Interim report

So this is what happens when post lengths keep on getting longer while blogging opportunities hit a period of work-induced scarcity: Not much. What's more, the time allotted to blogging matters has been taken up by non-literary pursuits that will bear fruit soon, though not quite yet.

In the meantime, I thought I'd try a revolutionary new idea. Short blog posts! Here we go...

Item! Yes, I stood in line with the geeks and bought myself a copy of Mac OS X 10.4 a few hours ago so I could spend my Friday evening installing it. Luckily, I was doing it as a public service so I could blog it for you all, and not for my own enjoyment.

First impression: Amazing, and not even for its two most anticipated features. I have yet to use Spotlight (the search function that I fully expect will forever change my relationship to my data) because it will take hours to index my files. And I am underwhelmed by Dashboard, the undeniably pretty eyecandy that lets you drop widgety mini programs all over your screen, because you can.

So the gripes first. The default Dashboard widgets are not all that well thought out. There is a dictionary widget, but you can't copy the results of your search to the clipboard. This gets even sillier when you find out there is a stand-alone dictionary application outside Dashboard that does exactly the same thing, except that here you can copy/paste, and that ó unlike with the widget ó you can keep it open next to your other applications, where it is useful.

The same goes for the calculator: There is a castrated version in Dashboard, and then there is a newly beefed up standalone version that includes a brand new mode (standard, scientific and now programmer).

So I guess I don't "get" Dashboard, but no doubt before long there will be plenty of pretty things you can do with it. Come to think of it, my parents will probably love it. It is undeniably simple, conceptually. (And by that I'm not implying that my parents are.)

On to the cool things. iChat now lets you use the Jabber protocol, so you can set up an account that lets you talk to MSN Messenger people. The ability to show iChat buddies what song or radio station you are currently listening to is now built in, with the added clever "feature" that you can click directly through to the song in the iTunes store. Sneaky.

Safari's RSS-reading ability is no replacement for the power-user features I like in NetNewsWire 2, but again, it makes RSS look extremely simple, and I predict this will finally lead to mass-utilization of RSS as a content consumption method. My parents don't currently use RSS. They will after they get their hands on this browser.

This focus on RSS gets leveraged in a luscious new screen saver, where the feeds get visualized as floating text snippets. It's a new favourite for staring at.

Automator, a GUI for AppleScript, sort of, finally provides simplicity where I've always wished things were simpler in the Mac OS, and I think I will find myself using it very often. BBEdit just today was upgraded to support it, and in conjunction with Mail and Spotlight and smart folders I can already see some possibilities. For example, if I were to write a PHP script that lets people RSVP on the web and which then sends the information via email, I could use my inbox as a sophisticated triage system, and then use BBEdit's text-handling prowess to collate the responses into a single snug text file. However often I want.

But by far the most impressive thing in OS X is the return of the Graphing Calculator, now called Grapher. Apple hides it in the Utilities folder. It's a real jawdropper, and simply gorgeous to look at. It lets you do all manner of fancy mathematical manipulation on equations (integrate, differentiate, find roots) and then graph the results in rotating 3D. Far too much to recount, so I'll just leave you with a screen shot.

That wasn't exactly a short post, though, was it?

Talking to aliens, part III: Khinchin's constant source of wonder

The first part of this series surveyed previous attempts at contacting aliens. The second part proposed a base-neutral notation system for encoding messages to aliens.In the previous post in this series, we used continued fractions to represent any real number as a unique sequence of whole numbers. Such sequences are ideal for sending real numbers to aliens via radio signals. Now we have to choose which numbers to send them, out of an infinite choice of candidates.

I propose sending them two numbers. The first of these is the topic of this post: Khinchin's Constant, KK equals 2.685452001065306445... in base ten, or [2,1,2,5,1,1,2,1,1,3,10,...] as as the sequence corresponding to its continued fraction..

What is so special about K? It is one of the very few numbers capable of giving the driest of mathematical texts exclamatory hiccups. Mathworld prefaces its introduction to K with "Amazingly, ...". The bible of mathematical constants, the stolidly named Mathematical Constants, irrupts with "Here occurs one of the most astonishing facts in mathematics."

And yet K is virtually unknown to a wider audience. Pi, e, i, the golden mean and the square root of two are all well ensconced in high school maths curricula, though not K.

To explain why I think K would make a excellent number to send to aliens, it will help to first derive it. This is easy to do, because we've already done all the hard work exploring continued fractions in the previous post. Pick any random real number — you know, one that in base ten would look something like 14.7631809156... with additional random digits continuing off to the right ad nauseam. Then, represent this number as a continued fraction to find the unique sequence of whole numbers that corresponds to it, just as we've done before.

Now consider the first n terms of this sequence — that's n whole numbers, starting with 14,1,3,4,... in our example. To find the geometric mean of this group of n numbers, we multiply them together and then take the nth rootTo find the arithmetic mean of n numbers, you add them up and divide the sum by n. To find the geometric mean of n numbers, you multiply them and then take the nth root.. What Aleksandr Yakovlevich Khinchin proved in 1934 is that as you make n larger and larger, the geometric mean of the first n terms of this sequence converges on our constant K, 2.685452001065306445..., regardless of the number we picked.

That, to mathematicians, was an utterly unexpected result. There are two reasons why, I think. First, most of the numbers we use every day correspond to sequences whose geometric means evidently do not converge on K. All rational numbers correspond to finite sequences, and therefore cannot possibly lead to KThe rational number 1.23, for example, corresponds exactly to [1,4,2,1,6,1]. (To be tedious but thorough: What if the number lies between 0 and 1? Divide the number into 1 first to get the same sequence without a zero as the first term. This works because there is a unique, one-to-one correspondence between a number and that number divided into 1. Or else just ignore the zero and start from the second term.). Nor can any irrational number that is not transcendental, because its sequence always obeys a pattern: The Golden Mean, for example, corresponds to the sequence [1,1,1,1,1,1,1,1,1,...], whose geometric mean is obviously 1. The sequence corresponding to the square root of 8, [2,1,4,1,4,1,4,1,4,...] converges on 2, not K.

Second is that by inspection, we can easily construct an infinite number of infinite sequences (all of them having a unique correspondence to a real number) that clearly do not converge on K. [1,2,3,4,5,6,7,8,...]'s geometric mean will grow to infinity. [100,100,100,100,...]'s geometric mean is 100. [101,101,101,101,...]'s geometric mean is 101, and so on.

So how can Khinchin's proof hold? It can because there are innumerably more real numbers that do obey Khinchin than do not. And if I asked you to choose one real number at random (as I did), the probability that you'd pick one that does not obey Khinchin is zero. Zilch. GuaranteedIf you really want to know more about why that is so, the answer involves countable vs. uncountable sets and Georg Cantor..

A couple of things about K, then:

The fact that K exists hints at a special kind of order amid randomness. Even a "meaningless" transcendental number (of which there are far more than any other kind of number on the number line) at least obeys Khinchin. In a deep way, K says something about the distribution of real numbers on the number line (though don't ask me what exactly)This should also mean that you can get a likely idea of whether a number is truly random or not by checking if it appears to converge on K (provided you have enough terms to play with)..

K is derived entirely from within number theory. It has nothing to do with the physical world — not even with geometry (that I am aware of). Its derivation requires nothing more than a careful observation of the number line, which is accessible by anyone anywhere in the universe.

Although it's been proven that virtually every number obeys K, nobody has ever proved that a specific number obeys. Pi very much looks like it doesThe convergence of pi to K, foisted from Mathworld (see link).
, because we've crunched enough numbers and had a look, but we don't know for sure. A few other useful mathematical constants seem to as well. Still, most of our workaday numbers do not converge on K, no doubt for the same reason that these numbers caught our eye in the first place — they concern themselves with ordered systems.

All this is very interesting. But the real clincher as to why we should beam K to aliens — the thing about this number that takes it to a whole new level, as it were, is this: It would appear that Khinchin's Constant obeys itself. The geometric mean of the first n terms of K, [2,1,2,5,1,1,2,1,1,3,10,...], also converges on K, for as far as we've looked. Khinchin's Constant appears to be autological.

Take a look for yourself. Convinced?

What does this imply? It implies that the sequence of whole numbers that describes K, [2,1,2,5,1,1,2,1,1,3,10,...], is simultaneously described by KHofstadter illustrates the notion with this Escher print:

He goes on to posit that such systems are the basic building blocks for self-awareness in far more complex systems, such as ourselves.. It implies that K is infused with that essential quality of self-loopiness, of continuous folding back on itself, that Douglas Hofstadter identifies in Gˆdel, Escher, Bach as being at the core of all self-referential systems.

What K embodies, then, is the seemingly paradoxical ability to describe the properties of the system that produces it. It's akin to what happens when a mind contemplates the laws of physics that govern the mind. Our aliens, which for our purposes here are really just stand-ins for complex self-aware systems, would not escape noticing this analogy — and not just because we're giving them a massive hint by sending K as [2,1,2,5,1,1,2,1,1,3,10,...].

By including K in our message, then, we are broadcasting that we consider self-referential systems to be special — a prerequisite for the kind of complexity that underpins self-awareness, which in turn allows for the understanding of messages from outer space.

The second number I propose to send will take a completely different tack.

Things I learned today

The Fahrenheit scale only preceded the Celsius scale by a few decades, and both were invented in the early 1700s.

Daniel Gabriel Fahrenheit, a German physicist, originally planned to place the 0 degree point at the temperature at which an equal water/salt mixture froze, the 30 degree point at where water froze and the 90 degree point at the temperature of the human body.

Unfortunately, he got those measurements wrong, and the freezing point of water was later revised to 32 degrees and the temperature of the human body to 98.6 degrees.

Swedish astronomer Anders Celsius's temperature scale originally placed the 0 degree point where water boiled, and the 100 degree point where water froze. This seems a bit absurd given today's conventions, but there is a logic to it: In quotidian use we almost never deal with temperatures hotter than the boiling point of water, though we do deal with temperatures colder than the freezing point of water; it would make sense, therefore, to use the boiling point as a kind of natural origin, and measure out from there.

And if you're a Swede inventing a new temperature scale, the idea of measuring a quantity of cold rather than a quantity of heat is not all that preposterous, certainly not if you've just recently been subjected to a Swedish winter.

Had Celsius's system not been tampered with, 76 (orthodox) degrees celsius would today correspond to 76 degrees fahrenheit, and we'd all assign that temperature some magical "ideal" quality, seeing how the value would be naturally endorsed by both scales. CNN's weather forecasts would use a special graphic to highlight 76-degree days.

Instead, in real life, both scales "endorse" -40 degrees. What happened? Sweden's most famous scientist ever, Carl Linnaeus, was heavily into plants, and since these tend to die around where water freezes, he felt this point was a more natural zero point. So he switched the temperature points around soon after Celsius died, in 1744.

This proved to be a good idea, in the long run. The concept of a quantity of heat would prove far more useful, scientifically, than a quantity of cold, as it would later lead Lord Kelvin to the Second Law of Thermodynamics, the concept of absolute zero, and the necessity of a scale that used it as a zero point. Whence kelvins.

Initiativ till initiativ

F! Det synes vara l‰tt starta upp ett eget politiskt initiativ som F!. Man samlar ihop nÂgra likasinnade m‰nniskor, skriver ett manifest, leker med en logotyp i Word, och ringer media. Det borde fler m‰nniskor gˆra, faktiskt. H‰rmed nÂgra fˆrslag:

F. Som F!, men med en mer nykter analys av frÂgan, utan skattefuskare eller sjukskrivna i styrelse, och med lˆftet att endast anv‰nda demokratiska metoder. Analysen skulle fˆrsˆka svara p varfˆr regeringens policy har fˆrs‰mrat lˆneskillnaderna mellan kvinnor och m‰n i j‰mfˆrelse med resten av Europa och USA, och varfˆr det finns mycket f‰rre kvinnliga VDar i Sverige ‰n i USA (1.5% mot 11%). Analysen skulle Âtminstone ifrÂgas‰tta om man behˆver mer av regeringens policy, eller kanske mindre.

F. skulle ocks pÂst att de flesta av v‰rldens kvinnor inte ‰r svenska, och om man vill hj‰lpa s mÂnga kvinnor som mˆjligt skulle man kunna gˆra det genom policy som fˆrsˆker gˆra U-l‰nder rikare s snabbt som mˆjligt, s att kvinnorna d‰r fÂr tillgÂng till egna resurser. Att det ocks betyder att m‰n blir rikare skulle inte vara ett problem, d‰rfˆr att F. tycker att m‰n ‰r helt okej, och att de flesta inte îvÂldtar kvinnor och flickorî eller îuts‰tter dagligen kvinnor fˆr vÂld.î

F? Som F., men riktad till feministnyfikna. Manifestet heter îFeminism for Dummiesî och de gˆr reklam p TV under pauserna i hockeymatcher. De skulle fˆrsˆka ber‰tta fˆr m‰n varfˆr de ocks borde vara feminister: Inte bara d‰rfˆr att ungef‰r 50% av deras ‰ttlingar kommer att vara kvinnor, men ocks d‰rfˆr att det betyder att samh‰llet kan utvecklas mycket mer effektivt, vilket ‰r bra fˆr alla. F? skulle ocks fˆrsˆka ˆvertyga m‰n om att vara feminist inte betyder att t‰nka som Schyman.

PFFT! Riktat till anti-feministerna, sÂklart. Skulle fˆresl samma policy som F! men med motiveringen att det hindrar kvinnor.

YF; Jag t‰nker faktiskt starta upp detta initiativ. IdÈen ‰r att fokusera p att fr‰mja och skydda yttrandefriheten p ett fˆljdriktigt s‰tt h‰r i Sverige. Det betyder att vara emot PUL som den ser ut nu, mot en bred tolkning av lagen mot hets mot folkgrupp, mot den otroligt dumma lagen betr‰ffande cookies, mot lagen som brottsfˆrklarar omodererade kommentarer, och mot lagar som kr‰nker yttrandefriheten bara d‰rfˆr att det underl‰ttar till‰mpningen av andra lagar ó vilket skulle h‰nda med maskeringsfˆrbudet, till exempel.

Motivering ‰r att fˆrst‰rka samh‰llet genom fri debatt. Men det ‰r ju inte en slump att YF;s syfte motsvarar till vad jag anser ‰r bloggarnas egen fˆrdel: R‰tt att uttala vad man tycker ‰r sant, ‰ven om andra tycker det ‰r pinsamt.

Fˆr att YF; ska lyckas, ‰r det viktigt att det inte blir ett hˆger- eller v‰nsterprojekt. ƒven om yttrandefriheten upptar en del av Frihetsfrontens manifest, skulle YF; inte befatta sig med de ekonomiska slutsatserna och inte heller frÂgor kring copyright eller ‰gande av IP. YF; skulle snarare vara en Svensk version av ACLU (American Civil Liberties Union), som k‰mpar fˆr yttrandefrihet och religionsfrihet (och frihet frÂn religion). I USA ‰r ACLU regelbundet demoniserat av hˆgern; detta borde fˆrs‰kra dem p v‰nstern att YF; inte ‰r en nyliberal komplott fˆr att ytterligare dela upp deras rˆst ‰nnu mer ‰n Schymans initiativ.

They like me! They really like me!

It would appear that my learned treatise On the applicability of the Juche Idea to the Nordics has found an appreciative audience. In my inbox tonight:

Hey
We are planning a Korea summit with the DPRK as theme in July.
Location: Kopparberg.
Invited: All friends of the DPRK, but of course also friends of the ROK.
An attempt at eclecticism [I think it means].
Very well written on your blog. On the applicability of the Juche idea.
Happy 15th of April to you!

Peter Bjˆrkman & Samuel West

Hej
Vi planerar en Korea-summit p DPRK-tema i juli.
Plats: Kopparberg. Inbjudna: alla v‰nner till DPRK, men fˆrstÂs ocks ROK-v‰nner.
Ett fˆrsˆk till ekletik.
Himla kul skrivet p bloggen. On the applicability of the Juche idea.
Trevlig 15:e april p dig!
†
Peter Bjˆrkman & Samuel West

That should provide some choice bloggage. And besides, I've always wanted to be the narrator in Eco's Foucault's Pendulum.

Jan Yoors redux

By the grace of Google, Kore Yoors found my recent post about him and his father, Jan Yoors, and contacted me. It was wonderful to catch up, and it seems like our parents will also be getting back in touch. It turns out that he's just gone live with JanYoors.com — a website dedicated to Jan Yoors' life and art that gives a great idea of his versatility as an artist. (If I'm not mistaken, this is Kore.) It's hard to capture the vibrancy of the tapestries in a picture, though.

Jan Yoors' photographs from his time with the Roma also fill a newly published book, The Heroic Present: Life Among the Gypsies.

So it looks like it might well be time for a resurgence of interest in his work, especially in his native Antwerp. Stay tuned.

Testing the limits, again.

In Dagens Nyheter this past Sunday, a TT newswire article about what looks likely to become the next battle for the free speech demarcation line in Sweden. A local court in a town north of Gˆteborg will on April 5 hear the case against a primitive Christian ("urkristen") and his website, on which hate speech against homosexuals can be found that, according to the article, is even stronger and more widely disseminated than ≈ke Green's sermon.

A quick summation of the charges, as related by the prosecutor, for those who do not speak Swedish: The site alleges homosexuals are the "origin of and the engine behind the AIDS epidemic," and also that homosexuality is a "sevenfold (?) dirty noise that wells up like an infernal flood through society and reaps millions of victims." Furthermore, according to the prosecutor, a bulletin board maintained by the site contains posts with the opinion that "homosexuals should be punished by death and hung on city squares."

The article does not mention the name of the site, nor the person behind it. I find that ridiculous. Society doesn't need to be shielded from such people — we need to seek them out, engage them, ridicule and shame them.

So, some discovery was in order, then. Googling the term used in the article, "oas fˆr urkristen tro och v‰ckelse" led me to the site, Bible Templet. The person behind this site is Leif Liljestrˆm, and it is immediately clear — if only from his complete lack of design sense — that he is something of a nutcase. In fact, I seriously question his sanity. He appears to have messianic illusions of grandeur.

From a rather cursory check (again, that design is unbearable) it would seem that Leif has taken down the passages referred to by the prosecutorGoogle does not seem to have a record of the quotes as related by the prosecutor. Leif does seem to maintain a weblog on Blogger as well, BTW., and in a post on his "guest book", he maintains that he himself disapproved of a commenter's call for the death penalty for homosexuals, and wrote as much in a response to the comment, which I could not find. He also appears to be saying that he rejects calls to violence (it's all rather confused). Finally, he says that the death penalty comment was posted as part of a discussion that was held "several" years ago, which would make it interesting from a legal point of view, as the hets mot folkgrupp law was extended to include homosexuals only around two years ago.

Still, it would appear that Leif is on shakier legal ground than ≈ke Green was, here in Sweden. Leif isn't preaching, and preaching is specifically what saved ≈ke Green when he appealed his conviction. Second, Sweden has a law which states that administrators of websites are legally responsible for the content of third-party contributions on unmoderated bulletin boards or comment sections.

I've previously argued in favor of my own preferred definition of hets mot folkgrupp, which is "incitement to violence," where speech is intentionally used to incite acts of physical violence against members of a protected group. On which side of this demarcation line for free speech would Leif's website fall?

The test I like most is actually just the one that the US Supreme Court used in its landmark 1969 case, Brandenburg vs. Ohio. It is described thus:

The Court used a two-pronged test to evaluate speech acts: (1) speech can be prohibited if it is "directed at inciting or producing imminent lawless action" and (2) it is "likely to incite or produce such action."

Here is another description of the test:

That link leads to a site that contains a whole range of possible tests for determining the free speech demarcation line — a far more nuanced range than any I have seen debated by legal scholars and legal authorities here in Sweden. I was at one such debate a few weeks ago under Mosebacke Terassen. The four panelists all held practically identicaly perspectives. The only variety of opinion was to be found in audience questions.

One more thing: If you don't agree with my choice of test, I'd be interested in knowing which test you'd prefer instead.

The Brandenburg test - Merely teaching or advocating unpopular ideas must be distinguished from teaching or advocating the duty, necessity, or propriety of acting on those beliefs. The right to speak and organize cannot be abridged no matter if the group's message and purpose are repugnant to American values (such as KKK speech). In order for government to intervene, the speaker must subjectively intend incitement (imminent evil), use words which are likely to produce action (imminent action), and openly encourage or urge incitement (suggesting, for example, it's a duty to commit a crime).†

It is clear to me that when it comes to Leif's own pronouncements, neither he nor ≈ke Green are engaging in speech that should be prohibited. The commenter, meanwhile, certainly sounds like he believes public executions of homosexuals are a good idea, and that is pretty strong stuff. But does this constitute incitement to violence as defined by the Brandenburg test? It does not. To be exact (and in such matters it makes a difference) the commenter does not propose extra-legal action (as in a KKK-style lynching) but rather a change in the law that would make such action legal — he talks about a death penalty. This removes the sense of a threat of "imminent lawless action" which the test requires for an incitement charge to stickIf you're interested, this page has some pretty thorny questions about borderline cases involving the Brandenburg test.. Additionally, I think that leaving an anonymous rant on a hideous-looking website is about as unconvincing a case as anyone can make.

At this point, it is worth asking again about Nazi rallies, and whether Nazi campaigns against gays and jews should be outlawed. I believe that they should, because Nazis and Nazi sympatisers have a history of violent action against homosexuals, even recently in Sweden. The US Supreme Court upheld such reasoning in an analogous situation with the KKK and cross-burning in Virginia, in the 2003 landmark case, Virginia v. Black, which I blogged hereA nice primer on the regulation of hate speech in the US, citing Virgina v. Black..

In sum, I think Bible Templet's content would be protected under the US Constitution's First Amendment, though it probably does not enjoy protection under Swedish law, unless Swedish courts were to interpret hets mot folkgrupp as narrowly as I would.

Why should they? Why should Swedish courts draw the line so that hate speech is protected (as it is in the US), even to the extent that you can call for capital punishment for groups of people you hate? Because by outlawing hate speech, rather than responding to it with more speech of our own — by pushing those ideas underground, where they will fester, not disappear — we are doing more harm than good to our society. I've argued this before, so I am not going to belabor the point, but in brief; We the people are smart enough to separate the good ideas from the bad ourselves — look at the progress we've made. The courts should restrict their focus to banning all calls to violent action, regardless of the ideas that might be used to justify them.

End of rant.