Kurtz-Fest

Stuart Kurtz turned 60 last October and his former students John Rogers and Stephen Fenner organized a celebration in his honor earlier this week at Fenner's institution, the University of South Carolina in Columbia.

Stuart has been part of the CS department at the University of Chicago since before they had a CS department and I knew Stuart well as a co-author, mentor, boss and friend during my 14+ years at Chicago. I would have attended this weekend no matter the location but a total eclipse a short drive from Atlanta (which merely had 97% coverage) certainly was a nice bonus.

Stuart Kurtz brought a logic background to computational complexity. He's played important roles in randomness, the structural properties of reductions, especially the Berman-Hartmanis isomorphism conjecture, relativization, counting complexity and logics of programs. I gave a talk about Stuart's work focusing on his ability to come up with the right definitions that help drive results. Stuart defined classes like Gap-P and SPP that have really changed the way people think about counting complexity. He changed the way I did oracle proofs, first trying to create the oracle first and then prove what happens as a consequence instead of the other way around. It was this approach, focusing on an oracle called sp-generic, that allowed us to give the first relativized world where the Berman-Hartmanis conjecture held.

The Crystal Blogaversity

A joint post from Lance and Bill

This blog started fifteen years ago today as  "My Computational Complexity Web Log". Bill came on permanently in 2007 after Lance retired from the blog, a retirement that didn't even last a year. We've had over 2500 posts and 6 million page views. We've highlighted great results, honored 100th birth anniversaries, mourned the passing of far too many colleagues and talked about the joys and challenges of being an academic and a theoretical computer scientist.

During the time of this blog, Lance held jobs at four different institutions, several positions in the theoretical computer science community and watched his daughters grow up. Besides his wife, perhaps the only constant in his life is this blog, and no matter how busy things get he still aims to post once a week. Writing keeps him sane.

Bill, who is somewhat of  Luddite, has seen technology change so much around him that he needs something to stay the same. This blog has kept him sane. Or at least more sane.

Computing has seen dramatic changes in the past fifteen years driven by cloud computing, big data and machine learning. Computing now drives society and we've only seen the tip of the iceberg so far. Precious few of these developments are grounded in theory and our community will have a large role to play in understanding what is and isn't possible in this brave new computational world.

Education has changes as well. The number of people majoring in Computer Science has skyrocketed, crashed, and is now skyrocketing again. We teach large lectures with PowerPoint and other technologies for both good and ill. Some people get their degrees online for both good and ill. We comment on all of these developments for both good and ill.

We're not done yet with the blog. We'll keep writing and hope you keep reading. To the next fifteen.

The World is Not for Me

I wanted to address diversity after the Google memo controversy but that shouldn't come from an old white man. I asked my daughter Molly, a college student trying to set her course, to give her thoughts.

The world is not for me. It never has been, and it never will be. This truth is bleak, but unavoidable. The world does not belong to women.

The possibilities for my life are not endless. The achievements in my sight are not mine to take. If I want them, I have to fight harder, prove more about myself, please people more, defy more first impressions. I’ll have to be smarter, stronger, more patient and more assertive. Every expectation of me has a mirror opposite, fracturing my success into a thing of paradoxes. I know this, and I’ve always known it, to some extent. As I get older, the more I learn and the more I educate myself, the more words I have to describe it.

So you’ll forgive me for not being surprised that sexism exists, especially in such male-dominated fields as technology and computing. You’ll forgive me for calling it out by name, and trying to point it out to those I care about. You’ll forgive me for being scared of tech jobs, so built by and for white men and controlled by them that the likelihood of a woman making a difference is almost none. And you’ll forgive me for trying to speak my mind and demand what I deserve, instead of living up to the natural state of my more “agreeable” gender.

I know this disparity is temporary. I know these fields could not have come nearly as far as they have come without the contributions of many extraordinary women who worked hard to push us into the future. I know that other fields that once believed women were simply incapable of participating are now thriving in the leadership of the very women who defied those odds. And I know, with all of my being, that the world moves forward, whether or not individuals choose to accept it.

I’m so fortunate to live the life I do, and to have the opportunities I have. This is not lost on me. But neither is the understanding that this world was not built for me, and still won’t have been built for me even when the tech world is ruled by the intelligent women who should already be in charge of it. The existence of people who believe genders to be inherently different will always exist, always perpetuate the system that attaches lead weights to my limbs, padlocks to my mouth.

But that doesn’t mean I’ll give up. It’s what women do, because it’s what we have to do, every day of our lives: we defy the odds. We overcome. The future includes us in it, as it always has, and it’s because of the women who didn’t give up. And I’ll be proud to say I was one of them.

What is unusual about this MIT grad student in Applied Math?

(Thanks to Rachel Folowoshele for bringing this to my attention)

John Urschel is a grad student in applied math at MIT. His webpage is here.

Some students go straight from ugrad to grad (I did that.)

Others take a job of some sort and then after a few years go to grad school.

That's what John did;  however, his prior job was unusual among applied math grad students







He was in the NFL as a professional football player! See here for more about the career change, though I'll say that the brain-problems that NFL players have (being hit on the head is not a good for your brain) was a major factor for doing this NOW rather than LATER.

How unusual is this? Looking around the web I found lists of smart football players, and lists of football players with advanced degrees (these lists were NOT identical but there was some overlap) but the only other NFL player with a PhD in Math/CS/Applied math was

Frank Ryan- see his wikipedia page here. He got his Phd WHILE playing football. He was a PhD student at Rice.

I suspect that a professional athlete getting a PhD in Math or CS or Applied Math or Physics or... probably most things, is rare.  Why is this? NOT because these people are dumber or anything of the sort, but because its HARD to do two things well, especially now that both math and football have gotten more complex. Its the same reason we don't have many Presidents with PhD's (Wilson was the only one) or Presidents who know math (see my post on presidents who knew math: here) or Pope's who are scientists (there was one around 1000 AD, see here).

If you know of any professional athlete who has a PhD in some science or math, please leave a comment on such.

(ADDED LATER- a commenter pointed out Angela Merkel who has a PhD in Physical Chemistry,
is chancellor of Germany, and there is a musical about her, see here.)

(ADDED LATER- some of the comments were for Olympic Athletes and hence not professional and another comment pointed this out. So I clarify: Olympic is fine too, I really meant serious athlete.)

Wearable Tech and Attention

Remember the Bluetooth craze where it seemed half of all people walked around with a headset in their ear. Now you rarely do.

Remember Google Glass. That didn't last long.

I remember having a conversation with someone and all of sudden they would say something nonsensical and you'd realize they are on the phone talking to someone else. Just by wearing a Bluetooth headset you felt that they cared more about a potential caller than the conversation they were currently having with you.

Google glass gave an even worse impression. Were they listening to you or checking their Twitter feed? [Aside: I now use "they" as a singular genderless pronoun without even thinking about it. I guess an old dog can learn new tricks.]

When you get bored and pull out your phone to check emails or put on headphones to listen to music or a podcast, you give a signal that you don't want to be disturbed even if that isn't your intent. Wearing a Bluetooth headset or Google glasses gave that impression all the time, which is why the technology didn't stick.

What about smart watches? You can certainly tell if someone has an Apple watch. But if they don't look at it you don't feel ignored. Some people think they can check their watch without the other person noticing. They do. I've been guilty of this myself.

What happens when are brains are directly connected to the Internet? You'll never know if anyone is actually listening to you in person. Of course, at that point will there even be a good reason to get out of bed in the morning?

Should we care if a job candidate does not know the social and ethical implications of their work (Second Blog Post inspired by Rogaway's Moral Character Paper)

Phillip Rogaway's article on the

The Moral character of Cryptographic Work (see here)

brings up so many issues that it could be the topics for at least 5 blog posts. I've already done one here, and today I'll do another. As I said in the first post I urge you to read it even if you disagree with it, in fact, especially if you disagree with it. (Possible Paradox- you have to read it to determine if you disagree with it.)

Today's issue:

Should a department take into account if someone understand the social and ethical issues with their work?

1) I'll start with something less controversial. I've sometimes asked a job candidate `why do you work on X?' Bad answers:

        Because my adviser told me to.

        Because I could make progress on it.

        Because it was fun to work on.

People should always know WHY they are working on what they are working on. What was the motivation of the original researchers is one thing they should know, even if the current motivation is different. If its a new problem then why is it worth studying?

2) In private email to Dr. Rogaway he states that he just wants this to be ONE of the many issues having to do with job hiring (alas, it usually is not even ONE). As such, the thoughts below may not be quite right since they assume a bigger role. But if you want to make something a criteria, even a small one, we should think of the implications.

3) In private email to Dr. Rogaway I speculated that we need to care more about this issue when interviewing someone in security then in (say) Ramsey theory. He reminded me of work done in pure graph theory funded by the DOD, that is about how to best disable a network (perhaps a social network talking too much about why the Iraq war is a terrible idea). Point taken- this is not just an issue in Security.

4) What if someone is working on security, funded by the DOD, and is fully aware that the government wants to use her work to illegally wiretap people and is quite okay with that. To hold that against her seems like holding someone's politics against them which I assume all readers of this blog would find very unfair.. OR is it okay to hire her since she HAS thought through the issues. The fact that you disagree with her conclusion should be irrelevant.

5) What if she says that the DOD, once they have the tech, will only wiretap bad people? (see here)

6) Lets say that someone is working on cute crypto with pictures of Alice and Bob (perhaps Alice is Wonderland and Bob the Builder). Its good technical work and is well funded. It has NO social or ethical  implications because it has NO practical value, and she knows it. Should this be held against her? More so than other branches of theory?

7) People can be aware of the social and ethical issues and not care.

8) The real dilemma: A really great job candidate in security who is brilliant. The work is top notch but has serious negative implications. The job candidate is clueless about that. But they can bring in
grant money! Prestige! Grad Students! I don't have an answer here but its hard to know how much to weigh social and ethical awareness versus getting a bump in the US News and World Report Rankings!

        What does your dept do? What are your thoughts on this issue?

What Makes a Great Definition

Too often we see bad definitions, a convoluted mess carefully crafted to make a theorem true. A student asked me though what makes for a great definition in theoretical computer science. The right definition can start a research area, where a bad definition can take research down the wrong path.

Some goals of a definition:

• A great definition should capture some phenomenon, like computation (Turing machines), efficient computation (P), efficient quantum computation (BQP). Cryptography has produced some of the best (and worst) definitions to capture security concerns.
• A great definition should be simple. Defining computability by a Turing machine--good. Definition computability by by the 1334 page ISO/IEC 14882:2011 C++ standard--not so good.
• A great definition should be robust. Small changes in the definition should have little, or better, no change in what fulfills the definition. That is what makes the P v NP problem so nice since both P and NP are robust to various different models of computing. Talking about the problems solvable by a 27-state Turing machine--not robust at all.
• A great definition should be logically consistent. Defining a set as any definable collection doesn't work.
• A great definition should be easy to apply. It should be easy to check that something fulfills the definition, ideally in a simply constructive way.

A great definition drives theorems not the other way around.

Sometimes you discover that a definition does not properly capture a phenomenon--then you should either change or discard your definition, or change your understanding of the phenomenon.

Let's go through an interesting example. In 1984, Goldwasser, Micali and Rackoff defined $k$-bits of knowledge interactive proof systems. Did they have good definitions?

• The definition of interactive proof systems hits all the right points above and created a new area of complexity that we still study today. 
• Their notion of zero-(bits of) knowledge interactive proofs hits nearly the right points. Running one zero-knowledge protocol followed by another using the GMR definition might not keep zero-knowledge but there is an easy fix for that. Zero-knowledge proof systems would end up transforming cryptography. 
• Their notion of k-bit knowledge didn't work at all. Not really robust and a protocol that output the factors of a number half the time leaked only 1-bit of knowledge by the GMR definition. They smartly dropped the k-bit definition in the journal version.

Two great definitions trump one bad one and GMR rightly received, along with Babai-Moran who gave an alternative equivalent definition of interactive proofs, the first Godel Prize.

Harvard punishes some social organizations. Why?

Over at  the blog Bits and Pieces my adviser Harry Lewis (is he still my adviser 32 years after I got my PhD? Yes) has written many posts about Harvard's decision to ban people who belong to same-sex organizations from being approved for Rhodes Fellowships and other things. He is against it. Not just that, he gives history, context, etc. While originally intended to stop some excesses of some male clubs, the ban  also punishes all-female clubs. But that's not the only reason the punishment is idiotic..

I could not possibly describe and argue against the policy as well as Harry Lewis can, (e.g., he never used the word idiotic) so I was going to write a post briefly describing the situation and then pointing to all of his posts.

AH- but then Michael Mitzenmacher did that in his blog My Biased Coin (Hmmm- I think its his biased coin).

I could not possibly give a short description and point to Harry Lewis's posts as well as MM did.

SO I point to MM's post and give some brief comments.

MM's post is here. Warning- MM's post  points to 16 Harry Lewis's posts. That is a lot to read but well worth it.

My two cents (that would be a good blog name!):

1) After MM's post HL posted again about the issue, this time pointing to several more  articles on the issue and commenting on them. HL's post is Here. That is even more to read but well worth it.
(UPDATE- After I posted this HL posted another post on this topic on his blog: here)

2) While I have seen many arguments against the policy I have not seen a single argument for the policy. I don't mean that I have seen arguments and they were not good, I really have not seen any arguments good or bad.

3) I would much rather have the debate be:

What are some clubs doing that is bad? If so then is there some policy that makes sense?

rather than

What business is it of Harvard what off-campus clubs a student belongs to?

Peter Wegner (1932-2017)

Peter Wegner passed away yesterday morning at the age of 84. As a child he escaped Stalinist Russia and Nazi-occupied Austria the latter via the Kindertransport to England. Wegner would go on to be an important computer scientist at Brown working on CS research and education.

With Dina Goldin, Peter Wegner developed a notion of interactive computation  and used it to argue for the incompleteness of the Church-Turing thesis. While I didn't agree with this interpretation, I appreciated Wegner's efforts to understanding the basic nature of computing. Peter Wegner later organized an ACM Ubiquity Symposium What is Computation? where he sought many view on the question, including my own.

Peter Wegner said "In computer science we work with possibilities and hope we’ll someday be able to solve them." Here's to all things possible.

Lessons from Norway

For the last two weeks, the wife and I took a vacation to beautiful Norway to see the fjords and the North Cape, effectively the northernmost point in Europe. It was a visit though to the Norwegian Petroleum Museum in Stavanger that inspired this post.

The discovery of oil in the waters off Norway in 1969 completely changed the Norwegian economy, changing the way of life from a difficult agriculture and fishing society to a more comfortable oil-based economy. The museum had a surprisingly good introductory movie "Oil Kid" describes the challenging relationship of a man with his father who drew a comfortable life as an oil worker. Oil may have made Norway complacent as it lags behind its Scandinavian neighbors in non-oil based technological innovation.

The Norwegian government declared that the oil belonged to the people and created a fund that now totals nearly a trillion US dollars, over $150,000 per Norwegian citizen. Nevertheless as the price of oil remains low, Norway risks challenges as a country reliant on its production.

Norway now aims to be energy-neutral in the near future with extensive hydropower and wind mills. Norway has the highest percentage of electric cars of any country. The tiny town of Eidfjord, population about 1000, has a Tesla charging station. Odd to see this from a major oil exporter.

As computer scientists we have "struck oil," also leading a revolutionary change to our economy with its winners and losers. In fifty years will we look back and regret what we have wrought? 

What are the top Computer science programs for women?

What are the top Computer Science Programs for Women?

How would one even answer the question?

Some people did a study based on National Center for Education Statistics and Payscale. The results are here.

1) While I believe the top X school listed are pretty good for women in computing I don't believe that (say) the Yth school is better than the (Y+1)th school for some values of X and all values of Y.

2) I appreciate that they put in the work for this.

3) Overall good news and bad news:

The number of female professionals in computer science has fallen by 35% since 1990

The number of women  finishing a comp sci degree has increased by 75% in the last five years.

4) Why do we care? If there are many talented people in group X who are being discouraged from going into field Y, but society needs more people in field Y then YES we should do something about that. Also, if a certain group of people is shut out then a group-think might occur.

5) What to do? Organizations like Girls who code are good. The younger they start the bettter.

6) Is there a social stigma for women to go into computer science? I think the answer is yes. How can we break that stigma? Realize that the notion of a female lawyer or doctor at one time had a stigma but I don't think it does anymore. What did they do right? What are we doing wrong?

7) Personal note:

I have mentored 58 High School Students. 56 were male, 2 were female.

I have mentored 45 ugrad students. 33 were male, 12 were female.

I have supervised 17 Masters students. 15 were male, 2 were female

I have supervised 7 PhD students, 6 were male, 1 was female.

The HS students stats are the most startling (at least to me). I don't have much control on this one as HS students seek me out and they happen to mostly be male. Reading that over it sounds weak on my part.

I would call these Galois Games but I can't

Here is a game (Darling says I only blog about non-fun games. This post will NOT prove her wrong.)

Let D be a domain,  d ≥  1 and 0 ≠ a₀  ∈ D. There are two players Wanda (for Wants root) and Nora (for No root). One of the players is Player I, the other Player II.

(1) Player I and II alternate (with Player I going first) choosing the coefficients in D of a polynomial of degree d with the constant term preset to a₀.

(2) When they are done, if there is a root in D  then Wanda wins, else Nora wins.

There is a paper by Gasarch-Washington-Zbarsky here where we determine who wins the game when D is Z,Q (these proofs are elementary), any finite extension of Q (this proof uses hard number theory), R, C (actually any algebraic closed field), and any finite field.

How did I think of this game?  There was a paper called Greedy Galois Games (which I blogged about here). When I saw the title I thought the game might be that players pick coefficients from Q and if the final polynomial has a solution in radicals then (say) Player I wins. That was not correct. They only use that Galois was a bad duelist. Even so, the paper INSPIRED me! Hence the paper above! The motivating problem is still open:

Open Question: Let d be at least 5. Play the above game except that (1) the coefficients are out of Q, and (2) Wanda wins if the final poly is solvable by radicals, otherwise Nora wins. (Note that if d=1,2,3,4 then Wanda wins.) Who wins?

If they had named their game Hamilton Game (since Alexander Hamilton lost a duel) I might have been inspired to come up with a game about quaternions or Hamiltonian cycles.

POINT- take ideas for problems from any source, even an incorrect guess about a paper!

89944 Hat Problems

I've blogged about different hat problems a few times (see here). The question arises: How many hat problems are there? The answer is really infinite (literally) but I will list some parameters and bound them reasonably to get an upper bound.  Some of the combinations don't make sense, but we'll live with that. (I am also working on a website of hat problem papers. Its nowhere near finished yet and maybe never will be, but its here for your benefit. And for mine-- if there are some obvious papers I've omitted then comment or email me.)

First off, what is a hat problem? Ignoring many parameters: There are n people and c different colors of  hats and they are put on people's heads and the people have to guess what color hat they have on. They can see some or all of the other people. I'll mention one that has someone's name on it:

Winkler's Hat Problem (Peter Winkler proposed it here along with some other hat problems and some non-hat problems that are also fun)

There are n people and 2 color hats. An adversary will put the hats no peoples heads. The people must guess simultaneously their hat color. Maximize how many get it right in the worst case.

(ADDED LATER: While I have seen the above referred to as Winkler's Hat Problem, Winkler
himself told me that hs problem has the hats put on RANDOMLY, not by an adversary.)

Peter Winkler and later a paper by Ebert  et al. (Not Ebert of Siskel and Ebert--- to bad, that would be awesome!) that I mention below seem to have popularized hat games somewhat.  But this post is not about their history its about

how many hat games are there?

Here are some parameters I've seen for hat games. If you know of any others please comment!


1) Is the number of hats finite, infinite (and assume AC), infinite (but don't assume AC). I could say that since there are infinitely many infinities this is an infinite number of parameters, but we'll stick to countable and say this is a 3-valued parameter.  A paper on infinite number of hats is here.

2) The two most common puzzles are to have the people either all see each other, or in a line where person i sees person j iff i ≤ j. This can be viewed as the people are on K_n or L_n.  There have been some papers on cycles (see here, here),  triangle-free graphs (see here), some directed graphs (see here), a PhD that studies the problem on cycles (see here), and a paper with several graphs (see here). Formally this would be an infinite-valued parameter, but we'll take the number of classes of graphs that actually have been studied to be 4.

3) Do the people all guess their hat at the same time OR is there some ordering OR in rounds  3-valued.

4) Are people allowed to pass or not? (if they are then usually we demand that at least one does not pass). 2-valued. The paper by Ebert-Merkle-Vollmer which allowed passing got a lot of attention and brought hat problems to the general public. Its here. A generalization of Ebert's version is here. Ebert's game but on a line is studied here

5) Are the hats put on by an adversary who can hear your strategy (I've never seen a paper about an adversary who can't hear your strategy) or uniformly randomly or random with some known probability. The last case has been studied in several papers by Theo van Uem (see here, here, here). 3 valued

6) The players strategy can be deterministic or randomized. 2-valued. Butler et. al's paper about deterministic strategies covers a lot of material: here. 2 valued.

7) What is the goal? To get as many right as possible all the time? To get the expected number right as large as possible (prob may be based on either the random placement of hats or the random strategy of the players). There are even more variations here such as you want for each color there is a guaranteed fraction that get it right (see here) 3-valued

8) Is there some other information available. Examples I've seen: (a) at least one hat is RED, (b) for each color there is a bound on how many hats there are of that color, (c) the hats are natural numbes x,y, and x+y. (see here) (d) there are n+1 colors, n people, and each perosn has a different color (see here). Many values depending on the information given, but we'll just say 4-valued, the info above and no info.

9) Can some other information be revealed first? I've seen a paper where first everyone who sees a RED hat raises their hand. 2-valued.

10) Is a delay allowed? There are some puzzles where the people do reasoning about what others might deduce, so there is a delay in answers. 2-valued

11) I've never seen this- but how about trying to make sure that everyone gets it WRONG. 2-valued

12) I don't count this as a hat problem but some do: they want to find collectively information about all of the hats. Aspnes et al has 0-1 valued hats and wants to simul vote on the parity, see here. 2-valued.

This puts an upper bound on the number of possible hat puzzles at

3 x 4 x 3 x 2 x 3 x 2 x 3 x 4 x 2 x 2 x 2 x 2 = 89944.

This figure is wrong for reasons for reasons that both argue higher and lower.

a) Lower: MANY of  these combinations do not work together. For example, if you have an adversary and a deterministic strategy you can't talk about doing well in the average case.

b) Higher: For many of the above categories my number-of-values is low. For example you could look at hat games on many different graphs.

c) Higher: there are other variants I have not listed. That's where YOU come in! If you know of a version I have not discussed then please comment or email it to me!

Solutions to some Hat Problem AND some points of interest.

In my last blog here I asked three (known) hat problems since they may be new to you (one of them I just learned last week) and I had a point to make about them. I have WRITTEN UP the proofs  here since html is clumsy with math (or I'm clumsy with html-math), so this post is mostly about the points to make about these problems. I would urge you to read the writeup pointed to before reading the post.

1) N people 1,...,N, two colors R,B, Hats put on RANDOMLY (no adversary).

People are in a line and pe sees person j's hat iff i ≤ j .

There is a well known strategy where nobody passes which guarantees n-1 get it right (see here), but that strategy has EVERYONE get it right 1/2 of the time. We want MORE than that. LOTS more.

The following strategy works: For i=1,2,..., N person i does the following: if nobody has said RED yet AND ALL of the hats i sees are BLUE then i says RED. Otherwise Red passes

This fails on B^n. It works on everything else with the last R getting it right and everyone else passing. So the prob of getting it right is 1- 1/2^n.

POINT: I originally didn't have one to make, but a commenter misread the problem (or I miswrote it) in an interesting way. My problem was: Hats put on randomly, players are deterministic. They thought it was Hats put on by an adversary but players can use a randomized strategy. That problem (which frankly is more intersting) has a similar solution to the above: the players get a random string of R,B of length n and treat that like I treat B^n above.

2) omega people: 1,2,3,... and as above. We want to get all but a finite number of people get it right. See my writeup of it pointed to above. The proof I use uses the Axiom of choice and this is needed (see here).

POINT: some of my students didn't like that the players need uncountable memory. How much does this bother me: not even a little. A fellow blogger thought this result was so non-intuitive that he now thinks the axiom of choice is wrong (see here) Personally I am a lot more bothered by the Banach Tarski Paradox (see here), though that paradox has lead to what my wife calls either the best or the most obscure math joke ever: what is an anagram of Banach-Tarski? Answer: Banach-Tarski Banach-Tarski.

3) omega people: 1,2,3,... and as above but now we want to get at most ONE wrong. You CAN do this! see the writeup.

POINT: When I first learned problem (2) I assumed you could not get it down to a finite bound. And I was sure I could prove it, though I never got around to it, prob because I thought it was true and easy. Well, my turn to eat humble pie (an expression only said on TV and not in real live)--- you CAN do this with only one error.  The problem where you have an infinite number of people, they all see each others hats, and they all shout at the same time- that one I am sure you can't do with at most 1 error. I might need to eat humble pie once again.

4) n people, c colors, everyrone sees everyone else's hat, simul shouting, deterministic, and want to maximize how many get it right. OH- and adversarial.

Can do it with floor(n/c) but can't to better. See writeup.

POINT: The argument that you can't do better is a probabilistic argument! That's great! It may help bridge the gap between recreational and serious math (is there even a gap anymore?) that we use a Prob method on a fun hat problem! 

Two hat problems you may or may not have seen but I have a point to make about one of them

Hat problems are fun and often require clever solutions. I have posted about one type of hat problem here.

In this post I ask three. For two of them I have a point to make which I will make when I post the answer later in the week. Feel free to post your thoughts and answers, BUT be warned that if you don't want to know the answer then don't look at the comments.

1) N people stand in a line and are numbered 1,2,3,..,n. If i < j then person i can see person j's hat color.

Hats are going to be put on the heads RANDOMLY- prob of RED or BLUE is 1/2. (so no adversary)

The people, in order 1,2,3,..., n either say RED or BLUE or PASS.

We want to maximize the probability that (1) someone does not say PASS, and (2) ALL who do not say PASS are correct.

They can meet ahead of time to discuss strategy but after the hats are on ALL they can say
is RED, BLUE, PASS and only when they are supposed to.

(Also try with 3 colors, 4 colors, etc.)

(ADDED LATER- some comments I got inspire a clarification and a new problem.

Clarify: NO adversary. The players are deterministic. So the prob of failure is based on the randomness of the hats. So you want to minimize the number of seq of R and B where the players mess up.

Another problem: Their IS an adversary but the players are allowed to flip coins. Now the prob of failure is based on the players coin flips.
)

2) omega people in a line are numbered 1,2,3,...  If < j then person i can see person j's hat color.

An ADVERSARY is going to put hats on peoples heads RED or BLUE.

The people in order 1,2,3,... either say RED or BLUE

They can meet ahead of time and discuss strategy as in problem 1. The Adversary KNOWS the strategy

a) Prove or Disprove: there is a protocol  such that they always get all but a finite number of hats right

b) Prove or Disprove: there is a protocol such that they always get all but at most ONE right.

3) N people in a circle (so they see each others hats).

An Adversary is going to put hats on peoples heads- there are c hat colors.

The people AT THE SAME TIME shout out a hat color.

Give a protocol that maximizes how many get it right (in the worst case).  Show there is no better protocol.

The Complexity of Rubik's Cube

In my book I use Rubik's Cube as an example of a puzzle we can computationally solve efficiently (as opposed to Sudoku or Rush Hour). How does this square with the new result of Erik Demaine, Sarah Eisenstat and Mikhail Rudoy that finding the shortest solution is NP-complete? New Scientist now proclaims It’s not you – solving a Rubik’s cube quickly is officially hard. No, it's still you.

To study the complexity of Rubik's cube we can't just fixate on the 3x3x3 cube with its finite state space but on the general NxNxN cube. (One could also generalize to 3-sided hypercubes in N dimensions but good luck constructing a 3x3x3x3x3 Rubik's cube.)  For a given mixed-up NxNxN cube we can find in polynomial time a polynomial number of steps to return the cube to the original state. A mixed-up cube is just a member of the permutation group of the 6N² small squares and we want to find a sequence of generators (allowable rotations of the cube) that yield the mixed-up cube. Group theorists have come up with very efficient algorithms to find these sequences which we can apply in reverse to solve the cube.

Group theory does not necessarily come up with the shortest possible sequence and only in 2010 did we discover that solving the worst-case 3x3x3 cube, the so-called "God's Number", required 20 moves. A year later Demaine et. al showed that the minimum sequence for an NxNxN cube is Θ(N²/log N).

Two weeks ago Demain, Eisenstat and Rudoy posted their proof that given a fixed NxNxN cube finding the shortest sequence in NP-complete. Their proof is combinatorial, showing that solving an NxNx1 cube is NP-complete and reducing to the NxNxN cube.

So there you have it, solving a generalized Rubik's cube is easy but finding the shortest possible solution is hard. Despite Rubik's Cube achieving popularity during my nerdy high school days, I never had the patience to solve it, but that's just me.

50 Years of the Turing Award

The ACM knows how to throw a party, a two-day celebration of the 50th anniversary of the Turing Award. Every recipient got a deck of Turing Award playing cards and the ACM unveiled a new bust of Turing perfect for selfies.

The conference featured a number of panels on different challenges of computer science from privacy to quantum. Deep Learning formed a common thread, not only did it have its own panel but the Moore's law panel talked about specialized hardware for learning and deep learning causes concern for the privacy and ethics panels. Even quantum computing used deep learning as an example of a technology that succeeded once the computing power was there.

The deep learning panel focused on what it can't do, particularly semantics, abstraction and learning from a small or medium amount of data. Deep networks are a tool in the toolbox but we need more. My favorite line came from Stuart Russell worried about "Grad Student Descent", research focused on parameter tuning to optimize learning in different regimes, as opposed to developing truly new approaches. For the theory folks, some questions like how powerful are deep neural nets (circuit complexity) and whether we can just find the best program for some data (P v NP).

The "Moore's Law is Really Dead" panel joked about the Monty Python parrot (it's resting). For the future, post-CPU software will need to know about hardware, we'll have more specialized and programmable architectures and we'll have to rely on better algorithms for improvement (theory again). Butler Lampson said "The whole reason the web works is because it doesn't have to." I don't remember how that fit into the discussion but I do like the quote.

The quantum panel acknowledged that we don't quite have the algorithms yet but we will soon have enough qbits to experiment and find ways that quantum can help.

You can watch the panels yourself, but the real fun comes from spending time with the leaders of the field, and not just theory but across computer science.

Best. STOC. Ever.

The Panel on TCS: The Next Decade

Last week I attended STOC as its first new TheoryFest in Montreal. Pretty much everything about TheoryFest went extremely well and for the first time in a long time I felt STOC played a role beyond a publication venue. Great plenary talks from both within and outside the community. The poster sessions were well-attended and caused our community to talk to each other--what a concept. Senior people took junior people to lunch--I had a great time with graduate students Dhiraj Holden (MIT) and Joseph Bebel (USC). I missed the tutorials and workshops but heard they went very well.

By the numbers: 370 attendees, 46% students. 103 accepted papers out of 421 submitted. These numbers are moderate increases over recent years.

The Panel on TCS: The Next Decade talked about everything but the next decade. A few of my favorite quotes: "Hard instances are everywhere except where people care" (Russell Impagliazzo, who walked back a little from it later in the discussion). "I never know when I proved my last theorem" (Dan Spielman on why he keeps trying). Generally the panel gave great advice on how to do research and talk with other disciplines.

Avi Wigderson argued that theory of computing has become "an independent academic discipline" which has strong ties to many others, of which computer science is just one example. He didn't quite go as far as suggesting a separate department but he outlined a TCS major and argued that our concepts should be taught as early as elementary school.

Oded Goldreich received the Knuth Prize and said that researchers should focus on their research and not on their careers. The SIGACT Distinguished Service Award went to Alistair Sinclair for his work at the Simons Institute.

Oded apologized for lying about why he was attending STOC this year. TheoryFest will be a true success when you need reasons to not attend STOC. All happens again next year in Los Angeles (June 23-27) for the 50th STOC. Do be there.

Joan Clarke (1917-1996)

I'm in San Francisco for the ACM conference celebrating 50 years of the Turing Award. I'll post on STOC and the Turing award celebration next week. Today though we remember another member of Bletchley Park, Joan Clarke, born one hundred years ago today, five years and a day after Turing.

Clarke became one of the leading cryptoanalysts at Bletchley Park during the second World War. She mastered the technique of Banburismus developed by Alan Turing, the only woman to do so, to help break German codes. Bletchley Park promoted her to linguist, even though she didn't know any languages, to partially compensate for a lower pay scale for woman at the time. Keira Knightly played Joan Clarke in The Imitation Game.

Joan Clarke had a close friendship with Turing and a brief engagement. In this video Joan Clarke talks about that time in her life.

Harvard revokes admission of students based on what was said in a private(?) chat room

Harvard revoked the admission of 10 students (see here) based on what the students said in a private (can't have been too private) chat room.

(ADDED later upon reflection- Harvard has only confirmed that there is a clause students are made
aware of about immaturity and moral character. As for the reason for the revoking- we only have
what is reported and that comes from the students. Are the students trustworthy on this?  Given that they are being expelled for moral reasons... But more seriously we really don't' know. I just want to caution that we do not know the full story and never will. Note that Harvard is not  legally allowed to disclose why they revoked, while the students can say what they want.  For an example of how off a reported story can be see this though I am sure you all know other examples.)

Normally I would be aghast (and I may still be aghast) because of the slippery slope:

Today you revoke admissions because students mock sexual assault, the Holocaust, and the death of children, and call the hypothetical hanging of a Mexican child ``pinata time''

Tomorrow you revoke admissions because a student is a Trump Supporter.  (Readers: I assume that you would find revoking admission because a student is a Trump supporter to be disgusting and absurd.)

I felt strongly against this and sought out some other viewpoints. Here are some:

1) Harvard is within their rights to do this legally according to what they agree to when they accept you. This is true. This is also irrelevant- I am interested in if its the right thing to do, not if its legal.

2) The content of the chat rooms indicates a lack of moral character.  This is a stronger argument. However the nebulousness of ``moral character'' reminds me of the origin of taking moral character into account: it was an excuse to let in less Jews (see the book t Harvard, Yale, and Princeton, see The Chosen: The hidden history of admissions and exclusion a review here).  Jews do not have less moral char, but it was used as an excuse to admit less of them.  Even though in the case at hand moral char is a legit issue, the history of the use of this issue bothers me. Slippery slope again.

3) For crying out loud bill, LIFE is a Slippery Slope! You have to draw the line somewhere! And wherever you draw it, these kids are over that line.  This argument, combined with the moral-point of item 2, I do find compelling.

4) Here is a one border (I do not know if it was crossed): If a student personally attacks another student then this is grounds for  revoking. Sounds good but what constitutes a personal attack?

Counter argument: : Whenever a disgusting point of view is censored or punished the conversation shifts from

                                              That is a disgusting point of view

to

                                         Free Speech! Oppressing unpopular views!

I would rather the conversation be about why the point of view is wrong (or disgusting)  rather than on Free Speech.

Right now I am 75% against the revoking of the students admissions. This has no effect- I am not in any position of power, I won't give less money to Harvard (I am an alum-Grad school, which is why I noticed the story in the first place). I find the question interesting and, more than usual, welcome your comments. Based on your comments that 75 might change! In either direction!