onsdag 29 februari 2012

Fred Singer Believes in Backradiation

Fred Singer states in the American Thinker under the title Climate Deniers Are Giving Us Skeptics a Bad Name

  • Now let me turn to the deniers. One of their favorite arguments is that the greenhouse effect does not exist at all because it violates the Second Law of Thermodynamics -- i.e., one cannot transfer energy from a cold atmosphere to a warmer surface. It is surprising that this simplistic argument is used by physicists, and even by professors who teach thermodynamics. One can show them data of downwelling infrared radiation from CO2, water vapor, and clouds, which clearly impinge on the surface. But their minds are closed to any such evidence.
Transfer of heat energy from a cold atmosphere to a warmer surface is the same as backradiation, and since I am a firm denier of backradiation, there is a high risk that Fred is aiming his attack on some-one like me, probably directly addressing my simple person.

OK, so I am giving skeptics a bad name? What have I done to deserve this evaluation?

Well, I have given a new proof of Planck's radiation law, which is closer to physics than Planck's original derivation, because it does not rely on statistics, understanding that statistics is not physics but just statistics.

My proof shows that backradiation is physically impossible because it is unstable and cannot be realized by spontaneous physics, as an expression of the 2nd law.

I don't think Fred has read my proof, maybe not even Planck's original one. I ask him to do so, and then compare the merits of the proofs, and after that possibly change his statement that I am giving him a bad name. How about that Fred?

And Fred, isn't it important also for skeptics to obey the 2nd Law? Isn't the 2nd Law more than a simplistic argument which one can discard without much thought?

I expand the argument in


tisdag 28 februari 2012

The Empty Postulate of CO2 Alarmism


CO2 climate alarmism is based on two basic postulates concerning the effect of doubled concentration of atmospheric CO2 (compared to pre-industrial time):
  1. Radiative forcing of 4 W/m2
  2. Global heating of 1 C from radiative forcing of 4 W/m2.
Let us see how are these postulates motivated: 1. is supposed to follow from measurements of spectra like the above from "Atmospheric Radiation", Goody (1989) observed for clear skies over the Gulf of Mexico, April 23, 1969. After Conrath et al (1970).

The idea is that the dip in the spectrum between 14 - 16 microns reflects the absorption and emission of atmospheric CO2, and that doubled CO2 will cause a certain widening of the dip which is translated to so called "radiative forcing" of 4 W/m2 according to Planck-Stefan-Boltzmann's radiation law (SB).

The so obtained radiative forcing of 4 W/m2 is then translated to 1 C of global heating by another application of SB which is the rationale of 2.

We see that both 1. and 2. originate from a spectrum which its translated first to radiative forcing and then to global heating with both steps relying on SB.

Is this a correct scientific mathematical argument? Is it so clear how to go from measured spectrum to estimated spectrum for doubled CO2 to radiative forcing to global warming?

No it is not at all clear, because SB describes radiation from a body into a surrounding of 0 K.

The Earth plus atmosphere radiates into a surrounding of about 3 K, and so SB may be applicable to the whole system, but SB does not in the same way describe the exchange of heat energy between the Earth surface and the atmosphere and this is where the radiative forcing is supposed to change global climate.

The net result is that the climate sensitivity of 1 C global warming from doubled CO2, cannot be viewed to describe any scientific reality, but is instead used simply as a definition or agreement. This is evidenced by the fact that all scientists are supposed to agree on the 1 C, from skeptics to alarmists. An they all do agree on the 1 C.

If you say that you the 1 C is not valid, you will meet the response that this it is not possible to say so, because all scientists agree on the 1 C and you cannot question a scientific agreement which is a definition. Or if you do, then you are silly.

To question that there are 100 centimeters on a meter will meet the same laughs as questioning the 1 C from doubled CO2.

But a definition has no scientific content and says nothing about reality. In particular it cannot be taken as point of departure for feedbacks, which is nevertheless done by both alarmists and skeptics.

Alarmists start with 1 C and jack it up to 3 C by positive feedback.

Skeptics start with 1 C and take it down to 0.5 C by negative feedback.

But a real skeptic would not start with 1 C, because it is not science. A real skeptic would seek to directly assess climate sensitivity, by measurements. Doing so indicates a climate sensitivity smaller than 0.5 C, thus so small that it cannot be identified.

The net result is that the basic postulate of climate alarmism of a climate sensitivity of 1 C is a definition empty of scientific content and as such of no value. Both skeptics and alarmists should be able to agree on this.

Also Judy Curry has now understood the emptiness of IPCC:
  • The IPCC might have outlived its usefulness. Let’s see what the next assessment report comes up with. But we are getting diminishing returns from these assessments, and they take up an enormous amount of scientists’ time.

tisdag 21 februari 2012

Can Roy Spencer Describe the "Greenhouse Effect"?


There is a new post on the Roy Spencer's description of the "Greenhouse Effect" at The World as Computation.

The comments show again how widely spread is the idea of "backradiation" although it is nowhere described in physics literature, not even on Wikipedia. Notable is also the complete absence of physicists in the debate, leaving room for all sorts of free inventions such as IR-photons busy traveling around the universe carrying little units of heat energy which they deliver to everybody without asking anything, in particular not about the temperature of the recipient.

But radiative heat transfer is a collective phenomenon of resonance between bodies in radiative contact, where the resonance is only causing heating in bodies with low temperature as an expression of the 2nd law as proved in Mathematical Physics of Blackbody Radiation.

söndag 19 februari 2012

Why Is Roy Spencer Not Serious?


Roy Spencer returns to the "The Issue of Backradiation" in More Musings from the Greenhouse with statements like:
  • The existence of this “back radiation” is disputed by some people because of two seemingly counter-intuitive features.
  • Imagine two plates at two different temperatures facing one another. Let’s say one plate is at 100 deg. C and the other is at 0 deg. C.
  • But now imagine that the cooler plate is nearly the same temperature (99 deg. C) as the hotter plate (100 deg. C). It will be obvious to most people that the net flow of IR energy from the 100 deg. C plate to the slightly cooler plate will be at a slower rate than it was before.
  • But why should that be? In both cases the 100 deg. C plate is emitting IR at the same rate, yet the NET flow of IR is reduced if the cooler plate is not as cold.
When I ask in a comment what the scientific evidence Roy has for his proclamation that "in both cases the 100 deg. C plate is emitting IR at the same rate", I get the following answer:
  • Yes, Claes you found me out. I have nefarious motives for using certain terminology. It’s simply to annoy you.
This is more than musing, it is nefariously amusing, with nefariously meaning "extremely wicked" or "extremely morally bad in principle or practice".

When I ask Roy to get serious, I get no response.

I ask him here again to get serious and answer my question: What is the scientific evidence Roy, supporting your proposition that emission of IR energy is independent of the surrounding temperature? You can reply as a comment to this post. I am serious.

PS Follow the debate as comments to Roy's post, and see how backradiation is deconstructed into the wardrobe of scientific ghosts.


How to Understand Climate Debate


Two basic issues dominate the climate debate:
  1. For CO2 emitters to prove that CO2 has no significant effect.
  2. For CO2 alarmists to prove that CO2 has significant effect.
We may compare with a legal process:
  1. For the accused to prove innocence.
  2. For the prosecutor to prove that the accused is guilty.
We understand that 2. is a necessary requirement for the prosecutor to win the process. If 2. is missing, the issue 1. does not come up.

The situation is the same in climate politics: If 2. is missing, then 1. does not come up. And the fact is that 2. is missing. There is no scientific evidence that CO2 has a significant effect.

But clever CO2 alarmists are turning the debate around to 1. instead of 2. asking CO2 emitters to prove that CO2 has no significant effect. Once one understands this trick also the climate debate becomes understandable and more managable.

lördag 18 februari 2012

What If They Are Wrong?



Judy Curry dares to report on her blog the questions posed on Mike Stopas blog:
  • Suppose it turns out that CO2 has essentially nothing to do with the earth’s climate. How will the history of this colossal mistake be written?
  • If someone were, for instance, to come up with indisputable evidence tomorrow that CO2 has essentially no impact on earth’s climate, could the world accept it?
  • With the development of frakking and the concomitant extension of carbon based energy resources hundreds of years into the future, what would they do with all the windmills?
  • Well, the truth of this issue should be apparent within about 15 years…at which point we may be allowed to buy incandescent light bulbs again.
Judy does not know what to say but says something anyway:
  • So, is a scientific revolution underway and/or needed for climate change?
  • I don’t know, it is certainly possible that the existing paradigm can be embellished as our understanding of the complex climate system increases.
  • However, as scientists, we need to acknowledge that the consensus needs to be continually challenged, and not dismiss anyone who challenges the consensus as ‘deniers.’
  • I think Stopa is about right when he says: Well, the truth of this issue should be apparent within about 15 years.
What Judy says is that "it is certainly possible" that CO2 has no effect on climate. This statement is in contradiction with the current consensus that "it is certain that CO2 has an effect on climate". Judy probably means by "certainly possible" that chances are somewhere between 25 and 50% that CO2 has no (detectable) effect.

So Judy challenges consensus, but does not want to be dismissed as "denier". Welcome then Judy to "the challengers".

As challenger, we do not have to wait 15 years for evidence of zero effect. We can right now scrutinize the existing scientific evidence that CO2 has an effect. Isn't that what we should do Judy? What is this scientific evidence in fact, Judy?



fredag 17 februari 2012

Numerical Analysis vs Mathematics at KTH


The President of KTH Peter Gudmundson decided on Feb 15 to move Numerical Analysis NA from computer science to mathematics with motivation:
  • far-reaching cooperation between NA and math
  • joint Ph D program in applied math
  • joint new Bachelors program in Simulation Technology
and objective:
  • integration of NA and math in basic engineering education.
The President starts from a fiction (cooperation) and ends with a fiction (integration of NA as computational math with math as traditional analytical calculus and linear algebra).

The intention of the President is admirable but the goal will be missed, in the same way it was missed at Chalmers. The net result of the integration will be:
  • math courses will remain the same as before integration
  • NA courses will simply disappear, because they have already collapsed to trivialities.
This will be the end of NA at KTH following the same fate as NA at Chalmers.

A successful integration requires non-trivial modern uptodate NA. This is offered by BodyandSoul Mathematical Simulation Technology MST.

But the President killed MST last fall in a media smear campaign. Integration of MST with math would transform math substantially, and this is why the math department opposes MST. The math dept is only capable of delivering the same calculus as always, and views MST with fear, for good reasons.

The current plan for the new Bachelors program in Simulation Technology is apparently standard calculus + standard trivial NA. It is not correct vs the students to invite to a new modern program and then simply serve old dishes which do not taste. The students will not be happy when understanding and the crucial recruitment will suffer. In fact, the program is not sold at all, as if the expectation is to get 0 applicants, in which case nothing will have to be delivered and everybody will be happy, at KTH.

Is the President interested in now seeing realities rather than fiction?

I ask him to comment this post, if he has anything to say, and will report, if there is anything to report on.


torsdag 16 februari 2012

The Education Index

The previous post made the observation that the ibook as interactive textbook opens to a new form of education, which can be termed iducation characterized by active learning combined with passive teaching.

The spectrum of education can be described as follows:
  1. active learning + passive teaching = iducation = motivated students + few lectures
  2. passive learning + active teaching = non-motivated students + many lectures
  3. active learning + active teaching = motivated students + many lectures,
  4. passive learning + passive teaching = non-motivated students + few lectures.
This leads into the Education Index EI defined as
  • EI = Learning Result/Teaching Cost = Course Grade per Euro ,
which is something a Minister of Education understands and is interested in knowing in order to properly allocate resources.

Let us compare the EI for the above cases 1 - 4 covering the spectrum of education:
  1. EI = 10/1 = 10
  2. EI = 1/10 = 0.1
  3. EI = 10/10 = 1
  4. EI = 0.1/1 = 0.1
Swedish Minister of Education Jan Björklund prescribes a system with many lectures for which the EI is at most 1, to be compared with EI = 10 for iducation.

But is it true that iducation forms motivated students?

Yes, the iPad as educational toy is met with great enthusiasm by both children, teachers and parents. With the iPad kids will learn to read, write and count already in preschool, because they want to learn, and they want to learn because they are motivated, and they are motivated by the iPad. If you don't think this is true, give a child an iPad and see what happens!

And if you know to read, write and count, then you are ready for a university education, right after preschool!

Active Learning - Passive Teaching



There is a new post on Mathematical Simulation Technology about the new possibilities opened by the ibook as the interactive textbook, of
to be compared with the traditional educational canon of Active Teaching - Passive Learning.

onsdag 15 februari 2012

The Death of Numerical Analysis

Archimedes 212 BC: Don't disturb my circles.

When I started my studies in the mid 1960's, Numerical Analysis NA was emerging as a new academic discipline developed by mathematicians attracted by the new capabilities of the electronic computer.

New departments of NA were formed outside departments of mathematics, as NADA at KTH by Germund Dahlquist, at Chalmers by Heinz-Otto Kreiss followed by Owe Axelsson, and in Uppsala again by Kreiss, while my former supervisor Vidar Thomee introduced mathematical NA at the mathematics department at Chalmers.

NA boomed and gave birth to new departments of computer science.

After finishing my Ph D with Vidar Thomee at the mathematics department and a post doc at the University of Chicago, I joined NA at Chalmers and when Owe Axelsson left in 1981 I had the chance to take over after him, but also a chance to return to the math department. I chose math and Axel Ruhe took over NA.

In the early 1990s NA was incorporated by math at Chalmers and when Axel Ruhe left Chalmers 10 years later, the life of NA at Chalmers was over. Today only a few residues of NA remain, and NA courses are no longer taught; they were simply assimilated into math courses without leaving any trace since the math courses are the same as before the computer. NA was born from math into a life outside math and now returned to math to die, as if nothing ever happened.

The development is similar at other universities in Sweden: NA first boomed but then lost momentum as we entered into the information age of 21st century ultimately based on NA.
It seemed as if NA became so widely used that there was no longer any need for any NA education.

The pillar of the old NA empire, NADA at KTH, is now meeting the same fate by being moved from its home at computer science to a mathematics department untouched by the computer.

Dahlquist managed to keep NADA outside mathematics, which allowed NADA to grow but when Dahlquist passed away the momentum was lost, and when now NA is being captured by mathematics, it has to face the same reality as NA at Chalmers (and Lund, Linköping, Umeå...).

The same is happening at the University of Chicago, where NA flourished within the math department in the 1970-80s under Jim Douglas Jr and Todd Dupont, while today NA faces extinction within computer science and math is again pure math without any NA.

Why is then NA dying when information science based on NA (like Googles search engine, imaging, simulation) is rocketing to the sky? If it is not eaten by math, computer science cleans the table.

When I look at the NA courses of today at NADA I see courses which are basically the same as those I met as an undergraduate almost 50 years ago: a bit of interpolation, Dahlquist stability and Gaussian elimination.

I see a petrified NA which is no longer fit for survival in the fierce competition of resources and students at the university of today, between math and computer science.

Old NA is dead and New NA is jet to be born, outside or inside mathematics departments.

Mathematics departments are in desperate need of revitalization by computational mathematics, but it seems that this hole cannot be filled with Old NA.

What may then New NA be? My (partial) answer is Mathematical Simulation Technology, but there are many other (possible) answers...

Test: Alive or Dead?

NA at KTH is in charge of the new Bachelors program in Simulation Technology scheduled to start in the Fall. This week NA will decide if this plan will be followed or the if the program will be shut down. Application opens March 15 and ends April 15. No publicity for the program has been made since the first announcement on Dec 1, 2011.

If NA is capable of upgrading to meet the requirements of the new program, then NA still has some life.

If NA decides to shut down the program, then NA is already dead.

I will report on the status as soon as the decision is made public.


tisdag 14 februari 2012

The Death of the Text Book


Apple predicts in its announcement of iBook Author that the traditional printed textbook will soon be replaced by the interactive ebook or ibook, because
  • textbooks are static
  • textbooks are heavy
  • textbooks are expensive,
while
  • ibooks are dynamic
  • ibooks have no weight
  • ibooks are cheap.
The argument is pretty convincing and the change is already taking place. In fact, even before the ibook students felt the change was coming and refused to buy all the expensive heavy text books listed in the course.

The traditional textbook served as the Bible presenting the accepted knowledge or scientific consensus of its time. The textbook was often written by authors without first hand knowledge as records of state of the art expressed in scientific journals by prime scientists, or in previous textbooks.

With Kuhn's terminology, "normal science" is what is written in the textbook, which thus serves as the Bible or canon.

The following questions present themselves:
  • What will be the effect of a Death of the Textbook?
  • Will "normal science" survive?
  • Is there a need of "normal science"?
  • What is the science of the ibook?
Lets us consider one specific example of major importance to all of us, climate science:

In climate science, the scientific consensus or "normal science" has been the science defined by IPCC in its textbooks, and this science is now falling apart as incorrect science identified by the scientific blogosphere, which is where the climate science is now being formed and which can be viewed as the ibook.

Another example is Calculus: No other area of science can count so many textbooks, all very similar and with very little change over 100 years. These textbooks have served to preserve mathematics education in a form untouched by the invention of the computer. But the ibook of Calculus is different and it is coming...my version is Mathematical Simulation Technology.

The shift from textbook to ibook thus can be expected to bring major shifts in both science and education. Interesting times are to come...


måndag 13 februari 2012

The Free Open Web-University

Wilhelm von Humboldt: True enjoyment comes from activity of the mind and exercise of the body; the two are ever united.

The free open university of Wilhelm von Humboldt of the 19th century, originating from the Enlightenment leading into the liberal arts education of our time, was in the second half of the 20th century replaced by the non-free closed university with the students locked into fixed educational programs characterized by ownership and control:
  • universities own and control educational programs
  • educational programs own and control courses, teachers and students
  • teachers own and control students in classrooms through text books
  • texts books own and control student minds by exercises and problems preparing for exam.
The program ownership generates income to the university, because students (or the state) pay and the control secures that students get prepared to pass exams, which is required to cash the money.

This non-free closed university is today troubled by decreasing enrollment and/or examination, and is now also challenged by the web-university as the modern form of Humboldt's free open university.

The web-university is run by the best scientists giving their science for free to free students owned by nobody. University bureaucrats have good reasons to be worried...

The Interactive Text Book

A classical math text book has limited interactivity.


Since the digital CD has replaced the analog vinyl record, it is natural to expect that the digital ebook will replace the analog printed book, and this is in fact already happening.

But how long will the CD and the ebook last?

The CD has already largely been replaced by iTunes and iTunes is now being replaced by Spotify and The Cloud: You no longer need to store your music yourself in your book-case or your computer, since it is better handled by The Cloud. With an Internet connection you can listen to any music you want, at a very small cost.

Will the ebook face the same fate? In particular, narrowing the question to the educational text book and learning, what will be the role and form of the text book in the education of tomorrow, in what can be called iducation?

I have met this question when trying to find the proper medium for math education as
  1. ebook,
  2. Apple iBook
  3. or something else?
Both 1 and 2 pose difficulties in conversion from pdf to ebook formats, and the lack of support of Latex in iBook Author, by Apple announced as a revolution in text books for education.

I have then been led into something else, into the idea of the interactive book as the new ibook
which I am now testing as Mathematics Simulation Technology on Wordpress.

The basic features of a ibook, making it different it from a standard ebook or printed book, are
  • an ibook is interactive
  • an ibook is connected to the web.
The idea of a classical book is to capture the mind of the reader and lock it into the book. Although the reader is supposed to be active, the reader cannot directly interact with the book, because the book is has no input window, only a loudspeaker for output.

Realizing that learning basically comes from trial-and-error in conjunction with interactive feed-back, it seems pretty clear that the interactive ibook with feed-back will be the best book for education.

The university of today seeks to lock the student into educational programs (to access the money coming with the student), which fits with the classical text book, but not with the ibook.

The idea of iBook Author is to open for authors to introduce interactive multimedia of the form offered on the web by HTML5.

One may the ask what iBook can offer which the web cannot?

torsdag 9 februari 2012

Royal Society and Royal Swedish Academy vs Science

Andrew Montford provides in Nullius in Verba The Royal Society and Climate Change:
  • a straightforward and unembellished chronology of the perversion not only of The Royal Society but of science itself, wherein the legitimate role of science as a powerful mode of inquiry is replaced by the pretence of science to a position of political authority
as expressed by Richard Lindzen in a foreword.

Since the Royal Swedish Academy of Sciences closely follows in the foot-steps of the Royal Society, the words by Lindzen also applies to its Swedish adherent.

The world now sees the alarmism of IPCC freezing away, because the science is cold and the scientific credibility supplied by the Royals has little weight. It seems that the Royals are aiming at the same influence in science as that of the King of Sweden in politics, as expressed by The Telegraph:
And if the RS is a joke, then so is the Royal Swedish Academy.

onsdag 8 februari 2012

Will KTH Simulation Technology Start 2012?

The KTH Bachelor program in Simulation Technology based on BodyandSoul scheduled to start in the Fall 2011 was stopped because of opposition to BodyandSoul at KTH.

The program is now scheduled to start in the Fall 2012 with BodyandSoul replaced by new material to be developed by people without connection to BodyandSoul. The "new material" is described as a "new view of mathematics" =
This leads to the contradiction of both using BS and not using BS. The program will thus both start and not start in the Fall 2012. The program is described in the program catalog as follows:
  • In education and entertainment the development of simulators, games and animation for film, web and mobiles, is based on increasingly advanced technology.
But contradictions are not allowed in mathematics, nor in reality.

Application to the new program is not yet open with applications due April 15.

No new information about the program has appeared on the web since December 1, 2011. No recruitment effort is visible.

KTH now has to choose (i) starting the program without new material, or (ii) closing down the program because of lack of new material. Bets are 50-50.

There is also a third possibility: If too few apply (because of lack of information) then the program will not start and the issue of new material or not will not arise. This may be a clever harmonious resolution following a principle of least resistance.

tisdag 7 februari 2012

The Truth about CO2 is Emerging


Media is now quickly switching from CO2 alarmism to criticism of the same, even in alarmist Germany:
related to the new book:
When will Swedish media also wake up? The game is over.


måndag 6 februari 2012

Swedish Minister of Education and KTH Put Ban on iLearning


1. Swedish Minister of Education Jan Björklund is threatening to put a ban on the use of iPads in learning to read and write for children in preschool and first years of school. These skills can only be allowed to be taught and learned using the traditional method of pencil + paper, says Björklund and threatens to send the School Inspection to any school using iLearning.

2. Several universities in Europe are effectively puttting a ban on scientific questioning of CO2 alarmism, see also Varenholt disinvited.

3. KTH has put a ban on my iLearning mathematics program BodyandSoul, in what has been termed KTH-Gate connecting to both 1. and 2.

We see in all three cases a narrow establishment in politics, science and eduction struggling to prevent (with inspiration from 1984) the new democratic iWave from reaching the people ....but the wave is strong...and it is coming...next year many children will learn to read and write and thus open the door to science using an iPad...

iLearning and iTeaching is Here!



Steve Jobs next goal after revolutionizing the music industry (iPod), telecom (iPhone), bookmarket (iBook), was to do something similar in education, and it is now here as iBook Author:
  • books in all subjects available to all students on the iPad.
This is what I have been dreaming of for many years and what I have been working on to realize in the BodyandSoul project. As a preparation for an iPad version of BS, I am collecting material and testing various modes of presentation on the Wordpress blog:
My plan is to come up with a finished version for various platforms including iPad in a couple of months.

It is clear that education will now quickly be reformed by the new possibilities of active iLearning and efficient iTeaching. Steve Jobs was right again!

The revolution has already started with an iPad to all children from preschool, to learn the "three r's" of reading, writing and arithmetics.


onsdag 1 februari 2012

Björklund Saboterar Lärande


Vår Utbildningsminister Jan Björklund läste igår i DN att Sollentuna kommun skall använda iPads istället för papper och penna i den inledande läsundervisningen för 6-7 åringar, och går i dagens DN till attack:
  • Jag blir oerhört provocerad när kommunala företrädare anser att böcker tillhör forntiden.
  • Man måste lära sig skriva för hand i skolan, det går inte att upphöra med det.
  • Man kan inte säga att bara för att det är svårare att skriva med penna så ska man sluta med det.
  • Jag blir rätt sorgsen när jag läser att man tänker så.
  • Även i framtiden måste man kunna både skriva och räkna.
  • Man kan inte alltid ha tillgång till en dator var man än befinner sig.
Både elever, lärare och föräldrar ser mycket positivt på de nya möjligheter till aktivt lärande som som digitala läromedel erbjuder.

Björklund saboterar med sin attack läsundervisningen i Sollentuna. Björklund förstör för elever, lärare och föräldrar. Björklund reagerar med reptilhjärna och har ingenting förstått.

Jag blir oerhört provocerad av att Sverige har en utbildningsminister som tillhör forntiden.

PS Mikael Damberg går till mot-attack på sin blogg. S har en unik chans att ta initiativet vad gäller skolans anpassning till det digitala samhället.