Alan Kay: Big Ideas are Sometimes Powerful Ideas

so we

actually are dealing with an  academic hour here

and be fitting with  our school setting

marvin minsky once  said school was the greatest

invention  anybody ever came up with to keep

you  from staying interested on anything for  any reasonable

length of time because of  course

it has all these schedules in  assembly line movements

and we have one  of those today and

I also wanted to  leave time for

questions but one of the  ways I want to leave time

for questions  is to encourage you to ask questions as  I

talk so I have no idea how long this

  talk is and I am going to stop after

50  minutes and regardless of what what

  happened so please don't be

shy ask  questions as we go if

you like and  because this talk is

not for me but for  you

so it's

in a series of ideas which  are

somewhat connected I hope so

one  contrast

I'd like you to think about is  the notion beach of

common sense that

  most people take

the world around them  as reality I

once came up with

at said technology is anything that  happened after

you were born because

the  technology that you're born into is

part of your world and it's taken to be  normal there and most

internet Prince the Internet is one of  the great inventions

of all time not the  web but the internet itself

one of the  great maybe one of the greatest  engineering

feats of all time and

it  worked so well that hardly

anybody  appreciates it particularly

in computing  where they should pay more attention to  why

it works so well so here's a

  common-sense deduction that

has been  made by most

people on the planet for  the slightly less

than 200,000 years  modern humans have been here

and that is  something like a king

  natural and normal

extension of the head  of the family

hunted leaders

of hunting  groups and etc etcetera so

this is just  regarded as common sense

and in fact was  not regarded as it as an idea

it was  just part of the part of the world that  people

lived in then in

January 1776  Thomas Paine

wrote a book which he  ironically titled common

sense everybody  here has heard of Tom Paine's Common  Sense

but he had a big idea in it which

  was instead of having the King be

the  law we can have the law be the king and

what he meant was we can design a much  better society

than the what the natural

  seeming hereditary monarchy as we can  take our

future into our own hands we  can come up with a better plan

this is  an idea that surfaced

a couple of times  in Greece but not

not before not after  and

this book

which pain published at  his own expense initially

just gave it  away had a press run

between six hundred thousand and nine  hundred thousand

in six months so

that's  a lot by today's standards and

there  were 1.5 million non

slaves in the  thirteen colonies

back then and so this  press run

encompassed somewhere between  almost a half

to more than a half of all  men women and children in

all 13  colonies so imagine just trying

to reach  that number of people today

there is no  medium that you could do it with except

  with the internet I try

to get sixty  percent of

300 million people no

  newspaper could do it so

so this is a  big idea but

  the powerful idea

and this is the  distinction I want to make was the

  Constitution as a

big idea is kind of an  insight and

often insights insights

are  wonderful but they're

lightweight  they're relatively easy to have compared

  to doing something about it so the

  Constitution said

we should shape  society into a self-organizing

  self-correcting shared idea and resource  system

and that is a very radical

idea  even for today for instance most  Americans

have no idea what the design  of the

United States was or is it's

imply not taught in schools it's not  the way American

history is is taught  and

so

most societies on earth haven't

  gotten this idea even at the societal  level

most human beings on earth don't  have this

idea but this is one of these  powerful ideas

that makes qualitative

  differences in almost every

area of life  and it's related to an even

bigger set  of ideas so

another common sense

whoops

  another another

common sense notion  which is

actually with most Americans  today according to the surveys

I've seen  which is the world is pretty much as it  seems

so we this

is what our nervous  systems are set up to do we're

basically  weren't set up by nature to think

we're  set up by nature to cope and so

primary mechanism is whatever  environment we

find ourselves in so the  answer anthropologists

know that you can  take a child at

birth from any culture  on the planet and take

on the planet  that child will grow up as

a member of  that culture you took it too that's

  because humans are rather more similar

  than they are different we have about  300

traits that anthropologists have  identified

that seem to be quite genetic  including

things like language having  culture telling stories

and those  mechanisms

get embodied with the

local  varieties of those and so the

reality  you grow up within the language you

grew  up with is the language and

the reality  of the culture you you're born in Q

so

now this big ideas

have been had a  number of times in history I happen to  like the

Talmud version of it

we see  things not as they are but as we are

so  this is a bit I'd love to know

what  actually

happened to the person who came  up with this

idea did they take it to  its logical conclusion

considering and

was interesting that was published in  this Talmud is part

of the commentary

  but this is one

of the great big ideas  of all time this

is a really hard one  because it

completely relative izes  what's

going on however it's not a  powerful idea

but had numerous

times and

powerful idea came in

the 17th century  and you

could point to a number of  people and you could point to various

  societies but

17th century has a has a  perfect

atomic

bomb place where science  started

because we had Galileo

and  Kepler and maybe Copernicus

beforehand  and a few other people but in fact

when  Newton did

the Principia he actually  revolutionized

human thought and it's  probably the largest leap in human

  thought of this kind that we know of  historically

this is why most scientists

think of Newton as being the greatest  scientist

and he was almost the first  scientist and

not just in

relative terms  but in absolute terms the amount

of  distance he was able to cover not just

in terms of knowledge but in terms of  about look and

the powerful idea of  science

is not so easy to state  everything

else comes out pretty nicely  as slogans and

there's more to science  than just

this but this is one half of  it which

is science is not about  knowledge  as

niels bohr said science is not there  to tell

us about the universe is what  most people think

most non-scientists  most kids in school

are taught what is  called science

as in roughly the same  way they learn religion in

when they go  to church or

synagogue or mosque but

in what science is at all it's not about  knowledge

it's about relating the

stuff  we can do and can't do in here

all the  things that we can do with

our  representational systems to stuff

out  there that we can't get to directly  because

everything we do is filtered  through our nervous

systems as filtered  through our culture's is

filtered for  through the the difficulties

we have  with making relationships

about things  and this was not an

easy idea to have  we'll

see in a bit but

what's happened  in the last 400 years in

many many  dimensions

has been more than has  happened

in the rest of the 200,000  years and you

know the cliche that

most  scientists 90 more

of all the scientists who ever lived  you're alive today

and most of the  things that

are happening today and some

of the problems and some of the  solutions to those problems

are all  caused this by different way

and much is made

particularly in the pop  culture of

bringing bright

this is  because pop

culture's or cultures  without a lot

of developed knowledge  basically

live by their wits and so you  out

with each other and you

compete at  the level of width but

imagine being  born with an IQ

of 500 who knows how

  smart leonardo was let's

just no 203 who  because

those figures don't what does IQ  me in any

way but let's just say hey  suppose

you're just a hell of a lot  smarter than anybody who ever lived

but  you were born in 10,000 BC

how far you  going to get so

you can probably out wit  everybody around you before

they burn  you at the stake

but in fact Leonardo

  who we know is very very bright could

  not invent a single engine

for any of  the vehicles that he designed so

he's  famous for designing things that look

like planes and things that maybe look  like helicopters

and I'll and they're  wonderful and he did a lot

hings but he couldn't make a single  goddamn one of

them work that is and  that's

because he wasn't smart enough to  think himself out

of the era he had been  born into as

far as we know if nobody  has the closest person who's ever

thought himself out of the era he was  born into his

Newton so

you have this  odd paradox

that whoops sorry that

Henry Ford who is not nearly as smart as

Leonardo just happened to be born in the  right time and

so he did revolutionize  one

of the areas that Leonardo wanted to  revolutionize

by being able

to do  adaptive engineering and a little

invention to the stuff that was already  around

so his knowledge was

processed  knowledge and this was very powerful and  what

was the difference between these  two these

two guys was this

change of  outlook that Newton

was one of the  promulgate errs of

so one of the ways I

  when I talked to grabs grad students

or  children I say well knowledge

is silver  but outlook is

gold our

world is built  on changes of outlook that was what the

  Constitution was that was what Tom Paine  did

and that's what science did and

IQ  is led

because there is no

we know of no  developed field knowledge in

which you  can get by with just talent there's

no  developed sport in which you can get by  with

just talent and some of the most

  difficult sports have been

excelled in  by people who are not as athletic

so for  instance Chris effort

as an example who  is not a particularly athletic

tennis  player but man that you know

how to work  and so she got very very

good at it and  most things have

this thing an Outlook  also

tells you what kind of knowledge to

  go after because of course every group

in history had a zillion amount of not  you going to the

Australian outback  without a

native Australian there

to  help you you're going to die whereas for

  them is just a walk in the park because

  everything is food they know how to get  water and

it's there just they know  where the dangers are they

it's no big deal  so every group

has lots of knowledge the  real thing to think about is

what kind  of knowledge is that what's the quality

level what's the level of flexibility  what can you

you do with it and these  outlook

changes are more pine Steiners  another

one so about a hundred years ago

something

that Newton in a

slightly  different Einstein was quite sure that

  Newton if he lived longer and had not

  been put in had a head

of the Treasury  in England that Newton would have  actually

come up with a theory of  relativity I don't

know whether he could  have could have actually

done that  because but Newton

didn't know that

he  thought it was ridiculous that his  equations

had action at a distance

so he  said so in letters as just

that nobody  could measure well enough

and what they  did measure the

gravitational forces  seem to

transmit instantly but

from  Newton standpoint that was ridiculous

okay so that was

the first section so  the second section is to look at

children can actually do under ideal  conditions and

this is not easy to find  so

a couple of these things are results  of

just dealing with hundreds

and  hundreds of teachers over more than 40

  years and in this case this was an

  accident because we were working in the  fourth

and fifth grades in the school  and of course I started

wandering around  the school and I happen to poke my

nose  into first grade and

what I saw was  quite shocking

to me i should mention I  have a

degree in mathematics and another  one in molecular biology

as well as the  computer science degrees

so when I  walked into this math this first grade  classroom

and SAT there for a few  minutes

  I gradually realize

that this teacher  was doing real math with

first graders  not school

math but real math the real  deal and

as I got to know her Julia  nishijima was her name

I found she was  that

she have not taken any math in  college but

she was like one of these  musician friends you

might have who was  just a natural musician she

was a net  she just saw the world in terms of math  and

her outlook was in the world of the

  kindergarten and first grade child so

  over a couple of years I saw some

most amazing things I've ever seen in  any classroom at any age

this one was  done after the kids have been there for

  about three months and the school

is a  busing school in LA and what

that means  is that the children in order

to induce  the parents

to get on the that have

their children but if you think about  bus driving

a car in LA as ridiculous so

  let's put our children on buses twice

  twice a day to

try and deal with some of  the racial imbalance

problems and but

  they did and there was

interesting inducements to get the  parents to do that but

the law was that  for each of the busing

schools had to  have the same demographic

as the city as  a whole so

these busing schools were the  perfect place for doing

educational  experiments because the city

forty-five percent Hispanic until you  have forty-five

percent Hispanic kids in  there and

just down the line in these  schools so

here's the thing she

had and  this is not unlike a lot of the things

  that she did with the kids so this one

  was fine to shape you like a square  diamond

a triangle a trapezoid and

make  a progression

of shapes just using these  shapes

so  next

larger size next larger size next  larger size and trapezoids

are coarser  are a tricky but

so 30 kids in the class  and

they all pick

the ones that they  like they all did did something and

then  she did something

that seems a little  strange to me which was to have

him now  go from these easy to handle wouldn't

  manipulatives to cutting

out the same  shapes out of cardboard so I asked

her  afterwards why she did this and she said  well little

kids are always jumping to  conclusions and this

part now that  they've done the thing I want them to  think about

it so this part slows them  down so the idea here

is make a we're  going to make a little thing to free to  take

home to your parents to show what  what

you're doing and so here's one of  them and

Laura in here

on this sheet she  wrote down what she

noticed that the  first diamond

here took one diamond the  total number of diamonds

was one and  then she had to add three

more diamonds  to get the next

diamond shape and the  total was four and then she had to add

  five to get the next one the total  number of tiles

was nine and she could  see

that she was adding to each time

  it's get the first column and then

up  you can see

she wasn't quite sure what  six times six was

but she knew the  square numbers

up to five times five

  then she worked this all out so this is  her sheet

then the teacher

julia had

kids all bringing their projects up to  the front of the room

there it is

kids

look to each other's projects and  they looked at the little

tables and  they went holy shit

technical term

  because everybody had filled

same table regardless of what the shapes  were the

growth laws were the same so

  this was hugely exciting I was there

I  just happened to be there that day and

I'm looking at this stuff with tears  running down my because

this is one of  the best mathematical

things I've ever  seen done in any classroom at any age  and

some of you

are we'll

have some  mathematical background and

realize what the kids were doing is  actually

deriving to

differential laws  one

is the differential law for smooth  progressions

sometimes called linear  progressions

that's that first column  and

of course if they used instead of  using two

they used one it would have a  different growth

but it would still be  smooth and linear

they could use three  or they could use 3.5 so

basic ideas are  just adding the same

thing in there and  in math that's

called the first order  differential equation if it were

in a  continuous space like we like

to teach  in school but for the kids this is the  screen

and there's a math for that its

a  math we don't teach but it's called a

  first order differential discreet  relationship

and the second one is

all  the square numbers

it's a quadratic one  so this is

called the second order  differential discreet

relationship and  it's built on the first an important

  thing here is that virtually everything

in high school physics and most things  in your first physics

course in college  can be handled with no more

mathematics  than this this is

actually the real  basis of the calculus

wind  using in high school and college his

  calculus has nothing to do with algebra  even

though it's cloaked in algebra for  historical

reasons most Mountain  mathematicians did not realize this

what  calculus is is actually an idea

quite  separate from the symbology that's

used  on so

and of course the kids could  calculate with this

so the

little rule  they had was you start with

one piece  and then you add to the new new pieces  column

add to each time and then you

add  from that column to

the total column to  get the next one and

a few if you act it  out you get something like this

so you  start off with ones and

you do a plus  two to get

the next guy there and then  you take that guy and the preceding

guy  to gets the next guy in okay

so that's  called a second

order differential  machine

and

it just happens to be what

  Babbage member Babbage what

did Babbage  do then the invented computer so first

hing he did was to actually make a  machine for computing

exactly those  numbers and it

was just he did it so you  could compute seven stages

of them  because again in mathematical

terms this  is a way of computing all of the values

  of all of the polynomials of up to a  certain

order and Babbage did it because  when he was

a kid he was 19 or 20 there

  were so many errors in his mathematical

  tables booked in the early 1800s he

  screwed across the room and he said to  his friend

herschel who became a great  astronomer he

said I wish to god these  calculations have been executed

by steam  meaning

gee whiz people make

so many  mistakes we can build a machine to just

  compute all its math we can

machine to compute all this duck  so

that's what this teacher intuited  from

these kids and now let's take a  look at

relationship

to the world that  you're more familiar with and

going to do is go through this thing  again and just watch

where the points

  are and I've drawn a line through

the  curves are so start

off again so there's  the ones

okay there's

a3 and a4

so you  can see the quadratic one is growing  very quickly now

it's next one will be  out of sight there

the difference here  is pretty interesting because

this way  of looking at

it is simply not what you  do in first grade because

the looking at

all the values at once which is the way  classical mathematics

likes to look at  them

in this case requires  multiplication

so even in the simple

guy  you have to multiply the slope

times X

  to get each succeeding y as you go  through

there and you have to square you

have a squared term to get the quadratic  so so this

way takes it completely out  of the child's world and yet the

idea  and the capturing

of what change is  actually is more fundamental

than the  algebraic way of looking at it

because  we've made a machine we

don't have to  solve in equations we can generate the  answers

so

in other words we can  mechanically in calculus terms

we can  mechanically integrate these things

instead of symbolically having to  integrate them and it just changes

  everything round this was see more paper

  it's great insight not this particular  example but

another one this this is an  example I did

  but the basic idea is if you have a  machine that

can help you do the  integration then all

of a sudden you can  chop ten years and change

outlook to  teaching

real math in terms that are  built into human beings

so one of the  reasons and it happened science

thinks  of math this way

because

scientists are  lazy mathematicians that's

because it  takes so much energy to deal with the  real world that

you don't want to spend  a lot of time messing around with

  mathematics so everything in science is

done by just adding things together and  these additions

are quantities that are  called vectors you've heard

of those but  there are fairly simple generalizations

  of what numbers are so this

whole area  is incredibly fruitful for

dealing even  with very young children

and of course  we have computers

so we can do things

  with them based on these ideas

and we're  used to using computers

in school not  for this stuff we're

used to using it to  imitate paper

in fact

it's expensive paper with a  little bit of magic

in their pay a  little extra money and we can run a  movie

in our book and we

can go look at  something in a library that spread

out  over the entire world rather than going  down the

hall to do it but by and large  pretty

much every use of computing in  most schools particularly

in elementary  schools is to do what business

people do  with their computers which is not to use  them for

anything interesting it's  basically automating the past

but if

take a look at what computers actually  are so

we can get our selves a little

  paint palette here

and I'll

make a  little car

and obviously

i'm not using  powerpoint here but

you can think about  this as a teacher as to whether

you  would

when you're trying to help

  children with examples and stuff you

  kind of would like to just be able to

  make things on

the fly because you do  have a dynamic medium

this has been one  of the hardest idea

is to make happen  because people

okay I've got my little  car and

the thing that's understandable  it's sort of a graphical

object and I'll  just call it a car here

and but I can  also look inside it and here's

something  that's a little less usual for

instance  here's cars heading it's

where the car  is pointing and if I click

over here and  start changing the angle you

can see  it's changing the car and conversely if

  you look over where it says heading and  notice

what happens when I change it

so here I have a visual representation  where

the car is pointing and here i  have a symbolic 1 and

similarly I have  little behaviors car

turn by five car 4  by 15 and

those of you tried logo you  recognize these are standard

logo ones  if I want to make a little script

  to take advantage

of these I can just  pull out some tiles and

now I've got my  car going and maybe

I'll get it to go 10  at a pop

okay so

in fact that I can  steer

my car so for instance if i

want  to make the car go straight i can take  it down to

zero that's a big one for  kids go

the other direction turned it in  the negative direction

so very young  children just

get a sense of concrete

  magnitudes and numbers but

driving a car this way is a little bit  like kissing your sister

so what you  really want to do is make a steering

  wheel so we'll paint another

little  drawing

and these drawings were all the  same entities and

when I look inside  this wheel I

see the same thing and

if I  turn this wheel

can see the number going  up and

negative and stuff and if you  remember the number

i put in here  determine

which way the car was going  which direction

to turn and how much so  it's kind of a invitation

to take the  name of those

the turn numbers coming  out of the wheel

and just dropping it  into the script here and

now as I change  the wheel

we can see that

the car is  turning by whatever the wheels heading

  is so here's an interesting thing to  think about

if you've ever had trouble  with teaching children about variables

a  child who learns variables this

way  learns it the first time and forever

  it's not the variables are hard for

children it's just that the way they're  taught is completely

unseated yes

  oh this so this is called squeaky

toys  if you go to squeak LAN

org runs on  every it's

free

yes that was so both of  these the

scratch was not the media lab

  and was also done on top of squeak so

  scratch and e toys or to scratch

was  done kind of four teenage

after school  kids as

a media thing they're both  relatively similar

and you can both do a  lot of the same things here

so the basic  idea

here is that you're trying

to  situate a

motivation if I want to I

to drive this car with a steering wheel  and

the fact that the number is coming

out of the steering wheel are going to  be different and so it makes sense to  have

them name and this script

icking over and over again so this  could hardly be simpler

and one other  little

thing is the car is a little  difficult to control

here and so

to the kids will want it why don't you  just put a gear and a

gear here being  for example dividing

the number coming  out by three

now you have to turn

the way the wheel  much further in order to get the same  influence

on the car so most 5th graders

have no idea why they should ever learn  how to multiply or divide

because in the  world that they're taught in school

math they're taught it's not  about scaling

it's about solving other  kinds of problems but

in the world of  science and

engineering it's not about  scaling

not about

multiplying as we as

we generally do but it's about scaling  things okay

so let

me try another little  idea on you i'm going

to make a little  script here so

i'm going to set cars  speed to 30 and

i'm

going to

set say

  increase the cars

horizontal position by  cars speed each time

so if I just do  this

or if I just let it go

stop

so does  does everybody see that

this is that

  first column that the six-year-olds did

  what I'm

increasing is the position

where they are so the

car is doing a  uniform

speed and these little dots i'm

dropping help us see the uniformity of  it but

what if i say okay instead

of  instead of doing that what

if I okay

look at this one really carefully now  what if I increase this by 30

each time  alright so the speed is going to start  off

0 36 d all

right so now the speed is  growing and

then I'm going to whatever

that has grown to i'm going to then bump  the car ahead

right so you see this is  the two columns

so the car is going to  go exponentially

so if i go do

it cow

and this gives us a visual way of

  thinking about acceleration because the

  distance between those two dots is the  distance

travel per unit time and the  distance travel

per unit time is the  speed

right so many so much distance

per  tick 30 miles per hour

and so what's  happening here is we can see

accelerating and the fifth graders love  to

know that the term for this is  acceleration

okay we have a question yes  I

know

your your commentary is focusing  on math

but my question has

to do with  the kids response to reading

and writing  or reading and typing in this case do

  you find that the kids

are more do they  get the transference from being able

to  use this high place and I try that after

  yeah

that's a good question though

reason I'm hurrying along here is I'm

going to be cut out regardless of how  interesting this talk is

it's going to  end at 10 minutes to

the hour okay let's  move

so I want the only comment here

is  does everybody

see that what you're  doing on the

computer can't be science  but

is only math that you can't do

  science on a computer

why

eah

I can simulate any goddamn thing I

  want on a computer I can live up one  side

and down the other so it's just all  math is is

a story that's consistent but

he problem is the degrees of freedom in  in any reasonable

human language are  larger than those the universe has

and  so this is this is why the Greeks

quite invent science except maybe  Archimedes

and the reason is they  thought God was a mathematician and

thought if they started off with  self-evident

first principles that they  could just

deduce the universe the same  way God did

could be true because that  this is a

lot of physicists think this  might

be true I doubt it so

let's take a  look let's look at the kids in the world  now

so you're a bunch of objects objects  that

you think will fall to the earth at  the same

okay

oh do not pay any  attention to

what anybody else the  grapefruit now

you two levels of shot  put sponge balls

are a couple

sleep  janet

is up on the roof  because

stopwatches by

the way to do it  but

when do you really not go

together  so put a sponge ball

okay I think we  should do the shot

right and the sub  ball because

they're two totally  different ways and if

you drop them at  the same time but they'll drop

at the  same speed drop

okay so

if you do this  so Aristotle

did not ask any children  when

he came up with the wrong theory of  this he

just deduced it using

a using a  wrong a common-sense way of thinking  about

what's actually going on but we  found that one

child in 30 roughly so if  you if

you have a class of 30 kids

you've got an excellent chance that one  child will do what that little girl

did  which is to pull the Galileo and just

  cut to the chase and say hey wait

a  minute that's

the I'm already in the

place

where all I have to do is just  listen and of course the

scaffolding in  the Leaning Tower of Pisa was

what  Galileo listen to it was under repair at

  that time so

but that's

quality could  call that a big idea

however

can also do  something

a little bit more here so we

  take a video these

might look like funny  video frames but video is just

part of  the objects that these this language  deals

with so we can make the frames  convenient to take every fifth frame

you  can stack them sideways or

you can stack  them like this if

you look at this what  do you think the kids say

when they see  that pattern

acceleration four months later

so four  months previously they did the  horizontal

thing with the car four  months later remember the

visual path  what kind of acceleration

so well

let's  measure

so we measure from the bottom of  one

guy and so we can just use these  little

translucent rectangles to do it

pre-measured these so

i don't have to  fiddle while I'm rushed

for time as it  is but then the cool thing

is i can just  stack these up

like

okay what do you think these

things mean  what are these

these are the differences

  between the speed at each time tick

  right each rectangle is the speed at

  each time tick in i'm doing a visual  subtraction

there and what i'm showing  is their progressive if I just subtract

hem off they're all the same what kind  of acceleration is

that acceleration

so  the kids immediately write this

little  script right here

let's listen to Tyrone  here

and to make sure that I was

doing  it just right I got

a magnifier which  would help me

so I figure out if the  size was just

right after I'd done that  I would

go and click on the little basic

  category button and then a little mini

  would pop up and one

of the categories  would be geometry so I click on that and

  here it has many things have

to do with  the size and shape of

the rectangle so

I  would see with the Heidi I kept

going  along the process until I

had them all  lined up with their height i subtracted

the smaller ones height from the big one  to see

if there was a kind of pattern  anywhere there

could help me I'm not as  this worked so

in order to show that it  was working

i decided to leave a doc  copy so that it

would show if the ball  was really the exact right speed Henry

  simulated ball is tracking the movie

  this is how he's showing that his model

  is in accord with the real world at

least two within a pixel so what you got  here so

here's something to think about  lily and mcdermott of

Washington is a physicist who looks at  college kids seventy

percent of all  college kids including science majors

in  this country fail to understand Galilean

  gravity that's what this is ninety

  percent of the children going doing it

  this way actually derive the equations

themselves actually  make the simulations from scratch

  themselves and show within

the limits of  the accuracy hear

that their model is an

  accord with physical reality and in fact  the difference

between Galilean gravity  14

feet above the ground and Newtonian  gravity is only one part

in a million  and so we can think of get

Galileo is  very lucky that

he couldn't measure that  one part

in a million or he would have  been very confused right

this way had to  be done first before the

Newtonian way  hat okay so let me I think I'm

getting  to the point where I have to finish up

  so

let's think about serious stuff now

e

live inside of systems and we are  systems so

it's a nice unification  through all of the

sciences engineering  and art

so if you're going to make up a  middle school science

curriculum for say  the eighth grade I would

not pick a  science like biology but I pick

a  uniform unifying rubric

like systems and  I teach all of different Sciences

the  systems aspect of those and

use  mathematics to deal with those

things  and my romantic ideal

would be the  planet is in trouble and we need to  learn

how to save it

and

what we've got  going in general is

something like this  if you hit

this mystery object with a  hammer it

returns to equilibrium but if

  I raise it up far enough it

doesn't come  back

so

what we got here

the most systems

are  like this the equilibrium

they have is  actually dynamically

stable but not  statically stable so

if you just tap  this thing

it won't do anything but if

tap it enough to get it passed its  center of mass bunk

and

thing to  understand here is that's

that's what  we're doing so what we're doing is  stressing

the earth and

little bits of  stress like

burning the river in  Cleveland can

be fixed up in large  amounts of stress

can topple the system and think

about  systems is when they get toppled they

  don't stop but it's in a new state

now  and it's going to resist

getting it back  it could so

for instance when the  climate has toppled in the past

aken between ten thousand a hundred  thousand

and five hundred thousand years  to restore all

of those numbers are a  lot larger than our lifetime

okay

let me  just try it

so

what we've seen here is a Jerry

  Bruner idea but I've tried to show you

  is that the

most important idea here is  that you have to heed the level of

development of the person you're trying  to teach and

if you know yourself like  it doesn't

make sense for a non  mathematician to try and teach math to

a  six-year-old it just doesn't

because the  six the

six-year-old doesn't think in  the same way as a teenager or an

doesn't if you want to teach real math  you

have to be a mathematician or have a  mathematician

in the loop because the  mathematicians job is to figure out what

  kind of real math is within the  wheelhouse

of the six-year-old

that's  really the job

so discovery learning so

here's the thing we have two poles in  the United States back to

basics and  discovery learning

both of this both  these are absolute

vs it

so it's very  complicated going into a meeting with

educators because they tend to polarize  long those and you

know any scientist  and mathematician guys think Oh No

and  the

the joke here is about discovery  learning is is

whoops is the teacher

saying oh no they're discovering the  wrong things why

are they discovering  the wrong things well consider

our  200,000 years on the planet

we had to go  almost all the

way to the present to  just do agriculture Greece was

only  2,500 years ago that was modern math and

  real science was just 400 years ago

  think about that the

u.s. know a stable

  dynamically stable democratic government

is only a few hundred years old these  ideas are

not easy so what you need is a  guide

so

it's not Hillary climbing  Everest it's Tenzing

and Hillary and

  sure we'd love to have Socrates and  Fineman

as guides but these guys don't

scale this is one of the problems with  school

books are great because you can  get some

of Fineman and Socrates but

I  used books a lot but I needed to have

real teacher that teacher had something  libraries didn't

have which is a table  full of junk you could make things and  learn things with

libraries should have

these but they don't know that they  should and I have

my dad who is a  physiologist to ask questions of

so what  we're thinking about

today is what

kind  of use could we make

out of the computer  since it has booked like properties

but  it also is active enough to

be able to  sense what the user is doing

so here's a simple

thing that's very  popular guitar hero

so the interesting  thing

about guitar hero is that people

don't have to go to school to learn how  to play it like

most video games

now the  bug with this is that

real guitar I used  to be a professional guitar

player jazz  guitar it's just

like a thousand times  harder than guitar hero guitar hero

is  it like simple drumming if

you ever  tried drumming is very like

just having  a snare and a high hat

and that's tricky  enough if

you've ever tried it you have  to get a couple of things going it's  tricky

you can think it's the entire  world because

this trick Ian of itself  and there's all these great sounds

coming out but it's absolutely a snare  and a delusion and

most here's the  prediction most schools

States are going to wind up using  computers in

classrooms to do a form of  guitar hero

for most of the important  subjects

because most teachers in

the  united states are not guitar players

alright so this is a huge

problem and  yet

without

replacing humans it's

  absolutely possible to make some

a  fantastic tutoring system for learning  any level

of guitar playing at any level

without having to have a human in the  loop that's what's interesting

you don't  get everything you get with

a human but  you get about ninety-five

stuff that you need to be able to do  anyway you

can do it and that's what

I  want you to think about is not replacing  teachers

here but to listen

to our  smarter than the average President as

talked to the National Academy last  spring he

gets it the

only way we're  ever going to get enough science

savvy  knowledge into schools is to help

existing teacher with media that  understand

  the science as children can practice it

  this is going to be a revolution

going to happen over the next year and  it is a grand challenge it's

as  difficult as the challenge that we faced

  40 years ago where the challenge was  everybody

should have a personal  computer pervasively network worldwide

  and

we have the funding for it and

we  were able to invent it now several  billion

people have it and it's time to  use the computers

for what they're  really good for what

do you think thank  you very much