The Internet of the Present

On this blog we rarely get non-spam comments on posts more than a few days old. Sometimes I can bring up a topic I had posted on just a few months ago and no one will notice. When people said they enjoyed my blog I used to ask them what posts they liked. I would just get a blank stare. I don't ask anymore.

In theory you can look at our old posts through the "Blog Archive" section on the left column (if you are reading this on the blog website). I doubt anyone actually does. Occasionally people get to old posts via Google searches but I've come to the realization that most posts I wrote more than a few weeks ago will never be read again.

That's too bad. Many of them are still quite relevant. But we live in the present. I'm just as guilty as everyone else. Sometimes I'll discover a great new blog and subscribe to its posts. But I'll never go back and read the old posts.

Blogs seem to be going out of style. Twitter don't even try, one cannot easily see someone's old tweets, and any brilliant tweet I make will expire in usefulness in a just a few hours. Google+ is similar. Interestingly Facebook with their new Timeline makes it possible to explore someone's early posts. The past remains there just in case someone cares.

I have no great insights or solutions to this problem. But what does it matter. A week from now you'll forget this post even existed. 

Turing's Titanic Machine!

In the March CACM, Barry Cooper writes

We quote Peter J. Denning introducing the ACM Ubiquity Symposium on "What is Computation?" as saying: "Researchers in biology and physics have claimed the discovery of natural computational processes that have nothing to do with computers."

With Lance Fortnow distinctly underwhelmed: "Some people outside of computer science might think that there is a serious debate about the nature of computation. There isn't."

As often happens when experts disagree, the truth lies somewhere in between.

No it doesn't. My extreme point of view: A strong belief in the Church-Turing thesis that Turing machine captures the true notion of computation now and forever.

What's next? Casting doubt on 1+1=2? Sure no one has yet proved 1+1=3 but that doesn't mean it won't happen someday.

The Erdos- de Bruijn theorem

The mathematician Nicolaas Govert de Bruijn passed away on Feb 17, 2012. The number of things named after him is quite large. I will discuss the Erdos-de Bruijn theorem.

Erdos-de Bruijn theorem: An (infinite) graph G is k-colorable iff every finite subgraph is k-colorable.

I will sketch the proof for the case where G is countable. We can assume the vertices are {1,2,3,...}. Let COL_i be a k-coloring of G restricted to {1,...,i}. We will use the COL_i's to obtain a k-coloring of the entire graph G. We can assume the COL_i's use colors {1,...,k} so we can speak of the least color j such that blah blah.

We color node 1 by the least color that an infinite number of the COL_i's color 1. Then REMOVE all of the COL_i's that do not use that color on 1. (We kill all those that disagree with us! as I told my students.) Note that there are still an infinite number of COL_i's left.

We color node 2 by the least color that an infinite number of the COL_i's THAT ARE LEFT color 2. Then REMOVE all of the COL_i's that do not use that color on 2. Note that there are still an infinite number of COL_i's left.

And so on.

End of Sketch of Proof.

1. This type of argument can be used to proof the following:
   1. If we already have the infinite Ramsey Theorem on N, we can obtain the finite Ramsey Theorem and (with a small trick) the Large Ramsey Theorem.
   2. If we already have the finite dilworth theorem (any FINITE partial order of width w can be covered with w chains) then we can obtain the infinite version of Dilworth's theorem: if an INFINITE partial order has width w can be covered with w chains.
2. The method is called compactness argument and is very general. It is related to topological compactness, but I won't to into that here. (If a reader has a short explanation or pointer, please post.)
3. The method is noneffective in that if you are given a Turing machine that tells you, for all i,j, COL_i(j), then the proof does not appear to be able to give you a Turing machine for a coloring of G. There are two ways this has been formalized, though I list three since the third one strengthens the second one. (For details see my survey of recursive combinatorics here.)
   1. (Bean, 1976) There is a computable graph (Vertex set N, Edge set decidable) that is 3-colorable but there is no computable finite coloring whatsoever. (He also made the graph planar, which was not needed but nice.)
   2. (Carstens and Pappinghaus, 1983) For every k ≥ 3 There is a highly computable graph (Vertex set N, the function that, given a graph, outputs its finite set of neighbors is computable) that is k-colorable but not computably k-colorable. (NOTE: if a highly comp. graph is k-col then IT IS computably 2k-1 colorable.)
   3. (Schmerl, 1980) For every k ≥3 There is a highly computable graph (Vertex set N, the function that, given a graph, outputs its finite set of neighbors is computable) that is k-colorable but not computably (2k-2)-colorable.

Nash and the NSA

By now most of you have heard about Nash's recently released letters to the NSA (press release, letters). Not only did John Nash think about computation and cryptography, there are many ideas in these letters that were a bit ahead of their time when Nash sent these letters in 1955.

• Expressing a cryptographic process as a Boolean function with input bits. 
• Breaking the cryptographic system as a function of the key length.
• Exponential in key length as computationally hard and polynomial in key length is computationally easy.

His conjecture is quite striking.

For almost all sufficiently complex types of enciphering, especially where the instruction given by different portions of the key interact complexly with each other in the determination of their ultimate effects on the enciphering, the key computation length increases exponentially with the length of the key, or in other words, with the information content of the key.

The significance of this general conjecture, assuming its truth, is easy to see. It means that it is quite feasible to design ciphers that are effectively unbreakable. As ciphers become more sophisticated the game of cipher breaking by skilled teams, etc. should become a thing of the past.

The nature of this conjecture is such that I cannot prove it, even for a special type of cipher. Nor do I expect it to be proven. 

Nash's conjecture, even for a specific cipher, would imply P ≠ NP, 16 years before Cook defined the problem, and the significance resonates with the Diffie-Hellman article written 21 years later

Theoretical developments in information theory and computer science show promise of providing provable secure cryptosystems, changing this ancient art into a science.

Given Nash's insights, why did the NSA react so cautiously to these letters.

• This was not a letter from Nobel Laureate Nash but from Assistant Professor Nash.
• There is a strong positive correlation between people who claim they are not a crank and those that are.
• Nash's arguments didn't apply that well to the relatively slow digital computers of the time.
• Nash didn't give a particularly useful cryptosystem.
• I don't even believe Nash's conjecture: There are plenty of complex enciphering techniques, such as the Engima machine, which the NSA did know how to break. Hard to break cryptosystems come from more structured ciphers based on algebraic properties like AES and RSA.

Is 99.8% Secure Secure?

Guest post by Janos Simon

A group of researchers (Arjen Lenstra and collaborators  from EPFL Lausanne and James Hughes from Palo Alto) published a study, Ron was wrong Whit is right, of new vulnerabilities of cryptosystems. The New York Times picked up the story. Although Lenstra et al discuss several cryptosystems, their results are particularly relevant to those based on RSA. The title mirrors their conviction that cryptosystems based on a single random element have fewer key generation problems than RSA, that uses two random primes.

The technical problem they identify in RSA is the following: The RSA cryptosystem uses a modulus n that is the product of two large "random" primes p and q. Actual keys may not be truly random, and this may cause several possible problems:

1. Different users may end up with the same n. Since a user knows the factors p, q, she will be able to decrypt the data of any user with the same modulus.

2. If two users share one of the factors, (user A's modulus is pq, user B's is pr) they will be able to decrypt each other's data. Given two moduli, one can use the Euclidean algorithm to determine whether they have a common factor, and find it if it exists.

Note that the second vulnerability is more insidious: in the first only the user with the matching key can decrypt the messages of its mate, while anyone can  explore the web looking for pairs of keys with a common factor.

The lack of randomness in key generation may be caused by bad choices for the seed of a random number generator. As an extreme example, devices may be shipped with a standard common seed. In this case all devices would generate the same n. In general, if the collection of seeds is a low entropy set, with high probability insecure keys will be generated.

The EPFL group collected 11.7 million public keys "while avoiding activities that our  system administrators may have frowned upon" and essentially found that about 99.8% of the keys were not insecure (to the extent that they did not suffer from the vulnerabilities above.)

Is this secure enough?

Note that .2 percent of 11 million is tens of thousands of bad keys.

To make matters murkier, another group with researchers from the University of Michigan and UCSD did a somewhat similar experiment. Their results are not published yet, but one of the authors, Nadia Heninger blogs about their results in Freedom to Tinker. They find a similar proprtion of bad keys, but they claim that the vulnerability mostly occurs with embedded devices like firewalls and routers, so "important" keys like bank certificates are not affected. Lenstra et al disagree.

Perhaps we should be happy that these vulnerabilities are not due to weak Theory, but to bad implementations of good theoretical ideas....

The Envelope Please

The conference that shares its namesake with this blog has announced their accepted papers. The 27th Conference on Computational Complexity itself will be held in Porto, Portugal June 26-29. If you go, stop by England on the way and celebrate the 100th anniversary of Turing's birth (June 23) in either Cambridge or Manchester.

Lots of great papers accepted to the conference. For biased reasons I like Limits on Alternation-Trading Proofs for Time-Space Lower Bounds by Sam Buss and Ryan Williams. They give some compelling logical reasons why we've hit the limit of current techniques in proving time-space tradeoffs for Satisfiability. Alon, Shpilka and Umans found connections between Sunflowers and Matrix Mulitplication. Finally a plug for my student Josh Grochow's first Complexity paper Matrix Lie Algebra Isomorphism.

Presidents Day Poll- what does the youth of american think about....

(In honor of President's day which was two days ago.)

On Presidents Day last year I had my classes fill out a form saying who they thought was the best, second best, third best, and worst president. I gave them a list and asked them to just mark 1,2,3 (for best, second best, third best) , BAD (for worst) on it. I omitted Obama, Bush Jr, Clinton from the list since they are too recent. So, what does the youth of America think? Or at least the youth taking Honors Discrete Math or Automata theory?

Here is the list or presidents ranked by roughly how well they did. (Some are not included since they did not get any voters pos or neg.) I (somewhat arbitrarily) gave 3 points for each ONE, 2 points for each TWO, 1 point for each THREE and -3 points for each BAD. Are these the best weights to use? Is there a way of arguing which weights are best? This is a variant of a standard voting problem. The standard problem does not include the option of BAD for negative points. I don't think there is an optimal answer. Weights that would NOT be good to use would make the ONES's get a lot more than the TWO's since I suspect this gap was not so large in peoples minds. Or I could have had THEM give point values between (say) 1 to 100 for the ONE, TWO, THREE and between -1 and -100 for the BAD. Maybe I'll do that next year.

1. Abraham Lincoln: 15 ones, 10 twos, 10 threes: 75 points.
2. Theodore Roosevelt: 8 ones, 8 twos, 4 three: 44 points.
3. Franklin D. Roosevelt: 11 ones, 7 twos, 7 threes, one B: 51 points.
4. George Washington: 7 ones, 4 twos, 8 threes, one B: 34 points.
5. Thomas Jefferson: 6 ones, 5 twos, 5 threes: 33 points
6. Dwight Eisenhower: 1 one, 3 twos, 5 threes: 14 points.
7. John F Kennedy: 2 ones, 5 twos, 6 ones, 1 B: 14 points.
8. Woodrow Wilson: 1 one, 1 two, 3 threes: 10 points.
9. Harry S Truman: 2 twos. 6 points.
10. James Polk: 1 one, 1 two: 5 points.
11. John Adams: one 1, one 2, one B: 4 points.
12. William Henry Harrison: one 1: 3 points.
13. Lyndon B. Johnson: one 2, one 3, one B: 2 points.
14. Andrew Jackson: 2 ones, 1 two, 2 B's: 2 points.
15. Ulysses S. Grant: 1 two, 2 B's: -4 points.
16. Zachery Taylor, Rutherford B Hayes, Chester Arthur, Millard Fillmore, Warren Harding, Gerald Ford: 1 B: -3 points.
17. Jimmy Carter: 1 one, 1 two, 4 B's: -5 points. CORRECTION ADDED LATER: SHOULD BE -7. ARITHMETIC MISTAKE. MAKES HIM RANK BELOW BUCHANAN AND TAFT!
18. James Buchanan, William Taft: 2 B's: -6 points.
19. Ronald Reagan: 1 one, 3 twos, one 3, 8 B's: -12 points. CORRECTOIN ADDED LATER: SHOULD BE -14. ARITHMETIC MISTAKE. RELATIVE ORDER UNCHANGED.
20. Herbert Hoover: 5 B's: -15 points.
21. George Bush: 6 B's: -18 points.
22. Richard Nixon: 1 one, 1 two, 10 B's: -25 points.

My thoughts

1. I thought George Washington would do better.
2. I'm surprised that Theodore Roosevelt did so well. Bart Simpsons likes him, though Lisa Simpson prefers FDR (From the episode Bart stops and smells the Roosevelt's.
3. The person who ranked Hayes as the worst president of all time either knows much more about the Hayes administration then I do or was just putting things down at random.
4. The vote for William Henry Harrison was a joke- the guy who voted for WHH is named Henry and liked that his first name was WHH's middle name.
5. Dwight Eisenhower did better than I thought he would.
6. Richard Nixon did worse than I thought he would. I thought today's youth didn't know about Watergate. George McGovern (who Nixon beat in 1972 and is still alive) recently said that if he had won in 1972 then Nixon's legacy would be much better (going to China, Detente with Russia, EPA, Okay on Civil Rights.) Nixon would be considered a left wing democrat today.
7. George Bush did so bad that I think people may have confused him with his son W.
8. Some of my opinion: (1) I rank George Washington first since the very act of STEPPING DOWN after two terms set the tone for peaceful transitions of power. Note that young democracies today the most important election is the one where the person in power has to voluntarily step down. (2) For worst prez I wouldn't call someone BAD just because I happen to disagree with their policies. It has to be someone who (in contrast to Washington) did things that undermine our democracy. Two that come to mind are Nixon (Watergate) and John Adams. (Alien and Sedition Acts). George W Bush (Patriot Act) might also qualify but its too early to tell. Other wartime restrictions on freedom (happened in many wars) might also qualify. The corruption of the Grant and Harding's administration were deplorable but I don't think they rise to the level of undermining our democracy. There are probably other presidents who qualify for this honor but not being an expert on Presidents, I don't know who they are.
9. In the book Hail to the Chiefs (a humorous though mostly accurate look at the presidents) in the first edition she said that Buchanan and Andrew Johnson were not looked upon kindly by historians, which is true. In the second edition she made the points many times with many presidents (including those two) that how well you do is VERY MUCH a matter of timing, luck, and History. To paraphrase Buchanan couldn't stop the Civil War. By that point nobody could. Andrew Johnson had to reunite the country and deal with the South after the Civil War. That's pretty hard too. I agree that there are many thing outside a presidents control, and they some blame or praise may be unwarranted.

Aggie for a Day

About 25 years ago I visited a college friend, David Jackson, then a grad student at Texas A&M. He was a Ph.D. student in Food Science doing his doctorate research on starch. He had a tortilla maker in his lab. Made me wonder if I was in the right field. David is now making tortillas in Nebraska.

Last week I made my second trip to College Station this time to visit the CS department, give a talk and meet lots of great researchers.

Landlocked Texas A&M has one of the world's leading Nautical Archaeology programs. We went to visit and a grad student came out, said "Howdy", and gave us a tour of models of the ships they have been excavating.

Robin Murphy arranged a tour for me at Disaster City (that's us pictured above). Disaster City is one of the largest training grounds for emergency responders with collapsed buildings, rubble piles, derailed trains and other sites to train people, dogs and robots, the last of which is Robin's specialty. Some of Robin's students were testing out a flying video drone that day. Robin gets involved in disaster areas such as Fukishima. Saving lives with computer science. Makes me wonder if I got in the right field.

People solve math problems for the prize money! NOT!

Why do people or organizations offer Prize Money for mathematics?

1. Paul Erdos: He offered money to solve problems that he found interesting. I assume he wanted them solved but he also wanted to encourage a line of research beyond the problem. He had a (well deserved) reputation as a brilliant mathematician, so if he couldn't solve a problem it was hard. People would somtimes not cash the check and frame it. I've heard that with color copiers people now copy it, frame the copy, and cash the check. Did he insist that it appear in a journal or just need to be convinced? I don't know but I would think just need to be convinced.
2. Bill Gasarch: He offered $289 dollars for one problem, which, as you know, was recently solved by Steinbach and Posthoff (see here). While Gasarch has nowhere near the reputation of Erdos and his problem was not a deep math problem, this problem caught on as a matter of luck and timing. The blog helped, and Brian Hayes picking up on it helped. Gasarch wanted to get this problem solved, but did not quite know if it would inspire a line of research. It did (according to the solvers) present a problem just on the edge of what is possible to solve of this type. Gasarch used paypal. Hence, alas, Steinbach and Postoff won't be able to frame a check or its copy.
3. Scott Aaronson: His 100,000 offer (see here) for ...demonstration, convincing to me, that scalable quantum computing is impossible in the physical world This is different than most prize offers in seveal ways: (1) He gets to decide, not a ``refereed journal''. (SIDE NOTE-here is an idea: a prize that pays out only if the article appears in a non-elsevier journal.) (2) He does not expect to pay out (but he happily will if someone really convinces him). I believe him on this, though 100,000 is a lot of money. He wants to inspire people to think about these questions. The only thing analagous I can think of is prizes for REAL parapsychology- they don't expect to pay out but would be happy to since the world is more interesting if parapsychology is true.
4. Millienium prizes: I believe these one million dollar prizes are the most ever offered for solving particular math problems by an order of magnitude (if that is not correct, please leave a polite comment correcting me). Clearly the Clay Instuite wants to encourage research in these areas. Why so much money? I assume to REALLY put these problems on the map. There is no mathematician of the stature of Hilbert nowadays who could state problems of importance in a way people would listen. Smale tried (see here) but those problems never got the status of either Hilbert's problems or the Millenium problems.
5. Godel Prize: Best paper in theory published in the last 14 years (used to be 7). I wonder- if someone posted a solution to P vs NP on arXiv and it was correct, would they really not get the Godel prize? I suppose not. A bit awkward in that if your publish in a period of time when many good papers come out you could be out of luck. Why did they extend the window from 7 years to 14 years? Speculation: people are getting worse at getting papers out into journals so they had to extend it. Enablers? Given once a year.
6. Turing Award: I am not quite sure if this is for one paper, a body of work around one idea, or a career. It can go to people who never proved a theorem since its open to all computer scientists. The prize money has gone from $2000 to $250,000. Given once a year.
7. Fields Medal: Given for a body of work. About $15,000. High Prestige, low dollars. How come the Turing Award was able to increase its money value but the Fields medal was not? I honestly want to know. Given once every 4 years to a set (group? locus?) of people.
8. King Faisal prize: I blogged about this here so I'll be brief: High dollars ($400,000), but low prestige. I assume the origin was to try to give glory and prestige to Saudi Arabia who gives out the prize. I don't think it worked. Aside from its origins it also has the problem of being unfocused in that they have awards for Sciene (which is sometimes math) and also for Muslim scholarship, and other areas.
9. Here is a list of other prize. Some thoughts
   1. Some are for solving a particular problem, some are for a body of work in a particular area, some are for a body of work and the area can be anything within mathematics.
   2. Some are restricted to a subset of people, some are not. Thats a tautology!
   3. People do not solve problems for the money. Most of the prizes are too small for that and those that are large are for really hard problems.
   4. There are many of them, more than I thought. I still doubt I'll win one. The closest I ever came was being linked to on the Wikipedia page on the Godel Prize (see this Blog Entry about why that happened.)

Sloans and More

The Alfred P. Sloan Research Fellows were announced today including Northwestern's own Nicole Immorlica. Other winners in theoretical computer science include Xi Chen, Nate Foster and Prasad Raghavendra. A shout out to TTIC who have their second Sloan Fellow in Jinbo Xu.

Computer science did well in the president's budget for FY 2013. CISE head Farnam Jahanian gives the details. Of course now the budget has to get through congress.

Tomorrow there will be a celebration of twenty years of the NITRD (Networking and Information Technologies Research and Development), an interagency program that has heavily supported CS research over the past two decades. Quite an impressive list of speakers. There will be a live webcast of the event.

FOCS call for papers is out. Submission deadline is April 4.

Barney the Evil Dinosaur

This is an old story from before I had a blog, but one of my favorite on when technology goes bad.

In the late 90's, the undergraduate CS coordinator at the time, Don Crabb, also wrote a column on technology for the Chicago Sun-Times and would get tons of tech stuff to review. One of these items was a robotic Barney the Dinosaur that interacted with the Barney and Friends show on PBS. I took Barney home and tried him out with my then 3-year old daughter Annie.

He worked as advertised, singing along with the characters on TV. But at one point Annie said "Let's read a book Barney". Barney replied "Let's watch TV". Annie said "OK". Definitely sending the wrong message here.

Later Annie was playing with Barney in the kitchen. Annie, who was toilet training, said to Barney "I have to go wee-wee". Barney said "Let's play a game". Annie said "OK". Soon I had a mess to clean up.

That was the end of Barney.

STOC 2012 accepts are posted

STOC 2012 paper accepts are posted here. Travel support for grad students (which I am involved with) is posted here. On a quick glance:

1. I tried counting the paper for how many were in which categories. I got dizzy so I stopped. Also, for some its hard to tell the area just from the title. There DO appear to be many papers on complexity.
2. I hope that when the papers are finished there are pointers to all of them on the website.
3. There will be four workshops (see here) Under Tutorials it says TBA, so there may be some of them. What is the difference between a workshop and a Tutorial? I ask nonrhetorically.
4. When I goto an MAA or AMS conference there are (1) invited papers, (2) contributed papers, (3) Math Jeopardy game, (4) demos, (5) other things. When I goto STOC or FOCS or CCC or just about any theory conference its (1) submitted papers that got accepted. There MIGHT be a rump sessions (CCC, Crypto does this) a workshop or tutorial (STOC, FOCS does this- anyone else?) an invited talk (FCRC has these, Sometimes others do) a poster session (FCRC has had these. Have others?) My objection here is NOT that STOC has the submitted paper format and that STOC and FOCS are other conferences are too highly valued. (That is another debate which we've had before.) My objection is that all of the theory conferences only have VERY FEW kinds of activity- talks on papers that were accepted. I would like to see more VARIETY in activities.
5. The word Quantum only appeared in two titles. Are there other Quantum papers (I would guess yes).

The 17x17 problem SOLVED! (also 18x18)

THE 17x17 PROBLEM HAS BEEN SOLVED!!!!!

On Nov 30, 2009 I posted here the following challenge:

If someone emails me a 4-coloring of 17x17 with no monochromatic rectangles then I will give you $289.00

Bernd Steinbach (Institute of Computer Science, Freiberg University of Mining and Technology, Freiberg (Saxony), Germany) and Christian Posthoff (retired from Department of Computing and Information Technology, The University of the West Indies, Trinidad and Tobago, but now in Germany) have found a 4-coloring of 17x17 without monochromatic rectangles!! The coloring is here. I have verified it (actually I asked Daniel Apon and Jim Purtilo to separately verify it, and they have. Also, Semmy Purewal and Brian Hayes did later.) The methods Steinbach and Posthoff used to obtain the coloring will appear in their paper

Most Complex Four-Colored Rectangle-free Grids - Solution of an Open Multiple-Valued Problem (ISMVL 2012. ISMVL stands for International Symposia on Multiple-Valued Logic). They will present this paper on May 14, 2012 during session B1 of ISMVL in Victoria, Canada.)

Once the paper appears there will be a post (with their help, perhaps guest posted by them) on the techniques they used.

Some thoughts:

1. Some very serious people had worked very hard on this. I actually began thinking that 17x17 is NOT 4-colorable.
2. CONGRATULATIONS to Bernd Steinbach and Christian Posthoff!
3. They also found a 4-coloring of 18x18.
4. The only grid that we do not know if it is 4-colorable is 12x21. This is still open and you are URGED to work on it. Sorry, no cash on this one. Do it for the glory!
5. If you are going to ISMVL 2012 then find Bernd and Christian and say hello. More important, talk to them about there work. (I won't be there alas.)
6. The reason I thought that 17x17 was 4-colorable is that there is a rectangle free subset of size 74, so I assumed that one of the colors would appear 74 times. WRONG- The max number of times a color appears is 73.
7. I thought that each color would appear 4 or 5 times in each row and column. WRONG- some appear 3 times in a row or column.
8. I am DELIGHTED to pay out the $289.00.
9. I asked them if they did it for the money (which I doubted). No, but the money made them more aware of the problem.
10. How did they do it? I do not know, but I am looking forward to reading their paper in May when it is available and blogging about it.

Competition

A few people have asked me my opinions on Oded Goldreich's essay On Struggle and Competition in Scientific Fields. I read through Oded's essay I expected to highly disagree with Oded, after all he attacks competition, which is just un-American, and he lays some blame on a small number of scientists "especially those holding administrative positions in the field" which as SIGACT chair puts me in that group.

But as I read the essay, I find myself agreeing with much of what he says. Our conferences have become too much more like competitions rather than focusing on distributing knowledge or bringing the community together. I also agree with many of his suggestions including having conference with more plenary talks, that program committees should create a "program" more than just choosing best papers and that hiring/promotion committees should focus more on the research itself rather than the decisions of program committees, awards committees and grant committees.

There is an faulty underlying assumption in Oded's essay that competition within theoretical computer science is a zero-sum game. Theoretical computer science competes within computer science for faculty slots and grant money. Computer science competes with other sciences and science competes with other needs.

SIGACT is not in the business of choosing winners and losers within the community but rather to promote the field to help increase the number of jobs and grants available to theoretical computer science. As I mentioned last week, awards are an important mechanism that lets us highlight the important research in theory.

Competition for grants, jobs, awards and just attention of other computer scientists helps make us all better allowing us to push for more resources for theory. It would be nice to say that we should just all do good self-motivated research, but the reality is we need those resources if we want theoretical computer science to continue to thrive.

Why do we have awards?

You have a month to get in your nominations for the Donald E. Knuth Prize and the SIGACT Distinguished Service Award.

Why do we have these awards and others like the Gödel Prize, The Turing Award, conference best paper awards, ACM Fellows, Nobel prizes and so much more. Are we just creating CV stuffers? Are we giving departments another measure to rank people? Are we trying to encourage good research through competitive awards? Does anyone have the conscious thought, "I wouldn't normally work on this problem but it could win me the Turing award so I'll do it"?

None of the above. We have awards for the publicity. We want to tell the world about the great researchers and work that they produce. A major award rises above the clutter and let's us say "Les Valiant must be a great computer scientist, he won the last Turing Award" or " Håstad's optimal approximation bounds are a great work in theoretical computer science as you can see from the Gödel Prize." Not a surprise that almost every award comes with a press release.

Are all awards fairly given? Of course not, prize committees are full of humans often comparing apples and oranges. But that's not the point. Awards let us celebrate what's great in computer science with ourselves and with the world.

Dusting off my bookshelf I find a book on FORTRAN

The following quote is from the back of a book that I dusted off and took off of my shelf recently:

FORTRAN is one of the oldest high-level languages and remains the premier language for writing code for science and engineering applications. (NOTE- The back of the book uses Fortran but the spell checker I am using insists on FORTRAN. As a fan of capitol letters, I don't mind going along.)

Was this book written in

1. The 1960's
2. the 1970's
3. the 1980's
4. the 1990's
5. the 2000's (meaning 2000-2009)
6. the 2010's (meaning 2010-2012)

Some questions and thoughts about FORTRAN:

1. How much is FORTRAN used? Perhaps more than you might think: Its in packages that have been running smoothly and quickly for a long time. It may not be worth it to swap it out for C or C++ or something else. However, it may be hard to modify.
2. How much new code in FORTRAN is being written? I suspect not much. UMCP does not have a course in it. Does your school?
3. Since people are not learning FORTRAN we will we become like one of those Science Fiction Aliens who says: Our ancestors left us these machines,but over time we only know how to operate them, not how to fix them or build new ones.

So, when was the book written?

The book is Modern Fortran by Clerman and Spector. The book came out in 2012 (I really need to dust my shelves). I doubt that FORTRAN is the premier languages for writing code in science and engineering. But how far off the mark is this? As always I ask non-rhetorically.

A result of Specker in Recursive Combinatorics

Ernst Specker passed away in December. He has 91. He was not the oldest living mathematician. That title likely belongs to Sergey Nikolsky. A former student of Specker's, Martin Furer, posted about his life and his math on this blog here.

In this post I discuss a results of Specker that is not his most famous (that seems to be the Kochen-Specker theorem) but instead a result that I actually know. Hope you like it.

Background: Ramsey's theorem states that if COL is a 2-coloring of pairs of naturals then there exists an infinite homogenous set H (so every pair from H has the same color). The standard proof is non constructive.

More background: What if you were GIVEN a Turing Machine for a 2-coloring. Could you GIVE ME BACK a Turing machine for a homogenous set? The standard proof does not give this to you, so we are really asking if there is a more constructive proof. So, what is known?

Specker showed that there is a computable 2-coloring of pairs of naturals so that there is NO computable Homogenous set. Here is the proof in brief:

1. Let A be a bi-immune set (no subset of A or its complement is decidable) that is decidable with oracle HALT. You can easily construct such by an initial segment argument.
2. By the Shoenfield limit lemma there exists computable f(x,s) such that A(x) = limit_{s→ ∞} f(x,s). (Easy proof of the direction we need: if A is computable in HALT via oracle Turing machine M let f(x,s) be the result of running M for s steps and using as oracle the first s elements of HALT in some enumeration.)
3. Let COL(x,y) = f(x,y), for x< y. (NOTE- This is a correction, I earlier just had COL(x,y)=f(x,y).)
4. Assume, by way of contradiction, that there is an infinite homogenous set
   
   x₁ < x₂ < x₃ < x₄ < x₅ ...
   
   For all L we have f(x_L,x_L+1)= f(x_L,x_L+2) = f(x_L,x_L+3) = f(x_L,x_L+4) = ... (NOTE- I corrected this- I originally had x_1, x_2, x_3, x_4 where I now have x_{L+1}, x_{L+2}, ..)
   
   Since all of these values equal they also equal limit_{→ ∞}f(x_L,s) and hence equals A(x_L). Hence either ALL of the x's are IN A or all of the x's are NOT in A. Hence an infinite homogenous set yields an infinite subset of either A or the complement of A, which contradicts that A is bi-immune.

More has been proven since then:

1. Jockusch showed that (a) there is a 2-coloring of pairs so that no homogenous set is Sigma₂, and (b) every 2-coloring has a Pi₂ set.
2. More is known- see the paper by Cholak, Jockusch, Slaman On the strength of Ramsey's theorem for pairs

Specker's result is probability the first theorem in infinite combinatorics to be proven to be non-constructive.

Guest post on ITCS by Chazelle

(Requested announcement: Calling all Women PhD Students (and a few undergrads) We will be having our bi-annual Women in Theory (WIT) Workshop this year in Princeton. The dates are June 23-27, 2012. Applications are due on: Feb 29, 2012. Go here for all the relevant information. Hoping to see you in June. From: Shubhangi Saraf, Lisa Zhang, Moses Charikar and Tal Rabin.)

(Guest Post by Bernard Chazelle) Why ITCS?

Thanks to Lance and Bill for their kind hospitality. I am delighted to be here. With the third edition of ITCS (formerly ICS) behind us, I thought it would be good to share a few personal, biased thoughts on the subject -- "personal" because I do not claim to speak for the Steering Committee; "biased" because I happen to chair that august body.

First, let me reach for my big bucket of gratitude. Shafi Goldwasser and Silvio Micali did an amazing job as PC & local chairs and I cannot thank them enough. A big shout-out to both. Toda Raba to Yael Kalai, too, for her great help, and to Omer Reingold, Nir Shavit, and their fellow actors for a fabulous "playback" show. If you missed it, fret not. If future organizing committees have any sense, the Nir-Omer show will soon come to a conference near you.

This year's ITCS had about 100 submissions, roughly a 20% growth from previous years, and 118 registrants. Talk attendance never seemed to dip below 90, a heart-warming figure that would be the envy of many conferences. In Shafi's and Silvio's deft hands, innovation came out swinging in all sorts of endearingly creative ways, from session chairs giving annotated previews of the talks to postdocs and graduating students making 5-min pitches to introduce themselves and their research. Brilliant! After watching the new generation of theorists in action, I can tell you that the future of theoretical computer science looks very bright, indeed!



And the future of ITCS, you'll ask, how bright is that? When I chaired the PC last year, a reviewer's comment struck a chord: "This submission would be good for STOC but might not be innovative enough for ICS." Now, that's the spirit! Of course, plenty of ITCS papers would fit in nicely at STOCS/FOCS. (Apparently, more than a few tried to fit in.) That said, it would take an advanced case of color blindness to miss the contrasting hues between ITCS and the rest. All PC members were instructed to add an innovation axis to their evaluation space, and, by golly, they did! (And when I use the word "golly," you know I mean business.)

STOC/FOCS has been accused of all sorts of dastardly deeds unmentionable on a family blog -- from accepting too few papers to boosting trends to rewarding technical wizardry. No less. STOC and FOCS might be four-letter words to some, but to me they're venerable legacy institutions that serve worthy professional functions, such as allowing junior researchers to trade these four-letter words for Theory Club membership cards. Nothing to sneer at. Over at Michael Mitzenmacher's corner, here, Umesh Vazirani bravely suggested merging STOC and FOCS into one mega-conference --- SFOCS, I guess. Much as I love the idea, beginning with the soothing effect of pronouncing the word SFOCS out loud, I didn't come here for a food fight, so I'll fall back on old New Jersey wisdom and say we cross that landfill when we come to it. Yet definitely something to mull over.

ITCS provides a venue for quality outside-the-box thinking. Not without reason, a few have wondered whether the best place outside the box is inside a new conference. On the plus side, conferences provide ideal platforms to publicize new work and, for younger scholars, increase the visibility of their research. With its particular focus on the uncharted, ITCS offers a welcome new outlet for a glut of quality papers. A conference is a big heads-up, a "breaking news" banner flashing on the Theory Channel. It's also a chance to initiate lasting collaborations and meet extraordinary people in pursuit of extraordinary ideas. It's fun.The downside is that a human being can attend only so many conferences before "their budget glares red and their head bursts in air" (as they say before kick-off at the Super Bowl).

This dichotomy, however, isn't quite right. It ignores the tangled web the online revolution has woven into our lives. Whereas in the past I'd have to go to a conference to hear a new result, this is no longer so. The PDF will come to me. It's a given that attendees at many talks will already know the results, perhaps even the proofs. This has diminished the relative importance of attending a conference while at the same time increasing its reach, and hence its influence. Don't get me wrong. I am not saying ITCS is so cool you don't even have to go. I am saying that, in the age of instant downloads, missing this month's Jay-Z & Kanye West "UGC" gig at the Garden ain't gonna be the heartbreak it would have been in the days of old. So, while I recognize that the burden of extra travel is a drawback and the timing always an issue, our wired world alleviates these concerns somewhat. And if you find this argument too subtle for its own good, well, remember, there's always the Umesh option.

Another worry heard on Theory Street is fragmentation. I don't get that. The sociological makeup of all these conferences is pretty much the same, anyway, so the risk of fragmentation is about as high as that of Dr. Jekyll and Mr. Hyde parting ways -- OK, make that Superman and Clark Kent if you prefer. In fact, this has it exactly backwards. Theory has yet to penetrate many geographical markets. Eurotheory shares a name with our kind, and little else. With Asia a promising growth area for our field, it is of more than symbolic value that ITCS was born in China. All theory conferences today are regional (North America, Latin America, Europe, Asia, etc). Maybe ITCS can be the exception. At any rate, to expand both the intellectual footprint and the geographical reach of Theory is a central goal of this conference.

To close on a personal note, let me get my crystal ball out of its dusty case and tell you what I see. As the new sciences of the 21st century further embrace their algorithmic nature, I see ITCS getting enriched with a growing flow of conceptual imports from physics, biology, economics, etc (and vice-versa). While the letter T was added to ICS for mundane reasons -- an ACM conference had a previous claim on the acronym -- I hope ITCS remains unabashedly theoretical. Yes, you heard right. And as you watch me adroitly duck the tomatoes sure to be hurled my way for this impolitic stand, you might even spot a contradiction or two. I mean, how can computing theory reach out to the sciences without losing its theoretical core? Well, well... Leaving aside the fact that math developed with precisely that sort of outreach, the answer is easy. What the "new" sciences (bio, neuro, socio, and all that) lack more than anything is a conceptual framework. Theoretical computer science can do for them what mathematics did for physics. Why? Because algorithms are the differential equations of the 21st c. They are the language of modern science. That's why. At this point, you expect me to clear my throat and indulge in a tasteful round of name dropping: "Moreover, as Newton and Einstein used to say, blah blah..." (I got that from my physicist friends. Works every time.)



But not today. Truth is, delusion won't help our cause one bit. Neither will diffidence or skittishness, however. These are heady times for computing theory, my friends. Hand wringing over fine tactical points should not distract us from our common goal, which is to allow Theory to expand and flourish, to unite and conquer. ITCS aims to do just that. It is an exciting experiment worthy of your support.

Thanks for your attention and, in a nod to ITCS' roots, a happy Year of the Dragon to all!

Bernard Chazelle

Ernst Specker (1920-2011)

Martin Fürer remembers his former advisor. 

While traveling, I received the unexpected sad news that Ernst Specker passed away on December 10, 2011. He was born in Zürich in 1920. After receiving his doctoral degree at ETH Zürich in 1949, he spent a year at the Institute for Advanced Study in Princeton. Then he returned to ETH in 1950 and stayed there with the exception of two visiting appointments at Cornell University.

Ernst Specker was teaching Linear Algebra when I started my studies at ETH Zürich in 1967. His teaching style was different from the typical polished and streamlined presentations of that time. He was looking for interaction, and did not hesitate to interrupt a proof to insert an example when he sensed that the audience was not following.

Outside the classroom, it was a turbulent time. The youth movement started to question many long established rules of society. For a long time, it seems that the majority of people, without ever thinking about it, had accepted the claim that the US with its war in Vietnam was defending western values. Quite suddenly, this consensus was widely questioned.

ETH had its own little problem. A new law governing the ETH (the only federal university in Switzerland) had just been adopted by the parliament. Many students took issue with the idea that the main goal of ETH was not to satisfy a general human right for education, but to prepare the students to serve the interests of business and industries.

Ernst Specker, who always liked discussions, never accepted anything based on authority without asking some critical questions, had quickly established a relationship with the young students at this time of evolving political turmoil.

Here are two examples, typical for Ernst. The mathematics and physics students of each semester had an open discussion about the ETH law. One professors came to our group to tell us, we should not complain, its our fault, we should have had this discussion a year ago, when it was the proper time to voice any opposition. He was not happy, when Ernst disagreed, noticing that this group of students has only been here for half a year.

A more important move was Ernst Specker's engagement for the Manifesto of Zürich, a public declaration against police brutality after some excesses when the "establishment" was shocked and fearful of the demonstrations in downtown Zürich.

During our studies, we all had to give talks in four seminars in different areas of mathematics. This rule was widely followed with one exception. A large group of students participated in the logic seminar, and they came back ever since (naturally in addition to the other seminars). Every semester, there was a different theme. My first subject was the solution of Hilbert's tenth problem, presented with all background information and details. The seminar was conducted with Hans Läuchli. Paul Bernays, who had started the seminar when he came from Göttingen before the second world war, was still a regular participant. He often followed the talks reading the blackboard with a two minute delay.

Ernst conducted the seminar still long after his retirement, because unfortunately ETH no longer had a position for mathematical logic. I participated in Ernst’s last logic seminar during my sabbatical in 2002. We ended the semester with a talk of Ernst that was intended for a general mathematical audience. I reserved the beautiful and rather spacious Aula of the ETH for this purpose. Luckily, we could still switch to the Auditorium Maximum, in the last minute, when we saw the people  arriving.

Scientifically, Ernst Specker has worked in many areas as illustrated in by the Selecta volume published by Birkhäuser on the occasion of his 70th birthday.  In his dissertation with Heinz Hopf, Ernst worked on cohomology groups. Then he moved on to investigate constructively in analysis, and the foundation of set theory, in particular Quine's new foundations. He also solved one of the early Erdős problems. Ernst’s most famous results are the works with Simon Kochen on the foundations of quantum mechanics, proving that certain hidden variable theories are not possible, and thus colliding with the assumptions made in the famous Einstein-Podolsky-Rosen paper. The results of Kochen and Specker are still discussed today in the physics literature. Early on and in his additional weekly seminar with Volker Strassen starting in the early seventies, he reached out to complexity theory.

Ernst Specker will always be remembered for his teaching and his scientific work, but most of all for his friendship, his openness and his engaging discussions.

Martin Fürer
Pennsylvania State University

What should we do?

Time for a post by tweet request.

Is a wave of action against big publishers' practices brewing?gowers.wordpress.com/2012/01/21/els…thecostofknowledge.com Should CS do more? @fortnow
— Tugkan Batu (@tugkanbatu) January 22, 2012

Quite a lot on the Internets on Tim Gowers' promise not to work with Elsevier anymore. I'm not as anti-Elsevier as Gowers or many of my readers but I understand the frustrations.

It's easy to make a promise not to publish, edit or referee papers, especially when you don't need to improve your academic reputation. Still a mathematician of his magnitude really puts a spotlight on that publisher.

Because of the Elsevier stigma we've had for several years, all the theoretical CS journals of Elsevier are not nearly as strong as they have been in the past. So you don't accomplish much more just by boycotting Elsevier.

Making a difference means what you do, not what you don't do. Be sure and support journals that are worthy of support by submitting and refereeing papers and serving on editorial boards. The best attack on publishers that you don't like is to have several strong alternatives. The best way to make them strong is by having your support.

No journals is completely free of cost, they require money or time. Open access journals without page charges generally have no revenue stream and require effort to make to publish the journal. For these journals you can volunteer your time as well as submitting, refereeing and editing.

Remember it's easy to complain and say what you won't do but it is what you do do that makes the difference.

Teaching an Honors Section of Discrete Mathematics

A few years ago I was assigned to teach the HONORS section of Discrete Math (a course for sophomores who have had a year of programming and a year a calculus). They told me it was up to me to figure out what to do to make it an honors course. (My section had 30 students, the non-Honors has about 60.) There were several options:

1. This could be taught separate from the non-honors course. Diff homework, diff exams.
   PRO: the homework and exams can be more interesting since you do not have to worry about how they are for the non-honors student.
   1. CON: If a student would have gotten (say) an A in the non-honors course, but gets a B in the honors section, that is not good. OR the teacher could grade inflate so that the students who got a B in the reg section gets an A in the honors section.
2. You could give the same exams and homework to the honors students but REQUIRE them to do more work- extra problems on the homework, extra problems on the Exams.
   1. PRO: They will get to do more fun problems.
   2. CON: They are being penalized for taking an honors course.
3. Same Exams and homework as the regular class. The regular class meets Tu-Th for 75 minutes. The Honors class meets MWF for 50 minutes each. What the Regular class does on Tu-Th, the honors class does on MW. On FRIDAY the honors class has an HONORS DAY- they work in groups of 3 or 4 on problems of more interest than usual. (example: For Logic devise a way to do do AND, OR, and NOT if the variables take on values BETWEEN 0 and 1 (including 0 and 1)). There is a LIGHT homework on this work just to keep them honest. But its not graded seriously.
   1. PRO: They get to learn more stuff in a fun way.
   2. CON: More work for the professor to make up these kinds of problems. (To brag- this is the sort of thing I am good at so not a problem for me.)

I did the last one and I think it worked, for some definition of worked. That is, the students liked it and found it interesting, but its hard to compare it to other ways of doing it. (Doing real studies that tell you things in the field of Education is hard.)

How have you, or would you, run an honors course in discrete math? How about for a programming course?

How important are the Fib numbers in math? in Nature? In History of Math books?

The following quotes is from In the book Algebra in Ancient and Modern Times by V.S. Varadarajan.

Fibonacci numbers thus grow very fast with N, indeed in geometric progression. This is often called exponential growth. They remained as curiosities till in the 1960's they were found to be crucial in certain studies in mathematical logic.

I suspected they were refering to its use in Hilbert's tenth problem even though that was really 1970 (a quibble) and I would hardly call it crucial (a more substantial objection). In fact Fib Numbers are not even needed in the end. I asked Chris Lastowksi who is a Model Theorist at UMCP and he told me the folowing:

Yes. Matijasec showed that the Fibonacci sequence was diophantine, and this sufficed to solve Hilbert's tenth problem (actually to show it could not be solved), by earlier work of Davis, J. Robinson and Putnam. However, Davis almost immediately showed that the exponential function is diophantine, which yields the solution to H-10 more easily, so I would hardly call that a deep connection.

V.S. Varadarajan wanted to make the Fib numbers interesting and important. The attempt was not quite right.

1. How bad is it for a history-of-math book to exaggerate how important some concept is?
2. How important are the Fib Numbers? Do they come up in Mathematics?
3. Could V.S. Varadarajan have picked a better example of their use in mathematics?
4. It has been said that the Fib Numbers come up in Nature. According to Fib Flim Flam most of the statements made about Fib numbers and nature are suspect.

The Information Flood

Twitter, Facebook, Google+. Information now comes to us as a faucet. If you don't drink it all it disappears forever. Try to find status updates and tweets from even a few days ago. Many of you wouldn't have seen this blog post if you didn't catch it on Twitter or Google+.

I try to keep my faucet turned relatively low. I still like RSS feeds like Google Reader. Stuff stays until you discard it. I try not to have too many Twitter followers or Facebook friends.

But the trend is for people, especially the younger generations, to subscribe to whatever fills their fancy. They get a continual stream of information and ignore what they don't see. So Google and Facebook develop algorithms based heavily on what the crowds and your friends are looking at, to determine the order of what you see. Twitter will surely have to follow. Google even tries to decide which of my emails are important.

As goes the Internet goes so does academic knowledge. How do we cut through the research clutter? Will we have algorithms and the crowds tell us which research papers to look at? That used to be the job of journal editors, conference program committees and my grad students.

Being Random and Trivial in Dagstuhl

This week I'm at the Computability, Complexity and Randomness workshop at Dagstuhl in Germany. This meeting brings together two groups, complexity theorists and computability theorists, who share a common love of Kolmogorov complexity.

From the logicians I learned about K-trivial sets. Let K(x) be the prefix-free Kolmogorov complexity of x, i.e., the size of the smallest program that generates x. There are several equivalent definitions of K-trivial sets, here is two of them. A are K-trivial if

1. For some constant c, for all x, K(x) ≤ K^A(x)+c, where K^A(x) is the smallest program generating x with access to oracle A.
2. For some constant c, for all n, K(A_1:n) ≤ K(n)+c, where A_1:n are the first n bits of the characteristic sequence of A.

Lots of interesting properties about K-trivial sets.

• All computable sets are K-trivial and there are K-trivial sets that are not computable.
• There are only a countable number of K-trivial sets. In fact there are only a finite number of K-trivial sets for each fixed constant c above. 
• Every K-trivial set is super-low, that is the halting problem relative to a K-trivial set is non-adaptively reducible to the halting problem.
• Every K-trivial non-adaptively reduces to a computably-enumerable set.
• Every set reducible to a K-trivial is K-trivial.
• The disjoint union of two K-trivial sets is K-trivial.
• Random sets are still random relative to A.

More about K-trivial sets and everything else computably random in a great book by Downey and Hirschfeldt. 

Us complexity theorists started thinking about polynomial-time versions of K-trivial sets but probably won't have as many nice properties. 

The Conjunction Paradox

In Yesterday's post you were told about Susan:

Susan is 31 years old, single, outspoken and very bright. She majored in philosophy. As a student she was deeply concerned with issues of discrimination and social justice and also participated in anti-nuke demonstrations.

You were asked to rank the probabilities of certain things about Susan. Two of the choices were

a bank teller

a bank teller and an active feminist

LOGICALLY bank teller and feminist would have a HIGHER probability than bank teller and and active feminist. Some people (including me when I first was given this exercise) ranked bank teller lower bank teller and active feminist. Why? I think that either people are not good at logic in real-world situations or people implicitly view bank teller as bank teller and NOT an active feminist. This problem has been extensively studied and there are other opinions.

Of the 30 responses I got before posting this roughly 10 ranked bank teller higher than bank teller and and active feminist (which is correct), 10 ranked bank teller and and active feminist higher than bank teller, and 10 of the answers were not relevant (e.g., clarifications of the question). (One person I blocked since he explained the above and would have given away the game, and one person who left a comment 5 minutes ago I will let through but only after I post this.)

I recommend giving this exercise to students in a class that covers logic and/or probability to see what they say.

Clyde Kruskal told me about this problem. He found it here though its also at other sites. This source credits the following (which I would guess is correct). Tversky, Amos; & Kahneman, Daniel (1983), Extensional Versus Intuitive Reasoning: The Conjunction Fallacy in Probability Judgment", Psychological Review 90(4) (October): 293-315. They are famous for these sorts of psychology questions. The latter won the Nobel prize in economics for joint work with the former.

The notion that A is less likely than A AND B is called The Conjunction Fallacy. The article pointed to only gives the two choices: (1) Bank Teller, and (2) Bank Teller and an active feminist. I think its better to give all of those choices as is done here other presentations of this exercise.

Rank these possibilities by probability

Readers- I want you to answer this question and post your answers as comments. I will tell you WHY I am asking tommorow.

Susan is 28 years old, single, outspoken, and very bright. She majored in philosophy. As a student she was deeply concerned with issues of discrimination and social justice and also participated in anti-nuke demonstrations.

Please rank the following possibilities by their probability. List them LOW to HIGH. (Just post your answers. Other comments I may block so that others can enjoy the question.)

1. a kindergarden teacher
2. works in a bookstore and takes yoga classes
3. an active feminist
4. a psychiatric social worker
5. a member of the Sierra club
6. a bank teller
7. an insurance salesperson
8. a bank teller and an active feminist

Starting the Year with Turing

This week I was in Boston for the Joint Math Meeting, a combined meeting of the AMS, MAA and a couple of other three-letter math societies with 7000 of my closest math buddies. This is the main American meeting of mathematicians one part of which are interviews for math jobs which seem few and far between.

The conference didn't seem large to me because I spent most of the meeting at the AMS-ASL Special Session on the Life and Legacy of Alan Turing. I got to see some exciting speakers I haven't seen before including Martin Davis, Andrew Hodges (who authored the famous Turing biography soon to be re-issued) and my great-grand advisor Marvin Minsky. Minsky talked mostly about the sorry state of AI over the past few decades including how the Watson people were working on the wrong problem. I found myself in the strange position of defending AI before my talk the next day.

Craig Bauer, a math historian, talked about the early days of voice encryption during Work War II, basically digitizing and then applying a one-time pad. Turing developed a mechanism that used a hardware PRG improving the quality of the audio and reducing the space needed from a large room to small box, though it was never deployed in the field.

Ted Slaman send me this link with Turing suggesting that PRG can help in searching. I guess Turing did care about running time after all but we still haven't found his lost letter on P v NP.

Interesting fact: Gödel and Turing both admired each other's work but there is no evidence that they ever met or had any direct communication of any kind.

A fun workshop but I'm all Turing'd out and it is only the first week of the Alan Turing Year though I am still looking forward to June to attending the ACM Turing Celebration in San Francisco and CiE in Cambridge.

Next week I'm off to Dagstuhl for Computability, Complexity and Randomness. The fun also continues in the Boston area with ITCS.

Is there a NICE gadget for showing PLANAR HC is NPC?

(I have already posted this question on CS Theory Stack Exchange.)

If you know that 3-COL is NPC then you can prove that PLANAR 3-COL is NPC by a NICE gadget that removes crossings (see here for some lecture notes on it. They are not mine. The original link is here but I can't figure out the real author, though it is likely whoever taught Algorithms at CMU in Spring of 2004.)

Lets say we know that HAM CYCLE is NPC (we do!). Is there a gadget to remove crossings so you can show that PLANAR HAM CYCLE is NPC? The problem of PLANAR HAM CYCLE is NPC so there sort-of has to be a gadget; but is there a NICE one? (The proof that PLANAR HAM Cycle is NPC is from SAT and I find it rather complicated (see here for the original paper.) I have tried to extract an uncrossing gadget from it but have not been able to it.

SO- I ask you, do you know of a NICE gadget for removing crossings in a graph so that we can easily go from HAM CYCLE NPC to PLANAR HAM CYCLE NPC.

I'll be happy with HAM PATH or HAM CYCLE or DIRECTED HAM PATH or DIRECTED HAM CYCLE.

Complexity Year in Review 2011

Result of the Year goes to the new bounds on Matrix Multiplication by Andrew Stothers and Virginia Vassilevska Williams. It's not every year that we see progress on an important problem where we've had no progress since the 80's. Well there was last year. But not every year.

Some other notable results: Impagliazzo's relativized separation of Algorithmica and Heuristica, The Power of Simple Tabulation Hashing by Pătraşcu and Thorup and Property Testing Lower Bounds via Communication Complexity by Blais, Brody and Matulef

We celebrated Les Valiant's Turing Award. We remember Patrick Fischer, Phillipe Flajolet, Steve Jobs, John McCarthy and Dennis Ritchie.

Thanks to our guest posters Daniel Apon, Lauren Cowles, Annie and Molly Fortnow, Nadia Jones, Samir Khuller, Ryan O'Donnell, John Rogers, Jeffrey Stein, Aaron Sterling and Anonymous.

2011 will go down as a year when computer science started changing the world (again). Watson won on Jeopardy. Social networks brought down dictators and congressmen. Obama opens Robotics Center at Carnegie-Mellon. My daughter's high school had their first computer science class in a very long time and Stanford's AI course goes big time. The New York Times has sections on Computer Science's Sputnik Moment and the Future of Computing. The director of the Mathematical and Physical Sciences at the NSF declares "software is the modern language of science". Is there nothing CS no longer touches?

In 2012 we celebrate the man who started it all with a series of events celebrating the 100th anniversary of the birth of the father of computer science. I'll get it started next week talking on "Turing's Influence on Computational Complexity" during the AMS-ASL Special Session on the Life and Legacy of Alan Turing at the Joint Math Meeting in Boston.

Game Changers

Two announcements on Monday connected to my two Alma Maters mark the changing face of universities.

New York City chooses Cornell and the Technion to create new technology campus on Roosevelt Island

It didn't hurt that Cornell got a $350 million donation and that their main competitor, Stanford, dropped out.

Foreign countries have been creating campuses for some time now, like Northwestern's Qatar campus. Great to see this happening in my own country, a realization of the importance of technology and that New York knows it must make these investments. May this lead to other cities building tech campuses like they build sports arenas. Unlike sports, we can have many winners.

What's going to happen on this tech campus? Education, research, start-up incubators? Will there be a separate CS department in New York or just a branch from Ithaca? I can find very little details on the web, though there is this cool fly-over.

MIT launches online learning initiative

Following up on Stanford's online courses, MIT is creating their own tools for teaching online courses and will share these tools with other universities. Those taking the courses may receive a certificate but will have to pay a small fee to do so and the certificate will not bear the MIT name. According to the FAQ "MIT plans to create a not-for-profit body within the Institute that will offer certification for online learners of MIT coursework. That body will carry a distinct name to avoid confusion. MIT awards MIT degrees only to those admitted to MIT through a highly selective admissions process." Nevertheless these courses will allow people to get access to great MIT courses at little cost.

In the 90's, Newspapers decided they could better serve the public by putting their news stories online. How did that work for them? Are universities starting to go down the same path today?

Romney vs. Aaronson

How are Mitt Romney and Scott Aaronson similar? Different?

Similarities:

1. Both live in Massachusetts. Actually, Scott lives there but its not clear where Mitt lives since he's been running for president for the last four years.
2. Both, deep in their heart and soul, believe that Global Warming is a real problem.
3. Both use money to make a point:
   1. Mitt tried to to bet Rick Perry $10,000 that Mitt was never in favor of the individual mandate here.
   2. Scott blogged that if Deolalikar's proof of P ≠ NP is correct, Scott would give Deolalikar $200,000 here.
4. Both were somewhat misinterpreted: Some thought that Scott was insulting Deolalikar. He was not. He was just expressing his certainly the proof was not correct. Some thought Mitt showed he was out of touch with Middle Class American (who normally can't afford to casually bet $10,000 on anything). While Mitt might be out of touch, I think this was more of a way to forcibly express that there is no evidence that he was in favor of the individual mandate.
5. Both Mitt and Scott seem to be right. Deolalikar's proof is no longer believed to be correct, and fact check says that Mitt never supported the individual mandate.
6. There exists people who say Scott is smart. There exists people who say Mitt is smart. I don't know if this means anything since there exists people who say Newt is smart.
7. They both seem smarter than Michelle Bachmann, Herman Cain, and uh,uh, I can't think of the third candidate they both seem smarter than. Oops.

Differences:

1. Scott believes his belief that Deolalikar didn't prove P ≠ NP. Mitt has no beliefs.
2. Mitt can easily afford $10,000. Scott would have to struggle to raise $200,000.
3. Mitt's bet made him look bad. Scott's offer made him look good. He put-his-money-where-his-mouth-is unlike other bloggers who just asserted the proof was likely not correct.
4. Mitt made a bet partially in jest- it is unlikely to really involve an exchange of money. Scott made a real offer- if Deolalikar's proof had been correct he really would have paid out.
5. There is one of them that I would vote for. The other was once Governor of Massachusetts.
6. Scott knows a bit more about Quantum Computing than Mitt.

I emailed the Romney Campaign this post (without this paragraph), and the information that I would post it on Monday Dec 19, in case they had a comment. They did not respond. Perhaps Mitt is miffed about my saying Scott knows a bit more about Quantum Computing.

Algorithmic Driving

In my post last week, my commentors took me to task on my prediction that cars will drive us in ten years. Some thought Americans would wise up and learn to love mass transit. They don't know Americans.

Others thought the hardware cost would even in ten years remain out of reach. Google did not build an autonomous car by creating the hardware but by harnessing and training good machine learning algorithms. No amount of hardware would have given you a car able to navigate the streets of San Francisco five years ago.

What hardware do you need for an autonomous car, beyond the car itself? A good camera, a GPS device, wireless Internet access, gigabytes of RAM and a fast processor. I carry all that in my pocket. Google does use other sensors including lasers and radar but as the algorithms get better, the cost and need for this hardware can be reduced. Wiring the car to drive itself won't be difficult, already the steering wheel and pedals are mostly just a user interface into a computer that is controlling the car.

I have no doubts that technologically we will have autonomous cars in ten years adding at most a couple of hundred dollars over the cost of the car itself.

Other problems could get in the way. One is legal but Nevada is already changing their laws that will allow a testbed for autonomous cars in that state. Once the cars are viewed as safe one would expect the law to expand and other states to open up as well.

The other issue is social. As with every technological change we will have the usual technological life cycle: Innovators willing to pay the big bucks to try stuff first, Early Adopters who love to jump on new technology (where I usually sit), the early and late majorities following the crowd and finally the laggards who still insist on manual transmission and pumping their own brakes.

There are other issues like patents and industries, like auto insurance companies, that will try to fight autonomous cars. Autonomous cars will be too much of a win, in terms of parking, fuel efficiency, shorter and more productive travel time and most of all safety, not to prevail.

Solution to the reciprocals problem

In my last blog I asked you to look at this problem, try to solve it, and tell me if you think it is too hard for a HS competition. (I meant to post this on WED so I posted it at 12:06AM East Coast Time. I didn't know that the blog is on Chicago Time. So it got posted on Tuesday. Oh well.) Here is the problem:

Prove or disprove: there exist natural numbers x₁,...,x₁₀ such that

1. 2011=x₁+... +x₁₀ and
2. 1=1/x₁+... +1/x₁₀.

Several solutions and some other points of interest about this problem are here. The answer is YES and here are the solutions that I know of -- both my solution and the ones emailed to me. (The explanation of how they were obtained are at the paper pointed to above.)

1. My Solution: 2,4,5,80,80,80,160,320,640,640. This used known theorems.
2. Sam Solution: 2,4,5,40,120,160,300,300,480,600. Sam is a HS senior who is very good at these contests. It took him 30 minutes,
3. David Eppstein Solution: 3,4,7,16,16,16,20,43,80,1806. This used a bit of advanced knowledge and some hand computations that were probably above what you want for a UMCP Math Competition.
4. Matt Howell Solution: 2,4,5,50,100,100,250,500,500,500 This solution could have been found by a HS student (it is similar to Sam's solution.) Matt has a BS in Math and Engineering and did the problem in 20 minutes.
5. An anonymous commenter send me 6,6,10,10,12,15,15,15,62,1860. This solution could have been found by a HS student (it is similar to Sam's solution.)
6. Another one from same anon: 6,8,8,8,12,15,16,16,62,1860 This solution could have been found by a HS student (it is similar to Sam's solution.)
7. Mike Roman Solution: 5,5,6,8,8,12,15,32,960,960

So what to make of this?

1. Much to my surprise, enough people got it right and in ways that a HS student could have gotten it. And one did- Sam took the real exam.
2. The systematic solution that I got required very little hand calculation. All of the others, which includes the one I think a HS student could have or did get, required quite a bit of hand calculation. That may be a reason to not ask it.
3. I wonder how many solutions there are. This could be figured out by a Dynamic Program but there may be issues with large ints. (See later in this blog.)
4. I wonder if there are any that have distinct numbers. This can also be figured out by a Dynamic Program, though there may be an easier way.
5. I wonder about the computational complexity of the following problems:
   1. Problem 1 Given a,b in N, does there exist x₁,...,x_a such that x₁+...+x_a=b and 1/x₁+...+1/x_a=1. (Can also ask with the stipulation that the x's are distinct.)
   2. Problem 2 Given a,b in N and r in Q, does there exist x₁,...,x_a such that x₁+...+x_a=b and 1/x₁+...+1/x_a=r. (Can also ask with the stipulation that the x's are distinct.)

Possible Dynamic Program (more likely you would do it as a recurrence but save all answers found and check to see if you have already computed it, to avoid recomputing.) Let f(a,b,c,r) (where a,b,c are naturals and r is rational) be

num of sols to x₁+...+x_a=b and 1/x₁+...+1/x_a=r. where c ≤ x₁ ≤ ... ≤ x_a.

Note that

1. f(1,b,c,r) = 1 if r=1/b and r ≥ c
2. f(a,b,c,r) = sum as x in {c,c+1,..., min(b,floor(a/r)) } of f(a-1,b-x,x,r-1/x)

(NOTE- Use f(a-1,b-x,x+1,r-1/x) if you want to enforce distinct solutions.)

A math point: Ronald Graham showed that, for all n ≥ 78, n can be written as a sum of natural numbers whose reciprocals sum to 1. The lower bound of 78 is tight: 77 cannot be. A sketch of a proof of this is in the file pointed to. (The proof I give is inspired by one of the comments on the blog. YEAH BLOG COMMENTERS!) (ADDED LATER- Ronald Graham actually proved that for all n &ge 78 n can be written as the sum of DISTINCT natural numbers such that... . The proof I presented in the pointed to document just gives nat numbers, not necc distinct ones.)

Is this problem too hard for a HS Math Competition

The Univ of MD HS Math Competition has two parts. Part I is 25 multiple choice questions in 2 hours (4 points for a correct answer, -2 for an incorrect answer). If you do well on it (the threshold changes from year to year) then you can do Part II which is 5 problems in 2 hours, 30 points each. The winner is the person who does best on the sum of the two parts.

This year I submitted a problem for Part II. The people on the committee who tried it couldn't do it so we decided to NOT put it on the exam. I only knew the answer because I read a theorem and build a problem around it. The people who couldn't do it are very sharp. Since they could not do it the problem was too hard. But... lets see what you think?

I would like YOU to try it without consulting any resources, (and don't look at the comments- someone might post questions that lead to a hint, or the answer) and keep in mind that you can't use advanced techniques (I'm do not think they would help anyway). See if you can do it so I can get a sense if it really is too hard. Post your opinion on if its too hard for a HIGH SCHOOL math competition. Here is the problem:

Prove or disprove: there exist natural numbers x₁,...,x₁₀ such that

1. 2011=x₁+... +x₁₀ and
2. 1=1/x₁+... +1/x₁₀

(ADDED LATER- A commenter thought that the x_i's in the first and second condition could be different. They are not. We want x₁,...,x₁₀ that satisfy both of these simultaneously.)

I'll post a pointer to the solution next time I post. (Probably Wednesday.) ADDED LATER- a commenter wants to know if there is a solution or not and can't wait until WED. Also wants to know if there is a solution is it constructive or proof of existence. To answer the question but NOT ruin it for others, I put it in a file you can click on (or NOT) over here: here.)

A Great Time to be a Computer Scientist

Ask your friends if they'll be driving an electric car in ten years. The answer: No, cars will be driving us.

Today is the 105th anniversary of the birth of computing pioneer Grace Murray Hopper and Computer Science Education Week is being held this week in her honor. If only she could see what we have reaped from what she has sown.

The New York Times this week devoted Tuesday's Science Times to the Future of Computing. The section includes a series of essays from CS researchers including Daphne Koller, Stefan Savage, David Patterson, Kai-Fu Lee and fellow theory blogger Scott Aaronson. Scott also blogged about the experience. Though what would you do with a quantum computer on your desk? The factoring number thing could get boring pretty quick.

The Times also has a crowdsourced interactive timeline of future computing events. Try to guess which one I submitted. Almost all the advances listed are realistic and should keep CS very active for the long future. The most exciting future computer science advances will be the ones we haven't even thought of.

Finally the new class of ACM Fellows includes many theorists including Serge Abiteboul, Guy Blelloch, David Eppstein, Howard Karloff, Susan Landau, Joe Mitchell, Janos Pach and Diane Souvaine. A great year to be an ACM Fellow because the awards ceremony in June will follow a workshop celebrating the Turing Centenary featuring over 30 former Turing award winners.

What is a Breakthrough?

The recent discussion on Matrix Mult inspires the general question of WHAT IS A BREAKTHROUGH? Last year I tried to get an intelligent discussion on this topic but I failed. After saying what some criteria were I applied them in a silly way to several results. This derailed the discussion. My bad, my fault. SO, I'll try again to get an INTELLIGENT discussion on this topic. (NOTE- some of this post is a reworking of the old post.)

Here are some criteria. The first three are extracted from a comment Gowers made on Scott's Blog. I do not know how many a result has to have to be a breakthrough or even if such a threshold makes sense. Perhaps some sort of weighted sum, but would be hard to define.

1. The result breaks a long standing barrier.
2. The techniques introduce a fundamentally different method.
3. The result is practical (or close to it).
4. The problem being discussed is important. This may be a bit circular in that it then depends on What is Important?
5. The result has to make substantial progress on the problem. This may depend on What is substantial? That notion may depend on how long the problem has been open.
6. There has to be a reason why the problem was thought to be hard. E.g., a proof that a new technique is needed, problem has been open for a long time, people in the field say its hard.
7. A paper that STARTS an important field could be a breakthrough. Cook's Theorem and Valiant's PAC learning qualify here.
8. A paper that FINISHES a field could be a breakthrough if the field is important. Again this may be a bit circular in that it then depends on What is Important?
9. The techniques are new. One might end up debating what is new.
10. The techniques can be used on other problems.
11. The paper inspires other papers. For this criteria you need to wait a few years. Some papers are not appreciated for a while.

The notions of important, substantial, new are not Boolean. As Gowers pointed out in his comment, the notion of breakthrough is not Boolean.

Do you have other criteria, examples, counterexamples, constructive criticism of my criteria, or anything that is an intelligent contribution to this topic? Is so, please post a comment!

Probability

On Saturday, Terrence Fine gave a talk on probability at a workshop at Northwestern. Before the talk he asked who thought probability was subjective (an individual's belief in the chance of an event) or a frequentist (a probability represents what happens if an experiment can be repeated many times). Someone noticed I didn't raise my hand either time so I said that I had a computational point of view of probability, since I have a computational point of view of everything.

I didn't mean computation as in Turing machine but as a process. A process that creates events according to some distribution. How does this process work? I don't care. That's the beauty of computational thinking, we abstract out the notion of probability and just make use of it. I've written papers on quantum computation having no idea of the physical processes that create entanglement. I study nondeterministic computation where we have no physical counterpart. Probability works the same way, at least for me.

My contribution to the workshop was to explain Kolmogorov complexity, the universal distribution and its relationship to inductive learning to the mostly economics crowd. Perhaps I could have explained things a bit more clearly as one econ student said to me afterwards "You lost me at prefix free". 

Analysis of Boolean Functions blog/book (Guest post by Ryan O'Donnell)

(Guest post by Ryan O'Donnell)

Lance and Bill have graciously let me plug my recently begun book/blog project, analysis of boolean functions. I am writing a textbook on analysis of Boolean functions and serializing it on the blog as I go. When I'm done, the book will be available online; hopefully it will also be published in the conventional format. (NOTE FROM BILL- its also linked to off of our blog page.)

The topic is sometimes called Boolean Fourier analysis, though my perspective is a bit more from probability theory than harmonic analysis. I hope the book will be accessible and of interest to grad students and researchers in theoretical computer science and other areas of mathematics. Each chapter will end with a "highlight" illustrating the use of Boolean analysis in problems where you might not necessarily expect it. To give you a flavor of the contents, my planned list of highlights is:

• Testing linearity (the Blum-Luby-Rubinfeld Theorem)
• Arrow's Theorem from Social Choice (and Kalai's "approximate" version)
• The Goldreich-Levin Algorithm from cryptography
• Constant-depth circuits (Linial-Mansour-Nisan's work)
• Noise sensitivity of threshold functions (Peres's Theorem)
• Pseudorandomness for F_2-polynomials (Viola's Theorem)
• NP-hardness of approximately solving linear systems (Hastad's Theorem)
• Randomized query complexity of monotone graph properties
• The (almost-)Polynomial Freiman-Ruzsa Theorem (i.e., Sanders's Theorem)
• The Kahn-Kalai-Linial Theorem on influences
• The Gaussian Isoperimetric Inequality (Bobkov's proof)
• Sharp threshold phenomena (Friedgut and Bourgain's theorems)
• Majority Is Stablest Theorem
• Unique Games-hardness from SDP gaps (work of Raghavendra and others)

If you're interested, you can think of it like an online course -- I've been publishing Mondays, Wednesdays, and Fridays, and there are even exercises. (Also like a course, I'll go on break for a few weeks around the new year.) Come see why "juntas" are important, what hypercontractivity "really" means, and why functions on Gaussian space are the "easy special case" of Boolean functions...

PS: I'm using MathJax for the posts; if anyone has suggestions for me or for readers on how to make it look nicer or load better, please do let me know.