## söndag 29 maj 2011

### Mathematical Secret of Flight 1

Computed Lift and Drag of a 3d NACA0012 wing for different angles of attack by Unicorn (blue) compared with different experiments.

My talk on June 15 at Svenska Mekanikdagar 2011, is now available for preview as
describing joint work with Johan Hoffman and Johan Jansson.

Based on accurate solution of the incompressible Navier-Stokes equations we identify the true mechanism for the generation of large lift L at small drag D of a wing with lift to drag quotient L/D of size 10 - 50, which is not described in the literature.

We combine the Navier-Stokes equations with a slip boundary condition on the wing motivated by the experimental fact that the skin friction is small for a slightly viscous fluid such as air or water, and we exhibit the role the slip condition in two crucial aspects:
• prevention of separation at the crest of the wing generating large lift
• 3d slip-separation at the trailing edge not destroying large lift and causing small drag.
Text books claim following Prandtl, named the father of modern fluid mechanics, that both lift and drag result from a boundary layer arising from a no-slip condition.

We obtain lift and drag in full accordance with experiments by solving the Navier-Stokes equations with a slip condition, which does not generate any boundary layer, and we thus present strong evidence that lift and drag do not originate from any boundary layer.

In short, we show that solutions to the Navier-Stokes equations with slip are computable and
Compare with state-of-the-art as expressed by Moin and Kim in Tackling Turbulence with Supercomputers:

• To solve the Navier-Stokes equations for, say, the flow over an airplane requires a finely spaced computational grid to resolve the smallest eddies.
• Consider a transport airplane with a 50-meter-long fuselage and wings with a chord length (the distance from the leading to the trailing edge) of about five meters. If the craft is cruising at 250 meters per second at an altitude of 10,000 meters, about 10 quadrillion (10^16) grid points are required to simulate the turbulence near the surface with reasonable detail.
Kim and Moin express the necessity dictated by Prandtl to resolve thin boundary layers to correctly compute lift and drag of a wing or an entire airplane, which would require 50 years of Moore's law to increase the computing power with a factor 10^10 to reach the dictated 10^16 points.

We show that this is possible already today using 10^6 points by using slip without boundary layers to resolve.

### Monstrosity of Quantum Mechanics 6: Collapse of Wave Function

Is quantum mechanics a physics beauty contest with all possibilities collapsing into one actuality upon observation? Who would you choose?

Since the multi-dimensional wave function of quantum mechanics is supposed to represent a probability distribution over all possibilities, the high dimensionality has to be drastically reduced to become an actuality of some interest.

This is supposed to happen in an interaction with an observer, referred to as collapse of the wave function, where the observer somehow picks one of all the potentialities and makes it into an actuality, as when Miss America somehow is chosen among many candidates by some educated physics observers.

Is then quantum mechanics a beauty contest? Well, ask your favorite physicist about the nature of the collapse of the wave function. Is it real? What is collapsing? Physical reality or our knowledge about reality.

Or is it quantum mechanics itself which collapses upon critical observation?

## lördag 28 maj 2011

### Monstrosity of Quantum Mechanics 5: Passive Observation Impossible

Is passive observation really impossible in the world of quantum mechanics?

David Albert, together with Barry Loewer inventor of a version of the Many-Worlds Interpretation referred to as Many-Minds (different from the one I suggest), tells us that the physical process of making an observation in the quantum world necessarily interferes with what is being observed. In other words, the ideal of fully passive observation of classical mechanics, cannot be upheld in quantum mechanics. The observer will always interfere more or less with what is being observed. Albert tells us that this is the big difference between classical and quantum mechanics.

But is this true? Is fully passive observation impossible in quantum mechanics? Maybe, or maybe not, depending on what is meant by an observation. A human being can make observations in different forms:
1. Inspection of an analog physical apparatus capabable of measuring some phenomenon.
2. Inspection of digital simulation of the phenomen.
Here 2. represents a digital simulation based on solving the Schrödinger equation describing the phenomenon, e g the ground state of an atom, and observing its energy, while 1. would be to directly observe the emission spectrum.

Th nice thing about 2. is that it is a completely passive observation, in the sense that the computational process is independent of the observer making the final observation of the energy as a number coming out of the computation.

So maybe passive observation is possible in quantum mechanics. Maybe quantum mechanics is not so different from classical mechanics. Not so mysterious?

## fredag 27 maj 2011

### Monstrosity of Quantum Mechanics 4: Quantum Computers

The belief of the modern physicist that the linear multi-dimensional Schrödinger equation
describes the quantum world of atoms and molecules, has led to the idea of the quantum computer:
• device for computation that makes direct use of quantum mechanical phenomena, such as superpositionand entanglement, to perform operations on data.
• Experiments have been carried out in which quantum computational operations were executed on a very small number of qubits (quantum bits).
• Government and military funding agencies support quantum computing research to develop quantum computers for both civilian and national security purposes, such as cryptanalysis.
I have noticed in previous posts that the linear multi-dimensional Schrödinger equation is a monster, which cannot be solved, not even on any thinkable supercomputer with any thinkable known microprocessor technique. The dimensionality is simply overwhelming.

We have noticed that the impossibility of solving the multi-dimensional Schrödinger equation
results from the fact the equation describes all possibilities rather than specific actualities, which is overwhelming for microprocessors limited to performing computations on specific data.

The Schrödinger equation is thus a monster computationally, and to handle such a beast a monster computer is needed, a computer which computes all possibilities rather than specific actualities, which computes on all data rather than on specific data: In other words a quantum computer is needed.

Are there any quantum computers? No, only with a few quantum bits.

Is it possible to construct a quantum computer? Nobody knows. Few seem to believe one can.

Does the multi-dimensional Schrödinger equation give a realistic description of the atomic world? Nobody knows because solutions cannot be computed and compared to experimental observation.

Can you solve a monster equation on a monster computer, that is a device which simulates a real analog monster by being a real digital monster?

What if the multi-dimensional Schrödinger equation is just an invented fictional monster, which will disappear as soon you stop talking about it?

Compare with the post today on The Reference Frame singing praise to the Copenhagen Interpretation of the multidimensional Schrödinger equation, as if it has a meaning. Read yourself and ask if you understand anything.

## tisdag 24 maj 2011

### Monstrosity of Quantum Mechanics 3: Many-Worlds

The monstrosity of quantum mechanics is expressed in full bloom in Everett's Many-Worlds interpretation reflecting that solutions of the linear multi-dimensional Schrödinger equation can freely be superimposed.

The Schrödinger cat in its closed box thus can be in a state of superposition of both alive and dead and only upon opening the box for observation does the cat have to collapse into either alive or dead, as if there were two possible parallel universa prior to collapse into one actual universe.

The solution of the linear multi-dimensional Schrödinger equation thus is interpreted as a universal wave-function supposedly representing all possible universa, out of which a specific actual universe is singled out in one way or the other.

How to react to this breath-taking ocean of possibilities? In this case there seems to be two possibilities:
1. Accept the linear multi-dimensional Schrödinger equation as given by God.
2. Replace the linear multi-dimensional Schrödinger as a basic model of quantum mechanics with something more reasonable.
I would vote for 2. and I explore one possibility in Many-Minds Quantum Mechanics.

After all, it was Schrödinger and not God who wrote down the equation. It was Schrödinger who understood that his equation had serious flaws and should be replaced by a version describing actualities instead of possibilities.

What do you say? 1 or 2? One actuality or all possibilities? Would you prefer all possible lives
before one actual life.

Compare with the title of the biography: A Life of Erwin Schrödinger.

Nobody would be able to write a biography with the title All Possible Lives of Erwin Schrödinger, and even if somebody could, nobody would be interested in reading it.

## måndag 23 maj 2011

### Monstrosity of Quantum Mechanics 2

The simplicity (linearity) of the Schrödinger equation is seductive and has misled many minds.

Quantum mechanics as a description of the microscopic world of atoms and molecules is based on Schrödinger's wave equation, which as a mathematical object is (see above)
• scalar
• linear
• multidimensional in 3N coordinates for N electrons/kernels
with solutions called wave-functions commonly denoted as Psi:
• Psi (x1, x2, ..., xN, t)
with xj representing the three position coordinates of particle j with j=1,...,N, and t denoting time. The wave function Psi thus depends on 3N independent real variables plus time.

The simplicity of the Schrödinger wave equation (scalar and linear) as a description of a complex reality, is thus balanced by an extreme richness of the wave function depending on
3N + 1 independent variables.

The richness of the wave-function thus makes it impossible to give it a physical meaning as
representing a configuration or distribution of electrons and kernels, which threatened to kill quantum mechanics at birth but was rescued by Max Born declaring that
• | Psi (x1,....,xN,t) |^2
represents the probability of the configuration given by the coordinates (x1,...,xN,t), and by Niels Bohr declaring that the wave function as a probability distribution, upon observation could collapse into a definite physical state, as when opening the box containing the Schrödinger cat.

Born and Bohr thus developed the Copenhagen Interpretation (of quantum mechanics), which is today the officially accepted truth although contested by alternatives as hidden variables and many-worlds interpretations, without any winner.

Schrödinger himself left quantum mechanics as soon as the Copenhagen Interpretation captured the minds of most physicists.

The richness of the wave function is in fact a monstrosity already for small systems with N = 100 say, not to speak of real systems of 10^23 particles in a mole of gas, as pointed out by Walter Kohn, Nobel Prize in Physics in 1998:
• The wave function does not exist for N larger than 100.
• Why? Because it cannot be computed, because of the many dimensions.
Kohn got the Nobel Prize for computing electron densities instead of probabilities as solutions of a non-linear version of the Schrödinger equation in 3 space dimension, referred to as density functional theory.

If now the wave-function as solution to the Schrödinger equation does not exist, there must something fishy about the Schrödinger equation. What? We saw that the equation is scalar and linear and thus has a simple structure, which is not problematic in itself, but if it necessitates a monstrous richness in dimensions, it seems that one should question the very formulation of the Schrödinger equation as a scalar linear multidimensional equation.

From where did Schrödinger get his equation? Did he derive it from basic principles? Not really. It is more of an ad hoc invention expressing particle interaction by
electrostatic Coulomb potentials combined with a new mysterious form of kinetic energy.

How can we know that the equation is a good model of physics if it cannot be solved? How can we check that its solutions give correct predictions if they cannot be computed and thus determined?

Nevertheless it is mantra of modern physics that the Schrödinger equation is a good model, but it is a mantra without physical meaning about an equations which cannot be solved. It is like claiming that a certain truth is hidden in a riddle which cannot be solved.

Thus, new versions of the Schrödinger equation are needed. I explore one such line of thought in Many-Minds Quantum Mechanics in the spirit of the Hartree method as a non-linear coupled system of one-electron/kernel Schrödinger equations.

The simplicity of linearity (and superposition) of the multi-dimensional Schrödinger equation is here replaced by a non-linear complexity, but the system solutions only depend on three space dimensions which makes a direct physical interpretation possible, without probabilities and wave function collapse. This is a realist approach as compared to the non-realist Copenhagen Interpretation.

Compare with Lars-Göran Johansson: Interpreting Quantum Mechanics: A Realsist's View in Schrödinger's Vein suggesting a form of realist wave-particle duality as continuous waves for propagation and discontinuous particles for exchange of energy.

## söndag 22 maj 2011

### Charles Mackay: Madness of Crowds and CO2 Alarmism

published in 1841, Charles Mackay debunks witch-hunts, alchemy and economic bubbles.

Today Mackay would have been writing about the crowd madness of CO2 alarmism, with the witches being the polluters of CO2, the alchemists the CO2 alarmists and the bubble the green economy.

Mackay said many clever things obviously anticipating CO2 climate alarmism, while giving hope to skeptics of CO2 alarmism:
• An arrow may fly through the air and leave no trace; but an ill thought leaves a trail like a serpent.
• Men, it has been well said, think in herds; it will be seen that they go mad in herds, while they only recover their senses slowly, and one by one.
• Money, again, has often been a cause of the delusion of the multitudes. Sober nations have all at once become desperate gamblers, and risked almost their existence upon the turn of a piece of paper.
• Aid the dawning, tongue and pen: Aid it, hopes of honest men!
• He who has mingled in the fray of duty that the brave endure, must have made foes. If you have none, small is the work that you have done.
• Truth... and if mine eyes Can bear its blaze, and trace its symmetries, Measure its distance, and its advent wait, I am no prophet - I but calculate.

## fredag 20 maj 2011

### Monstrosity of Quantum Mechanics

Schrödinger trying to slay the many-headed monster of the wave function (assisted by Einstein) however without success.

Basically, classical physics is Newtonian mechanics and modern physics is quantum mechanics.

Quantum mechanics is supposed to be described by Schrödinger's equation, worshipped by modern physicists. The equation was formulated by Erwin Schrödinger in 1925 seeking an equation with wave-like solutions called wave functions describing the dynamics of atoms and molecules resulting from an interplay of positive kernels and negative electrons under attractive and repulsive electric Coulomb forces. Nothing strange in principle, but what Schrödinger had created showed to be nothing but a Monster.

Monster? Why? Well, the wave function for the simplest case of the Hydrogen atom with one electron depends on 3 space coordinates and and time, but the wave function for an atom with N electrons depends on 3N space coordinates (and time), which makes it into a Many-Headed Monster beyond direct physical interpretation:
• Instead of describing an actuality in 3 space dimensions, the wave function describes all possibilities
• Instead of describing a specific actual sequence of 1000 coin flips, the wave function describes the 2^1000, much more than 10^100 = googol, possible sequences of coin flips.
• Instead of describing the life of one specific actual human being, it describes the lives of all possible human beings.
As soon as Schrödinger understood that he had created a scientific monster, he tried to kill it but failed and then he withdrew from physics, while the Monster captured the minds of all the modern physicists (except Einstein's) who quickly formed a whole army under the leadership of Niels Bohr and his Copenhagen Interpretation of the wave function as a probability distribution of all possibilites.

To get from possibility to actuality, the idea of collapse of the wave-function was invented,
a Monstrous Idea to handle a Monster. Before collapse the Schrödinger Cat in the box would be in a state of superposition of alive and dead with all possibilities still present, and only upon opening of the box and inspection, would the Cat collapse into an actuality as alive or dead.

This Monstrous Idea has led modern physics into an endless desert of Multiverses and Many-Worlds of all possibilities. A recent contribution to this monstrosity is the
Raphael Bousso and Leonard Susskind:
• We argue that the many-worlds of quantum mechanics and the many worlds of the multiverse are the same thing, and that the multiverse is necessary to give exact operational meaning to probabilistic predictions from quantum mechanics. Decoherence - the modern version of wave-function collapse - is subjective in that it depends on the choice of a set of unmonitored degrees of freedom, the "environment".
Read and try to understand where physics is today...

For a new approach without monsters, see Many-Minds Quantum Mechanics based on a different non-linear version of the Schrödinger equation as a coupled system of one-particle three-dimensional equations.

The thesis of Hugh Everett III behind the many-worlds interpretation exhibits the difficulties or rather monstrosities of the usual scalar linear multidimensional version of Schrödinger's equation. We will return to Everett's thesis in search of a connection between many-minds and many-worlds physics. Since we all have different conceptions of the world, maybe we in fact live in a many-worlds universe, one for each mind. Of course, the following questions then comes up: What is a mind and how many are there?

Another monstrosity perturbing the minds of many modern physicists is the Greenhouse Gas Effect, but there are some physicists fighting this monster, as e g William Happer: The Truth about Greenhouse Gases referring to Charles Mackay's Extraordinary Popular Delusions and the Madness of Crowds first published in 1841.

The development of modern physics into monstrosity is described in Dr Faustus of Modern Physics.

### Free Will and Finite Precision Computation 5

The question if animals have some sort free will is addressed by BBC in Free Will Similar in Animals, Humans - But Not so Free based on the
• The free will that humans enjoy is similar to that exercised by animals as simple as flies.
• Animals always have a range of options available to them...perceived as conscious decisions.
• The idea tackles one of history's great philosophical debates.
• What has been long established is that "deterministic behaviour" - the idea that an animal poked in just such a way will react with the same response every time - is not a complete description of behaviour.
• Even the simple animals are not the predictable automatons that they are often portrayed to be.
• However, the absence of determinism does not suggest completely random behaviour either.
• Experiments has shown that although animal behaviour can be unpredictable, responses do seem to come from a fixed list of options.
• Free will is not that lofty metaphysical thing that it was until the 1970s or so.
• It is a biological property, a trait; the brain possesses the freedom to generate behaviours and options on its own.
• The exact mechanism by which brains - from those of flies up to humans - do that generation remains a matter for experiments to more fully prove.
• There is no way the conscious mind, the refuge of the soul, could influence the brain without leaving tell-tale signs; physics does not permit such ghostly interactions.
• Brembs and others have used mathematical models to simulate brain activity on a computer, finding that what worked best was a combination of deterministic behaviour and what is known as stochastic behaviour - which may look random but actually, in time, follows a defined set of probabilities.
• Tethered fruit flies proved their choices to be neither deterministic nor random.
• The strong, Cartesian version of free will—the belief that if you were placed in exactly the same circumstances again, you could have acted otherwise—is difficult to reconcile with natural laws.
• There is no way the conscious mind, the refuge of the soul, could influence the brain without leaving tell-tale signs. Physics does not permit such ghostly interactions.
In short, free will seems to be expressed through a combination of goal-oriented determinism (as concerns big things) and indeterminism (as concerns little things), with a clear connection to finite precision computation.

It seems that the discussion has passed from sterile metaphysics into a more constructive analysis of finite precision computing minds...

## torsdag 19 maj 2011

### Free Will and Finite Precision Computation 4

Daniel Dennet advocates a compatibilism of determinism and free will, expressed as a capacity of human beings developed by evolution to avoid (unpleasant) things by voluntary action:

Seeing a brick being thrown at us by some unfriendly agent, we typically choose to duck. Dennet argues that we do that by free will, since it would also be possible to choose to not duck and take the hit to get a case to bring to court.

Dennet argues that either the future is fully determined by the past (Laplace demon) or the future is fully undetermined in the quantum sense that the next position of an electron is not determined but subject to throwing a dice.

In either case we cannot really influence what is going to happen, and thus we cannot exercise any free will: whatever happens, happens. Yet Dennet claims that we have a free will in the sense that we can decide to avoid certain things, but not all: We will not have time to duck if the brick is replaced by a bullet.

I get the impression that Dennet's resolution of the apparent contradiction between a free will and full determinism/indeterminism, is a scholastic resolution in the sense that something essential is being missed and nothing really new is brought in to solve the eternal free will problem.

Would finite precision computation be helpful? The idea here is that little things may be left to be decided by the dice while major things are predetermind by a finite precision Laplacian demon. More precisely, we know that
• there are major things that we cannot do even if we would like to (limited free will): e g fly like a bird.
• there are major things we can do which we have decided to do (according to a predetermined master plan): e g go to college.
• there are little things which we can decide by free will, which we could leave to the dice if we cannot decide: e g meat or fish for dinner.
This opens to a finite precision resolution of the free will problem:
• big things determined by a finite precision Laplace demon/master plan of ours
• little things decided by a dice.
In extreme cases a small thing could become big and would then be described as a strike of luck or accident: to win on the lottery or get hit by a falling brick.

### A Dark Side of CO2 Alarmism and The Royal Swedish Academy

The Royal Swedish Academy of Sciences hiding behind a statue of Anders Retzius, father of racial biology with his cephalic index.

The CO2 climate alarmism behind the 3rd Nobel Laurate Symposium on Global Sustainability, organized by the Royal Swedish Academy of Sciences, goes back to the Swedish physicist/chemist Svante Arrhenius, who
The Stockholm-Memorandum signed by an invited group of Nobel Laurates states that
• Humans are now propelling the planet into a new geological epoch, the Anthropocene
and makes the following Call:
• Fundamental transformation in all spheres and at all scales to stop and reverse global environmental change.
• reduce birth rates.
What is "reproductive health services"? How to "reduce birth rates"? Is there a connection to Arrhenius, or is it just a fantasy? Why was the Symposium held behind closed doors?

I have already expressed my protest against the uncritical support of CO2 alarmism by the Royal Academy in a symbolic resignation.

### Basic Science: Climate Sensitivity Less Than 0.3 C

For the convenience of the reader I here collect the links to a couple of basic arguments showing that the effect of doubled atmospheric CO2 at most could be a global warming of harmless 0.3 C, that is that the climate sensitivity is smaller than 0.3 C.

The idea is to combine observation with simple mathematical models, where observation is used to determine the coefficients of the model, thus allowing prediction. Stefan-Boltzmann's radiation law for an ideal blackbody is not used, since it does not describe the complex Earth-atmosphere system.

I thus only use simple models with coefficients determined by observation, which is the basic scientific method leading to the basic mathematical models of physics, such as the heat equation, potential flow equation and radiative transfer equation.

I assume that doubled CO2 could correspond to a change of the radiative properties of the atmosphere of 1%, or a "radiative forcing" of 3 W/m2 = 1% of a total insolation of about 300 W/m2.

I assume that the "atmospheric effect" is 33 C corresponding to raising the temperature of an Earth without atmosphere (= observed mean temperature of the Moon) of - 18 C to the observed temperature of the Earth with atmosphere of 15 C.
These are three different arguments using different data and different simple models, all giving the same result of a climate sensitivity smaller than 0.3 C, where 0.3 C is to be viewed as an upper bound, with the real value probably a factor 2 - 3 smaller.

IPCC claims a "best estimate" which is 10 times bigger = 3 C, which is obtained by confusing definition with physical fact and free invention of positive feed-backs.

IPCC has invented a factor 10 for which there is no scientific basis. In economics a factor 10 would be swindle and it is the same in science, or even worse.

## onsdag 18 maj 2011

### What is a Princess Allowed to Say? About CO2 and Great Transformation?

Crown Princess Victoria of the Kingdom of Sweden stated in her presentation at the 3rd Nobel Laureate Symposium on Global Sustainability organized by the Royal Swedish Academy of Sciences:
• Burdens must be shared by everyone (including masses of poor people).
• Wind turbines, solar connectors, panels and geothermal energy, why is it that countries are using soo little of renewable energy sources despite having the knowledge and technique?
• We can and must change our life styles and the manner in which we use energy.
• What are we waiting for? The work has to start here and now.
• The world succeeded to come together and decide upon removal of freons.
• To succeed we need to reconnect humanity with the biosphere.
• This is no small task. I see no better persons though than Nobel Laurates to carry this critical message to the world:
• The need for a Great Transformation.
• Our generation has the knowledge and ability to create a sustainable world for future generations.
The presentation poses the following questions
• Does the Princess make political statements?
• Is the Princess allowed to make political statements?
• Is the Princess allowed to advocate specific techniques for generating energy?
• Is the Royal Swedish Academy influenced by Royals?

The Princess speaks the same words as Hans Joachim Schellnhuber, main organizer and ideolog of the symposium, according to New York Times known for his "aggressive stance on climate policy":
1. Earth’s population could be devastated by buildup of greenhouse gases.
2. In a very cynical way, it’s a triumph for science because at last we have stabilized something –- namely the estimates for the carrying capacity of the planet, namely below 1 billion people.
Does the Princess understand what she is saying?

PS1 The verdict of the Jury of Nobel Laurates of the Symposium is expressed in the Stockholm-Memorandum:
• Humans are now the most significant driver of global change, propelling the planet into a new geological epoch, the Anthropocene.
• Our call is for fundamental transformation and innovation in all spheres and at all scales in order to stop and reverse global environmental change.
• Introduce strict resource efficiency standards
• Launch a major research initiative on the earth system.
• Scale up our education efforts to increase scientific literacy.
This is nothing but A New Brave World......but is there place for a Princess in this New Brave World? A resource efficient renewable Princess?

## tisdag 17 maj 2011

### Free Will and Finite Precision Computation 3

This is a continuation of Free Will 2:

So can we make it rain tomorrow by leaving the car window open? Can the flap of a butterfly in Brazil set up a tornado in Texas?

How can we tell? Well we have already answered this question: Take away the butterfly and observe tornados anyway, close the window and observe rain anyway. Or let the butterfly flap and observe no tornados, open the window and observe no rain.

Evidently we are talking about a big effect (tornado, rain) from a small cause (butterfly, car window), which is only possible if the system under consideration is unstable. Why? Because the definition of an unstable system is that a small cause can have a big effect.

If the effect of any small causes is small, then the system is stable. Most of the systems we can observe are (more or less) stable, because unstable systems tend to break down or explode into non-existence.

Is the weather unstable? Well, we say that the weather is unstable when changes are unpredictable, and we know that this is often the case. How unstable can then the weather be?
Can it be so unstable that the flap of butterfly can cause a tornado? Probably not.

We expect that sufficiently small perturbations cannot change the major features of the weather and cause a tornado. This means that it is irrelevant whether a butterfly flaps or not, or if we leave the car windows open or not, as concerns tornados and rain.

If we accept that small causes do not change major features, that is, that we are dealing with a (more or less) stable system as a typical system which we may be confronted with, then we could say that we could leave certain little things to be determined by chance, by throwing a dice:
• It would not change anything essential.
• It would save us time for essentials by avoiding getting drowned into pedantry.
• In fact, it would be necessary to not get bogged down by details.
• In other words, we would have to act with finite precision in order to not get stuck on the spot at a specific point in time.
• Time is advancing and so we have to advance as well and thus we have to take decisions with finite precision only, because we have no time to do everything with infinite precision.
We are now approaching the question of free will. Can we do anything we could of think of doing? No, our abilities are limited, but within these limits we would say that we have some form of free will.

We could decide what to study at the university, with whom to engage, how to dress, what to eat, what to say, but all these decisions could fit into some form of master plan for our life, which we probably should search for if we don't have any. Our free will would not be entirely free but subordinate to a master plan, which we may have chosen by free will or inherited from our parents, spouse or friends or society. So maybe our free will as concerns big things is not that free, as if the main pattern of our life largely is predetermined.

We could still argue that we have a free will to decide little things, what movie to see, what to have for dinner et cet, but we could also say that we will only spend limited time on these issues to find the "optimal solution". We could even use a dice to decide if we cannot easily make up our mind or come to some agreement with somebody.

But you would not like Luke Rhinehart decide big things, such as getting divorced or not, by throwing the dice, because that would quickly ruin your life.

In short, you would act with finite precision and feel that you have some form of free will in particular for little things, possibly exercised using dice, while you may feel that the main path of your life (or at least other people's lives) is more or less predetermined.

This corresponds to something between full determinism (no dice) and full indeterminism (all dice) as a for of finite precision determinism (dice only for little things). In other words, a free will which is not completely free, but not completely unfree either:
• a finite precision free will.
PS Suppose Tom wants to show Harry that he has a free will. Consider the following conversation:

Tom: Look, I can decide to lift my left arm or my right arm according to my own free will.

Harry: How you decide to lift the left or the right? Do have some predetermined preference?

Tom: Of course not, then it would not be free will.

Harry: OK, but if you are completely neutral, how are going to decide?

Tom: Let me think...should I lift the right arm...or should I lift the left...what could be a good reason to lift the right arm...instead of the left...well, I cannot really decide...I need more time...
but even so I don't how to choose while staying fully neutral...

Harry: Can I offer some help? What about flipping a coin?

Tom: Flipping a coin? Yes, that must be the only possibility which is completely neutral, without any perdetermined predjudice for right and left. That's what I will do to not get held up by this silly test...

### What Does a Nobel Laurate Understand about CO2? 1

Murray Gell-Mann, Nobel Prize in Physics in 1969 for the Standard Model of elementary particles, is one of the Nobel Laurates to decide about the future of humanity at the Nobel Laurate Symposium on Global Sustainability at The Royal Swedish Academy of Sciences, May 16-19,

• Evidence that the Earth is warming by human emissions of greenhouse gases is unequivocal
• fossil fuel raising CO2 above the limits of the Holocene
• exit door from the Holocene had been opened
• Great Acceleration: human population tripled, consumption in the global economy grew many times faster
• Great Acceleration has not been an environmentally benign phenomenon
• eroding the Earth’s resilience, ocean acidification.
The agenda for the meeting is presented by The German Advisory Council on Global Change, chaired by Prof. Dr. Hans Joachim Schellnhuber, as a Summary for Policy Makers: World in Transition, A Social Contract for Sustainability:
• carbon-based model unsustainable
• low-carbon society is a Great Transformation
• global energy system decarbonised
• greenhouse gas emissions absolute minimum
• low-carbon societies
• quantum leap for civilisation
• universal consensus
• Global Enlightenment
• new social contract
• science subservient role
• sustainability is a question of imagination.
The purpose of the meeting is to get Nobel Laurates of Physics and Chemistry to confirm on scientific grounds that CO2 emission is the big threat to human civilization.

The Nobel Laurates will form the jury of a Tribunal facing Humanity with charges of destroying the Earth (by CO2 emission).

• Do Nobel Laurates understand the role of CO2 for global climate?
• Do Nobel Laurates say that society will have to be decarbonized by 2050?
and will report on answers..stay tuned...

PS Johan Rockström (organizer) and Andreas Carlgren (minister) write in DN Debate to prepare the Swedish opinion:
• To avoid catastrophical climate change, many scientists believe that CO2 emisssion from fossil fuels must stop by 2050.
• This requires resources to renewable energy of unprecedented size.
Note the term many scientists, not as before all scientists... This seems to be an acknowledgement that there are also many scientists who consider CO2 emission to not be harmful at all.

What if the jury was changed to the latter group of scientists? What would then the charges be? Who would then sit on the accused bench?

## måndag 16 maj 2011

### Free Will and Finite Precision Computation 2

Continuation of Free Will 1:

David Foster Wallace studies the logical argument of the fatalism of Richard Taylor going back to Aristotle stating that we cannot do anything other than what we actually do, in other words that the future is predetermined and free will is only an illusion.

The logic is that a statement of the form "Tomorrow it will rain" is either true or false: If it is true then it will have to rain, and if it is not true then it cannot rain, in both cases showing that what will happen tomorrow is predetermined.

Of course, this is a simple logical trick based on the idea that a statement must be either true or not true. But nothing says that this must apply to the statement "Tomorrow it will rain". It is a statement without definite truth value when (today) it is uttered; only in retrospect knowing the outcome is it possible to assign it a truth value and then the predetermination disappears.

But there are other arguments showing that the future is determined by the present. The best one is that of Laplace's demon:
• We may regard the present state of the universe as the effect of its past and the cause of its future.
• 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 would be uncertain and the future just like the past would be present before its eyes.
Laplace's demon would thus be able to tell today if it is going to rain tomorrow by simply computing the solution to the equations of motion describing the evolution of particles (atoms, molecules) making up the climate system, and would thus be able to make a necessarily true prediction of a coming event, thus showing that it is predetermined.

But is there a Laplace demon? Human computing power is capable of solving the equations of motion for particle systems of millions or billions of particles (10^6 - 10^9), but not the octillions (10^30) of real systems.

We are all too familiar with the fact that human intellect cannot tell for sure if it is going to rain tomorrow. But is the weather still predetermined?

Is there anything we can do by free will to make it rain or not? Can we make it rain tomorrow by leaving our car windows open? The investigation continues...

I have published the following new books of mine on Google Books as fullview with free PDF download:
The idea is to compare direct publishing on Google Books with self-publishing on e.g. Amazon CreateSpace, or to conventional publishing through an established publisher as ebook or printed book.

It appears that Amazon CreateSpace requires conversion of pdf to a different ebook format, which is not automatic and tricky if math formulas are involved. Maybe somebody has some good advice to give.

## söndag 15 maj 2011

### Free Will and Finite Precision Computation 1

In recent books I have shown that the concept of finite precision computation, in reality in analog form and in simulation of reality in digital form, can be used to give rational deterministic (mathematical) explanations of the following phenomena:
• direction of time
• 2nd law of thermodynamics
which have evaded explanations using both classical deterministic exact mathematics and classical statistical physics. Finite precision computation opens classical exact determinism to some imprecision or indeterminism, without going all the way to the full indeterminism of statistical physics, and thus avoids the impossibility of both extreme determinsim and extreme indeterminsim.

In finite precision computation, little things may be decided by throwing a dice, corresponding to chopping a decimal expansion into a finite number of digits, while big things still may be fully deterministic.

The concept can be described as one of the following options for using dice throw to decide what to do:
• Full Determinism: Calculate everything exactly. Never throw a dice.
• Full Indeterminsim: Calculate nothing. Always throw a dice.
• Finite Precision: Calculate the big. Throw a dice to decide the small.
Full Indeterminism is represented by the cult novel The Dice Man by George Cockcroft about the psychiatrist Luke Rhinehart, who decides to let the dice decide everything with catastrophical results from using it to decide big things like getting divorced or not.

Full Determinsim is represented by the fatalism of Richard Taylor exhibited by the cult author David Foster Wallace, who took his own life on Sept 12 2008, maybe after asking the dice to decide to pull the trigger or not.

Wallace wrote a college thesis on Taylor's fatalism with title Fate, Time, and Language: An Essay of Free Will, republished in 2010 by Columbia State University.

Can Finite Precision Computation be used to shed some light on the eternal philosophical problem Free Will? I will address this question in a sequence of posts, while reading a bit of Wallace. I will start with the following question:
• Is it helpful to let a dice decide little things?

## onsdag 11 maj 2011

### Har Professorn Avskaffat Sig Själv?

I den nya Högskolelagen är det prefekten som "leder verksamheten", dvs bestämmer vad som skall göras och sägas, medan professorn/läraren "har hand om" utbildning och forskning, dvs gör jobbet, på order av ledningen. Jag tar upp detta i ett inlägg på Newsmill:
med utgångspunkt från mina erfarenheter av censur och munkavle på KTH, redovisat under KTH-gate.

Naturligtvis refuserades artikeln av Svd och DN var ju inte att tänka på. Munkavle på!

Ytterst handlar det om akademisk tankefrihet, om vem som skall bestämma vad som är aktuell vetenskaplig sanning, professorn/vetenskapsmannen eller administratören/politikern?

Mina professorskollegor i landet är anmärkningsvärt indifferenta till frågan, som om den inte berörde dem:
• Kan det verkligen vara så att professorn avskaffat sig själv utan att någon har märkt något och än mindre sagt något?
• Utan att professorns fackförbund SULF haft någon invändning?
• Kanske det i den nya högskolan inte behövs några professorer med uppgift att tänka självständigt?
• Har professorn utan att protestera låtit sig förses med munkavle?
Debatten på Newsmill kanske ger svar.

PS1 Vad gäller munkavle, censur och tystande av kritiska röster, så är det naturligtvis effektivt så länge det funkar till 100%, men det förutsätter att alla kanaler stängs och att övervakningen är total. Detta är dock svårt att uppnå i dagens nya informationsvärld:

Debatten i klimatfrågan har nu tagits över av den fria blogg-sfären och det politiskt korrekta tänkandet har tappat sin hegemoni på vetenskaplig sanning. Något för KTH, DN och SvD att betänka, kanske. Det finns ju också skygglappar att sätta på.

PS2 Lustigt nog arrangerar KTH ett Symposium om Akademiskt Ledarskap 13/5 till ära av Ingrid Melinder (som inte är professor), där naturligtvis de administratörer som satt munkavle med benäget bistånd av Melinder, talar: Peter Gudmundson och Folke Snickars.

Kanske läge att ta upp KTH-gate? Nog inte: det är bara administratörer som får tala om akademiskt ledarskap. Professorer får hålla tyst, i den nya högskolan (utom Mathias Uhlen med sina 800 milj/år), medan Scoutförbundet får utveckla sin ledarskapsfilosofi, för högskolan.

## måndag 9 maj 2011

### SULF om Censur och KTH-gate

Efter att ha blivit utsatt för censur med ett direkt personangrepp av KTH backat av Rektor Peter Gudmundson, vilket jag redovisat i en serie poster under KTH-gate, vände jag mig till mitt fackförbund SULF för att se om jag kunde få något stöd.

Jag presenterade mitt fall vid ett möte med förbundsjurist Carl Falck, som därefter deltog i ett möte med Rektor stöttad av sin adjutant Anders Lundgren, varvid mycket tydligt framkom att Rektor inte hyste minsta betänklighet att genom sitt agerande allvarligt skada min professionella verksamhet.

Anders Lundgren var noga med att påpeka att KTH aldrig (aldrig) kommenterar uppgifter i pressen som tillskrivs Rektor, även om de är grovt felaktiga och hårt drabbar den som utsätts för felaktiga nedvärderande uppgifter. Aldrig! KTH har principer, och KTH följer sina principer, även om det är tufft. Peter Gudmundson är gammal hockeyspelare och är van vid hårda puckar.

Carl Falck meddelar mig kort därefter, efter att ha träffat Anders Lundgren utan min närvaro:
• Vi har diskuterat frågan vid flera tillfällen inom förbundet, men har nu kommit fram till att det idag inte finns utrymme för oss att föra denna fråga vidare. Det svar jag kan ge dig, och det är vårt gemensamma svar, är att vi inte kommer att agera fortsättningsvis i detta ärende.
Förbundordförande Anna Götlind bekräftar med:
• Som SULF:s förbundsjurist Carl Falck tidigare meddelat dig kommer SULF inte att bistå dig vidare i ditt ärende.
• SULF är alltid positiva till debatt om den akademiska friheten, men som förbund kan vi inte debattera i enskilda ärenden.
Tja, vad skall man nu säga om detta? Ja inte kan man säga att SULF givit mig något vidare stöd. Ur min synvinkel har SULF snarast försvårat min situation genom att till synes helt liera sig med KTHs ledning.

Carl Falck säger att det idag inte finns utrymme medan Anna Götlind använder argumentet att SULF inte tar upp enskilda ärenden, som om det trots allt skulle finnas utrymme bara inte mitt ärende vore så himla enskilt.

Jag har snällt betalat min avgift till SULF i 40 år (minst 100.000 kr) utan att någonsin besvära med något enda litet ärende. När jag till slut vänder mig till SULF i en utsatt situation får jag kalla handen.

Det är klart att jag känner mig ganska korkad som gått på en sådan nit. Men jag är väl inte ensam i den gamla trogna skaran som trodde att facket var till för medlemmen. Bland de unga är det väl inte så populärt att betala fackföreningsavgift.

• SULF har till uppgift att tillvarata och bevaka medlemmarnas fackliga, sociala och ekonomiska intressen samt att företräda medlemmarna i sådana frågor.
Skall jag tolka detta som att mina professionella intressen i min roll som professor ligger utanför SULFs ansvarsområde? Tar inte SULF upp enskilda ärenden utan bara ärenden som gäller alla medlemmarna? Skall alla medlemmarna ha utsatts för censur för att SULF skall ta upp frågan? Vi får höra vad Anna Götlind svarar:
• Jag svarar inte. Jag har redan svarat att SULF inte bistår dig i detta ärende.
Så småningom får jag väl sammanfatta mina erfarenheter av SULF i ett debattinlägg i förbundets tidskrift Universitetsläraren, såvida inte detta också censureras bort...men Newsmill finns ju alltid....nytt inlägg kommer snart...

### Definition as Physical Fact

In science and philosophy the distinction between synthetic and analytic statements is fundamental, according to Kant's Critique of Pure Reason.

An analytic statement is about language and its truth can be evaluated by checking the meaning of the words forming the statements. A definition is analytic as a specification of the meaning of a new word in terms of previously defined words, e.g. bachelor as unmarried man.

A synthetic statement is about some reality and can in principle be checked by observing the reality.

The statement "1 meter is equal to 100 centimeters", is analytic, while the statement "this stick is 1 meter long", is synthetic.

To subject an analytic statement to experimental observation would be ridiculous: To check by experiment if there are 100 centimeters on 1 meter would not give a Nobel Prize, just laughs.

So if an experiment is set up to test a statement, that is a sign that the statement is viewed as synthetic.

In modern physics the distinction between a definition (analytic statement) and synthetic statement is sometimes blurred into statements which are viewed to be both analytic (true by definition) and synthetic about some reality, or rather sometimes analytic and sometimes synthetic, sometimes definition sometimes fact.

Such a statement makes it possible to say something about reality which cannot be denied, and it is directly recognized as such. When you hear a physicist making a statement claiming that something cannot be denied, then the statement is such a double analytic-synthetic statement.

Here are some key examples:
1. The speed of light in vacuum is constant.
2. Heavy mass is equal to inertial mass.
The constancy of the speed of light is a definition since according to the 1983 standard length
unit of a meter is defined as a certain fraction of a lightsecond = the distance traveled by light in one second. The speed of light is thus by definition equal to 1 lightsecond per second, no more no less.

On the other hand, a physicist is convinced that the speed of light is constant as a physical fact. A physicist would say that because the speed of light is constant in reality, it can be used to define the length standard. So we have a definition which is a physical fact at the same time: Double analytical-synthetic.

Einstein was a master of this form of double-play: The basic assumption of special relativity is that the speed of light is constant, and Einstein uses this statement sometimes as analytic and sometimes as synthetic. Very clever and very confusing. But according to Kant it is not reasonable.

In general relativity Einstein uses the equality of heavy and inertial mass both as definition and physical fact. In this case experimental verification of equality could give a Nobel Prize.

In climate science the following statement is the very basis of climate alarmism:
• No-feedback climate sensitivity is equal to 1 C,
with climate sensitivity the global warming from doubled atmospheric CO2.

This is presented as an undeniable fact and as such is an example of a double analytic-synthetic statement. The 1 C comes from a direct application of Stefan-Boltzmann's radiation law Q = sigma T, in its differentiated form dQ ~ 4 dT with Q ~ 240 W/m2, T ~ 288 K and dQ = 4 W/m2 as "radiative forcing" from doubled CO2. Thus dT = 1 C as climate sensitivity.

This statement is analytic because the simple algebraic law Q = sigma T cannot tell anything
about the reaction of the complex Earth-atmosphere system upon a small perturbation.

So climate sensitivity = 1 C is a definition but it is used as statement of factual global warming of 1 C. It is a double analytic-synthetic statement, and it is recognized as an undeniable fact about reality.

It is so undeniable that even skeptics like Lindzen, Monckton and Spencer, are convinced that it is a true fact and not just a definition.

We just learned that a double analytic-synthetic statement can be extremely powerful, the very basis of climate alarmism, yet it is easy to discover as soon as one is aware of the double-play.

I hope the reader is stimulated to find other examples of double analytic-synthetic statements
used in the debate today. They are not difficult to find once the light is on. For example, what about the statement:
• Educated people are superior to no so well educated people!
Definition or fact, or both?

## söndag 8 maj 2011

### The Final Solution by The Royal Swedish Academy

• Together with Stockholm Environment Institute, Stockholm Resilience Centre, Beijer Institute for Ecological Economics and Potsdam Institute for Climate Impact Research, the Royal Swedish Academy of Sciences will bring together some of the world’s most renowned thinkers and experts on global sustainability, 16-19 May 2011 in Stockholm. Only for invited guests.
The agenda for the meeting is presented by The German Advisory Council on Global Change, chaired by Prof. Dr. Hans Joachim Schellnhuber, as a Summary for Policy Makers: World in Transition, A Social Contract for Sustainability:
• Normatively, the carbon-based economic model is also an unsustainable situation.
• The transformation towards a low-carbon society is therefore as much an ethical imperative as the abolition of slavery and the condemnation of child labour.
• This structural transition is the start of a "Great Transformation" into a sustainable society, which must inevitably proceed within the planetary guard rails of sustainability.
• By the middle of the century, the global energy systems must largely be decarbonised.
• Production, consumption patterns and lifestyles in all of the three key transformation fields must be changed in such a way that global greenhouse gas emissions are reduced to an absolute minimum over the coming decades, and low-carbon societies can develop.
• The extent of the transformation ahead of us can barely be overestimated.
• In terms of profound impact, it is comparable to the two fundamental transformations in the world‘s history:
• the Neolithic Revolution, i.e. the invention and spreading of farming and animal husbandry, and the Industrial Revolution, meaning the transition from agricultural to industrialised society.
• This would be something of a quantum leap for civilisation.
• It should in principle also be possible to reach a universal consensus regarding human civilisation's ability to survive within the natural boundaries imposed by planet Earth.
• This necessarily presupposes an extensive "Global Enlightenment".
• So nothing less than a new social contract must be agreed to.
• Science will play a decisive, although subservient, role here.
• Ultimately, sustainability is a question of imagination.
In other words, a Final Solution to the Carbon Question will be presented by the Royal Swedish Academy of Sciences. The basic idea is to comb Europe through from West to East from North to South for carbon and transport it to Eastern Poland, where it will be gassed (in special camps, see picture above).

This will secure a carbon-free sustainable Europe, which will serve as a model for the rest of the world including its 3 billion people who still do not have access to essential modern energy services.

The Symposium will conclude with a memorandum signed by key Nobel Laureates, crowned by a
dinner hosted by King Carl XVI Gustaf.

Among the invited 50 of the world’s most renowned thinkers, we find:
• Martin Rees, President Royal Society,
• Mikhail Gorbachev, Nobel Peace Prize 1990
• Andreas Carlgren, Swedish Minister of Environment
• Murray Gell-Mann, Nobel Prize in Physics 1969 for his contributions and discoveries concerning the classification of elementary particles and their interactions.
• David Gross, Nobel Prize in Physics 2004 for the discovery of asymptotic freedom in the theory of the strong interaction.
• Johan Rockström, Stockholm Resilience Center
• Anders Wijkman, Stockholm Environment Institute.
Note that the key Nobel Laurates when signing the memorandum accept that science will play a subservient role.

It is natural to compare with Manifesto of the Ninety-Three and the suppression of quantum mechanics and relativity in the Soviet Union as "idealistic" and "bourgeois", and in Nazi-Germany as "Jewish physics".

## fredag 6 maj 2011

### Presentation at Stockholm Initiative: The IPCC Trick

The Hustler (1886-1905) by Ernst Josephson (student at the Royal Academy of Fine Arts in 1867)

Here is a summary of a short presentation at the annual meeting of the Stockholm Initiative
at the Royal Academy of Fine Arts, May 7.

1. IPCC Climate Sensitivity = 3 C
• The CO2 climate alarmism of IPCC is based on an estimate of climate sensitivity (global warming by doubled CO2) of 3 C obtained by positive feedback from a no-feedback sensitivity of 1 C.
• No-feedback sensitivity is obtained by definition from Stefan-Boltzmann dQ ~ 4 dT with dQ = 4 W/m2 assumed "radiative forcing" from doubled CO2.
• Note: A definition says nothing about reality. The 4 W/m2 of "radiative forcing" is a theoretical assumption rather than observed reality. Insolation constant.
2. The Question
• What is the global warming effect of a 1 % change of atmospheric radiative properties?
• 4 W/m2 is about 1 % of gross insolation of 360 W/m2
• 3 C = 1 % of gross temperature 288 K
• Reasonable?? Unreasonable??
3. Observation + Simple Models: Climate Sensitivity = 0.3 C

Combining basic mathematical models and direct observation of
• temperatures, lapse rate, insolation and thermodynamics,
one obtains a climate sensitivity which is 10 times smaller than IPCC:
• 1 % change of atmospheric radiative properties
• 0.3 C is about 1% of "atmospheric effect" of 33 C (= 288 - 255 K)
• wellposed (stable): 1% forcing gives 1% = 0.3 C
• Real radiative exchange between surface and atmosphere: 30 - 60 W/m2
• 1 % change of atmospheric properties: 0.3 - 0.6 W/m2 net radiative forcing
• IPCC backradiation exchange: 300 - 400 W/m2
• 1 % change of atmospheric properties: 4 W/m2 gross radiative forcing
• view 3 C as 1% of gross temperature 288 K, not 1% of "atmospheric effect".

In Computational Blackbody Radiation I give a new mathematical derivation of Planck's radiation law showing that backradiation is fiction. This is mathematical evidence that the 3 C of IPCC is based on fiction: 10 times too big.

5. Wellposedness: Butterfly in Brazil vs Torando in Texas

IPCC claims that a small cause (1% or 0.1% change of atmospheric properties) can have a big effect (global warming of 3 C = 10% of atmospheric effect 33 C).

6. The Lorenz Model

Can a butterfly in Brazil set off a torando in Texas?
• Can be disproved by removing butterfly and observing tornados.
• Can never be proved, because a very precise model is required (both butterfly and tornado).
Requires unstable system: small cause - big effect.

7. Is global climate unstable?

Observations say No rather than Yes. Atmosphere as air conditioner: Radiative forcing changes intensity of thermodynamics with little temperature change.

Compare with boiling water: heat forcing gives more vigorous boiling at steady temperature.

8. KTH-gate

KTH censored my mathematical analysis of climate models. Unique in (Swedish) modern academic history (after 1632). At present my professors union SULF hesitates to take up my case, as if my union and KTH were acting in tandem to silence my voice. How is this possible?

Well, in the new university system in Sweden 0f 2011, it is the administrative hierarchy of rector, dean and prefect, which determines the scientific truth and not the professor (as during 1632 - 2010).

The censorship of my work is therefore fully logical and apparently accepted even by the professors union, and also by Swedish professors. Only one has questioned the censorship, Ingemar Nordin.

## torsdag 5 maj 2011

### The IPCC Trick 6

The variation of the Earth surface temperature over day and night (shown in the above picture) with its diurnal temperature range DTR and phase lag L, can be used to determine the heat capacity C and damping A in the following simple model of the Earth-atmosphere system:
• C dT/dt + A T = F sin(t),
where T(t) is the Earth surface temperature deviation from its mean as function of suitably scaled time t, and F = is the mean radiative forcing of the Earth-atmosphere system. Fitting this model to the data DTR = 20 C, F = 240 W/m2 and L = 3 h, we obtain
• A ~ C ~ 0.7 x 240/10 ~ 16 .
An additional forcing of 4 W/m2, by IPCC attributed to doubled CO2, could thus be estimated to require an increase of the mean temperature of 4/16 = 0.25 C, to restore heat balance.

In other words, the observed diurnal temperature variation suggests a climate sensitivity of 0.25 C.

We have now seen two different arguments based on simple models and observation, indicating that climate sensitivity is smaller 0.3 C.

We compare with the climate sensitivity of IPCC of 3 C underlying CO2 climate alarmism obtained by a clever use of the IPCC Trick, which is 10 times larger.