So now we have Kerry Emanuel, who's
a colleague of mine, a professor in Earth and Planetary
Sciences.
And he's interested in moist dynamics, tropical meteorology.
A great expert on hurricanes.
He's co-director of the Lorenz Center
and was also very close to Charney and Lorenz,
and was one of Charney's last students.
Thank you very much, and good morning.
Before I begin my remarks on Ed Lorenz,
I can't resist adding a little vignette to what you just
heard about Charney.
I was also a student of Charney's and really
loved interacting with him.
We did like to argue with each other a lot
in a very productive and friendly way, sometimes very
vigorous.
And I'll tell you one such argument we had in his office
when I had been arguing with him about a finer
point of something called the Howard semicircle
theorem, which is quite a well-known theorem
in fluid dynamics.
And we went back and forth and back and forth,
and it got a little bit heated.
And finally, Charney said, all right.
And he picked up the phone.
And the next thing I heard him say is, Lou?
I've got this kid in here, Emmanuel.
Would you talk to about such and such?
He put me on the phone with him.
And there came a barrage over, a very polite barrage
over the phone, and I clearly lost that argument.
And Jule was very magnan--
he never smirked or looked at me.
We just never discussed the subject again.
He was great that way.
What I'd like to do with you this morning
is to tell you a little bit about the life of Ed Lorenz
and interweave that with his scientific accomplishments.
I'm going to go a little bit back and forth
between those two.
Many in this room will have remembered Ed very well
as a beloved colleague, mentor, and teacher.
And he was, of course, the author of one
of the greatest intellectual advances of our time.
It's particularly wonderful, by the way, that today we also
have all of Ed's children with us,
and I hope I can do a little bit of justice
to the life and legacy of their father.
Ed was born in West Hartford, Connecticut,
in 1917 to Edward Henry and Grace Norton Lorenz.
And one of the reasons I mention this is they both
had connections to MIT already.
Edward Henry majored in mechanical engineering here.
And although he was, like his son, small in stature,
he held, at the time, the MIT record for the two-mile run.
Grace's father had developed the very first course
in chemical engineering here at MIT within the chemistry
department.
That was back in 1888.
And her mother founded the department of Home Economics
at the University of Chicago, the institution from which
Grace ultimately graduated.
Ed always attributed his love of games,
which you heard a little bit if he were at the dinner
last night, particularly chess, to his mother Grace's
influence.
Ed's parents met at Waterville Valley, a summer resort
in New Hampshire.
And after they were married in 1916
continued to summer there, imparting to their son
a deep and abiding love of the outdoors.
Ed's fascination with numbers was
apparent at a very early age.
And not long after he learned how to multiply,
he taught himself all the perfect squares up to 10,000.
He had a really great ear for music, and by the time
he was three, he could already tell that his mother
was singing off-key.
His passion continued to develop, and many of you
will remember attending concerts with him
and his wife, Jane, at Chautauqua Resort in Boulder,
where they often spent part of the summer,
or at MIT, where they were both avid patrons of the student
symphony orchestra.
Well, like his father, Ed was small in stature,
and he didn't excel in team sports.
But he could swim underwater farther than any of his peers
and, owing to his light weight, he could reach mountaintops
faster than most.
He later related that mountains and music were his greatest
spare time interests.
Curiously enough, Ed was only seven undergraduates
entering Dartmouth in the year 1934
who would major in mathematics.
In 1938, he entered Harvard's graduate school
and he worked on a problem in mathematical physics
under the guidance of George Birkhoff.
Ed relates that during his graduate years,
he seldom saw any number other than 0, 1, and 2.
Such was the nature of the math he was engaged in.
In 1942, just months before he expected
to receive his doctorate, though, the war intervened,
and he chose to become part of a team of weather forecasters
for the Army rather than to be drafted.
He enrolled as a cadet in the Army Air Corps
in a special eight-month master's program at MIT
to train as a weather forecaster.
While the forecaster training was rigorous,
MIT's illustrious faculty, which included
the likes of Herd Willett, Henry Houghton, and Bernhard Horwitz,
couldn't resist teaching their students some theory.
But Ed had trouble understanding the connection.
In Ed's words, "not only were we never
shown how to use the dynamical equations to make
weather forecasts, which I had naively assumed
was the reason for our studying dynamic meteorology,
but we were not even told whether they
could be used in this manner.
I also learned that there were outstanding meteorologists
at other universities who believed
that it was impossible."
And I think it's very important for particularly
the younger people here to understand that in those times,
it was not accepted very universally at all--
I should say it wasn't accepted at all--
by people in the field that you could actually
do this kind of deterministic forecasting.
So the dichotomy between the theory of weather
and the practice of weather forecasting
fascinated Ed throughout his career.
In the summer of 1944, Ed was sent
to Hawaii, where he absorbed another two months of training
in tropical meteorology.
And then he flew to Saipan in October.
There he helped to set up weather forecasting
operations in support of airborne bombing raids.
These forecasts relied heavily on observations
made in previous raids, but Ed complained
that the pilots, to save time, would often
simply repeat the forecast as the observation.
This made for really good forecast verification
but hardly help the forecasters make the next forecast.
In the spring of '45, the weather operation
was transferred to Guam, and Ed was made
head of the upper air section.
And some insight into Ed's character during this period
is provided by one of his fellow forecasters
from back then, Patrick [? Soupis. ?]
And Patrick says that although Ed was not
a strongly outgoing individual, it
turned out he rather liked conversation on many topics.
And of course, as those who knew Ed will find unsurprising,
he knew a lot and was prepared to talk
about a great many different subjects.
Those who know Ed principally through his research
contributions might easily overlook his interest
in the practical art of weather forecasting
and his love of weather in general.
But generations of students and colleagues here at MIT
will remember many occasions when Ed would appear silently
in their office as if by magic and enthuse over
some feature of the current weather map.
After the war, with much deliberation,
actually, Ed decided to formally switch from mathematics
to meteorology.
In his own words, "mathematicians
seem to have no difficulty in creating new concepts
faster than the old ones become well understood.
And there will undoubtedly always be many
challenging problems to solve.
Nevertheless, I believe that some
of the unsolved meteorological problems were more fundamental,
and I felt confident that I could contribute
to some of their solutions."
Ed received his doctorate under Jim Austin in 1948,
and shortly thereafter, married Jane Loban,
who'd been working as a research assistant
in the meteorology department at MIT.
Jane was born in Dayton, Ohio, in 1919
but spent most of her childhood in Cedar Falls, Iowa.
Her consuming interest was flying,
and she flew small airplanes before she
was old enough to drive a car.
You'll remember some of the problems that Ed later
had with Jane's piloting abilities,
being treated to terrifying flights around New Zealand
and so forth.
But she was a good pilot.
Her interest in flying led naturally
to studies in meteorology, which in turn led her
to an appointment at MIT.
Following their marriage, they settled in Cambridge
and lived in the Boston area for the remainder of their lives.
Their three children shared Ed's love of game and the outdoors.
According to Ed, "Many of my winter weekends
were spent taking all of them--
one of them or all of them, usually with my wife,
as well-- to some ski area north of Boston.
This, of course, was just what I'd hoped would happen."
Ed's devotion to his family was evident to everyone
who came to know him well.
Ed accepted a job as a research scientist
on a project to study the general circulation
of the atmosphere, headed by Victor Starr, who
had come to MIT from the University of Chicago the year
before.
Starr became Ed's mentor and close friend
and was, next to his parents, the most important influence
on his intellectual development.
One of the most important events during this period-- and Joe
[? Galosky ?] alluded to this in his talk--
was a visit to Jule Charney, Norm Phillips,
and others working under the direction of John Von
Neumann at the Institute for Advanced Study in Princeton
to apply the newly developed digital computer
to the problem of numerical weather prediction.
At this point, Ed and Victor were not convinced
that numerical solution of the equations governing
atmospheric flow was even possible.
Although Ed was not entirely persuaded during this visit,
by the mid-1950s he saw that this was the way of the future.
Ed must have made a positive impression on Charney
because, as you've just heard, a few years later,
Charney made his own acceptance of the offer of a faculty
position at MIT contingent upon the promotion of Ed.
It was during this period of the early 1950s
that Ed made his first lasting contribution to meteorology.
Victor Starr had speculated that some fraction
of the potential energy of the atmosphere
could be converted to kinetic energy,
and this fraction became known as
the available potential energy.
Ed took some time to work out the physics and math of it.
In his words, "It finally occurred to me around 1953,
I think it was-- actually, it was one night
when I couldn't sleep.
I was turning these things over in my head and it suddenly
occurred to me, why not define available potential energy
as just the excess over the minimum that you could get
by redistributing the mass [INAUDIBLE]?? "
And this led to his first and very highly influential paper,
published in 1955, on available potential energy.
Now, I'd like to do, because it's
impossible to cover everything, but I
want to skip directly now to the origins and evolution
of the discovery that changed the world, in many ways,
and made the name Lorenz known to many.
And here I'd like to gratefully acknowledge
the help of my colleague Dan Rothman in getting
the facts straight of this rather fascinating story.
I'd like to just begin by putting this whole development
of chaos theory in the longer history
of the concept of determinism.
Because I think it's very hard for us in 2018
to imagine how people viewed the material
world before the Renaissance.
Causality was a theological question,
and the word "science" had not even been invented yet.
And as you know, the great thinkers of the Renaissance,
like Galileo, Copernicus, Kepler and, ultimately, Newton,
changed all that, so much so that by 1814, Pierre-Simon
Laplace could write, in his philosophical essay
on probabilities, that "an intellect which
at a certain moment would know all forces that
set nature in motion and all positions of all items of which
nature is composed, if this intellect were also vast enough
to submit these data to analysis,
it would embrace in a single formula
the movements of the greatest bodies of the universe
and those of the tiniest atom.
For such an intellect nothing be uncertain
and the future, just like the past,
would be present before its eyes."
This very bold statement of universal determinism
marked the dawn of an age of astounding scientific discovery
and technological progress.
Determinism reigned for about 150 years,
and it was not even much perturbed by Henri
Poincaré's 1903 deduction, stemming from his work
on the three-body orbital problem,
that certain dynamical systems could be practically
unpredictable owing to their sensitive dependence on initial
conditions.
A more serious challenge arose in the mid-1920s in the form
of Heisenberg's uncertainty principle,
which asserted that the product of a particle's position
in velocity cannot be known to better than a definite finite
accuracy.
Yet many physicists believe that this
had little implication for the behavior
of the macroscopic world.
Now, it's very important to note here
that Ed never intentionally entered
this fray of determinism.
He had a very different battle to fight,
and I think it's important that we
realize what that battle was.
By the middle of the 1950s, there
was a dispute among meteorologists
about whether numerical weather prediction could ever, ever,
even theoretically, outperform purely statistical forecasts
based on linear regression.
You see, at that time, if there was a science of weather
forecasting that was actually being applied,
it was statistical forecasting.
And I remember-- some of you may remember--
taking a course in statistical weather forecasting from Ed
Lorenz here at MIT in the '70s.
But Ed felt that the advocates of statistical forecasting
had misinterpreted a theorem by his MIT chess
partner, the mathematician Norbert Wiener.
It seemed to suggest that in principle,
statistical forecasts could perform at least
as well as integrating equations in any deterministic system.
Now, we think that's really kind of a crazy idea now.
But the reason we think it's a crazy idea
is really because of Ed's work, ultimately.
Ed just felt that it had to be wrong,
and he set out to prove it.
At a meeting in Madison, Wisconsin, in 1956,
he told an assembled group of statistical forecasters
that he proposed to test their hypothesis--
that is, the hypothesis that you would always
outperform or at least reproduce a deterministic forecast
statistically.
He said he was going to test that
by integrating a set of nonlinear equations
on a computer, producing a set of optimum linear prediction
equations using standard methods and finding out
whether they could actually reproduce
the numerical solution.
He knew that to do this, he had to find
a set of solutions or equations that did not repeat themselves.
That is, he set out to find some deterministic system that
was not ultimately periodic.
And he wanted these equations, ideally,
to be relatively simple.
But he also needed a computer to integrate them.
Now, in those days, computers were just in their infancy.
They were largely confined to big computing centers.
But at this point, he had been made a faculty member here
at MIT, filling a position vacated by Tom Malone,
and one day a post-doctoral fellow by the name of Bob
White, who later became the head of the Weather Bureau,
suggested that Ed purchase a computer of his own.
Now, this concept, back then, was unheard of.
But they set about shopping around
for something for months, and they settled on the Royal McBee
LGP-30.
And think we had an issue of one of those yesterday
up in the Green Building.
It was noisy and it filled his office,
but it could perform 60 floating point operations per second,
or flops, a huge improvement over mechanical calculators,
and could store--
get this-- 4 kilobytes of data.
Your smartphone performs at about five billion flops
and may have 64 gigabytes of storage.
By 1959, Ed had settled on a set of 12 equations representing
a highly reduced model of the global atmosphere
and had found, for certain combinations,
parameters, solutions that seemed never to repeat.
Here is a description of his 12, sort of in compact notation,
his 12-equation system.
It was a nonlinear system.
And the solutions, he did ultimately
find by trying many different combinations of parameters,
a solution.
This is taken directly from a conference report
he submitted to a conference in Tokyo that took place in 1960.
He did ultimately find a solution
that didn't repeat itself.
That was what he was after.
He'd proven what he said.
Well, then he applied these optimal set
of statistical equations, and lo and behold,
only after a short time, they diverged from this.
And he could not reproduce the solution
with statistical equations, so he actually
proved what he set out to prove.
Now, during the period when he was performing
these calculations, there came the much-celebrated moment
when he restarted one of the calculations
by re-entering the values of the 12 variables
at a particular time step.
He stepped out-- and this is according to him--
for a cup of coffee, and on returning
noticed that the output didn't resemble that
of the original simulation.
He suspected that this complicated machine
with lots of vacuum tubes, that one of the vacuum tubes
had failed, and that turned out not to be the case,
and came to realize that it was the rounding he had done,
which we heard about yesterday, when he re-entered
the numbers that that caused a small perturbation that grew.
And it ultimately grew to the point
where the difference was as large
as the difference between any two random realizations.
I think it's telling that in the body of his 1960 Tokyo
conference report, he didn't mention this incident.
He was focused on the non-periodicity of the solution
and the inability of the statistical equations
to simulate it.
As was traditional in those days with papers,
the paper itself, the printed paper,
concluded with a summary of the discussion that
took place at the meeting following its presentation.
Bert Bolin had asked Ed, "Did you
change the initial condition just slightly
and see how much different results were
in the forecasting this way?"
Ed related that they had tried that with the result
that the perturbed solution diverged from the control
exponentially in time.
After the conference, Ed turned his full attention
to the predictability problem.
He now wanted to understand the relationship
between aperiodicity and loss of predictability.
And he felt he needed to work with a much simpler system
to get at this problem and worked hard at first
to simplify the set of 12 equations.
But he failed at doing that.
And much later in his career, he showed that, in fact, it
was impossible to simplify this particular set of equations.
So Ed's search for a simpler system
bore fruit, actually, when he visited Barry Saltzman in 1961.
Saltzman showed him a set of seven equations that
represented convective flows.
Those 12 equations were a reduced model, by the way,
of the general circulation of the atmosphere.
Barry was interested in the periodic solutions,
but he did show Ed one solution that refused to settle down.
In this solution, four of the seven variables
decayed toward zero, and Ed realized
that the chaotic solution could be
represented by equations dealing with only three variables.
And so with Saltzman's blessing, he
published this three-equation set in 1963,
and these are now known as the Lorenz equations.
The variables could be plotted in a three-dimensional
perspective or in 2D sections, and the nature
of the strange attractor could be revealed in all its glory.
Ed showed that this peculiar and beautiful fractal geometry
of the attractor was intimately tied to sensitive dependence
on initial conditions.
And some consider this to be, this recognition,
to be Ed's greatest achievement.
So here is a slide showing the Lorenz equations and the values
that he took in the published paper.
And if you happen to have an iPhone,
you can get an app called My Attractor,
and you can integrate those equations in less than a second
and display them on your phone.
And it's actually quite fun to do this, so I recommend it.
It just shows you how far we've come.
And as you are probably aware, the interesting thing
about the solution of these equations
is that they essentially never repeat themselves.
And they occupy this very fascinating and, I think,
beautiful fractal geometry.
Now, the 1963 paper is interesting for a variety
of reasons.
Here is just a Xerox, if you will,
or a copy of its title page.
Very simple, beautiful, short title.
Beautiful short abstract.
No abstracts that fill pages.
And it's kind of interesting that for the next 10
years, a little bit more, 1963 to 1974,
this paper was cited three times by people
outside of meteorology.
That's all.
It just took a long time for it to filter out.
When I was here as a student in the early '70s,
the first time I heard of it was a course
in dynamics I took from Ed Lorenz.
And I was really shocked that I hadn't heard of this before.
I thought this was some failure of my education.
And I started asking people who were majoring
in physics if they'd heard of it,
and I ultimately discovered that it
was just simply not very widely known, except in mathematics.
It was beginning to be known by then in meteorology, of course.
So finally around '74, Ed's work was
brought to widespread notice in the mathematics community
by James Yorke, Allan Fowler, and Steven Smeal.
The topological properties of Ed's strange attractor
were of special interest, and the explosion of research
in chaos theory ensued.
But by then, Ed had discovered something arguably
more profound than his earlier work on non-periodic systems.
As illuminating and exciting as his 1963 paper was,
it posed no real threat to the basic idea of determinism
because the predictability horizon--
that is, the amount of time you could go forward
before you lost any resemblance to the true solution--
the basic predictability horizon of the '63 system
increases without limit as the initial condition error
becomes vanishingly small.
But in 1969, he presented a system
of equations representing flow with many different interacting
scales.
The key feature of such systems is that the amplification time
scale gets shorter sufficiently rapidly with the spatial scale
of the disturbance.
In Ed's own words, "It's proposed
that certain formerly deterministic fluid
systems which possess many scales of motion
are observationally indistinguishable
from indeterministic systems--
specifically, that two states of the system differing initially
by a small observational error will
evolve into two states differing as greatly
as randomly chosen states of the system within a finite time
interval--
within a finite time interval which cannot be lengthened,
by reducing the amplitude
of the initial error.
That is, the predictability time horizon
approaches a finite number as the initial condition error
becomes arbitrarily small.
It's a singular limit of the system.
If nothing else, quantum uncertainty
prevents the initial error from actually becoming zero."
So this is, I think, the really profound result
of that 1969 paper expressed graphically.
So on the bottom axis, we have the size
of the initial perturbation that you're
going to add to the system and, on the vertical axis,
the predictability time horizon.
For certain kinds of chaotic systems, like the 1963 system,
as you reduce the initial error to zero,
the predictability time horizon recedes without limit.
But for the 1969 system, it doesn't.
Even as you approach the limit that the initial condition
error is zero, the predictability time horizon
remains finite.
That is, these systems are formally
indistinguishable from systems that can't be predicted.
Now, no one has yet succeeded in proving
that this is true of the actual Navier-Stokes equations,
but most of us suspect that it is.
So history may well record that Ed Lorenz
had hammered the last nail into the coffin
of Cartesian universe.
Ed himself wasn't immune to some of
the philosophical implications of his work and, in his book,
The Essence of Chaos mused in characteristic Lorenzian
fashion on the problem of free will.
This is what he said.
I love this.
"We must wholeheartedly believe in free will.
If free will is a reality, we'll have made the correct choice.
If it is not, we shall not have made an incorrect choice,
because we shall not have made any choice at all,
not having the free will to do it."
Those of us privileged to have known Ed Lorenz will remember
him as a gentle, quiet soul, almost painfully
shy and modest to a fault. But if you engage him
on a favorite topic, a fine point
in atmospheric or dynamical systems
theory, the virtues of a particular mountain trail,
or anything to do with his extended family,
with a twinkle of his bright blue eyes,
he would come to life.
And at such times one always felt
as if he were inwardly smiling at life.
Ed was a true gentleman and, in his own quiet way,
showed a deep affection for his wife, Jane, and their children
and an old-fashioned sense of chivalry toward Jane.
We all miss him.
Thank you.
[APPLAUSE]
Thanks a lot, Kerry.
Do we have any questions for Kerry?
Please come down to the microphone.
Hi, Kerry.
Thank you very much.
That was so interesting and filled
in some things I don't recall but am glad to know.
I'm just-- I was thinking as you mentioned--
you sort of alluded a little bit to the development
of turbulence.
You didn't mention it exactly, but I would like to ask you,
do you know what interaction Ed had with people developing
the turbulence theory?
I'm thinking-- I don't know if he interacted directly
with Obukhov or Kolmogorov or Monin or any of them.
But there was a theory making somewhat related discoveries
more or less in the same decade.
So I'd like to hear your comments about that.
There were.
And I don't know specifically of interactions
he might have had with the people you mentioned here
at MIT.
Does anybody else know the answer to that question?
I just-- I didn't come across any description
of such interactions.
Doesn't mean they didn't take place.
I think Joe had--
Joe [INAUDIBLE] did.
Joe?
Is there a straightforward explanation
of what was different between the '69 and the '63 models that
led to this remarkable change?
I guess it all hinges, Joe, on one's interpretation
of the word straightforward.
In my mind, it is the continuous interaction
among scales and the fact that in that system, as you
went to smaller and smaller spatial scales,
they sort of exponential--
you know, the e folding time of disturbances got faster.
It depends on the shape of spectrum of the turbulence.
And if that's true, if that slope is sufficiently shallow
or sufficiently steep, then the fact
that the smallest disturbances grow very fast and interact
ultimately with the larger disturbances
is the source of the loss of predictability.
Tim Palmer?
Kerry, you mentioned the fact that before the war,
Ed had done a master's degree in mathematics under Birkhoff.
And Birkhoff was, in some sense, the natural successor
of Poincaré that you mentioned, about the three-body problem,
and clearly the leading figure in the theory of nonlinear
dynamical systems at that time.
Is there any evidence that any of that
rubbed off on Ed, either consciously or subconsciously,
and influenced, then, his work in the '60s, '50s and '60s?
That's a really interesting question, Tim.
The only way I can illuminate it-- and it's probably not much
of an illumination-- is that in The Essence of Chaos,
Ed relates that at the time he was developing the 1960
12-equation set and the Barry Saltzman set in '63,
he says he was unaware of the three-body problem work.
And I think that's curious, because his advisor had
worked on that problem.
I just don't know how to resolve that, but yeah.
Bruno.
Hi.
We are all friends, so let me correct you
on a piece of history.
Before Copernicus, Nikolaus von Kues
is called in French Nicolas [? Lecuse. ?]
He was a German theologian.
He was a [INAUDIBLE] on his own.
He introduced the idea, of course,
that the Earth was not at the center of the universe.
There could be many universes.
He was not a deterministic person.
And people tend to forget about him.
Then OK, this piece of history.
Then coming back too shorter time,
when they arrived at Princeton, [INAUDIBLE] was dead already
and Jule Charney was already at MIT.
But do you know anything about [INAUDIBLE] understanding
of chaos?
For he was a rather deterministic person--
your language.
You're asking about Charney's knowledge?
No, I don't know about that.
I think what-- my guess is that what he learned about it,
he learned directly from Ed.
But I don't know for a fact.
Thank you.
Last question before coffee break.
Yeah.
Regarding this interesting question about whether anything
from Birkhoff on dynamical systems rubbed off on Ed,
it always fascinated me that in the early '60s papers
on strange attractors by Ed he essentially uses the concept
of the Poincaré return map to analyze what that thing is
doing.
But I don't think he used the term "Poincaré map."
So I don't actually know whether he just independently
reinvented this just out of pure thought,
which he could well have done, or whether something
had sat there subconsciously and came back
when he really needed it.
But it is essentially the same technique
that had been used in analyzing three-body problems
of dynamical systems.
Ed has an interesting comment about this, Ray, in his book,
where he says one of the things that
got him excited about the Saltzman equations,
the '63 work, was that he could finally
apply this form of mapping.
I don't recall whether he actually used the term
Poincaré.
But he knew about that mapping.
Or he says he knew about it.
Yeah.
Yeah, in fact, he gave a seminar to the applied mathematicians
in '63 or '64 at MIT.
And he was fully prepared to talk about his work on chaos
using those concepts and using that terminology.
Thank you very much, everybody.
So we're now going to have coffee break, up the stairs
and off to the left.
And we'll be back here at 11:00
[APPLAUSE]