Combinatorics use to not get any respect. But because of Erdos...

(This blog is based on things I heard at the Erdos 100th Bday Conference)

I have spend the last week at the Erdos 100th bday conference. One point that was made many times: the acceptance of Combinatorics by the mathematics community and Erdos's effect on that.

In the 1950's combinatorics was seen as recreational but not as serious math. In the 1970's you could get a PhD in it but it was still seen as suspect. Even at the time of Erdos's death (September 1996) it was still not that well regarded. Now it is, as evidenced by Szemeredi getting the Abel Prize (Gowers and Tao getting the Fields Medal is also evidence, though not as strong since one could argue that they are not really combinatorists). What changed?

1. I would have thought Szemeredi's theorem (1975) would have turned people around on combinatorics. It didn't. Roth proved the k=3 case in the 1950's, using Fourier Analysis (``Real Math'') but Szemeredi's proof of the general case was ``purely combinatorial'' and hence of less interest. Furstenberg's proof that used Ergodic theory helped put it on the mathematical map (is the Mathematical map a bijection?) but combinatorics still was not well regarded.
   
2. Erdos got many people interested in combinatorics and the connections of it to other areas such as number theory. He had incredibly good taste in problems in that the problems he suggested often lead to deep mathematics of interest, and to more problems of interest. His emphasis on asymptotics, which now seems so natural, was revolutionary at the time and later had applications to computer science. His constant pushing for better and better results, his concept of Proof from THE BOOK his encouraging epsilons and deltas to pursue mathematics, all had a profound affect on mathematics and mathematicians.
   
3. One of the reasons for the disdain was that it was seen as recreational math. This was damming for two reasons (1) the problems were not important, and (2) the proofs were easy. Both are unfair. This may have been true at one time but they became less true over time.
   
   1. Problems not important: P vs NP is certainly important. Ramsey Theory reveals hidden
      regular structure and is important. Much of the work that has gone into better bounds
      on the VDW numbers is very important and involves deep mathematics.
      
   2. Proofs are easy: People are using Fourier analysis and ergodic theory and others tools that are rather difficult. Here we have the No true Scotsman Fallacy where people claim that if it uses these tools then its not combinatorics. This raises the question of if a field is defined by its methods or by its problems. In any case, people are solving problems in combinatorics using hard methods. But even among so-called easy proofs, they often exhibit the NP-phenomena where they are easy to verify and hence LOOK easy, but are hard to come up with.
      
4. One of the reasons for the respect is computer science. Just as Continuous math was just the right tool for physics, discrete math is just the right tool for computer science. This lead to a rich source of problems for combinatorists that in turn lead to interesting techniques.
   
5. Erdos stressed asymptotics which was just the right approach for computer science.
   

How much was Erdos responsible for the respect combinatorics has now? For those who believe in The Great Person theory of history, one person CAN make a difference and perhaps Erdos is one of those people. Would combinatorics have moved into the mainstream without Erdos? I think combinatorics would have gotten respect in year n where n might be large. With Erdos, n is smaller. Perhaps much smaller. I leave it to the reader to work out the proper asymptotics.

AltaVista versus Google

Today Yahoo is closing AltaVista, the best search engine before Google. The news caught me by surprise, AltaVista still existed? A number of commentators attribute bad management for AltaVista losing its dominance to Google. But it was an algorithm that killed the search engine.

AltaVista made its claim to fame in the mid-90's by indexing a large number of web pages. AltaVista did very well for obscure search terms like "fortnow" but didn't do so well for more common searches. I used to run a test on search engines by looking for "Holiday Inn", a popular hotel chain in the US. When you search AltaVista for Holiday Inn, the first thing listed was a Holiday Inn in Buffalo, New York. The Holiday Inn home page was nowhere to be found on the search results.

For searches like Holiday Inn, one had to use Yahoo, which back then was not a search engine but a directory tree of web sites. We needed our own directories as well. Ian Parberry maintained the TCS Virtual Rolodex, a list of home pages of theoretical computer scientists, most of which had names common enough that AltaVista wouldn't find them.

A Stanford professor (I can't remember which one) came to give a talk at the University of Chicago around 1997 and he mentioned a research project at Stanford developing a new search engine known as Google. I tested Google with my Holiday Inn test and was in shock when the Holiday Inn home page showed up as the first time. Google passed every other test I could throw at it and I've rarely used any other search engine since. Google made AltaVista, the Yahoo directory and the TCS rolodex irrelevant. Google's PageRank algorithm simply took search to a new level, like the way that Steve Jobs didn't create the first smart phone but completely changed the game with the iPhone. AltaVista managed to survive for another 15+ years but never recovered market share.

The AltaVista story leads to a lesson we still tackle today. Collecting and storing big data is a huge technical challenge but data by itself is of limited value without the algorithms to find the important parts among the muck.

Computability in Europe

Bill and I are both in Europe this week. I'm in Milan at Computability in Europe and Bill is 500 miles away in Budapest for the Paul Erdős Centenary. The US 4th of July holiday doesn't seem to sway the the Europeans from holding workshops. Bill will report on the star-studded Erdős celebration when he gets back.

So what is "Computability in Europe"? Don't the Europeans use the same Turing machines that we do? Wasn't Turing European?

Or course computation is the same, whether we do it in the US or Europe, Japan or Jupiter, but the emphasis is different. In the US we typically deal with traditional models of computers and see how much time and memory we need to solve various problems. The theme of this year's CiE is "The Nature of Computing" with "nature" being the key word. The conference is co-located with the Unconventional Computation and Natural Computation conference that focuses on different models of computing, especially those that rise from nature like biological computing. The two tutorials this week come from Grzegorz Rozenberg, talking on computing modes based on living cells and Gilles Brassard (whom I didn't recognize without his trademark beard) on quantum models.

Me, I like my computation served straight up on Turing machines, thank you very much.

Friends Don't Let Friends Carpool

The AAA foundation measured cognitive distraction while driving and reported that having a passenger in the car is as dangerous as using a cell phone. On a scale of 1 to 5, a handheld cell phone caused a distraction level of 2.45, a passenger 2.33 and a hands-free phone 2.27. On top of this, distraction causes risk to a passenger as well as a driver, whereas the other side of the cell phone conversation can't be harmed by a driver's distraction.

Since the popular media ignores this risk, as a public service I present some guidelines:

1. Avoid carpooling whenever possible. While there are some advantages (less traffic, pollution and loss of natural resources), it is worth putting lives of the driver, passengers and others at extra risk?
2. If you do carpool, do not talk to each other except in case of emergency.
3. If you need to talk, pull over to a safe place and turn off your engine before engaging in conversation.

Car manufacturers must share some of the blame by building cars with multiple seats and not physically separating the driver from the other passengers.

In the same study, the AAA foundation rated solving difficult math and verbal tasks at the top distraction level of 5. So some words of advice particularly for readers of this blog

Don't Drive and Derive

Quantum Tecniques/Gen Functions- don't be afraid of new techniques

Ronald de Wolf gave a GREAT talk at CCC on the uses of Quantum techniques to Classical Problems. He made the analogy of using the Prob Method to prove non-prob results. This reminded me of the following false counterarguments I've heard about new techniques:

1. The Prob Method: Isn't that just counting?
   
2. Kolg complexity: Isn't that just the Prob Method?
   
3. Information complexity: Isn't that just Kolg complexity?
   
4. Counting: Isn't that just Information Complexity?
   

In all of the cases above the complaint is idiotic--- while one COULD translate some (all?) proofs using Prob Method to Counting, it is easier to think in terms of Prob. The translation would be harder than just getting used to thinking probabilistically. By coincidence I spend some of my time at CCC looking for simple examples of generating functions where it would be difficult to do it any other way. I found one and liked it so much that I did a write up FOR YOU MY READERS! I suspect that it COULD be done using just algebra (or something) but you wouldn't want to. Here is the theorem and a link to my write up:

(Schur's Theorem) Let a₁,a₂,...,a_L be denominations of coins such that no number ≥ 2 divides all of them. Then, for large n, the number of ways to make change of n cents is

n^L-1/((L-1)! a₁ a₂ ... a_L) + O(n^L-2)

For full proof see here. My writeup is based on that in Wilf's book generatingfunctionology (the title page really does use a small g for the first letter).


The above was my INTENDED POST. However, when I showed the Gen-function proof of Schur's theorem to some students, one of them, Sam (a HS student), came back the next day with a purely combinatorial proof. It was not completely rigorous but I am sure that he and most of my readers, could make it so without too much effort. While having two proofs (Gen-function and Combinatorial) is MORE enlightening for me and for my readers, it does dampen my point that this is a theorem for which the gen-function proof is easier. I COULD argue that the gen-function proof did not require as much cleverness, or that once you put in the rigor it is harder, but I don't really have confidence in those arguments. I include the combinatorial proof in the writeup pointed to above. Which proof is better? A matter of taste. However, I hope you enjoy both of them!

Automate Me

An economist friend asked me if there were still productivity gains to be had for office workers (like us). After all, we have email, social networks, skype and other easy ways to connect with everyone not to mention search for everything. Most tasks are pretty straightforward to do online. How much easier can it get?

There are some obvious answers to his question, such as better automated filtering of all the information thrown at us. But here's what I really would love to see--an automated electronic me.

I have about 115000 email conversations in Gmail not counting spam. Google must have tens or hundreds of billions of emails from everyone combined.

So Google can learn both how many emails are typically answered and also my particular email style. So when I hit reply, Gmail should be able to pre-fill a reasonable reply. I can edit as needed and then send. Saves me much time.

Of course Google will learn from the changes I make and get more accurate each time. After a while I can trust Gmail just to answer a subset of my email. After a while it can answer most of my email. In the future Google can referee papers, write my blog posts and prepare my class lectures.

I can hide out and proof theorems while Google does everything else for me. Until Google proves its own theorems and then I'm just out of a job.

Fraud or not ?

For each of these, are they frauds?

1. The Turk was a chess playing ``computer'' (around 1770) that was later discovered to be cheating--- a human made the moves. As Ken Regan knows well, we now have the opposite problem- humans who cheat by having a computer make the moves. Note that the Turk still played an excellent game of chess and hid the human element. This IS an achievement--- just not the one people wanted. Fraud? Yes
   
2. I once heard a rumor (NOTE- this may not be true, that's why its called a rumor) that Hybrid cars get good gas mileage NOT because of the battery but because in their effort to get good mileage they rethought other things like the aerodynamics and how the gas powers the car. If I buy a hybrid car that gets 45 miles and hour but then find out that it gets this NOT because of the battery, but because of really really good enginnering- was I cheated? My sense is NO since I wanted good gas mileage. I may wonder why I need to replace the battery, or even if I need to. Fraud: I'll say NO but its certainly debatable.
   
3. Someone sells a single-purpose quantum computer to factor numbers and it works REALLY WELL but later it is discovered that it didn't use quantum at all(!)---it instead used a new classical algorithms (e.g., an extension of the Number field Sieve)--- would the buyers consider themselves cheated?
   
   1. If the buyers were people who just want to factor really large numbers then perhaps they wouldn't care.
      
   2. If the device was meant to fool granting agencies or venture capatilists to fund more quantum, then it is fraud. One may wonder why the device-maker didn't just apply for funding in crypto.
      
   3. If the buyer is an academic who then writes an article about how quantum computing is finally practical, when the truth is discovered he may have his credibility (unfairly?) tarnished.
      
4. What if someone had a quantum computer that factored really well but was advertised as a really good classical algorithm that used hard number theory? Somehow that seems very funny to me as a scenario so I won't even ponder fraud or not.
   
5. I have heard that the current quantum computers that do such miraculous things as factor 15 (darling says `factor 15? I could do that without breaking a sweat') or find R(3) (I always thought it was 6 and now I know!) may not be ``really quantum'' . This is problematic since nobody really wants to factor 15 or find R(3)--- that is, there is no analog to the people who want good gas mileage or the people who want to factor large numbers in my two examples above. These devices are JUST for demonstration purposes. If its not quantum, its not demonstrating anything. Fraud? Yes, but are they really fooling anyone?
   

The Internship

Last weekend I took my teenage daughters to see The Internship, the Vince Vaughn-Owen Wilson vehicle where they play two forty-year old interns at Google. It basically follows the standard underdog story Vince Vaughn so greatly spoofed in Dodgeball.

We went since most of the Google scenes were filmed at Georgia Tech last summer, with the climatic final meeting filmed in the atrium of the Klaus building that houses the School of Computer Science.

The movie was at best mildly amusing and not too often do you see an Emacs vs Vi discussion in a major motion picture. Mostly the movie played as an homage to Google, what a wonderful magical place it is and all the great things they do for the world. To some extent that worked: Both of my daughters came out of the movie wanting to work at Google.

Larry Page, talking about the movie said "The reason we got involved with the movie ‘The Internship’ is that computer science has a marketing problem. We're the nerdy curmudgeons." I do think CS has a marketing problem, though recently of a very different nature.

The US government is using big data as big brother. The US-China discussions on cyber attacks remind me of the US-USSR talks on nuclear weapons in the 70's. Let's not mention how some people believe computers are destroying jobs and widening the gap between the haves and have-nots.

But of course I remain very bullish on computer science and the great things we can achieve with computing. And sometimes it takes silly movies like The Internship to drive that point home.

STOC: Some NON-radical ideas

At the STOC business meeting Joan Feigenbaum (PC chair) raised some very good points. There was no real discussion (or perhaps the burning car was the discussion). Here are the issues and some thoughts as I see them. Note that I am not speaking in any official capacity. I speak of STOC but many of my comments apply to other conferences.


What is the purpose of STOC? Initially it was to help spread knowledge of the latest results, through both talks and lunch. Even though we can now tweet the latest VDW numbers, STOC still serves this purpose. Another (likely unintended) purpose of STOC is to give researchers a quick yet prestigious way to publish. Hiring committees and Tenure committee's DO ask questions like How many STOC/FOCS publications does she have?. Some people think this is an awful system since these papers are not refereed carefully. I am not going to debate that here. My only concern is making STOC better at spreading knowledge.

What are some of the problems with STOC?

1. People don't want to serve on the program committee since its a lot of time and they can't submit. The two-tiered system used for STOC 2013 seems like a good solution to this.
   
2. Referees Reports (can we even call them that?) are often not very informative. The two-tiered system COULD help this since each committee member has less work and there is a small oversight committee. Another solution that some conferences use is to give the authors a chance to rebut a report and/or rewrite the paper. I'll discuss this more in the next point.
   
3. Since the reviewing process is rushed there have been papers that are just plain WRONG. This can be confusing for someone coming to the literature. Also there are throw-away- comments like This can easily be extended to the case of weighted graphs. where this is not easy at all. How big a problem is this? How much worse than Journals is it? I DON"T KNOW. Would the Rebut/Rewrite help this? PRO: Referees don't have to decide RIGHT NOW what to do and can ask the authors things? CON: More back and fourth, more work. CAVEAT: This might make STOC more like a journal with fast turn-around time.
   
4. Some of the papers never get into Journal Form. Again Rebut/Rewrite may help in that the STOC version is better, but this is more giving in to the problem rather than solving it. Demanding full versions of papers (now possible since with e-proceedings page limits are less of an issue) is a good idea (and I think IS being used now by STOC).
   
5. Many good papers get turned down. Going to three parallel sessions would help this. There may be logistical problems here, but I think this is a good idea. Are there enough good papers to make this work? I think so- and the committee would have the freedom to NOT use all the sessions in case there aren't quite enough papers. I do not think this would make STOC's prestige decline.
   
6. It has been said that only narrow technically hard stuff gets in and not simple short new ideas. Its hard to know if this is really true. But in any case the three-parallel sessions may help this since there would be room for diff types of papers.
   
7. Personally I get more out of the workshops and invited talks then out of the refereed talks. Hence I would like more of those. Posters are good also. More to the point- I would like more VARIETY in whats at a conference since people get knowledge in different ways.
   
8. Can you really communicate your latest and greatest result in a 20 minute time slot in a crowded room where the adjacent bathroom is out of order? Even though we've made great advances in technology (I call PowerPoint PROGRESS but some disagree) and in plumbing (in the old days STOC people had to use an outhouse- do young people even know what an outhouse is anymore?), is there a better way to do this? It was suggested that ALL talks be POSTER sessions (NIPS does this). This should NOT be viewed as inferior or demeaning so long as we still have published proceedings (whatever that means in the days of arXiv) and high standards. The only relevant question is: Would posters be a better way to convey results? I DO NOT KNOW, but I think it would be worth trying out.
   

So in summary I want to see (1) more workshops, invited talks, and student posters, (2) Full papers in the proceedings, (3) two-tiered program comm. (4) either go to three parallel sessions or have posters. Some of these could be combined-- like a workshop on max flows, and them posters on the max flow papers that got in. The rebut/rewrite I am more ambivalent on but that may also be a good idea. These ideas are NOT radical (and not even original) and it is NOT my purpose to drain STOC of its prestige. Whether that is a good idea is another debate.

Complexity Typecast

Lance: Welcome to another exciting typecast coming from sunny Stanford University. I'm with Bill at the 28th Conference on Computational Complexity. Hi Bill, I see you're now at Mizzou.

Bill: Yes, my name tag says Univ. of Missouri but the body is still at Maryland. But Missouri is the Show-Me State and I don't believe theorems until you show me the proof.

Lance: Interesting name tags going around. Joshua Brody is at the University of Aarhus in Windsor, Vermont. But outside the name tags, this has been a well-run meeting.

Bill: Indeed. So Lance, anything seem different this year.

Lance: I'm noticing a few trends at both STOC and Complexity. Both have strong attendance this year, especially for West Coast meetings, and more papers than usual. Though fewer women attendees and I'm not sure why.

Bill: I was at a computability meeting at Iowa recently where there six women but they were the same six women from twenty years ago. That does not bode for the future.

Lance: I think that says more about computability as I'm guessing all the attendees were there twenty years ago.

Bill: I resemble that remark. Let's talk math. At one you were a Kolmogorov skeptic, now you are a believer.

Lance: Yes once I actually used it for a theorem I saw the light.

Bill: Speaking of light, are you now a quantum believer? Ronald de Wolf gave an awesome talk on the applications of quantum techniques to classical theorems. Were you convinced?

Lance: There are times that thinking quantumly can help generate good theorems. Nice to see quantum is good for something.

Bill: They didn't have quantum back in the days of the first complexity conference in 1986.

Lance: Yes the world was classical back then, just like the world was flat in 1400. No one here remembers that complexity meeting in 1400 but I have seen a few people from the original 1986 meeting.

Bill: Besides us, Eric Allender, Jonathan Buss, Steve Homer and Osamu Watanabe. Whether we remember anything from those days...

Lance: I remember meeting you for the first time. I was just a first-year grad student and I walked into a room with you and David Barrington talking at light speed. I thought you were both so smart.

Bill: Sorry to disappoint you. So Eric is the last man standing?

Lance: Yes, since I missed complexity last year, Eric Allender is the only person to have attended all 28 Complexity meetings. He does not want that to be his claim to fame.

Bill: Back in '86 I could follow 2/3 of 3/4 of the talks. Now I can follow 1/8 of 1/4 of all the talk. Have I gotten dumber or have the talks gotten harder?

Lance: Yes.

Bill: Thank you Lance, how about you?

Lance: Yes. More the techniques are quite different than the more computability type tools we used back in the day.

Bill: A field must change or die. I'm glad we're changing unlike certain areas of math I will not mention.

Lance: Speaking of change...

Bill: There are 242 ways of changing a dollar into pennies, nickels, dimes and quarters.

Lance: I did not know that! Moving on, what do you think of Joan Feigenbaum's suggestions on changing STOC?

Bill: I'll do a blog post on this later, but I'm generally in favor of more people on the PC (2-tiered), more papers in conference (3 parallel sessions) and more workshops, invited papers and posters.

Lance: So Bill ready to wrap it up?

Bill: Yes, it's time.

Lance: So remember, in a complex world best to keep it simple. And buy my book.

STOC is Burning

Bill and I are in Palo Alto this week for the co-located meetings of STOC and Complexity. In a new ACM policy, the STOC 2013 papers are freely downloadable by all for the next month. Check out the best papers and best student papers.

Last night smoke from a burning car preemptively ended the STOC business meeting.

Photo from Moritz Hardt

Before the fire I live tweeted the business meeting. In short, a possible record attendance for a west coast meeting (364), one less than New York last year. Next year's STOC will be in the same hotel in New York. A record number of accepted papes (100). PC chair Joan Feigenbaum talked about her two-tiered committee and several potential experiments for future STOCs (eliminate proceedings and just point to Arxiv papers for instance). Read her blog interview for more. 

Lane Hemaspaandra received the SIGACT distinguished service prize for running the SIGACT News complexity column. Gautam Kamath won the STOC 2012 best student presentation award. No award this year because there aren't videos for the talks.

Gary Miller gave the Knuth Prize lecture. He talked about new techniques for solving systems of equations based on graphs that has many applications including new almost linear time algorithms for approximating undirected max flow. 

More from Palo Alto later this week. 

The High Quality Research Act

Lots of talk, mostly negative, about the proposed High Quality Research Act.

Prior to making an award of any contract or grant funding for a scientific research project, the Director of the National Science Foundation shall publish a statement on the public website of the Foundation that certifies that the research project
(1) is in the interests of the United States to advance the national health, prosperity, or welfare, and to secure the national defense by promoting the progress of science;
(2) is the finest quality, is groundbreaking, and answers questions or solves problems that are of  utmost importance to society at large; and
(3) is not duplicative of other research projects being funded by the Foundation or other Federal science agencies.

On the whole, doesn't sound like a bad thing. So why the fuss? Because the bill's sponsor Lamar Smith, republican congressman from Texas and chair of the house science committee, also sent a letter to the NSF acting director asking for the reviews on five grant proposals. So the High Quality Research Act is an attempt to give congressional approval to the grants process and perhaps requiring justification of individual grants. Nothing good can come from that.

The NSF bravely said no to Smith's request for the reviews. That was two weeks ago and I haven't seen any new news on the topic. Let's hope that High Quality Research Act just simply disappears.

Theory Jobs 2013

Time for the annual spring jobs posts. Like last year, I set up a Google Spreadsheet that everyone can edit so we can crowd source who is going where next year.

A reminder of the rules

• I set up separate sheets for faculty, industry, postdoc/visitors and students.
• 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

Quantum Computing Fast and Slow

I just read two very different science books, Daniel Kahneman's Thinking, Fast and Slow and Scott Aaronson's Quantum Computing since Democritus. Not much to connect the two except both deal to some extent about probability and computation and I want to write a blog post for each chapter, for much I disagree with both authors. But that's what makes them so much fun, so rare to find science-oriented books both worth reading that have the guts to say things that one can disagree with.

In full disclosure, Scott and I agree that he would post about my book if I wrote about his but what a deal. Scott's book is a pleasure to read. He weaves the story of logic, computation and quantum computing into a wonderful tour. You can get an idea of Scott's style by how he explains how he will explain quantum.

The second way to teach quantum mechanics eschews a blow-by-blow account of its discovery, and instead starts directly from the conceptual core - namely, a certain generalization of the laws of probability to allow minu signs (and more generally, complex numbers). Once you understand that core, you can then sprinkle in physics to taste, and calculate the spectrum of whatever atom you want.

He approaches the whole book by this philosophy.  Every now and then he moves into technical details that are best skipped--either you already know it or will get lost trying to follow. But no problem, the story remains. You need to appreciate Scott's sense of humor and his philosophical tendencies, and he does get way too philosophical near the end, particularly a strange attack on Bayesian that involves God flipping a coin. At the end of the book Scott contemplates whether computer science should have been part of a physics department but after one reads this book the real question is whether physics should be part of a CS department.

Kahneman gives a readable tour of behavioral economics with a variety of examples, though I don't agree with his interpretation of many of them. His fast and slow refers to decisions we make instinctively and quickly (like judging a person based on first impressions) versus more slow and deliberative (like multiplying numbers). There is a computer science analogy, in that his fast refers to what we can do with machine learning, simple trained models to make quick judgments that occasionally gets things wrong. I'm not a huge fan of behavioral economics, but it is useful in life to know the probability mistakes people make so you can avoid making them yourself. The wikipedia article has a nice summary of the effects mentioned in the book.

While these two books cover completely different areas, the themes of probability and computation pervade both of them. One simply cannot truly understand physics, economics, psychology and for that matter biology unless one realizes the computational underpinnings of all of them.

Do you KNOW how you KNOW what you KNOW? I don't KNOW.

When watching Jeopardy with Darling if I get a question correct that is NOT in my usual store of knowledge (that is NOT Ramsey Theory, NOT Vice Presidents, NOT Satires of Bob Dylan) Darling asks me How did you know that? I usually reply I do not know how I knew that. Recently I DID know and I'll get to that later, but for now the question arises: Do you know how you know what you know?

1. As an undergrad I learned mostly from taking courses. Hence I could say things like I Know Group theory from a course I had in Abstract Algebra in the Fall of 1978 (Side Note- I know why I should care about groups from reading the algorithm for graph isom for graphs of bounded degree---in 1988). I learned a few things on my own- I learned that a graph is Eulerian iff every vertex has even degree from a Martin Gardner article. But since most of my knowledge was from courses I knew how I knew what I knew.
   
2. As a grad students I still took courses but more routes to knowledge emerged. Papers! I could say things like
   I know the oracle constructions about P vs NP because I read the Baker Gill Solovay paper on October 23, 1981. It helps that Oct 23 is Weird Al's birthday. But even here things get a bit murky- someone TOLD ME about the paper which lead me to read it, but I don't recall who. So one more route to knowledge emerged- people telling you stuff in the hallways.
   
3. I saw Anil Nerode give a talk on Recursive Mathematics and that day went to the library (ask your grandmother what a library is) and read some articles on it. This was well timed- I knew enough recursion theory and combinatorics to read up on recursive combinatorics. In this case I know exactly how I know what I know. Might be the last time.
   
4. As a professor I read papers, hear talks, hear things in hallways, and learn stuff. Its getting harder to know how I know things, but to some extend I still could. Until...
   
5. THE WEB. The Web is the main reason I don't know how I know things. I sometimes tell Darling I read it on the web which is (a) prob true, and (b) prob not very insightful.
   

So- do you know how you know what you know?

On Jeopardy recently the final Jeopardy question was as follows.

TOPIC: Island Countries.

ANSWER: No longer Western, this one-word nation has moved to the west side of the international Date Line to join Asia and Australia.

BILL: What is SAMOA!?

Darling wondered how I know that:

DARLING: How did you know that? Is there a Ramsey Theorist in Samoa?

BILL: Not that I know if, but that's a good guess as to how I knew that. Actually Lance had a blog post Those Happy Samoans about Samoa going over the international dateline and losing the advantage of having more time to work on their conference submissions.

DARLING: Too bad there isn't a Ramsey Theorist there to take advantage of that!

Thanks Lance!- In this one case I know how I know what I know!

The MOOCs Degree

Earlier this week Georgia Tech announced the Online Masters of Science in Computer Science, a MOOCs-based degree with a total tuition of about $7000. This degree came out of a collaboration between Sebastian Thrun of Udacity and my dean Zvi Galil with some significant financial support from AT&T. We've spent several months getting faculty input and buy-in to the program and we're very excited about taking a new leading role in the MOOCs revolution.

We will roll out slowly, with a smaller scale courses to corporate affiliates to work out the kinks and the plan to go to the general public in fall 2014. Read the FAQ to get more information about the program.

It's been fun watching the development of this degree, in particular hearing Sebastian talk about his MOOC 2.0 plans to scale courses with a small amount of expense that we pull from the tuition. No doubt we will have challenges in making this degree truly work at a large scale but I'm truly bullish that we'll a self-sustaining quality Masters program that will reach tens if not hundreds of thousands of students.

Here we go.

Mother's Day Math

Problem: On Mothers day (May 12 this year) restaurants are very crowded because many people take their mothers, grandmothers, great-grandmothers, etc out to lunch. (Grandparents day is in September but I think most people ignore that and honor their grandmothers on mothers day and their grandfathers on fathers day.)

My solution: Take mom out to lunch the FOLLOWING week. Some of my friends tell me NO- you can't just MOVE Mothers day- what are you--- The Master of Space and Time? The key is that my mom AGREES with me and in fact raised me with these values: (1) Never do X when everyone else is doing X, its too crowed, and (2) Learn the polynomial VDW theorem.

While this solution may work for me, it may not work for everyone. Here are some options to alleviate the restaurant crunch:

1. Declare the second WEEKEND in May to be MOTHERS WEEKEND. People take their moms out to lunch SATURDAY or SUNDAY. This would split the restaurant load in half.
   
2. Declare May MOTHERS MONTH. People take their moms out to lunch ONE Sunday in May. This would split the restaurant load by 4.
   
3. Declare May MOTHERS MONTH. People take their moms out to lunch ONE Saturday OR Sunday in May. This would split the restaurant load by 8.
   
4. Declare May MOTHERS MONTH. People take their moms out to breakfast OR lunch OR Dinner ONE Saturday OR Sunday in May. This would split the restaurant load by 24.

How would people DECIDE which day to do:

1. The last day of April have mom either (depending on which of the above schemes) flip a coin, role a 4-sided die, or role an 8-sided die or role two 12-sided dice to determine which day to be taken to lunch. Fortunately, due to the Dungeons-and-Dragons craze that girls got into about 40 years ago, most mothers have these dice. But in case she does not, here is a nice MATH PROBLEM (I am sure already solved): USE fair coins and fair 6-sided dice to simulate other random choices fairly. In our case 4-sided, 8-sided, and 24-sided. Which random choice can be simulated? Which can't?
   
2. Say we do the Saturday/Sunday/breakfast/lunch/dinner solution. Everyone with last name beginning with A goes to breakfast on the first Saturday. Everyone with last name beginning with B goes to lunch on the first Saturday. etc. There are only 24 lunches and 26 letters, so merge P and Q, and merge Y and Z.
   

How likely is any of this to come about? It would need to evolve naturally as a social custom. It also would have to not be that hard to implement. As such the 24-meal-plan probably won't catch on. Also, if Mother's Day become Mothers one-of-24-meals-day it may lose something. Hence the 2-meal-plan solution is probably the best.

However, the entire tradition of taking mom out to lunch on mothers day may fade. The origin is that mom cooks for the family most days, so this ONE day they take her out. Nice! But more and more households share responsibilities (NOTE- I have no facts or stats to back this up but it has a certain truthiness about it) hence the notion of taking mom out to lunch may seem more and more odd over time. Then again, its still nice being taken out to lunch.

GPU Computing

Back around 1980, I used to write computer games for the Apple II. Plotting a point on the Apple II screen required dividing by 7, a lengthy process for the 6502 microprocessor. Asking around, we learned how to make division by 7 much faster--lookup tables.

As computer gaming got more intense in the decades that followed, we first had graphics cards designed to speed up the process and later Graphics Processing Units or GPUs, dedicated processors devoted to graphics.

Around the turn of the century, people started using GPUs for more than just graphics. GPUs did certain kinds of vector manipulation quickly and one could use these for a variety of mostly scientific computing. But GPUs weren't really well designed for other purposes. Following the cupholder principle, GPUs began to evolve to allow easier to access APIs from more common programming languages becoming General Purpose GPU or GPGPUs. Several systems researchers at Georgia Tech and elsewhere are now redesigning chip layouts to make the best most efficient uses of CPUs and GPGPUs.

The theory community hasn't seem to catch on yet. There should be some nice theoretical model that captures the vector and other operations of a GPGPU and then we should search for algorithms that make the best use of the hardware. The theory world writes algorithms for non-existent quantum computers but not for the machines that we currently use.

Are you smarter than a fifth grader? I'm not.

My darling sometimes watches TV in the middle of the night when she can't sleep.So I found myself watching (actually listening) to the quiz show
Are You Smarter than a Fifth Grader? They asked the following Math Question:

What number do you need to add to 3 to get a double fact?

I had never heard the term double fact! I really didn't know and there was no way toderive it! I don't recall what my guess was but it was incorrect.See herefor what they are.

Is this a common term? If you Google

"Double fact" math

You get roughly 6,000 hits. (Down from 17,000 a few months ago when I first sketched out this post.)Is that enough hits to be a real term? Is number-of-hits a good measure?

Are there other math terms that are being taught in elementaryschool that are not that well known to people like us? (Though if you have children perhaps you know them.)Note that no matter how much math you know, there may be terms you don't know and can't derive (though you can make an intelligent guess).

My name is Bill Gasarch, and I am NOT smarter than a fifth grader.

Map Coloring Revisited

Following the coloring theme from Bill's last post, a few years ago I asked you readers for natural examples of maps that were and were not three colorable. Chris Bogart gave a nice non-trivial example of a three-colorable country, Armenia.

But I also wanted a natural example that was four-colorable even though every interior region had an even number of neighbors. In my book I ended up making up my own fake country map.

(Sorry for the hand-drawn picture and getting East-West wrong. Looks better in the book)

So once again I'd still like to see a natural example. Here's a simple 7-node graph with every interior node with even degree but not 3-colorable. 

There must be some real world map that captures this graph.

I'll make the same deal I made before, an autographed copy of my book for the best example of a real-world example of a non-three colorable map with interior regions with an even number of neighbors. Should be a real political unit--not just a collection of states.