OK With thank you very much for
the AOPA you need to do is be here and

to try to do so the things that they
will be talking about mostly where we.

Deem blasts and
I want folks who was here last year.

And I was also saying that you know at the
end they pulled seven or less live reviews

whether we thought like satellite
we take it in good but so.

Do I like it.

So so let me just try to tell you
a little bit what is the situation so.

So many common parlance so
you can see that.

You know the almost but you don't think so
and you typically have a flow right and

if it's any stationary flow then
you know what things happen but

suppose I just start protecting it and
then the things become more interesting

if you come up you know the what
I question but the question for

example I was sewing this
morning in my government

class they are float right when it becomes
a question you know that that's one of

the examples that we want to look so
the question that we want to ask these

two questions one is where they would cast
their export that would be cuts mixing so

I am not going to describe transport
by mixing but means that you start you

know face a space and then you go into
another part of the face of space and

make seeing something that just started.

And then everything gets completely as
spread out more or less evenly right so

I mean this is not a mathematical name and
so on but you can see that the two were.

Completely different concepts for

example in the first picture of that they
pulled things have been exported but

they're not mixed right so
they are moved from one site building but

they keep being together in the second
case of course in some ways mixing in.

Nice transport but
then you want to be for them when he's.

So know what these they may not hear
actually that he said maybe interesting

idea is that they may know if
the action that happens to.

Do all these properties transport them
mixing is that there is some object that

remains seen by the young.

And separate as they do right so and
I am very careful about the words so

you say the main that I'm not saying the
only one there is some very interesting

paper by in the vehicle for
me where he was proving that.

They become system side of
the building which is often best if.

It were just based on the assumption that
the only thing that separates the Senate

will surface and
that this that the thing and yet

at the other kind I mean of course for
me was I mean even when he was

wrong he was not wrong I mean it
was a very interesting thing and

actually this is almost through in some
sense I mean it's actually one of the main

invariance I mean that old old sort of
crazy sense cunt of said can happen but

they're not so interesting somehow.

So when we have time to go.

Basically And
then also the thing that happens is that.

So.

These embody and projects if you can for
example anybody and she then

in kind of stop things from moving from
one side to you know they're right but

on the other hand if you have for example
something that I mean you have people

nobody well like me a homo clinic dangle
and I was social Big yourself about it

then these can move things from one faces
pace to another like embodied in money

force or something so this is the type
of things that we have going to study so

I will concentrate on three thought I.

Write and all of them are OK I'm told
I and there's some kind of fine.

Interesting behavior so the.

The idea is that there are seven
are there are two types of I mean K.

in thought are you will define them more
precisely so they are going to be two

dimensional objects in which
the motion is like of rotation OK And

these come into flavors one which I am
going to call Prime many I know that one

which I will call secondary OK I'm They
have completely different proper of

the sun they play completely different
worlds they primary carry and

thought I have but we have to transport
that mixing on the second that I thought I

allowed transport but they just
make it this low but they allowed

transport completely and then on the other
hand they have but we have some mixing and

then I would talk about you know one of
the mentioned I thought so this is not.

That he says Who or all that things
are going to happen but I would not try to

go over the whole slew I mean you know
I want to be when I was going for.

There are many people that I have so
I would be talking about

to see dimensional mobs.

Because I mean the events
from maps have more.

To do to a study they have to have
naturally when you're going to see that

time period the throws For example if
you're looking at there they were flow

after the first bifurcation So the sum
up right because I mean when you look at

their body every P.T.O. then this gets you
a map and he's going to stand right so

these have things that they would
you say all these things but

they were of course I mean
the theory is a little bit.

General I mean going to the theory and
then you try to the if you're unsure of

course everything works and
the mention of money flows but

of course no magical person knows
that to go from any well to do and

equal to see them decisive the computer
is nice to be significant in the end and

equal to ten these of
course of the question.

OK but
there is something they wanted to poke.

About which is that we will formulate the
theory and I don't put that about the way

and then we don't need the system is close
doing they have also which is something

that appears very often in the later to
let me try to give you one example to

keep in mind this is what people
call there is done that mop.

All the volume preserving is done
there Bob So if you take away and

I screw up with the width you have then
he said he had a set up with a prime.

So what Google is that so
there is that out of the one goes on So

You Think Of these seven
nights the room with a waltz

identify the mark on the fourth item.

On the front they then defy them that
the sites say that if I write and

then there is One Direction so would you
though is that you change the height by

some function that depends
on their on their own their.

Own the position on the angles and then
use change the angles with something that

depends on the new height
this should be on a prime so.

This would be any problem there is some
number that they will give you a little

bit so let me just try to explain a little
bit I should have been there were several

there is life that I am missing.

Which Because I mean I want to explain
what the world is Venus of primary and

secondary thought I but
let me tell you a little bit about my

need to be the last of what I am now.

I am completely lost now all right.

All right so this is the thing so
let me I started to tell him to read so

we have gone to try to find to
the mention I thought I get so

how do you find do you mention I
thought I have come out of patience so

this is the finish and if you want of
you know the right so question because I

thought I had ordered meats and then you
look at the order beads and then they

are to be it's going to be expressed with
Finally many frequencies but you are.

I put the where they have the frequencies
right so you have the frequencies and

then you move by you combined them we
think that years you combine them with

into years and then age of people
passing along so if you look at this.

This is basically you have the function K.
which people call the whole function and

then basically what you're doing is that
you have an internal face which is moving

along but a fairly well with this
impression of frequency these will be

They've actually frequency and then.

By you moving along the state gives you
the position so this is the case like I

think doesn't have phase which
is moving like a cloak and then.

I mean in this case and of course and
then he said maybe a small calculation

saying that looking at the fact that
these functions at this phase these

property which is that of course is you
advance then you need time of opposition

if you have one time by the opposition
that my face advances by my God So

if your are functional Emilie's then you
say all of these bodies copy of The Sun I

know this is a function on the question
which is you know nice a function and

that's what they would
they have to be fighting.

OK So this is the picture right and
you have over here

a they I've talked about you know
of the time on the seas moving with

going to them to speed and then you look
at the through your older landscape and

then these lens case tracing of any
complicated develop dictates it.

The same idea works for flows now you want
to explain what does the equation for

Frozen is very similar so as you give
a back to the feedbacks then the equation

is just that.

In the Total they ought to be
moving around but figure well

they ought to be moving around perfectly
well and then when you look at the.

In they might be gay.

A you they need they sold this
complicated object in their right so

I mean you see that this is a little
bit of a more complicated differential

equations where of course that
people are very happy but

the function of not only says I need to be
complicated because this equation involves

that these so that's a little bit
more elegant in some sense so

I don't want to go into technicalities and
then it involves vector fields comparing

comparing bones except that as
well their idea is that of course.

I mean on these things that we have any
general proceed you have to try to do

all these business of chaos theory and
then things have been

implemented in many ways for
many different objects etc so

that he said book by I there in
the audience and your viewers forget us.

Aleksandr on looking at Mondello.

So the idea is that I mean and
I am going to musing my.

Well I should have said what I mean
the well the main idea is to the right

side question you don't mess up
the study they embody and sequential and

then this does Newton methyl to the choir
to use to do my thing properties

that allow you to cancel things and
then we would need to adjust but

I mean there's some of them up I
mean I am cheating a little bit.

On the lease on and I'm going to
explain the thing in I mean it so

when you have the feeling with this when
you have looking for two dimensional

thought I think the minute you know mops
then sell then you need to adjust but

I mean that's when I will explain
ways this situation and then.

But on the other hand they're.

Not to complicate right.

On Well let me give you an advance
of the things that we will but

they are going to ask them that we will
give me sixty really efficient for

the medical analyses I mean in particular
one of the things that they want to know.

Is that if you're looking for
two dimensional objects you have to find

the function K. and the function
case a function of two volumes so

they do maybe even fifty seven dimensional
space but then you're dealing with

functions of divide able shortly
which of course it's a big advantage.

I'm of course if you have these good
deicing functions of many more variables

the cost to very well except that I think
that I am going to go to the things you

need that there they start it's barely
more than it is going to be and

you don't methyl but
one misstep that basically that was

the number of places young these doubles
the number of the is that you have got

right requires basically or
they're in Logan operations on or they're

in a store it's where it is their points
in which you have these great pricing so

if you think about the Dean and you don't
methyl once you describe by scene or

then then you will need all of that
in a square to storage I mean if

your matrix is beyond the then you've got
to simplify everything to be of course but

but but then you're required or there in
a square operation storing Q I mean that

if the matrix is fully reviewing
it when it's just awful.

OK Also I want to call the attention that
the formulation of the main theory it

it's not opposed to the only theory which
does you that if you have an approximate

solution which says satisfy some condition
numbers then you come about through

solution the other by OK So this is their
idea of a post that you only see them show

up as dearie theorem sees something in
which you would try to find solutions so

far something you wanted to see but
I think you lack in my case

do we see like that then no but I think
the other sects will be the embedding and

it will be that but I mean right but this
is like I mean this is not a theorem but

it's kind of like there is sketch
of how a theorem should look like.

OK so
they feel them typically there's the.

It is that we want to prove
kind of the form that you have

something that satisfies the equation
without any approximate ever

right with any small ever then you're
ready Faisel going this your numbers and

then your take with it you'll
never be sufficiently S.

ball and then you conclude that
there exist at the solution and

then the solution is close to the self
in that you want it so for example

there exceed you don't have to just be
five how do you will stay in that seat so

exceed Could be there are so
too far completely nondrinker of.

Them include me that you are that I
believe that night that you could be that

you really believed what they were OK but
once you come once you can.

Verify that it satisfies the equations
approach you might leave then you know

that he said the solution so that he and
I you know this approximate or right.

Or right so these are posted here if
you have something because he proved by

just describing anything
race your mental and

then he said that he said mental
showing that in combat it is.

To us Aleutian.

And of course they idea is that I
mean once you have these methods and

then you bring forth in Afghan situations
so that you can prove all your estimates

then you have they never any official
in the medical who are with him.

So let me just read to tell you
a little bit which is how you can read

the hospital room and I will try
to describe why you need that but

I mean it well this is how many
simple example I know you and

I again I for got pulled over so this is
anything I will see them right there you

see you think I will system in which they
hide to be remains constant Right OK So

when you pull tapes you don't need to see
it you see that the set of frequencies

that that is the range of is the brain to
form they got right so you let all these

things come on then you move my God why
don't they get so this is our curve so.

If you look at the set of frequencies from
I got one hundred made up to that appear

right so this is a curve.

Right then if you are then all that
is more power to replace your own

right juggernaut that is more brittle base
and then the curve goes into a number of

things like that so there is no
frequency that gets preserved so

this is very different from
the situation the cup in C.

and I mean Tony and systems so you come
into a system so everybody has heard of

about the fact that certain motions
with good frequencies have preserved yet

you cannot guarantee that the system
with a certain frequency get yourself

even if you make up of the direction that
remains the system into it I will write.

For purity I mean if you make this
instant to remain I mean think I will

then that's there that
is there there's there.

There's the situation.

OK So there you there is you can yeah
use something buried it's thinking

which is a little be good but they will
maybe try to sort of say these things so

that he have so the idea is that they do
water but I mean there are so you have

some artificial but I mean that isolation
right and then would you try to go East so

this is something which is so
you have these have to feel but

I mean this right so you have these
are difficult but I mean there's and

then when you will so is that you
kind of think something is likely so

you get the frequency if Mueller
from a guy satisfies these are and

then you can fix their height they have
any tight so this is an I will explain

you how you look at it but
then they would you'll thing is that these

meal it's had differentiable function of
the date of your program which is from

a guy named SIEGEL So this is something
we call program except that up and

then good you can do is that
you can solve the equation and

you will fail my guy well to see it
right you can try to solve this mule for

make I want.

SEATO and of course then he said Let
them eat the fat thing they got a little

difficulty which is that
the Omega rang just so leo but

I kind of said except that I but
never mind it does the same so

typically I mean if these things where
there you've got functions would you

expect is that on that some mild
degeneracy conditions you can get

the Omega functional facio us this will.

This turns out to be like I said
that a few things these but

these things got a lot of silly
what I would buy with me OK So

what you have pain is that at the end
then you get these curve and then

you they call it holds which happen to be
then six at that but that is just the in

a set of let's measure it and then these
have the frequencies that you can find.

OK so that's more or less the story and
that I said the next month that just

because in many of these situations
that we will be discussing.

That he's not doing that no none
degenerate icy conditions in there and

put the system so that you can try
to sort of if you have an extra But

I mean then you can then the things
become much easier because

while he was told to do that even if
these things but if you have you need

much less on the Genesee conditions if
you have more but I mean there's and

then you can prove all these is multi
students by the silly OK this is the type

of things that they wanted to discover the
thing that they were looking for before so

when you look at these two dimensional
thought I right so remember that that

embedding but they can be sitting in this
space into the foot in ways right so

they can be seething in one way
that they were putting over here so

that they have in this way that always
that's a good half over there if

if I want I mean to fight do it right so
these are things that you know or

they can be like deleted roles that
go from one side to another right so

this is so
that mathematical description is that.

You look at these waves but I might have
thought I they cannot be contacted through

all over the mention of the right but
they're blue ones they can be contracted

to one dimension I thought I right OK the
one dimensional so called because I mean

these things but you know I remember that
different than they were back at that and

they say they're right on the left and
right so these things go across and

you cannot sort of move the foreman into
sort of such a way that they go into

something low where they mention but
if these things have rolled then they go

across like a few then you can sort
of a squeeze these that action and

get them into a row where
the mention on thing right.

Well you can see what I was telling you so
if you look at these red and

these list of suspicion here you can
not go from here to the top right so

these things prevent the transport
completely and the second that he thought

I do not prevent that transport OK
because you can wind that on them right.

On the other hand the secondary thought
I they prevent you the mixing because

anything that this they seemed
sorry remains inside and

doesn't mix with the things that I.

Write So this isn't like the thing
when you're making a cake and

then just steering the steering and then
all of a sudden then you find that clump

will roll flower right and
that's that sort of thing so

everything is very thought only makes but
that only still

leaves them perhaps a flower floating
around and that's my kind of thing.

And and you have moved things from one
site to go that are very quickly so

this clumps of flower.

But assume sort of lower the mentioned
I thought I was happy having your cake

mix in there but he will yes.

So you see this is the situation so

the sum of the two things they come
extremely different properties for.

Mixing having steam.

Different properties for
all these other things.

And so this is the remark that I was going
to say over here on there is one all that

remark that I would like to make which is
also very interesting which is that when

you look at the in thinkable systems
in which the thing is pretty set of and

then things just move on
depending on the height OK and

the surfaces these things don't
have secondary thought I right so

what these the sequence of these when.

There is no reason I would put it there
is no we see put the racial theory before

they say so the second that he thought
I do not continue do they think

I will system OK they become singular when
they so basically will compensate and

I will show you some pictures will
compensate that they become like

a singular particular racial theory and
there is no way that you can get something

has moved on then you can guess how the
second thought are you happy by this but

will that ever ways of doing it then so
one so that's one of the things which.

There is also know that of any import of
them properly that would play every girl

which is not the primary three and
require that that he see them in flux and

the second that he thought are you
exist even in systems with

mean flux which is something that So
this is what they mean they mean flux.

They mean flux appropriately of
the system which sees that so

I would just putting it into their
mentions because that I had to make sure

that I'm going in through them insurance
is very hard but I think I thought it was

like this right which is one of these
no contract people daughters right so

then think they mates right and
then calling the things that have going up

with paucity of mesure on the things
of cover going down with negative so

then you have thing and I'm bored which
is called to see them in flags right for

the she's there you know that they've
been in black we all should be

the area that they put the green with and
I got it right OK now

it's very easy to take that these
number that's in the pen on which some.

Gold you took right because for example if
you take another set of gold that piece

a little bit below then the SO THAT
THING WE GO will show that on right on

because of the UP A celebration there
we go of this history is the area

of the steeple of the image and
then this does you that.

Mean flags you see independent of
the circle that you have taken.

But what is your convincing that I mean
this is appropriate give them up and

if you have one embody and
photos then it would be seen so

the seed only influx the sun necessary
condition for the existence of a second

that a total of all part of a primary
thought but for secondary thought I.

They don't care about the mean flux
they have sitting around here they

don't see whether the mob he's moving up
or down and so on so you can see that for

example you can make up in the relation
where you have something thing here you

can move these so that apart up and then
you can destroy the tsunami in flags but

you impacts the secondary totems So
the secondary thought I it's a very

interesting property that we're going to
think a lot of the thing is that they.

They have systems with me in flux and
this has been an important game sequences.

Be close it tells you that even if
you're flashing a channel etc then you

can still tough things that but
a system don't mix.

Right that produces them don't mix and
these are the things that happening I mean

actually I was looking at these if
things are going to hear because.

So let me formulate some conjectures
now I mean these things but

you have any import them girl.

For Baby things so
if you if you take the system that example

that I was telling you which is just
this this see if done to see which is so

very deep you've got more than.

Of many things that is happening.

In many fluid systems then
why would you think you know

up at a basement if you think
somebody if you think enough but

the ration if you think one of these
things that you did then then you do

the see have been the primary thirty These
have be it for large enough seeking.

The secondary thought I think would get
to these that they then disappear so

they did that even if so if you're having
something that is flushing you're sinking

right area and you're going to
create the mess sold them right so

you're flushing then try not to say
something that people are more or

less a little except that
have been then you find.

This field I mean so I mean.

I was trying to say these things so
that's this conjecture is true for

the mission I learned up instead of
being it than that and it was proved by

one side of the conjecture was proved
by your not there and the other.

The other side was proved by
people who are so over the.

There is something I mean this I am
putting these as propaganda because I mean

we actually have studied for example
things like that I mean since February is

one of my heroes study there for
me bust out that bright and you look

at the fed me bust out on system I may
be well the that he sat of recovery and

success except that I was right and then
everybody says it's a thought I exit that

well they like several of the things
that we study is that if you

if you look at their second body if you
look at the ratio of volume between right

many thought I am second that he thought I
they play my thought I have explained in

Celia smaller in the number of degrees
of freedom compared with this that is so

if you type the little thought
of all they not mix of so

both of them might make legible eventually
that's what these that conjecture but for

sure there are but I might be out of much
more than if you go down the secondary So

if you are trying to find our current
scene from the past now a lot more.

Systems like big molecules
are something that

most of them are covering says given
to you by a second that he thought I.

Had going back to or so I mean if.

There's hope to be false I don't know but
but but

I think I mean we gave quite And
I mean he's not just.

You know just a formula I mean in class
I think I think I just if you Casey

has to do with every normally
say she had many things of class

some medical experiments behind it.

So let me just have to tell
you what these delegates them

to compute their justice but I mean
that's and everything I would go but

he quickly over the I'll go with
him because I want to emphasize

that Delaware thing works just as well
I mean this is one of the reasons why I

didn't want to use at all
the fact that we have me have.

Taken I will which is World Cup and
see most of the league that shooting chaos

theory because they want to get these
secondary thought I would tell you how to

compute that makes it so just added with
an approach in its rules you don't like

that and then you try to do on your own
method what is then you can method where

you change the game to Kate Plus there's
the and then you change mewling do you

plan to meet them in such a way that
first thought of that if they kill they

ever write so how much that changed
first how much does the change

changing first part of the way this is
just the change rule right so if you

took a pleasant thought these thought of
changes in the least right the second time

changes into these That's very easy
because he's leaning I think a right and

then this is the effect of changing
the parameters of the right and

then you want that this is equal to my
city if you look at this equation this

equation is like the most that we
go to this thing up you have seen

two points and then the summit that it's.

A little bit hard to evaluate except that
I and if you try to do it by would force

like you're seeing what they are and
I think then you're out of there because

then you're very quiet or they will
finish stories one over there often you.

Operations and
then you realize I mean so think and

do we like a million that's the thing that
we have are going to be using more or

less right so or
that in this thought it's.

Repeat if you need to compute that I
mean you need like eight gigabytes or

so if you just keep one of the functions
but you know if you don't need fifty then

needs like four hundred if you go
by these I mean these things well

the main idea is I do try to use so this
is something which is called sometimes

I think I do see reality which is the
following yourself so you think that he

about the use of them by the I'm sick and
then you've got a pretty dramatically and

if you think that he got these this
is just the chamber All right so

what disturbs you Jim I think Ali is that
there is these back door to the policy of

with respect to K one.

So these these gets transformed into
just it's corresponding back to

the things I have found to make those
that move very nicely on their way and

the video at the right so you might think
well it does you that there are these two

back to get that out for me to each other
so they think that they do is I think so

but this is not the frame so what you
do is that you take a perpendicular to

the previous two which in this case I just
think they're there they cross product

line and then they normalize it so
the volume is one way so

yes normalize it so
that the volume is one and then so

they the idea is that if you can see that
of these flame then there anybody even

explaining this frame it has I made
a simple form which is that it's happened

I mean because lots of C. dose and
there you are going to lose one so

this is the main idea there is a picture
of the goes with it which tell you let me

see if I find the picture or
maybe I should.

I still have the pictures someplace but.

I apologize but the picture is
very simple let me try to the.

But here because you have these things
this is so you have these two vectors and

these two men those going to themselves
right so these two characters

of the SHE'S ONE goes wrong and
who goes into the corresponding thing and

now you think the I know you
think they're not about.

Now you've taken over my life not mine so

when you look at these
put it in the pipe it.

Right so this president by playing cards.

Volume One you look at the minutes.

And the maids because it's everything is
volume percent of me is going to be up but

I will if I play the Volume one right so
what do you know if this but I lead pipe

and goes in to be told that by only by
play them both of them couple one well

there you are in the race is there any in
the base right because they get reset and

now so the only thing that you have
pain is of course the height is one.

Right so that's what you have thing that
of course these one on one come because

these two are in body young right
in the right way and then you

get these one a with you have because
of the geometry right and then the so

that one's I call the mass because they
have C.R.S. right and they can be computed

without them I think only I mean you can
compute them better you see me right so

this is their formula that you get which I
mean the way to that pretty dramatically

is that that that he what the experience
in this frame is just these matrix that.

So this is fantastic because then when
you look at this equation if you express

anything in these equations so you express
the corrections into the right frame

then they go to extremes
I think these form which

is very easy equations to study because
basically they have a constant coefficient

diffidence equations which you can
deal with by fourteen analyses so

these equations some of the prototype
of the equations that you get so

they're equations and I think that
he said all that type of there.

There should be a your feet I know say
your feet up let's all make these right so

it's only about the so
if you see say your feet.

Mine and say your feet up let's Omega.

Equal to a year.

Of that right so you give me at that and
then I have to prove you say

well they are the eyes of many simple
leave you think for your analysis right.

Shifting is that you're going to have
serious right is just multiplying by

the by the exponential so this is
the formula that you have pain right

when you divide and
of course you have one condition so

this is I mean I mean I don't think but
I mean if so you get one condition but

then you get one free them so
this is like the freckle Malcolm at

the result the first one thing but
it's like if it was find a dimension so

they can think of but
I mean this works as if it was fine and

they mention you get one condition but
then you get one three but I mean that

because then you're going to have
the constants right so that's not too.

Too too too difficult and then that he
suddenly sees that I mean I'm not going to

these because I have too much so
when you get into I want a component and

then he said that we define magic thing
that happens which is that the when you

look at these equations that you have here
this set of comporting there is something

magic and so on I knew this is things I've
seen all mean flacks then you can solve

the third of the equation the abstraction
Viney says because when you look at the if

you have some totals like these when you
look at the average of these thing over

here to judge the flux
in first thought there.

Never mind so let me just try to say
these things have been here and then but

are sold of has been established at the
end is something that if you have the your

front numbers so much place should not
degenerate I see conditions except that

having you can try to have these.

So anyhow so this is what the scene in
they wanted with us and then these.

I mean that remark is that this is
completely up of studio the system which

said there was you that if you think
I'm not a computer solution then.

And they assume satisfies the equation
with accuracy they you have.

The solution everybody OK And once you get
that done that I've said that all the.

Conditions give so.

Let me just try to sort of make a few
remarks from the calculations I mean I

went through they.

Really are going to think with detail
because I want to convince you that I mean

all the steps that you need to go
are composing functions a culture but

I corporations think that he about
Dave's shifting from one place to

do it to another to be duplication and
then solving diffidence equations so

there's steps that I might act but

that I might you know are fast if you
would just use this going to say sure and

I agree that there are things that I mark
in day are there fast if you take forty

of coffee since right so by street seeing
a couple of times between full of coffee

since I'm getting the set that I which of
course you're going to buy you food fast

food that's for there you have.

That's where they look and

comes because you have to use a couple
of times that fast furious that half.

And of course the first full day
of times when we send Logan but

of course he has been
optimized to do this and

there are people that have them hardware
except that I show him so if for

once the theoretical estimates and
Logan I've not really gives Lehi.

Already made sense but
actually they had underestimations.

Because I mean thanks to the number of
people that have worked in doing so

anyhow so if you're someone I mean this
is something which comes how dramatically

from the mathematics and I think that's
going to tell you one is the one.

You have these supposed to be only
theaters then you can prove out of

the gully there is more dependence on but
I mean this right which is very useful for

these thinking of but I mean there's
no we have that side then that is so

soft I mean I would just drop of
where you live in which is that.

If you have solutions which
have sufficiently regular and

then get out them I think Ali and

the only thing is there might be some
at least they could set there and

then that he said think that you're in for
a breakdown that is when I still have

ceased to exist all day if I you know if
so will it in order to have to grow up so

that's also something like that and
then if you put all these things but here.

Even if you implement this I'm going
to make said that even with a million

Confucians you can run into our.

Regular laptop I mean you know.

And then also I want to mention that I
mean this is some I thought that the.

Continuation method right because if you
have an approximate solution you polish it

and then you can amend your part
I mean it's accepted and so

then you can get pretty close to that.

So exactly these methyl
goes implemented by you

I mean by I don't focus on Jimmy's most of

the paper almost I mean over
a year I go in the archive and

I'm this paper actually so I mean I cannot
do it justice because it's not just

an implementation of this I'm going to
think I mean it's actually much more

because they give you
great video which is.

Which is something that they call their
method they go by they compared with their

green screen Didio in an approximation by
you know they go to be they also do of any

exhaustive thing except that I buy
well how that's what those get

approximated by if you know the quarter
beats and so on and this is actually

even from the point of view of mathematics
the episode is really amazing because.

Mathematicians simple don't use that
you're fronting up books you mention these

very hard to write but
they managed to actually.

Group some of the results are in
my opinion one of the things that

is really fantastic in this case
is that of course they discover

that when these stories are yet
about to break down they actually cry for

help they start coming in scaling
relations we make it actually

very easily do that they accept it and
then there are all these fantastic it's.

That of course I've been writing for
after Molly sation group explanation so

let me give you some so this is one of
the total says that I have computed by by

by folks I'm missing this
paper that I mention and

they go on this is basically seven hundred
thousand points except that I like two

hundred two hundred I think one hundred
twenty eight hundred twenty eight so

a fairly large number of things so
this is so subtle that.

I mean this is a little bit of a different
story so this is have all the implicit

remop but it's have all been presented
remop of a very special kind

that you have seen so the there's
the physics and this is something that.

Lasts And I mean this is already I mean
it's much easier than the Berlin that

folks and me see in some sense but
I mean it's.

But it's something which more or less
tells you what the thing that happens for

the thought I think right so
they have to be not very regular and

we have pretty sure that this is
within like six figures of the now and

then you see that there's something that
have somebody in that extra good start to

it because so many streaks accept it and
then this is another view of the same

object except that I so this is what I'm
really a specific weapon not going to lead

the way he had but this up you have
seen I probably means only the physics.

Of it a lot of symmetries
that allow us to compute but.

OK So let me try to tell you a little bit
about the role of secondary thought I

thought that was Perth and mixing so
this is basically paper the.

I am.

Groat Well he was here and so
they they do celebrations let me just read

to say a little bit what is
the situation is that they

in THINK I WILL system does not contain
second that he thought I was right but

nevertheless if you make up at the ration
of the system which removes they

don't think I really the then secondary
thought are you all of a sudden Apia

where do they come from well they come
from grace from Lance is right so

this is very similar to the situation
that everybody knows that when you have

any epicenter being mappings and
you put it out of the my little bead

then just by getting these chains of
file and things like that right so

this is like and I'm not looking I have my
mentions of the same phenomena right so

everybody knows that if you
put a thought of a system

which he said represent a being then you
just are getting something like this and

so on so these were the global
already way poincaré Right so

you have to go the court of beads and
some of them my lipstick some of

them I what they were so the only thing
that happens is that now we have.

The next that I mentioned this.

OK is not the see do sort of just to
fight but but in cars being done so

you can use I would I didn't feel any so
that if you have a fresh one thought of

in the in thing I will system was you have
but at the base you it breaks up into

find a dimensional thought
I put it about the ME.

And now then you have to say Well so
then you can do up at the vision theory

then you have to learn all
the preparation of every.

And then this is that of things that
survive they will be menace you not

thought I saw wrong doing these elliptic
toto survive I mean the thought of them so

it's really funny they leave photos
does not survive typically And

you can prove that it doesn't survive but
they are but the things that sort of think

a seed do survive because of the theory
that they was brewing before.

The theater missile it'll be dead and

they want to mention I'm not really
hyperbolic thing social survive because of

normally hyperbole city theory now they
have responded This is slightly difficult

I mean the reason that this is this is
difficult and it was not done before is

because air here they're not beginning
to see conditions degenerate and

the same time that they have of
the generates so that to have them they

generate at the same time and you have to
be extremely careful and extremely granted

that the of about how do they entered
into these Wait six at that hour and

then being twenty that you've been deposed
if you only theorem space so if you have

to check that then on the unit or
sequin these things disappear at exit so

let me tell you what is there.

If they do the simple experiment
that we do company for

in one of these an episode of a billion
preserving mappings with known pseudo

flux then I mean this is you can imagine
that this is the type of things that you

can but I mean compute that for several
days and get the interesting things and

actually this is running
seven of my computers now and

so on so you pick on the southern of
them then you eat that eight right.

I mean you're flashing things right
just trying to do these things and

you put on them so you know mean flux then
you think something then you compute what

I mean you don't need the rates and now
these computers can do it even nothing and

then if it has moved too much
then you don't draw it and

if it has a state then it yes so
yes maybe so

you look at what happens and then they
the things that we claim I mean and

this is of course that the only
positive message or things that survive

are things that pairing case
by second that he thought I so

this is a plane which is
based on medical experiments.

So let me tell you more or

less if you run this experiment a little
read this is not the best picture but.

So this is what you get so
this is when it's done that I'm up.

For this experiment that they were still
in there which I mean of course you

can program it in an afternoon or
something when you're waiting for

an airplane or something.

And this is what you get so
you get these two and

these deals have been mistaken
Well then you look at them

a little bit more carefully and
then you look at the boundary and

then you look at my god these things had
a fool of a second that he thought I and

then you don't find anything else right.

OK So I mean I if you use theorem
six at that I think you know that

something else exists but these things
that you can probably say exactly so

you can be that he really did that they've
because then you say Well I'm I'm missing

something I'm missing something I'm I'm
using my you doing something like that

you know OK so let's try to be
a little be more careful and so

on because you say well all this depends
on how long you wait I mean what

happens if you wait a little bit longer
Well then cities know because that is so

many amazing thing that happens
which is that you try to feed

How long does he think they
ought to be to escape and.

It's just them then Osaka
by these three anyway and

this and they put up with this I mean
they've got the but I mean there's but

then you can feed with the but
I mean there's you can feel rather well.

Several million.

Is not there so I mean you know it's
impeding So all of these impeding and

so on and then he said relation between
the Fluxus I was telling you they're

going to cure that was that when you have
enough flux then everything gets tied up

except there but the interesting thing is
that the flux that you need is more or

less proportional to the size of the part
of the ration that you're creating OK So

this is a little bit surprising for

us because they may sort of the thought
I use basically a square root so but

the size of the thought I had that
destroys the size of the flags and.

The stories that thought I ease I
mean this thought I had a very big

because they had of this size square root
the flips alone but the other can get

a very fragile because I put the question
of say steps along can destroy them so

we don't understand that.

Also That's what I was telling over here
that when you look at these things so

this is more or less the volume of the
thing so when you don't have any flux then

these things come a size which is a square
root of types we learned which is fairly

big but then nevertheless do these throw
them with with up at the base in which

the size of the loan so
this is something which.

I mean and this sort of.

Thing by running all these for
what they want it is so you can cover

a lot of fun and then you feed they and
then you can have a lot of fun.

So anyhow so there.

They did the lower the mention of
the hyperbolic thought I I I'm not

going to describe didn't do much but
I'm going to yes show your picture so

this is a very simple case which is.

The question here legally but
based on that.

This is the picture of what
actually they are doing by me and

thought I and then that if they will and
if they will my knee folds.

So that I have to embody and
taught our young that if they will and

if they want money for.

This is the start so that when you look
at that this is the thing that The Times

says the mixing and
the transport right so let me give a cat.

They got these more or less like that OK
So this is the kind of this they will sell

that out of this to these days
because the quote we we we found.

Then the the little out of
this they were money force and

then that way that again if they were
money folks and these things had not be

you just that they fall onto each other
and so on and then they just have some.

The five getting into each other because
they're so there are these two things and

then you see that I mean the thing that
happens is that if you're caught up I mean

if you want to go for all he had there
right well they see a thing to go and

just coast along and then when you
go there when you come back right.

So if you were.

In Iraq it was something I knew what you
would hear and you want to go there when

there the thing would be to shoot
that rocket to go there but

if you just go along and
go along except that out the you're right

we're left with photos and then you jump
if you sort of select the time of jump

correctly then you can go with fuel.

So these sort of type of things that.

We have looking at except that I you
can apply them so all this element bang

goes that you look up I mean the beach
ball you need them I'm dead many including

Kate because I mean you can see that they
have to move through has been absolutely

somewhere because I mean if you look at it
has been sullied the means that by that I

mean I'm not zero so if you have to but
I mean there are things well.

Chances out of that the thing
will go to seat of some point so.

So just like that that
all these things and

then when you sume then they
just have it coming but

it could be exponentially well and then
this is reassuring so that they think us

all these extremely good accuracy because
I mean if you look at it then this is

what happens in the third of the of these
really when they said well did it or

when I mean sorry it's in the third of
this here it's in the second decimal digit

so that somebody is pretty good
that you can get the secular C. So

just to finish let me tell you seven I'll
mean this is like a long that at least.

And I just thought of course
with a cry for help right so

this is how long the least and if somebody
can for example one of the things that.

We would like to Luis if somebody has
some more at least exist thems right that

you want to look at the ad then I mean of
course we would be very happy if somebody

that's it except that I write so I used to
throw a I put all these on the release and

I just started from the most practical and
in my opinion a straightforward but but

of course we were quite a lot of work and
a lot of cleverness to go through their

mode of mathematical one which is to leave
them didn't want to speculate so all for

example that is something which is very
much the in yourself thesis that the even.

So when you look at them by remembering
you know I told you that in divine that he

you find the body and thought I where I
was kind of lying because then you find

also sort of all the things in
the bone that we try to blend there's.

And sold in the examples of things like
that and we don't understand those I mean

is the same situation that with happens
when you look into the mention of mobs

I mean to you mentioned on mobs then you
look at the bond that you have the islands

and there is a lot of where both Jean me
said all that about that when you mother

in them things like that so these
are not a lot of these going on here.

Martha can I they'll already have spoken
about the bond that you have hyperbole

cities so you have these well
where the mention of thought I

had to they break down how
do they lose credibility.

That out of all these so that objects
that we don't know how to compute like so

you know it's things of perhaps all these
had well defined math them I think I love

jokes but in the world he knows
how to compute them anyway.

Well let me just read to
mention a bit he have like

a they didn't have quite the number of the
genitive but the original series because I

mean there is something that they didn't
mention but this is what happens if you

have the meet the beat of the sea bass
you all these thing breaks down but

you can is the computer formal by what
C.D.'s so for help I would see a swath

of the giving you another question that
I think is very interesting from the my.

And I think I'm going to
be you will compensate for

the bifurcations of thought I just have
functional equates young bright and

then you're going to say well that should
be a double or something they all said

Baby Baby delegate because they spanked
through most dysfunctional equation he's

always been to the general that's some of
the theories that you've come through that

I mean you never find one eigenvalue
grossing units of value and

then of course since.

These things up yet also even several are
solid state physics more of those which is

something that Lisa makes but then he has
several other things to try to go and

as I told you we have spent some
time already thinking about.

Felony bystander and
lay song has been working also

in the question of
the crinkled Clinton Obama.

OK thank you very

much.

Yes

yes.

Yes.

Always made of reason I will know it's
not the movies and I will now but

he's not like them to the minus fifteen
always liked into the mind of seven of

them to minus eight these.

Is within the accuracy that you can
get we've that we're pretty sure he's.

No no it's I mean at least when I would
number of people out there doing always.

That this is something like what
the younger at least did like

the mind of the kind of knowing something
I would like into my nose for the money

It's completely.

Sold there so
you need that mean even see what that area

SEATO might be even that reset of value.

So yes.

Yes I mean the main the main issues
that percent of the volume and

regulated is not the.

Yes.

Yes.

I mean that's.

That's a very well known we sold them in
actually people have been using these for.

Many years I think.

And presumably it goes back to.

I mean the reason is very simple because I
mean you see there you have one told us he

have right so you have one and then you
look at the right if you were looking

at them all that one right if you were
looking at another one where the image of

the other one would be something
that goes like this right.

But if you look at their area here.

It is said you actually have to be
exactly the same as the SO that area.

So if you make ANY
the formation of the thing.

In three of these the same I mean yeah I
mean the only thing that you need this

doesn't make something that goes a little
bit below and therefore I see him and

then you get then his neighbor and
then this is Lee Rigby's I know it's hard

to the wall and I view them right through
the it in three dimensions because I mean

I use halfway succeeded but then when
I have said have succeeded in that

always you didn't see that
building seeing it but.

But you know if you're
stuck I do the drawing and

do you suffer enough to make it the very
least they need seem possible to see so

yes.

That's ideas.

Yes I know yes.

No I mean they did this statement I
was making is much more than all this.

Volume All right maybe the second
That is the essential I mean

they're going to firmly pressed on all of
these very interesting I mean they don't

give you the exact initial conditions
that they use except that I What do

you do I mean nowadays of
course you're going to do

we do that calculation in
minutes you know I mean it's.

It's sixteen mothers or eight it's
somebody can look I mean something that

looks to us as more numbers but they
excite only wide initial condition and

themselves that this is full of Russian
assess and then it's full of second.

Day and he said conditions that the they
I mean what they tell you about

the direction they need help
conditions they don't pin point

the initial conditions but but but you
can guess what they need conditions and

then you look at the place where
they did it and then if it's full of

second very very few.

And.

If you do they calculate how much I was
telling you and now I am doing it again

with these of you seeing
fluxes except there but

Alexander and I use all the techniques to
sort of identify the story and so on and

we just computed these low and so on and.

I feel I mean it's not just the medical
field it's there is I think

I think a lot of human behind it and
the two of them much even when so

we tend to believe it.

Yes I know I.

Yeah well if if you're typing on the cover
and I've been I will tell you what I think

but I mean it's very thin that the but
but of course I mean you know I know you.

Yes.

Yes.

Yes.

Yeah.