Yuri Gurevich from Microsoft Research [1] gave a very erudite and somewhat interesting Google Tech Talk on the Church-Turing thesis today. The reward for patiently listening to a poor video quality H.323 session across the Atlantic at midnight was the discovery of something totally new: Abstract State Machines.

Update (The Video is Up):

I have trouble understanding ASMs as a fundamental model for computation like Lambda Calculus or Post-Turing Machines. But apparently “States” and “State Transitions” are good enough for universality. The advantage over the Standard Models is supposed to be the expresiveness and better mapping to high level structures and algorithms. This makes them very suitable for Formal Models , Verification and Validation. The video of the talk should be out soon and I will post a link when that happens. But the two most interesting personal takeaways from the talk were totally unrelated to ASMs:

- Kolmogorov’s physical view of computation, entropy and information is completely fascinating. I should really find a readable text on Algorithmic Information Theory.

- Donald Knuth once remarked on Artificial Intelligence: There are two great unsolved problems in AI – What is A ? and What is I ?

Even if I didn’t make out much else from the talk, Don’s snide humor was totally worth an hour

[1] Yes, we do let people from Redmond into Googleplex – Stan needs to be fed once in a while.

Read this on Jonathan’s blog: http://blogs.sun.com/jonathan/entry/will_java_be_the_world

Its a great idea, no doubt. Just 11 years too late for Windows 98 – Long after people abandoned writing lousy desktop applications with ugly AWT or less ugly Swing. This time around Sun has a new secret weapon: JavaFX. But why would developers abandon Flash, AIR, Silverlight, OpenLaszlo, XUL and jump to a new platform ?

0) The language is horribly weird and doesn’t fit into the brains conditioned by ActionScript. F# and Ocaml appear benign by comparison.

1) Its not even multi-platform yet.

2) Dude, where is my IDE ? Not Netbeans. Something like that shiny “Adobe Flash” thing.

3) If the IDE doesn’t exist because this is targetted at “Enterprise Customers”, then where the fsck are the UnitTests ?

And somebody thought that developers will ignore these fixable pain points and jump right into JavaFX  ? Esepcially when Oracle is all set to take over Sun’s business and give lots of love and care to desktop applications ?

But the icing on top of most cakes made at Sun is the business plan. Mr. Schwartz writes:

“Candidate applications will be submitted via a simple web site, evaluated by Sun for safety and content, then presented under free or fee terms to the broad Java audience via our update mechanism. Over time, developers will bid for position on our storefront, and the relationships won’t be exclusive (as they have been for search).”

Really ? When was the last time you paid for a desktop application ? Impulse purchases on mobile phones by bored American Teenagers is a different market. It is a market where a *massive* quantity of high quality closed and open-source apps don’t exist to compete with you.

And “bidding” for storefront positions ? Thats like bidding for Search Result Rankings. There is no price-point equilibrium that would work favorably for both Apple and Mr.T to promote Mr.T’s Ringtone to No.1 on the IPhone Store. Thats simply not how the Free Market works – you cannot fool all the people all the time. That is why an unscrupulous company like Apple has to use “honest” metrics such as moving averages of downloads and ratings to determine rankings for Apps.

If neither consumers nor producers pay money for this App Store, where is the business ? Sun’s top brass doesn’t even know how to make profits out of selling “physical” commodities like servers. I take all this hand-waving about Desktop AppStores with a few tonnes of Salt.

Just as the US. Congress rapped Detroit CEOs on the knee for leading Ford, GM and Chrysler to doom, somebody should question hi-tech CEOs for wasting billions in capital and sending the output of thousands of the brightest engineers on the planet to /dev/null.

Doug Hofstadter might find it amusing. But I find it incredibly annoying that when I want to read news online, I see news about news or media reporting about media or celebrity gossip about media celebrities. Talk about self-serving institutions. Being very interested in Statistics, all this recent Trash-Talk about Television ratings for the Indian Premier League got me interested in the methodology used for measuring TRP ratings.

There are apparently just two main companies that engage in the business of measuring TRP ratings:

1. Television Audience Measurement: http://www.tamindia.com/tamindia/

2. Audience Measurement and Analytics: http://www.audiencemap.com/

Here is a detailed rundown on either: http://www.chennaitvnews.com/2008/09/tam-tam-i-am-topper.html (To my big surprise, they actually have devices installed in people’s homes to sample usage)

Whats incredible is that, in a country rampant with corruption where Price Waterhouse Coopers played Dogberry to Satyam, we actually have a multi-billion dollar TV-Ads Industry that rides on the data provided by two sources with possibly highly skewed interests. Online advertising has a very nice solution with Stable Equilibrium in the form of Second Price Auctions. But in a market with no regulatory authority, I don’t think there is even a theoretical model where the TRP Auditors have a high incentive to be truthful. Lying their assess off seems like a dominant strategy and I suspect that is what happens all the time. (Please leave a note if you know of prior research in Game Theory that applies here).

So what is a fair (if noisy) way to measure the impact of the IPL ? Here is a thought: The NIXI – India’s only Internet Exchange Point where all ISPs do Peering for local traffic has very pretty MRTG graphs that shows aggregate throughput across all the routers in the exchange point.

http://nixi.in/index.php?option=com_content&task=view&id=52&Itemid=79

And unless I am very mistaken, the time on the graphs is off by 12 hours and the 700 Mbps drop at 8 p.m (a.m on the graph), is when people stop watching Skateboarding Dogs and tune into the IPL. Be afraid of Geeks, TRP auditors – we haz graphs.

Far too much of my time in recent years has been spent by an all consuming obsession to understand Turing’s original proof as outlined in “On Computable Numbers with an application to the Entscheidungsproblem”. Much like Alice in Wonderland in pre-teen years and Super Mario Bros. of teenage yore, I suspect there was very little value in spending time thusly. But there is light at the end of the tunnel and for some vague definition of “complete”, I call my study of Turing’s paper done for the time being.

If you are happy with reading other people’s description of the proof and don’t intend to inflict pain upon yourself or like to have a life, try Martin Davis or Charles Petzold. For the rest, I am outlining the list of topics that were useful in understanding the proof and beyond:

- A passing knowledge of German and weird Gothic Fonts

- Diophantine Equations, Hilbert’s 10th Problem, Entscheidungsproblem

- Euclidean Geometry, Constructions and Euclidean Numbers

- Naive Set Theory, Cardinality of Infinite Sets, Continuum Hypothesis, Dedekind’s Theorem, Transfinite Numbers

- Type Theory, Russell’s Paradox

- ZF Set Theory, Axiom of Choice

- Cantor’s Diagonalization Argument, Godel Numbering

- Overview of the proofs of Kurt Godel, Alonzo Church, Stephen Kleene, Julia Robinson, Yuri Matiyasevich

- Integers, Reals, Irrationals, Transcendentals

- Crux of Turing’s Proof: Computable Numbers, Definable Numbers, Turing Machines, Circle Free Machines, Skeleton Tables, Enumerability of Computable Sequences, Description Number, Satisfactory Numbers, Standard Description and Universal Machines, Diagonalization applied to Description Numbers, Inability to construct Turing Machines for Circle-Free determination, Hilbert Functional Calculus a.k.a First-Order Logic and Automatic Theorem Proving using Turing Machines, Computable Functions, Universal Machine expressed via First-Order Logic, Equivalance of Propositional Provability and Circle-Free condition. Q.E.D.

Many of the above subjects require a lifetime’s devotion themselves and I was merely a tourist through that fascinating mathematical landscape. The initial part of the study was heavily dependent on Google, ArXiv and Wikipedia. But about a year ago, I moved to a country where Amazon.com delivers books and that made life much easier.

Much of the study overlaps with my next growing obsession, “On Formally Undecidable Propositions of Principia Mathematica and Related Systems”: Godel must be completed !

Pardon all the puns

Long long ago, before Claude Shannon modeled the distribution of English Words as a Markov process, before Larry and Sergey modeled the Random Surfer as a Markov Chain on the Graph of the Internet, before SciGen made Markov Chains the legend of Slashdot, before even Monte-Carlo and Metropolis-Hastings, there was Jonathan Swift.

Martin Gardner’s “Logic Machines and Diagrams” is a highly recommended book. Especially for those who are interested in the early history of computing from a symbolic logic processing perspective as opposed to the history of the numeric processing computer. The book opens with the curious character of Ramon Llull. If you ever studied AI from Russell & Norvig’s legendary AIMA and remember the cover image – Among Lewis Caroll, Turing, Frege, Babbage and Aristotle you can find this messy drawing in the left hand corner that belongs to Mr. Llull.

Ramon Llull was a curious character. He believed in logic and he believed in religion. (Much like Aumann or Kripke for contemporary examples). He believed that he could encode the principles of Christianity into a consistent formal system and use it as a tool to derive propositions, detect contradictions and convince the Crusading Muslims about the nature of God and Truth. He got killed for talking batshit and pissing people off before he got around to doing any of this but there was something interesting he did manage to concieve – The Lullian Circle – Seen in the cover of the aforementioned AIMA.

The Lullian Circle is a series of concentric disks with markings along the circumference. The markings represent words or phrases. By rotating and aligning them you generate a combinatorial number of sentences. For each of them, an Index is referenced as the answer which either asserts the truth value of the statement or offers a proposition for the question. Most of Lull’s works did not have Socratic appeal and was pseudo-scientific in nature. But the Lullian circle apparently inspired Leibniz in his syllogistic pursuits.

This is where Jonathan Swift comes in. In Book 3, Lemuel Gulliver visits the Grand Academy of Lagado, where he sees “The Engine” – A 20 x 20 grid of cubes inscribed with words on their sides. Each of the 20 rows and 20 columns are rotated by levers. The Professor calls upon his students to rotate the lever and randomly stops them. Whenever they encounter a sequence of 3 or 4 words that could be reasonably fit into a real sentence, they transcribe it and produce “great works of art and science without genius or study” as the parody goes.

According to Gardner, this is Swift pulling a fast one at the expense of Llull. Not only that, but we also have one of the earliest recorded instances of a Markov Chain in action. Instead of stochastically extracting words from a distribution, the students of Lagado generate random words and see if they fit a distribution. And they beat SciGen to it by a few hundred years.

Happy St. Patrick’s Day to everyone in Dublin [1]

[1] – As coincidences happen, Swift is interred in St. Patrick’s Cathedral here.

Strip Generator is awesome (via Harish) ! I couldn’t resist giving it a try:

(Click on the image for a readable version)

What is incomputable in two dimensions becomes computable in three. Fantastic intuitive explanation and visualization of Smale’s Paradox:

Smock Alley Theatre is a special place and the performance of the stage actors in “The Death of Harry Leon” is something else. Conall Quinn’s script itself is not the high point of the play as much as the magnificent intensity that the cast brought in. The backdrop is against the oh so familiar 1939 Europe with an imaginary twist of Nazi occupation and a Ghetto in Ireland.

The play starts with an engimatic question: “Are there passions more important than life itself ?”. It raises questions on what National and Cultural Identity mean and the role of  collective and personal history. Personally, I found parallels with Joyce’s Ulysses: Leopold Bloom’s Jewish identity and tribulations, Stephen Dedalus’s “History is a nightmare from which I am trying to awake”. There are several unexpected places with humor in the script from the stereotypical black-and-white characters – But none from the very gray Mr. Leon.

The high points of the script were the little gems of wit that kept constantly coming:

“The luxury of being a poet is to not have firms views on anything.”

“Wagner’s great legacy was not his music but the way he changed the music that came before him”.

“The French really won the war in 1812 but people remember only Napoleon’s retreat – That’s Tolstoy’s history.”

The performance of the cast was just mind-blowing. The high level of awareness and the hightened sense of being alive that stage plays usually induce was multiplied several times over. Highly recommended to Dubliners – Just two more performances left.

There are numerous literary artifacts and references in Dublin life that you tend to take them for granted after a while. One of the houses where James Joyce lived is less than a minute from my place. While Oscar Wilde, Bernard Shaw, Jonathan Swift, Samuel Beckett, Sean O’Casey and William Yeats loom large in one form or the other when I have to go to the SuperMarket or the Theater.

But the DART is apparently not so high on nationalistic fervor. Here is some interesting Welsh poetry I found on the train today:

Transcript follows.

Moorland
RS Thomas

It is beautiful and still:
the air rarefied
as the interior of a cathedral

expecting a presence. It is where, also,
the harrier occurs,
materialising from nothing, snow-

soft, but with claws of fire,
quartering the bare earth
for the prey that escapes it;

hovering over the incipient
scream, here a moment, then
not here, like my belief in God.

Cuz killin’ him is fun sez Calvin

And its snowin’ in Dublin