Well, the podcasting bug has finally bitten, late but hard. I’m currently addicted to the BBCs In Our Time and CBCs Quirks and Quarks, and several NPR shows. My commute to work has become far more enriching in the process. It’s like getting an few extra free lectures in history or science per week. Here’s hoping the effect will show over time.

My initial critical stance towards podcasting as a revolutionary force will therefore need revision. The following things are still true, however:

Unless new technology comes along (such as better voice to text), podcasts will remain opaque to the increasingly important pervasive search abilities of operating systems (well, my operating system) and Google. Podcasts won’t show up in searches based on what is inside them, unless you were to annotate or transcribe them, which is a nuisance. (But then again, we tend to annotate or tag pictures, don’t we?) This will continue to limit their efficiency as a searchable store of knowledgeI have also been skeptical of tagging as a meme. Why do something manually that Google does better automatically? For podcasts, however, it may be the best option for now, as it may be for pictures..

Podcasts are terrible unless they’re by people who know what they are talking about. That is also the case for text blogs, of course, but the cost of realizing that a blog is terrible is much lower in terms of time and effort than realizing a podcaster is terrible.

Furthermore, podcasts are useless unless they are the best medium for the message. If you aren’t blind, visually scanning text will always be a far faster method of soaking up informationThe blind can also use text-to-speech, or have the results of text searches read out to them., so podcasts need to exploit their limited competitive advantage. Podcasts work for interviews, lectures, comedy shows or learned debate, where the timeliness of the delivery is not so critical and the cost of transcribing the voices outstrips the value added from doing so. In other words, podcasts work for the delivery of natively oral niche discourses free from newscycle pressures.

In other cases, such as with comedy, the very nature of the delivery adds value, so podcasts of the BBC’s Hitchhiker’s Guide to the Galaxy shows would obviously be far preferable to the script.

For several years now, streaming on-demand delivery of radio programs via the interneet has complemented radio delivery by making them available A) anywhere in the world you have internet access, and B) whenever you want. Podcasts further improve on A) by letting you hear them anywhere, period.

I think the advantage of letting you take your on-demand audio that extra mile has yet to be fully exploited. When it is, there will be many more uses in the vein of architectural walking tours through cities, much as how museums today use audio devices to aid romps through exhibitions.

I’m less optimistic about the idea that podcasts of “working-class” rallies and meetings will somehow raise class consciousness among those who ostensibly don’t read (to reply to Mark Comerford’s podcast manifesto). That’s because the added value of such meetings comes from actual participation — the sense of belonging to something larger, and the fact that these meetings sometimes serve as decision-making opportunities. Listening to after-the-fact podcasts, on the other hand, is just as solitary an experience as reading or writing, and is not going to change the results of these meetings. You had to be there, so to speak. So to speak (haha).

(Not to mention that I believe the idea of class consciousness is no longer relevant. Class-based movements used to be a response to a lack of opportunities for social mobility in society. Ironically, labor movements today are trying to resist such mobility, favoring the protection of uncompetitive manufacturing jobs over retraining for jobs that have a much better competitive future. I put this down to a self-preservationist impulse on the part of labor unions, and the difficulty of letting go of mental constructs past their use-by date.)

Oh this is precious. John Hobbs over at Cinema Volta has concocted a Dashboard widget that gives you the GPS-derived ETA, in minutes, for the next blue bus at your local stop, much in the same way Stockholm’s high-tech busstops do. I took his widget and chose my own two stops, using the codes in the html of this page. (You might need a free trial version of BBEdit 8 to do this.) So here is my very own first (entirely plagiarized) widget. If they’re that easy to make, I take everything back I said about Dashboard yesterday, and I think I have just put another project on my to-do list.

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 — unlike with the widget — 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?

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:

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 Gödel, 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.

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.

If you want to, you can read Part I: Prelude first.Mathematical bases sure are a convenient shorthand when adding, multiplying and subtracting, and their invention was necessary for the kind of recordkeeping that allowed ancient civilizations to blossom — amphoras of wine shipped, monies owed to the emperor, sacrifices made to the gods — let’s hear it for property rights and central planning.

But bases are arbitrary. The Babylonians used base 60. The Mayans used base 20. The Greeks and others used base 10, while the geeks have adopted binary notation, base 2, as their own.

All these number systems have quirks, too. Modern systems use place to determine the value of a number (i.e the 5 in 350 stands for 5 groups of 10); the Romans used different numeric symbols (XXX stood for three tens, CCC stood for three hundreds). Without prior access to such rules, a stranger would need a good number of examples from which to glean patterns. It wasn’t until the 1820s that we deciphered the Mayan number system, for example, and it took all the lateral thinking the splendidly named Constantine Samuel Rafinesque-Schmaltz could muster.

Number systems have another weakness: Division. They have no neat way of precisely representing all rational numbers — numbers that can be represented by a fraction, such as 6/2, 7683/99746 or 1/7. All bases can represent some rational numbers precisely: In base 10, for example, 6/2 is precisely 3 and 1/4 is precisely 0.25. But 1/7 is 0.142857142857… the 142857 repeating forever, the actual number never quite managing to get nailed. In base 7, meanwhile, the number equivalent to 1/7 in base 10 can be precisely represented as 0.1, but 1/4 becomes 0.151515… ad infinitum.

Base 2 merits some special consideration. The received wisdom is that binary notation is somehow more natural, because it is the simplest system, requiring the fewest symbols (2) without having to resort to pebbles or prison wall notches as a counting tool. Base 2 is special, it is argued or assumed, because its ones and zeros (“bits”) lend themself perfectly to representing the trues and falses of Boolean logic, which in turn can be physically embodied in the presence (“on”) or absence (“off”) of electromagnetic charges in our computers’ transistors and circuits.

That amounts to attaching too much importance to historical accident, however. Alternative logic systems do exist. In ternary logic, for example, base 3’s zeros, ones and twos map to “unknown”, “true” and “false”. And base 3 is more efficient than base 2 at representing numbers, as this great article points outHow to measure this efficiency? Take a number, any number. Depending on your choice of base, you will require different amounts of digits to write out the number. For example, the number 66 requires two digits in base 10; the base 2 equivalent of that number, 1000010, requires seven digits; the base 3 equivalent, 2110, requires four digits. Clearly, the higher the base, the fewer digits you need. Using a higher base means having to differentiate between more number symbols, which uses up bandwidth or computing resources — though it also means needing fewer digits, which saves resources. You can measure the total resources needed by multiplying the base a number is written in by its length in digits. In our case, 66 requires 10 x 2 = 20 “units” in base 10, 2 x 7 = 14 units in base 2, and 3 x 4 = 12 units in base 3. It turns out that for almost all numbers, using base 3 provides us with the notation that is the most economical in terms of these “units”. (The same argument applies to using ternary logic instead of Boolean logic. Often, fewer steps are needed to obtain the same result.). Computers using “trits” instead of bits were developed in the 1950s, notably by the Russians, but these efforts never caught on. According to the article, which you still haven’t read (it’s worth printing out the PDF and unplugging for this one), the likely reason why base 2 became the Microsoft of information theory notation is that in those days we didn’t have the technology to make transistors that could reliably represent three states. We could do two states, and that was good enough, so people like Claude Shannon ran with the idea and we never looked back. The cost of switching would now be too great. (Or would it? When it comes to data transmission, the Swedes are all over this.)

If aliens assume anything, why shouldn’t they assume that since base 3 is the most efficient notation, this must obviously be the base to use for interstellar communication? Since radio transmissions use phase shifts variable signal strength to encode “on” and “off” bits, it would be trivial to encode multiple states. Why didn’t we do so in our data transmissions? I’m guessing at more anthropocentrism, and because we forgot that sometimes simplicity is not the same as efficiencyWay off topic: When quantum computing happens, and it will, there is every reason to consider using the opportunity to swith to ternary logic, and using qutrits instead of qubits. This paper [PDF] and this paper make the case. This one [PDF] even has pretty pictures!.

But I want to hold off on the aliens for a while longer. I’m trying to make a case here for jetissoning bases in favor of a more rigorous approach to describing the numbers that lie between whole numbers. That’s because no number system is precise when it comes to representing arbitrary rational numbers, and downright hopeless when it comes to irrational numbers — and I think it is some of those numbers that we should consider beaming to aliens. (But I’m getting ahead of myself.)

The solution to the division problem is ingenious, and therefore first discovered by the Greeks. I’d come across continued fractions before, in high school, but their deeper significance completely passed me by until Roger Penrose, of course, rubbed my nose in them in his The Road to Reality (Chapter 3)You might remember my commitment to blog each chapter of that book. It’s not feasible, and frankly boring to impose my half-baked solutions to his problems on you. Perhaps a wiki is in order. Later. Instead, there’ll be posts like this one, inspired by the eye-opening (to me) stuff from the book..

It turns out that every number on the number line is representable by a unique continued fraction that looks like one of these:

It’s not as bad as it looks, so bear with me. You can make these continued fractions yourself: Use a calculator to divide 13 by 11. The answer is 1.181818… Subtract the bit to the left of the decimal point (it’s a 1) and put it aside. Divide the remainder into 1, and you get 5.5. Again subtract the bit to the left (the 5), then again divide the remainder into 1, and you get 2, this time with no remainder (if your calculator is any good). The numbers you took away from the running total, 1, 5 and 2, are the terms along the left edge in the continued fraction, above, which uniquely describes 13/11. This is the “basic” way of constructing a continued fraction — there are other ways [PDF].

There is only one continued fraction of this kindBy “kind” I mean continued fraction where all the numerators are 1. for each number because if you changed any of the denominators you would (obviously) get a different number. Another way of saying this is that every real number (whole, rational, irrational, transcendental) has a one-to-one correspondence to a specific sequence of whole numbers. In the case of the number 13/11, this sequence is short and finite: 1,5,2. In the case of the square root of 3, the sequence is 1,1,2,1,2,1,2… with the 1 and 2 alternating ad infinitum.

You might be wondering why this is any better than the repeating “181818…” we got in the decimal notation of 13/11. I have two reasons. First, the whole numbers that make up these sequences do not change depending on the base we use to write them. The sequence is base-neutral. Second, these sequences are more elegant: They are always finite when it comes to describing rational numbers exactly, and they are far better at divulging patterns in irrational numbers than any number system you care to use.

Here are some examples showing off the elegance of continued fractions when describing some irrational numbers — the square root of 41, and Phi, the Golden Mean.

In decimal notation, and in any other base, the numbers following the decimal point convey no order; they might as well be random. Not so when it comes to the representation of these numbers via continued fractions; for the square root of 41, the sequence is [6,2,2,12,2,2,12,2,2,12,2,2,12,…] ad infinitum. The pattern is clear.

What about that special class of “really” irrational numbers, the transcendental numbers, such as pi and eTranscendental numbers are irrational numbers that cannot be the solution to a polynomial equation. There are in fact far more transcendental numbers than any other kind of number — pi and e are just the most famous ones.?

For e, there is pattern visible, though it is one that changes in a set way with each repetition. As for pi, there is no discernible pattern via this kind of continued fraction, though much has been [Swedish PDF] made of the sequence of numbers that corresponds to it.

In sum, what we now have is a means of representing any real number in a base-independent manner using only sequences of whole numbers. This is good for communicating with aliens: No bases means no opportunity for anthropomorphising, while whole numbers are about as close to made-for-radio blips as you can get.

So, now that we can unambiguously send real numbers to aliens, which numbers shall we send them? Stay tuned for part III.

Before talking to aliens, it would be helpful if we had some insight into what it is like to be one. Since we don’t, and won’t, we will have to do the next best thing — identify all our anthropocentric assumptions about intelligent life in the universe and then ruthlessly eradicate these from the messages we send them.

To that end, we need to ask ourselves: What common ground could there be between all forms of intelligence in he universe? What is the minimal definition of the term intelligence in this regard? And is there a medium for communication that is shared by all these intelligences?

Jules Verne implicitly had a go at some answers when he conjured up a scheme for communicating with moon dwellers, the “Selenites,” in From the Earth to the Moon:

Thus, a few days ago, a German geometrician proposed to send a scientific expedition to the steppes of Siberia. There, on those vast plains, they were to describe enormous geometric figures, drawn in characters of reflecting luminosity, among which was the proposition regarding the ‘square of the hypothenuse,’ commonly called the ‘Ass’s Bridge’ by the French. “Every intelligent being,” said the geometrician, “must understand the scientific meaning of that figure. The Selenites, do they exist, will respond by a similar figure; and, a communication being thus once established, it will be easy to form an alphabet which shall enable us to converse with the inhabitants of the moon.” So spoke the German geometrician; but his project was never put into practice, and up to the present day there is no bond in existence between the Earth and her satellite. (Found via the University of Zimbabwe)

Here a geometric proof of the Pythagorean theorem is proposed as something so fundamental that it must be one of the first discoveries made by a budding civilization’s mathematicians. The Greeks indeed discovered it first here on Earth, but still: How fundamental is it exactlyIn hyperbolic space, the angles of a triangle add up to less than 180 degrees. In elliptical space, they had up to more than 180 degrees — as is the case if you draw a triangle on a sphere, for example. We don’t currently know what kind of space the universe is made of. On a very small scale, the human scale, space certainly looks Euclidian, but that would also hold true in hyperbolic or elliptical universes. My own gut feeling is that space is hyperbolic. But aliens might know for sure.? The theorem only holds true in Euclidian space, which we think of as “normal” space, but not in hyperbolic or elliptical space. We’re biased that way, however. We’re instinctive flat-Earthers — we prefer to shoehorn the elliptical plane we call Earth into flat, Euclidian maps, replete with massive Greenlands. We exude pro-Euclidian sentiment in everything we do.

We shouldn’t expect aliens to know about this proclivity of ours. Actually, they probably wouldn’t even notice proofs transmitted at wavelengths suited specifically for our eyes — aliens have no reason to suspect we’d be broadcasting at those entirely arbitrary wavelengths. Or else they might be in a phase of their development where geometric proofs are unfashionable, not to be trusted, much as was the case for generations of our own mathematicians in the era between Descartes and Riemann — and they’d even be right in this caseIn Verne’s time, aliens might (correctly) have interpreted our depiction of the Pythagorean theorem across Siberia as a statement of our (unjustified) belief in a Euclidian universe; or else they might (incorrectly) have concluded that we think the theorem holds true on an elliptical plane (Siberia). Either way, they’d think we’re stupid..

We have on several occasions made real attempts to talk to aliens. In the early 70s we attached a plaque with an engraved diagrammatic message to the Pioneer 10 and 11 space probes, which we then sent on flyby missions to Jupiter and Saturn and on into outer space.

Pioneer 10 is travelling to Aldebaran, a giant aging star around 65 light years away. As of 2005, the probe is about 12 light hours from us — one 50,000th of the way there.

In the late 70s we launched the Voyager 1 and 2 probes on a similar, upgraded mission. They contain a more ambitious attempt at communication — a gold-plated phonograph record! With a supplied needle, no less.

Both attempts unintentionally reveal some less flattering aspects of humanity, though fortunately these should be way above aliens’ potential heads. For example, the naked woman on the Pioneer plaques has no genitalia. Apparently the plaque’s designer, astronomer Carl Sagan, left them out rather than risk rejection of the entire project. The fact that there were naked people at all on these plaques nevertheless led to angry letters accusing NASA of peddling smut to the stars. More embarrassing, at least to me, is that one of the two greetings on the Voyager records is by an ex-Nazi stormtrooper, Kurt Waldheim. How on Earth — literally — did we manage thatThe other greeting is by Jimmy Carter.?

I rather doubt aliens will ever “hear” the encoded sounds on the record. If they find a Voyager spacecraft they will conclude it was built by an intelligence, but in the absence of ears, atmosphere or human brain circuitry, the bits on that record will be as revealing to aliens as a jpeg of Monica Bellucci is to a blind personCue yet another reference to Thomas Nagel and his essay, What is it like to be a bat?. And how should aliens tell if they are seeing the plaque the right side up, given they have never met a human before? It’s just a load of Pollocks to them.

In 1974 we carefully aimed the Arecibo radio telescope’s transmitter at M13, a globular star cluster 25,000 lightyears away, and sent it a three minute message containing exactly 1,679 bits (around 0.2 kilobytes). The message, travelling at the speed of light, will unfortunately miss M13 completely, as the cluster will by then have moved out of the signal’s path, seeing as our galaxy rotates.

This problem aside, using radio was not an arbitrary choice. Radio transmissions offer a faster medium than plaques and a less anthropocentric medium than records or light. Radio is as fast as light, since both are just electromagnetic radiation made up of photons, but radio frequencies are far lower than light frequencies, so radio photons require much less energy to produce.

Which exact frequency to use for radio transmissions (and thus also for listening)? In this universe, one part of the radio spectrum — at around 1420 Megahertz — has far less background noise than other parts, so anybody who would want to maximize their signal-to-noise ratio would use it. We use it when we listen for aliens with SETI. So did we use it to send the Arecibo message? Not exactly:

It’s interesting to note that in 1974 the Arecibo message was transmitted at 2380 MHz, a frequency well above the “water hole” band. In Earth’s first “Active SETI” attempt we didn’t transmit at a well known and preferred frequency of either 1420 or 1665 MHz. Furthermore, 2380 MHz is the second harmonic of no particularly special frequency. The Arecibo transmitter was designed for S-band planetary radar experiments and SETI used it because it was available.

Luckily, it technically relatively easy for aliens to listen to many frequencies simultaneously, as this fuller discussion on making guesses about the medium makes clear.

The one thing the makers of the Arecibo message did get right, in my opinion, was to use the basic properties of whole numbers to encode it. Because the sequence of prime numbers is the same regardless of where you are in this universe, the prime factors of 1,679 — the number of bits sent in the message — will be 23 and 73 everywhere. Aligning the bits sequentially on a 23 x 79 grid produces the patterns that make up the message. That’s really clever, and hints at the kind of message I think we should be sending.

Do the patterns that comprise the Arecibo message make any sense to aliens? As there will not be any opportunity to start a dialogue, aliens won’t be able to ask for clarifications. I think mixing binary counting systems with graphical representations is therefore really just a way of not imparting any information at all. Aliens might think we look like the blobs representing binary representations of our DNA molecules. Maybe they look like the binary representations of our DNA molecules. Maybe our representative pinheaded human provides them with an unsolveable binary counting puzzle which they just can’t crack.

And why oh why do we have to count to 10 in our binary counting lesson at the start of the message? Haven’t we learned anything about anthropocentrism? Much better, I think, to drop using bases altogether when talking to aliens, and just focus on winking at them unambiguously. How? I have a plan.

I happened to me this morning, during the commute, on the 52 bus: the first verified multipod moment on Stockholm public transport. By multipod moment I mean me noticing two white iPod earbud-toting co-passengers in addition to myself on a bus or subway carriage. I’ve come across other iPod users individually before, while using my own, but as I don’t feel my presence should influence the results of measuring such chance occurences, true multipod moments really should exclude the observer’s iPod.

My first ever multipod moment happened in January 2002 in New York, on the N/R line on the way to Wall Street, some four months after the original iPod was introduced. iPod densities are likely the world’s highest right there. By now, I’d be surprised to find a rush-hour carriage there that does not have multiple iPods on it.

Multipod moments are not as arbitrary a notion as you might think. In the minds of the iPod-less people (iPLP) on the bus, one white earbud-clad person is weird, but two of them is fashion, and who doesn’t want to be in fashion? Multipod moments on public transport are Apple’s tipping point.

The iPod Shuffle arrived en masse in Stockholm yesterday, and I stood in line to acquire mine — they were selling like semlor and looked about as delicious.

Cut to the few things that struck me about the Shuffle that I have not yet read about:

Oh, and today I learned that att avfukta means to dehumidify in Swedish, and not what you might think it means.

Since everyone (OK, well, someone) is engaging in a bout of rank guessing about which companies are the rumoured suitors for the licensing of OS X on non-Apple boxes, I thought I’d join the funFrom Fortune Magazine: “Most tantalizing of all is scuttlebutt that three of the biggest PC makers are wooing Jobs to let them license OS X and adapt it to computers built around standard Intel chips. Why? They want to offer customers, many of whom are sick of the security problems that go with Windows and tired of waiting for Longhorn, an alternative.”:

What will obviously happen is that Apple is going to license OS X to IBM so that Big Blue’s customers have the option to run OS X on the next generation Cell-based IBM corporate servers; and Apple is going to license OS X to Sony so that every Cell-based PlayStation 3 is simultaneously a Mac mini on steroids — running the non-game home-entertainment-hub part of the PlayStation’s many promised abilities. (Who knows, maybe Cell-based Macs will in turn run PlayStation games.)

Notice how this strategy does not in the main cannibalize Apple’s own computer segments (this being the mistake Apple made last time it licensed an operating system)? By licensing to Sony, OS X shows up in far more households, and by licensing to IBM the whole corporate world finally opens up to Apple — at least to its OS, and thus later hopefully to its Xserve on the low end.

Meanwhile, going to Intel chips is not worth the risk of compatibility headaches, especially as Cell looks amazing from where we are standing right now.

As for who the third manufacturer might be, here is a clue: Three major companies are co-developing Cell.