The Digital Random Bit Generator

I started this month asking about the nature of randomness and how we generate it for our computers. Let me end the month talking about Intel's clever new digital approach to creating random bits.

Intel chips used to have an analog random bit generator based on noise in the circuits. But improved circuits reduced the noise limiting the effectiveness of these generators.

In the September IEEE Spectrum, Intel Architects Greg Taylor and George Cox give an overview of a digital random bit generator will sit in future Intel chips. The article is a short and fun read.

The heart of the article describe a simple digital circuit.

Initially when both transistors cause full voltage at both Nodes A and B. Intel had to use special inverters (NOT gates) that can withstand not being able to invert at this point. A clock signal slowly turns off the transistors and the inverters go to work reducing A and B to an equilibrium of half voltage each.

The magic now happens. This isn't a stable equilibrium so even the slightest noise quickly drives one of the nodes to full voltage and the other to no voltage. Which node goes to one depends on the direction of the noise and that's how you get your random bit.

Taylor and Cox find an idea that they might have sketched on a napkin and yet gives an incredible simple and elegant solution to an important problem. This is why I love computer science.

John McCarthy (1927-2011)

First Steve and then Dennis and now we have the death of a third computing pioneer this month. John McCarthy passed away earlier this week at the age of 84.

McCarthy was one of the founders and early promoters of Artificial Intelligence and gave the field its name. He developed Lisp for the same reason Newton invented calculus, he needed a system to do his research so he created his own. Lisp, built on Church's λ-calculus, was the first popular example of a functional programming language, an entirely different way to think about programming than the more structured languages. McCarthy received the ACM Turing Award in 1971.

McCarthy truly believed a computer could capture human intelligence and his pioneering work may yet help make that happen.

It's Open Access Week

Open Access Week starts today. Interestingly a number of traditional journal publishers, like Springer, are sponsors as they try to figure out how to modify their business model in a changing publication environment.

We'd love all our papers to be as widely available as possible but no journals are truly free. They either need a revenue stream whether that comes from authors, readers, libraries or some other outside source, or require a considerable amount of volunteer effort and coordination beyond just editing and reviewing.

I found out about Open Access Week from the ACM as they are promoting their Author-ize service that lets authors give a link on their home pages that allows their readers to freely download the ACM version of their papers. I consider ACM one of the good publishers, reasonably priced, and they've already allowed us to publish our own papers on their website and use them in other publications. David Rosenthal has other opinions.

There is a pledge Research Without Walls going around to "assist in the peer review process (as a reviewer, board/committee member, chair, editor, etc.) only for conferences, journals, and other publication venues that make all accepted publications available to the public for free via the web." Are you signers willing to forgo serving on a STOC or FOCS PC?

I heard a great (though hard to parse) quote second hand from an economist about the ethics of illegally downloading music.

If if I had to pay for it I would pay for it then I will pay for it.

The iTunes model addressed this concern by pricing music so cheaply that one would feel better paying for it than not. Academic publishers should learn this lesson and also price downloads of research papers at $0.99.

My biggest fear of the open access movement is that without a strong alternative model it will just lead to even less CS papers getting published in journals. Even open access won't give access to a paper never written.

The Cup Holder Principle

The story goes that when Toyota engineers started to design the first cup holders in the 80's, they went to a local 7-11 and got every different cup 7-11 had to make sure their design would work on all the cups in current use. These days the cup designers have to make sure their cups will work in today's cup holders.

This is one of the starkest examples of initial Technology for A being driven by B and now the technology for A drives the technology for B.

How much does this happen in theoretical computer science? Do we design algorithms to use an already established data structure? Do we modify our definitions of some object to make it group or a field? Do we create a cryptographic protocol so that some "standard assumption" makes it secure?

Are these good or bad things? Sometimes it is really useful to make square pegs fit into round holes and other times we miss new opportunities.

Theorems that are impressive at first but then....

Mission Impossible was my favorite show as a kid. As an adult it would not make my top 20, and I wonder why I liked it so much as a kid. (Actually I do know- at the beginning they are given a well defined problem and they solve it, which is how Math works.)

This inspired this post: Is there some theorem that you were initially impressed with but are now far less impressed? I list things I have heard of for this category. I request that you submit your own examples.

1. Every number is the sum of 4 squares. This is impressive and still is. Number theorist must use this all the time! Alas, aside from its use in Hilbert's 10th problem, and maybe a few few other places, I has never seen it used and is now less impressed. However, this may be unwarranted. Some theorems in math are impressive for the achievement, others for their use later. This one IS impressive for its achievement. But, as far as I can tell (and I could be wrong), not for its uses.
2. Every group is a group of permutations. Group Theorists must use this all the time! Alas the proof makes you realize its more of a tautology. Rarely used by Group Theorists. It is used in some of the proofs of Sylow's theorem. I do not know of any others uses. And this one is not impressive for its achievement.
3. The Prime Number Theorem. Since results that are very very close to it can be gotten with much much much less effort, getting the actual constant down to 1 seems like too much sugar for a cent. (For more on PNT and a link to an easy proof of a weaker version see an old post of mine here.) However, this one is an achievement certainly. And it inspired other great mathematics.
4. Poincare's Conjecture says that if something looks, feels, and smells like a sphere, then its a sphere. Is that really worth $1,000,000? Perhaps Perelman didn't think so either.

Teaching PCPs to Undergrads

The last few times I've taught undergraduate theory I cover the PCP theorem. It's not complicated if you state it the right way:

PCP Theorem: For any constant α > 7/8, there is a polynomial-time computable function f mapping 3-CNFs to 3-CNFs such that for all formula φ,

• If φ is satisfiable then f(φ) is satisfiable.
• If φ is not satisfiable then every assignment to f(φ) satisfies at most an α-fraction of the clauses.

I point out to the class you can satisfy 7/8 of the clauses by just choosing a random assignment.

Also I show how the PCP theorem gives some (weak) approximation bounds for Clique. For each variable in each clause of f(φ) create a node of a graph and connect two nodes as long as they aren't in the same clause or connect a node representing a variable with one representing its negation. That gets you an 8/7-ε approximation lower bound for clique. I give showing a constant approximation lower bound for Vertex cover as a homework assignment.

I don't even try to give an idea of the proof of the PCP theorem. I just say it would take an entire graduate class to cover the proof in its full detail. That's probably a lie, one of our ten-week quarter-long classes is not enough time to prove the very strong version of the PCP theorem stated above. 

Dennis Ritchie (1941-2011)

We lost another computing pioneer of a very different kind. Dennis Ritchie, who developed C and co-developed Unix, passed away last weekend. Ritchie and Ken Thompson received the 1983 Turing Award for their development of Unix.

In the early 80's I programmed extensively in assembly language on the Apple II and IBM 370. In both cases we needed speed a high-level language couldn't get us. C and Unix let us take advantage of high-level constructs and abstraction and yet retain the full power of the underlying machine. Ritchie changed the way we did computing.

If there is a moment that captures both Jobs and Ritchie, it was in 2002 when the Mac moved to the Unix-based OS X from which also the Apple iOS was later derived. As you play with the new iOS 5, you can't help but think of these great pioneers that made it possible.

If Bill Tweeted what would he tweet (Steve Jobs Edition)

1. A more nuanced view of Steve Jobs: here.
2. A less nuanced view of Steve Jobs: here.
3. The next Steve Jobs: here
4. A very nice NON-Steve Jobs post here.
5. Is this an appropriate use of logarithms? From Andrew Sullivan's Blog (the boldface is mine):

   In some ways, the emergence of a Republican candidate (Rick Perry) who takes every single aspect of George W. Bush's political persona and adds a logarithm, is a healthy sign. I'd rather have a candidate who is explicitly saying that his politics is based on religion and his political rallies are actually spiritual rallies, than one whose theocratically-driven conservatism is on the downlow.

6. A type of Math Anxiety
7. Should people learn math?
8. The president invokes math: here
9. A bad idea for a TV series: The intuitionist defense attorney: Just because you proved that A OR B did the crime, and then you showed NOT(A did it), does not mean that you have proven B did it.

More than East and West

The Obama Campaign is creating a Campaign Analytics Team.

Love Data, Predictive Analytics, Social Media and Politics? The Analytics team for the Obama Campaign is hiring full-time analytics engineers and scientists at our headquarters in Chicago!

To find out more, come meet us at the Stanford campus ...

To find good computer scientists, the Obama campaign feels the need to look 1850 miles away. A stark  reminder that especially in the tech world, people often forget that there is an America between Oakland and Philadelphia. Google, IBM, Microsoft and Yahoo have research labs around the globe but generally ignore middle America. Chicago is often considered at best a place to change planes.

Chicago has amazing arts, music, food, sports and architecture, everything you'd want in a city and considerably cheaper than the coasts. We know we have great universities and a strong intellectual core. How many cities have a battle for the minds between the Chicago Ideas Week starting today and the Chicago Humanities Festival beginning next week?

Chicago isn't as well known for its high tech. Computer science in Chicago is good but not yet as strong as it should be. We do have some very strong CS departments nearby at Illinois, Wisconsin, Michigan and Purdue. Chicago has had its successful startups most notably Groupon. Chicago should be a major high tech hub but we need to sell ourselves better.

Next time you are stranded at O'Hare, take the El to the Loop and check out our great city. Prepare to be amazed.

Steve Jobs 1955-2011

It's one of those events. You'll always remember where you were when you heard that Steve Jobs passed away. I was at dinner with several visiting computer scientists, holdovers from the CCC council meeting earlier in the day. Our iPhones started buzzing and the news quickly spread. We gave a toast to the great Mr. Jobs.

Steve Jobs put the algorithm in our pocket. Computation moved from big rooms to the desktop to something we carry with us every waking minute. Jobs make it happen not just for us tech heads but for everyone. Jobs did it without an algorithm that analyzes data to see what the public wants. Jobs realized it takes an inner vision, a true artist to make the power of computation something we all can use.

If you find a mistake in someone elses paper you should....

What do you do if you read a paper or book and find mistakes in it? My first impulse is to say: Email the author. Always be polite and admit (which is true) that you may be misunderstanding something. A few thoughts:

1. If you offer a suggested correction then MAKE SURE IT IS CORRECT. The author may say Oh, I guess that's a mistake, I better make the correction having thought that you read it carefully. While that may well be the authors responsibility, be very careful. The first rule of proofreading is DO NO HARM.
2. If the paper is a preprint then the author should be VERY GRATEFUL since they will be able to make the correction before it becomes official. But see next point.
3. If the paper is already in a journal the author might want to correct the version on their own website. I can picture a day when the version on the authors website or arXiv are BETTER than the so-called official version. So the author should be grateful here as well.
4. For arguments sake, lets say that in Karp's classic paper Reducibility Among Combinatorial Problems, where he proves 21 problems NP-compete, he made a mistake on 0-1 programming. The problem IS NP-complete and the correct proof is in many textbooks (also, anyone reading this blog can probably do it themselves). Is it worth wasting Karp's time with this?
5. Most authors will be surprised and delighted that someone read their paper.
6. Some authors won't care. Either they left the field or they don't care about the constant they got wrong or they don't want to be bothered. That is their right; however, what to do? You can't publish an erratum for them.
7. In High School while studying some Combinatorics I came across the following passage.

   The number of ways to arrange n distinct objects is n × (n-1) × ... × 1. For example, the number of ways to arrange 5 distinct objects is 5!.

   I did not understand why they were so excited about the answer. Using an exclamation point seemed over the top. And CLEARLY there were two mistakes!
   1. The answer of 5 is WRONG. The answer should be 5 × 4 × 3 × 2 × 1 = 120.
   2. There is a spurious period after the exclamation point.
   Unfortunately I did not contact them. The mistakes are still there.

What is Random?

One can get into great philosophical debates on what is randomness. Information that we can't compress. Information that's unpredictable. Information that we are willing to bet on. 

When I define a probabilistic Turing machine I give it a special "coin state" which it enters and magically lands in a special "heads" state and "tails" state uniformly and independently each time. I imagine a computer hooked up to a little box with a coin inside that gets flipped and some sensor or camera determines whether it landed heads or tails.

I have no problems thinking about probabilistic computation just like I have no issues with quantum machines which haven't been built yet or nondeterministic machines which will never exist.

We don't care where those random bits come from as long as they fulfill the right properties. Of course our computers don't have little coin boxes so they generate randomness using pseudorandom generators which don't fulfill all the properties we expect from true randomness. So we developed theories of PRGs and under what assumptions good PRGs exist. Whether we can use them depends on whether we use randomness for searching or hiding.

We can't disprove that BPP = NEXP (everything in nondeterministic exponential time can be solved in probabilistic polynomial time). Then true randomness will give us the secrets of the universe and PRGs won't help much. Random bits would be worth their weight in gold but can we get them? I'd make a fortune selling little coin boxes. 

Bibliographies

Lots of buzz about Princeton's new policy that prevents faculty from giving away the right to publish papers on their own web pages. Never seen faculty so happy to have their rights restricted.

Princeton is behind the game for Computer Science.  All the major publishers I use explicitly give the right to authors to publish their own versions of papers on their web pages including ACM, IEEE, Springer and Elsevier. Even before, publishers rarely went after authors' pages. I have posted FOCS and Complexity papers for years and IEEE just updated their policy last November. Also see this discussion about ACM giving authors links so their visitors can freely download the official ACM versions of their papers.

We have these rights so EXERCISE THEM. No computer scientist has any excuse not to maintain a page of their papers with downloadable versions.

It gets harder to maintain these pages. I have to keep an old bibtex-to-html system running and at some point I should redo the whole page. Sites like DBLP and Google Scholar let people find my papers easily without my intervention. But if I want anyone to see all of my papers I have little choice but to keep the page going.

A candidate for a new Millenium Problem

In a prior post I wrote that the Erdos-Turan Conjecture should be a Millennium problem. Today I am going to (1) suggest a generalization of the Erdos-Turan Conjecture should be a Millennium problem instead, and also suggest (2) a far harder problem be another candidate. For some history see here. (This is an excerpt from my still-being-written book on VDW stuff- so if you find a mistake or suggestions please comment or email me.)

Recall the poly VDW theorem:

Let p₁,...,p_k ∈ Z[x] such that p_i(0)=0. Let c ∈ N. There exists W=W(p₁,...,p_{_k};c) such that for any c-coloring of {1,...,W} there exists a,d such that a, a+p₁(d), ..., a+p_k(d) are all the same color.

Much like VDW's theorem was before Gowers result, (1) there is a proof that gives bounds that are not primitive recursive (Walters proof) (2) there is a density-type theorem that does not give good bounds, (3) there is a proof by Shelah that gives primitive recursive bounds, but they are still quite large.

We make the following conjecture which we hope will lead to better bounds on the poly VDW numbers.

CONJ: Let p₁,...,p_k ∈ Z[x] such that p_i(0)=0. If Σ_{x ∈ A} 1/x diverges then there exists a,d such that

a, a+p₁(d), ..., a+p_k(d) are all in A.

1. The case where all of the polynomials are linear is often called the Erdos-Turan Conjecture. It is still open.
2. The following is a subcase that is orthogonal to the Erdos-Turan Conj: If Σ_{x ∈ A} 1/x diverges then there exists two elements of A that are a square apart.
3. Green and Tao showed that the set of primes have arb. large AP's. Then Tao and Ziegler showed the following: Let p₁,...,p_k ∈ Z[x] such that p_i(0)=0. There exists a, d such that
   
   a, a+p₁(d), ..., a+p_k(d) are all primes.
   
   SO the CONJ is true for a particular set of interest.

We also pose a question which is more interesting but likely much harder:

If A is a set then let d_A(n) =|A ∩ {1,...,n}|/n. The lim sup_{n → ∞} d_A(n) is the upper positive density. We will be interested in the function d_A(n).

QUESTION: Let p₁,...,p_k ∈ Z[x] such that p_i(0)=0. Find functions e₁(n) and e₂(n) (not that far apart) such that e₁(n) ≥ e₂(n), and the following occurs:

1. If for almost all n, d_A(n) ≥ e₁(n) then there exists a,d such that a, p₁(d),...,p_k(d) ∈ A.
2. There exists A such that, for almost all n, d_A(n) ≥ e₂(n), and there is NO a,d such that a, p₁(d),...,p_k(d) ∈ A.

For the case of 3-AP's the following are known:

1. If for almost all n d_A(n) ≥ (log log n)⁵/log n then A has a 3-AP. (See this Tom Sanders paper.)
2. There exists a set A such that, for almost all n d_A(n) ≥ 1/n^{\sqrt(log n)} and A has no 3-APs (See Michael Elkin's paper for a slightly better result that I didn't have the energy to typeset.)

These two functions are NOT close together. So even in the case of 3-AP's we do not know the answer. I want to know the e1,e2 for ALL finite sets of polynomials with 0 constant term. We've got our work cut out for us.

It is my hope that progress on the question will lead to better bounds on some poly VDW numbers. A similar question DID lead to better bounds on the VDW numbers.

Moneyball

I saw Moneyball over the weekend. This movie gives a fictionalized account of the how the general manager of the 2002 Oakland A's used the right kind of statistics to build a strong team with a low budget. This article on the GM Billy Beane gives a nice follow-up to the movie.

A bit surprising one can get a good movie about the math in baseball. Moneyball was based on the book by Michael Lewis with a screenplay co-written by Aaron Sorkin who also wrote the screenplay to the Social Network. Sorkin writes nerdy things well.

Moneyball is really a computer science movie. It's not about the computers themselves which play a small role, but its about taking a large amount of data and deriving the conclusions that help make the crucial decisions in developing the team.

You can also see the difference in computer science over the last decade. At the time of Moneyball, people would try many statistical models and test them out. These days via Machine Learning we give the computer the data and the results and the computer determines the right models.

Oddly enough Billy Beane's actions led to an even greater separation between the large and small market teams. The statistical ideas that Beane pushed have been adopted by the other teams. Now we've hit an equilibrium so the teams that spend more win more as well.

Oddly the New York Times ran an editorial piece Not-So-Smart Cities by Greg Lindsey yesterday arguing that cities shouldn't rely on these kinds of statistics for planning because of a failed project from the 60's. Sounds like Lindsey needs to see Moneyball.

Mahaney's Theorem

Bill has a lot of posts where he questions whether to teach Mahaney's theorem in a graduate complexity class. Since it is one of my favorite theorems and most of you young folk won't see a proof in your complexity classes, I'll give it here. This proof is not the original of Mahaney but based on a paper by Ogihara and Watanabe.

Mahaney's Theorem: Let c be a constant and A be set such that for all n, A has at most n^c strings of length n. If A is NP-complete then P=NP.

Proof: We define the left-set of SAT as follows: Let B = { (φ,w) | φ has a satisfying assignment a with a ≤ w in lexicographic order}. We'll restrict ourselves to w that are (not necessary satisfying) assignments for φ.

Assume φ is satisfiable and let a' be the lexicographically smallest satisfying assignment. We have (φ,w) is in B iff w ≥ a'.

Since B is in NP by assumption B reduces to A via some function f computable in polynomial-time, (φ,w) is in B iff f(φ,w) is in A.

Fix φ and n and let m=n^k bound the number of strings in A of any length that f(φ,w) could query. Pick w₀ < w₁ < w₂ < … < w_m+1 evenly spaced from each other.

Let z_i = f(φ,w_i) for each i. Note that if z_i is in A then z_j is also in A for all j ≥ i.

Case 1: z_i = z_j for some j > i. We know a' cannot be between w_i and w_j.

Case 2: All the z_i are distinct. There are only m elements in A so z₁ is not in A and a' cannot be between w₀ and w₁.

Either way we have eliminated a 1/(m+1) fraction of the possible assignments.

We repeat the process choosing the w_i equally spaced among the remaining possibilities and eliminate another 1/(m+1) fraction of those assignments. We continue O(mn) times until we narrow down to a set S of m+1 possible assignments.

If φ is satisfiable then a' is in S so at least one assignment in S and will satisfy φ. If φ is not satisfiable then none of the assignments in S satisfy φ.

By trying all the assignments of S and seeing if they satisfy φ, we get a polynomial-time algorithm to determine if φ is satisfiable. Since Satisfiability is NP-complete we have P = NP.

Where do theorems go to die?

(Joint post by Bill Gasarch and Daniel Apon)

Recently I (Daniel) reviewed Dexter Kozen's Theory of Computation (it was AWESOME). You can find the review here. Many of the topics were standard but some we (Bill and Daniel) suspect are not covered in any complexity class (well... maybe in Dexter's). This DOES NOT detract from the book, however we now raise the question:

Where do Theorems go to die?

In some eras there are some theorems that are taught in EVERY basic grad complexity courses Then all of a sudden, they are NOT taught at all. (Both the EVERY and the NOT are exaggerations.)

1. The Blum Speedup theorem: In the 1970's EVERY comp sci grad student knew it. In the 1980's EVERY theorist knew it. In the 1990's EVERY complexity theorist knew it. In the 2000's (that sounds like it means 2000-3000) EVERY... Actually NOBODY knew it, except maybe students who took Dexter's class. I doubt Blum teaches it anymore. Blum's speedup theorem was proven before Cook's theorem when people were still trying to get complexity right. Blum has since said Cook got it right! Even so, Blum's Speedup theorem should be in the preface to God's book of algorithms (See here) as a warning that there might not be an optimal algorithm.
2. The Complexity of Decidable theories (e.g, Presburger, WS1S, S1S, S2S). We all know that by Godel's theorem the theory of (N,+,times) is undecidable. There are some subtheories that are decidable. However, the decision procedures are complete in various rather high up classes (WS1S is provably not primitive recursive). This material I (Bill) learned from Michael Rabin (who himself proved S2S undecidable) in 1981 but my impression is that it is not taught anymore. Was it ever widely? We think that students should know the STATEMENTS of these results, because these are NATURAL problems (Bill did the capitalization) that are complete in classes strictly larger than P. (See the second conversation here for comment on that.) One of us thinks they should also know the proofs.
3. omega-Automata. This is used to prove S1S decidable and we've heard it is used in fair termination of concurrent programs. Sounds like it should be more well known. But it is rare to find it in a complexity cousre. It may well be taught in other classes. (I (Bill) touch on it in undergrad automata theory.)
4. Jon Katz is pondering not teaching Ladner's theorem!!! The students should surely know the result (YES, and stop calling me Shirley) however, should they know the proof?
5. Spare Sets: Bill Blogged about no longer doing Mahaney's Theorem Karp-Lipton is still used A LOT, but Mahaney's theorem is not really used at all. Daniel thinks Mahaney's Theorem is AWESOME, however Daniel is bright eyed and bushy tailed and thinks ALL of this stuff is AWESOME.
6. Computability Theory: Friedberg-Muchnik, Arithmetic Hierarchy, Analytic hierarchy, Recursion Theorem. This is like Blum Speedup- this material used to be better known to complexity theorists but is hardly taught to them anymore. It IS of course taught in courses in computability theory. But such courses are taken by complexity theorists far less often then they were. When I (Bill) tell someone there are c.e. sets that are not decidable and not complete! they say Oh, just like Ladner's theorem. Its the other way around, Ladner's result came far later.
7. Part of this is that Complexity theory has changed from Logic-Based to Combinatorics-Based (see post on CCC Call for papers) We don't teach Blum Speedup (and other things) any more because we have better things to teach. However, are there results that the students should know even if the fields they come from are dead? YES, and Ladner's theorem is one of them.

Who decides such things? Textbook writers for one. A Proof Theorist who worked on lower bounds for Resolution told me he hopes that Arora-Barak's book would include this material. He even said If it does not, the field will die. Is this true? If so then Arora and Barak have more power than they realize.

Conferences Again

Lots of conference news and views going around. Let's sort it out.

FOCS early registration deadline is September 29th, fast approaching. Deadline for applying for student support is this Thursday September 22. Apply even if you don't have a paper there and take the opportunity to attend one of theory's most important meetings.

Also the STOC 2012 submission deadline is still November 2. There was a mistaken deadline listed on a theory events site.

The SODA 2012 accepted papers (and links to Arxiv) are out. Program Committee Chair Yuval Rabani explained the PC process. Seems pretty much along the lines of PCs I've been apart of. I wished they did penalize people who had poorly written papers, otherwise there's little incentive to write well. I'm also not a big fan of the "pet paper" idea, people tend to choose papers of their friends and colleagues.

Michael Mitzenmacher posted about the number of good papers not accepted and whether SODA should accept more (an issue at most of our major conferences). In this blog, Sami Khuller guest posted about whether it makes sense to have SODA in Japan. There are a handful of SODA accepts with primarily Japanese and other Asian authors but the vast majority of the authors are US-based.

Some of the comments on Khuller's post talked about having a virtual conference. How about this idea: We don't bother meeting and just collect the accepted papers into a single volume. We can give this idea an innovative name like a "journal".

In this month's CACM article, Moshe Vardi complains about the quality of conference talks. (I like the "journal  that meets in a hotel" quote but it didn't originate with me). You see this at STOC and FOCS too, people giving a talk only to other specialists in their field instead of aiming for a general audience.

Most of you readers know my position on conferences, that we need to get conferences out of the ranking business in CS so conferences can instead play their role of bringing community together and escape from the explosion of conferences just to give people who were rejected from another conference a place to submit their papers.

Happy Constitution Day

September 17th officially is known in the United States as "Constitution Day and Citizenship Day" but is celebrated today because the 17th this year falls on a weekend. I  have nothing but love for the our Constitution. Not only does the Constitution and its amendments provide the great freedoms we have in America but it also shows how to balance states of different sizes with a strong central government. The EU could do worse than by following its example.

What bothers me is a law that Robert Byrd snuck into an omnibus spending bill in 2004.

Each educational institution that receives Federal funds for a fiscal year shall hold an educational program on the United States Constitution on September 17 of such year for the students served by the educational institution.

With a few exceptions like the military academies, US universities are either run by the states, municipalities or are private institutions. It defeats the whole point of the Constitution for the Federal government to be dictating to US universities what educational programs must be held when.

Most universities do the minimum. Northwestern just points students to a website with Constitution related information and videos.

To help all of you celebrate Constitution Day here is the great preamble as I learned it as a kid.

Conventions in Math- just to make the rules work or more?

1. Why is

   a^1/2 = sqrt(a)?

   true? To make the rule

   a^x+y=a^x a ^y

   work out.
2. Why is

   (∀ x ∈ ∅)[P(x)]

   true? To make the rule

   (∀ x ∈ A ∪ B)[P(x)] iff (∀ x ∈ A)[P(x)] AND (∀ x ∈ B)[P(x)]

   work out.
3. Why is the sum over an empty index set equal to 0 and the product over an empty index set equal to 1? Same reason- it makes various math laws work out.

For the second and third item on the above list I would say its not JUST to make some rule work out, it also makes sense. But the first item, that a^1/2 = sqrt(a), seems to only make sense in terms of making a rule work out and not for any other reason. I have no objection to the rule; however, if you have a REASON other than it makes the rules work for this convention, please leave a comment.