Babai Strikes Back

"So it is quasipolynomial time again"

Short Version: Babai fixed his proof.

In November 2015 László Babai announced a talk "Graph Isomorphism in Quasipolynomial Time" at the University of Chicago, an incredible breakthrough for this important problem. The algorithm is a tour-de-force masterpiece combining combinatorics and group theory. The result sent shock waves through the community, we covered the result as did most everyone else, despite Babai's disclaimer that the result was not yet peer reviewed.

Robin Thomas at Georgia Tech immediately suggested we get Babai down to Atlanta to talk on the paper. Babai's dance card filled up quickly but he eventually agreed to give two talks at Georgia Tech. January 9-10, 2017, right after the Joint Mathematics Meeting in Atlanta. Robin scheduled the 25th anniversary celebration of our Algorithms, Combinatorics and Optimization PhD program around Babai's talks.

Around 4 AM last Wednesday we got a lengthy email from Babai with the subject "new development" and the first line "The GI algorithm does not run in quasipolynomial time." The email explained the new running time, still a huge breakthrough being the first subexponential time algorithm for graph isomorphism, but not as strong as before. Harald Helfgott had discovered the problem while going through the proof carefully preparing for a Bourbaki seminar talk on the result. The email asked if we still wanted him to give the talk (of course we did) and instructions for removing "quasipolynomial" from his talk abstracts. That email must have been very hard for Babai to write.

Babai posted an update on his home page which I too quickly tweeted. News spread quickly in blog posts and by Thursday an online article in Quanta titled Complexity Theory Strikes Back. Scott Aaronson picked a lousy day to release his new book-length survey on the P v NP problem.

On top of all this snow in Atlanta threatened to cancel the Monday talk. But the snow never came and Babai started his talk at 4:30 PM to a packed room. Without telling any of us beforehand, an hour earlier he had posted an update to his update and announced it in his talk.

We were watching history. From the talk I tweeted the new news though Bill Cook, also in the audience, beat me to the punch. Babai went on to describe the issue, an error in the analysis of the running time in the recursion, and the fix, basically a way to avoid that recursive step, but I can't do it justice here. At the end he proclaimed "So it is quasipolynomial time again". And so it was.

Today Babai talked about the group theory behind the algorithm as though there was never an issue in the first place.

Learning About Learning

Yesterday Scott Aaronson released his sweeping new P v NP survey. Babai gave an update on graph isomorphism, in short while he still has the first subexponential time algorithm for GI, he no longer claims quasipolynomial-time. We'll have more on graph isomorphism next week.

Having seen the power of neural networks for learning, how do they actually work? Over the break I decided to catch myself up. I worked through Michael Nielsen's online book Neural Networks and Deep Learning chosen mainly because he co-authored one of the great books on quantum computing followed by the beginning of the TensorFlow tutorial. To try out code I downloaded Python and TensorFlow and used PyCharm as my IDE (free for academics). I should really learn GitHub since that holds all the code samples. Where were all these cool tools when I was a kid?

So what did I learn? Here is my high level understanding, but read the above materials to get a fuller picture. A neural network is just a weighted threshold circuit, though instead of precise threshold functions you use more continuous and differentiable functions like sigmoid or a rectifier. If you fix the weights and biases (the negation of the threshold value), the network computes a function from input to output, for example from images of digits to the digits themselves. Typically you have a sample of labelled data and you can create an error function to see how well your network computes the solution. Fix the labelled data and now you have a new function from the weights and biases to the error.

You want to choose weights and biases to minimize the error. The general approach is gradient descent, improve a given solution by moving a small distance in the opposite direction in the gradient and repeat. I had naively thought you estimated the gradient numerically but in fact the gradient is computed symbolically using a dynamic programming-like algorithm called backpropagation based on the chain rule for partial derivatives.

Convolution nets has a special first layer that captures features of pieces of the image. Recurrent neural networks allow feedback loops.

Nielsen shows how from scratch to build and train a neural net. In TensorFlow you just design the network and then it automatically computes the gradient and has a highly optimized algorithm that can be run on GPUs or specialized hardware to minimize the error.

What caught my eye is how much of an art machine learning still is. How many nodes should you have in your network? How many levels? Too many may take too long to train and could cause overfitting. Too few and you don't have enough parameters to create the function you need.

What threshold function do you use and how to you aggregate results? Lots of various tricks to avoid overfitting and improve speed of optimization. There's no fixed procedure to choose the parameters, though you can test how well you do. So lots of trial and error to learning and experience (which I don't have) certainly helps.

So we have amazingly powerful learning tools but for now we still need humans to learn. For now.

Predictions for 2017

Lance's Complexity Year in Review, posted the last week of the year (lets hope that P vs NP is not resolved on Dec 31) is a tradition that goes back to 2002.  Bill posting predictions for the coming year is a tradition that goes back to 2016. Here is the last one: here.  My predictions were not very good- all of those that came true were obvious (P vs NP will not be resolved, CS enrollment will go up). My biggest goof- that Hillary Clinton would beat .. Ted Cruz, by accusing him of being born in a foreign country.

However, being wrong never stopped me before, so here are my predictions for 2017

1) Some people think Trump be more presidential once he takes office. Some point to Checks and Balances in the System - but the Congress is ruled by his party. Some point to the media as a watchdog. e.g:  here. A more accurate picture is  due to John Oliver here. Some say Trump is a closet liberal. But I doubt his true beliefs, if he has any, matter. Its going to be bad. I second Scott Aaronson's call to not normalize this:  here.

2) Not a prediction but a thought: Prior arguments against Trump were countered with `Well Hillary is just as bad'  They can't use this anymore. The following absurd conversation might happen:

NEWS: Today some democrats and John McCain questioned Donald Trumps nominee, Rex Tillerson for Sec of State, about his past dealings with Russia and Putin.

 FOX NEWS: But Hillary was the worst Sec of State ever! Bengazi!


3) I will be asked to review at least one paper claiming P=NP (or P NE NP or it won't be clear what they are saying) and at least one paper claiming to determine a Ramsey or VDW number.  They will be garbage. Cranks are  getting into more sophisticated areas so others may be asked to look at ``solutions'' to open problems in harder areas of math. The Navier-Stokes equations (A Millennium problem, see  here)  might be a good area for cranks since they might get out some numbers and think they've solved it.  I'm glad I'm not in that area.

4) Our Popular Posts links (which is determined by a program, not by us) will continue to have some of our most recent posts AND my very old post on Russell and Whitehead using 300 pages to prove 1+1=2. Why is that post seen as being so popular? I doubt it IS that popular. So--- whats going on?

5) Recall that Josh Alman and Ryan Williams showed that one method for lower bounds prob won't work  here . There will be more results that rule out techniques.

6) n-person envy-free cake cutting can now be done with number-of-cuts TOW(n).
There will be better upper bounds or some lower bounds on this proven this year.

7) There will be a big breakthrough on derandomization- possibly L=RL.

8) There will be a big data breach.

9) Some minor celebrity will die the last week of the year and hence not make either the
`who died in 2017' lists, nor the `who died in 2018' lists. In  2016 this happened to William Christopher. Why do people make the `end of the year lists' before the year ends?

10) Fake News will become worse and worse.  After Pizzagate there was NO apology or regret from the people who spread the false news.

11) Fake Journals, Schools, and accreditation agencies will continue to grow.

Complexity Year in Review 2016

Paper of the year goes to A Discrete and Bounded Envy-Free Cake Cutting Protocol for Any Number of Agents by Haris Aziz and Simon Mackenzie. Might not seem like a traditional complexity result but cake cutting is a computational process with a desired set of properties and this papers settles a long standing open question. Bill posted about the paper back in June.

Some other nice papers from 2016: Hadamard not so rigid after all and not usable for Valiant's lower-bound program, 2-source extractors from low-entropy sources which get near perfect randomness from two weak sources, query complexity separations, deterministic, randomized and quantum, in two wonderful constructions beautifully presented at STOC, space-efficient subset-sum,and learning algorithms from natural proofs.

2016 will go down as a watershed year for machine learning with AlphaGo, huge advances in translation, self-driving cars and with tools like TensorFlow out in the open we'll truly see learning everywhere. Prediction didn't have such a great year with bad calls on Trump's nomination, Brexit and Trump's election. Machines learning humans still has a way to go.

We thank our guest posters MohammadTaghi HajiAghayi, Samir Khuller and Avi Wigderson.

We remember Erich Bloch, Hartmut Ehrig, Carrie Fisher, Rūsiņš Freivalds, John Glenn, David Johnson, Marvin Minsky, Peter Naur, Seymour Papert, Hillary Putnam, Lloyd Shapley and Boris Trakhtenbrot.

As the surprises of 2016 lead us into an uncertain 2017 let me leave with my usual advice: When in a complex world, best to keep it simple.

Hidden Figures

Yesterday in our tradition of seeing math movies on Christmas, we saw Hidden Figures, the story of African-American women who worked as "computers" at NASA in 1961 Virginia in the last vestiges of "separate but equal". The movie focuses on three women, Katherine Johnson, Dorothy Vaughn and Mary Jackson as they dealt with and crossed racial and gender boundaries. But this isn't just a movie you should see, rather a movie you will enjoy watching and I highly recommend it when it goes into a wide release in the US on January 6. Some minor spoilers ahead.

Beyond the struggle, Hidden Figures does work as a math movie. The major storyline follows the group of mathematicians who compute the trajectories of the Mercury flights with Katherine Johnson playing a main role in figuring out how to pull John Glenn out of an elliptical orbit into a parabolic safe entry back to Earth.

The movie also serves up lessons about computers. The new IBM mainframe comes and threatens the need for human computers, women (here segregated into two groups) who did the tedious manual calculations that NASA relied on. In the movie Dorothy Vaughn recognizes the threat and retrains her team to learn Fortran, perhaps a parable for how technology changes jobs today.

The majority of the audience for the sold-out theater were African-American women and they laughed and cheered as the heroines of the movies succeeded. While we have made much progress in the last 50 years we still have far to go.

Moneyball for Academics

MIT and Tel Aviv business school professors Dimitris Bertsimas, Erik Brynjolfsson, Shachar Reichman and John Silberholz wrote an intriguing paper Tenure Analytics: Models for Predicting Research Impact about using metrics in tenure decisions, Moneyball for academics. The paper is behind a firewall but here is a preprint (with the Moneyball title), an essay by some of the authors, and an article from Inside Higher Ed.

Brynjolfsson works extensively on metric-based decision making and gave early warnings on the loss of jobs to ML. I still have the HiPPO (Highest Paid Person's Opinion) from his EC 2010 invited talk. I like it for the complexity class on its back.

In this article, Brynjolfsson and his co-authors use properties of the co-author and citation network graphs to predict future paper-citation based metrics, like the h-index for professors at top ranked OR departments. The paper claims that their metrics do a better prediction job than tenure committees.

The IHE article captures an alternative view:

Many professors oppose the use of bibliometrics in hiring, tenure and promotion decisions, saying that scholarly potential can’t be captured in a formula most often applied to pursuits with a bottom line, like winning games or playing the stock market. Such a system inevitably will be “gamed" by academics, critics say, and time-consuming but ground-breaking research will be sidelined in favor of “sure things” in terms of publishing -- the academic equivalent of clickbait.

I have a different issue--the use of bibliometrics to judge the current value of a professor. In baseball, the original Moneyball, there are measurable goals: runs, wins, championships. So you can use data analytics to both measure the current and future potential of a player. In academics, what makes a great professor? I hope the sole answer isn't the h-index. And without a subjective method to measure a successful professor, how do you train a model to predict for it?

I'm not against using metrics to help with tenure and hiring decisions but I still put most of the weight on the letters.

The article does talk about predicting INFORMS fellows from the network centrality model, predicting a subjecting decision from objective statistics, though doesn't compare that to tenure decisions. I wonder how well one can predict ACM Fellows as well. Another challenge here: As CS is a constantly changing field, can one use an algorithm that predicts today's fellows from 20 year old data to predict future fellows from today's data?

The very first Ramseyian Theorem

Many years ago I noticed that in several books on Ramsey Theory  mention that  Hilbert proved the first   Ramseyian theorem.  The theorem is the Hilbert Cube Lemma (HCL) which in modern language is:

DEFINITION: Let x, y1, y2,...,yn   be natural numbers. Then the n-cube on x, y1, y2, ..., yn is

{ x+ e1*y1 + ... + en*yn : e1,...,en \in {0,1} }

HCL: for all c there exists H=H(m,c) such that for all c-colorings of {1,...,H} there exists a monochromatic cube.

Here are some quotes about this theorem from texts on Ramsey Theory:

Graham-Rothchild-Spencer's book Ramsey Theory: In the middle of Szemeredi's proof of a cube lemma with double exp bounds on H (Hilbert's proof gives tower-type bounds) they write:

Historical Note: In 1892 D. Hilbert proved that, for any k\ge 1, if N (the naturals) is
finitely colored then there exists in one color infinitely many translates of a k-cube.

THATS IT! No mention of WHY Hilbert proved this. According to the index this is the only mention of Hilbert in the book.

From Landman and Robertson Ramsey Theory over the Integers:

The results that are generally accepted to be the earliest Ramsey-type theorems are due,
in chronological order, to Hilbert, Schur, and van der Warden.

Later in the exercises he asks the reader to prove HCL from VDW's theorem.

THATS IT! No mention of WHY Hilbert proved this According to the index this is the only
mention of Hilbert in the book.

Andrew Soifer's The Mathematical Coloring Book.  This is a very scholarly work about the history of coloring theorems. (For my review see here .) I expected to get MORE on why Hilbert did. Soifer  does devote two pages to Hilbert. But as for WHY Hilbert did it all he says is:

As far as we know today, the first Ramseyian-type results appeared in 1892 as a little noticed
assertion in [Hil]. Its author was the great David Hilbert. In this work Hilbert proved the theorem of our interest merely as a tool for his study of irreducibility of rational functions.

I wanted to know what Hilbert proved (this was easy- I looked up the Hilbert Irreducibility
theorem) and how he used his Cube Lemma to do it.  I assumed this would be known and out there
in English since the Hilbert Irreducibility Lemma is very important.

But NO- I found the original German Version but THATS IT.

Well, if you want something done, best to do it yourself. Except that I don't know German.

YADDA YADDA YADDA

Here is a paper with Mark Villarino and Ken Regan, in English, that has the proof.
In some later post I'll describe how the paper came about.

For now I will state the Hilbert Irred Theorem, two-variable case:


If f(x,t) is in Z[x,t] and is irreducible then for infinitely many natural numbers t,  f(x,t) is irreducible.

Freedom of Speech

Bill and I have always strongly believed in the principle of freedom of speech, guaranteed to us by the constitution of the United States.  The government block speech only in extreme circumstances, fraud, libel, threats to people and property, but allows people's opinions, no matter how abhorrent we find them. 

Speech used to be tempered by complexity. You could only talk to a small number of people at once. You had to physically print and distribute materials spouting your points of view. So while people could say what they wanted, they had some barriers to distribute that information. We believed in free speech but speech wasn't free.

Now with the Internet, particularly through social media, speech flows quickly and cheaply. Excitedly people could express their views easily. People also discovered that others could do so as well.

We should welcome this diversity of opinion, never available at this level before. We should listen to what people have to say, challenge their views and even their claimed facts, but more importantly challenge ourselves and our own viewpoints with the arguments of others. Never trust anything you see on the Internet but never be afraid of it either.

Instead we see calls protect people from ideas that fall significantly outside the mainstream and decide for them which facts are true or false, whether by blocking accounts or making it more difficult to distribute information. Free speech may have helped elect a president whose views and actions they find abhorrent but that's not a reason to restrict the speech. One must fight words with words, not block the words of others.

We must always fight for the rights of people to express themselves and avoid the path of limiting the spread of ideas. Once we start restricting the distribution of ideas we take a walk down a tough path, and someday you may find you'll have to keep your own thoughts to yourself. 

Guest post by Samir Khuller on Humans, Machines, and the Future of Work (a workshop)

Guest Post from Samir Khuller on

Humans, Machines, and the Future of Work
(A Workshop)

On Dec 5th and 6th I attended, at Rice University,
a workshop on Humans, Machines, and the Future of Work.
I had a wonderful lunch with John Markoff  of NY Times,
and Moshe Vardi of Rice University (Moshe is the brains
behind this workshop).

I have rarely ever attended such meetings, that are so different
from the usual conferences I attend where the talks are all
rather technical and half the audience is lost half way through the talk.

The main theme poses the speculative question about the evolving
nature of work and how technology, and especially recent
advances in AI and Robotics (Self driving cars, Robots to look
after the elderly, self checkout machines that can simply
recognize your shopping order) can render huge categories of
jobs redundant. Why hire a human, when a robot will cook
dinner, and clean your home every day? What will people spend their time doing?

Will the work week reduce greatly? Yet, for many, their devices and

24/7 connectivity means we are working more than ever! The

speakers had varied backgrounds, from Economics to Social Science

to Roboticists.

In the end, its clear that the nature of work is constantly evolving.

Our children could have job titles, our parents could never dream of

when they were selecting a profession. However, the rapidly growing

interest in Tech and Computing is clear - these are powerful societal

forces at work. New job titles - Robot fixer, Robot Programmer,

Virtual Reality Expert, Lawyer for the protection of Robots. Demand

for graduates with those skills will continue to increase, and the

Universities that invest quickly and early will become the dominant

players. CMU,  Georgia Tech and others invested very early in colleges

of computing, and this has paid of handsomely for them. The demand for

CS degrees is going to increase even more in the next decade

with research moving more closely to the impact that technology is

having on society. We as researchers, need to pay attention to

societal impact, since its very real and immediate.

The workshop speakers were pretty amazing - talks were accessible,

and extremely well delivered. I suppose such talks meant for a really

broad audience (there actually were not many CS people in the audience)

and thus the points being made are pretty high level.

I would recommend that we all become better acquainted with some of

the social issues that interact with Computer Science, and going

to workshops like this is a great start.

Fixing the Academic Job Market

Last month I posted about the craziness of the computer science academic job market due mainly to the decentralized nature of our field. Here are some ideas of what we can do better. I've stolen some of these ideas from other fields such as math and economics.

Single Job Market System

A single website that every CS department uses to advertise positions and accept applications. Easy for applicants to apply to multiple places and, if they wish, make their materials open for any department to see. Recommenders need only upload their letter once. We could add some additional controls, methods for applicants to indicate say geographical preferences or two-body issues.

We could have an opt-in site for candidates to list where and when they have interviews. It would make coordination of job interview dates and offer timing that much simpler.

Annual Meeting

A meeting in early January that brings together all the subfields of computing so we can work as one community instead of twenty. As part of this meeting, members of recruiting committees and job candidates come and schedule short interviews with each other to make preliminary choices for on-campus interviews. CS hasn't had annual meetings since the 80's but math and econ still do.

Virtual Meetings

Every time I bring up annual meetings, people complain that we already have too many conferences in computer science. So if no physical meeting, we can set aside days to have a virtual meeting with recruiting committees and candidates talking over Skype.

Common Dates

Have some common fixed dates, just a couple of times in the spring, when departments can present offers, and when candidates must make a decision. That should reduce how long departments have to hold a position before it settles.

These last two ideas require no centralization, just willing job candidates.

Job Market Paper and Video

As the recent CRA Best Practices Memo suggests, candidates should choose a single paper to highlight their research. Each candidate should also post a short (3-5 minute) video where they describe this research at a level that any computer scientist could follow. The job talk should cover this paper only, instead of trying to wow with multiple works.

Candidate Web Page

If you are publicly looking for a job, set up a web page, linked from your home page, to your job materials: CV, research statement, teaching statement, list of references, pointers to all your papers with links to PDFs, with the aforementioned job market paper and video highlighted. Also give a pointer to your Google Scholar profile page and make sure that page is correct and up to date.

A students unusual proof might be a better proof

I asked a student to show that between any two rationals is a rational.

She did the following: if x < y are rational then take δ << y-x and rational and use x+δ

This is correct though more complicated then what I had in mind: (x+y)/2

I then asked her to prove that between two irrationals is an irrational.


She did the following: if x < y are irrational then take δ << y-x and rational and use x+δ

SAME PROOF!

I had a different proof in mind: the number of reals in (x,y) is uncountable while the number of rationals is countable, so there must be at least one (in fact uncountable many) irrationals in (x,y).
(NOTE- I originally had `the number of irrationals in (x,y) is ...' which, as comment by stu below
points out, is assuming what I want to prove. Typo on my part.)

These proofs raise questions about our criteria of goodness-of-proof.

1) Which proof for rationals is better:

The delta-proof or the (x+y)/2 proof?

The (x+y)/2 proof is simple, but the delta-proof also works for irrationals.

2) Which proof for irrationals is better:

The delta proof or the uncountable proof?

Which one is simpler?

The uncountable proof gives more information (the number of irrationals is unctble)
but is nonconstructive.

3) Are there other proofs for either theorem?

Which proof do you prefer? Why? What is your criteria?

Guest post by Samir Khuller about Visiting the Simons theory Inst for Computing

Guest post by Samir Khuller on his visit to the Simons Inst. of Computing

Visiting the Simons Institute for Theory of Computing

A few days back I had the good fortune to spend four days at the
Simons Theory inst. at UC Berkeley (for a workshop titled
Learning, Algorihtm Design, and Beyond Worst Case Analysis,)
Not only was the workshop extremely well run, the entire Institute is
amazing - from wide open spaces for collaboration to an excellent staff
and amenities for visitors (especially long term visitors who have
shared office space). We were missing a Dagstuhl like venue in the US
for a long time, and I think the Simons Theory Center partially makes
up for this deficiency. Dagstuhl is of course a bit isolated, so people
have no-where to go but interact, and work, and that is part
of the charm. Berkeley isn’t isolated and has some of the most amazing
cafes and restaurants right next to its charming campus. I ended up staying
on campus at their Faculty Club.

Simons workshops are over-subscribed and in high demand, but even on
Thursday evening (my last day there) I noticed that scores of badges
had not yet been picked up. Part of the problem lies in the fact that
registration is free. Perhaps charging $10/day for registration will

ensure that people sign up for the days that they intend to be there,

so others who want to attend are not locked out (to be fair, I don’t

know how many were locked out, but I have the impression that due to

high demand, workshops have closed registration in the past).

Kudos to both the Simons Institute  organizers as well as the ones

for the special semester and workshop! I did visit Simons once in 2014,

for just 15 minutes when we were visiting places to see for the design

of our very own Brendan Iribe Center for Computer Science and Innovation.

The construction of which launched in summer 2016, and we hope to be done

by August 2018.  Come and visit after that! This project has consumed the

last 30 months of my life.

One of the main benefits of attending these workshops is to see sub-fields

as they form - long before new courses emerge covering these topics - and

it’s inspiring to meet the leaders in our field running the

program on Algorithms and Uncertainty. Finally, if you missed it,

videos of talks are available online here.

A Few Interesting Computer Science Papers

Probabilistic Rank and Matrix Rigidity by Josh Alman and Ryan Williams

Leslie Valiant outlined an approach to proving circuit lower bounds from matrix rigidity. A matrix is rigid if you need to change many entries to significantly reduce the rank. Valiant showed that one could create a function with high algebraic circuit complexity from a rigid matrix. Of course one needs a rigid matrix and the Hadamard matrices (rows are Hadamard codes) seemed the perfect candidate. Alman and Williams say not so fast, in fact the Hadamard matrices are not that rigid and won't work for Valiant's program.

Ryoan: A Distributed Sandbox for Untrusted Computation on Secret Data by Tyler Hunt, Zhiting Zhu, Yuanzhong Xu, Simon Peter, and Emmett Witchel

You want to use Intuit's TurboTax to prepare your taxes but you don't want to actually let Intuit or their cloud provider to see your income sources. Sounds like a job for homomorphic encryption, a good solution in theory but not yet practical. Ryoan, an OSDI best paper awardee, takes a systems approach to the same problem, creating a computing sandbox where one can do secure computation without allowing the cloud or software provider access.

Google's Multilingual Neural Machine Translation System: Enabling Zero-Shot Translation (and related blog post) by Melvin Johnson, Mike Schuster, Quoc V. Le, Maxim Krikun, Yonghui Wu, Zhifeng Chen, Nikhil Thorat, Fernanda Viégas, Martin Wattenberg, Greg Corrado, Macduff Hughes and Jeffrey Dean

Google now using a single system to translate between different pairs of languages, even pairs of languages for which it has no examples. Their analysis shows a potential internal representation of the language and the beginning of a universal translator.

Music Theory for Theorists

I fully completed and passed my first MOOC, Fundamentals of Music Theory, a Coursera course out of the University of Edinburgh. I played the tuba in college and grad school but really just practiced scales and (usually) hit the notes. I didn't really understand keys, intervals, chords and the such and I wanted to learn.

Music theory has the same problem as C++, too much overloaded notation before you really understand what's going on. So here's a quick view of music theory without the mess.

Think (theoretically) of an bi-infinite sequence of notes. Every note is equivalent to notes a factor of twelve away from them (though in different octaves). Pick a note, label it 1, then the notes labelled 1, 3, 5, 6, 8, 10, 12, 1 (an octave higher) form a major scale in the key of note 1. There are twelve major scales, depending on which note you label 1. If you start at 10, i.e., 10, 12, 1, 3, 5, 6, 8, 10 you get the relative minor scale in the key of note 10. Also twelve minor scales.

Start a new major scale starting from 8 you'll get 8, 10, 12, 1, 3, 5, 7, 8, just one number off from the previous scale. Repeating this process will run through all the major scales. This is called the circle of fifths (since 8 is the fifth note of the scale). You can go through the circle backwards by starting at 6.

A chord is typically three or four alternating notes of a scale, for example 1, 5, 8 (the tonic) and 8, 12, 3, 6 (the dominant 7th). They can be inverted using different octaves and all sorts of other good stuff.

So notation wise, there is a mapping of {A,B,C,D,E,F,G} X {Flat, Natural, Sharp} to the twelve notes with several notes getting two different names in such a way that each note of any scale can get one of the letters in cyclic order. For example the D-Major scale would be the notes D-Natural, E-Natural, F-Sharp, G-Natural, A-Natural, B-Natural, C-Sharp and back to D-Natural. You put it all together in a diagram called a musical score.

Many undergrad computing courses now use Python instead of C++ to get around the notational challenges. Alas music notation goes back a millennium or so, I don't expect any changes soon.

Should I tell HS students that if they do well I'll write them a letter OR do I want them to ...

I teach a 3-week intense course for HS students on cryptography during the summer. Some of the students are very good, interested, and working hard. I also give out some extra credit assignments that some of them do.  For such students I am glad to write letters of rec for college. I want to reward them for working hard and being interested not knowing that they will get a letter for it.

These students don't quite know about colleges and letters and that stuff. I have two choices:

1) The first day tell them that if they do well I could write a letter for them.

PRO- this will encourage some of them to work harder

CON- I want them to work hard and BE interested (not just SHOW interest, though I doubt they are that good as actors) NOT because of some reward but because they really are interested. Contrast:

Bob showed an intense interest in computer science

to

Bob showed an intense interest in computer science but it may have been just for show to get this letter. Gee, I can't tell.

2) Don't tell them. This way when they work hard and show interest its more likely genuine.

PRO- as noted, their behavior is genuine

CON- They may not work as hard.

I tend to do (1) now- tell them. One thing, don't tell them too much and make it simple. I used to say that I would write a letter even for a B student if there were extenuating circumstances or if I could tell they really were good and just happened to blow an exam, or something like that. But this just invites more questions about what they need to get a letter, and I've never  had one of those cases where a B-student is better than he looks. (This could be because my exams are of the type where there is no time pressure as evidenced by half the students leaving about half way through. They are not easy, but they depend on knowledge not cleverness, so more time does not help. Or it could be something else about my teaching and grading.)

So- better to tell them about a letter option or not?

Computer Science Academic Hiring

My faculty recruiting season in 2016 never stopped. The spring recruiting season bled through summer right into various fall recruiting activities. How I envy my friends in other fields whose faculty recruiting season runs in less than three months.

Economist Noah Smith writes about the process he went through in the econ job market in 2012.

After applications go out, employers contact grad students for interviews. These interviews take place at the AEA's Annual Meeting in early January, which is a gigantic confab where most of the economists in the country go to eat free food and hobnob. As an interviewee, you generally don't have time to go to any of the presentations or speeches; you're running back and forth from hotel to hotel, going to interview after interview. This year's AEA Meeting was in Chicago. 

You then wait a week or two, and the employers who are interested in you call you back and schedule a flyout. Flyouts, which happen in February and March, involve going to the place, meeting the people, getting taken to dinner, and presenting your research. After that, offers go out.

Ahh to be done with recruiting before April Fools Day. Why can't we do this in Computer Science? In one word: Decentralization.

Academic fields act administratively like their field. So econ creates a structured market with the goal of an efficient (in their sense of the right people get the right jobs) outcome.

Computer science abhors centralized control. We lack a strong central authority and have very little coordination between different departments. So we have a process that takes a long time to work its way through and quite often fails to get that efficient outcome. Even the CRA's modest 2010 proposal for some common earlier deadlines went nowhere.

What can we do? I welcome suggestions and will give some of my own in a future post.

Did you do research when you were an undergrad? Well.. it was a different time.

Dan is a high school student who has worked with me and is now an ugrad at College Park

DAN: Bill, did you do research when you were in high school?

BILL: No, things were different then, there wasn't really a mechanism for it. Or, as you young people would say, it wasn't a thing.

DAN: When as an undergrad did you begin to do research?

BILL: Well, I never did research as an ugrad either.

DAN: Then how did you get into Harvard? Did they accidentally put your folder in the wrong pile?

BILL: Good question. I'll ask my adviser if he recalls what went wrong back in 1980.

DAN: Really? You'll ask him?

BILL: NO!

Okay, the real question here is:

At some point (before 1980) doing research at an ugrad in college was not really a thing many people did.

And now its quite common.

What changed? Is the change for the good? I'll phrase my thoughts and questions in the form of a question (the opposite of Jeopardy).

1) Are there more magnet schools and more ways to funnel students into research early?

2) Do computers allow students to to more research than they could have back before (say) 1980?

3) Is the phrase `HS research' a bit odd-  it is more learning then doing?

4) Is there a cycle going on- since more students are doing research, more have to do research to keep up in order to get into grad school? Is this even an issue for college admissions and/or scholarships?

5) Has the quality of research at HS science competitions increased ? Ugrad research? Grad student research? Prof research?

6) Does having HS or ugrads do research with you increase or decrease your productivity? (That depends on the students of course)

7) Do colleges give faculty kudos for guiding HS or ugrad research? (That depends on the school of course)

8) Are there more grants for ugrad research then before 1980? Are REU programs fairly new?

9) Does an ugrad now NEED to have done research to get into one of the top X grad schools? If so is this a good thing or not?  Does this hurt those without the oppurtunity  to do research? Do REU programs help alleviate this problem?

10) Are students entering grad school knowing far more than they used to?

11) Some magnet schools REQUIRE HS students to do research. Is this a good thing?

12) I've been using 1980 as a reference for no good reason- when did HS research and ugrad research increase? Was it gradual or was there some big increase over some X years where X is small?

Our Role and Responsibility

It's Trump but not just Trump. Brexit. Right-wing politicians gaining power in France, Netherlands, Austria and beyond. We worry about the future of our country and the whole world at large.

But what role have we played? By we I mean those of us who work in technology-related fields and have benefited the most from the new economy. 

There's a large population who's lives haven't gotten better. Not just the poor, we're talking the lower 80% of the economy. Our changing economy hasn't greatly improved the life of the middle class. 

Our technologies have put people out of jobs. We tell them our technology will create more and better jobs, our own version of trickle-down economics. They just need to learn what we have created, drive our Ubers, at least until the Ubers can drive themselves. 

We love working at universities where we can educate the very top students. But many don't get the opportunity to go to college at all. They are honest people willing to work hard and not seeing their lives improving. And we just call them "uneducated". 

We have learned how to mine data but often forget the people behind the data and get caught by surprise when things don't go the way we expected from the data.

We've created new communication channels. But we also control those channels. We often make the choices between usability, security, privacy, fairness, free speech and preventing hatred and discrimination. But who are we to make those choices. They have little say.

Who are they? They are us, fellow Americans. We need to make sure that all of us benefit from our changing world and everyone feels that they contribute to making it better and everyone has a say. Democracy, messy as it is, means that if people don't feel they the world looks out for them, they will find someone who promises change no matter the baggage they carry. And we need to listen or we end up with Donald Trump.

And the winner is... Harambe

Tomorow is the Election for Prez of the USA! This post is non-partisan but, in the interest of full disclosure, I state my politics: I will be voting for Hillary Clinton. I urge you to read the posts by Scott Aaronson: here and by Terry Tao here or John Oliver's segment here to see why. I would have thought that 99% of  their readers, and mine, are voting for Clinton, but looking at the comments on  Scott's an Terry's blog I realize that might not be true. (ADDED LATER- A nice article that summarizes the entire election, I put it here for you and for me: here)

However, I am not blogging about who you should vote for.

I had the teachers of Discrete Math and Algorithms (two diff courses)  give their students paper ballots with the four candidates on the Maryland ballot (Clinton, Trump, Johnson, Stein, write-in) and had them vote. But with a difference:

Discrete Math did the standard voting where you vote for ONE candidate

Algorithms did approval voting- where you mark all those you approve of.

DISCRETE MATH RESULTS: 428 students.
Clinton: 305
Trump: 44
Johnson:21
Stein:11:
Abstain (or some variant like `f**k all of them')-7
Sanders-6
Harambe. The Gorilla  who was shot (see here)-3
Hugh Mungus (word play - you figure it out. Also see here)-3
Ken Bone (he asked a good question at the Town Hall Debate. Then...)-2
Vermin Supreme (Policy: All Americans must brush their teeth. See here)-2
Joe Yecco (don't know who it is. Maybe a student in the class) -2

For the people who got 1 vote see here. There were 22 of these.

ALGORITHMS RESULTS. 251 students (won't add up since its approval voting)
Clinton-155
Johnson-63
Stein-59
Trump-40
Sanders-18
Abstain-14
Clyde Kruskal (who teaches the course)-13
Tom Reinhart (a CS lecturer at UMCP)-5
Larry Herman (a CS lecturer at UMCP)-3
John Kasich-3
Evan McMullen (Third Party Candidate who is doing well in Utah)-3 See here
Vernin Supreme (see above)-3
Harambe the Gorilla (really!) -2
Michelle Obama-2
Eric Sim (don't know who this is- Maybe a student in the class)-2

For people who got 1 vote see here

For more complete information see here

What to make of all of this?

College Students are largely Liberal so the pro-Clinton vote is not surprising. Also Maryland is a strongly democratic state, though I think being a college is more of a factor than being in Maryland. I suspect that students at UT Austin are also liberal even though the state isn't.

I've had large classes vote before, but not by approval voting. Both of the classes above had more  write-ins than usual- though that is less surprising for approval voting.

Approval voting shows that Trump is very few people's second choice. That is, those that don't like him REALLY don't like him. Again, this  is among the narrow demographic of college students taking Algorithms at UMCP CS.

Any odd candidate who gets ONE vote does not surprise me. If ONE person votes for Aliko Dangote, a real (see here) Nigerian Billionaire (he has NOT emailed you) that is not surprising.

If someone who is sort-of out there get TWO or more votes  (Vernin Supreme, Hugh Mungus) I am not surprised. Those two have websites and a following, though small.

The three votes for Harambe the Gorilla surprised me. I've looked on the web, and this is NOT a thing- there is no Harmabe for Prez websites, even as a joke (I assume if they existed they would be a joke). So I am surprised he got 3 votes in DM and 2 vote in Algorithms. One of those voted for Clinton, Johnson, Stein, and Harambe. I'm assuming that's a strong anti-trump vote.

Does this poll have any predictive value? The winner of the Discrete Math Poll ended up being the real winner in 1992, 1996 (though there were more Ross Perot Votes then I would have thought),
2008, and 2012. Note that in all these cases the democratic candidate won. Not a surprise.

Some  personal opinions:

1) If Trump loses what will the republicans learn from this. NOTHING since Trump was such an odd candidate. I wish it would have been Hillary (or someone like her) vs Cruz (or someone on the hard right) so that if they lose the reps can't say, as some have, we lost because we weren't conservative enough. And one can hope that Hillary vs Cruz would have more of a contest of ideas.

2) I'm not sure what would be better for the Rep Party- a Trump loss or a Trump win.

3) Predictwise says a Hillary win is around 85% likely. Nate (the only pollster known by his first name!) says 65%. If Hillary wins it won't be clear who was right? If Trump wins then Nate would have been more right, but not sure what that means. More generally:

If two people give different predictions, in the end you can see who was right

If two people give different probabilities of an event, then its harder to see who was right.

Do We Still Need Great Minds?

An anonymous comment on a recent post on alternate histories.

As far as science is concerned I don't believe that the great minds are needed anymore. They only speed things up that would later have been developed by an industry of a great mass of brilliant but more mediocre researchers. The best examples are Godel's and Turing's work which would have been done necessarily by the next generation of logicians or theoretical computer scientists. Regarding your own contributions it is fair to say that "the future doesn't need you." Anything important would also be created sooner or later by others, only some idiosyncratic work of minor importance could be left undone forever.

Depressing. So we do either mediocre work or work that others would later do anyway.

Of course we can never know. We can't tell if some great idea today may not have existed if a single genius didn't create it. We also don't know what technology we don't have because of someone who became a playwright instead of a scientist.

I don't doubt we'd have the P v NP question without Cook, Karp and Levin, though our understanding of the problem would have a very different flavor.

Take someone like Manuel Blum. Through him and his students we got formal models of cryptography that led to zero-knowledge proofs, interactive proofs, probabilistically checkable proofs, lower bounds on approximation and major advances in coding theory, among so much more. Would we have all this work if Manuel never existed? Maybe, eventually, but we'd live in a whole different theory world without him. And that world would always look different until we find a new Manuel to unify it.