A Critical Analysis of the Ideology of Mathematics

The Ideology of Mathematics as presented in the documents of the previous blogpost can be summarized as:

• Mathematics has a double character: It is both the most original, complex and beautiful free creation of the human spirit with its own internal standards, and a universal practical tool.  The miraculous double character is described by the Physics Nobel Laurate Eugene Wigner as:
• The unreasonable effectiveness of mathematics in the natural sciences. The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. 

Mathematics education is based on this mystification, this true miracle:

It allows mathematics education from early grades and on to focus on the language and logic of mathematics learning the words "and", "or", "not", "there is/are", "for some", "for every", "for all", in the safe conviction that this will be most useful to all students in their practical lives. 

It allows mathematics education to focus on axiomatics in the safe conviction that human knowledge can be axiomatized.

It allows mathematics education to focus just about anything in the safe conviction that mathematics is universally applicable.

But there are no miracles, trivialities are trivialities, axiomatization of knowledge is impossible, and no mathematics is universally applicable. To build education on a mystery which is neither understood nor deserved, is not a good idea, because learning is about understanding and students do not profit from free gifts which they do not understand nor deserve and which they cannot use.

For a discussion of how mathematics education can and should be reformed see my blog posts

on mathematics education. In particular notice Mathematics and Religion vs Self-Help

showing close similarities between mathematics and religion sharing the double character of uplifted divinity and universal practicality. In both cases the idea is to study the language of the Divinity to learn about the World. This is still practiced in Islamic schools, but no longer in Western schools.

The two characters of mathematics clashed in the great war between the logicist/formalist and constructivist schools in 1920-30s. The constructivists won on technical knockout but they were soon cleansed from mathematics departments filled with logicists/formalists still in control and forming the ideology of mathematics today, so well expressed by the Committe on Logical Education. For more war reports, see my knols on mathematics.

The Ideology of Mathematics

What is the ideology of mathematics underlying mathematics education as presented by professional mathematicians? Let us seek an answer in the following typical texts to be analyzed in the next blogpost:

American Association for the Advancement of Science explains in Science for All Americans:

• Mathematics relies on both logic and creativity, and it is pursued both for a variety of practical purposes and for its intrinsic interest. 
• For some people, and not only professional mathematicians, the essence of mathematics lies in its beauty and its intellectual challenge. 
• For others, including many scientists and engineers, the chief value of mathematics is how it applies to their own work. 
• Because mathematics plays such a central role in modern culture, some basic understanding of the nature of mathematics is requisite for scientific literacy. To achieve this, students need to perceive mathematics as part of the scientific endeavor, comprehend the nature of mathematical thinking, and become familiar with key mathematical ideas and skills.
  

The Committee on Logic Eduction offers the following comprehensive summary:

• There are creative tensions in mathematics between beauty and utility, abstraction and application, between a search for unity and a desire to treat phenomena comprehensively.
• Mathematics was originally linked with science and technology; however, it gradually became independent of science and technology, and present-day mathematicians think freely about virtually everything possible.
• Therefore, mathematics is said to be a free creation of the human spirit. Special characteristics of mathematics are the clarity and precision of definitions, including usuage of words in ways that differ from their use in everyday language, and the certainty of mathematical truth based on deductive mathematical reasoning.
• Given what Wigner call the "unreasonable effectiveness of mathematics", all students should learn the basic nature of mathematics and mathematical reasoning and its use in organizing and modeling natural phenomena. 
• In the practice of mathematics, typically some concepts and statements are taken as given. They may be applied or serve as the foundation for the development of further mathematics. Additional concepts can be defined carefully in terms of the given ones. Conjectures can be developed on the basis of experience with examples. Further statements can be proved deductively based on what has been assumed. 
• This process has been repeated extensively, resulting in mathematics having its own intricate structure, with concepts and areas of specialization that require considerable time and study to grasp. Moreover mathematics is interconnected in many interesting ways. 
• It may be useful to think of students learning mathematics along the lines of a generalized structure of reasoning: (1) recognition, (2) analysis, (3) informal deduction, (4) formal deduction, (5)  axiomatics. 
• In early grades, students learn the basic language including the critical logical words "and", "or", "not", "there is/are", "for some", "for every", "for all". They see multidigit numbers being built from single digit numbers. They match the trajectory of a kicked ball with the concept of line. They recognize patterns in sequences of numbers and shapes. In middle grades students develop habits of reasoning "locally", clarifying the assumptions of a particular problems and examining the steps involved in the solution to determine correctness. 
• For example, one of us recently observed a fifth grade teacher asking her students for the definition of polygon. They knew, for example that triangles, squares and hexagons were polygons. It was exciting to see the students wrestling with abstraction, differentiating polygons from circles, and finally focusing on polygons as figures with sides. 
• By the end of high school, students should be aware of the global deductive nature of axiomatic mathematics. They should be familiar with the connections between our number systems and algebra, between algebra and geometry. 
• They should be comfortable reasoning with short sequences of statements, with Venn diagrams and other visual and diagrammatic methods. They should have experience with modeling, recognizing for example that certain natural phenomena obey linear relationships and that linear relationships make prediction so easy that we try to approximate other more complicated phenomena by linear ones. 
• It is important both to understand how algebraic relationships can describe particular problems and to understand the power derived by working abstractly with the mathematics which applies to many different situations.

Everybody Counts: A Report to the Nation on the Future of Mathematics Education describes The Nature of Mathematics as follows:

• Mathematics reveals hidden patterns that help us understand the world around us. Now much more than arithmetic and geometry, mathematics today is a diverse discipline that deals with data, measurements, and observations from science; with inference, deduction, and proof; and with mathematical models of natural phenomena, of human behavior, and of social systems.
• As a practical matter, mathematics is a science of pattern and order. Its domain is not molecules or cells, but numbers, chance, form, algorithms, and change. As a science of abstract objects, mathematics relies on logic rather than on observation as its standard of truth, yet employs observation, simulation, and even experimentation as means of discovering truth.
• The special role of mathematics in education is a consequence of its universal applicability. The results of mathematics--theorems and theories--are both significant and useful; the best results are also elegant and deep. Through its theorems, mathematics offers science both a foundation of truth and a standard of certainty.
• In addition to theorems and theories, mathematics offers distinctive modes of thought which are both versatile and powerful, including modeling, abstraction, optimization, logical analysis, inference from data, and use of symbols. Experience with mathematical modes of thought builds mathematical power--a capacity of mind of increasing value in this technological age that enables one to read critically, to identify fallacies, to detect bias, to assess risk, and to suggest alternatives. 
• Mathematics empowers us to understand better the information-laden world in which we live. During the first half of the twentieth century, mathematical growth was stimulated primarily by the power of abstraction and deduction, climaxing more than two centuries of effort to extract full benefit from the mathematical principles of physical science formulated by Isaac Newton. 
• Now, as the century closes, the historic alliances of mathematics with science are expanding rapidly; the highly developed legacy of classical mathematical theory is being put to broad and often stunning use in a vast mathematical landscape.
• Several particular events triggered periods of explosive growth. The Second World War forced development of many new and powerful methods of applied mathematics. Postwar government investment in mathematics, fueled by Sputnik, accelerated growth in both education and research. Then the development of electronic computing moved mathematics toward an algorithmic perspective even as it provided mathematicians with a powerful tool for exploring patterns and testing conjectures.
• At the end of the nineteenth century, the axiomatization of mathematics on a foundation of logic and sets made possible grand theories of algebra, analysis, and topology whose synthesis dominated mathematics research and teaching for the first two thirds of the twentieth century. 
• These traditional areas have now been supplemented by major developments in other mathematical sciences--in number theory, logic, statistics, operations research, probability, computation, geometry, and combinatorics. In each of these subdisciplines, applications parallel theory. 
• Even the most esoteric and abstract parts of mathematics--number theory and logic, for example--are now used routinely in applications (for example, in computer science and cryptography). Fifty years ago, the leading British mathematician G.H. Hardy could boast that number theory was the most pure and least useful part of mathematics. Today, Hardy's mathematics is studied as an essential prerequisite to many applications, including control of automated systems, data transmission from remote satellites, protection of financial records, and efficient algorithms for computation.
• In 1960, at a time when theoretical physics was the central jewel in the crown of applied mathematics, Eugene Wigner wrote about the ``unreasonable effectiveness'' of mathematics in the natural sciences: ``The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.'' 
• Theoretical physics has continued to adopt (and occasionally invent) increasingly abstract mathematical models as the foundation for current theories. For example, Lie groups and gauge theories--exotic expressions of symmetry--are fundamental tools in the physicist's search for a unified theory of force.During this same period, however, striking applications of mathematics have emerged across the entire landscape of natural, behavioral, and social sciences. 
• All advances in design, control, and efficiency of modern airliners depend on sophisticated mathematical models that simulate performance before prototypes are built. From medical technology (CAT scanners) to economic planning (input/output models of economic behavior), from genetics (decoding of DNA) to geology (locating oil reserves), mathematics has made an indelible imprint on every part of modern science, even as science itself has stimulated the growth of many branches of mathematics.
• Applications of one part of mathematics to another--of geometry to analysis, of probability to number theory--provide renewed evidence of the fundamental unity of mathematics. Despite frequent connections among problems in science and mathematics, the constant discovery of new alliances retains a surprising degree of unpredictability and serendipity. 
• Whether planned or unplanned, the cross-fertilization between science and mathematics in problems, theories, and concepts has rarely been greater than it is now, in this last quarter of the twentieth century.

The mathematician A N Whitehead, who wrote the bible of the logicist school Principia Mathematica together with Bertrand Russell, explains to us in Mathematics in the History of Thought:

• The science of pure mathematics, in its modern developments, may claim to be the most original creation of the human spirit. 
• The originality of mathematics consists in the fact that in mathematical science connections between things are exhibited which, apart from the agency of human reason, are extremely unobvious. 
• Suppose we project our imagination backwards through many thousands of years, and endeavour to realise the simple-mindedness of even the greatest intellects in those early societies. Abstract ideas which to us are immediately obvious must have been, for them, matters only of the most dim apprehension. For example take the question of number.
• We think of the number 'five' as applying to appropriate groups of any entities whatsoever-to five fishes, five children, five apples, five days. Thus in considering the relations of the number 'five' to the number 'three,' we are thinking of two groups of things, one with five members and the other with three members. But we are entirely abstracting from any consideration of any particular entities, or even of any particular sorts of entities, which go to make up the membership of either of the two groups. We are merely thinking of those relationships between those two groups which are entirely independent of the individual essences of any of the members of either group. This is a very remarkable feat of abstraction; and it must have taken ages for the human race to rise to it. 
• During a long period, groups of fishes will have been compared to each other in respect to their multiplicity, and groups of days to each other. But the first man who noticed the analogy between a group of seven fishes and a group of seven days made a notable advance in the history of thought. He was the first man who entertained a concept belonging to the science of pure mathematics. At that moment it must have been impossible for him to divine the complexity and subtlety of these abstract mathematical ideas which were waiting for discovery. Nor could he have guessed that these notions would exert a widespread fascination in each succeeding generation.
• The tremendous future effect of mathematical knowledge on the lives of men, on their daily avocations, on their habitual thoughts, on the organization of society, must have been even more completely shrouded from the foresight of those early thinkers. Even now there is a very wavering grasp of the true position of mathematics as an element in the history of thought. 
• When we think of mathematics, we have in our mind a science devoted to the exploration of number, quantity, geometry, and in modern times also including investigation into yet more abstract concepts of order, and into analogous types of purely logical relations. The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities. So that for example, no mathematical truths apply merely to fish, or merely to stones, or merely to colours. So long as you are dealing with pure mathematics, you are in the realm of complete and absolute abstraction. 
• All you assert is, that reason insists on the admission that, if any entities whatever have any relations which satisfy such-and-such purely abstract conditions, then they must have other relations which satisfy other purely abstract conditions.
• Mathematics is thought moving in the sphere of complete abstraction from any particular instance of what it is talking about. So far is this view of mathematics from being obvious, that we can easily assure ourselves that it is not, even now, generally understood.
  

Short-Time Accuracy Test of Climate Models?

The climate of the Earth results from turbulent flow of air in the atmosphere and turbulent flow of water in the ocean, which is heated by incoming solar radiation and cooled by outgoing infrared radiation, both of which critically depend on cloud formation, which requires presence of particles in the air or aerosols acting as condensation kernels.

Burning of fossil fuels produces aerosols which can enhance cloud formation. Low clouds  can decrease incoming radiation and thus act as negative feedback to global warming from fossil fuels, while high clouds can decrease outgoing radiation and thus act as positive feed-back. The net effect appears to be unknown and uncertainties in modeling of cloud formation propagate to uncertainties in global climate modeling.

A main goal of climate modeling is to predict climate sensitivity, that is the increase of global temperature from doubling of CO2 in the atmosphere. In the  IPCC 4th Assessment Report climate sensitivity is predicted to likely be between 2 and 4.5 degrees Celcius, which thus could be the global warming in 2100 without CO2 emission control. The UK Met Office explains to us:

• There have been major advances in the development and use of models over the last 20 years and the current models give us a reliable guide to the direction of future climate change.
• Computer models cannot predict the future exactly...
• Current models enable us to attribute the causes of past climate change, and predict the main features of the future climate, with a high degree of confidence.
• As well as producing CO2, burning fossil fuels also produces small particles called aerosols which cool the climate by reflecting sunlight back into space. These have increased steadily in concentration over the 20th century, which has probably offset some of the warming we have seen.

IPCC and the Met Office thus inform us that even if climate model predictions are incorrect over year and decade, they can be correct over centennials. But is this really possible from a mathematical point of view? Are there dynamical systems which allow computational modeling with this surprising property? Long-time accurate while short-time inaccurate? We are familiar with models which are short-time pointwise accurate and long-time pointwise inaccurate, but the opposite?

There are trivial such systems, like modeling an oscillation between -1 and +1 by a constant 0 state, but is the climate such a trivial system? Probably not. 

There are dissipative systems which forget initial data over long-time, so if initial data are incorrect this affects accuracy only for short-time. Climate models are dissipative and thus partly forget initial data, but that is not enough to secure long-time accuracy. 

The previous blog Climate and Turbulence Modeling recalled the analysis of turbulent flow in Computational Turbulent Incompressible Flow, showing that long-time meanvalues of turbulent flow may be predictable even if pointvalues are predictable only over short time, because of cancellation effects.  It is likely that climate models can share this property, but it requires short-time accuracy.

Altogether, I see no real reason to expect that short-time inaccurate climate models can be long-time meanvalue accurate, as suggested by IPCC and the Met Office. 

If this observation is correct, one could require climate models to be short-time accurate, which can be tested in short-time,  as a necessary requirement for reliability of long-time meanvalue prediction of climate sensitivity. 

Concerning the predictive capabilities of current climate models, see the US Senate Report: Dissent over Global Warming Claims.

The lecture Considering the Human Influence on Climate by R. A. Pielke Sr, is also informative. 

Mathematics and Religion vs Self-Help

There are similarities between traditional education in religion and contemporary education in mathematics based on an idea that God = Mathematics. To see this, consider the following common statements which express the fundamental beliefs which religious/mathematics education seeks to imprint in the blank minds of the students:

• Religion/Math is a supreme creation of human thought.
• Religion/Math is a high perfect art as daring as the most secret dreams of imagination.
• Religion/Math is a fundament of society.
• Religion/Math helps us to understand the World.
• Religion/Math helps us to cope with the problems we face in our lives.
• God/Math is everywhere present but invisible.
• God/Math is allmighty but with very limited practical utility.
• Religion/Math can be properly understood only by a selected few; the others have to accept it without understanding.
• A life without Religion/Math is a miserable life.
• Religion/Math has an intrinsic beauty and coherence.
• Religion/Math Mathematics plays a pivotal role in the progress of society and its continued growth relies on the encouragement and teaching of the next generation religious/mathematical thinkers, and outreach to the public and schools. 
  

Traditional education in religion was very successful in implanting these beliefs, but nevertheless today confessional religion has vanished from the school system, at least in the Western World. 

Similarly, even if the school system still succeeds in making all students believe in the greatness and importance of mathematics, whether they succeed or fail miserably, mathematics education is today in a state of permanent crisis in the footpaths of religious education. 

Religious education is today being replaced by a flood of self-help psychology and traditional mathematics is being replaced by self-help laptop technology:

• how to handle words, pictures, sound and videos
• how handle social life using facebook and blog 
• how to get information and get to understand the world, using search engines
• how to play computer games and music
• how handle gps, mobile and bank account. 

If not mathematics education is going to vanish from the school system, it has to be reformed into self-help laptop technology, and come down form the higher spheres of religion. This is further motivated on my blogs about mathematics education.

Climate and Turbulence Modeling

Global climate models are based on turbulence models, since the slightly viscous flow of air in the atmosphere and water in the oceans is turbulent. Turbulence modeling, in the form of  analytical mathematical models, is a main unsolved problem of fluid mechanics.

In our book Computational Turbulent Incompressible Flow, with prel. version for download, Johan Hoffman and I present a new approach to turbulence modeling based on ab initio numerical computation with turbulence automatically modeled by the stabilization of the numerics, thus without any explicit analytical turbulence model.  

We show that mean-value quantities of turbulent flow such as drag and mean temperature can be accurately computed without analytical turbulence model, thus circumventing the main unsolved problem of fluid mechanics. We plan to test this approach on climate modeling with hopefully a connection between turbulence and the main unsolved problem of climate modeling: cloud formation. 

We will report as soon as we have something to report on...hopefully before the Copenhagen meeting in December...since the outcome of this meeting critically depends on computational modeling of turbulence and cloud formation...and dark clouds over the meeting are already forming... 

Coin Tossing: Cold or Warm?

Newscientist reports:

• Forecasts of climate change are about to go seriously out of kilter. One of the world's top climate modellers said Thursday we could be about to enter "one or even two decades during which temperatures cool."People will say this is global warming disappearing," he told more than 1500 of the world's top climate scientists gathering in Geneva at the UN's World Climate Conference.
• "I am not one of the sceptics," insisted Mojib Latif of the Leibniz Institute of Marine Sciences at Kiel University, Germany. "However, we have to ask the nasty questions ourselves or other people will do it.
• "Few climate scientists go as far as Latif, an author for the Intergovernmental Panel on Climate Change. But more and more agree that the short-term prognosis for climate change is much less certain than once thought.
•  "In many ways we know more about what will happen in the 2050s than next year," said Vicky Pope from the UK Met Office.

The message is that global climate models cannot predict year or decade meanvalues, but can predict centennial meanvalues. How can this be? What is the mathematics behind such a belief? 

The first idea that come to mind is the law of large numbers of statistics offering prediction of the meanvalue 0.5 of many cointosses between 0 and 1, but no prediction of the meanvalue of a few tosses. But is climate modeling the same as coin tossing between cold and warm? 

Newscientist concludes:

• The world may badly want reliable forecasts of future climate. But such predictions are proving as elusive as the perfect weather forecast.
  

The future of mankind thus seems to lie in the hands of mathematicians running the climate models...but coin tossing statistics does not seem to be enough...what can be done or said? 

Well, let us recall that the 0.5 probability of heads in coin tossing is computed mathematically using the fact that a rotating coin has head up half of the time, that is using a short-time-accurate mathematical model, see the discussion in Chapter 13 Turbulence and Chaos in Computational Turbulent Incompressible Flow. Without a short-time-accurate model, nothing can be be predicted about long-time...Compare with the UK Met Office assurement:

• There have been major advances in the development and use of models over the last 20 years and the current models give us a reliable guide to the direction of future climate change.
• Computer models cannot predict the future exactly...
• Current models enable us to attribute the causes of past climate change, and predict the main features of the future climate, with a high degree of confidence.

What are "the advances in the development and use of models"? What is meant by "direction of future climate change"? Colder or warmer? Does "direction" indicate that the size of the change cannot be predicted? What is the meaning of "computer models cannot predict the future exactly"? That computer models can predict the future almost exactly? Who is the inventor of this form of newspeak? Note the clever construction of the following key statement by Met Office:

• As well as producing CO2, burning fossil fuels also produces small particles called aerosols which cool the climate by reflecting sunlight back into space. These have increased steadily in concentration over the 20th century, which has probably offset some of the warming we have seen.
  

Note the clever use of "probably" and "some of the warming". Very clever doublespeak: Clearly suggesting something, without saying anything! This is not the language of science. 

Can really these semantic tricks help save the World?

US Senators Freeze Despite Global Warming

The Guardian reports that The US Freezes on Climate Change:

• The stalled US climate change debate has killed the hope of reaching a final agreement at the Copenhagen summit
• Without concrete action in the Senate, there will not be an actual deal ready to sign in Copenhagen. With no Senate action, there's no guarantee that the US will commit to binding targets. And with no US targets, there will be no firm agreement from China, India or other emerging powers.
• It won't be a failure if there's no deal in Copenhagen, but it will be hard to gauge success with no new expectations.

What is the true reason that US Senators hesitate? Is it because most US Senators are not convinced about the reliability of present computational climate models predicting catastrophical global warming from CO2 emission? Is this because the Senators knowledge of mathematics and computer simulation is not deep enough? If so, would some education help?

Or is it because the Senators realize that they can only convince voters about the necessity of costly emission controls, if they themselves are convinced about the predictive power of present climate models, and they do not feel convinced? 

It seems that the only possibility is that the Senators sit down and carefully study mathematics and computational simulation, and after this experience check if they are convinced or not. It should be possible to bring them to the research front in a couple of weeks, with good math teachers. I guess this effort cannot be spared? 

I guess we here touch the essence of democracy? You cannot dictate, only convince others by first convincing yourself by first thinking yourself. Not even President Obama can get around this predicament. In his campaing Obama talked like a convinced: "the science is beyond dispute, the facts are clear", but today he has to face a disputable reality of unclear facts. How is Obama going to handle this situation? By joining the Senators math class?

Financial Times reports:

• The cost of reducing China’s total greenhouse gas emissions is likely to reach $438bn a year within 20 years, and developed economies will have to bear much of that cost, according to a group of Beijing’s leading climate economists.The figure, equivalent to about 7.5 per cent of China’s estimated gross domestic product in 2030, is likely to be deployed to support Beijing’s argument at December’s climate change summit in Copenhagen that industrialised nations must share the cost of cutting emissions in developing countries.
  

Another math lesson for both US President Obama and EU Chairman Reinfelt? 

Scoping the 5th Assessment Report of IPCC

                                                       The core of a climate model.

The upcoming 5th Assessment Report of IPCC AR5 was scoped in IPCCs 30th Session in Antalya, April 21-23, 2009, as a Proposal for an IPCC Expert Meeting on Assessing and Combining Multi Model Climate Projections:

• Climate model results provide the basis for IPCC projections of future climate change. Previous  assessment reports included model evaluations but avoided weighting or ranking models.  
• Defining a set of minimum criteria for a model to be 'credible' or  agreeing on a metric of performance is therefore difficult and the criteria are likely to depend on the  variable and timescale of interest. Combined with an estimated data volume exceeding 1000  Terabytes, the AR5 faces immense obstacles in trying to make sense of the deluge of model runs and  data that it will produce. 
• Recent studies have started to address these issues by proposing ways to weight or rank models, based  on process evaluation, agreement with present day observations, past climate or observed trends.  While there is agreement that 'the end of model democracy' may be near, there is no consensus on how  such a model selection or weighting process could be agreed upon. 

Reading these reservations, we get a warning that we should not expect any significant improvement of climate model reliability from AR4 to AR5. World leaders preparing far-reaching reductions in CO2 emissions thus have to look to the stars for guidance, or simply rely on the predictions of IPCC based on climate models of unknown but most likely low reliability.

 

Bara En Liten Miljon Till, till Matematik

I gårdagens SvD föreslår fem matematikprofessorer en blygsam satsning på matematiska vetenskaper genom adekvat stöd till Institut Mittag-Leffler på en miljon eller två. Motiveringen beskriver den rådande krisen inom matematik som akademiskt ämne:

• Den accellererande utvecklingen mot ett alltmer kunskapsbaserat samhälle tar stöd i matematiken.
• Idag är en satsning på matematik accepterad som ett fundamentalt villkor för ett lands utveckling. 
• För att bevara vår position som kunskapsnation ... måste Institut Mittag-Leffler få ett rimligt och långsiktigt stöd.     
  

Huvudargumentet är att matematik är fundamentet till vårt moderna Sverige, ett fundament som emellertid är osynligt och därför tyvärr lätt glöms bort i den nuvarande forskningspolitiken styrd av strategiska satsningar på lättbegripliga breda ämnesområden.

Således: Eftersom matematik är detta allestädes närvarande, men tyvärr osynliga och något obegripliga fundament, måste Sverige satsa inte en utan två miljoner på Institut Mittag-Leffler.

De fem matematikprofessorerna söker alltså skjuta en mygga med kanon: Om nu matematik är så väsentligt för vårt samhälle, vilket är riktigt om man tolkar matematik som dator/beräknings-matematik = basen för informationssamhället,  så räcker det inte med ytterligare en miljon till ett matematiksintititut i Djursholm, utan då måste matematikutbildningen på alla nivåer reformeras så att den motsvarar dagens behov.

Om detta behov finns att läsa på mina Knols on Mathematics/Science Education.

A Modest Proposal for Research Money

The Royal Society has published a report on the feasibility and possible dangers of technologies for cooling down the Earth, known as geoengineering. The ideas include artificial trees that draw CO2 from the air, mimicking volcanoes by spraying sulphate particles a few miles above the Earth to deflect the Sun’s rays, cloud seeding or launching trillions of small mirrors into space to act as a sunshield. For more ideas see news article in DN. 

The panel of 12 scientists who produced the report called for a £100 million annual global research fund to study geoengineering technologies and said that Britain should contribute £10 million a year, ten times the amount being spent now on such research. Professor John Shepherd, who chaired the panel, said:

• It is an unpalatable truth that unless we can succeed in greatly reducing carbon dioxide emissions we are heading for a very uncomfortable and challenging climate future, and geoengineering will be the only option left to limit further temperature increases.
  

However, Professor Shepherd admitted that he had no firm opinion on how likely it was that the world would need some form of geoengineering: 

• My opinion ranges from maybe to possibly to probably, depending on what I had for breakfast.
  

In the report Professor Shepherds breakfast ambivalence is expressed as:

• It is likely that global warming will exceed 2°C this century  unless global greenhouse gas emissions are cut by at least  50% of 1990 levels by 2050, and by more thereafter. There  is no credible emissions scenario under which global mean  temperature would peak and then start to decline by 2100.  
  

What to say about this? Is the Royal Society joking or not? Well, let us take a look at its Climate Change Controversies, A Simple Guide, in particular how the Society counters what it presents as Misleading Argument 5: "Global warming computer models which predict the

future climate are unreliable":

• Modern climate models have become increasingly accurate in reproducing how the real climate 'works'. They are based on our understanding of basic scientific principles, observations of the climate and our understanding of how it functions.
• Using this understanding of the climate system, scientists are then able to project what is likely to happen in the future, based on various assumptions about human activities.
  
• It is important to note that computer models cannot exactly predict the future, since there are so many unknowns concerning what might happen.  
• While climate models are now able to reproduce past and present changes in the global climate rather well, they are not, as yet, sufficiently well-developed to project accurately all the detail of the impacts we might see at regional or local levels. 
  
• They do, however, give us a reliable guide to the direction of future climate change.  The reliability also continues to be improved through the use of new techniques and technologies.  
  

These statements seem to support rather than refute Misleading Argument 5 stating that climate models are unreliable. How is it possible that the Royal Society without blushing can present nonsense like: Modern climate models have become increasingly accurate...the reliability also continues to be improved...they do, however, give us a reliable guide to the direction of future climate change... 

Notice in particular the Misleading Statement: the climate models are not, as yet, sufficiently well-developed to project accurately all the detail of the impacts we might see at regional or local levels... intended to give the impression that global climate models are accurate, without in fact saying anything. Clever or just stupid? Which is the audience addressed by the Royal Society?

The Royal Society, in good company with the Royal Swedish Academy of Sciences, seems to uncritically repeat whatever the political organ IPCC says, but why?