Why didn’t anybody tell me?

I remember staring at the first drafts of the MathML definition almost two decades ago and obsessively clicking “reload” for checking the next browser version to implement it. After the web had facilated communication around the globe in various human languages and alphabets, I eagerly awaited support for that single, universal language that made it all work: mathematics.

Alas, it didn’t happen. Since then, I’ve revisited current standards and adoption states for maths on the web every few years. The situation was dismal.

For years, everybody has been able to read, write, and communicate “square root of two” with all kinds of funny squiggles: “roten ur två”, “квадратный корень из двух”, “השורש הריבועי שלשְׁתַּ֫יִם”, “二的平方根”. But try to put the symbol “2” under the radical √ on the web? No way. As the information age progressed, we became unable to communicate in its underlying language, because the web suddenly became the playground of nonmathematical people.

Turns out: instead of bitching about it, somebody solved it. Just like that.

The technology is called MathJax, written in javascript. It produces beautiful, scaling, copyable maths on the web. And it’s been around for a while, apparently. I just didn’t notice it—I seem to work too much and spend too little time procrastinating on the web.

Since recently, it works on Wikipedia! As of May 2012, log in, go to “my preferences”, choose the “appearance” tab, and select MathJax as your default rendering engine for maths at the bottom. Then, go to some page like Tutte Polynomial; and feast your eyes. Increase the font size just because you can!

On the MathJax page you can see which other websites support it. This looks like a very healthy system.

Only grumble: Since it requires javascript, the solution doesn’t work with my current blogging platform. The easiest solution seems to be to host a wordpress.org blog on a separate server. 

I am an eager public speaker and have several crowd-pleasing talks that I can take off the shelf, say about how Google works. In March, I had the opportunity to record a lecture for Swedish TV’s educational channel Utbildningsradion. That audience is as “general” as it gets, so I wanted it to be broad and accessible. Something everybody immediately relates to. Something concrete and tangible.

What better choice than separation results for nonderministic polynomial-time computation? That’s right! In a fit of misguided ambition I decided to make a 20 minutes talks about honest-to-Karp theory of computation. P versus NP. Also, I did it in my fourth language: Swedish.

Here it is:

• Utopier i Science Fiction och Datavetenskap

I haven’t had the guts to watch it yet, maybe I never will. But as far as I remember, it came out well.

Some comments:

1. P and NP are the worst complexity class names ever invented, maybe the worst named concepts in all of science. I found it much easier to talk about Impagliazzo’s five worlds and focus on the dichotomy between Cryptomania and Algorithmica. These are meaty, sexy, fuzzy concepts rich with association and meaning. This is what we should talk about to the public. P and NP are just very cold, different, specific, nerdy instantiations of the same basic question.
2. Puzzles are good when explaining algorithms and their absence. I have a bunch of these talks, using paper folding, sudoku, or (as in this case) tiling puzzles. It gives you something tangible in a talk, and when you talk about something as abstract as computational complexity, you need all the tangibility you can get.
3. Science Fiction is our friend. I used various tropes from SF to ground the talk in a shared cultural space, and as an underlying theme. Here: the existence of hard artificial intelligence and the Singularity!. (I always say Singularity! in a booming voice. Hence the italics and exclamation point.)
4. The Singularity focus (sorry, Singularity! focus) was largely inspired by some transhumanistic alarmism on the blogs of Chalmers maths professor Olle Häggström (Okunnigt om artificiell intelligens och mänsklighetens framtid) and fantasy author R. Scott Bakker (The Posthuman Paradox). For some reason, the Singularity! exerts a strange attraction (ha!) on brilliant people like Olle and Scott. I simply can’t get myself worked up about it, and assume it’s simply the result of nonalgorithmic thinking that assails people who work in formal, possibly even quantitative, but nonalgorithmic settings. (Scott is a philosopher, Olle a statistician.) Alternatively, they could be right and I could be wrong. Still, it’s certainly fun to think about, and a great conduit for evangelising about algorithms to the public. The point of the talk is that the Singularity! is morally equivalent to P = NP. I think I manage to convey this point pretty well, given the constraints of the setting. In some sense, this is the maximally ambitious core of the talk. Neither Olle or Scott will be convinced by the argument, but the production values sure outshine their puny blog entries! Proof by intimidation.
5. I think I made the rhetorically correct decision of leaving the talk by moving the dystopias down to Earth in the end, with a bit of “algorithms are everywhere” internet evangelism.

In summary, the Singularity! is far. But then, the time-travelling nanobots paid me to say that, promising me a simulated eternity filled with cybervixens and Nutella.

Edit to add: I have been informed that I shouldn’t say “NP-hårt” in Swedish, but “NP-svårt.” Thanks, these things are beyond my linguistic intuition.

Related: Views of Impagliazzo’s Five Worlds.

“Computer scientist, public debater.” Next stop: “International man of mystery.”

In fact, the epithet comes from a poster for a panel debate about the blessings of the Internet arranged by the Social Sciences at Lund University, Debatt i Lund. I was really happy to be invited and had a good time; I hope this sets a precedent for more involvement of academics from the technical and natural sciences. The nerds.

In preparing for the debate, I spent some time reading or re-reading a few general-audience books about various societal aspects of the Internet, including the relatively recent The Filter Bubble and Program or be Programmed. I remain impressed by Blown to Bits, which combines a minimal amount of alarmism with an honest ambition to actually explain what is going on. It’s written by nerds, so the facts are correct. For nonspecialists, this should be the one book to read.

I also refreshed some sociological aspects. As a newly minted public intellectual I feel it behooves me to drop Foucault into conversation at regular intervals, instead of my usual spiel of an intertextual hodgepodge of Star Trek, Monty Python, and fantasy novels.

Foucault is topical because of his treatise on discipline and punishment that includes a famous description of modern society in terms of prison architecture. This design goes back to the English utilitarianist Jeremy Bentham and is called the Panopticon: the prison is circular, with a centrally placed warden able to inspect all the cells on the perimeter. This is clever not so much for the actual surveillance, but for the inmate’s constant knowledge of being potentially watched. It’s a correction facilty by design.

Foucault uses this design to make some point about modern society, with several institutions (such as schools) playing the role of the warden. This is good stuff; I had a chance to reacquaint myself with these notions recently when reading the spectacular The Judging Eye by R. Scott Bakker. (Fantasy novel reference duly dropped.)

As with all dystopias, Foucault’s Panopticon is of course an old hat by now. We’re living it, just as the London of Orwell’s 1984 is in fact the London of today. Some media theorists have taken Foucault’s Panopticon to the next level and speak of a Panspectron to describe our society: instead of us surrounding a centrally placed warden who sees us, we’re now surrounded by countless sensors that measure us in many other ways than just optically. I think Branden Hookway is the one to read about this. (Which I haven’t done.)

While I think this is a valid concept, I’m not too fond of the name. Panspectron. It’s basically the same word as Panopticon, with Latin replacing the Greek.

Thus, wearing my “public intellectual” mantle (which is, in fact, just a well-poured glass of Scotch) I will release a new word into memetic space that I find superior to Panspectron. Here it comes:

Panmnemonicon n. 1. A device or set of devices that records and stores everything. 2. A society operating under the influence of such a device.

Panmnemonicon translates to something like “all-remembering”, which I think is the point of our brave new world. After all, nobody actually watches you or me; mostly because nobody cares about you or me. Instead, everything is stored with the possibility of later being retrieved and mined, should you or I suddenly become interesting. That’s the worrying point, and the one that has potential impact on behaviour.

So there it is. A new word minted. Remember it, as it surely will remember you.

At the time of writing, Panmnemonicon has a total of 0 hits on Google. Panspectron does have some hits, but not enough for me to Google Trend it. We’ll see how it goes. It’s so on, Panspectron.

The talk was recorded by Swedish TV and will be broadcast somewhen during the Spring of 2012 on their education and facts channel Kunskapskanalen. Because of the potentially high impact I decided to apply a bit more spit and polish to the visual side of the talk. In particular, I made 5 posters to represent Impagliazzo’s five worlds of computation. These worlds provide a metaphor that I find more intellectually stimulating than the relatively stuffy formulation, “Is the complexity class P equal to the complexity class NP?”.

I think some of them came out well, even typographically. (Five points for guessing which typeface was used for Heuristica.) I hereby release them under the CC BY-SA 3.0 license; maybe somebody else can use them in a similar talk. The talk was in Swedish (or at least in whatever language I use to approximate Swedish); if an anglophone wants Kryptomanien changed to Cryptomania, or wants the PDFs, I’m happy to oblige.

Next up: mugs, mouse mats, lingerie, and a perfume series of five fragrances.

References

Five worlds of computation are from Russell Impagliazzo: A Personal View of Average-Case Complexity. Structure in Complexity Theory Conference 1995: 134-147. [online PS]

Image sources: The dice are by ed_g2s at Wikimedia Commons. HAL 9000 is by Cryteria at Wikimedia Commons.

Relationship between Cahen’s constant and who you’re gonna call

Since a while back I’ve used weekly, small, well-defined programming exercises for all my courses. It’s a lot of work to develop these, but also a lot of fun.

The book I’m using, Sedgewick and Wayne’s Algorithms (4th ed.), makes it natural to have an exercise about the four sum problem early on, involving a bit of coding, parsing, simple experimental and theoretical running time analysis, and a clever idea or two. Rasmus Pagh had a brilliant idea how to turn this exercise into something fun, inspired by xkcd 687. After all, finding deep-looking product formulas is just a question of looking (after taking logarithms) for values that add to 0. Given enough interesting numbers, some pattern has to emerge.

I’ve played around with Rasmus’s exercise it a bit more since yesterday, added some spit and polish, and made it slightly crazier. The best new law of physics I’ve discovered this way is shown at the top. It relates

• the energy equivalent m_uc² of the atomic mass constant in in MeV,
• the energy equivalent m_dc² of the mass of a deuterium atom in Joule,
• Cahen’s constant (roughly 0.643410), defined by a sum of Sylvester numbers a_k, and
• G, the phone number of the Ghostbusters, 5552368.

You can’t make that up. It’s correct up to rounding errors and a cavalier attitude to dimensions.

The finished exercise, with data files, is at the course blog at ITU; I’m slowly getting myself organised to publishing these things on GitHub to make them more useful for other teachers. (That would include the TeX file for the exercise description, for example.) Stay tuned.

Edit to add: I guess the real conclusion of this formula is that the world finally knows the unit and dimension of US phone numbers, assuming that Cahen’s constant is dimension-less. Phone numbers express inverse energy squared, measured in mega electron Volt Joule. You heard it here first.

Edit to add (25 May 2012): xkcd 1047: approximations

Illustration of Yates’s algorithm from my talk. I finally found a way to simultaneously depict the lattice structure and the symmetries of the circuit.

Many computer science fields in France are organised in national, cross-institutional groupes de recherches, not completely unlike the ACM SIGs in the US. The TCS group (“Mathematical Informatics”) encompasses some 400-500 people, as far as I understand.

As in most of Europe, theoretical computer science in France includes many more fields more than US-style theory of computation. Amazingly, they meet once a year for two days, and give well-attended talks to each other. The 2012 meeting had 170 registrants, an impressive number.

This struck me as particularly noteworthy after just attending SODA, where the various subfields of algorithms become increasingly fragmented and estranged, to the point of hostility and mutual incomprehensibility.

At the Paris meeting, a steering committee selects a number speakers from the various working groups in the GDR IM, who give meaty, 45-minutes talks to a general TCS audience: Computational logic, computational geometry, distributed systems, process calculi, extremal graphs, ….

In addition, the meeting includes two 1-hour invited talks recruited outside of the French GdR. Ashwin Nayak talked about communication complexity, and I used to opportunity to present an overview of zeta transform algorithms and applications, culminating in our SODA 2012 result from last week. [slides]

Thanks to everybody who attended, and to the nice organisers for putting me into a disarmingly charming hotel in the middle of the Latin quarter, where you couldn’t swing a dead Marsipulami without hitting a comic store. I had a splendid time.

“Coded cultural choice” on the cover of SvD’s Arts section, illustrated by badly indented Java code.

The article is about the effect of algorithms on the consumption of culture. One of the arguments that I’ve been trying to make for a while is that (a) the human condition is increasingly determined by access to information (b) the main force affecting information is algorithms. Thus algorithms are a worth understanding for other reasons than (a) intellectual curiosity or (b) technological progress.

The web version of the article is online at svd.se.

Such an article are the result of an interview that takes over an hour, and where I say a lot of things about a lot of things, and some subsequent emails. What ends up in the final article is a bit of hit and miss. This time, I’m pretty happy with the outcome.

Some highlights and comments:

• My physics envy is in full display: “We teach 1960’s science like physics and chemistry in school, but you don’t learn more about algorithms now than 20 years ago.” This statement is of course not universally true; many countries do have programming and other computer science as part of the high school curriculum. But even with that proviso I think it’s safe to say that “what science should be thought in school” has changed relatively little since Sputnik. But the point of the article is of course something else: algorithms have an effect on culture (and democracy and whatnot), so the bold claim is that algorithmic thinking should be part of the Social Science curriculum. (It goes without saying that recursion ought to stand proudly next to Pascal’s law in the Science and Maths curriculum as well.)
• The article contains a nice-looking attempt at actually Explaining What’s Going On. You can see some pseudocode in the web version, where nice-looking brand icons serve as objects that are polled for various signals about previous user behaviour. There is even a collaborative filtering aspect (since the hypothetical Facebook object is queried about what your friends like). Given the constraints under which such a page is produced, I think this came out well. The real point is of course that this code is not written by a human, but by another algorithm, so “the algorithm” performs at a meta-level. I did not find a good way to communicate that, so I didn’t try.
• The code on the section’s front page is from the very nice data mining research done at ITU: Andrea Campagna and Rasmus Pagh, Finding Associations and Computing Similarity via Biased Pair Sampling, The Ninth IEEE International Conference on Data Mining, Miami, Florida, USA, 6-9 December 2009 pp 61-70. Proper indentation or choice of a non-proportional font is not something the newspaper graphics guy cares about. (Hell, my own students don’t.) I proudly showed this to ITU’s vice chancellor Mads Tofte, but he “would have been more impressed if it had been in ML.”
• Lest somebody misattributes pithy quotations to quotable me, the phrase “program or be programmed” is from Douglas Rushkoff.

The European Association for Theoretical Computer Science has around 1000 members, including many European TCS researchers and everybody who attended conferences like ICALP and ESA in a particular year. Traditionally, EATCS has had a close relationship to scientific publisher Springer, who publishes the proceedings of EATCS’s “flagship conference” ICALP.

A recurring theme at the EATCS general assembly meetings for the past many years has been the publication model for ICALP. Should “we” continue with Springer, or move to an open-access publisher like LIPIcs? After considerable deliberation, a ballot among EATCS members was held in late 2011.

For more background:

1. EATCS general assembly at ICALP 2010 on my blog.
2. EATCS general assembly at ICALP 2011 on my blog.
3. EATCS ballot on Luca Aceto’s blog.

I have been absolutely thrilled that the EATCS council decided to send this question to its members. Well done. I want to see more of this.

Unfortunately, the outcome is not what I would have hoped. The EATCS council required a quorum of 25% of EATCS members for the ballot to be valid. I think this is a reasonable requirement – the ICALP publishing model is an important decision that should be safely moored.

Alas, the quorum was not reached. On 9 November 2011, EATCS president Burkhard Monien informed the EATCS that out of the 1094 members, only 260 had voted. And that’s just slightly less than 1 out of 4. It’s 23.8%.

Informative graphic explaining the magnitude of the value 13 in relation to the value 1094

Monien adds,

However, I also want to let you know that the majority of the 260 votes were in favor of LIPIcs. EATCS will observe the further development carefully.

So at least we know the opinion of those EATCS member who care. Next time we just need to remember to inform intelligent adults of the importance to actually vote.

A 9-input sorting network in action

IT University of Copenhagen opened its doors to the public last Friday in connection with the city-wide “Culture Night”, so I used the opportunity to implement the Sorting Networks activity.

ITU has a big stair case in its atrium, which had the proper size for a 9-input sorting network. I measured everything up, found a good-looking network in Knuth’s The Art of Computer Programming, and sketched the layout for the friendly folks at Facilities Management.

The network was “drawn” on the stairs using adhesive tape, which took a few hours on the day before the event. It looked absolutely splendid. The activity was manned with enthusiastic undergraduate students for several hours, who herded eager and intrigued guests of all ages through the maze of comparators. A smashing success.

Also, a student volunteered to translate the Wikipedia page on sorting networks into Danish, so the outreach activity had a permanent, digital result as well: Sorteringsnetværk.

Originally, I had also promised myself to produce a large poster or two next to the activity, which should explain what’s actually going on, why sorting is important, and (in particular) show a few more concrete networks of various sizes. This would have given the whole activity a bit more scientific muscle. Alas, I failed to get this done in time. Better next time.

I also failed to show up in time for the kick-off, instructing the student volunteers in how the whole thing was supposed to work. Apparently, they spent a good number of attempts running the network in the reverse direction (from the top of the stairs and down, which arguably is the obvious direction), and tried to find the bug! So now they know that sorting networks don’t necessarily work in both directions. (But insertion sort does!) This may be a fresh research question: find an optimal bidirectional sorting network for 9 inputs.

All in all, a splendid event. Thanks to everybody who helped, or just wanted to get themselves sorted out.

Based on my quick perusal of list of accepted papers [PDF], here’s a list of papers related to exponential time computation, together with references to online version — I’m probably missing some. Updates are welcome.

• Counting Perfect Matchings as Fast as Ryser [arxiv.org 1107.4466], by Andreas Björklund
• Fixed-Parameter Tractability of Directed Multiway Cut Parameterized by the Size of the Cutset, by Rajesh Chitnis, Mohammadtaghi Hajiaghayi and Dániel Marx
• Co-nondeterminism in compositions: A kernelization lower bound for a Ramsey-type problem [arxiv 1107.3704], by Stefan Kratsch
• Weak Compositions and Their Applications to Polynomial Lower-Bounds for Kernelization [ECCC 2011-072], by Danny Hermelin and Xi Wu
• Subexponential Parameterized Algorithm for Minimum Fill-in [arxiv 1104.2230] by Fedor V. Fomin and Yngve Villanger
• A Satisfiability Algorithm for AC₀ [arxiv 1107.3127], by Russel Impagliazzo, William Matthews and Ramamohan Paturi
• Compression via Matroids: A Randomized Polynomial Kernel for Odd Cycle Transversal [arxiv 1107.3068] by Stefan Kratsch and Magnus Wahlström
• Fast zeta transforms for point lattices, by Andreas Björklund, Thore Husfeldt, Petteri Kaski, Mikko Koivisto, Jesper Nederlof and Pekka Parviainen
• Shortest Cycle Through Specified Elements [PDF], by Andreas Björklund, Thore Husfeldt and Nina Taslaman
• Kernelization of Packing Problems, by Holger Dell and Dániel Marx
• Linear Kernels for (Connected) Dominating Set on H-minor-free graphs [PDF], by Fedor V. Fomin, Daniel Lokshtanov, Saket Saurabh and Dimitrios Thilikos
• Bidimensionality and Geometric Graphs [arxiv 1107.2221], by Fedor V. Fomin, Daniel Lokshtanov and Saket Saurabh

An amazing number of kernelisation (and, I presume non-kernelisation) papers. And lots and lots of exciting papers in many other fields as well.