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All right, and a lovely welcome back to
the stage this evening
here to present, you talk about
models and science opportunities
and mechanisms, limitations by Michael's
voter.
He will be talking about scientific
models, what they do,
how they work, what are
they.
And they are quite
in the news right now because of the
coronavirus and climate
change.
And with models, you can do a lot.
You can model things.
But for the public, it's not always
quite apparent how they work and
what they do. So we have
our own streaming site with an I.R.S.
and no JavaScript.
If you don't like that, go to live dot
dot media there. You can also ask
questions in your city or via Twitter
with hashtag or RCF
three huc.
And apart from that, I
think we're good to go, so I'm
giving over to Marcus.
All right, so talk,
it's scheduled for 90 minutes, I might
take a little bit longer, but it should
be interesting.
All right. So I want to talk about
models.
I'll cover topics like
the difference between a lot of
analytical, numerical, parametric models,
forecasting versus explanation,
abstraction and simplification,
statistics forecasting the past
sounds stupid, but is useful.
Sensitivity analysis, optimization,
forecasting versus scenarios, fitting
of data, fake numerical precision,
chaos, emergence and unknown unknowns.
That's quite a lot of stuff.
So I'll run rather fast.
As you'll notice, the examples will
be taken from cranes, pendulums,
weather and climate flight simulators,
sheep and ant's gravitational
waves.
The LHC, the Event
Horizon Telescope. Cellular Automata
attribute Terk.
And you might ask yourself, why
the hell is this guy talking about you
have some background. I'm a physics
engineer and a computer scientist, but
more importantly, over the last 12
years, I ran a science podcast
called Omega Tau and Artists and
Engineers for about 600
hours.
And that.
Basically, where all of the material
of this talk comes from,
the podcast also gave me.
Our in the backseat of an F-16, which,
of course, was the highlight.
All right, so let's get started.
Let's get started.
You probably have all seen these large
steel monster.
And if you look.
Closely at these little traffic
light kind of thing, the cabin
Haisla.
Right here, it signals
to outside personnel the
load of the
and not the weight that is
on the hook, but the actual stress
on the crane, the load on the crane.
And, of course, obviously there's been
what you'd expect, OK, be careful and
at the limit.
And so what is the load of the crane?
Well, one is the bending of the boom,
right? The boom is a long stick.
That is, of course, bent from the weight
that's at its tip on the hook.
And of course, also the stability, the
balance of the
lift mass and the counter
mass, I should say, counterweight.
So how does the crane know all of these
things? Well, there's a model that
calculates this and drives the traffic
lights. And let's investigate what goes
into that mold. Well, one, of course,
there's the weight that is currently
being lifted. The more weight,
the higher the bending moment on
the boom, the length
of the boom is relevant.
Of course, these booms are telescopic,
and if they're longer, you have for the
same lifted weight you have
or mass you have more bending moment,
the angle of the boom, obviously, you
can lower it and also,
you know, make the angle steeper and the
lower the angle of the boom
again, the higher the bending moment
because the radius is larger.
There are additional wires
and poles you can use to stiffen
up the whole construction.
And if you have those installed, then
you're bending. Moment is less for a
given lifted weight.
And finally, wind, because if
the wind moves, you're
lifted it sideways.
This leads to sideways bending
of the boom, which lowers the overall
stability.
So that's for the bending, for the
balance. Obviously, the relationship
between the lifted
weight and the counterweight and
their respective radii
is relevant. So that is something that's
taken into account. And the distance
radius of the stanchions,
the further out you have moved them,
the bigger is the, if you will, a
footprint of the crane and the more
stable it stands.
So these two
aspects of overall load
are calculated separately.
And whenever one of them reaches
a critical level, that is
that drives the traffic light.
So how is this done?
Well, for the stability, for the balance,
we simply lose the use
that the lever principle.
Right. So you basically calculate
the two moments that the actual
lifted weight is measured from the
pressure in the hydraulic cylinders.
The counterweight is configured.
And then, you know, the two radii,
you can calculate those as well from the
angle and the length of the boom.
And then you can just simply figure out
whether the crane is stable.
The balance is is imbalance for
the bending.
It's a little bit more interesting
because here
what you basically do is
you run an FM analysis, finite
element analysis, where
you basically simulate
every little discrete
piece of boom material
and run a numerical simulation, a
numerical model that
figures out where the load is high
and when it reaches a limited any of
these discrete, small, finite
volumes, volumes.
And of course, you can't run this
in real time in the crane, which
is why the results of this analysis
are abstracted into basically lookup
tables.
Right. This is called a parametric model.
We'll get back to these model
categories later, but that's basically
how it works.
And so there is an interesting thing
that happened this year or maybe it was
last year. This is a 750
ton crane, the LTM 1750
dot dash nine dot one
manufacturer by Lepo and
again, it can lift 750 tons.
Well, it was able to do 750
until earlier this year, last
year, because now it can do 800
only because of a software update.
Nothing changed in the actual
construction of the of the of the
machine.
In fact, existing cranes can
be updated retrospectively.
So how does this work? Well, there's a
something I translated from the Leaphart
website. It says, We completely
recalculated the crane, more and more
precise FAA models, more
and more precise models, I should say,
on Fossler computing hardware permit
a less conservative approach.
The latest regulations regarding the load
bearing capacity in compliance with all
the applicable standards, other blah,
blah, blah. So basically they they
have newer modeling
tools, both in terms of algorithms
and software and machinery,
computers. And now that.
Can be a little bit less pessimistic
conservative about what the crankin left
and so they've the software updated
update basically installed new
lookup tables and now the
same machine can lift 50 tons
more.
Regarding the balance.
I talked to a bunch of crane operators
this year, obviously, and one told me
today it's basically impossible to
to knock over a crane to to bring
it out of balance so that it actually
falls over.
Oops. This is from 2013
where one of these large people
tracked cranes, fell over
in Brazil during
the construction of their Olympic
stadium, and the problem there
was surface stability so that the ground
gave in.
These cranes produce a significant
pressure on the ground.
And if the ground isn't suitably
prepared, then the whole thing falls
over. And obviously, the model
that, you know, takes that considers,
as we have seen, that the the levers
of of the weight and the counterweight
can't know about this.
So this problem.
Here's another example of something that
went wrong.
A large ship bought Crane
in Rostock, Germany,
completely crashed.
And so, again, is this
a modeling problem?
Well, no, not really.
It was very likely a material
fall. The production mistake in the hook
itself, the hook broke and then
the whole boom basically snapped over
backwards, completely destroying
the crane. Millions of millions of,
you know, money lost and several people
hurt. Big, big drama.
So what can we learn about this?
We have to be really careful about what
goes in a model.
The model sounds trivial, but the model
doesn't make any statement
about whatever hasn't been put into it,
like, for example, the status of the
ground or the material quality
of the hook. And these assumptions and
constraints must be well-defined, that
they must be communicated to the users.
So is this a useful model?
It's a Lego.
Uh, actually, yeah.
It's a Lego model of one of these LTM
1750 cranes.
It's not useful for understanding
the load capacity because obviously the
Lego has no
relationship to the real thing in terms
of stability. But you can explain
in principle how the crane
works, you know, with with extensions and
telescopic booms and stuff.
So it can serve as a model
for illustrating that it might serve as
a model for work site planning.
You know, if you have to work side in the
same scale, then
why not? Right.
So this model also has
its purposes, but it's not the same
purpose as these mathematical
models that we've talked about before.
So, again, the user of a model
has got to know what's in the
model, what the purpose is and
the model, or has to decide what is
important, what impacts the results.
So let's define the notion of
model. It's an abstract representation
of something that exists in real life, in
the real world, expressed in a suitable
language like chemistry, physics, math,
LEGO should be an Omaha
for the purpose of understanding,
prediction, optimization,
proof or production of that
real world thing the proof and production
part will ignore. In this talk, we're
going to look at understanding prediction
optimization.
So when you build a model, you have to
think about what part of the reality
you want to represent in your model.
What is relevant to represent that
part faithfully in the model, how to
represent and compute.
Right? I mean, you have to somehow make
it quote Runnable mathematically
calculated or in other ways executable.
You have to think about how do you
observe parts of the reality that serve
as input to the model and then
what is the relevance and trust of the
output? Again, if you don't input
something about the ground, then
you are okay. If you can only measure
that unreliably, then the
relevance of the output and the trust
level of the output is low.
We'll get back to that.
So let's revisit analytical
numeric and parametric models.
Here are a very simple analytic model.
It's a differential equation
of the movement of a pendulum,
right? It basically says that the angular
acceleration, which is what the left
term says, basically
depends on the angle itself, on
the sinus, on the sign of the angle.
And then you multiply it basically
by the
fraction of the earth acceleration
and the length of the pendulum.
And so an analytical model
is basically a regular use, precise or
approximate.
Equations, as we'll see this one
as approximate and
then for dynamical systems, these
are often differential equations which
relate a quantity to its
first or second or whatever a
derivative. Again, here it relates the
angle of the
angle five to the
the second derivative of that same angle.
And so, again,
a numerical model, sorry, analytical
model. This is what we all know from
school as formulas, equations.
Now, numerical model is more
interesting because it in practice
plays a more relevant
role for what we
hear about models today.
What you do is you discreetness your
world and the finite element
analysis we saw in the context of cranes
before you basically democratized
the overall boom into finite small
volumes of steel and climate
and weather models.
You describe the atmosphere
and the volumes of air.
If you do epidemiology, you have
sets of subsets of the population
and then you assemble
the overall system by basically
joining all these little volumes
and computing
a whole bunch of properties for
each of these.
I called these properties E
for I changed at
the properties.
And you then again from
from the calculated properties of each of
these small volumes, you
reassemble the overall story.
So and then you also
typically, if this is a system that
evolves over time, you iterate over time.
Right. So again, for the whether you
have small volumes of air,
you calculate various properties for each
of them and then you run
this thing over time.
There is a bunch of constraints.
One is that
you have to make sure that the
changes are plausible both
in time and space.
But I mean by that is if you have a
weather forecast and it says,
you know, at time T equals one,
the temperature at some location is 20
degrees and
10 minutes later it's 10 degrees.
There's probably something wrong.
Same is for spatial plausibility.
You if you have 10 degrees in Stuttgart
and 20 degrees in Esslinger in a city
nearby, it's probably strange.
So you have to make
sure that either by design
the model doesn't jump both in
time and space or whatever other
democratization dimension you've used.
Or if if this is an outcome,
then your model is wrong if things jump.
So basically, you still calculate with
equations in numerical models, but
these are descriptivist and
often spatially and temporally, these are
the most obvious democratization.
But of course, others might
be used as well
if you use smaller boxes,
smaller discrete volumes to
get higher resolution, same if
you use smaller time steps.
So this gives you increased precision.
In some cases, it gives
you correctness.
For example, in control theory,
if you have two large
time steps, you
might not get a
control algorithm that is stable
because it's because
of its large timestamps.
It can see oscillations and control
those so that the algorithm
isn't just imprecise, it doesn't work
if you don't use a fine
grained high resolution
time. Same thing in some cases
for space. If you want to forecast
thermals, you know the stuff that propels
gliders up warm air rising
above mountain peaks, and you have
a chorus grained resolution
of your terrain.
Then these peaks
are averaged out and you will not be able
to produce correct
predictions of how and when thermals
develop above those peaks.
It's something glider pilots know very
well when they fly in mountainous areas,
that the forecasts are often wrong.
And then, of course, the drawback of a
high resolution is that you need more
computational power.
And even today, with
faster and faster computers, it's still
quite plausible.
I mean, scientists will have to make
lots of compromises in various
ways, for example, in resolution to
make it feasible to run on existing
machines.
And then, of course, you can compose
these. For example, the ECM, WCF,
the European Center for Medium Range
Weather Forecasting runs a worldwide
weather model.
They use nine by nine kilometers
horizontal resolution and five hundred
meters vertical resolution, up
to 80 kilometers, by the way.
And then the German Weather Service,
the DVD, um, they have
a higher resolution model,
but only for Germany.
And
basically they use the the more
constrained model from the MWF
as as a boundary condition
for what the and also a
means of initialization in initializing
data for the final grant model.
And by the way, weather models calculate
around 50 of these properties.
So lots of stuff going on there.
And so you can see easily why even
large computers can be
utilized completely
with this approach.
So let's look at parametric models again.
We look at cloud formation.
You can see a beautiful picture of clouds
here. And the question is, you know,
what kind of cloud forms,
how much of the sky
is covered by clouds?
What is their lower and upper limit
called base and ceiling?
And there's a lot of parameters that
go in the position of the sun,
basically time of day.
How much high clouds you have
that limit the energy
imparted by the sun.
Then, of course, humidity, pressure,
temperature, properties of the ground,
the elevation of the ground.
And so you want to if you want to compute
this algorithmically, there's lots of
chemical and physical processes going on.
Some of them are theoretically not even
known.
Lots of small things happening,
lots of complex interactions.
So basically
what you do in principle,
again, is you you democratize
and you associate all these
interesting properties with each of these
democratized er volumes.
But you can't
really run this
as a numerical model because again,
some things aren't known.
Interactions are complex.
It would take too long.
So what do you do, you basically put
all these things into a series of lookup
tables. Right. So for example, you know,
properties E one and E two from
let's say, observations.
And from those you calculate some
property X and then this Property
X together with properties three
and four, you put that into a simple
equation which gives you a property Y,
which would then use in another lookup
table together with property E five
and you get the result.
So this is basically a very simple lookup
table and or set of equations.
And of course, those
are, as we've seen, with a grain filled
by numerical models, analytical models
and experiments, experiments.
Even if you don't know how something
works, you can easily just
take the experiment results and package
them into a parametric model which would
then run to make a forecast.
Another example of a very simple,
parametric model comes from medicine.
This is actually the only software
example. I think in my whole talk
I build an application in the health care
domain not.
Who long ago, where you, for example,
from the systolic
and diastolic blood pressure,
depending on the ranges they're in, you
calculate a risk factor
which you then use, for example, together
with the age and the weight of the
patient to make further decisions
regarding treatment.
At combining these different
kinds of models,
this is a picture of
a.
Aircraft, which many of you do probably
know from the movie Top Gun,
although this is not actually a picture
of a real aircraft.
This is a screen shot from the D.C.
Azer.
Here's another one.
Looks beautifully realistic.
So that would be another example
of models. How do you model these
surfaces and how.
Like that, but we're going to talk about
something else, and that is the modeling
of the Arrow mechanical properties
of let's say we are
a maverick
and you know, you know, we
are flying around and Top Gun with Goose
on the boost that is going to turn right.
So he'll smash the stick to the right.
What happens next?
Right. How does the simulator simulate
reacts and the pilot
moves the stick to the right?
So we have to stick movement,
which basically is translated simply,
you know, stick angle becomes a
percentage of deflection.
And that's the input to the
hydro mechanic flight control system.
And now you have to think about
to what degree the aero surfaces.
In this case, it's elevons and spoilers
on the wing, to what degree they are
deflected. And interestingly, they
actually calculate that
in the simulator and they calculate
that based on the current hydraulic
pressure and the simulated hydraulic
system, because if Rick, 28,
shot away half of it, you know, remember
Top Gun, then you have less
pressure on you in your hydraulic
system and the deflections are
slower.
Then you get
the you find out what your
flap settings are.
You find out what the wing sweep
angle is.
As you remember from Top Gun,
the wing, the A14 has wippel
wings right to adapt the wing to
different speed table.
What is the coefficient of
lift for that
deflection for this flap setting
and this thing sweep?
And this is a parametric model, which
happily NASA
did in the 70s.
They put one of these aircraft into the
wind tunnel and measured
all of these things. And those guys
somehow got hold of this wind tunnel
data.
And now that we have the coefficient of
lift, we can basically calculate the
actual lift force.
And we do that by multiplying the
coefficient with a bunch of properties
of the aircraft, but also
specifically with the speed of the
aircraft, which they get from the
simulation environment.
So that's another calculation.
And then they look at, again,
the wing speak wing sweep angle,
which gives them an inertia.
And they know how much fuel is in the
wing in the simulator because they know
how much energy fuel the engine has
burned since they took off.
And they take this information
to actually calculate
the inertial moment that acts
against the movement from the
differential lift of the two sides.
So, you know, that done gives
you a roll roll movement.
So the point is that I'm trying to
illustrate here how this overall model
uses analytical meaning,
calculations and parametric
models jointly in
one, if you will, big calculation,
relying on previously calculated
numerical data in this case,
stuff that NASA has figured out
in the wind tunnel.
Now, models aren't just
relevant for controlling a simulated
airplane on a PC.
That's also actually a model very
prominently used in the flight control
system of an Airbus 320 and
of course, of all subsequent Airbus
airplanes. So the way you actually
fly an Airbus is that you move the stick.
And what this does literally,
is that the stick?
Flies an idealized
airplane, a model of an idealized
airplane in the computer,
then the various
altitude sensors and air data
computers they measure, what is
the state of the physical
aircraft, things like, you know,
angle of attack, role, angle, stuff
like that. And then there is
obviously a difference between the model
that the pilot flies, the idealized
airplane and the real one.
And then you have control algorithms
that decide how
best to get the state of the real
aircraft in sync with what
the pilot wants the aircraft to fly,
like based on its input into the
idealized aircraft model.
And it's interesting because if, for
example, one of the flight computers
has failed and you cannot control your
ailerons, then
you still use the same flight inputs.
But of course, the system then figures
out how to use, for example, Despoilers
to produce the role.
Right in order to bring the state
of the real aircraft in line with
the model.
So to wrap up that part of the talk,
we have analytical, numerical and
parametric models, analytical models
are basically functions, if you will,
equations that take a bunch of inputs and
you can calculate the output you're
interested in directly for every
point in time, for every kind of
combination of inputs, the quantities you
calculate with are usually continuous
and the equations are physics or whatever
else, chemistry, biology.
But it's the real science in
an American model you describe
as basically the analytical world.
You iterate then and typically
the iteration.
Well, almost always your
iteration will depend on the
on the previous state of,
you know, in the last time step, for
example. And this means that you can't
just say, hey, model, give me
the state at T equals
five thousand seconds, because in order
to know that the model has to calculate
for all five thousand previous time steps
and that makes these kinds of numerical
models much less flexible.
On the other hand, they're much simpler
because solving
complex
systems of equations numerically is much
easier than analytically.
The equations are still basically the
real science, but the quantities are
discrete. In a parametric model,
you can again have a direct look up.
It's not expensive, but the
quantities are usually much more coarse
grained and the equations are not
necessarily somehow
resembling the real
science. They might be completely opaque,
right? They might be completely just
numbers you figured out somehow.
And, you know, they kind of work and
you use them, but they don't tell
you anything about how the real world
works. They make a prediction, but
they don't explain.
So let's elaborate on that difference.
Let's say you have the real world
changing somehow as shown in this
lower dark gray box.
And the you know, the reality changes
basically as a straight line.
This warbly change is
sensed by your model
as a step function.
The model calculates and outputs
some kind of reaction.
OK, that's fine.
That is a prediction.
So the model expresses or gives
you information about how reality
will change as a consequence of whatever
impulse you
are interested in. Like how does
the weather change if temperature
increases, how does the virus
spread rate change
if 60 percent of people will
wear FFP to masks and stuff
like that? But there's no explanation
going on, which raises the question
what actually is an explanation?
And I struggled with this quite a bit
because what is the difference between
the how and the why isn't
the Y also also kind
of how, you know, how do you make the
difference? And I interviewed somebody
from from CERN and
he gave me a very, very interesting
definition of what Y means
in this context. He says that if a model.
Produces its prediction
through applying
a more general theory to this
particular case.
Right, if you don't have, if you will, a
theory specifically for this problem.
But if you have a more general theory
and the model, if you will, configures
that theory in order to produce
a correct prediction, then
if you look at the configuration of
that model, you have the Y,
you have the explanation.
Examples for such general theories
are, of course, Newton's laws or Quantum
Croma Dynamics or Darwin's evolution
or some kind of
reaction to genetics and chemistry.
Right.
And so this really is
a better model because it just doesn't
just predict.
It also explains
why it makes that prediction.
It explains the underlying mechanisms,
which is, again, more useful.
Now, here is an exciting category of
models that don't do that right.
You have probably all know what this
resembles here.
This is a neural network which has a
bunch of inputs and a whole bunch of
weights and an output.
So the neural network makes a
prediction, right?
It's the ultimate form of a parametric
model because each of the weights
here in that neural network and there
are millions in real networks
is a parameter and it
is not at all transparent what each of
these millions of parameters means and
what the model has learned.
You can test and that's what people do.
But if you forget to test certain things,
you have no idea how the model will
behave. And there is this funny example
where people were trying to build
a machine learning
model neural network to
recognize sheep.
Right. The idea was to oh, should be
idea. The idea was to
make the model learn the shape of
sheep. But of course, what that
particular model learned was, you
know, the green of the grass on
which shapes a sheep's are usually
photographed.
And so, you know, when you
showed the thing just green pastures,
it also detected sheep.
And so basically
such an opaque,
pure, parametric model will produce
wrong results with some probability
for new situations.
And the problem is that you don't
necessarily know what a new situation
is because you have no clue.
You know, what the thing has learned.
Obviously, you test, but testing,
as we all know from programing, but not
sure if we all know. But as programmers
know, testing can only prove the
presence of the bug, never the absence
of bugs. And you have that problem here.
So this really doesn't matter for
advertising. It's annoying if they try
to sell me the same shoes that I just
bought. Right. Or tried to sell me,
I don't know, you know, orange hats,
which I will never buy.
But it's not really a problem.
It is more of a problem if people aren't
given credit because some stupid machine
learning algorithm has basically,
you know, incorporated some
discriminatory decision
based on stupid training
data. And it's really a problem.
It's potentially fatal in autonomous
driving. So there is a whole thing about,
you know, trustworthy machine
learning and understanding what a model
learn. But that's and it's in its early
stages.
So let's look at abstraction
and simplification again, back to our
simple pendulum and we
can ask how quickly will this thing
pendulum back and forth?
And yes, an open duel is not an English
word, but I thought it's funny.
So what's the period of this pendulum?
And if you look at the Wikipedia
article for this, you get a very
long formula and you can see the three
dots. So it continues.
I did actually a screenshot of Wikipedia
because I was too lazy to type
this up in a formula editor
myself because it's so long.
The point is that you can see that this
period depends on the angle.
So if you.
You know, move the pendulum further out,
it oscillates with a different
rate than if you move it out only
a little bit and
you can make a simple simplification for
very small angles where
the science of the angle
is basically the number
Dangl itself sine X equals X,
then you can simplify for small angles
that the period is two pi
square root of L over G.
And that is probably the formula you
learned in school, which is completely
fine. It gives you the right result.
You stay within that
range for which the simplification
is valid, right, and it gives you wrong
results outside of the validity range.
So this is another one of these things
if a model has been.
Built for a certain limited
parameter range, if you will, a range of
inputs and you use it outside the
forecast is wrong that the obvious
example here also is Newton's mechanics,
because Newton's mechanics are wrong,
right? Because Einstein showed
that things are quite a bit more
complicated with a special and general
relativity. But we also know
that for our everyday world, because
we are at low speeds and relatively low
gravitational forces, Newton
is good enough. But you have to be aware
of this. If you try to calculate the
path and trajectories of spaceships
with Newton, you will
not get the rest of
the results at the required position
that you expect.
So another question, will
this thing oscillate forever?
And if you look at this formula again,
there is nothing that seems to slow
this thing down. So it's actually this
formula is actually given with
no damping. Right.
So this thing will just continue forever.
And we know experientially that
that's not the case.
You know, stuff will stop oscillating
at some point because of aerodynamic
drag of the of the weight and
also because of internal friction within
the the wire that holds the weight.
So actually, it looks like this.
Right. So it will become less
and at some point it will stop.
Now, again, importantly for your
pendulum clock.
Right. I think it's called grandfather
clock in English.
Right. I'm not sure.
Um, it doesn't really matter because
you'll, you know, add additional energy
to the clock every evening, you know,
right around Takizawa anyway.
And so doesn't really matter.
But if you try to work with this
kind of problem, then it is
a concern.
Not sure if you recognize
this picture.
It basically zori
represents the
how a gravitational wave looks
like in twenty sixteen, the legal
gravitational waves detectors have
heard gravitational waves for the
first time.
And again here, here's the thing again.
This shows time on the x
axis and the frequency of
the wave on the y axis.
And the darker the shape,
the more intense, the louder,
the stronger the wave.
So they called this a chirp
because it basically sounds like
rap, right?
Because the high frequency increase,
it becomes louder like a birds chirp.
So how do those guys
detect gravitational waves?
Well, they have a interferometer,
which basically sorry, which means
that they send in a laser
pulse along one arm.
The laser is reflected, passes
through a semi transparent mirror along
another arm that is orthogonal to the
first one reflected again.
And then back to
a place where the two,
um, the two
laser beams that went
through either or both arms are
interfered.
And if the two beams
arrive in phase, that
will be constructive interference,
whereas if they arrive exactly
out of phase, then the output
will become dark.
So any difference in
length between the two
arms will change the interference
pattern at the output.
That's the idea.
And so if the gravitational waves
possessed by and makes one
arm longer and the other one shorter,
I hope you can see this on my great,
wonderful animation here.
Then you can see this thing
basically vibrate.
The output vibrates visually.
Well, I mean, lots of detectors going
on, but principally, of course, this
only works if these mirrors
here on either end don't vibrate
just so right.
They told me the story when I visited
the geophysics 100th detector.
Whenever the post you know, the
package delivery guy drives too
fast along the way to their
to their site there, they
can see the mirrors vibrate and they're
telling the, you know, the post guys
to go slow. And whenever a new post guy
shows up, destroys the measurement.
So what they do is they attach these
mirrors to two level pendulums
because pendulums actually, when they
have a high mass, have a very good
damping, about one thousand.
And so with this triple pendulum here,
they can get a damping,
a passive damping of,
I think, one thousandth of
the power of three. That would be ten to
the power of nine.
Right. And then they do some active
temping as well.
They precisely understand the behavior
of the laser.
They even optimize and understand
and measure and change
and, you know, try to limit shot noise.
And so my point here is
you don't have to understand that damping
of a pendulum for your stupid clock,
but you do have to understand it very
precisely.
If you want to distinguish the natural
pendulum behavior from,
you know, environment, postal
guys and little earthquakes, if you want
to distinguish that from whatever
a gravitational wave does.
So all models are simplifications,
even the one for the
gravitational wave detector.
But how and how far depends on
the model's purpose.
Let's look at another example.
I visited the Bantustan seven
x stellar radar fusion experiment
in Greifswald and I asked
them, so how do you guys model
the plasma in the reactor?
And they told me, well, it's not so easy
to have a.
One model that models it as a fluid
called Magneto Hydrodynamics,
the other one model said as a mix of two
gases, right, that the electron gas and
the nuclear gas, basically,
they can also model it as small particles
that our dislike and that can
model it? S point like particles
that move on this disc as
on the circle around
on this disk because of the magnetic
field configuration.
And they use all of them.
Right. Depending on what they want to do,
they use all of them. Obviously, the
Maged model on the left doesn't
give you detailed information about the
particular particle.
But if you want to characterize the
overall behavior of the fluid
as sorry, off the plasma
as a body that is
inside the reactor, then that's good
enough. And obviously,
each of these models have to
make the same prediction when
you get to a boundary case
from which on you use the other
representation, another
kind of physical constraint.
Let's look at this example.
Not sure if people recognize
this is the configuration of
the various accelerators at CERN,
the big ring is the Large Hadron Collider
and the smaller rings are earlier
colliders that are now used as
accelerators, as pre accelerators
before the hadrons
enter the large storage ring.
And these.
The LHC has these huge experiments,
you see the person standing there at the
bottom, these
huge experiments which
capture what happens
when particles from these beams
collide.
And again, here is another picture here.
And again, consider the people
for reference.
The way these detectors work is basically
that you have a whole bunch of different
detecting elements arranged around
the central collection point.
And when particles fly
out, then they
hit these detectors
as they are called, and produces
some kind of electronic signal.
And that is then used.
Quick comment to the
technical people here.
I get a lot of noise on my mumble
channel.
Not sure who should make a mute.
Their their microphone, their.
All right, so here is a
an illustration of one of these collision
events. You can see how
the particles stream in from the well,
can see the particles, but you can see
the beam pipe at the center
through which the two particles that
collide travel.
And then you can see how the various
collision products stream out and
how they light up the various
detector surfaces.
And what this shows here is the collision
of two protons, which forms a
Higgs boson, which then decays
to the bottom quarks and to a W
boson, which then also decays.
How do we know?
Right. How the heck do they know what's
happening, what's going on here?
So let's first understand a little bit
how these detectors work.
Fundamentally, what they do is they
have a very strong magnetic field.
And if a particle that has some
electromagnetic charge and most of them
have otherwise, it's hard to
detect them actually.
Then, you know, again,
a little bit of school physics,
Lawrence, for us and stuff like that, the
particle will be bent around
a circular track by the magnetic
field and then they have different kinds
of detectors.
And for example, if you look at a
electron here, the second
example from the top, it moves
it leaves a trace in what's called the
silicon tracker. And then is
it decays in the
electromagnetic calorimeter.
And so if you look at the various
different particles, each of them leaves
traces in a different combination
of detecting elements.
So this gives you the type of particle.
And then through the bending,
you can measure its momentum.
And basically through time and
momentum, you get a unique
characterization of what's going on.
You can even, you know, calculate
the overall energy balance and stuff like
that. And the moment, moment, momentum,
balance and very sophisticated, really
interesting stuff.
So and
so in this case, in the example I gave,
we have an expose on the decays in
various ways. I've just called these
particles A through F here.
Doesn't really matter what they are.
And these decays, they are multi step.
So what the detector actually sees
is what they call the final state, which
is these decay products.
What the scientists are interested in is
what actually happens in the collision.
And so the challenges after
observing the final
state, the decay products with the
detector, you want to calculate
back what actually happened in
the collision? Was there a Higgs or
wasn't there? And what is the mass of the
Higgs boson? That was the big question
back then. And I think 2013
when they discovered it.
By the way, Einstein has nothing to do
with this. I just used the picture.
So
in German, we say
there are Haken, right?
It's not so easy. There are
there are problems. And so I used this
picture of a hook. It doesn't really work
in English, but so what are
some of the challenges I have to
overcome? Well, we have seen that the
Higgs decays in multiple ways and each
of these decays happens with a certain
probability. So they have to somehow
untangle that.
That decays our non-unique.
As you can see in this example, this
hypothetical e particle can either
arise from A to B to E
or from age to A today to eat.
So just because you see an E, you don't
really know what happened in between
then. These collisions are not
unique, depending on how exactly
you know how well the the protons
align in their collision.
You either get hard collisions or soft
collisions or any intermediate state.
And so the
created particles, the kind their
energy depends on whether it was a soft
or a heart collision and all kinds of
other parameters. So that is also a
source of complexity.
And then finally, this detector,
I mean, these detectors are marvels
of engineering. They are also terribly
complex. Each of these components has
their own failure modes and
failure models, and
these are complex systems in themselves.
So, again, how do they know
what they're observing and how do they
know that with a you know, with
a with five sigma.
Five Sigma is.
A measure of the
basically a measure of the trust and the
result, five sigma is the
threshold in physics for a discovery
and five sigma means that that
there is a probability of zero point zero
zero zero zero five seven something
percent, that the observation happened
by chance and not and
is not the effect
that they assume in terms of physics.
And this is also quite related
to the p value that's used in statistics.
It's inversely proportional
to the amount of data.
The more data you have, the higher the
trust and of course, also inversely
proportional to the size of the effect.
The bigger the effect, the higher the
trust.
By the way, it's interesting to compare
these five zigmas to the P
values they using in medical trials,
right?
They are happy if they get five percent,
not zero point zero zero zero zero zero
five seven.
So it's quite a big, big difference.
So how the hell do they do that?
Well, statistics, right.
They simulate billions of events
to understand the distribution of what
will happen. So how does this work?
So they have what's called an event
generator. It's a software model that
simulates the physics of
decay after a collision.
Right. So you basically specify
collision parameters. Is it a hard or
soft collision? And then this thing gives
you a distribution of particle vectors
of basically what streaming out of these
of this collision site?
Then they have what's called an
experiment model.
It's called G and four.
It is a complete well,
obviously it's a simplification, but is a
a representation of the actual detector
and of the physics in the detectors
themselves, because, I mean, the
detectors work by
basically running certain physical
processes when the particles interact
with the detector material that is
simulated in this model.
This gives you then simulated detector
hits.
Then they have basically an electronic
simulator that has a noise model
for all of the electronics of
these detectors. And this gives you
simulated raw data and
they run billions of these simulated
collisions in order to get what they
call the background, which is how
what what would they see in
this detector statistically
if there wasn't any Higgs?
Right. So they run these simulations
without Higgs, just the other
nuclear processes, and then they take
the measurements and they compare.
And then this is the screenshot of
what Atlas saw.
And you can see that at one hundred
twenty five giga electron volts, there is
some kind of peak and that is the Higgs
boson. And they
basically find this out through
statistical calculations
based on huge amounts of data.
Right. This is why they have some
of the largest computing centers.
They run millions and
billions lines of code in these
various simulators developed over
decades. Of course, good old Fortran
is still the backbone.
They also use Python for a lot.
And they have I think it's terabytes
of data.
There's a whole world wide distribution
and scheduling infrastructure for,
you know, calculating and running all
these simulations. It's a huge
infrastructure behind this in order to
get enough data to
find out with some
degree of trust that in this case
they discovered the Higgs.
So how can we build trust in models?
Well, one way we can run
lots of experiments with lots of data
and then do statistics.
Now, experiments are nice because they
give you controlled conditions, they
allow you to isolate various influencing
factors by controlling for them.
Right. And so you can
if you see stuff correlated, it's
relatively easy to derive causality.
So, you know, instead of just saying, you
know, this happens and that happens.
And whenever this happens, that happens,
you can also say, because this
happens, that happens.
That is that is causality.
But sometimes you can't do experiments
in climate or epidemiology
or economics or many societally relevant
questions. You can't really run
an experiment. I mean, you know, in
some sense we run an experiment with our
atmosphere, but but you can't build
another planet and run, you know,
a climate experiment in that sense.
So what you have to do then is you have
to fall back on just observation,
but you do not have controlled
conditions.
You cannot isolate influencing factors,
at least usually you can't.
And so you really just get correlation
and then you have to make an attempt at
deriving causality.
But that's much harder
sometimes. You're lucky, right?
You have natural experiments.
The economics profession,
you know, tries to use that when
they say in this country when they
did this and that it gave them
inflation.
And in this other country where there was
the following difference, there was no
inflation. And so then because of that
following difference, they claim this
is what produces inflation.
But of course, again, you never know what
else has changed.
Right.
It's harder.
It's maybe a bit easier in epidemiology
these days.
You know, the factors aren't that
different. So maybe maybe looking at
other countries that to a stronger
lockdown's is a good idea.
Different story.
So what can we do again if
we don't really have a way of
running experiments in that sense?
Let's say we want to run some kind of
forecast and we know that this forecast
depends on some kind of parameter.
P is a parameter that we have to
tune in our model for
the forecast to be correct.
But again, we can't run,
we can't validate easily.
So we have no data for comparison because
we want to forecast the
future. Weather forecast is a good
example. Well, what we can do is we can
forecast the past, right.
So we can move back in time and run
the forecast from a point in the past
where we do know what actually happened
in the real world and then we can tune
our parameter P in this case P
to some value.
P2 is the best setting
for P in order to fit our
forecast best with the
actual, you know, data that
we know because they happened in the past
and then we can continue using this
parameter for the future.
This actually happens in weather
forecasting there. It's called re
forecasting.
And these weather models
that are continuously run the various
weather services, they
continuously basically go back
and forth between re forecasting for a
parameter tuning and also for
filling in inputs
that they don't know because,
you know, there is not a
way to find the temperature everywhere
above the ocean, only where there are
ships. Right.
And a bunch of weather buoys.
So that ship has to go back and forth
to do this kind of stuff.
And so this is really the backbone of of
weather forecasting.
So another way of building trust
in models is re forecasting the past.
Now, all models are simplifications.
We've talked about that. Right.
And so the question is, if we simplify
which of potentially many parameters
can we ignore which are important?
Right. So here is another model M, it
has three parameters, P1, P2 and P3.
I realize I used P2 as
a value on the previous example here.
It's the name for a different parameter,
not a good decision. I'm sorry.
So we have three parameters, P1 through
three and we don't know which of them is
important. Well, what we can do is we
can scan through the ranges
of all of these parameters and see
which, which, which scan has the largest
output or the, I should say, the largest
consequence on the output of the model.
In this case, we can see Delta time for
P three is the largest one.
Right. So we know P three has the
largest influence.
By the way, there might be an even larger
influence when we combine
the scanning of P1 P three.
So we have a combinatorics problem.
I don't know.
I forget which scientist I talked
with when I asked about that and
they said, well, we don't we don't do
these combinations. It's too complicated.
So that's another simplifications.
They treat each of these parameters as
uncorrelated with others, which
might or might not be correct anyway.
So we find out that this model here
is sensitive to the value
of P three.
And so what does this mean?
Well, it means we have to.
Invest effort or computational
power into determining
P3 precisely, or
if we can do that again, because we might
not have a way of finding the value
because we don't have, you know,
temperature sensors all over the ocean,
maybe satellites can help.
But different topic then we have to
always very P3 and
whenever we make a forecast, make it
for the whole range of P3 and see what
this gives us.
And this is, well,
more or less this is what ensemble
forecasting is called in meteorology,
where they run different models,
different parameters of the same models
and also different values of the input
conditions.
Well, that where they are not known
in order to basically get a probability
distribution of outputs.
Right. So they might vary the temperature
at a given point, run the forecast
and they get a probability distribution
of the output. And then they either
communicate the probability distribution
to their users or they
just give you the result that is most
probable.
There is a weather forecasting service
called Metro or Blue, and
I like them because if you look at the
screenshot from the left, you can see in
Germany, of course, the traffic.
So you had a better prognosis.
The reliability of this prognosis
is three is medium, and
now you can click on a button and
you now get what they call the multi
model. This is essentially
a, if you will, sensitivity analysis.
It shows you what the different
models forecast.
And you can easily see if you actually go
to the page how they diverge more over
time.
They even give you the verification.
They they basically tell you how
good this model was in the last three
days. So they give you a lot of
information in actually, if you want to
invest the time in
analyzing which how reliable
the model is. And this particular one
is used by a glider pilots.
I used the example from Goup.
It's a favorite gliding site
in southern France, and people spent half
the morning over this and other forecast
to figure out what the weather will be
now in epidemiology.
Things are really simple, right?
It's exponential growth.
Meaning?
The infection rate will grow
exponentially with some factor,
this B here is
kind of what we know as are not
exactly the same, but for now, it's good
enough.
Right. But we also know
it's not really like that.
Right. If there are no more people left
that can be infected or more generally,
if there are no more resources,
resources which an exponential
growth can, if you will, grow into,
then the growth has to stop.
It's called the logistic growth model as
opposed to an exponential growth model.
And we know everybody knows now
that, if you will, that the
herd immunity is the step or is
the amount of infection where there
are no more people left
to be infected or where at least the
infection rate becomes,
quote, inefficient from the perspective
of the virus and the growth becomes
slower and at some point increased
infection stops.
So what else could there
be? Right. Simple.
Well, there is this website
called Korvettes by a company called
Explosives, and they have discovered
simulator.
And actually, there's a whole
bunch of differential equations
they use, like the number of susceptible
individuals, you
know.
The individuals in various periods of
infection, the number of recovered
individuals, people of number of people
who have died, so it's quite a bit more
complicated, actually, it's way
more complicated.
There's lots of different dynamical
equations.
There are intervention effects you might
want to model.
And there's a whole long range of
parameters that you can set and that
you have to set.
Right. And so there's
an interesting effect that I figured
out when I talked to one of these guys.
The the ratio
at which the population
reaches herd immunity depends
on how they
break down the age groups.
Now, I'm not talking about the actual
H h distribution
in the population.
Obviously, if you have more old people,
more people will die. We know that,
right? That's our experience.
What I'm talking about here is whether
you split, you know, your population
into three groups, zero to 30,
30 to 60, 60 to
infinity, or whether you split
that same.
Age pyramid into 10 or 15
subgroups.
The model makes different predictions,
who'd have thunk? Right?
So this is an example of a sensitivity
analysis where you have to somehow figure
out what is a good way for
this age structuring
in your model.
There's another nice example for
sensitivity analysis and fusion,
so one thing they might want to optimize
in their reactor is how do you maximize
the distance between the plasma and
the reactor wall?
Because as you perhaps know, that the
plasma is very hot.
It's stabilized through a magnetic field.
And if the reactor Asara if the plasma
hits the wall, well, it might damage the
wall. But more importantly, the plasma
will be damaged and might collapse.
So you want to keep the plasma away from
the wall. And again, that's the point of
the magnetic field. So one parameter
you can tune is you can increase or
decrease the field.
You can increase or decrease the gas
density. You can increase or
decrease the number of neutral particles
that are injected in as a way of
injecting energy.
Basically, you can change the temperature
of the plasma
point is that it's 10 to 100
combinations.
And how do you
do that? Right. So how do you make this
optimization? Well, one way is you have
to use the simplest of these various
representations of the plasma I mentioned
before. So this is something they do with
the Ph.D., the fluid representation,
because it's the simplest, it's the most
efficient.
But also, again, even
then, you know, we only have 10 to the
power of 10 to the 80 fifth
atoms in the universe.
So 10 to the power of 100 combinations
won't work.
So this is where in these numerical
models, computer science comes in, right,
where you have various different
optimization algorithms, numerical
solvers, you know,
things like her climbing, simulated
annealing, not something I want to cover
in this talk.
But I thought it was important
to point out that it's not just
about finding the right model and the
right abstractions and the right
sense, you know, deciding on
the right parameters.
There's a lot of cleverness going
on here in the programing and how
you perhaps then also run this on
a parallel computer.
By the way, little anecdote.
I talk to a meteorologist a few
days ago, actually, for a podcast
interview, and he said it's
going to be really painful when in the
next or next
next generation of supercomputers,
everything will be computed on graphics
cards because we can basically throw away
all our code and have to rewrite
everything that it's going to be painful.
So how can we build trust in models?
We can vary parameters, do a
sensitivity and analysis and
analyze the impact.
Now, I want to re-emphasize
something because somebody recently on
Twitter told me that
this modeling for covid
seems to be shit because the
forecasts were wrong
and this person understood something,
misunderstood something completely, and
that is forecasting versus scenarios.
So let's say you have
a model and you
want to make the model correct.
You know, make the right predictions.
But you have but you can't take into
account all of these millions of
different parameters. You have to find
out which ones are the most relevant.
So that's when you as we just learned,
you run a sensitivity analysis.
Right. For example, you want to
find out the cloud formation depending
on temperature and humidity, the radiated
energy by the earth, depending on cirrus
cloud coverage or the amount of
precipitation, depending on layering of
the atmosphere. Right.
Once you figure that out, you put that
into your model and then you can actually
measure various data in the world and
make forecasts, actual forecasts
that the output of the model claims
that this is how the weather will
behave.
OK, that's what we do in forecasting.
Now, let's look at another example.
Let's say we want
to figure out or we want to understand
how the one-to-one infection rate
are depends
on how much virus
people shed when they breathe,
how the virus shedding depends on
the kind of mask you wear and how
the one to many infection rate depends
on the rate of interpersonal contacts.
In this case, you can then also
make a sensitivity analysis,
run it on simulated data, and
then what you get isn't the forecast
because you don't know how people
will behave.
But what you get is scenarios.
You can say that if you guys
behave in the following way, then,
you know the infection rate
will increase. So there's no point
in saying the covid forecast was wrong
because it didn't make a forecast.
It gave us scenarios that,
you know, give us hints about how we
should behave.
And of course, it's a bit frustrating,
right? We have a health care model that
says that early and hard lockdown works
best. Right, because it's easier to
slow down exponential growth when the
absolute numbers are low and economical.
Model told us that early and hard
lockdowns work best because shorter
lockdown's.
All the reasons above means less total
cost. There's also psychological analysis
that says, well, early and hard lockdown
works best because if you become harder
over time, people are already fatigued.
They have lockdown fatigue so they won't
comply.
So Germany still started a lockdown
light and did it too late.
So it's quite a bit useless if
you have all these models that make these
useful and I guess
rather reliable scenario
forecasts, if you will.
But then we don't care.
OK, but that's just a side note.
It frustrates me a great deal.
So I had to include that into the talk.
All right.
So again, going back
to building trust in models, we were at
this parameter variation story.
But there is another way how we can build
trust in models, and that is if we
do have an explaining model,
one that doesn't just tell us the how,
but also the why, then we
can inspect that model and and
see if this makes sense.
Right. Is this explanation plausible?
Does it make sense, for example, if
your plasma optimization thingy
comes up with a great solution for
maximizing the distance of the plasma
from the rack, the wall, but it predicts
a pressure that is twice
as high then what your reactor
vessel can bear.
It's not a good forecast.
It's not a good result. Right.
But you can only do this because you
can inspect the solution, the model
created for sensibleness, if you
will, so you can check
explanation's if they are
there. So let's look at how you
get from data to the model.
You probably all remember this picture,
right? It's the first ever image of a
black hole. Well, it's sort of
an image or I should rather say this is
an image, but what the Event
Horizon telescope imaged
wasn't really an image.
Right, because of how
that works.
Let's let's see how this works.
So that is a radio infirmaries
interferometer, which means
you computationally combine
several telescopes and there's
lots of computing going on.
So in this case, they combined
a bunch of telescopes all over the world
in something that's called very large
baseline interferometry.
The very large baseline comes from
the distance between the telescopes.
And that is relevant because the
resolution, the the
whole computational
thing can resolve
depends on the length of these
baselines.
So the longer the further you can
distance these telescopes, the higher
resolution is the picture.
Well, picture this thing is going to take
here is a picture of one of these
telescopes. OK, this particular
one at its bulk is not used
because it can't observe at the
respective wavelengths.
But these kinds of telescopes
smaller, some of them
all over the world.
Now, how does this work?
So these different telescopes, they look
at the same spot in the sky.
Right. But because they are some
distance apart that the distance
from the telescope to that point in the
sky is different. Right.
So they see the same wave, the
light wave that arrives,
you know, with a certain phase difference
because there is this difference D
in distance offset.
Right. And of course, because light speed
is constant, this is proportional to some
time difference as well.
Now as the
Earth rotates
and also as you look
at different points in the sky,
this difference also sorry, this distance
also changes because the angle
of the object in the sky is different
from each of the telescopes.
So if you take these two observations
or realizations and then apply
a whole bunch of mathematics, which I'm
not going to go into, I
probably also couldn't in detail
you get the following equation, which
again, not important in detail,
but what this equation shows is
a Fourier transform of the sky.
So the HD actually observes
a Fourier transformation, a spatial
it. It observes the spatial
frequency distribution of
the radiation across
the sky. OK,
and then the actual
data point is basically there is
a way that
we can we can we can basically observe
this amount of radiation
with this frequency.
And by that I mean spatial frequency
at the following orientation.
And then they
combine all of this data and
the more different lengths of baselines
they have and the more different
orientations of baselines they have,
the better. But still, in any case,
you know, they only have like whatever
seven telescopes.
So they have 10
different baselines.
And the orientation of these baselines,
well, there's only a limited number of
these orientations, sure, the Earth
rotates, giving them a bit more,
but still it will be incomplete
data.
So what they'll have to do is they have
to do an inverse Fourier
transformation of incomplete
data. The question they're answering is,
which is which mathematical description
of the object in the actual
space domain
represents or approximates best
the data that has been seen
by the telescope in the frequency domain.
Right.
And so let's look at a simple example
of this kind of problem.
On the left side, you can see a bunch of
measurements, right? Some data.
And on the right side, you
see a mathematical model.
In this case, a horizontal line, a simple
equation Y equals Y zero,
no dependency on X and
the total error.
Of that model relative
to the observation is you can imagine
that as the sum of all the red bars,
right, that the difference between what
the model predicts, what was actually
observed.
So there could be different
mathematical models.
Right, that approximate
that same data.
Question is which one is
the right one? Right.
So, again, in the case,
what visual shape actually
fits best to the observe
observed incomplete data in the
frequency domain?
And this example here
on the right is best,
right? Because it has a total error of
zero.
But actually, what this is, this is an
overfit if you put enough
terms into your polynomial, you can
fit every data with some kind of
polynomial.
But while
it reproduces the data perfectly, it
makes no useful prediction because
there's no way you can tell what the next
like if you extrapolate to the right
would be. And it's no it's no
abstraction. It's not a useful model.
It's just the encoding, if you will,
of the measurements as a formula.
So, by the way, this is what's called
over learning in neural networks, just as
a side note.
So how do you decide between the three
remaining ones while you decide based
on knowledge about the system at hand?
Right. You know something about
how your observed
system should look like because
you understand the physics.
You have a simple, analytical, intuitive
model about what's going on.
So in this case, the model
of the black hole tells us
that between
the center of the black hole and
a distance of two point six times
the so-called Shwartz radius,
you will see black because in
the middle you look at the black front
side of the black hole a little bit
further out the your race
or the lad coming from the black hole are
actually bent by the strong gravitation
so that you can see the back side of the
black hole, which is also black.
So we know that,
you know, up to two point six hours
it'll be dark.
And outside there, we will see
a glow from radiation
that is accelerated around
the black hole from the gravitational
force. So there must be something glowing
and there must be a black thing
in the middle. And we even know roughly
how big business because we can calculate
the Schwarzschild radius through other
means or at least guesstimate it.
And so we kind of know what it will look
like. We'll kind of look like this donut.
And so knowing that we can
use this knowledge and
basically help interpreting the
incomplete data.
Now, of course, the problem is how is
that not self-fulfilling?
How do we avoid observing
exactly what we want to observe?
You know, then we don't have to observe
it because we know what to look like
anyway and will fake it.
So what they did here is they used
different three different DE convolution
algorithms to do this kind of inverse
four year transformation with three
different software packages for
independent teams who weren't allowed to
see everybody else's data.
They also worked with synthetic data.
They used the same magneto hatada
hydrodynamic magneto
hydrodynamic simulations of
black holes.
And of other shapes, right, they they
they produce such data of,
I don't know, rectangles and and, you
know, if if the if the software
is still produced a donut
as a result, then something fishy is
going on. Right.
And of course, they still minimize the
error of the feting.
So there's a lot of work going
into this reverse
analysis of the
of the data. It's fascinating to read
this nice book by Ficca, one of
the leaders of the project.
I think it's called Light in the Dark or
something that talks about that
and other things.
So again, that's the explanation.
Makes sense, right?
We know how the physics works so we can
say something about what what we expect.
So how far can we trust models?
Here's a statement I've read.
If we had started the lockdown one week
earlier, thirty six thirty
six thousand three hundred seventy two
fewer people would have died.
This is what I call pointless precision
because the precision of whatever
your model predicts must be proportional
somehow to the precision of the input and
the parameters.
And obviously we there's a lot of things
we don't know precisely for this virus
and how society reacts.
Right.
So this leads us to this observation
that there are models that are
qualitative in nature.
It only tells us tendencies.
Right? If input increases output,
X will also increase.
There are relative models
which give you comparative influences
like input, a influence the output X
twice as much as input be useful.
And then there are quantitative models
which actually give you numbers.
Right. If you increase by 10 percent, the
input A, then output B decreases
by thirty three point three percent.
Now formula doesn't mean
numerical sorry formula doesn't
mean quantitative.
There is this Drake equation which tells
you how many civilizations there are in
our galaxy. Right.
And it's this equation, it has all kinds
of factors, like the average rate of star
formation, the fraction of planets that
could support life, fraction of
civilizations that sent detectable
signals, blah, blah, blah.
Right. It's a formula has lots of
factors. So it's numeric, right?
It gives you quantitative outputs.
No, it doesn't.
This is really just a simple parametric
model because none of these
parameters has really
known quantities.
We have rough boundaries or,
you know, boxing for each
of those, but not really.
So using
an IT just because you have an equation
doesn't mean that it's a quantitative
model. It might just be
it basically just says which things
influence this thing and whether it's
proportional or a..
Proportional.
So let's look
at fundamental limitations
of this whole modeling business.
So first is chaos,
which means that a small change in the
initial conditions leads to huge effects
over time. So you've probably all seen
this chaos pendulum, right?
It's a pendulum with two
hinges that the word don't know.
And if you take the pendulum and
put it into a certain, you know,
position and let it go,
it will oscillate in some way.
And if you then take the pendulum and try
to put it into the same position again
after a few seconds, it will move
completely differently because the
behavior is chaotic and you're
not able to
put the pendulum
in exactly the same initial condition.
Also, you don't know exactly what
other factors influence it.
You know, there might be some wind going
on or whatever.
So the other example
that everybody talks about in the context
of chaos is like if the butterfly
leaves, you know, starts flying
in Brazil somewhere, this leads to
thunderstorms in Europe.
I did ask various meteorologists
here whether they actually think that's
true. And I mean, nobody disagrees
that the weather is chaotic.
But I think they said that
this very small effect,
but very likely not lead to a
thunderstorm, although in theory it
could. So the point is that both
of these systems are deterministic,
right? There is no randomness.
Right. There's no randomness in the
physics of the weather of the of the
atmosphere.
The quantum effects really aren't
relevant on that level.
There's also no randomness
in this and this pendulum.
But we don't know the
interactions, for example, the friction
in these two hinges and the initial
conditions precisely enough.
If we if we if you knew them
precisely enough, then we
could make a perfect prediction.
Right.
So or stated
less. Absolutely.
More input gives you
a better prediction.
More weather stations, more satellites,
more ships, more airplanes with sensors
gives you a better prediction.
So this chaotic
behavior of the weather really is
the fundamental limit for weather
forecasts because.
Right for any given data quality
and computational power.
Right. So that's why I think
what they told me was that roughly
every 10 years,
the useful range of weather forecasts
becomes one more one day more.
Right. And so that is
not just because the computers get
faster. It is also just because they have
more inputs
and of course, because to understand the
mechanism better.
So if we can't predict the weather,
you know, for more than a few
days, how then
will the climate skeptics say how
then can we predict climate?
Right. This is all fake.
They can't even predict the weather.
And of course, this is bullshit because
climate is a statistical prediction.
It's not relevant if it will rain
on 5th March,
two thousand thirty eight in Stuttgart.
Right. That's not what climate models
do. They make statistical predictions.
And just to draw home this difference,
again, going back to the
fusion example, we really
cannot because of chaotic
behavior, we cannot predict the
precision of each molecule or
element atom in this
mix of two gases, kinetic model
here. But what we can do is we can
calculate the averages.
In this case, the averages of these
movements is called temperature and
pressure. Right.
And so we can calculate that
precisely, but.
You know, despite not being able to
forecast every molecule
precisely so there is an interesting
thing in climate science,
it's called attribution science.
And so what these guys ask is, is
this extreme weather event that happened
there? Is this caused by climate change?
Right.
Really what they're asking is with which
probability is this kind
of weather event caused by climate change
at this location on the Earth at this
time of year? Right.
How do they do that? Well, they take the
current atmosphere.
They modify the initial conditions
like temperature, humidity, pressure,
stuff like that.
They they scan through these and
then they run the,
you know, climate models or weather
models.
Well, this the same models anyway.
It's a question of prioritization these
days.
And they figure out with how
many of these modified of
these initial conditions will we get
this kind of extreme weather event?
Then they take the atmosphere without
the human impact.
They remove the CO2 that we've introduced
over the last, whatever, 50
years.
And the methane, because,
I mean, that is relatively well
known how much disease they do.
The same modification of
animals run the weather forecasts
and they get another ratio of extreme
weather still happening versus not
happening. So basically they get
different degrees of robustness of
that extreme weather phenomenon,
depending on whether they run the real
atmosphere or the one without human
impact. And then they basically take
the difference between the two.
And this gives you the probability
of this, um,
weather event being caused by climate
change. I thought that's a very ingenious
use by climate models.
Of course, it also really takes a lot of
computational power because you have to
run these models lots and lots and lots
of times.
Now, you could say, well, this
whole chaos stuff, it's not
really fundamental.
It's just because we can't measure
precisely enough.
Really, there isn't any chaos.
It's just because our engineering is too
bad.
Well, let's look at cellular
automata.
A cellular automaton is
a mathematical abstraction that
has a row of cells.
A cell can be either alive or
dead. And then we observe
how the cells evolve over
time or generations
so that generations our time is the y
axis. And then we have a whole
bunch of cells on the x axis.
And of course, Generation Y depends
on the previous generation.
And each value of a
cell depends on
the value of the
two neighbors in the previous
generation.
So there is an X, so we can see this
here in this in this diagram we have
generation Y minus one.
And the value of the cell with a question
mark in Generation AI depends
on whether, you know, the three
other gray boxes, cells,
whether they were alive or dead.
And then we have an example rule, the one
here that says, you know, if the if
all three predecessors were alive,
then next time next in the next
generation, we are dead.
If it's you know, in this case,
it's only if the
three three predecessors
were all dead, then
the next one in the next generation is
going to be alive. So some kind of birth
from nothing.
Point is, if we plot this
rule one, there is a way of classifying
these rules and giving them names.
If we run this rule one over
20 or 100 or thousands or whatever,
how many steps you can see that a regular
pattern occurs.
Right.
And.
So we can give
a formula for this,
um.
Rule in this case, it's very simple
because only if
well, only in one case do
we basically we basically flip
the values of the
of the previous cells, except for these
two cells in the middle next and right
to the center, they always stay zero.
So point is, there is an iterative
formula. Right.
And it takes into account the value of
a previous generation.
That's why it's iterative.
But we can also give a closed Formula
One that does not rely
on the previous generation.
Right. We can't distinguish between even
and odd generations and just state
which ones are
alive and which ones are dead.
So that's fine. That's deterministic
behavior. We can predict it for
any number of generations and
we don't have to iterate.
Now, here is another rule, rule 13.
Here is how this one looks after 20
steps. And here is how
it looks after 100 steps.
And in these two other illustrations,
top right, you can see how a
simple change in the initial conditions,
how it spreads through
the chapter that the whole basically the
whole row. So this is actually chaotic
behavior and it's chaotic behavior
in pure math. There is nothing going on
with measurement. It's a property of the
math. So we
cannot predict.
The value of a cell in the IV
generation, we have to run the iteration,
this is also called computationally
irreducible.
In fact, it's a very good, secure,
random generator because the behavior is
random. It has been proven to be
random. It's all work by
Stephen Wolfram, who has written this
book, A New Kind of Science.
It's interesting, not everybody takes
it too seriously.
But these this work on cellular
automata is is not
disputed. So it's it's it's called stuff.
So chaos is a fundamental property
of our universe, and we
have to somehow, you
know, if it occurs in our systems
because our systems are complex, as we'll
see, this limits
the range to which we can say something
useful with models.
Another example is emergence.
You've all heard about how and
colonies exhibit these very
sophisticated group behaviors,
even though presumably the brains
of these ants are rather small and
simple.
So.
What's going on here? Well, we have
what's called agents, it's each and it's
an agent, it has simple rules.
It behaves based on,
for example, based on pheromones and
smells and stuff like that.
But then we have lots of interacting of
these agents to interact in different
ways, and then they produce some
kind of complex ultimate outcome.
And the point is that we cannot
predict the outcome
just by observing and understanding
the rules.
We have to actually run,
also iteratively the system and see
what can potentially come out.
And the thing is that in lots of
systems we care about, they work
exactly this way.
Right. Politics sets rules.
And then we all as society
behave in some way.
We interact based on rules,
maybe not based on rules.
People know there's lots of game,
theoretical personal optimization
going on. Right.
And so we really can't predict.
Right. So I did
an interview
with somebody from Delft,
Igor Nikolic, about socio
technical systems.
He investigates how a society
interacts with technical systems
and what resulting behaviors
could come out. And again, he can't
really predict because of this emergence.
But what he can do is he can run these
ancient models and then look at
the scenarios that could
potentially happen and then discuss this
with stakeholders, potentially
go back to change the rules and run
again and maybe iterate to
a better set of rules.
There's no proof there, right?
There's no guaranteed, you know,
understanding, but it can help.
He has lots of interesting cases there.
There's also a very nice counterexample
from from from politics in Germany.
Recently in Berlin, there were
setting an upper limit for Rentz.
Right. So the idea was to therefore
have lower rents and so less affluent
people will find apartments.
What actually happened, at least
initially I haven't checked in the last
few weeks, is that 70,
37 percent more apartments were
sold instead of being on the market
for rent.
Because, you know, this just became
less interesting
for people. For the renters,
28 percent fewer apartments were on the
market, 200 percent more
inquiry's per apartment.
And there was a shadow rent for the case
when the law was to comply with the
German basic law. So the point is, this
failed, right?
And it failed because, you know,
one tried to set simple
rules in an obviously complex
system with lots of emergent
behaviors now.
I do think that one maybe could
have anticipated that even without
running complex agent based simulations,
but still it's an example of
how rule making in politics
really is challenging because you
just don't know how the system will
react once you put some kind of
stimulus on it by changing regulations.
There is also an interesting example
from Cellular Automata, Game
of life. You've probably all heard it
right? It's basically a 2D cellular
automaton where the question
whether the
cell marked with X
in the next generation depends
on not just, you know, but
it depends on what happens around it.
So this phenomena like,
you know, dying from loneliness,
dying from overpopulation, healthy
environment, reproduction, the rules
don't really matter.
So here is something.
So this runs a game
of life simulation for I
don't know how many oscillations here or
how many runs, and you can see there are
things oscillating back and forth.
There are so-called spaceships,
there are glider guns.
These are the technical terms for
these seemingly coordinated
behaviors. Right.
So who would have thought that
from this relatively simple set
of very local rules,
seemingly coordinated phenomena
can happen? Almost looks like ants
walking around a
track, right.
So, again, pure math
can produce complex
or coordinated seeming behavior
from simple rules
that do not somehow
presuppose
presuppose that kind of coordinated
behavior.
So what can we do here?
Right. We we just said we cannot
predict behavior of the whole
system by examining the rules.
But we can what we can do is we
can set a new we can define
a new set of rules that
specify that that are valid for
the system as a whole, like whatever.
If you have more than 100 ants and the
temperatures over 30 degrees, they'll
come out of their bunk or whatever that's
called, and we'll start rummaging around,
you know, stuff like that.
You can observe or create
higher level theories.
In fact, this happens all the time,
right. Because the behavior of
ants might be based on biology,
but biology is just applied.
Chemistry and chemistry, as we all know.
It's just the physics of the of
the of the electrons.
Right. It's a joke among physicists.
So but the point is, we couldn't predict
the behavior even of a single
and if we tried to do but do that with
physics, even though it is physics
that drives the and everything is driven
by physics. Right.
We could try with chemistry, but that's
probably also a bit too low
level. We can maybe be more
successful with biology or medicine
by doing an MRI or an
fMRI of the brain of an
ant. Right. I mean, I'm not a biologist,
as you can probably tell.
But the point is what we are doing all
the time with we're stacking
abstractions on top of another of one
another. We are building models
of aggregated
subsystems in order
to understand those.
There is a very nice quote by Edgar
Dykstra, a famous computer scientist who
says the purpose of abstraction is not
to be vague, but to create and
but to create a new semantic level
on which one can be absolutely precise.
Right. This also relates to this
averaging stuff in the in the
fusion reactor. So very,
very cool kind of framework
that that humanity has has built for
themselves. They're another
example of stuff that can go wrong in
modeling path dependance.
Right. So there is a complex
structure of decisions we've made over
time. I don't know, just the cool
screenshot. Right. But we are somewhere
out there on the outer edges of this
path. How did we get here?
And the answer is we got here because
there were all these random and context
and resource dependent and cultural and
political decisions that we've made over
time for lots of phenomena.
If you ask, so why
the hell is something
like the way it is in our society,
there really isn't a good answer.
It could just as well be different.
But because of all these random
things over the decades
and centuries, we've just ended
up there. There isn't a good reason it
just happened.
Right. And the only way to
predict, if you will, is by
going the path you cannot simplify.
You can run an analysis and say,
well, obviously, you
know, I don't know, the
society has to do things this way.
It's not like that. Even the obvious
example is evolution, right?
Evolution is not a deterministic
process. It just, you know, because of
all kinds of constraints and randomness
and, you know, a meteor impacted the
earth. Stuff happened.
All of these things are examples of
complexity.
There are other things like hidden links,
feedback cycles, tipping points,
power loss.
If you listen closely, you
have heard all of those in the
discussion about climate.
Right. Which just drives home the point
that our climate is a complex
system, which makes it hard
to control it in a deterministic way
and back control.
I don't necessarily mean just
geoengineering.
Right. It's really
hard to understand and decide
what to do. I mean, obviously, we have to
reduce CO2. I'm not discussing
that. But in detail, um, I
guess maybe the point is that
geoengineering is risky.
So last point before we wrap up this
talk.
Unknown unknowns.
Models almost
always represent somehow
model knowledge and experience.
There's no completely unknown stuff
in models because nobody could have put
it in there. Right.
So there might be also biases
and prejudices.
And we won't ever run the sensitivity
analysis for unknown unknowns because
we don't know them.
We were not aware that they're unknowns.
So we are not testing the model for
what it would mean if that unknown
parameter would have a different value.
We don't know it. Right.
So the really nice example,
uh, I forget where I have
it from. It's very well known.
Um, I actually know where I have
it from, but I forget that whatever.
It doesn't matter. So, you know,
Turkey Turkey
gets fed by the former.
Turkey likes the farmer
because, you know, it's the guy who
brings food. So based on Bayesian
reasoning, updating its
own perception, the
turkey builds a model of the farmer
in their brain and, you know,
becomes more and more, you know,
on the good side.
But then on day one hundred,
Thanksgiving, the farmer comes and kills
the turkey.
Of course, the model could not have
predicted that. Right, because there was
nothing in the experiential world
of the turkey.
There was no indication based on
which the turkey could have
updated the model in their
brain to maybe not be
so optimistic because, you
know, one day Thanksgiving
comes around. So again,
so this means that when we think
about what we will all die
from, we as a as
humankind.
Right. We can do some probabilistic
modeling that estimates the likelihood
of dying from volcanic super volcanic
eruptions or meteors hitting or
natural pandemics because we have
experience from the past.
But we cannot use this approach
to predict, well, how how likely it
is we're going to die from our own
nuclear wars or A.I.
eating us or a manmade
pandemic. I did an interview with Toby
Art, who wrote a book called The
Precipice, where he discusses these
likelihoods as well.
Interesting story.
So was this crane accident
here consequence of an unknown
unknown?
I don't think so, because they
knew how important it is that
the hook doesn't break.
Right. So they put a safety factor of
three, they told me, into the hook
design.
But if the process in manufacturing
fails, well, what do you
do? Right.
You can't your model won't predict.
So. All right, models, they're not
perfect. But what else?
There is a nice example that maybe,
you know, gives a bit of a counterpoint
to detailed modeling.
There is something called a fast and
frugal tree, which is a very simple
decision tree, basically, to
decide whether a patient who
shows up in the emergency room should
be moved to the intensive care unit or to
a regular care unit.
And as you can see,
there is only basically
very few.
Three.
Yes, no answers.
We don't have to discuss what this mean
in detail.
This thing performs better
than a machine learning model
that takes dozens of factors into
account. So the doctors would say
something like how much stock market,
which is German for?
Well, we've always known that we don't
need the stupid machine learning stuff.
Right. But the point is, more
data, more detailed modeling
doesn't always mean better outcome.
Right? Sometimes common sense and
just experience of humans is
something that is relevant, especially
also when interpreting models.
And of course, models change over time.
Right. That's science.
As we get new insights, we update
how our models work from Newton
to Einstein to a
grand unified theory, maybe at
some point. So models
are everywhere that the use of models
allows us to forecast developments and
quantity quantified uncertainties as cool
models make. Influencing variables and
their effects, explicit write, the
explanatory models can even help
understand something.
Models are the basis for constructive
discussion. This is really important.
When you have a model, you can
constructively disagree whether
some additional parameter should be taken
into account or whatever.
You cannot do that if you just run around
and claim shit.
Right, as some people do in this
pandemic.
But of course, boundary conditions and
limits of modeling must be considered.
And in the end, you know, in case of
doubt, creep in, crÃªpe out is always
true here as well.
All right. This brings me to the end of
the talk.
Interestingly, I took two minutes
longer than in my in my trial.
Sorry for running a little bit over time,
but I'm done now.
There is a book that you might want to
check out. And of course, there are the
podcast episodes listed here
that are most relevant to the
stuff we talked about, obviously,
300.
30 more, but these are the ones
that have direct influence on this talk.
Second was the weather
path dependance isn't just a lack
of proper accounting of state,
or if the person asking missed
something, they're sure.
I mean, it's similar to this
problem with chaos, right?
If you could if you could track
everything to arbitrary
detail and could keep track of
everything, then
maybe path dependance
would not be a thing.
But we know that's not possible in
practice.
I think that's it
from my standpoint right now, there
aren't any more questions I am aware of.
So.
Chad has sent you more.
There was something more in the I.R.S.,
doesn't look like it.
I think we can into.