Sunday, August 13, 2017

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.)

Thursday, August 10, 2017

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?

Sunday, August 06, 2017

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?



Thursday, August 03, 2017

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.

Monday, July 31, 2017

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?

Friday, July 28, 2017

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.

Thursday, July 27, 2017

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? 

Sunday, July 23, 2017

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.

Thursday, July 20, 2017

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!




Monday, July 17, 2017

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 Kn or Ln.  There have been some papers on cycles (see herehere),  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 hereherehere). 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!



Thursday, July 13, 2017

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! 

Sunday, July 09, 2017

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.






Wednesday, July 05, 2017

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.

Thursday, June 29, 2017

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.

Monday, June 26, 2017

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.

Saturday, June 24, 2017

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.

Tuesday, June 20, 2017

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!

Wednesday, June 14, 2017

The Power of Economic Inefficiency

I grew up in a time when long distance domestic phone calls from AT&T costed $0.20/minute off peak ($1.30 in today's dollars). I also grew up close to AT&T Bell Labs, a mecca that claimed more PhDs than any university many doing independent research. Now I get all the phone minutes I can use and Bell Labs is a tiny fraction of what it once was. Was it a good trade?

Technology has helped eliminate many of the economic inefficiencies. Usually for the better but sometimes these inefficiencies has good side effects. For another example take airlines--we can now so easily compare airlines on price so they often compete on price at the cost of service. Don't even get me started on newspapers.

Universities remain one of the institutions where technological change has not had the cost savings effect that we've seen in communication and transportation. That's one of the reasons that universities have become more expense. We can't keep raising tuition and being pushed to focus on eliminating inefficiencies, seeking new ways to deliver classes for example. Will the research university as we know it survive?

Monday, June 12, 2017

Climate Change: The Evolution of the Deniers/Does Paul Ryan Hate His Grandchildren?


I went to the Mach for Science and then Drumpf pulled out of the Paris Accords. Causation or Correlation? I then posted about climate change (CC). That's caustation.

1) Deniers:

  The deniers have gone through several phases:

There is no CC

There is CC but its not caused by humans.

There is CC and its caused by humans but since China and India and other countries aren't doing anything about it, if only we do it will have no effect except to ruin our economy.
(Counter argument: the effects of climate change are economically devastating- are insurance companies trying to pressure governments to do something about CC since CC's effects cause damage which hurts their bottom line?)

Intermixed with these arguments have been:

Just because 87% of all lung cancer victims  smoke, that's just a correlation. Maybe people the lung cancer gene is also the smoking gene. Correlation does not equal causation. OH, sorry, that's a flashback to the Correlation NOT causation arguments made by the Tobacco companies. Do they still believe that? Mike Pence does (see here). How can they stay in business? (here's how) ANYWAY, some are making the correlation NOT causation argument for why Polar bears are dying, etc.

AND the classic

Technology will bail us out. (This would be a better argument if it was followed by hence we will give lots of funding for such technology  which is NEVER what its followed by.)

OKAY, so where are we in 2017?

The economist had an argument about how Solar and Wind will soon be MORE cost effective than Oil and Gas- though we still have the problem of what happens on a cloudy, windless day- so we need technology to store (see here though its behind a pay wall). China and India ARE doing things about CC. How much? Effective? Hard to say- though both are really concerned with pollution.

I predict the new argument will be:

We're all doomed anyway so why take our economy down at the same time.

Unfortunately this argument might be correct.

(ADDED LATER- a commenter says that I conspicuously left out religious arguments to not do anything about CC.  I now conspicuously ask you to read his comment.)

2) Take Paul Ryan. Please.
Seriously-- I assume he KNOWS that CC really is a problem and the longer we put it off the worse it will be for his grandchildren, and perhaps his children. So why does he fight ANY attempt to even admit we HAVE a problem (And note there ARE some market-based solutions- a Carbon Tax, Cap and Trade.)  Some speculation

a) Despite being smart he's in deep deep denial. Okay, but why is that? If you believe in small government then if something comes along that REQUIRES big government, you just DENY it since it does not fit into your world view.

b) Paul Ryan hates his Grandchildren.

c) Paul Ryan thinks that HIS grandchildren will be among the few people who survive and live in a VERY gated community. He's probably wrong about that as even those in gated communities will suffer the effects of CC.

d) Paul Ryan is stuck. If he tries to do ANYTHING then it will not work AND he'll lose his speakership and possibly his seat in congress. And there are a large number of congressman and senators who feel the same way but they're all afraid to say. If they ALL said so then... they'd ALL lose their seat in congress. One of the downsides of politics is ending up STUCK on the WRONG side of history and KNOWING it. Well, at least there won't be much history left so he won't be stuck on the wrong side for long.

3) Game Theory. I used to think that it was in NO countries SHORT term interest to do anything serious about CC (that is, do it alone) and hence we were all DOOMED! Doomed I say! And part of the problem is that if Country A emits greenhouse gases its bad for THE ENTIRE WORLD EQUALLY, and not for Country A in particular. But a few things make me more optimistic:

Pollution is a here-and-now problem for China and India so they will tackle that. That somehow has to be part of the solution.

Technology- as mentioned before Solar and Wind is catching up to Gas and Oil. (downside of technology- Fracking and oil extraction are also getting better and cheaper. Hubbert's Peak Oil Theory doesn't seem to be true) But the real advantage of Solar and Wind will be that you don't have to Extract and ship Oil (or Coal or whatever).

4) I wrote that last positive point before President Drumpf. Having a CC denier in the white house means four more years of no action which sounds really bad- especially since the longer we put off doing something about the problem, the harder and more expensive it will be to slow down CC (Some ponders that Trump won't be that bad for the environment: here)

5) Okay Bill, what would YOU do? Carbon Tax will give financial incentive for companies to curb Carbon emissions. And its simple. The Tax has to be high enough to have an effect. Another added bonus will be to help America pay down its deficit. ALSO more research into renewables. Oddly enough I would also recommend NOT forcing Gas to contain Ethanol- make Ethanol compete with Solar and Wind. (Recall that Ethanol is funded only because of the Iowa Caucus. If you don't know what I'm talking about, don't worry, its too stupid to explain.) Some may disagree and have other ideas. Thats FINE- I would rather be having a debate about what to DO about the problem rather than one about whether or not there IS a problem. Though even a debate about what to do about the problem should be SHORT so we can begin DOING something.

Thursday, June 08, 2017

Theory Jobs 2017

In the fall we point to theory jobs, in the spring we see who got them. Like last year and years past I created a fully editable Google Spreadsheet to crowd source who is going where. Ground rules:
  • I set up separate sheets for faculty, industry and postdoc/visitors.
  • People should be connected to theoretical computer science, broadly defined.
  • Only add jobs that you are absolutely sure have been offered and accepted. This is not the place for speculation and rumors.
  • You are welcome to add yourself, or people your department has hired.
This document will continue to grow as more jobs settle. So check it often.

Edit

Monday, June 05, 2017

Big News on W(3,r) !

This is a JOINT POST with   Evangelos Georgiadis who brought this problem to my attention.)

In 2010 I posted about how dense a set of integers has to be before you know there is a 3-AP in it (a 3-AP is a set of three numbers equally spaced). Such results were motivated by and are applied to getting upper bounds on

W(3,r) = the least W such that any r-coloring of {1,...,W} has a monochromatic 3-AP.

That blog, which also has history and context, is here

At the time of that post the following was known (and had just been proven by Sanders see here)

If A ⊂  {1,...,N} and |A|  ≥ N*(log log N)5  / log N  then A has a 3-AP

and hence

W(3,r) ≤ 2r(log r)5





(Added later: Bloom's paper (see link on next line) reports that Sanders result is a bit weaker than claimed- the 5's should be 6's, calculation error.)

This has now been improved!. Thomas Bloom, in this paper has shown

If A ⊂  {1,...,N} and |A|  ≥ N*(log log N)4  / log N  then A has a 3-AP

and hence

W(3,r) ≤ 2r(log r)4

An easy prob argument gives

W(3,r)  ≥ r3/2


So is W(3,r)'s growth rate poly? Exp? in between? Is there a connection to SAT?

One can phrase the question  W(k,r)=m as asking of a certain Boolean Formula is it satisfiable.  IF we can get theorems about that kind of formula, that might help.

However, I doubt that it has much real connection to the general SAT problem.

I don't know if the consensus of the community is that W(3,r) is poly or exp.

(Warning: I've seen W(3,r) to mean something else: W(3,r) is the least W such that any 2-coloring of {1,...,W} with colors 0 and 1 has either a 0-colored 3-AP or a 1-colored k-AP. This is NOT the function we are talking about, though that one is also interesting. )

ADDED LATER: Knuth's Volume 4, Fascicle 6 has theorems about this W(3,r)

ADDED LATER: A commenter said that a simple prob greedy algorithm using salem-spencer sets
yields

W(3,r) ≥ exp(C (ln r)2)

I reconstructed the proof from these comments, though using Behrends sets instead of SS

The proof is here: here









Thursday, June 01, 2017

Who Sets Policy?

In April the New York Times Magazine ran an article Is it O.K. to Tinker with the Environment to Fight Climate Change?  The article asks about the ethics of even running tests on such methods and has this quote froms David Battisti, an atmospheric scientist at UW.
Name a technology humans have developed that they haven't used. I can't think of any. So we can work on this for sure. But we are in this dilemma: Once we do develop this technology, it will be tempting to use it.
The article skirts the question on who makes this decision. Maybe the United Nations after some unlikely agreement among major powers. But what if the UN doesn't act and some billionaire decides to fund a project?

As computer scientists we start to face these questions as software in our hyper-connected world starts to change society in unpredictable ways. How do we balance privacy, security, usability and fairness in communications and machine learning? What about net neutrality, self-driving cars, autonomous military robots? Job disruption from automation?

We have governments to deal with these challenges. But the world seems to have lost trust in its politicians and governments don't agree. How does one set different rules across states and countries which apply to software services over the Internet?

All too often companies set these policies, at least the default policies until government steps in. Uber didn't ask permission to completely change the paid-ride business and only a few places pushed back. Google, Facebook, etc. use machine learning with abandon, until some governments try and reign them in. The Department of Defense and the NSA, in some sense industries within government, set their policies often without public debate.

What is our role as computer scientists? It's not wrong to create the technologies, but we should acknowledge the ethical questions that come with them and what we technically can and cannot do to address them. Keep people informed so the decision makers, whomever they be, at least have the right knowledge to make their choices.

Tuesday, May 30, 2017

Google Scholar thinks my Hilbert Number is 1

(I want to thank Lane Hemaspaandra for bringing this to my attention.)

When I google:

google scholar  William Gasarch

I get  this

(I wonder if what you get depends on who you are- I describe below what I get.)

The first entry on it is

Methods of  Mathematical Physics by Courant and Hilbert.

The first page page that Google brings up has all papers with Hilbert as a co-author except the book

Handbook of discrete and combinatorial mathematics edited by Rosen

I have a short article in that book.

The second page has the paper of Hilbert:

Uber die irreducible ganzer rationaler blah blah

which I have a connection to since Mark Villarino, Bill Gasarch, and Ken Regan have a paper explaining this paper in modern terms here. Could this have confused google scholar into thinking I am Hilbert? Seems unlikely.

In fact, the first two pages are all papers with Hilbert as an author. The third page has

Some connections between bounded query classes and non-uniform complexity by Amir, Beigel, Gasarch.

And after that the pages are a mix of Hilbert's papers and mine, though mostly his since he had so many more papers than I did.

This raises some questions

1) How did this happen? Did I hack google scholar? Many theorists at one time in their lives were excellent programmers- however, I am not one of them.

2) How common is it for google scholar to be this far wrong?

3) If I wanted to get this fixed who would I tell?  In the past whenever I've tried to tell a company something FOR THEIR OWN GOOD I get the same run-around as when I am trying to get information not on their website, so I have STOPPED even trying. Same here?

4) Should I want to get it fixed? I am proud to be affiliated with Hilbert!

Thursday, May 25, 2017

Graduation from the Other Side


I've attended many graduations in my time, mostly as faculty, a couple of times as a student or a brother. This last weekend I attended my first university graduation as a parent as my daughter Annie graduated from Brandeis University in Waltham, Massachusetts. Brandeis has a big graduation ceremony with lots of speeches and then different departments or groups of departments have their own diploma ceremonies with their own speakers and where they give out the actual diplomas.

Brandeis gives out a number of honorary doctorates each year and for the first time gave one to a computer scientist, Turing Award Winner Leslie Lamport. Lamport received his PhD at Brandeis in math in 1972 before they had a CS deparment but now he has an (honorary) PhD in Computer Science. Lamport gave an eight-minute talk in the School of Science ceremony. But when you are a parent the weekend is about your child and my daughter didn't graduate from the school of science so I didn't see the Lamport talk.

In the main ceremony, Brandeis has not only an undergrad give a speech but also a grad student. Sounds like a crazy idea, but Vivekanand Vimal, Neuroscience PhD, gave what could be best described as a performance art. Since I can't find the video of Lamport and you probably don't want to see my videos of Annie, enjoy the new Dr. Vimal's ode to the craziness of the PhD and saving society.

Thursday, May 18, 2017

The Optimizers

Last week the Georgia Tech School of Industrial and Systems Engineering honored the 80th birthday of George Nemhauser and the 70th of Arkadi Nemirovski at an event naturally called NemFest. The Nems are powerhouses in the optimization community and this event drew many of the greats of the field.

In theoretical CS we often take NP-complete as a sign to stop searching for an efficient algorithm. Optimization people take NP-complete as a starting point, using powerful algorithmic ideas, clever heuristics and sheer computing power to solve or nearly optimize in many real-world cases.

Bill Cook talked about his adventures with the traveling salesman problem. Check out his British pub crawl and his tour through the nearly 50,000 US historic sites.

Michael Trick talked about his side job, schedule MLB baseball games, a surprisingly challenging problem. Like TSP, you want to minimize total travel distance but under a wide variety of constraints. "There's something satisfying about being at a bar, seeing a game on the TV and knowing those two teams are playing because you scheduled them." Can't say I've had that kind of satisfaction in my computational complexity research.

Tuesday, May 16, 2017

If an ugrad asks `is field X worth studying' the answer is almost always yes

An undergraduate Freshman recently emailed me that he was very interested in Quantum Computing and wanted to know

1) Who on the fCS aculty works in QC (Answer: Andrew Childs though you should ask him about postdocs, grad students, and Physics faulty in the area.)

2) What are good books on QC for a bright ugrad. I said the following:

QC since Democritus by Aaronson
QC-A gentle introduction by Rieffel and Polak
QC for CS by Yanofsy and Mannucci
QC and QI by Nielsen and Chuang
Some of Scott's blog posts.
Ask Andrew Childs for more.

my webpage of book reviews for SIGACT NEWS here and search for Quantum to get some other books- read the reviews and pick one.

on Amazon type in quantum computing and see what reviews say- though they might not be reliable.

There are likely other good books but I do not know of them. (You can leave comments.)

3) Is QC a good topic to get into? I said YES of course. My reasoning is that they would of course LEARN something by studying it.

 But this raises the question: When would I say `that field is not worth studying' ?

1) If they really want to do RESEARCH and the topic is either too dead or too hard and they want to actually do research (as opposed to learning the topic without wanting to to research).

2) If there was nobody around to help them in that topic. Might still be okay if they are both highly motivated and very smart.

3) If the topic was bogus AND they would learn NOTHING from studying it. Are there topics that are bogus but you still learn from studying them? Does studying astrology seriously teach you some astronomy? Some history? How about Alchemy and Chemistry? Fine if the students KNOWS that Astrology is bogus and Alchemy is not correct.

The points is that I really do not want to dampen someone's enthusiasm for a topic.

SO- aside from the reasons above, can you think of any other reason to discourage a student from a topic they are interested in? I ask, as always, non-rhetorically.



Sunday, May 14, 2017

William Tutte (1917-2002)

Today we celebrate our mothers of course, but also the 100th anniversary of the birth of Bill Tutte, best known for his role in decrypting the Lorenz cipher used by the Nazi high command. Tutte also made many important advances in graph theory and algorithms.

For this post, let's look at one very powerful concept, the Tutte Polynomial, with a rather technical looking definition. Fix a graph G with vertex set V and edge set E with n = |V|. For a subset A of E, let kA be the number of connected components of A and nA be the number of vertices of the vertices of G induced by A, and k=kE the number of connected components of G.

The Tutte polynomial T(x,y) is the sum over all subsets A of E of the quantity
(x-1)kA-k(y-1)KA+nA-n.

What makes this problem interesting? For some fixed values of x and y we get various properties of the graph.

T(2,1) is the number of forests of G.
T(1,2) number of spanning forests (or spanning trees if G is connected.
T(2,0) is the number of spanning subgraphs.
T(0,2) is the number of strongly connected orientations.
The value (-1)n-kqkT(1-q,0) counts the number of q-colorings of G.

Computing T can be difficult. Counting the number of 3-colorings is #P-complete, equivalent to counting the number of satisfying assignments of a Boolean formula. So even computing T(-2,0) for a given graph G is #P-complete. Leslie Goldberg and Mark Jerrum show that even computing the sign of a Tutte polynomial, just determining whether it is positive, zero or negative, on certain values is still #P-hard.

This is only a sampling of the many applications of the Tutte polynomial. Let's remember Tutte for creating a single function that captures so much information about a graph and helping to defeat the Nazis. Not a bad life. Must have had a good mother.

Thursday, May 11, 2017

How to Solve It

Today a guest post from Periklis Papakonstantinou, coincidentally not unrelated to Bill's post earlier this week. I'll be back with a special post on Sunday.

I'm teaching in an undergrad program that is half computer science and half business at Rutgers, but the CS part taught there is the real thing (I assume for Business too). This term I taught a very theoretical course in cryptography and I realized that (1) the students enjoyed it and (2) that they were lacking basic reasoning skills. I ended up teaching for a few weeks how one can structure basic logic arguments. I am not sure if they appreciated things like the hybrid argument but I believe I convinced them that without rigorous thinking one cannot think clearly.

So, I decided to teach a much more fun class (hopefully next year) titled "How to solve it" -- à la Pólya. The goal is students to develop rigorous problem-solving skills. At the same time, I'd like to use this course as an excuse to introduce basic concepts in combinatorics, linear algebra, and theoretical stats. I'm not sure whether the original book by Polya is appropriate for this and that's why I thought of reaching out to my peers for suggestions. Any ideas and thoughts on possible texts, topics, or notes would be greatly appreciated.

Sunday, May 07, 2017

Students try to memorize rather than understand! Who knew! (everyone)


Discrete Math. Required for CS majors, taken mostly by Sophmores.  Goal is to teach them how to think  rigorously. Topics are logic, number theory (not much), induction, sets, functions, relations, combinatorics (includes Pigeon hole prin, henceoforth PNP), prob, countability, uncountability.

We taught the Pigeon Hole Principle and gave MANY examples and HW of the following type:

Let A be a subset of {1,...,50} of size 10. Show there are two subsets of A that have the same sum.

ANSWER: There are 2^{10} = 1024 possible subsets.

MAXSUM is  41+..+50 = (1+...+ 50 )-(1 +...+ 40) = 50*51/2 - 40*41/2 = 455

MINSUM is 0 (the empty set). So the NUMBER OF SUMS is 456

Since 1024 > 456 there are two subsets of A of the same size.

The EXAM covered PHP, combs, prob, and induction. Hence they should know n choose k

On the HW and in class we NEVER did a problem where we only cared about the subsets of a fixed size. Conceptually this is really the same problem but if you had MEMORIZED  the proof template and tried to apply it you would get it wrong.

I asked the following on the exam: which was worth 20 points.

(20 points) Let A be a subset of {1,...,21} of size 8. Show that A has at least two subsets of size 3 which have the same sum.

ANSWER: There are (8 choose 3) = 56 subsets of A of size 3.
MAXSUM = 19+20+21 = 60, MINSUM = 1+2+ 3 = 6,
 So the NUMBER OF SUMS is 60-5 = 55.

Since 56> 55 there are two subsets of A of size 3 that have the same size.

Grading rubric:

If they got (8 choose 3) thats 3 points.(Many said 2^8- I suspect incorrect memorization)

If they got the MAXSUM and the MINSUM both right (aritj errors- NO penalty) then 3 points
(Many had MINSUM=0- I suspect incorrect memorization).

If they knew to use these PHP then 3 points.

If they got all three right then 20 points

So they got 0,3,6, or 20.

Here is the final tally:

0 points: 85

3 points: 190

6 points: 71

20 points: 167

(For the entire exam: 39 100's, 55 90-99, 77 80-89, 77 70-79, 76 60-69, 70 50-59, 47 40-49, 24 30-39, 24 30-39, 17 20-29, 3 10-19, 3 1-9)

This all raises the much harder question- how can we get students to UNDERSTAND rather than MEMORIZE

Telling them: DO NOT MEMORIZE! TRY TO UNDERSTAND!- I did this. Oh well.

Allowing a cheat sheet (which I did) is both good and bad for this issue.

Giving them a much wider variety of problems of this type. Either they would understand OR they would memorize several different templates.

I WELCOME your thoughts on either my grading or on how to get them to try to UNDERSTAND rather than MEMORIZE.


Thursday, May 04, 2017

Summer Conferences

Ahh summer. No Classes. Baseball. Opera Festivals. Time to focus on research and starting a new book. But, of course, many computer scientists travel the world to various conferences. I went to too many last year and trying to cut down but many great options abound.

The STOC 2017 Theory Fest, June 19-23 in Montreal, five days of conference talks, tutorials, invited lectures and so much more. Sanjeev Arora has the details over at Windows on Theory.

The ACM celebrates 50 years of Turing Awards with a special conference June 23-24 in San Francisco. Tim Berners-Lee takes home this year's prize.

The Computational Complexity Conference, that meeting that shares its domain with this blog, holds its annual get together July 6-9 for the first time in Latvia. Latvia gave us Juris Hartmanis, one of the founders of the field. Travel grants available for students and "needy researchers", you don't have to be an author to apply.

Computability in Europe, June 12-16 in Turku, Finland. Economics and Computation, June 26-30 at MIT. Computational Geometry, July 4-7 in Brisbane. ICALP, July 10-14 in Warsaw. Random/Approx, August 16-18 in Berkeley.

If I missed your favorite events, well that's why we have comments.

Monday, May 01, 2017

A Celebration of Computer Science at Harvard in Honor of Harry Lewis's 70th Bday

My adviser Harry Lewis turned 70 recently. I blogged about how things have changed since I got my Phd in this post. I now post on

A celebration of Computer Science at Harvard in Honor of Harry Lewis's 70th Birthday

(for video of all talks in order see: here)

The title was accurate: most of the speakers (1) were Harvard ugrads, (2) went on to do great things, and (3) Harry Lewis had inspired them. The talks were mostly non-technical and fun!
went on to do great things. Margo Seltzer, a prof at Harvard now (who I TAed many years ago in Aut Theory) orgnaized the event, though she gave lots of credit to her helpers.

0) Marty Chavez was one of Harry Lewis's teaching assistants for a CS programming course and recalled Harry's harsh (but fair) grading polices on code which he later saw the wisdom of.

1) Marty Chavez never thought he would use that HALT is undecidable (I think I might have been his TA for that course). But he found himself telling an egghead of economists who wanted to VERIFY all code to avoid future crashes that... Can't be done. Actually, while that is true, attempts to verify some of it might be a good idea.

2) James Gwertzman noted that:

in 1991 10% of all ugrads at Harvard  had email, and there was no web

in 1995 100%of all ugrads at Harvard had email, and there was web (though primitive).


He then pointed out that a company can do very well by using LOTS of packages that are already out there to use. He named #slack, salesforce, trello, jeaking, mailchip, greenhouse, phabricator, pingdom (just deals with pings- really!), datadog, strips, statuspage, zendeski.

The future will be serverless and codeless.

4) Guy Steele gave the most technical talk and it was, as the kids say, awesome (do adults still say `as the kids say' ?) Here is a version of the talk:

A Logial Concern

Its about how papers at POPL and some other conference have been informally using a language to specify protocols and by now its all bent out of shape. There is also some nice history of math embedded in the talk of which I'll say one thing: one way to group terms together is by placing a bar over them. The most common use of this now is the squareroot sign which didn't always have that bar over the quantity.

Guy's talk even had some slides about his notebooks from Harvard, from a course Harry taughtback in 1974 (the first course Harry taught at Harvard). Part of the course was on the sequent calculus which relates to Guys work and the current paper. Guy's notebook had both material relevent to the current paper and doodles of things like a picture of a Church next to Church's thesis.

The paper was very labor intensive since you can't just use a search program to search for some of the notations he was talking about. For example overbar and underbar. So he had to go through ALL of the POPL proceedings (and a few others) by hand. In 2017. Will that ever be easier?

He also had a two quotes about proofs:

Its not enough to prove something. You must seduce people into believing it

One man's truth is another man's cold broccoli 

I leave it to you to figure out who these quotes are credited to (different people).

5) Stuart Shieber's talk was WWHD (What Would Harry Do).

Care

Promote Character over knowledge (see Harry's book Excellence without a soul- How a great university forgot education)

Pursue the right over the popular

A late talk by Rebecca Nessin told of some things Harry did as Dean that were RIGHT but NOT POPULAR:

The housing at Harvard used to be you chose the house (dorm complex) you lived in. When I was there Dunster was KNOWN to be the Math-house, and others had other reputations that were somewhat accurate. Harry made housing RANDOMIZED (did he use a hardness result to derive a pseudo random generation?) His goal was to increase diversity- people should get to know other kinds of people that are not like themselves.

He made polices do curb underage drinking.

He raised standards for when students get WARNINGS about their performance in classes.

These were all unpopular BUT the right thing to do.

6) There was a panel discussion on teaching.  I'll save this for a later blog post since my random thoughts on this may make this post longer than it should be. I WILL say it was excellent.

7) Rebecca Nessin is the head online course development at Harvard. The courses are  (1) open enrollment  (2) No faculty- all are borrowed from the usual faculty, (3) some courses are online.  She developed a course where the students ARE avatars. Helps with shy students. And text based conversation allows students to get out coherent complete thoughts (CONTRAST- I find myself saying to my students questions ``that was a random sequence of math words'')

That was the first part of her talk.

THEN she began talking about her journey through Harvard and Harry's place in it. Unlike her fellow students she did not what she wanted to do. She took random courses (ancient greek! Multivar calc!) After graduating she still did not know what she wanted to do so she went to... Harvard Law School. While there she took a CS course (what!  You can do that?) and soon after had Aut Theory with Harry. Her PhD was with Stuart Shieber with Harry on the committee and lots of Grammars in it.

Then she told a great story: There was a discussion of raising the min age that someone can get an ugrad  degree at the Harvard extension school. Harry asked who this would affect. The answer was

A small number. Students who can't go to a residential full time school for some reason. This includes competitive athletes, performance artists, deployed military personal, youthful entrepreneurs,  and people with disabilities.

to  which Harry replied:

These are the oddballs. Are we trying to say there is no room for oddballs at Harvard?

Rebecca ended her talk by pointing out that with her crooked path to where she is now she is an oddball and
that all of the oddballs should celebrate that they will also have a place at at Harry Lewis's Harvard.

8) Cliff Young declared Moore's Law Dead (some disagree- see here) - and the solution is to go back to special purpose machines- which, contrary to popular belief, Do NOT just do one thing and
ARE programmable, He also talked about Amdahl's law which is about the limits of parallelism and about how  parallelism research seems to fight the same battle over and over again (RISC vs CISC,
SIMD vs MIMD, and VLIW)

9) Danielle Feinberg from Pixar had the following quote about animation:

Long hair is an unsolved problem

But they did solve it (for the movie The Incredibles). She also pointed out that they can sometimes spend lots of time and energy and creativity on a scene that will take 3 second, or on something just in the background.

Much like Rebecca, Danielle also appreciated Harrys appreciating for oddballs.

10) Harry Lewis- He spoke some about his career but also about CS in general.

 His career and where his now is sort-of an accident. He was originally going to get his PhD in Systems but Theorists got out faster.

 Computer Science has changed a lot in the last X years- but the change he remarked on the most is that it CS is at

The twilight of the Amateur Era

I'll let you debate what that means.

11) Later at the reception Bill Gates and Mark Zuckerberg send their recorded greetings, though only Mark Z's is on the you tube video- towards the end. Its short so rather than summarize it- I urge to to view it yourself.





Thursday, April 27, 2017

So Was I

While Bill marched at the main March for Science in DC, I marched at the satellite march in Atlanta, my daughter Molly in Chicago, Scott Aaronson in Austin, Hal Gabow in New York, and Donald Knuth (pictured) presumably in San Francisco. I thank the many of you who participated in your local march. Science appreciates the support.

Most of the marchers I saw did not come from the ranks of academia or professional scientists. Rather people from all walks of life who believe in the important role science and scientists have in shaping our future. Parents dragged their kids. Kids dragged their parents.

There have been some worry about politicizing science and whether the march would be a bad idea. The march won't have much effect on policy positively or negatively. But we mustn't forget that scientists need to deal with politics, as long as the government continues its missions of funding science and using proper science to help guide policies that require understanding of the world.

If there's one positive sign of a Trump presidency, as Molly explained to me, it's inspiring a generation. We would not have had a March for Science if Trump wasn't president, but what an wonderful movement and we should march every year around Earth Day no matter who sits in the oval office.

Monday, April 24, 2017

I was at the March for Science on Saturday

(Will blog on Harry Lewis's 70th Bday next week-- Today's post is more time sensitive.)

I was on the March for Science on April 22. Here are some Kolmogorov random comments

1) Why should I go to it? One less person there would not have matters. AH- but if they all think that then nobody goes. The Classic Voting Paradox- why vote if the chance that your vote matters is so small (even less so in my state- Maryland is one of the Bluest States).  In the case of the March For Science there is another factor- since I live in Maryland I really CAN go at minimal effort. Most of the readers of this blog cannot (Though there were some other marches in other cities. Scott was at a March in Austin Texas.)

2) One of the speakers said something like `and the fact that you are all here in the rain shows how much you believe in our cause!'  While the rain might have made our being there more impressive, I wish it had been better weather.

3) Here are some of the Signs I saw:

What do we Want!
Empirical  Based Science!
When do we Want it!
After Peer Review!

Trump- where's your PhD? Trump University?
(This one is not fair- most presidents have not been scientists and have funded science. Trump himself not have a PhD  is not relevant here.)

A sign had in a circle:  pi, sqrt(2) and Trump and said: These are all irrational.

A 6-year old had a sign: Light travels faster than sound which is why Trump looks bright until he talks (I think her mother, who was there, made it for her).

Science is the Solution (with a picture of a chemical Flask)

If you are not part of the solution you are part of the precipitate

Truth is sometimes inconvenient.

So severe even the nerds are here

I can't believe I'm marching for facts!

There is no planet B (this refers to if Global Warming kills the planet we can't go elsewhere- a play off of `Plan B')

I'm with her (pointing to the earth) (The person with this sign told me she used the same sign for the Women's  March- so recycling!)

Science has no borders

Science doesn't care what you think.

Its not Rocket Science- well, some of it is.

4) The March For Science was the same day as Earth Day and many of the talks mentioned global warming and pollution. Many of the talks mentioned the contributions of women and minorities. One of the speakers was transgender .Hence the March had a liberal slant. BUT- if believing in Global Warming and wanting to open science up to all people (e.g., women and minorities) are Liberal positions, this speaks very badly of conservatives. First ACCEPT that Global Warming is TRUE- then one can debate what to do about it--and that debate could be a constructive political debate.  One talk was about Indigenous Science-- I can't tell if its a healthy alternative  view or ... not.

A more telling point about the march having a liberal slant is the OMISSION of the following topics:

Technology has

(a) helped Oil people extract more oil, and fracking to be cost effective

(b) GMO's  have helped feed the world and have had no ill effects (I think anti-GMO in America is a fringe view-- I don't know of any elected democrat who is anti-GMO, though I could be wrong. I think its a more mainstream view in Europe.)

(c)  make the weapons that keep us safe (that's a positive spin on it)

(d) DNA used to prove people GUILTY (they did mention DNA used to prove people INNOCENT).

So the March LOOKED like it was a bunch of Liberal Scientists. Does this make it less effective and easy for Trump and others to dismiss? Or are we so far past any hope of intelligent conversation that it doesn't matter?


5) Many of the machers, including Darling and me,  had lunch at the Ronald Reagan Center. Is this an IRONY?

NO: Reagan funded the NSF as well as other presidents, see this blog post of Lance's from 2004. That post is interesting for other reasons: at the time Dems and Reps seemed to both RESPECT science. Trump may be the first one not to- though its early in his term so we'll see how it all pans out. Second, Lance has been blogging for a LONG time! (since 2003, and me since 2007).

YES: See these quotes by the Gipper (ask your grandparents why Reagan is called that):here

6) Will it have any effect? Short term I doubt it, Long term probably yes. An article about the impact of the the Women's March: here

7) There have been Women's Marches, The Million Man March, Civil Rights Marchs, pro-life, pro-choice, anti-war, pro-gay, anti-gay marches before. Has there ever been a March for Science before? Has there ever been a need before? I don't think so but I am asking non-rhetorically.

Cutting EPA because you don't believe in Global warming is appalling, (see here) but I understand politically where that comes from.

Not allowing funding of gun violence because you are pro-gun is appalling, (see here) but I understand politically where that comes from.

IF they cut funding on the study of evolution (Have republican presidents done that?) then that would be appalling but I would understand politically where it came from.

But cutting the NIH (see here) or the NSF (has he done that yet or is he just thinking of doing that?) I really DON"T understand- It does not even fit into the Republican Philosophy.

There should NOT be a NEED for a MARCH FOR SCIENCE, Or, to quote one of the signs

I can't believe I"m marching for facts!