineral diversity (there are more than 4000 different kinds) did NOT come from evolution, it comes from phsysics and chemistry! It comes from the capabilities of different kinds of atoms in the periodic chart (lab 74). Explore the radically different behaviors of protons, neutrons and electrons, just becase there are different nuumbers of them. Or different geometries, or different solutions to differential equations?
Again when we take water molecules and separate them into vapour in our breath and then we exhale and they drift about into clouds and come down as rain (a different state as vapour) and the raindrops take on a distinct shape because of intermolecular bonds)... or even more drastically when we breath on a cold window pain we get those cool complex jack frost patterns... How? (lab 75)
At this stage in our labs, we are getting close to the heart of the matter: Mathematics. before chemistry, before physics, there is math:
VIII) IT ALL COMES FROM MATH
Now, we've already seen crazy examples of order from simple mathematical rules, but those were kind of complicated since we had to keep iterating the system to build up the complexity, but what about just proposing a simple system of logical rules and see what must be true about a system that follows them?
The definition of a prime number is simple: any number who's only factors are itself and one is a prime number. 7=7*1 is prime, 12=6*2 or 3*4 is not. well lets list the prime numbers:
2 3 _ 5 _ 7 _ _ _ 11 _ 13 _ _ _ 17 _ 19 _
_ _23 _ _ _ _ _ 29 _31 _ _ _ _ _ 37 _ _ _
41 _ 43 _ _ _ 47 _ _ _ _ _ 53 _ _ _ _ _ 59_
Is there any pattern to them? The gaps are funny. Is it chaotic or is there a pattern? It seems chaotic, but not totally so... The number of primes less than N tends to N/ln(N) (lookup the "prime number theorem") and look there seem to be pairs 5;7, 11;13, 17;19, 29;31, 41;43... as far as we've looked these pairs happen, but no one can prove that they keep occuring...
Lets create some more exciting patterns out of simplicity, lets enumerate the finite graphs out of balls of clay and toothpics (lab 87)
the rules: a ball of clay at each end of the toothpick. all toothpicks same length, can't bend them, can't connect two toothpicks together at BOTH ends like O====O.
what happens? the shapes we get. we get loops, we get interlocked loops, we get 2 dimensions, we get 3 dimensions.... note that this doesn't require OUR MINDS to construct. this is pure math. If you don't believe it, i suppose we could build an experiment to shake these parts and sort the results by weight and get all these patterns.
This creativity of mathematics shows you where the creativity to make all those crazy states of matter and minerals from simply protons, neutrons and electrons comes from.
A more involved example of this type of interesting but not chaotic complexity coming from simple rules is the classification of all finite simple grouups.
(81) classification of finite simple groups
IX) PUTTING IT ALL BACK TOGETHER: EVOLUTIONARY BIOLOGY
...
Monday, May 11, 2009
3n+1: A Simple Number Game With Complex Behavior
3n+1
Here is a dirt simple game that requires only 4th grade arithmetic, yet leads to a hard puzzle.
Pick a number, say 5. It's odd, so let's multiply it by 3 and add one. We get 16. That one is even so we will divide by 2. We get 8. It's even again so divide by 2. We get 4. Then we get 2. Then we get 1. Oh, that's an odd number, so multiply by 3 and add one. We get 4. Then we get 2. Hey wait a minute, we just did that! so this little game ends up looping around! Ok, let's try starting with another number.
Remember the rules:
If the number you get is even, divide it by 2.
If the number you get is odd, multiply it by 3 and then add one.
How about 7? what happens?
It ends up in that 4,2,1, loop again, right?
This is called a mathematical dynamical system. you have a set of rules that you repeatedly operate on a given number with. The sequence of numbers you get is called an orbit. the loop 4,2,1 is called a closed orbit.
Try some more numbers, and see where they end up. Try 19. Hmm... that one is interesting, but it still ends up in our closed 4,2,1 orbit.
Do they all? Did you try 27? Oops, you will need a calculator! Even with a calculator It's too much work. Let's write a computer program to do it for us.
def iterate[n]
if int(n/2)=n/2 then 'if the integer portion of n/2 =n/2 then there is no remainder, so even
n=n/2
else
n=3*n+1
endif
return
simple program:
input n
while n<>1
iterate[n]
print n
wend
print "we've reached the loop"
program to calculate an orbit for each n:
for start_n = 1 to largest_n
print start_n; print ": ";
n=start_n
while n<>1
iterate[n]
print n; print ", ";
wend
print
next start_n
here's all the orbits for numbers less than 27:
1 4 2 1
2 / (i write a slash if we hit a number we've already tried)
3 10 5 16 8 4 2 1
4 /
5 /
6 3 /
7 22 11 34 17 52 26 13 40 20 10 /
Note here that if n is odd, 3n+1 is even so you always divide by 2 after 3n+1ing, however SOMETIMES you can divide by 2 TWICE, and as with 5, you can divide by 2 THREE times. So in general it's a little crazy. we can't tell on average how many times we mult by 3 vs divide by 2. So no trends.
8 /
9 28 14 7 /
10/
11/
12 even numbers are boring we already hit them all!
13 /
15 36 18 9 /
17 /
19 58 29 88 44 22 11/
21 64 32 16 8 /
(as an aside, is there an odd number n such that for each m, 3n+1=2^m? say 2^7.. so what is 2^m mod 3?
1 1
2 2
4 1
8 2
16 1
32 2
64 1
128 2
ah. half of them)
23 70 35 106 53 160 80 40 20 10 5 /
but note that 3*53+1 does =32*5, hmm..
25 76 38 19 /
Here is 27:
27 82 41 124 62 31 94 47 142 71 214 107 322
(odd, why ending in 1s and 7s? well, 3*1+1=4 and half 4 is either ending in 7 or 2 and half 2 ends in 1! 3*7+1 ends in 2 and half that ends in 1. how would the pattern break? half 2 is sometimes ending in 6! oh, so this IS odd!)
161 484 242 121 364 182 91 274 137 412 206
(see the pattern breaks finally)
103 310 155 466 233 700 350 175 526 263
(woah! whats going on here, this one is different than all the other's we've done so far, it keeps growing!)
790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1,
WOW! That's a complicated pattern for such a simple set of rules to produce. in fact we can do something curious here's the program i wrote to produce that list of numbers:
n=27
while n<>1
n=iterate(n)
print n;", ";
wend
wait
function iterate(n)
if int(n/2)=n/2 then
iterate=n/2
else
iterate=3*n+1
end if
end function
here's the entire orbit it produces
82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1,
the program produced a sequence of characters longer and more complicated than the sequence of characters in the original program. or is it more complicated? or is it random? These are difficult concepts to pin down. One of the major themes to this complexity lab is to ask what does it mean to ask whether a simple system can produce complex behavior. It is difficult to pin down what we mean by 'complex'.
Remember, ultimately we are motivated by the question "can a simple set of laws of chemistry and physics produce a complicated living organism from scratch?"
Here's orbits for more numbers:
29 88 44 22 11/
31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 (oh, 310 is in the orbit starting with 27, so we already know what happens)
33 100 50 25 /
35 /
etc... We need to keep a list of nums we've already found, so that we don't keep calculating orbits we've already spent time calculating!
we can write a program to do that too.
Now what is going on here? notice that most of the numbers lead to short sequences that end up in the repeating loop 4, 2, 1. But 27 goes wild. It looks like it never will settle into that loop, but it eventually does! Notice the seemingly chaotic nature of the alternation of odd even here. (and we will have to come up with a careful definition of what we mean by chaotic) very chancy.
Now if you want, you can try to delve into the nature of the numbers. All the factors of 2 and 3, are there any patterns going on? Can you estimate on average how often we multiply by 3 or divide by 2 and try to guess whether the sequence can grow without end? Or is there any rhyme or reason why we might not hit a number with a large power of 2 as a factor and that sends the sequence all the way back down to a small number again...
So now we have some questions.
Is there any order to this game or is it totally chaotic?
Is there any sequence that keeps growing forever and never settles down to 4,2,1?
Are there any other loops like 4,2,1 that a sequence might settle down to?
If all sequences settle down to 4,2,1 or some other loop, how far can they go before settling down?
If there are other loops how long can they be?
It is not hard to write a computer program to play this game and even keep track of all the old numbers and detect when you've reached a loop.
Guess what? After x years of study, mathematicians do not know the answers to ANY of these questions. Though we've calculated sequences out to the gazillions and SO FAR, they seem to all settle to 4,2,1, but no one knows how to prove that that ALWAYS happens.
Curious, eh?
There are more games like this in the complexity lab manual.
Here is a dirt simple game that requires only 4th grade arithmetic, yet leads to a hard puzzle.
Pick a number, say 5. It's odd, so let's multiply it by 3 and add one. We get 16. That one is even so we will divide by 2. We get 8. It's even again so divide by 2. We get 4. Then we get 2. Then we get 1. Oh, that's an odd number, so multiply by 3 and add one. We get 4. Then we get 2. Hey wait a minute, we just did that! so this little game ends up looping around! Ok, let's try starting with another number.
Remember the rules:
If the number you get is even, divide it by 2.
If the number you get is odd, multiply it by 3 and then add one.
How about 7? what happens?
It ends up in that 4,2,1, loop again, right?
This is called a mathematical dynamical system. you have a set of rules that you repeatedly operate on a given number with. The sequence of numbers you get is called an orbit. the loop 4,2,1 is called a closed orbit.
Try some more numbers, and see where they end up. Try 19. Hmm... that one is interesting, but it still ends up in our closed 4,2,1 orbit.
Do they all? Did you try 27? Oops, you will need a calculator! Even with a calculator It's too much work. Let's write a computer program to do it for us.
def iterate[n]
if int(n/2)=n/2 then 'if the integer portion of n/2 =n/2 then there is no remainder, so even
n=n/2
else
n=3*n+1
endif
return
simple program:
input n
while n<>1
iterate[n]
print n
wend
print "we've reached the loop"
program to calculate an orbit for each n:
for start_n = 1 to largest_n
print start_n; print ": ";
n=start_n
while n<>1
iterate[n]
print n; print ", ";
wend
next start_n
here's all the orbits for numbers less than 27:
1 4 2 1
2 / (i write a slash if we hit a number we've already tried)
3 10 5 16 8 4 2 1
4 /
5 /
6 3 /
7 22 11 34 17 52 26 13 40 20 10 /
Note here that if n is odd, 3n+1 is even so you always divide by 2 after 3n+1ing, however SOMETIMES you can divide by 2 TWICE, and as with 5, you can divide by 2 THREE times. So in general it's a little crazy. we can't tell on average how many times we mult by 3 vs divide by 2. So no trends.
8 /
9 28 14 7 /
10/
11/
12 even numbers are boring we already hit them all!
13 /
15 36 18 9 /
17 /
19 58 29 88 44 22 11/
21 64 32 16 8 /
(as an aside, is there an odd number n such that for each m, 3n+1=2^m? say 2^7.. so what is 2^m mod 3?
1 1
2 2
4 1
8 2
16 1
32 2
64 1
128 2
ah. half of them)
23 70 35 106 53 160 80 40 20 10 5 /
but note that 3*53+1 does =32*5, hmm..
25 76 38 19 /
Here is 27:
27 82 41 124 62 31 94 47 142 71 214 107 322
(odd, why ending in 1s and 7s? well, 3*1+1=4 and half 4 is either ending in 7 or 2 and half 2 ends in 1! 3*7+1 ends in 2 and half that ends in 1. how would the pattern break? half 2 is sometimes ending in 6! oh, so this IS odd!)
161 484 242 121 364 182 91 274 137 412 206
(see the pattern breaks finally)
103 310 155 466 233 700 350 175 526 263
(woah! whats going on here, this one is different than all the other's we've done so far, it keeps growing!)
790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1,
WOW! That's a complicated pattern for such a simple set of rules to produce. in fact we can do something curious here's the program i wrote to produce that list of numbers:
n=27
while n<>1
n=iterate(n)
print n;", ";
wend
wait
function iterate(n)
if int(n/2)=n/2 then
iterate=n/2
else
iterate=3*n+1
end if
end function
here's the entire orbit it produces
82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1,
the program produced a sequence of characters longer and more complicated than the sequence of characters in the original program. or is it more complicated? or is it random? These are difficult concepts to pin down. One of the major themes to this complexity lab is to ask what does it mean to ask whether a simple system can produce complex behavior. It is difficult to pin down what we mean by 'complex'.
Remember, ultimately we are motivated by the question "can a simple set of laws of chemistry and physics produce a complicated living organism from scratch?"
Here's orbits for more numbers:
29 88 44 22 11/
31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 (oh, 310 is in the orbit starting with 27, so we already know what happens)
33 100 50 25 /
35 /
etc... We need to keep a list of nums we've already found, so that we don't keep calculating orbits we've already spent time calculating!
we can write a program to do that too.
Now what is going on here? notice that most of the numbers lead to short sequences that end up in the repeating loop 4, 2, 1. But 27 goes wild. It looks like it never will settle into that loop, but it eventually does! Notice the seemingly chaotic nature of the alternation of odd even here. (and we will have to come up with a careful definition of what we mean by chaotic) very chancy.
Now if you want, you can try to delve into the nature of the numbers. All the factors of 2 and 3, are there any patterns going on? Can you estimate on average how often we multiply by 3 or divide by 2 and try to guess whether the sequence can grow without end? Or is there any rhyme or reason why we might not hit a number with a large power of 2 as a factor and that sends the sequence all the way back down to a small number again...
So now we have some questions.
Is there any order to this game or is it totally chaotic?
Is there any sequence that keeps growing forever and never settles down to 4,2,1?
Are there any other loops like 4,2,1 that a sequence might settle down to?
If all sequences settle down to 4,2,1 or some other loop, how far can they go before settling down?
If there are other loops how long can they be?
It is not hard to write a computer program to play this game and even keep track of all the old numbers and detect when you've reached a loop.
Guess what? After x years of study, mathematicians do not know the answers to ANY of these questions. Though we've calculated sequences out to the gazillions and SO FAR, they seem to all settle to 4,2,1, but no one knows how to prove that that ALWAYS happens.
Curious, eh?
There are more games like this in the complexity lab manual.
57) The Iterated Logistic Map and The Mandelbrot Set: An Intro To Mathematical Dynamical Systems
An Integer Dynamical System With A Curious Array Of Orbits
fn+1= (fn+fn-1)/2 if even odd else (fn+fn-1)/4 if even even or odd odd
58) Iterates Of The Unimodal Map: Intro To Concepts In Mathematical Dynamical Systems
Xnew=mXold(1-Xold) and Mandelbrot set stability, sensitive dependence on initial conditions, repellors, periodic orbits, chaos, phase space, bifurcations
Pick a number, say 3. double it, 6. double it again 12, well you see where that goes.
pick a fraction like 1/2, double it, 1, double it again, 2, double it again, 4
what if we square numbers: 2, 4, 16, 256 grows wildly
how about start with 1/2? 1/4, 1/16, 1/256... that one keeps shrinking forever, but at least it's not unbounded. in fact it approaches a particular number: 0.
what if i decide to multiply a number by -2? start with 3, we get -6, 18, -54, 162, that one bounces back and forth wildly
what if i decide to multiply by -1/2? start with 2, -1, -1/2, 1/4, -1/8, 1/16... that one swings back and forth but the swings are smaller and smaller and that one zeros in on 0.
what if i decide to multiply by -1? 2, -2, 2, -2.. huh, this one keeps oscillating back and forth between two values.
god it would take days to write this! can i make an anthology instead? or at least pilfer a chapter from Devaney and rewrite it to emphasize my own points?
find a system with period four i.e. multiply i
then look at exp(2pi/3) for period 3.
now follow mx(1-x), look at fixed, periodic, attractor, repellor, bifurcation,
structural stability
sensitive dependence on initial condition
wandering orbit
infinite many orbits
chaos
whole bifurcation cascade
cantor dust
then look at z^2+c
the space of bifurcations on c
Mandelbrot set.
what were the concepts from Liu: singularity theory? structural stability, genericity? ...
fn+1= (fn+fn-1)/2 if even odd else (fn+fn-1)/4 if even even or odd odd
58) Iterates Of The Unimodal Map: Intro To Concepts In Mathematical Dynamical Systems
Xnew=mXold(1-Xold) and Mandelbrot set stability, sensitive dependence on initial conditions, repellors, periodic orbits, chaos, phase space, bifurcations
Pick a number, say 3. double it, 6. double it again 12, well you see where that goes.
pick a fraction like 1/2, double it, 1, double it again, 2, double it again, 4
what if we square numbers: 2, 4, 16, 256 grows wildly
how about start with 1/2? 1/4, 1/16, 1/256... that one keeps shrinking forever, but at least it's not unbounded. in fact it approaches a particular number: 0.
what if i decide to multiply a number by -2? start with 3, we get -6, 18, -54, 162, that one bounces back and forth wildly
what if i decide to multiply by -1/2? start with 2, -1, -1/2, 1/4, -1/8, 1/16... that one swings back and forth but the swings are smaller and smaller and that one zeros in on 0.
what if i decide to multiply by -1? 2, -2, 2, -2.. huh, this one keeps oscillating back and forth between two values.
god it would take days to write this! can i make an anthology instead? or at least pilfer a chapter from Devaney and rewrite it to emphasize my own points?
find a system with period four i.e. multiply i
then look at exp(2pi/3) for period 3.
now follow mx(1-x), look at fixed, periodic, attractor, repellor, bifurcation,
structural stability
sensitive dependence on initial condition
wandering orbit
infinite many orbits
chaos
whole bifurcation cascade
cantor dust
then look at z^2+c
the space of bifurcations on c
Mandelbrot set.
what were the concepts from Liu: singularity theory? structural stability, genericity? ...
A Selection Of Representative Labs With Commentary
CHAPTER 1
LIFE
How varied and detailed is life on Earth?
6) Key Out 100 Plants In A Local Park [6WKS] [or a two session blitz just to collect 100 different plants and press them]
By learning to key out and LOOK at organisms hard enough to distinguish their varieties, we learn two things:
there is a bewildering variety
organisms are incredibly DETAILED. As close as we look at them as much as we magnify and look inward, we find levels and levels of complex details. How does it happen?
And how complex is their behavior?
2) collect insects and watch their behavior in a terrarium
after much observation you can find out:
4.5) List of 270 Skills That a Honeybee Has
Can we get a handle on it from computer science? In the past 60 years we have learned to build some complexity ourselves. Follow the levels of complexity as we build up from transistors a computer with elaborate software.
CHAPTER 6
COMPUTERS
It's not so easy to see how animals work, maybe we can at least try to make some robots that act as complex and see from scratch how it might work?
8) from logic gates to computer [1/2 hr?] show them, or make some simple circuits in digi-lab.
61.2) write simple computer programs in machine code: binary search, sort, rule 30 etc... [hr]
61.3) program John Horton Conway's game of life, Mandelbrot set, and Lorenz attractor in basic or something or maybe the lego bot language
[hr?] show them?
Researchers in the field of Artificial Intelligence are now asking themselves, what it would take to build an animal, to build clever behaviors from the bottom up. We are trying to check our understanding of intelligence by building complex things and seeing if they can ACT intelligently.
9) show them well programmed lego bots ( (intro to another whole workshop) and listings of 1000 lined programs [1/2hr]
But we still Can't do it! Our robots are clunky and stupid in comparison with a honeybee!
CHAPTER 1
SO BACK TO CRITTERS FOR HELP
16) watch videos of animal development
This is an amazing process. And it works because animals are colonies of living cells, all talking with each other, feeling each other out and reproducing and sending their kids to the right places. We build machines from the outside in factories, but animals and plants are built from within by cells. What are cells?
CHAPTER 2
CELLULAR LIFE
Some critters are a single cell all in one, lets watch some:
22) watch single cell pond creatures [hr]
Take some time to watch the intricate behaviors of living single celled organisms. Already at this level, there is so much capability. The capabilities that make life so rich are not concentrated at the top, the most centralized level, but are distributed throughout every size scale! Even at the cellular level, and below...
So what kind of 'things' are cells?
27) molecular video "inner life of cell" [10min] more?
cells are hierarchical structures of organelles, macromolecular assemblies, macromolecules, small molecules. The properties of cells are also due to the most common molecule in them: water.
They are whirlwinds of swirling interacting molecules. The structure and organization goes in several more levels deep, as complex as a whole giant city.
and finally the most common machinery: proteins. they can self assemble into complex structures like undulipodia, they can change shape, travel along tracks, act as a complex logic elements in processing information, respond to EM radiation
25) grow oscillatoria in water and glass jar. watch it move. then at second to last session, weigh it, dry it, last session, burn it, weigh the ash
[10min sessions a few times]
PART 2
PHYSICS AND MATH
So how do cells do it? Well, no need to go to biology for the complexity of cells, the capabilities of cells. Physics, chemistry, and mathematics already gives us this. We are slowly whittling away at the divide between chemistry and life!
Physics and math gives us:
1) Patterns at far from equilibrium: energy flow through systems creates ordered dynamism
2) But even at equilibrium, rest, pattern comes ultimately from mathematics
3) And the clay that physics and math get to sculpt into organisms?
molecules!
CHAPTER 3
WHAT IS THE MOLECULAR WORLD?
So what is the molecular world like that it gives life it's subtle creative qualities? What are we 'made of'
Well, how many molecules are there in a cell?
73.2) Brownian motion: hints at the existence of many tiny molecules, constantly in motion due to heat, and hints at how small they are, how many in a drop of water.
73.3) monomolecular lipid layer: another clue to how big molecules are. Then we sketch out how the number of molecules in a glass of water can be calculated from experiments like these
[hr]
Atoms, molecules are not building BLOCKS, they are little machines, not clunky, but fuzzy, sensitive to their environment and each other, reactive, each atom is a complex of electron orbitals which are solutions to wave equations... molecules are flexible, constantly wiggling, not alive, but... can't describe what they are in common every day terms.
any labs we can do to show how molecules interact? orgo reactions, soap/oil/water, collisions? orientations? chirality..
72.2) show how many ways an ethanol molecule can respond to its chemical environment?
At the molecular level you already have a kind of trial and error mechanism for fitting together puzzles. one of the roots of our intelligence. molecules are always moving, wiggling, interacting with each other 10^10 times a second! molecules in a warm universe with energy flow are not like a jumble of cold automobile parts just sitting there, molecules can self assemble!
Show diagrams/video of how simple molecular interactions cooperate to form complex structures and processes:
31.2) Distributed Brownian Motion Machinery: Clathrin Coated Pits
molecules pass energy to each other in reactions, store energy in bonds, thus networks of their reactions can be ordered by energy flowing through systems of molecules.
molecules react with EM radiation. vision comes for free at the lowest level
44) Play With A Candle Flame
CHAPTER 4
DISSIPATIVE STRUCTURES: FLOW OF ENERGY THROUGH SYSTEMS CREATES PATTERNED DYNAMISM
If molecules aren't simple building blocks, then organisms are not 'things' at all, 'phenomena' would be a better adjective, or, to be less academic; 'dances'? What kind of phenomena are living cells? they are chemical systems animated by energy flow.
Our usual experience is that things wear out after a while and run down. You may have heard of the second law of thermodynamics which says "all closed systems (nothing coming in or out) run down and become less, not more ordered. If this is so, then how can life oppose this 'universal' tendency? Well, life is not a closed system!
One process that helps is positive and negative feedback. Lets explore some machines and simple processes that can do this.
64.2) chaotic waterwheel, thermostat and heater, door buzzer [hr]
In our next labs
33) show steam engine (with governor?) can i show that it needs hot and cold?
34) Then Benard convection
[hr]
We show the basic system animated by energy flow: Benard convection: We start off with wood (or some kind of fuel, highly ordered in any case) and air (unusual, out of equilibrium with all its oxygen..) and light the wood into flame. It is important that the flame is much hotter than the air above It.
The flame will heat from below a pan of shallow water. As the bigger closed system of wood and air and water run down to ashes and luke-warm carbon dioxide and water, for a while, a wondrous thing happens. Our pan of water (not closed, open to heat flowing through it) becomes ordered into an hexagonal array of gyrating convection cells.
We call these subsystems FAR from thermodynamic equilibrium systems or Dissipative Systems (they dissipate heat).
And what makes CELLS swirl? this time it is the flow of chemical energy. High energy bonds come in (sugars) and again low energy bonds come out in the form of carbon dioxide. In the meanwhile the cells swirl with activity. here are some simpler examples.
Can life even arise spontaneously from chemistry?
42) The Beloussov Zhabotinsky reaction : a simple far from equilibrium chemical system that you can watch forming periodic spatial patterns
Put convection and chemical reaction cycles together and you get:
44) play with a flame: [hr]
They are more complex than you think! And they contain complex networks of chemical reactions reminiscent of the metabolic chart!
CHAPTER 5
MATHEMATICAL DYNAMICAL SYSTEMS: EASY LABORATORY, ALL YOU NEED IS PENCIL, PAPER, COMPUTER
But living creatures are more complicated then these. Can chemistry really result in the complexity we found in living cells? Where do all those different patterns and structures come from? MATH! Mathematics gives us so much pattern for free. Simple rules repeated over and over again between many identical simple units can create surprising unpredictable patterns.
48) John Horton Conway's Game Of Life: a simple system of simple rules wherein there are patterns of many classes of behaviors, and simple patterns can develop into surprisingly complex ones. we can even make a finite pattern that results in an endlessly interesting one
53) One dimensional cellular automata rules 30 and 110 even dirt simpler set of rules that produces an endless stream of creativity
[1/2hr] [1/2 hr]
56) 3n+1: a simple number game with complex behavior we have yet to fully understand
57) e/o Fibonacci system: another one with much more complex behavior. these only involve addition and division.
58) Iterated logistic equation to Mandelbrot set: simple math rules give the most complex geometric structure we've ever imagined
60) Lorenz attractor: a simple dynamic system that results in a curious subtly behaving system with a sprinkling of unpredictability. By the way, it is very similar in behavior to the chaotic waterwheel.
[hr]
CHAPTER 7
EVEN AT EQUILIBRIUM: PHYSICAL AND CHEMICAL PATTERN FORMATION
Even without the dynamical systems set into motion by energy flow, the laws of physics are fecund: We find pattern formation even at equilibrium.
The wonder is, why isn't the universe a seamless haze of psychedelic chaos? Why isn't it just a bland grey blob of continuous matter? Why isn't the universe simply one huge neutron or quark or is THERE anything at the bottom? Somehow the physics and math give us all these phase transitions, clumpings for free.
74) show periodic chart with samples of diff elements: gas, liquid, metal, graphite, sulfur, semiconductor..
76) phases of sulfur: even with one kind of atom, depending on temperature, we get wildly different behaviors
75) and breath on a window pane: ditto for water molecules, how do they 'calculate' the beautiful patterns of 'jack frost' on window panes?
[1/2 hr]
70) mineral exhibit a dozen elements, a dozen transition metals and 2000+ combinations all for free.[1/2 hr? depends where]
CHAPTER 8
IT ALL COMES FROM MATH
At root, why is this universe so full of patterns? MATH!
From mathematics alone, we get surprising complexity but not total chaos from the simplest static logical rules
And why do we have this interesting periodic chart of elements, each with their potent particular properties? Physics and math again! Propose a simple set of rules and let them play out and you often find that you get a set of discrete entities which follow them that is interestingly diverse but not infinitely chaotic! This is the core of pattern formation in our universe. It's built in at the very basic logical structure of it.
87) enumeration of finite graphs: keep adding one more edge to a graph and you discover radical new behaviors. clues to things like how we get the behaviors in the periodic chart of elements?[1/2 hr]
81) classification of finite simple groups: example of simple static rules giving surprisingly diverse but only a tiny bit of chaotic pattern [1/2hr]
PART 3
THE BIG QUESTIONS: EVOLUTION, ORIGINS OF LIFE, AND MIND
CHAPTER 9
PUTTING IT ALL BACK TOGETHER: EVOLUTIONARY BIOLOGY
Then we put it all back together again and tackle the most fascinating subject: what is it that brings us all those wonderful critters we found outside at the beginning of our exploration? Evolutionary biology.
96) Tierra a system of programs that can reproduce, evolve, and form ecosystems [hr]
CHAPTERS FOR FURTHER STUDY:
CHAPTER 10
THE FINAL FRONTIER: CAN WE UNDERSTAND HOW GEOCHEMISTRY CAN BECOME LIFE?
The final frontier: is life SOLELY a consequence of chemistry and mathematics? If you perform labs in this topic, you are at the forefront of the scientific adventure.
CHAPTER 11?
MIND
Bar, why do you leave off discussing mind and consciousness? because I'm not greedy? but the labs watching behavior of single cells, the computer science topics, 260 skills of honeybees, building AI programs to simulate critters is the start.
CHAPTER 12?
SUPERORGANISMS
And finally we come back to the ants! This is the most recent hierarchical level of complex behavior to evolve on earth. not only critters with minds who can explore and learn about and manipulate their world, but some organisms come together and build highly cohesive societies:
Ants, honeybees, wasps, termites, naked mole rats, wolves and... humans.
LIFE
How varied and detailed is life on Earth?
6) Key Out 100 Plants In A Local Park [6WKS] [or a two session blitz just to collect 100 different plants and press them]
By learning to key out and LOOK at organisms hard enough to distinguish their varieties, we learn two things:
there is a bewildering variety
organisms are incredibly DETAILED. As close as we look at them as much as we magnify and look inward, we find levels and levels of complex details. How does it happen?
And how complex is their behavior?
2) collect insects and watch their behavior in a terrarium
after much observation you can find out:
4.5) List of 270 Skills That a Honeybee Has
Can we get a handle on it from computer science? In the past 60 years we have learned to build some complexity ourselves. Follow the levels of complexity as we build up from transistors a computer with elaborate software.
CHAPTER 6
COMPUTERS
It's not so easy to see how animals work, maybe we can at least try to make some robots that act as complex and see from scratch how it might work?
8) from logic gates to computer [1/2 hr?] show them, or make some simple circuits in digi-lab.
61.2) write simple computer programs in machine code: binary search, sort, rule 30 etc... [hr]
61.3) program John Horton Conway's game of life, Mandelbrot set, and Lorenz attractor in basic or something or maybe the lego bot language
[hr?] show them?
Researchers in the field of Artificial Intelligence are now asking themselves, what it would take to build an animal, to build clever behaviors from the bottom up. We are trying to check our understanding of intelligence by building complex things and seeing if they can ACT intelligently.
9) show them well programmed lego bots ( (intro to another whole workshop) and listings of 1000 lined programs [1/2hr]
But we still Can't do it! Our robots are clunky and stupid in comparison with a honeybee!
CHAPTER 1
SO BACK TO CRITTERS FOR HELP
16) watch videos of animal development
This is an amazing process. And it works because animals are colonies of living cells, all talking with each other, feeling each other out and reproducing and sending their kids to the right places. We build machines from the outside in factories, but animals and plants are built from within by cells. What are cells?
CHAPTER 2
CELLULAR LIFE
Some critters are a single cell all in one, lets watch some:
22) watch single cell pond creatures [hr]
Take some time to watch the intricate behaviors of living single celled organisms. Already at this level, there is so much capability. The capabilities that make life so rich are not concentrated at the top, the most centralized level, but are distributed throughout every size scale! Even at the cellular level, and below...
So what kind of 'things' are cells?
27) molecular video "inner life of cell" [10min] more?
cells are hierarchical structures of organelles, macromolecular assemblies, macromolecules, small molecules. The properties of cells are also due to the most common molecule in them: water.
They are whirlwinds of swirling interacting molecules. The structure and organization goes in several more levels deep, as complex as a whole giant city.
and finally the most common machinery: proteins. they can self assemble into complex structures like undulipodia, they can change shape, travel along tracks, act as a complex logic elements in processing information, respond to EM radiation
25) grow oscillatoria in water and glass jar. watch it move. then at second to last session, weigh it, dry it, last session, burn it, weigh the ash
[10min sessions a few times]
PART 2
PHYSICS AND MATH
So how do cells do it? Well, no need to go to biology for the complexity of cells, the capabilities of cells. Physics, chemistry, and mathematics already gives us this. We are slowly whittling away at the divide between chemistry and life!
Physics and math gives us:
1) Patterns at far from equilibrium: energy flow through systems creates ordered dynamism
2) But even at equilibrium, rest, pattern comes ultimately from mathematics
3) And the clay that physics and math get to sculpt into organisms?
molecules!
CHAPTER 3
WHAT IS THE MOLECULAR WORLD?
So what is the molecular world like that it gives life it's subtle creative qualities? What are we 'made of'
Well, how many molecules are there in a cell?
73.2) Brownian motion: hints at the existence of many tiny molecules, constantly in motion due to heat, and hints at how small they are, how many in a drop of water.
73.3) monomolecular lipid layer: another clue to how big molecules are. Then we sketch out how the number of molecules in a glass of water can be calculated from experiments like these
[hr]
Atoms, molecules are not building BLOCKS, they are little machines, not clunky, but fuzzy, sensitive to their environment and each other, reactive, each atom is a complex of electron orbitals which are solutions to wave equations... molecules are flexible, constantly wiggling, not alive, but... can't describe what they are in common every day terms.
any labs we can do to show how molecules interact? orgo reactions, soap/oil/water, collisions? orientations? chirality..
72.2) show how many ways an ethanol molecule can respond to its chemical environment?
At the molecular level you already have a kind of trial and error mechanism for fitting together puzzles. one of the roots of our intelligence. molecules are always moving, wiggling, interacting with each other 10^10 times a second! molecules in a warm universe with energy flow are not like a jumble of cold automobile parts just sitting there, molecules can self assemble!
Show diagrams/video of how simple molecular interactions cooperate to form complex structures and processes:
31.2) Distributed Brownian Motion Machinery: Clathrin Coated Pits
molecules pass energy to each other in reactions, store energy in bonds, thus networks of their reactions can be ordered by energy flowing through systems of molecules.
molecules react with EM radiation. vision comes for free at the lowest level
44) Play With A Candle Flame
CHAPTER 4
DISSIPATIVE STRUCTURES: FLOW OF ENERGY THROUGH SYSTEMS CREATES PATTERNED DYNAMISM
If molecules aren't simple building blocks, then organisms are not 'things' at all, 'phenomena' would be a better adjective, or, to be less academic; 'dances'? What kind of phenomena are living cells? they are chemical systems animated by energy flow.
Our usual experience is that things wear out after a while and run down. You may have heard of the second law of thermodynamics which says "all closed systems (nothing coming in or out) run down and become less, not more ordered. If this is so, then how can life oppose this 'universal' tendency? Well, life is not a closed system!
One process that helps is positive and negative feedback. Lets explore some machines and simple processes that can do this.
64.2) chaotic waterwheel, thermostat and heater, door buzzer [hr]
In our next labs
33) show steam engine (with governor?) can i show that it needs hot and cold?
34) Then Benard convection
[hr]
We show the basic system animated by energy flow: Benard convection: We start off with wood (or some kind of fuel, highly ordered in any case) and air (unusual, out of equilibrium with all its oxygen..) and light the wood into flame. It is important that the flame is much hotter than the air above It.
The flame will heat from below a pan of shallow water. As the bigger closed system of wood and air and water run down to ashes and luke-warm carbon dioxide and water, for a while, a wondrous thing happens. Our pan of water (not closed, open to heat flowing through it) becomes ordered into an hexagonal array of gyrating convection cells.
We call these subsystems FAR from thermodynamic equilibrium systems or Dissipative Systems (they dissipate heat).
And what makes CELLS swirl? this time it is the flow of chemical energy. High energy bonds come in (sugars) and again low energy bonds come out in the form of carbon dioxide. In the meanwhile the cells swirl with activity. here are some simpler examples.
Can life even arise spontaneously from chemistry?
42) The Beloussov Zhabotinsky reaction : a simple far from equilibrium chemical system that you can watch forming periodic spatial patterns
Put convection and chemical reaction cycles together and you get:
44) play with a flame: [hr]
They are more complex than you think! And they contain complex networks of chemical reactions reminiscent of the metabolic chart!
CHAPTER 5
MATHEMATICAL DYNAMICAL SYSTEMS: EASY LABORATORY, ALL YOU NEED IS PENCIL, PAPER, COMPUTER
But living creatures are more complicated then these. Can chemistry really result in the complexity we found in living cells? Where do all those different patterns and structures come from? MATH! Mathematics gives us so much pattern for free. Simple rules repeated over and over again between many identical simple units can create surprising unpredictable patterns.
48) John Horton Conway's Game Of Life: a simple system of simple rules wherein there are patterns of many classes of behaviors, and simple patterns can develop into surprisingly complex ones. we can even make a finite pattern that results in an endlessly interesting one
53) One dimensional cellular automata rules 30 and 110 even dirt simpler set of rules that produces an endless stream of creativity
[1/2hr] [1/2 hr]
56) 3n+1: a simple number game with complex behavior we have yet to fully understand
57) e/o Fibonacci system: another one with much more complex behavior. these only involve addition and division.
58) Iterated logistic equation to Mandelbrot set: simple math rules give the most complex geometric structure we've ever imagined
60) Lorenz attractor: a simple dynamic system that results in a curious subtly behaving system with a sprinkling of unpredictability. By the way, it is very similar in behavior to the chaotic waterwheel.
[hr]
CHAPTER 7
EVEN AT EQUILIBRIUM: PHYSICAL AND CHEMICAL PATTERN FORMATION
Even without the dynamical systems set into motion by energy flow, the laws of physics are fecund: We find pattern formation even at equilibrium.
The wonder is, why isn't the universe a seamless haze of psychedelic chaos? Why isn't it just a bland grey blob of continuous matter? Why isn't the universe simply one huge neutron or quark or is THERE anything at the bottom? Somehow the physics and math give us all these phase transitions, clumpings for free.
74) show periodic chart with samples of diff elements: gas, liquid, metal, graphite, sulfur, semiconductor..
76) phases of sulfur: even with one kind of atom, depending on temperature, we get wildly different behaviors
75) and breath on a window pane: ditto for water molecules, how do they 'calculate' the beautiful patterns of 'jack frost' on window panes?
[1/2 hr]
70) mineral exhibit a dozen elements, a dozen transition metals and 2000+ combinations all for free.[1/2 hr? depends where]
CHAPTER 8
IT ALL COMES FROM MATH
At root, why is this universe so full of patterns? MATH!
From mathematics alone, we get surprising complexity but not total chaos from the simplest static logical rules
And why do we have this interesting periodic chart of elements, each with their potent particular properties? Physics and math again! Propose a simple set of rules and let them play out and you often find that you get a set of discrete entities which follow them that is interestingly diverse but not infinitely chaotic! This is the core of pattern formation in our universe. It's built in at the very basic logical structure of it.
87) enumeration of finite graphs: keep adding one more edge to a graph and you discover radical new behaviors. clues to things like how we get the behaviors in the periodic chart of elements?[1/2 hr]
81) classification of finite simple groups: example of simple static rules giving surprisingly diverse but only a tiny bit of chaotic pattern [1/2hr]
PART 3
THE BIG QUESTIONS: EVOLUTION, ORIGINS OF LIFE, AND MIND
CHAPTER 9
PUTTING IT ALL BACK TOGETHER: EVOLUTIONARY BIOLOGY
Then we put it all back together again and tackle the most fascinating subject: what is it that brings us all those wonderful critters we found outside at the beginning of our exploration? Evolutionary biology.
96) Tierra a system of programs that can reproduce, evolve, and form ecosystems [hr]
CHAPTERS FOR FURTHER STUDY:
CHAPTER 10
THE FINAL FRONTIER: CAN WE UNDERSTAND HOW GEOCHEMISTRY CAN BECOME LIFE?
The final frontier: is life SOLELY a consequence of chemistry and mathematics? If you perform labs in this topic, you are at the forefront of the scientific adventure.
CHAPTER 11?
MIND
Bar, why do you leave off discussing mind and consciousness? because I'm not greedy? but the labs watching behavior of single cells, the computer science topics, 260 skills of honeybees, building AI programs to simulate critters is the start.
CHAPTER 12?
SUPERORGANISMS
And finally we come back to the ants! This is the most recent hierarchical level of complex behavior to evolve on earth. not only critters with minds who can explore and learn about and manipulate their world, but some organisms come together and build highly cohesive societies:
Ants, honeybees, wasps, termites, naked mole rats, wolves and... humans.
Saturday, May 9, 2009
44) Play With A Candle Flame
back to top back to best labs summary contents
Materials
candle, matches, bunsen burner, chart of reactions, white cards to catch soot, high temp cooking thermometer, a container to keep out random air currents?
are there differences between the two flames? do flames have boundaries? how stable are they? map out the temperatures, how do they spread? what are those blobs that sometimes form on the wick?
look at the chart of reactions in a flame, there are dozens of reactions!
Materials
candle, matches, bunsen burner, chart of reactions, white cards to catch soot, high temp cooking thermometer, a container to keep out random air currents?
are there differences between the two flames? do flames have boundaries? how stable are they? map out the temperatures, how do they spread? what are those blobs that sometimes form on the wick?
look at the chart of reactions in a flame, there are dozens of reactions!
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