söndagen den 28:e februari 2010

Klimatdebatt i Public Service Sveriges Radio

Climategate och den svenska klimatdebatten har nu nått SRs Godmorgon Världens satirprogram Public Service. Till slut tar alltså SR sitt public-service uppdrag på allvar och rapporterar objektivt och sakligt!

Godmorgon Världen har också ett icke-satirisk (mindre sakligt/objektivt) inslag, 
där man får höra: 
  • Debattens vågor går höga. (Karl-Johan Bondesson)
  • Frågan väcker starka känslor. Går vi mot katastrof, då stiger tonläget.
  • Det är ett skyttegravskrig där alla medel är tillåtna.
  • Bland klimatskeptikerna finns seriösa forskare.
  • I sak har inget ändrat sig, men så ser det inte ut i medierna...(Sverker Sörlin)
  • Klimatfrågan har fått sig en rejäl törn.
  • Entydiga forskningsresultat. Ingenting har förändrats (Maria Wetterstrand).
Ingenting har ändrats, påstår SR. Kanske inte på SR, men utanför...

I UK utfrågas Phil Jones av MPs i direktsändning av Channel 4 från kl 16 March 1.

När kommer KVA att utfrågas av våra MPs?

fredagen den 26:e februari 2010

Pachauri Facing Independent Inquiry

Rajendra Pachauri, the controversial Chairman of the Intergovernmental Panel on Climate Change (IPCC) is to face an international inquiry into the performance of his organisation.

Since the Royal Swedish Academy of Sciences is supporting IPCC and Pachauri, it may seem motivated to let also the Academy face an independent inquiry.

Why bother about a statement of the Academy in support of IPCC? Because Swedish climate policy is based on this statement as a statement of the highest scientific authority: If the Academy would change position and withdraw its unconditional support of IPCC, then Swedish climate politics would have to change.

But the Academy has not modified its statement/support of IPCC after the scandals hitting IPCC since Climategate in November 2009. Nor has Swedish climate politics changed after
Copenhagen. But this is unreasonable, and in science unreason does not last...

  • The Institute is concerned that, unless the disclosed e-mails are proved to be forgeries or adaptations, worrying implications arise for the integrity of scientific research in this field and for the credibility of the scientific method as practised in this context.
But the Academy does not seem to be worried...

Mona Verkar Inte Förstå Matematik

Mitt försök att nå kontakt med Socialdemokrater beträffande skolans matematikundervsining,
verkar inte ha lyckats. Det tycktes ganska nära ett tag,  när jag fick svar på mitt Öppna Brev till Mona med invitation till möte med Marie Granlund från Pelle Rödin 18/1:

  • Bäste Claes Johnson, Marie Granlund, vår utbildningspolitiska talesperson och vice ordförande i utbildninsutskottet, skulle gärna vilja ha ett kort möte eller lunch med dig. 
  • Tisdag till torsdag i någon av de kommande veckorna är lättast för oss. Om du är intresserad kan du väl skicka mig ditt telefonnummer och några förslag på tider i nästa och näst-nästa vecka? 
Sedan den 18/1 har jag dock inte hört ett ljud  om detta, trots flera påstötningar, och kontakt med Oskar Stenström som skriver 12/2
  • Pelle kommer att höra av sig. 
  • Vi är inne i ett mycket intensivt arbete i Sverige Riksdag just nu. Snart stängs fönstret för regeringen att lämna in nya förslag för behandling innan valet, därför är arbetsbelastningen extra hög nu. 
  • Jag vädjar om förståelse om att vi ibland inte kan svara direkt. Trots att vi är det största partiet med flest anställda har vi en fullständigt omöjlig uppgift att ens hinna besvara alla förfrågningar som kommer in. 
  • Självklart har vår partiordförande ambition att veta så mycket som möjligt om alla politikområden, så även om matematikens utveckling inom svensk utbildningsväsende. 
Vad skall man tro? Är Mona intresserad av Matematik-IT? Förstår Mona att Björklund är ute och cyklar? 

Eller är det bara hushållsnära tjänster som tar upp hela tankeutrymmet?

torsdagen den 25:e februari 2010

Better Resolution = Worse Results? No!

Nature reports in Earth Science: The Climate Machine about the the Met Office/Hadley Center new climate simulator HadGEM2-ES supposed to produce the scenarios underlying the upcoming IPCC AR5 Report:
  • A new generation of sophisticated Earth models is gearing up for its first major test. 
  • But added complexity may lead to greater uncertainty about the future climate.
Is it true that added complexity = better spacial and temporal resolution, increases the uncertainty of a flow simulation like a climate simulation? Can better resolution give worse results?

No, in general you would expect that better resolution gives better accuracy. However, in flow simulation it is possible that you can fool yourself into believing the opposite, because of the presence of turbulence, as explained in The Secret of Turbulence with the following essential feature:

In a simulation on coarse mesh the flow may come out as laminar, because a coarse mesh introduces substantial artificial numerical viscosity preventing transition to turbulence, while
the real flow with smaller real viscosity is turbulent. A coarse mesh laminar solution thus 
can upon mesh refinement turn into a very different turbulent solution. 

Now, a laminar solution may look nicely ordered and stable, while a turbulent solution 
may seem messy unordered and unstable, and if you are naive you could draw the conclusion that mesh refinement gives a worse result.

But this is not so: The nice-looking laminar solution carries no information of value, while 
the ugly-looking turbulent solution carries valuable information. This is shown in the book Computational Turbulent Incompressible Flow to depend on cancellation effects in turbulent flow, with the main message that computational simulation is possible without resolving the flow to its physical scale, only so that turbulence develops.

The conclusion concerning climate simulation is that the mesh has to be sufficiently fine for turbulence to develop, which requires a mesh of about 100 x 100 x 100 = 1 million mesh points,
(on a cubical domain), which is no problem on a supercomputer. For the Globe, 100 million mesh points could suffice and be possible.

In general, coarse mesh simulation producing laminar nice-looking solutions cannot be trusted.
 

tisdagen den 23:e februari 2010

KVA to Testify to the Swedish Parliament?

Senator James Inhofe (R-OK) today asked the Obama administration to investigate what he called “the greatest scientific scandal of our generation” — the actions of climate scientists revealed by the Climategate Files, and the subsequent admissions by the editors of the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4).

Senator Inhofe also called for former Vice President Al Gore to be called back to the Senate to testify.“In [Gore's] science fiction movie, every assertion has been rebutted,” Inhofe said. He believes Vice President Gore should defend himself and his movie before Congress.

Since the Royal Swedish Academy of Sciences is backing IPCC, the Academy should similarly be asked to testify to the Swedish Parliament. Who is the Swedish Mr. Inhofe to make such a proposal?



The Swedish IPCC representative Erland Källen meanwhile testifies to Swedish Public Radio SR that it will get "very much warmer". SR also expresses the logic that if there was no global warming, then SR would not have such a massive reporting on how to solve this problem...or the other way around: Since SR reports on global warming, there must be global warming...
This is the advantage of state-controled public radio...

Note that The Government Office (Regeringskansliet) reported on a hearing on April 27 2009
  • We know that a large part of the temperature increase during the latter half of the 20th century is very likely due to an increased concentration of greenhouse gases in the atmosphere by human activity.
  • In addition, projections of possible future climate change can be made.
In the light of Climategate these key statements now seem to lack scientific support.

The need of a new hearing (by the Commission on Sustainable Development or better a new Commission) is obvious and urgent.

See the recent article A Pending American Temperaturegate.


söndagen den 21:e februari 2010

Ny Världsordning?

Bo Ekman, Chairman and Founder of Tällberg Foundation (with Board including Jan Eliasson, Former UN Special Envoy toSudan, Minister of Foreign Affairs and former Ambassador to the USA, Johan Rockström, Executive Director, Stockholm Environment Institute and Stockholm Resilience Centre and Anders Wijkman, Vice chairman of the Tällberg Foundation Member of the European Parliament) skriver idag på DN Debatt Ny världsordning ett måste efter debaclet i Köpenhamn:
  • Världen behöver en ny demokratisk ordning som säkrar ekonomisk tillväxt, social stabilitet och ekologisk restabilisering. 
  • Historien lär oss att ingen världsordning har evigt liv. Den viktiga frågan är nu hur en demokratisk grundad ordning ska formas i denna nya värld. 
  • Uppgiften är enorm. 
DN meddelar i anslutning till artikeln att Tällberg Foundation  finansieras av både privata och statliga medel. Störst bidragsgivare är Svenska postkodlotteriet. Även lokala dalaföretag bidrar, liksom bland andra UD, Närings- och Miljödepartementen.

Att lokala dataföretag (och postkodlotteriet) stödjer inrättandet en ny världsordning är kanske inte så mycket att säga om (även om uppgiften är enorm), men att UD skulle göra detta kan väl ifrågasättas? Har Sverige i demokratisk ordning beslutat att verka för en ny värld med ett folk/ett styre? Vad säger Carl Bildt?

Samtidigt meddelar Statskontoret att Rockströms Stockholm Environment Institute brister i kontroll och styrning och att regeringen bör minska sitt beroende av SEI.

Kanske Statskontoret efter vidare granskning skulle komma fram till att UD borde minska sitt beroende av även Tällberg Foundation? Eller vad säger Carl Bildt? 

lördagen den 20:e februari 2010

Det Politiserade SvD

Thomas Gur skriver i dagens SvD Kolumn om Den Politiserade Klimatvetenskapen:
  • Att ingå Faustkontrakt med politiken kan vara lockande för vetenskapen – ens ämne kommer i debattens centrum, forskningsanslagen strömmar till och som expert hamnar man i rampljuset tillsammans med andra celebriteter.
  • Politiker som beslås med fel eller inte lever som de lär får löpa gatlopp.
  • När vetenskap politiseras får den vara med om samma sak.
  • Vägen tillbaka är enkel i teorin. Det gäller att frikoppla sig från den politiska dagordningen, dela med sig av forskningsdata och välkomna den kritiska granskningen. Men så hade också Faust svårt att komma loss från sitt kontrakt.
Men det kontrakt Gur skriver om har ju också ingåtts av SvD, som bedrivit politiserad klimatrapportering. Skall SvD nu få löpa gatlopp? Finns en väg tillbaka för SvD?

Compare with this example of serious unbiased climate journalism.

onsdagen den 17:e februari 2010

Law vs Science in Climategate

The Independent Review into the allegations against the Climatic Research Unit (CRU) headed by Sir Muir Russell will only consider legal aspects (open data software FOI) and not scientific (if the science is true/correct or false/incorrect). This raises an interesting question concerning the relation between legal and scientific truth, in Climategate and in general. There are four possible combinations:
  1. Legally correct and scientifically correct.
  2. Legally incorrect and scientifically correct
  3. Legally correct and scientifically incorrect
  4. Legally incorrect and scientifically incorrect.
Sir Muir Russell is supposed to decide between legally correct or incorrect, irrespective of
scientific correctness. However, the real question is scientific correctness, irrespective
of legal correctness. If the science is correct, it is more or less irrelevant if some legal aspects
are incorrect. If the science is incorrect, it is irrelevant if legal aspects are correct.

In other words: You can lose your academic position if your science is wrong, but not if you lose data or reject your competitors work on false grounds.

How can this be? Maybe because science has a very special nature as something which belongs
to all of us, which no-one can own and prevent others from using, which is endless. Which like Solar radiation is just there, irrespective of legality? Maybe, like in war and love, only the
result counts?

In any case, the Inquiry Team headed by Sir Muir does not appear to be correct.

  • All this is being driven by breakdowns in the science behind global warming theory and in the global resolve to respond.
  • The failure of Copenhagen to reach agreement reflected the two main problems:
  • If the science is perceived to be shaky, and the global economic situation is shaky, if follows that the politics will head in the same direction.


tisdagen den 16:e februari 2010

Vem Granskar KVAs Uttalande om Klimat?

SvD rapporterar under rubriken "Granskningen fungerade inte" att Kungliga VetenskapsAkademien nu bryter sin tystnad och försiktigt börjar ifrågasätta sitt eget oreserverade stöd av FNs klimatpanel IPCC och dess ordförande Rajendra Pachauri. KVAs ständige sekreteraren Gunnar Öquist:
  • Nu måste FN granska klimatpanelens arbete och vidta åtgärder.
  • IPCC har i några fall uppenbart dragit förhastade slutsatser som baseras på ett undermåligt underlag. Kontrollen och granskningen har inte fungerat tillfredsställande i dessa fall. FN måste gå till botten med vad som har hänt och vidta åtgärder för att förtroendet för klimatpanelen inte ska äventyras.
  • KVA tar inte ställning till om IPCC:s ordförande bör avgå, men tror att avslöjandet får konsekvenser.
  • Sådana här saker brukar kräva sina offer.
Ett av offren skulle kunna vara KVA som uttalat sitt stöd till IPCC and Pachauri, och inte ändrat sig. Ännu. När kommer KVA att krypa till korset?

Lennart Bengtson, initiativtagare till KVAs yttrande, verkar dock ta saken med ro:
  • Min uppfattning är att IPCC har en viss tendens att hårdra i sammanfattningen till politikerna. Man vill ha ett enkelt budskap.
  • IPCC har ett stort ansvar och måste ha höga etiska normer.
  • Men man ska inte överdriva det som hänt.
  • Det kan bli misstag.
  • Men det finns inte anledning att ifrågasätta hela IPCC:s arbete för det.
Det kan bli misstag. Ingenting att haka upp sig på enligt KVA.

KVAs granskning fungerade inte. KVA har dragit förhastade slutsatser som baseras på undermåligt underlag. Men KVAs uttalande ligger fast.

Vem granskar då KVA? Vem skall gå till botten med detta? Vilka åtgärder skall vidtagas för att förtroendet för KVA inte skall äventyras? Vilka offer kommer att krävas? Skall någon tvingas avgå? Skall KVA i likhet med FNs panel granska sig själv?

Eftersom svensk klimatpolitik bygger på KVAs uttalande, har detta uttalande en viss betydelse.

måndagen den 15:e februari 2010

d'Alembertgate

Another example of the (mal)practice of peer-review in science revealed in Climategate, is my own experience with the reception of my resolution of d'Alembert's paradox with Johan Hoffman, first submitted to the leading journal in the field Journal of Fluid Mechanics and rejected with the following referee's reports:

Referee 1:
  • I strongly recommend that you reject this paper.
  • 1. The authors show no understanding of fluid mechanics, of how small viscosity leads to experimentally verified thin boundary layers, and of how experimentally verified these boundary layers detach when the external flow decelerates.
  • 2. The authors show no understanding of mathematics, of how in the Euler equations streamlines leaving a surface will be vortex sheets which divide the domain into regions in which there is separately potential flow.
  • 3. The authors show no understanding of numerics, of how finite element methods introduce an artificial viscosity (or hyper-viscosity in high-order methods) through the truncation error, and so their solutions are not solutions of the Euler equation but solutions of a Navier-Stokes equation.
  • I am alarmed that these authors have another paper accepted by JFM: I recommend that someone checks it for logic.
Referee 2:
  • THE AUTHORS PROPOSE RESOLVE D'ALEMBERT'S PARADOX BY SHOWING THAT THE ZERO DRAG POTENTIAL SOLUTION OF EULER'S EQUATIONS IS UNSTABLE AND INSTEAD A TURBULENT (APPROXIMATE) SOLUTION DEVELOPS WITH A NON ZERO DRAG, EVEN WITHOUT BOUNDARY LAYER EFFECTS.
  • THEY BASE THEIR RESULT ON NUMERICAL CALCULATION MOSTLY DONE IN 2006 WITH THEIR OWN NUMERICAL PACKAGE.
  • THE EQUATIONS THEY STUDY (2.1) HAVE NO PARAMETERS OTHER THAN THE VELOCITY SO THAT THEIR CONCLUSIONS MUST APPLY TO ALL REYNOLDS NUMBERS.
  • SINCE TURBULENCE DOES NOT DEVELOP AT LOW RE THEIR RESULT GOES TOO FAR. I DO NOT KNOW HOW THEY GET VORTICITY WHEN THE INTIAL FLOW IS IRROTATIONAL, BAROTROPIC AND WITHOUT SHEAR LAYERS.
  • I DO NOT NOT UNDERSTAND THEIR USE OF SEPARATION WHEN THERE ARE NO BOUNDARY LAYERS TO SEPARATE. I HAVE ATTACHED A CITATION FROM LIGHTHILL IN WHICH HE ADVOCATES REPLACING d'ALEMBERTS PARADOX WITH d'ALEMBERTS THEOREM.
  • THIS PAPER SHOULD BE REJECTED.
  • I DID NOT READ THEIR NUMERICAL PAPERS WHICH ARE VERY NEW AND APPARENTLY NOT VALIDATED AGAINST EXACT SOLUTIONS AND OTHER TURBULENT CODES.
It is clear that these referee's are out kill, and they do it! The paper was then submitted to Journal of Mathematical Fluid Mechanics and was accepted and published in Dec 2008.

The story is told in my previous post The Sciencegate of Fluid Mechanics: It shows how a small group of scientists can control a whole scientific discipline by suppressing new information and new discoveries showing classical "truths" to be empty/false. See my interview with the Editors of Journal of Fluid Mechanics JFM.

It shows how this small group of scientists also controls Wikipedia, and blocks any reference

Climategate has shown that some of climate science has been a dirty business, and I have experienced similar practice in fluid mechanics. The Climategate drama is now unfolding and its consequences must be far-reaching...carbon trading is losing momentum...Maybe the emails behind dAlembertgate will also be made public...maybe according to FOI...

If you look into the details of dAlembertgate you will discover that the new resolution of d'Alembert's paradox fundamentally changes the mathematical basis of fluid dynamics and that the attitude of JFM is untenable...

For more insight into the essentials of peer-review see an example from 1945.

söndagen den 14:e februari 2010

Time for Fight, in Climate Science

The basic scientific questions in climate science are
  • (i) Is there today unequivocal unprecedented global warming?
  • (ii) Is there scientific evidence of major AGW?
In a BBC interview Phil Jones as central scientific advocate of AGW, answers No to (i) and Maybe Not to (ii), as evidenced in:

Question A - Do you agree that according to the global temperature record used by the IPCC, the rates of global warming from 1860-1880, 1910-1940 and 1975-1998 were identical?

Phil Jones: An initial point to make is that in the responses to these questions I've assumed that when you talk about the global temperature record, you mean the record that combines the estimates from land regions with those from the marine regions of the world. CRU produces the land component, with the Met Office Hadley Centre producing the marine component.Temperature data for the period 1860-1880 are more uncertain, because of sparser coverage, than for later periods in the 20th Century. The 1860-1880 period is also only 21 years in length. As for the two periods 1910-40 and 1975-1998 the warming rates are not statistically significantly different (see numbers below).I have also included the trend over the period 1975 to 2009, which has a very similar trend to the period 1975-1998.So, in answer to the question, the warming rates for all 4 periods are similar and not statistically significantly
different from each other.

Question D - Do you agree that natural influences could have contributed significantly to the global warming observed from 1975-1998, and, if so, please could you specify each natural influence and express its radiative forcing over the period in Watts per square metre.

Phil Jones: This area is slightly outside my area of expertise. When considering changes over this period we need to consider all possible factors (so human and natural influences as well as natural internal variability of the climate system). Natural influences (from volcanoes and the Sun) over this period could have contributed to the change over this period. Volcanic influences from the two large eruptions (El Chichon in 1982 and Pinatubo in 1991) would exert a negative influence. Solar influence was about flat over this period. Combining only these two natural influences, therefore, we might have expected some cooling over this period.

Question E - How confident are you that warming has taken place and that humans are mainly responsible?

Phil Jones: I'm 100% confident that the climate has warmed. As to the second question, I would go along with IPCC Chapter 9 - there's evidence that most of the warming since the 1950s is due to human activity.

Question V - If you have confidence in your science why didn't you come out fighting like the UK government's drugs adviser David Nutt when he was criticised?

Phil Jones: I don't feel this question merits an answer.

Both question (i) and (ii) are scientific questions which can be answered today, or not. It is up to the scientific community including the Royal Society and Royal Swedish Academy of Sciences to present answers or if this is not yet possible, to make this clear.

It is time for Phil Jones and the Royals to come out in the open and fight. This is how science is performed, unlike business and politics taking place in closed boards behind closed doors, and how merits in science are gained.

Or rather, this is how science is supposed to work, but the practice is different, as now being
brought into light in Climategate and Climategate Analysis by John Costella
  • So what reception do they get? Instead of embracing this diversity of knowledge—  thanking them for their experience (no one knows everything about everything)  and using that knowledge to improve their own calculations—these power-brokers  of climate science instead ignore, fob off, ridicule, threaten, and ultimately black-  ball those who dare to question the methods that they—the power-brokers, the  leaders—have used. 
  • And do not be confused: I am here talking about those  scientists within their own camps, not the “skeptics” which they dismiss out of  hand.    
  • This is not “climate science”, it is climate ideology; it is the Church of Climatology.    It is this betrayal of the principles of science—in what is arguably the most  important public application of science in our lifetime—that most distresses  scientists. 

A parallel story, on a much smaller scale but with the same ingredients, is my own experience with my resolution together with Johan Hoffman of the 250 year old d'Alembert's paradox as a central problem of fluid mechanics.

tisdagen den 9:e februari 2010

Should IPCC be Replaced by The Royals?

The Guardian concludes in The case for climate action must be remade from the ground upwards that
  • The IPCC panel should arguably be replaced by a body controlled by national scientific academies rather than governments.
This is because IPCC has lost all scientific credibility. Fine, IPCC should be dismantled. But is it such a good idea to hand over to the Royal Society of London and the Royal Swedish Academy of Sciences? 

Probably not, because the Royals have been very loyal supporters of IPCC  all along and have been keen to express official endorsements of IPCC, which have not been revised because of Climategate and all the other scandals connected to IPCC and its chairman Pachauri.  

Not yet at least, but the time to leave the sinking ship is near, right?

  • This service will be a vital part of our growing body of knowledge on climate change, and will be held to the highest standards of scientific integrity and transparency.

lördagen den 6:e februari 2010

Björklunds Läsa Skriva Räkna


Jan Björklunds vision av dagens skola  är folkskolan: 
  • disciplin, betyg
  • LÄSA SKRIVA RÄKNA.
Detta skall nu åstadkommas genom att förlänga en lärarutbildning, som i sin nuvarande form inte lyckats lära ens lärarna att RÄKNA = de fyra räknesätten, än mindre eleverna.

Björklund spenderar 525 miljoner på sin Matematiksatsning för att hitta en lärare i Sverige som kan RÄKNA och kan lära ut att RÄKNA. Ännu har ingen påträffats.

Med 525 miljoner skulle man kunna ge varje elev en laptop vid skolstart och därmed ge alla elever en ingång till både svenska, IT och matematik och därmed till vårt moderna samhälle. 

Finns det verkligen ingen som kan hjäpa Björklund att lyfta blicken från den fyraåriga folkskolan?

Jag har försökt få Mona att reagera, men det verkar som inte heller Mona kan se framåt.
Nog är det väl konstigt?

Men detta är vad DNs huvudledare Bryt Cirkelgången ber om:
  • Man måste inte alltid gå bakåt, Jan Björklund. Man kan kombinera det bästa av det gamla med det bästa av det nya.
Kan Björklund läsa? Räkna kan han i alla fall inte.

onsdagen den 3:e februari 2010

No Apology from the Royal Swedish Academy

The Guardian reports:
  • The embattled chief Dr Rajendra Pachauri of the UN's climate change body IPCC has hit out at his critics and refused to resign or apologise for a damaging mistake in a landmark 2007 report on global warming.
  • Pachauri said it would be hypocritical to apologise for the false claim that Himalayan glaciers could melt away by 2035, because he was not personally responsible for that part of the report. "You can't expect me to be personally responsible for every word in a 3,000 page report," he said.
The Royal Swedish Academy of Sciences neither apologizes for its unreserved endorsement of
the IPCC 2007 report, probably using the same argument. Of course, an Academy of Sciences cannot be responsible for whatever science it endorses, and cannot be expected to apologize for endorsing incorrect science...or maybe it can...because the pressure is building up...

What the Geological Society of America can do, is also possible to do for the Royal Academy...

The Spectator has the story: The Global Warming Guerillas:
  • Matt Ridley salutes the bloggers who changed the climate debate. While most of Fleet Street kowtowed to the green lobby, online amateurs uncovered the spin and deception that finally cracked the consensus.
Science is no longer controled by secret societies in closed academies, but now performed in the open blogosphere...amazing...Even Aftonbladet takes the blade from the mouth...and even New York Times...

måndagen den 1:e februari 2010

Mathematical Simulation Technology: Body&Soul

I am preparing the following text for the new Bachelors program in Simulation Technology at KTH:
which consists of the following basic parts:
  1. Icarus and Daedalus
  2. Newton's World of Mechanics
  3. World of Games
  4. Leibniz' World of Mathematics
  5. Tool Bags
  6. World of Differential Equations
  7. World of Finite Elements
  8. World of Applications
combined with the following parts serving as a unified source of material for more detailed studies (with 1-11 embedded in the above main document):
  1. Derivatives and Geometry in R3: Body&Soul Vol I
  2. Integrals and Geometry in Rn: Body&Soul Vol II
  3. Calculus of Several Variables: Body&Soul Vol III
  4. Computational Differential Equations
  5. The Mathematical Secret of Flight
  6. The Secret of Thermodynamics
  7. Mathematical Theory of Flight
  8. Mathematical Theory of Sailing
  9. The Clock and the Arrow: A Brief History of Time
  10. Mathematical Relativity and Quantum Mechanics
  11. Mathematical Blackbody Radiation.
  12. Computational Turbulent Incompressible Flow: Body&Soul Vol IV

The text is complemented by interactive Sessions covering basic mathematical tools, prototypes of simulation software and computer games, and short videos introducing key concepts 

The student is encouraged to create his/her own web-based version of Mathematical Simulation Technology with text, picture, movie and sound in simulation and presentation.

Here is a demo of the first chapter with movies of simulations and introductory lecture
by Tutor (2 min) embedded into the pdf. Maybe it is necessary to download the file to see
the movies.

A simplified version for high-school will also be prepared and to be tested at Kunskapsskolan in the Spring.