tisdag 30 september 2014

En invariansprincip

Bland oss som inte sympatiserar med Sverigedemokraterna talas det i dessa dagar mycket om hur vi bör förhålla oss till dem. Är de rumsrena? Bör de behandlas som vilket annat riksdagsparti som helst? Eller är deras åsikter av sådant slag att vi inte bör ta i dem ens med tång?

Min avsikt med denna bloggpost är inte att sätta ned foten i dessa frågor. Istället har jag en synpunkt på vad för slags övervägande jag tycker bör (respektive inte bör) beaktas när man besvarar dem. Ofta hörs i dessa dagar synpunkter i stil med "Nu när de faktiskt har fått nästan 13% i ett riksdagsval (och till och med besitter posten som riksdagens andre vice talman) är det hög tid att behandla dem med respekt och som vilket annat parti som helst". En sådan synpunkt är enligt min mening irrelevant.

Inom fysiken talar man om invariansprinciper eller konserveringslagar, vilka anger hur någon viss kvantitet under vissa omständigheter måste förbli konstant: kända exempel är energikonserveringsprincipen och lagen om rörelsemängdens bevarande. I analogi med detta vill jag (dock fullt medveten om att analogin inte är perfekt, inte minst då jag överträder gränsen mellan fakta och värderingar) formulera följande politiska invariansprincip:
    Givet den politik ett parti för, dess ideologi, och de åsikter som deras företrädare uttrycker, så är den respekt och den rumsrenhet vi bör tillerkänna partiet konstant, oberoende av hur många anhängare det har.
Antag, hypotetiskt, att jag får ta del av partiprogram, ideologiska dokument, och yttranden och utspel från företrädare för två för mig tidigare okända partier A och B. Antag att jag på basis av denna information känner att de båda partierna står för lika förkastliga ideologier och åsikter, och att båda ligger strax bortom min gräns för vad jag finner respektabelt, rumsrent och något som det går an att förhandla med. Antag att jag sedan får reda på att A-partiet har stöd av 0,001% av den svenska väljarkåren, medan B-partiet har stöd av nära 13%. Om jag under de omständigheterna bestämmer mig för att upprätthålla min hårdföra linje mot A-partiet, medan jag gentemot B-partiet mjuknar och säger att "ett sådant parti måste man ju ändå respektera och tala med som med vilket annat som helst, allt annat vore ju odemokratiskt", då gör jag mig till en principlös ynkrygg och en efter-vinden-kappvändare.1 Lite grand som om jag vore högstadielärare och vände mig till klassen med följande besked:
    Hallå där Kalle, tag genast av dig din keps märkt Ljungskile SK, vi har faktiskt kepsförbud här i klassrumet! Lite ordning och reda får det väl ändå vara! Ni tiotalet ynglingar som sitter där med Hammarby-kepsar får däremot behålla dem på, ty ni representerar en så utbredd uppfattning att den måste respekteras.

Fotnot

1) Min invariansprincip är ett ideal. Jag vill inte vara så självförhärligande att jag påstår att jag aldrig någonsin skulle förfalla till kappvänderi. Det är naturligtvis härligt att försöka föreställa sig att man i Nazityskland skulle uppträda lika rakryggat som August Landmesser, men hur jag skulle agera under sådana extrema omständigheter (måtte jag aldrig utsättas för dem!) kan jag inte veta säkert.

söndag 28 september 2014

Hur vi kan undvika att lura oss själva

Kom och lyssna till mitt föredrag
    Hur vi kan undvika att lura oss själva:
    matematisk statistik som en korrigering av
    felkalibreringar i den mänskliga hjärnan
    1
på onsdag i nästa vecka klockan 12.00! Lokal är Sällskapsrum Birgit Thilander i Academicum, Medicinaregatan 3 i Göteborg.

Klicka på bilden för en större version!

Fotnot

1) Feg som jag är vågade jag inte använda Johan Wästlunds förslag till alternativ (och i stort sett synonym, men lite spänstigare) rubrik:
    Varför jag har rätt hela tiden och hur ni lagar era hjärnor

fredag 26 september 2014

tisdag 23 september 2014

Högskolan - ett orimligt krav på skattebetalarna?

På DN Debatt idag skriver professor Bo Becker vid Handelshögskolan i Stockholm om den brain gain som USA och Australien erhåller genom att deras främsta universitet attraherar utländska toppstudenter, och han oroar sig över hur svenska lärosäten skall klara konkurrensen. Hans svar är...

TERMINSAVGIFTER!

Ja, ni läste rätt: terminsavgifter! Det är med terminsavgifter som vi skall attrahera utländska studenter.

För att nu vara lite rättvis mot Becker så är det nog inte terminsavgifterna i sig som han tror skall attrahera de utländska studenterna, utan hög kvalitet i utbildningen.1 Och kvalitet kostar. Becker frågar retoriskt hur vi skall ha råd med hög kvalitet i universitet och högskolor "utan att ställa orimliga krav på skattebetalarna". Mitt svar är enkelt: den högre utbildningen skall även fortsättningsvis vara skattefinansierad. Detta är inte ett "orimligt krav på skattebetalarna", utan ett högst rimligt sådant, som vi hittills varit överens om (frånsett måhända en och annan medlem i Skattebetalarnas förening - huruvida Becker har medlemskort där vill jag inte spekulera över).

Det vore väldigt olyckligt om vi började rucka på principen att högre utbildning skall finansieras via skattsedeln och alltså vara gratis för studenten.2 Becker talar visserligen om att gå försiktigt fram: vi bör börja med ett tak på "10.000 kronor per termin", och "de lärosäten som vill får ha lägre avgifter" (åh tack snälla snälla schysstaste hygglo-Becker för att du så generöst vill ge oss den möjligheten!). Icke desto mindre skulle hans förslag innebära att vi slår in en kil mot det gamla systemet, tillkommet för att ge våra ungdomar rättvis tillgång till högre utbildning, så att det inte blir en exklusiv förmån för dem som kommer från välbärgade och studievana hemmiljöer.

Det finns även annat i Beckers framställning jag inte gillar. Han talar t.ex. om att det behövs incitament (eller, som han formulerar det, en "morot") för att vi på universiteten skall göra ett bra jobb, och han ser avgifterna som ett ekonomiskt sådant. Well, I've got news for you, Bo Becker: vi har redan gott om incitament. Framför allt består incitamenten i den yrkesstolthet som vi universitetslärare känner och som driver oss att göra vårt bästa (undantag finns givetvis, men huruvida Becker hör till dem vill jag inte spekulera över). Vi har till och med ekonomiska incitament, i fall att nu Becker har fått för sig att det endast är sådana som fungerar, ty de skattemedel vi får till våra utbildningar är inte ovillkorade. Det vore också bra om Becker satte sig in i vad den psykologiska forskningen säger om vad ekonomiska incitament gör med våra drivkrafter.

Fotnoter

1) Att kvalitetsproblem föreligger här och var i det svenska universitetsväsendet vill jag inte bestrida, men Beckers argumentation för att så är fallet är beklämmande svag. Han skriver att "inget svenskt universitet utom Karolinska institutet rankas numera bland världens topp 100", men detta är inte en indikation på att kvaliteten i svensk högre utbildning är låg, utan att den är hög.

Eftersom den beckerska argumentationen på denna punkt är vanligt förekommande (jag har hört den från både professorer och rektorer) tar jag mig friheten att förklara hur det ligger till. Världens befolkning är i runda slängar 7 miljarder, vilket betyder att om de 100 främsta universiteten i världen vore jämnt utspridda skulle det finnas ett per 70 miljoner invånare. Ett land som Sverige, med cirka 9,5 miljoner invånare, skulle väntas ha 0,14 sådana universitet. Nu är siffran istället 1 enligt vilken ranking det nu är som Becker stödjer sig på (han anger inte sin källa), vilket rimligtvis får anses vara ett gott utfall. (Det finns gott om universitetsrankingar, och utfallen varierar, men det kan i sammanhanget vara värt att nämna att enligt två av de mest välkända - såväl Shanghairankingen som (den tidigare i år här på bloggen omnämnda) Times Higher Education-rankingen - har vi inte mindre än 3 universitet på topp 100, vilket är en fantastiskt fin siffra med tanke på vilket litet land vi är!)

2) Noga taget så har vi redan börjat rucka på den saken, genom den avgiftsbeläggning för utomeuropeiska studenter som infördes 2011. Men denna bör tas bort, snarare än att vi som Becker föreslår fortsätter längre in på denna olyckliga väg.

fredag 19 september 2014

Superintelligence odds and ends: index page

Nick Bostrom's Superintelligence: Paths, Dangers, Strategies is such an important, interesting and thought-provoking book that it has taken me several blog posts to comment on it. Here, to help the reader find her way in my writings on this topic, I provide a list of links to these posts, plus a few others.

After two initial mentions of Bostrom's book when it had just been released in July this year... ...I posted my review of the book on September 10: I then quickly followed up my review with a sequence of five blog posts with further comments on the book, under the joint heading Superintelligence odds and ends: That exhausts, for the time being, my list of blog posts devoted explicitly to Bostrom's Superintelligence, but I have a large number of further blog posts that treat the same or closely related topics as his book, such as the following: For those readers who, due to their weak or non-existent knowledge of Swedish, feel prevented from reading some of these posts, perhaps Google Translate can provide some assistance. Its translations are neither beautiful, nor perfectly accurate, but in many cases they can help readers identify the gist of a blog post.

torsdag 18 september 2014

Superintelligence odds and ends V: What is an important research accomplishment?

My review of Nick Bostrom's important book Superintelligence: Paths, Dangers, Strategies appeared first in Axess 6/2014, and then, in English translation, in a blog post here on September 10. The present blog post is the last in a series of five in which I offer various additional comments on the book (here is an index page for the series).

*

The following two-sentence paragraph, which opens Chapter 15 of Superintelligence, is likely to anger many of my mathematician colleagues.
    A colleague of mine likes to point out that a Fields Medal (the highest honor in mathematics) indicates two things about the recipient: that he was capable of accomplishing something important, and that he didn't. Though harsh, the remark hints at a truth.

At this point, I urge the angry mathematicians reading this not to stop reading, and not to conclude that Bostrom is a jackass and/or a moron unworthy of further attention. There is more to his "harsh" position than first meets the eye. And less, because to those of us who continue reading, it quickly becomes clear that he is not saying that the mathematical results discovered by some or all Fields Medalists are unimportant. Instead, he has two interesting and original points to make about research in mathematics (and in other disciplines), one general, and one more concrete. The general point is that the value of the discovery of a result is not equal to the value of the result itself, but rather the value of how much earlier we, as a consequence of the discovery, learned the result compared to what would have been the case without that particular discovery.1 The more concrete point is that even if deep and ground-breaking results in pure mathematics are valuable in themselves (as opposed to whatever scientific or engineering applications may eventually grow out of them), then there may be a vastly more efficient way to advance mathematics (compared to what the typical Fields Medalist engages in), namely to contribute to the development of AI or of transhumanistic technologies for enhancement of human cognitive capacities, in order for the next generation of mathematicians (made of flesh-and-blood or of silicon) to be in a vastly better position to make even deeper and even more ground-breaking discoveries. Here's how Bostrom explains his position:
    Think of a "discovery" as an act that moves the arrival of information from a later point in time to an earlier time. The discovery's value does not equal the value of the information discovered but rather the value of having the information available earlier than it otherwise would have been. A scientist or a mathematician may show great skill by being the first to find a solution that has eluded many others; yet if the problem would soon have been solved anyway, then the work probably has not much benefited the world. There are cases in which having a solution even slightly sooner is immensely valuable, but this is more plausible when the solution is immediately put to use, either by being deployed for some practical end or serving as the foundation to further theoretical work. And in the latter case [...] there is great value in obtaining the solution slightly sooner only if the further work it enables is itself both important and urgent.

    The question, then, is [...] whether it was important that the medalist enabled the publication of the result to occur at an earlier date. The value of this temporal transport should be compared to the value that a world-class mathematical mind could have generated by working on something else. At least in some cases, the Fields Medal might indicate a life spent solving the wrong problem - perhaps a problem whose allure consisted primarily in being famously difficult to solve.

    Similar barbs could be directed at other fields, such as academic philosophy. Philosophy covers some problems that are relevant to existential risk mitigation - we encountered several in this book. Yet there are also subfields within philosophy that have no apparent link to existential risk or indeed any practical concern. As with pure mathematics, some of the problems that philosophy studies might be regarded as intrinsically important, in the sense that humans have reason to care about them independently of any practical application. The fundamental nature of reality, for instance, might be worth knowing about, for its own sake. The world would arguably be less glorious if nobody studied metaphysics, cosmology, or string theory. However, the dawning prospect of an intelligence explosion shines a new light on this ancient quest for wisdom.

    The outlook now suggests that philosophic progress can be maximized via an indirect path rather than by immediate philosophizing. One of the many tasks on which superintelligence (or even just moderately enhanced human intelligence) would outperform the current cast of thinkers is in answering fundamental questions in science and philosophy. This reflection suggests a strategy of deferred gratification. We could postpone work on some of the eternal questions for a little while, delegating that task to our hopefully more competent successors - in order to focus our own attention on a more pressing challenge: increasing the chance that we will actually have competent successors. This would be high-impact philosophy and high-impact mathematics.

If this is not enough to calm down those readers feeling anger on behalf of mathematics and mathematicians, Bostrom furthermore offers the following conciliatory footnote:
    I am not suggesting that nobody should work on pure mathematics or philosophy. I am also not suggesting that these endeavors are especially wasteful compared to all the other dissipations of academia or society at large. It is probably very good that some people can devote themselves to the life of the mind and follow their intellectual curiosity wherever it leads, independent of any thought of utility or impact. The suggestion is that at the margin, some of the best minds might, upon realizing that their cognitive performance may become obsolete in the forseeable future, want to shift their attention to those theoretical problems for which it makes a difference whether we get the solution a little sooner.
The view of research priorities and the value of mathematical, philosophical and scientific progress that Bostrom offers in the above passages may seem provocative at first, but in fact it strikes me wise and balanced. Are there any aspects of this issue he has failed to take into account? Of course there are, but the question should be whether there are any such aspects that are sufficiently relevant to overthrow his conclusion. Here's the best one I can come up with for the moment:

Perhaps the main value of a mathematical discovery lies not in the result itself, but in the process leading up to the discovery, and perhaps it is important that the cognitive work is done by an ordinary human tather than an enhanced human or some super-AI. Well, a bit of enhancement is OK - many years of education, plus some caffeine - but anything much beyond that reduces the value of the discovery significantly.

Something along those lines. But, honestly, doesn't it sound arbitrary, artificial, and more than a little anthropochauvinistic? It is certainly not an argument with which the mathematical community can hope to convince tax payers to support research in mathematics. Perhaps some similar argument might work for music or for literature, as the audience might have a preference for songs or novels they know are written by ordinary humans rather than by some superintelligence.2 But the case is very different for mathematics, because the population of people who can appreciate and enjoy, say, Wiles' proof of Fermat's Last Theorem or Perelman's proof of the Poincaré conjecture, is very small and consists almost exclusively of professional mathematicians. So using the argument for mathematics comes very close to asking taxpayers to support mathematical research because it is enjoyable to mathematicians.

The process-more-important-then-result objection fails to convince. All in all, I think that Bostrom's new perspective on the value of research findings, although of course not the only valid viewpoint, is very much worth putting on the table when discussing priorities regarding which research areas to fund.3

Footnotes

1) This notion of the value of a discovery is not entirely unproblematic, however. Consider the case of my friends Svante Linusson and Johan Wästlund, and their their solution to the famous problem of proving Parisi's conjecture. On the very same day that they announced their result, another group, consisting of Chandra Nair, Balaji Prabhakar and Mayank Sharma, announced that they had achieved the same thing (using a different approach). For the sake of the argument, let us make the following simplifying assumptions:
    (a) the two works and their timings were independent (almost true),

    (b) there is no extra value in having the two different proofs of the result compared to having just one (plain false),

    (c) without the two works, it would have taken another ten years for the scientific community to come up with a proof of Parisi's conjecture (pure speculation on my part).

With these assumptions, Bostrom's way of attaching value to research discoveries has some strange consequences. The work of Linusson and Wästlund is deemed worthless (because in view of the Nair-Prabhakar-Sharma paper, they did not accelerate the proof of Parisi's conjecture). Similarly and symmetrically, the Nair-Prabhakar-Sharma paper is deemed worthless. Yet, Bostrom has to accept that the two papers, taken together, are valuable, because they gave us proof of Parisi's conjecture ten years earlier than what would have been the case without them.

Such superadditivity of values is not unusual. A hot dog on its own may be worthless to me, and the same may go for a bun, but together they constitute a highly delicious and valuable meal. But the Linusson-Wästlund and the Nair-Prabhakar-Sharma papers, exhibiting the same superadditivity, still does not fit the hot-dog-and-bun pattern, because unlike the hot dog and the bun, each of the papers contains, on its own, the whole thing we value (the early arrival of the proof of Parisi's conjecture). Strange.

2) And chess. As a chess amateur, I enjoy studying the games of world champions and other grandmasters. For more than a decade, there have been computer programs that play clearly better chess than the very best human chess players. And yet, I do not find even remotely the same thrill in studying games between these programs, compared to those played between humans.

3) It will be interesting to see how this statement will be received by my friends and colleagues in the mathematics community. My hope and my belief is that the position I'm endorsing will be appreciated for its nuances and recognized as a point of view that merits discussion. But I am not certain about this. If worst comes to worst, my statement will be widely condemned and perhaps even mark the end of a 15-or-so years period during which I have received a steady stream of invitations and requests to take on various positions of trust in which I am expected to defend the interests of research mathematics. I would not welcome such a scenario, but I much prefer it to one in which I refrain from speaking openly on important issues.

tisdag 16 september 2014

Superintelligence odds and ends IV: Geniuses working on the control problem

My review of Nick Bostrom's important book Superintelligence: Paths, Dangers, Strategies appeared first in Axess 6/2014, and then, in English translation, in a blog post here on September 10. The present blog post is the fourth in a series of five in which I offer various additional comments on the book (here is an index page for the series).

*

The topic of Bostrom's Superintelligence is dead serious: the author believes the survival and future of humanity is at stake, and he may well be right. He treats the topic with utmost seriousness. Yet, his subtle sense of humor surfaces from time to time, diverting nothing from his serious intent, but providing bits of enjoyment for the reader. Here I wish to draw attention to a footnote which I consider a particularly striking example of Bostrom's way of exhibiting a slightly dry humor at the same time as he means every word he writes. What I have in mind is Footnote 10 in the book's Chapter 14, p 236. The context is a discussion on whether it improves or worsens the odds of a favorable outcome of an AI breakthrough with a fast takeoff (a.k.a. the Singularity) if, prior to that, we have performed transhumanistic cognitive enhancement of humans. As usual, there are pros and cons. Among the pros, Bostrom suggests that improved cognitive skills may make it easier for individual researchers as well as society as a whole to recognize the crucial importance of what he calls the control problem, i.e., the problem of how to turn an intelligence explosion into a controlled detonation with consequences that are in line with human values and favorable to humanity. And here's the footnote:
    Anecdotally, it appears those currently seriously interested in the control problem are disproportionately sampled from one extreme end of the intelligence distribution, though there could be alternative explanations of this impression. If the field becomes fashionable, it will undoubtedly be flooded with mediocrities and cranks.
The community of researchers currently working seriously on the control problem is very small - if their head count even reaches the realm of two-digit numbers, it is not by much. Bostrom is one of its two most well-known members; the other is Eliezer Yudkowsky. I'd judge both of them to have cognitive capacities fairly far into the high end of "the intelligence distribution" (and I imagine myself to be in a reasonable position to calibrate - as a research mathematician, I know a fair number of people (including Fields Medalists) in various parts of that high end). Bostrom is undoubtedly aware of his own unusual talents, as well as of the strong social norm saying that one should not talk about one's own high intelligence, yet his devotion to honest unbisaed matter-of-fact presentation of what he perceives as the truth (always with uncertainty bars) leads him in this case to override the social norm.

I like that kind of honesty, even though it carries with it a nonnegligible risk of antagonizing others. Yudkowsky, in fact, has been known for going far - much further than Bostrom does here - in speaking openly about his own cognitive talents. And he does receive a good deal of shit for that, such as in Alexander Kruels's recent blogpost devoted to what he considers to be "Yudkowsky’s narcissistic tendencies".

All this makes the footnote multi-layered in a humorous kind of way. I also think the footnote's final sentence about what happens "if the field becomes fashionable" carries with it a nice touch of humor. Bostrom has a farily extreme propensity to question premises and conclusions, he is well aware of this, and I do think this last sentence (which points out a downside to what is clearly a main purpose of the book - namely to draw attention to the control problem) is written with a wink to that propensity.