Well thank you for the very generous
introduction this lecture is

I actually gave something similar to
this in Shanghai a few years ago and

for the purpose of the Shanghai audience
I had some Chinese characters and

I thought that.

Well first of all so
you probably don't Chinese characters so

why should I take a vowel.

And secondly so you don't know Chinese
characters and I want to remind you that.

Science is a cultural force is global and
international So

either you know these characters and you
can enjoy them or you don't know them and

I hope you enjoy them also.

But anyway I want to explain
a story which is new but

old and it is deep.

So.

I want to give an example of the history
of mathematics and its uses.

So main ideas.

This is really the centerpiece
of what I want to discuss.

Because otherwise we have examples and
sort of gee whiz Isn't it nice.

We did this we did that but I tried to
stand back a little bit and say how is it.

How is it that we did this and
this and this and this and this and

why does it actually happen.

And so there are some organizing
principles or sort of a rash and now.

At least that's you know my effort
to be a historian or something.

Whatever.
So you can take that as you wish but

I think that the that will be
the centerpiece of this talk is the ideas

of linked together and
show you where these examples.

Come about.

So first of all I want to make
the point is that there's nothing very

new about mathematics having
applications and just to make that

point I go back to Archimedes so that you
know far enough back but Isaac Newton on.

So now what did Isaac Newton teach us.

A teaches us that the laws of
physics are written as mathematical

equations and he is better at
calculus in order to do that and

that's new mathematics to write
down the laws of physics and

of course have been new laws
of physics and new things.

Since then but
basically that was a watershed.

From that point forward.

Any problem that was properly
understood in physics was understood by

means of a mathematical equation.

Now questions and
solutions are quite a different story.

And we struggle along for
several centuries doing what we

could basically the linear things
somehow could be done one way or

another and
the nonlinear things were hopeless.

John von Neumann who is also noted for
foundations of quantum mechanics.

But I want to emphasize here is role
in the development of the computer and

of computational science and
his deep contribution to

this collection of problems
is that he can solve

non-linear equations of physics
the nonlinear equations can be solved

effectively Here's an effective method for
solving even the nonlinear equations.

So.

Newton says we have equations one Norman
says we can solve nonlinear equations.

Now you might think that
that was the end of it and

after nine hundred sixty and so on.

It was all ancient history.

Well that isn't quite the case.

So he wrote a story in one
thousand nine hundred sixty about.

Can you imagine people are still doing
weather forecasting while the old

fashioned method like
looking out the window and

saying whether it's cloudy words you
could do it all on computers and

there's a long way from
ninety six you today.

But we still have.

Observation is still as vital a part
of weather forecasting as computer

simulation.

And.

Even today climate forecasts are limited
in their ability to use computers.

So this is an evolving.

Revolution which is taking so for
half a century and isn't finished.

And I have more to say about that.

Why is it that he was so wrong.

He would both profoundly right.

But also profoundly wrong and
being a little but

personally I will tell
you why he was wrong and

he was profoundly wrong because
the computers can handle

basically one like scale and
maybe if you're lucky one and a half just

if you know it just marginally on the next
one cannot handle mall the scale problems.

And many of the problems are not only
non-linear but there are multi scale.

So I have more to say
on that tomorrow but.

There is there is a there is work for

us even after a Von Neumann when
he didn't finish everything.

So let me continue with
some overall ideas.

So.

The first thing is that
the applications are not

narrow they're not specifically physics.

Physics engineering climate and
weather forecasting geology chemistry.

And those are sort of the line
of work of solving the partial

differential equations that define physics
based problems in science or science and

engineering but there's another set of
ideas involving geometry and symmetry.

Crystallography and Stein and
general relativity.

Who he started with some equations and

he said Well that should be invariant
under coordinate transformation and

that's a symmetry principle and out of
that principle came general relativity.

So he derived by pure.

Thought.

The equations in general
relativity now usually

equations in physics a long slog
with a lot of data and all that and

general relativity there isn't a lot of
data so it had to be done by pure thought.

And that was basically mathematics
although I think everyone would say he

was a physicist but we might as
well claim him as a mathematician.

The same story with regard to
young males and gauge theory.

Discovered independently
by Yang who didn't

realize that the mathematician had already
done all this stuff and that was also

a matter of exercises symmetry giving rise
to the derivation the biological sciences.

Have a huge number of scales and you can
go anywhere from population dynamics and

the epidemiology of say the AIDS
epidemic it's a very macro scale

down to the molecules the HIV virus and
the individual atoms that make that

viruses do what it does and everything
in between chemical pathways and

fluids and
electrical signals and so on and

then there's management science and
we have economics and we have finance but

beyond that we have in fact Georgia Tech
is a center for operations research.

So this is one of your one of
the stars in your firmament is.

Decision making optimization and
so on planning schedules.

They are aligned breeze diet and live and

die on their ability to have good
schedules and when something

goes wrong like this under storm and they
have to risk Rampal all the schedules.

Somehow get you there with minimum hassle.

And so they re re re optimize
there's a perfect schedule.

There was perfect at eight
am in the morning but

it's not perfect by
three in the afternoon.

Computer science says.

A huge number of mathematical issues which
are quite distinct from the ones about

network security and
things like that linguistics.

There is a large government agency
that deals with mathematics and

linguistics I don't know what his name
is that has no such name in fact.

And sociology which is maybe
the newer treatment to

this list with but
people do highway traffic patterns and

decide what is a disruption
due to putting in say a repair

at certain times of day you close down the
traffic and what will the consequences be.

And there is agent based models that do
that you can have mathematical theories of

voting behavior there is something
called the mark of process for the.

For those mathematicians among you for
those who are not mathematicians it's

a law of probability whereby
if you did something rather

today how likely are you to do something
either the same or different tomorrow.

And so you can do not only
the voting with the opinion.

But as to who you're going to vote for
today but

if you look at the rate of change you
can say well somebody is moving up or

moving down and you have so
many days the election and so.

Try to make a prediction with some
time variable in addition to the.

Instantaneous statistics.

And so on social networks which have

gotten a lot of prominence recently
that's of interest to add to advertisers.

Also interest to people who
are concerned with terrorists.

So there's many many
of these applications.

So in one nine hundred sixty.

Eugene Whitner wrote a paper which
is probably the most famous for

its title I'm not sure how
many people read the paper but

the title has been very widely quoted and
I think it says it all.

So I give you the title there and
you can go back and

look at the paper if you want to but.

Whitner was certainly possible but
why this all happens.

So what is the Edel actual force
that is driving these events.

So I already went through an outline form
there are equations and with computers

even non-linear equations you can not
always but often solve them as symmetries.

And then there is this business
of models that transcend scales.

Combining the large in
the small That's I would say.

As much for the future is
that as the present that one.

Pattern recognition and
the meeting hidden in data.

So these are some of
the intellectual forces.

And one of the technological forces.

Well the computing power
to solve the equations has

been one of the great achievements of.

The last century and
probably will be for the next the.

At least the first half
of the century also.

But it isn't to solving the equations.

The same technology is
used in data acquisition.

So you have sensors and automated data
collection so people say that for every.

Computational grid cell in
the weather forecasting or climate.

Calculation.

There is there is one data measurement.

There's about as many data
measurements as you have grid cells so

you have grid cells.

Roughly in the order of a thousand cubes.

For your large calculation so

that's a thousand million a billion you
have a billion data cells and so the.

The assertion which I can't
independently verify but

people claim that there's also a billion.

Units of data acquisition.

So there's a huge explosion of data
acquisition all over the place.

And then you need mathematical methods
both for solving the equations and for

the data analysis and for
the integration of the two.

And you need to understand it all and

those are basically mathematical
theories sometimes not done by

a professional mathematician in the sense
that they may get their paycheck by

working in some other department where
we know they're mathematicians anyway.

So what are the technological forces now
there's something called Moore's Law.

And I think more is a very lucky
fellow because he stated a rather.

Circumspect version of this law but
it turns out that it was so

powerful that people called Moore's Law
anything that looks at all like it.

And so he gets credit for

something that goes way beyond
what he originally claimed.

But that's fine that's.

You know we sometimes I think a lot.

It's fair to have luck in life so

I don't I don't I don't argue
with that interpretation.

And I will take the strong
view of Moore's Law.

And that strong view says that
the computer power doubles every

one point two years.

And that's about roughly two thousand and

eight when I gave this talk in Shanghai
but now it's two thousand and ten.

So that's fifty years
fifty years of doubling.

So.

Two point four So
more than a factor of forty.

Now I would say that there is absolutely
nothing in the history of civilization

that has doubled in its power by
a factor of two to the fortieth power.

Is not a factor of forty.

I'm not talking about forty times
I'm talking about two to the power

forty every one point
two years you double.

That is just an unprecedented event.

In the history of civilization.

And I think we all sort of recognize
even the nontechnical among us that

something's going on out there
that we don't quite understand but

there's some force that's
driving driving change in this

world that we don't know
quite where it's coming from.

And this isn't the only thing but

this is right at the heart of
everything else that happens.

And the data acquisition has
on a similar trajectory and

it's in fact very similar hardware
because there's a lot of silicon in the.

In the in the sensors.

And then as mathematicians we like to
remember that the methods are making all

this work has also moved forward
just about as fast and so

the methodology for using these
these tools progresses you also and

so all in all this is something that.

I think has no parallel and civilization
in the history of civilization.

It is a unique event in
the history of civilization.

So if you think about
something like the Iron age.

And that was certainly very profound
when you move from Stone the iron

from stone to copper to iron.

And you look at the timeline for
the Iron Age and it probably came in over.

I don't know what a couple centuries or
something like that it didn't.

Double every year one point two years.

Now maybe if you believe in going from
walking on foot to taking a space shuttle.

There is a big factor there and that
that might be roughly in that ballpark.

But.

It just basically it doesn't happen so
word.

I want to put this in a context and
let's pretend that you're

Charles Darwin and you're on the big
hole and so you write down all this

former you know jihad today I saw this
little flower and it looked like this and

tomorrow I saw this little bug
going to look like that and.

So the.
The descriptive stage of

human understanding and
botany for years was.

A little but in a Project Argus sense was

considered to be a descriptive
science that's really not true today.

But he wasn't satisfied with that.

And he wanted to organize his description.

And so out came the origin of the species.

One of the most profound
pieces of science in that era.

And in which he explained all of
the descriptive things that he saw

in terms of certain
patterns of evolution and

that is what I would call
a qualitative understanding.

Now and then we will.

Fast forward and
people write down a creation for the.

Way in which the genome when
it does different things.

When it combines it not only
has Point insertions but

you have whole the whole lump
of genome gets disconnected and

reconnected over there and so you can do
rather large jumps as well as small ones.

And so there are mathematical
formulas that tell you

what is the probability for
such an event to happen.

Now then you take something
that very practical and this is

an engineering college so you forgive
me for being practical I assume and

look at the HIV virus and that is known
to evolve very rapidly and that's why.

Treatments are not so good because you
have a good treatment and then the virus

evolves and goes around your treatment and
goes forward and infects people anyway.

So a little bit later on about the.

Methods for understanding the virus
in terms of finding out where it is

points of high rates of you Taishan where
it has points of low rates of mutation and

numerical methods for
targeting drugs that will block.

Versions of the virus with
lower rates of mutation.

So those are numerical and
algorithmic advances which then all of it

lead lead to you would
say engineering success.

So this is the progressive stages
of human understanding and

this happens not just for
our G. and not just for

AIDS It happens across the whole
spectrum of human experience.

And so it is really transforming our
life practically everywhere we look.

So you might have if you were my age.

You might remember being taught and

driving learning driving
to pump your brakes.

So you don't skid but the younger
people probably never got that lesson.

Why don't you get that lesson
because there's something smart

put into your break it's
called an add a lock for

a mechanism and
it does it automatically for you.

And it was first put in these large
tractor trailers but eventually got down

to ordinary automobiles and
I believe that's probably why you never

got that piece in your education about
pumping your brakes if you don't have to.

So the forces that are driving

these changes or advances in hardware and

as I say that's unprecedented advances in
the algorithms the software the use of

the hardware equally important and Moore's
Law Well I already went over this and

this is the one of the main points
no technology in human history.

In my belief has ever achieved
anything near like this rate of

progress over such a period of time.

So here's the proof.

And this is starts in two thousand and
eight but

if I had two more years of data
that would look just the same.

And the.

These are the top five hundred computers
and the top line is the total of the top

five hundred and the bottom is
the bottom of the top five hundred.

And the middle line which is a little
more drag it is the individual computer

which it has received
the fastest performance for

that particular year so
it's the one computer top five hundred and

you can see that's a little bit and
the reason is giant it is very important.

And that is that progress is sort of level
and people say well Moore's Law is dead.

So.

Here you can if you go back and
look in the literature at

this point I'll say Moore's Law
is dead computing is at the end.

We've had it.

We've had a road block a stone wall and
that's the end of it and what happens when

it hits a stone wall is that something
new comes up a new a new technology or

disruptive technology and jumps up again
and then it hits a stone wall and so

on and to stonewall for quite a while.

So that's a little the top computer
is a little noisier but all in all.

That's a story Moore's law is very.

It's still still alive in
spite of periodically being.

We've been informed that it had a.

Hit a brick wall.

So here's The New York blew it.

Brookhaven jointly by Brookhaven
a story broken wide a lot of

the work of present tomorrow will
have been done on this computer.

So what are the human forces
that are driving these events.

Well first of all any
time you do something.

Well sure enough people come back and
say What have you done for us recently.

You know that's yesterday
Now how about tomorrow and

then but in addition there's a whole
new set of issues that are coming up.

So we used to think we're pretty
good if we got the answer.

Well now that people
actually want to build.

I can use it.

The answer isn't good enough.

You need the answer was an error or so are
there any experimentalist in the audience.

Maybe not but if there are there.

You certainly know what an error war is
probably everybody knows what an error war

is it's an error of ours is a noose that
you voluntarily put put around your neck.

And then you wait three years and
see what happens.

That's what an air of war is so you can
go at this was a little bit of caution.

And once you decide what the error bar
is in this is an enduring University.

You need safety margins that if
you're going to find designed

something on the computer and
you don't even have a mock up or anything.

You still need safety margin so

you need a computational basis for
engineering safety margins that cetera and

for instance take the same thing and
apply it to the automobile industry.

And the auto billings are used to that
four or five years between models and

they always got creamed because
they did take them four or

five years to build those model every
two years people wanted a different car.

And they're always going to cream.

But they went on the computer and

it wasn't just that they could
do it with fewer engineers.

It wasn't just that they could build
a better car but they could build it in

a bad eighteen months they could get
the car onto the showroom floor.

And that way they could get it
while build it while people

still want the car they were building.

So it was a huge advantage and

the companies they couldn't make
it are just not with us anymore.

And this happens across
all kinds of technologies.

So every technology is
investing in this kind of

transformation because they can do
something better than their competitors or

else they fear their competitors
will do something better than them.

But one way or the other this
just is has a life of its own.

So this is not the conclusion of
the talk but it's a conclusion of the.

The Ideas section of the talk.

So mathematics.

Is not the only force here but
it is has a strong.

Role in this larger enterprise and

it is aiding in human understanding it
is vital central mainstream and growing.

So that's good news for
mathematics lots of other people win too

we are not unique and in fact we succeed
by cooperating and collaborating.

So as we win a lot of
other people when also.

So now I want to give some examples.

And I will take them from biology
engineering and physics and

management science and these
are basically pretty much examples taken

from my own experience so
they have a strong.

Stony Brook centric.

Flavor to them but I'm not.

There's nothing special these things exist
all over the world they must exist in

Georgia Tech and they exist everywhere
else but I'll just give examples that I

know about personally so
that's the basis for the selection.

Now the first example was done by
Sony Sonic and she did this actually in

the universe if used and but she was
a student of ours at Stony Brook So I feel

that it's OK to include her within this
and she did a study in the blood vessels.

And.

I will give you a discussion of how you
how she improved the design of a stent

which is something you insert
into a weakened blood vessel

we can block the vessels called an Ism and
if you're an Is if it bursts.

The chances are you're going to
be dead in about ten minutes so

if you're not in a hospital.

Chances are you're going to be done.

So a naturism isn't a small issue.

And so people put in stents where they
disc discover an aneurism it's a kind of.

Liner like a little plastic thing that.

Strengthens the blood vessel where it
was weak and so it gives it a normal.

And sort of bulging out
of this on a resume.

And that will do some drug design.

So the question is how to
repair weaken blood vessels so

this was being done all along and.

Sunny sonic worked in direct collaboration
with doctors and medical school.

She would never have done
this without without them.

And I believe they I'm sure they
would not have done this without her.

So it was a very good collaboration.

So the bad old stance and the good new
stance or what I want to describe.

And the battle stance.

Were a piece of plastic constant
strength and it just ended and

where it ended there was a discontinuity
because you strengthened it and

then you stop the strengthening and
so you have a normal blood vessels so

a stress at the end of the stent and

that led to a lot of wear and tear and
damage to the blood vessel and

loss of strength and
eventually the stent stopped working.

And furthermore they had
the branching ratios wrong.

I don't know how they did that I
think you do and they could have done

that correctly but you have a certain
diameter tube and it splits.

So common sense says that the diameter
of the two tubes it splits into

should total the diameter
of the one going in.

I mean that's sort of you know I don't
think you have to be a engineer or

Hydra dam assess the figure that out.

If you have a pipe and
you have a big pipe and

it splits into two little pipes you want
the total diameter of the two little

pipes to equal the diameter
of the big pipe.

But yes.

The area.

In fact you probably want
a little more than thank you for

correcting me you want the area to
be the same roughly speaking but

there's probably more drag on
the little ones in the big so

maybe the area should be
slightly bigger than double.

So on.

The way that's what she dealt with and
these are some pictures that.

Part of she was kind enough to
share her presentations with me and

these are pictures from from her.

I won't go through a lot of detail but
I think I've explained the ideas.

And so what this involved was first
of all experimental measurements

of the stand and its mechanical
properties both the bad one and

when they replace and got a new once
they could measure the new one.

Then they did mathematical modeling of
that and to see what was going on and

computer simulations and
they came up with a new stat and

then they had to put it in
I hope they put in a peg or

something like that to begin with but
they put it in something and it worked.

And so
now it be has become actually standard for

this is now the standard step for
for repair of a of an aneurism.

So this is has to do with
the ratios splitting and.

So those are the two main ideas and.

I'll go on now to
a problem in drug design.

And so
this is the first stage in drug design you

start with a library of possible chemicals
and you see if they do anything.

And so normally you have this
warehouse full of rats and

some kind of automated thing that will
put different things in their feed and

you look and
see what happens to the rats and

it's a sort of an ugly way
to do science but that.

That's the that's the old
fashioned method and still.

Still quite a lot of that around.

But this is the computer based so
you have these computer things that

are replacing the rats at least for
a portion of the step.

It is not correct that you can
replace rats or animals in.

Medical Discovery but you can reduce
their use and the point of this.

Is that you can cut years.

In years off the development time and
cut way down on the budget.

You can explore a larger search space.

So I don't think they ever do these
million libraries with rats I think they

have a much smaller number
of trial chemicals.

And the idea is just to try
all these chemicals and

see which one binds you have a an idea
where you want to bind on the HIV virus.

If you bind there or you disrupt
the virus and it doesn't reproduce and so

it's a good thing to do and.

Let's see how my doing
on time when I start.

Twenty minutes OK good.

So you it's a Sest the binding

energies of the lake and
on to this part of the wire.

If you're trying to get it to disrupt and
you can take a million or

whatever number you can afford with
your computation which is surely a much

bigger amount than you would afford
if you're doing it with experimental.

And typically drug discoveries ten
to fifteen years in the initial

stages then can be replaced
by computational modeling we

are plying this at Stony Brook to H.
I.V. and also to.

Flu.

And in addition you can target
drug resistance by finding.

Target portions of the virus
which are evolving more slowly so

that there are drugs that are blind
zero have a bigger be more

had less drug resistance buildup.

So this is just some schematics of the.

Of this thing this red thing is a leg and
then it sticks into the green thing.

And you can see the way it's the picture
suggests that it was really happy to be

in there so that gives you
a good binding energy and so

that would be a good link in the family
according to the qualitative picture.

They're the suggested picture.

And at the bottom on
the right there is an actual

picture of the of the simulations
with a lake and then there.

So the search.

Has sort of hierarchical and
you start with a large number and

you have to have a very
approximate energy function.

And you get rid of all the stuff
that doesn't do very well.

And you get things that work more or
less and

then you have a more accurate
energy function you redo

a more accurate calculation you
could do this hierarchically.

And.

Then you need to decide where you
set your threshold which which.

Which chemicals you throw
out which ones you keep and

so there's a probability involved
there because there's a type

one type two errors you can
keep too many bad things or

you can throw out of the small number of
good things and never find the answer.

So you have can make a probability
a model that tells you how to get through

all of that.

And I think I will skip over the I
have a section on fruit flies.

I will skip over most of that but
I want to show you one.

This is a gene network for
regulation of genes and

a fruit fly skipping over most of this.

With a lot of mathematical equations and

some green went between equations
in the data so that's nice.

And with this explained
something called canalization.

Me coming from the word can now.

The idea is that.

In evolution or
in rather than in not in evolution but in.

Morphogenesis in the in the maturing
of an immature organizations.

You have a lot of errors and
many of the errors are corrected.

So you have sort of.

The genetic code you might say is this.

Correct in code.

So you have a lot of things that
go wrong but they don't go wrong.

Seriously.

And then you end up end
up in the right story

ending spot no matter that you
didn't start in the right.

Perfect starting spot and
it's called channelization.

And it's a well accepted principle
in biology in the biology.

I would say the foggiest
idea of where it came from.

So here is some more pictures now I want
to emphasize the lower right hand corner.

Which is a set of trajectories of the
solution of these differential equations.

And you can see that purple trajectory or
and

you can see the blue the green
trajectories the green

trajectories and the point is that you
can start out wherever you want and

the solution of these equations
flows up to a fixed point.

Now that's a very simple principle and

I think that probably most of
the graduate school students.

Might have learned that within one or
two years of your graduate studies so

differential equations.

Sometimes have fixed points and
if they have a fixed point that

means that point as a solution
the equation doesn't change in time.

But furthermore it could and
often does have a neighborhood.

And in that neighborhood things
flow into the fixed point.

So there's a loss of information.

Sometimes they just go around in circles.

You know like the solar system.

It just goes around in circles and

it doesn't get anywhere but sometimes if
there's a little dissipation in the system

things sort of wind downhill and
they fall into the fixed point.

And the fixed point then is
an attractor and it tracks.

A big area of the initial
condition there is a call

this the domain of attraction
as a technical term.

If you're in the.

Domain of attraction of the fixed point.

You're going to end up with
a fixed point no matter what

a very simple mathematical principle.

And that principle connected
through these equations that.

My colleague John Ryan it's discovered and

validated against experiment
through those equations.

If you start at of sort of a random
location of it's not too bad you're going

to end up at the same spot and
that's canalization So he explained.

A biological principle.

Why a mathematical fact and
the mathematical fact is so

simple that I believe.

Probably most of the graduate
students in this room understand.

Understand that idea.

So anyway that was I think
a big triumph in that work and

he's continuing with that.

And now I'm going to get into physics and
engineering applications and.

Use comparable processing I think I
will skip over that set of issues this

is a schematic of how you make a parallel
computer how you make a modern computer

it has many Basically many pieces
together with a switch and

they all do a little piece
of a big problem and this.

This is supposed to explain that.

But I'm not going to go into details but
here is just an example of

a design of a high energy accelerator and
you deposited a huge

amount of energy in the center of a tube
of mercury and it sort of flying apart and

you can see that thing in the center
looks worse flying apart.

And this is part of the design process for
building a new high energy accelerators So

that is an example of
sort of an engineering or

applied physics calculation
using fluid dynamics.

And we are also involved in the nuclear
fusion there's an eater tokamak

experiment being conducted in France.

It's an international thing with the U.S.
supplying the computation.

And so my colleague Roman Samuel yok has
been involved in the fueling of this.

The fueling is by deuterium power to tear
him as heavy water or as sea hide its

heavy hydrogen that would then if it had
oxygen would be heavy water so they do.

Terry must have a high view that has
has double the number of nuclei as

a regular hydrogen and it is very
reactive from the point of view a fusion.

So you can get a lot of energy
by combining deuterium.

Into Turkey and I don't know what you get
you probably get helium or something.

So they have these do Terry in college so
they put it into this very hot plasma and.

So the idea is to figure out where
that pellets going to end up and

shoot it out of a gun and
if it doesn't get very far.

It won't get heated up and
won't do anything and if it goes too far.

It hits the other wall and
it doesn't do anything so

you want to get sort of right in
the middle of the hot plasma and.

Very complicated physics I'm
not going to go into that but

this involves a lot of simulation.

And this is some of the details which
I'm not going into over this is I'm just

trying to convince you that there was
a lot going on in this prediction.

So many issues involving computation
modeling physics mathematics and so on.

And then something I'm working on myself
is a design of a scramjet a scramjet

is a mock seven aircraft is experimental
it's been flown about three times and.

It's a little bit mysterious how you
aren't sure you're not going to carry

passengers when they get
through having a work.

I wouldn't really want to be one of them.

But anyway it flies up and
it runs for a little bit and

then crashes and our job was not to
design it was already designed but

we're working for
the Department of Energy and

they were curious how you can do
error margins for calculation.

So we're doing the error margins for this.

Calculation and
it has a way of stopping it.

They called on START.

I don't know why they call it and

start when they should call it stop
with anyway that's the terminology.

So I'm starts and it doesn't start because
it burns too much and it pushes everything

upstream instead of going downstream and
trucks off the oxygen and so on.

So anyway we're trying to model
the top is an experiment and

the bottom is a simulation.

And we were sort of happy about that
we didn't put in any combustion yet

where if the bottom of the top
has compression so it.

It's not an A B. comparison but
it looked pretty reasonable and

here is the simulation that we did and
this is still without the combustion.

And this is we will use them to
study the on start phenomenon and

this is a matter of trying to
understand the calculations so

we change the grid and
we change the some of the turbulence

models we change the new
Basically the algorithm and so on.

We get different answers.

And the final step is to get our
engineering safety margins and

that is the project of the whole
team not just of what I'm doing.

So that's an ongoing effort.

And this is the schematic of
the picture the orange stuff is words

burning the burning hydrogen is the fuel.

Has a lot of shock waves bouncing back and
forth in fairly complicated flow.

So I think I went through this.

I want to.

So the.

Quantified margins of uncertainty
this is the safety margin you have to

take the distance the distance is
the distance to the bad stuff.

If you're in a good spot and you want to
make sure you're in a good spot you're not

sure you take the distance for
the bad stuff and

you said practice off
the uncertainties and that's for sure.

For sure.

Honest.

You know put up your hand in the distance
you have your safety margin but

that has units and
you want to be sort of dimensional So

you divide by the uncertainty and that's
a measure of of your safety margin and

then depending how important it
is you want to say positive or

you want to be one hundred ten or
something.

Whatever your management decision
what they need for a safety margin.

And then I would say a little bit
about the electric power grid is

something we're getting into
now I guess everybody is.

So we're studying resource requirements.

How many units are needed
to meet expected demand.

If you have solar panels or when there's
a lot of randomness in the electricity.

So we need a random source term and

then you do a simulation basically that's

the Monte Carlo It means you're doing
something random like the Monte Carlo

gambling the Monte Carlo is
a famous gambling center.

And this is the same thing you do
a lot of trials and see what happens.

So that's how we're doing a simulation.

And this is a map of

all the different generating units
in New York City New York State.

Something we're targeting We have
several different aspects of this smart

grid business.

And then we have just for fun some
logos from our simulation package.

So this is to remind you
that the talk is now over.

And I will just say thank you.

So.

Just seems like you feel that
the truck was given in China.

And I found a Chinese mathematician and
I would have to go back and look

at the name right because it doesn't stick
in my mind that's a very good question.

In fact I had to stretch to do that.

It's hard to write all the Chinese Europe
with that was I couldn't find someone

I couldn't find a familiar name familiar
in the West and the ancient Chinese

mathematics as

well yes I think we're all

right so
well it's not entirely true because

the general relativity
the general to the lot of

the young males was dissipated
by the mathematicians about

maybe twenty years before
the physicists discovered it.

So in fact it goes back and
forth I think crystallography is

I'm not sure of the first quarter
crystallographer as were were physicists

are mathematicians but certainly the a lot
of that was curiosity driven research.

So if I gave that impression.

I want to correct it and I thank you for
giving me the chance to do that

it

was a pretty.