Sunday, April 11, 2021

Is the following reaction to getting the first COVID shot logical?

 Alice works at a charity that puts together bag and box lunches for children.


They all wear masks and they are 12 feet apart and very careful, and nobody there has gotten COVID.

Then Alice gets here first COVID shot and says:


I am not going to work for that charity until I have had my second shot and waited  4 weeks so I am immune. 


She is really scared of getting COVID NOW that  she is on the verge of being immune. 


Is that logical? She was not scared before. So does it make sense to be scared now? I see where she is coming from emotionally, but is there a logical argument for her viewpoint? I ask nonrhetorically.


bill g. 

Thursday, April 08, 2021

Quantum Stories

Scott Aaronson wrote last month about the hype over quantum computing. I'd thought I'd drop a few stories.

I was once asked to review a grant proposal (outside the US) that claimed it would find a quantum algorithm for NP-hard problems. I wrote a scathing review but the grant was funded because I failed to prove that it was impossible. I replied that they should fund my research to teleport people from Chicago to Paris because they couldn't prove I couldn't do it. I never got a response.

I was at an NSF sponsored meeting on quantum computing. I suggested, as a complexity theorist, that we need to explore the limits of quantum computing. A senior researcher said we shouldn't mention that in the report or it might hurt our chances of funding the field if they think quantum computing might not be a complete success.

I went to a Microsoft Faculty Research Summit which had a big focus on quantum computing. I complained of the quantum computing hype. My friends in the field denied the hype. Later at the summit a research head said that Microsoft will solve world hunger with quantum computing.

I was meeting with a congressional staffer who had worked on the National Quantum Initiative which coincidentally was being announced that day. I said something about high risk, high reward. He looked shocked--nobody had told him before that quantum computing is a speculative technology.

Quantum computing has generated a large number of beautiful and challenging scientific questions. Thinking about quantum has helped generate classical complexity and algorithmic results. But quantum computing having a real-world impact in the near or mid-term is unlikely. Most scientists I know working directly in quantum research are honest about the limitations and challenges in quantum computing. But somehow that message is not often getting to the next layers up, the policy makers, the research managers, the university administrators, the media and the venture capitalists. 

But who knows, maybe some quantum heuristic that doesn't need much entanglement will change the world tomorrow. I can't prove it's impossible.

Sunday, April 04, 2021

Do any NP-reductions use deep mathematics? Non-rhetically

BILL: Lets say we didn't know that FACTORING NPC --> NP=coNP.
then what direction would we think Factoring in P or NPC? 

STUDENT: In P. After all, Number Theory is a deep subject and I can imagine some deep Theorem in it leading to FACTORING in P. 

BILL: That cuts both ways. I can imagine some deep theorem in NT being the key to showing 

FACTORING poly-reduces to  SAT

STUDENT: 
Deep mathematics HAS been used for algorithms. Factoring algs is one example, The graph minor theorem yielding MANY problems in P is another. Can you give me an example where deep mathematics has been used for an NPC reduction?

BILL: Oh. Gee. I do not know of any. 

STUDENT: If only you had some mechanism to ask the theory community. Maybe you could call it a web log, or weblog.

BILL: If only...

QUESTIONS
1) Are there any NPC reductions that use deep math? (I realize that the phrase `deep math' is not well defined,)

2) Are there other reductions that use deep math?

3) If P NE NP then: 
For all epsilon there is no approx-alg for MAX3SAT which yields  \ge  (7/8 + epsilon)OPT

For all delta  there is no approx-alg for CLIQ which yields > n^{-delta} OPT

No approx-alg for SET COVER which yields \ge (ln n + o(1))OPT. 

All of these proofs use  the PCP machinery or something similar. My impression is that the original PCP theorem, while long, hard, and impressive, did not use deep math. I have a vague memory of some paper or PhD thesis stating that the ONLY theorem needed was that a poly of degree d over a finite field has \le d roots. 

However to get the optimal lower bounds seemed to use some deep math. But I am more ASKING than telling. 

Thursday, April 01, 2021

Want to Buy a Theorem?

This is embarrassing to admit but after a few badly timed trades on GameStop options I find myself a bit tight on money. To raise some cash, I reluctantly decided to sell one of my prized possessions, one of my theorems.

For Sale: Boolean formula satisfiability cannot be solved in both logarithmic space and quasilinear time. For a more formal and slightly more general statement and a proof, see this paper.

Bidding starts at 12 BTC (about $705,000). 

The winning bid, upon verified payment, will receive:

  • The ability to give the theorem the name of your choice such as your own name, your best friend's mother's name or "Teddy McTheoremface".
  • A non-fungible token (NFT) attesting ownership of the theorem and the name you have chosen for it.
  • Anyone citing this result will be required to note that you own it and use the name you chose above. You cannot, however, limit the use of the theorem or receive compensation for its use. 
  • By virtue of owning this theorem you will a Fortnow number of zero. This immediately gives you an Erdős number of 2. If you have previously written a paper with Paul Erdős then both of us will now have an Erdős number of 1.
Frequently Asked Questions

Q: Why this theorem?

A: The theorem is in one of my few solely authored papers and I can't afford to share the proceeds of the sale. 

Q: Doesn't Ryan Williams and others have stronger theorems?

A: The results are incomparable. Ryan gives bounds on a single algorithm with low time and space. My theorem allows different machines for the time and space bounds.

Also, to the best of my knowledge, Ryan's theorem is not for sale.

Q: Doesn't the proof of the theorem rely on other people's theorems such as Nepomnjascii? Shouldn't he get some of the value from this sale?

A: I'm not selling the proof of the theorem, just the theorem itself.

Q: If I purchase this theorem will I get to write next year's April Fools post?

A: No.

Monday, March 29, 2021

Slicing the Hypercube

Here's a neat result I heard about at virtual Dagstuhl last week, a new lower bound on the number of hyperplanes that cuts all the edges of a hypercube.

A n-dimensional hypercube has 2n vertices corresponding to the binary strings of length n. Edges are between two vertices that differ in exactly one bit, for a total of (n/2) 2n edges. Hypercubes played a large role in Hao Huang's recent proof of the sensitivity conjecture. 

A hyperplane is just a linear inequality in x1,…,xn the bits of the string corresponding to a vertex. An edge is cut if the inequality is true for one vertex and false for the other.

With n hyperplanes you can cut all the edges in two very different ways. 

  • The hyperplanes xi > 0 for each i. These are n orthogonal hyperplanes.
  • The hyperplanes x1+…+xn > i for each i from 0 to n-1. These are n parallel hyperplanes.
Do you need n hyperplanes to cut all the edges? Mike Paterson found 5 explicit hyperplanes that cuts all the edges of a 6-dimensional hypercube (see survey by Mike Saks). Scaling that up means you need 5n/6 hyperplanes to cut an n-dimensional hypercube. That remains the best known upper bound.

For the lower bound, in 1971 Patrick O'Neil showed that any hyperplane can cut at most O(n0.5) fraction of the edges (sharp by the hyperplane x1+…+xn > n/2). Thus you need at least O(n0.5) hyperplanes which for 50 years was the best known bound.

Gil Yehuda and Amir Yehudayoff have given a new lower bound of O(n0.57). The paper gives a O(n0.51) bound but Yehudayoff said in a talk last week the bound has been improved.

Yehudayoff didn't go into much details in his 20 minute talk but the proofs uses geometry, probability and antichains. 

The result has some applications to complexity, namely you need at least n1.57 wires in a depth-two threshold circuit for parity. But the main fun is the question itself, that we finally made progress and there is still a long way to go.

Thursday, March 25, 2021

The key to my Taylor series problem: Buddy can you spare a penny, nickel, dime, or quarter

 In my last blog post I posed a question about finding the coeff of x^100 in a particular Taylor Series. The question and answer are given  here:


The key to the problem was to recognize that it was asking how many ways you can make change of a dollar using pennies, nickels, dimes, and quarters. This can be done by hand (its 242). 

1) Someone who I gave the problem to solved it by available software, but when he saw the answer was 242 he realized how to do it via making change.


2) How hard would this problem me to do completely by hand- say as a Putnam Problem? Its hard for me to say since I started with the trick and then found the problem. 


3) Is this a well known trick? 



Monday, March 22, 2021

A Taylor Series Problem

 I post a problem today and its solution on Thursday.

Comments are fine, though if you don't want to get a hint, don't read them. 


Find the coefficient of x100 in the Taylor series for the rational function which has 


numerator 1 

and denominator


x41 - x40 - x36 + x35 -x31 + x30 + x26 - x25- x16 + x15 + x11 - x10 + x6 - x5 -x+1


For better readability see my pdf file with the problem in it here


Is there a clever way to do the problem?  If the way to do it was to actually do the Taylor series then 

1) I wouldn't post it

2) I probably could not do it (or it would take too long to bother)  though maybe there are freely available programs that could. 


So yes, there is a clever solution. At least I think it's clever. 



Wednesday, March 17, 2021

I read the news today oh boy



I'm absolutely elated that Lázló Lovász and Avi Wigderson won the Abel Prize. More from the New York Times, Quanta Magazine and Gil Kalai. Another example of how complexity theory and theoretical computer science has reached the upper echelons of mathematics.

I'm horrified of the spa shootings in Atlanta. I've driven by those spas many times when I lived there. 

I'm saddened by the closing of Mills College in Oakland, California. I lived in a dorm Berkeley rented at Mills College during my crazy year there.

I've got mixed emotions about the death of James Levine. What he did musically with the Metropolitan opera and orchestra was nothing short of incredible. What he did to the young people he abused is inexcusable. I remember watching a Met taped videocast of Die Walküre with my daughter, enjoying the production but telling her "Do you realize we are watching an opera composed by an anti-Semite and conducted by a child molester?"  Can you separate art from artist?

Monday, March 15, 2021

I didn't understand The Art Market before the NFT sale, and I understand it less now

 (This post is a sequel to my post from Feb 13, 2007 which you can find here. While the gap from 2007 until 2021 seems large, its not as long as the gap between Knuth Vol 3 and Knuth Vol 4, nor as long as the gap between Stan Freberg Vinyl Record History of America Part I and his CD History of America Part 2, both novelty records, and quite good.)

My 2017 post was about people posting a clip on youtube and calling it `rare footage of...' 


My point was: How can something be rare if its on you tube?

I also pondered: if someone can make a REALLY REALLY GOOD copy of the Mona Lisa, that is at talent that should be respected and such a person should be able to sell it for about the same price as the original (not sure if I want the copy to be worth A LOT or the original to be worth LESS than it is.)

IF Art is to-look-at-cause-its-pretty then it should not matter who the artist is. 

IF Art is an investment then that could be risky since it does not have intrinsic value. 

IF Art is neither to-look-at or an investment then... What is it? We'll see below that one answer might be Bragging Rights. 

This is NOT a RANT, this is an admitance of my lack of understanding. (Spell check things admitance is not a word. Maybe its admitence. No, Hmmm.) 

And now there is a new wrinkle in all of this: 

69 million for a NFT (Non-Fungable Token) of an art work:story here

1) What is the buyer getting? Bragging rights?

2) Can anyone SEE the art but doesn't OWN it? I don't know..

3) If someone hacked in and got a perfect copy of the art and posted it on a website, would that be theft? Nothing was taken. 

4) In the normal art world does it happen that prices go DOWN because people wake up and say WHAT? Why did I EVER think that White on White was worth 10 million dollars? 

5) Might this happen here also? 

6) Is My Feb 13 blog, which is in a diff format (or I didn't know how to use the blogger interface then) going to one day be worth something?


Friday, March 12, 2021

Cake Cutting in Overtime

There's a new proposal out of Baltimore for a new way to handle overtime in National Football League games. This post is about American Football, soccer has its own overtime issues we won't talk about here.

Instead of randomly choosing who gets the ball, which gives an advantage to the team on offense, the Raven's coach John Harbaugh suggests a "spot and choose" rule based on cake cutting. One team picks a starting position and the other team decides whether to be on offense or defense.

Sounds intriguing but there's a problem. In cake cutting, if you cut off a crumb, everyone would definitely choose the rest of the cake. But in football suppose the spotting team chose the offensive's team one-yard line (99 yards needed for a touchdown). For spot and choose to work the one-yard line would have to be an obvious choice for defense. But many teams might still choose starting at the one-year line on offense. There's a chance you can march down the field and if not you can always punt it away. So the team that gets to choose whether to be on offense could get an advantage no matter what the spotting team did.

I still like the idea of "spot and choose". Maybe you let the first team choose not only the yard line but what down to start. Because no one would start at their one yard line at 4th down.

Are there variations for spot and choose in other sports? I like using game theory to figure out how to play actual games. 

Sunday, March 07, 2021

When do I need to warn about Spoilers?

In a recent post here I mentioned in passing a plot point from the last season of The Big Bang Theory. Note that the last season was in 2019.  WARNING- do not read that post if you are watching The Big Bang Theory and do not want a plot point revealed. 

Someone who perhaps thinks Lance and I are the same person (are we? See here) left Lance a tweet complaining about the spoiler. At least I think they are complaining. The tweet is in Spanish and its here.

Either

1) Some country is two years behind America on showing The Big Bang Theory. 

2) The person who tweeted has them on DVR (or something like that) and is watching them a few years after they air (I watched Firefly on a DVD I borrowed from a friend 10 years after it went off he air. Ask your grandparents what a DVD used to be.) 

3) They are kidding us and making fun of the notion of spoilers.

This raises the question: When is it okay to post spoilers without warning? A few random thoughts:

1) ``Don't tell me who won the superb owl! I have it on tape and want to watch it without knowing who won!''  This always seemed odd to me.  Routing for events to happen that have already happened seems weird to me. When I was 10 years old I was in New York listening to a Knicks-Celtics Basketball game on the radio and during halftime I accidentally found a Boston radio station that had the game 30 minutes later (I did not realize that the channel I was on originally was 30 minutes behind). So I heard how the game ended, then switched back listening to a game knowing how it would end. I didn't route for my team (the Knicks, who lost) but it just felt very weird listening to it. If I had thought of it I might have noticed how the different broadcasts differ and got a paper out of the data, but as a 10 year old I was not thinking about how to pad my resume quite yet. 

2) I like seeing a mystery twice- first time I don't know who did it, second time I do but can look for clues I missed the first time.

3) I would have thought 2 years after a show is off the air its fine to spoil. But... maybe not.

4) It also matters how important the plot point is. I didn't think the plot point I revealed was that important. 

5) Many TV shows are predictable so I am not sure what `spoiler' even means. If I said to Darling:

 The bad guy is an unimportant character we meet in the first 10 minutes.

that does not show I've seen it before. It shows that I am a master of TV-logic.

6) With Arc TV shows this is more of a problem. While it was possible to spoil an episode (Captain Kir will survive but Ensign Red Shirt will bite the dust) it was impossible to spoil a long-term arc. TV has gotten to complicated. And I say that without having watched Game of Thrones. 



Sunday, February 28, 2021

Using number-of-PhD's as a measure of smartness is stupid.

In Thor:Ragnorak Bruce Banner mentions that he has 7 PhDs. Gee, I wonder how he managed to slip that into a conversation casually.  Later in the movie:


Bruce: I don't know how to fly one of those (it an Alien Spacecraft)

Thor: You're a scientist. Use one of your PhD's 

Bruce: None of them are for flying alien spaceships.


On the episode Double Date of Archer (Season 11, Episode 6) Gabrielle notes that she has 2 PhD's whereas Lana only has 1 PhD. 


I am sure there are other examples of a work of fiction using number of PhDs as a way to say that someone is smart. In reality the number of PhD's one has is... not really a thing. 

In reality if a scientist wants to do work in another field they... do work in that field.

Godel did research in Physics in the 1950's, but it would have been silly to go back and get a PhD in it.

Fortnow did research in Economics, but it would have been silly to go back and get a PhD in it. 

Amy Farrah Fowler worked in neurobiology and then in Physics. Her Nobel prize in physics (with Sheldon Cooper) is impressive, getting a PhD in Physics would be ... odd. Imagine someone looking at here resume: She has a Nobel Prize in Physics, but does she have a PhD? Did she pass her qualifying exams?  This is the flip side of what I mentioned in a prior post about PhD's: Not only does Dr. Doom want to take over the world, but his PhD is from The University of Latveria, which is not accredited. 

There are other examples.

There ARE some people who get two PhDs for reasons of job market or other such things. That's absolutely fine of course. However, I wonder if in the real world they brag about it. I doubt it. 

Is there anyone who has 3 PhDs? I would assume yes, but again, I wonder if they brag about it. Or should. 

WHY do TV and movies use number-of-PhDs as a sign of genius? I do not know- especially since there are BETTER ways say someone is a genius in a way the audience can understand:  number-of-Nobel-prizes, number-of-times-mentioned-in-complexityblog,  number of Dundie's (see here), etc. 








Thursday, February 25, 2021

Complexity is the Enemy of Speed

The title of this post came from an opinion piece in the Wall Street Journal yesterday on vaccine distribution. Many attempts to get the vaccines to the right groups first have slowed down distribution and sometime even caused vaccines to go to waste. Rules to help spread vaccines across minority groups often backfire. Often when some rules lead to inequity, we try to fix it with more rules when we need less much less. Attempts to distribute vaccines to multiple medical and pharmacy sites have made it difficult to get appointments even if you are eligible.

Randomness is the simplest way to fairness. The movie Contagion got it right, just choose birthdays by picking balls from a bin to distribute the vaccine. Then people can just show up at a few chosen sites with proof of birthday. No need to sign up.

You could argue to add back conditions like age, medical conditions, jobs but that just leads you down the same problematic path. The fastest way to get past this pandemic is to get vaccines into arms. Trust the randomness.

Monday, February 22, 2021

Good Names and Bad Names of Game Shows and theorems

 In my post on Alex Trebek, see here, I noted that Jeopardy! is not a good name for the game show since it doesn't tell you much about the show. Perhaps Answers and Questions is a better name.

The following game shows have names that tell you something about the game and hence have better names: 

Wheel of Fortune, The Price is Right, Lets make a Deal, Beautiful women have suitcases full of money (the original name for Deal-No Deal), Win Ben Stein's Money, Beat the Geeks. 

In Math we often name a concept  after a person. While this may be a good way to honor someone, the name does not tell us much about the concept and it leads to statements like:


A Calabi-Yau manifold is a compact complex Kahler manifold with a trivial first Chern class. 

A Kahler manifold is a Hermitian manifold for which the Hermitian form is closed.

A Hermitian manifold is the complex analog of the Riemann manifold. 

(These examples are from an article I will point to later---I do not understand any of these terms, though I once knew what a Riemann manifold was. I heard the term Kahler Manifold in the song Bohemian Gravity.  It's at about the 4 minute 30 second place.) 

While I am amused by the name Victoria Delfino Problems (probably the only realtor who has problems in math named after her, see my post here) it's not a descriptive way to name open problems in descriptive set theory. 


Sometimes  a name becomes SO connected to a concept that it IS descriptive, e.g.:

The first proof of VDW's theorem yields ACKERMAN-LIKE bounds. 

but you cannot count on that happening AND it is only descriptive to people already somewhat in the field. 


What to do? This article makes the  ballian point that we should   STOP DOING THIS and that the person who first proves the theorem should name it in a way that tells you something about the concept. I would agree. But this can still be hard to really do.


In my book on Muffin Mathematics (see here) I have a sequence of methods called

Floor Ceiling, Half, Mid, Interval, Easy-Buddy-Match, Hard-Buddy-Match, Gap, Train. 

There was one more method that I didn't quite name, but I used the phrase `Scott Muffin Problem' to honors Scott Huddleton who came up with the method, in my description of it. 

All but the last concept were given ballian names.  Even so, you would need to read the book to see why the names make sense. Still, that would be easier than trying to figure out what a Calabi-Yau manifold is. 



Sunday, February 14, 2021

Two examples of Journalists being... Wrong. One BIG one small

 Journalists sometimes get things wrong.

This is not news, but it is interesting when you KNOW they are wrong. 

1) Scott Aaronson has a GREAT example regarding an IMPORTANT story. I recommend you to read his blog post here. Most of the comments are good also, though they go off on some tangents (e.g., is the Universal Basic Income a progressive idea?)


2) I have my own example. It is far less important than the one Scott discusses; however, inspired by Scott, I will discuss it. My example also involves Scott, but that's a coincidence. 

Quanta Magazine emailed me that they wanted to talk to me about an upcoming article on The Busy Beaver Problem. Why me? Because Scott's (same Scott as above!) survey/open problems column appeared in the SIGACT News Open Problem Column that I edit. 

This sounded fine (Spoiler Alert: It was fine, the errors they made were odd, not harmful).

Here is the Quanta Article (though I do not know if it is behind paywalls- I can never tell if I am getting access because I have a UMCP account of or anyone can have access or if I am breaking copyright laws by posting the link):    here

Here is Scotts article: here

The interviewer asked me 

a) Why did I ask Scott to write the article?

ANSWER: He had a blog post on it, and I was skeptical of why these numbers are interesting, so I asked a question in the comments. He gave a great answer, so I asked him if he wanted to write a column for my open problems column. Actually I asked him if either he or perhaps a grad student would do it- I assumed he would be too busy since his `day job' is quantum  computing. However, much to my surprise and delight he said YES he would do it.

b) Is the Busy Beaver Function important?

ANSWER: In my opinion the actual numbers are not that important but its really neat that (a) we know some of them, and (b) they are far smaller than I would have thought. Also these numbers are interesting for the following reason:  there is some  n so that proving 

BB(n)=whatever it equals

 is Ind of Peano Arithmetic. When I hear that I think the number must be really large. Its not. Its 27. NEAT! And stronger theories are related to bigger numbers. This is a way to order theories. For  ZF they have something in the 700's- MUCH SMALLER than I would have thought. Scott and others can even relate BB to open problems in Math! 

There were some other questions also, but I don't recall what they were. 

SO when the article came they mentioned me once, and its... not quite wrong but odd:

William Gasarch, a computer science professor at the University of Maryland College Park,

said he's less intrigued by the prospect of pinning down the Busy Beaver numbers than by 

``the general concept that its actually uncomputable.'' He and other mathematicians are mainly interested in using the yardstick for gauging the difficulty of important open problems in mathematics--or for figuring out what is mathematically knowable at all. 


The oddest thing about the paragraph is they do not mention my connection to Scott and the article he wrote! I reread the article looking for something like `Scotts article appeared in the SIGACT News Open Problems column edited by William Gasarch' Nothing of that sort appears. 

Without that its not clear why they are soliciting my opinion. My colleague Clyde says this is GOOD:  people will ASSUME I am some sort of expert. Am I an expert? I proofread Scott's paper so... there is that...

Also I come off as more down on BB than I really am. 

Did I claim that Mathematicians are more interested in using it as a yardstick. Actually I may have said something like that. I don't know if its true. That's my bad- I should have said that I am interested in that.

After the article came out I asked the interviewer why my role was not in the article. He said it was cut by the editor. 

NOW- NONE of this is important, but even on small and easily correctable things, they get it wrong. So imagine what happens on hard issues that are harder to get right. 


MISC: One comment on Scott's blog was about the Gell-Mann amnesia effect, see this article on it:

here


Sunday, February 07, 2021

The Victoria Delfino Problems: an example of math problems named after a non-mathematician

 If you Google Victoria Delfino you will find that she is a real estate agent in LA (well, one of the Victoria Delfino's you find is such).  After this blog is posted you may well get this post on the first Google page. 

If you Google Victoria Delfino Problems you will find a paper:

The fourteen Victoria Delfino Problems and their Status in the year 2015

(ADDED LATER: a comment pointed me to an updated version, so  you can see that- I got to a pay wall.) 

How did a real estate agent get honored by having 14 problems in descriptive set theory named after her?

Possibilities before I tell you which one.

1) Real estate is her day job. Her hobby is Descriptive Set Theory. Recall that Fermat was a lawyer (or something like that- see his Wikipedia page) so perhaps she is similar. Doubtful- I think math is too hard for that now.  Or at least descriptive  set theory is too hard for that now. 

2) She just happened to remark one day, Gee, I wonder if

 ZFC + SEP(Sigma_3^1) + #   implies DET(Delta_2^1). 

Its just the kind of thing someone might just say. That was problem 4 of the 14. 

3) There are two Victoria Delfino's- one is a realtor, one is a mathematician. While plausible, that would not be worth blogging about. 

4) And now the truth: Victoria was the realtor who helped Moschovakis (a descriptive set theorist who I will henceforth describe as M) buy his house. When Tony Martin (another Desc. Set Theorist) moved to UCLA, M referred him to Victoria and she did indeed help Tony find a house. Victoria gave M a large commission which he tried to turn down. She did not want it returned, so M used the money to fund five problems. Later problems were added, but for no money. The article The Fourteen... linked to above has the full story. It also has the curious line: 

Contrary to popular belief, no monetary prize is attached to further problems. 

I didn't think any of this was so well known as to have popular believes. 

ANYWAY, this is an example of a math problem named after a non-math person. Are there others? Will the name stick? Probably not- already 12 of the 14 are solved. I have noted in a prior blog (here) once a conjecture gets proven, the one who made the conjecture gets forgotten. Or in this case the person who the conjectures is named after. 

So are there other open problems in math named after non-math people? How about Theorems?

Near Misses: 

Pythagoras: Not clear what he had to do with the theorem that bears his name. 

L'hopital's Rule: the story could be a blog in itself, and in fact it is! Not mind, but someone else: here. However L'hopital was a mathematician. 

Sheldon's conjecture (see here) was named after a FICTIONAL physicist. Note that Sheldon inspired the conjecture but did not make it. It has been solved. 

The Governor's  Theorem (see here) was named because Jeb Bush was asked for the angles of a 3-4-5 right triangle (not a fair question). 

The Monty Hall Paradox.

SO- are there Open Problems, Theorems, Lemmas, any math concepts, named after non-math people? I really mean non-STEM people. If a Physicist or an Engineer or a Chemist or Biologist or...  has their name on something, that would not really be what I want.

(ADDED LATER - someone emailed me two oddly-named math things:

Belphegor's prime, see here

Morrie's law- odd since Morrie is the FIRST name of who the name is honoring, see here 

)


Are there any other open problems in descriptive set theory  named after realtors?




Wednesday, February 03, 2021

A Blood Donation Puzzle

In the US you can donate whole blood every eight weeks. Suppose Elvira does exactly that. Will she hit every date of the year? For example, if Elvira gave blood today, will she in some future year give blood on the 4th of July? Can we figure it out without having to rely on a computer simulation or even a calculator?

Let's make the assumptions that the blood center is open every day and that Elvira gives blood exactly every 56 days for eternity. 

A year has 365 days which is relatively prime to 56=23*7 since 365 mod 2 =1 and 365 mod 7 = 1. By the Chinese remainder theorem her next 365 blood donations will be on 365 distinct dates. If Elvira started giving blood at age 17, she will have hit every date at age 73.

That was easy but wrong. We have to account for those pesky leap years.

In a four year span, there will be one leap day. The total days in four years (using modular arithmetic) will still be odd and 5 mod 7, so still relatively prime to 56. So Elvira will donate on every day on the calendar exactly four times, except February 29th which she will hit once, over a period 56*4=224 years. 

Alas not quite. Years ending 00 are not leap years, unless the year is divisible by 400. 2000 was a leap year but 2100 won't be. Any stretch of 224 years will hit at least one of those 00 non-leap years.

In 400 years, there will be 97 leap years. Since a regular year is 1 mod 7 days and a leap year is 2 mod 7 days, 400 years will be 497 mod 7 days. Since 497=71*7, 400 years has a multiple of 7 days. Every 400 years we have exactly the same calendar. February 3, 2421 is also a Wednesday.

The cycle of blood donations will repeat every 3200 years, the number of years in the least common multiple of 56 and the odd multiple of seven number of days in 400 years. But we can no longer directly apply the Chinese remainder theorem and argue that every day of the year will be hit. In those 3200 years Elvira will have over 20,000 blood donations. If the dates were chosen randomly the expected number to hit all dates would be 2372 by coupon collector. So one would expect Elvira would hit every day, but that's not a proof.

So I had to dust off my Python skills and do the computer simulation after all. No matter what day Elvira starts donating she will eventually hit every date of the year. If Elvira starts donating today, she would give blood on the 4th of July for the first time in 2035 and hit all dates on January 8, 2087 after 431 donations. The longest sequence is 3235 donations starting April 25, 2140 and hitting all dates on February 29, 2636.

Sunday, January 31, 2021

Grading policies during Covid-No easy answers

 Because of COVID  (my spellecheck says covid and Covid are not words, but COVID is) various schools have done various things to make school less traumatic. Students already have problems, either getting COVID or having their friends got family get it (I've had four relatives get it, and one died) . Some do not adjust to learning online.  Some do not have good computer connection to learn on line. So what is a good policy? Here are some things I have either seen schools do or heard that they might do.


1) Be more generous with Tuition-Refunds if a student has to withdraw. 

2) Be more generous with Housing-Refunds if a students comes to campus thinking it will be courses on campus and there are no courses on campus. Or if a student has to withdraw. 

3) Make the deadlines for dropping-without-a-W, or taking-it-pass-fail, later in the semester. 

4) Tell the teachers to `just teach them the bare min they need for the next course.'

5) Allow students to take courses P/F in their major and still allow them to count, so a student might get a D in Discrete Math and be able to go on in the major. 

6) How far to extend deadlines? How is this: extend deadline to make it P/F until the last day of classes (but before the final) and then after the final is given, the school changes its mind and says - OH, you can change to P/F now if you want to.

7) Allow either an absolute number (say 7) or a fraction (say 1/3) of the courses to be changed to P/F by the last day of class.

8) Combine 6 or 7 with saying NO- a D is an F for a P/F course. Perhaps only if its in the major, but that maybe hard to work out. since majors can change. Some schools do A-B-C-NO CREDIT, where the NC grade does not go into the GPA.

9) Give standard letter grades and tell the students to tough it out. Recall the following inspirational quotes

When the going gets tough, the tough go shopping

When the going gets tough, the tough take a nap

If at first you don't succeed, quit. Why make a damn fool of yourself. 

If at first you don't succeed, then skydiving is not for you. 

10) Decide later in the term what to do depending on who yells the loudest. 

11) Any combination of the above that makes sense, and even some that don't. 


On the one hand, there are students who are going through very hard times because of COVID and should be given a break. On the other hand, we want to give people a good education and give grades that are meaningful (the logic of how to give grades in normal times is another issue for another blog post). 

What is your school doing? Is it working? What does it mean to be working?

The problems I am talking about are first-world problems or even champagne-problems. I know there are people who have far worse problems then getting a bad grade or dropping courses.


Thursday, January 28, 2021

PhDs and Green Cards

Joe Biden's immigration policy has some interesting policies for PhDs. 

Biden will exempt from any cap recent graduates of PhD programs in STEM fields in the U.S. who are poised to make some of the most important contributions to the world economy. Biden believes that foreign graduates of a U.S. doctoral program should be given a green card with their degree and that losing these highly trained workers to foreign economies is a disservice to our own economic competitiveness. 

Biden will submit an immigration plan to congress soon but it is not clear if the above will be in the bill, whether it will survive negotiations or even whether an immigration bill will be passed at all. 

Nevertheless I worry about the unintended consequences of this policy. It will encourage students to apply and come for a PhD who have no interest in research, but want the green card. It gives too much power to professors who may abuse their students who need the PhD. Conversely it will pressure professors and thesis committees to grant PhDs because there would be a big difference between graduating with a PhD and leaving early with a Masters. By making the PhD so valuable, we may devalue it.

The solution is to give green cards to Masters students as well. We shouldn't limit talented researchers and developers who can help the United States keep its technology edge. They don't take jobs away from Americans, but instead help create new ones.

Tuesday, January 26, 2021

Answers to the Prez Quiz, and some interesting history


I posted a presidential quiz (that is, a quiz about presidents, not a quiz that is so majestic it can be called presidential) on Thursday Jan 21.

Here is the link to the post: The Post

Here is the link to the quiz:The Prez Quiz

 I now post the answers here: The Prez Quiz Answers


Looking back at the quiz and some prior ones I realize that some questions are TRIVIA while others are not- that is- they tell us something interesting beyond the answer. Some thoughts on that: 


a) Asking who the oldest prez ever has to be better defined. But however you define it, the answer is Joltin Joe. I will ask it as Age-when-sworn-in, which for Joltin Joe is 78. Second is Trump who was 70 when sworn in.  INFO: Presidents seem to be getting older. Is this a trend or will 2024 and 2028 feature younger folks? I note that both VP's are in their 50's. 

b) Presidential first via xkcd; here

c) Between Nixon-Kennedy 1960 and Bush-Kerry 2004 EVERY election had one of he candidates being either a former or current Prez or Vice Prez.  (This was a question on the 2008 quiz, but since the streak is broken it is no longer as interesting.) INFO: It was hard to break into the prez business unless you were already somewhat known. Having said that, note that some of the non-VPs and non-Prezs DID win. 

d) Between 1948 and 2008 at least one of the candidates for Prez had served in the Military. How did they do? In many cases both served so I am not going to to a chart of how well the Military ones did. (This was a question on the 2012 quiz, but since the streak is broken it is no longer interesting.) INFO: At one time a lot of people were in the military. At one time a lot of people knew someone in the military. Now it seems like the military is rather far removed from civilians. 

e) Kennedy was our first Catholic Prez in 1960. Biden is our second one in 2020. My impression is that it was an issue for the Kennedy Campaign but not for the Biden campaign. Romney being a Mormon seems to have not been an issue in the General election, but some of the other candidates brought it up in the primaries. INFO: Religious bigotry within different denominations of Christianity is declining. 

f) Reagan was our first divorced Prez, in 1980. Trump was our second in 2016. It don't think it was  an issue for either one. INFO: We need to couple this with Rockefellers divorce being a problem for him getting the nomination in 1964. Peoples attitude on divorce has changed A LOT. 


Contrast: Knowing which president had a fictional street gang named after him  does not tell us anything about History .I will remove that question when I do the quiz in 2025. 













Friday, January 22, 2021

Alan Selman (1941-2021)

From a 1994 Dagstuhl Workshop. Selman is the one wearing a cap.
Alan Selman, one of the early leaders in structural complexity and the co-founder and first chair of what is now the Computational Complexity Conference, passed away this morning. He was one of the true greats in our field both for his research and his service.

Selman was a good colleague and a friend. I hosted his sabbatical at the University of Chicago in 1998 which produced a paper with Selman's student and my later postdoc Pavan Aduri. In Spring of 1999 Selman ran a NSF workshop in Chicago on Challenges for Theory of Computing.

In a desire to create a community of complexity theorists and foster publications of their results, Selman led the efforts to establish the Structure in Complexity Theory conference, first held in 1986 in Berkeley, California. As a student in Berkeley I attended that meeting and the next twenty-five. The conference would join the IEEE in 1987, in 1996 renamed the IEEE Conference and Computational Complexity and in 2015 drop from the IEEE to become the Computational Complexity Conference, still going strong. Alan served as the first conference chair and as PC co-chair of the first meeting. 

For all his service for the field, Selman received the ACM SIGACT Distinguished Service Award in 2002.

Selman joined University at Buffalo in 1990 to serve six years as department chair and then as a professor until he retired in 2014. Lane Hemaspaandra wrote a highly recommended appreciation for Selman and his research in honor of his retirement where he mentions some of Selman's research programs, including his seminal work on P-Selective sets, non-deterministic functions and his work with Joachim Grollman on one-way functions. Selman came down hard on anyone who got the wrong number of l's in Grollman, so we would often joking cite it as Grollman and Sellman or just Grollman et Al.

In my favorite Selman paper, in work with Hemaspaandra, Ashish Naik and Mitsu Ogihara, looks at witness reduction. If there is a set A in P such that for all satisfiable formula φ there is a unique satisfying assignment a of φ such that (φ,a) is in A then the polynomial-time hierarchy collapses. The more general question of whether NP=UP implies the polynomial-time hierarchy collapses remains open.

Also Selman's paper with Steve Homer giving an oracle where Σ2P-complete sets were isomorphic was instrumental to my own work on the isomorphism conjecture.

Bill wanted me to mention the Selman paper that most influenced him. Selman and Theodore Baker and gave the first oracle separating the second level of the polynomial-time hierarchy in 1979. It would take Yao and Håstad over five more years to get the whole hierarchy infinite relative to an oracle. The Baker-Selman proof could easily extend to show that AM games did not sit in Σ2P, a bit surprising as MA is in Σ2P.

In addition to his research, Selman wrote an introductory theory textbook with Homer as well as editor and co-editor of two editions of Complexity Theory Retrospective.

It would be no exaggeration to say the field of computational complexity and my own research within it would have been much different without Alan.

Alan drove a car with a "P NE NP" license plate. One day someone came up to him in a parking lot and said "Yes, but can you prove it?" Possibly the one thing in complexity he couldn't do.

Thursday, January 21, 2021

Presidential Quiz: Three ways to take it

 Every four years around the time of the inaugural I post a presidential Quiz! I do that today, and I will post the answers on Monday.  I am tempted to joke that I am posting it AFTER Joltin Joe gets sworn in just in case something happens; however, I always posted it after the prez is sworn in. 

The quiz is here: quiz

 GRADING CRITERIA

33 questions, 3 points each, and 1 free point.

If the answer is a list of L elts and you get x correct, you get x/L points. If any are wrong then 0 points.

You can take the quiz one of three ways.

1) Take it WITHOUT using the web and see how many you can get right. Take 3 hours.

WARNING- its a hard quiz so this may not be fun. 

2) Take it and use the web and try to do it fast. Stop when you want. Your Score is as follows:

If  R is the number if points and  T be how many minutes you took,  your score is 

 (180R/T)+ 1.

If  you get all 33 right in 60 minutes then you get a 100. You could get more than 100 if you do it faster.

3) The answer key has all kinds of other information in it and is fun to read. So do not take the quiz and enjoy  reading the answers on Monday. That's what I did. 


I was curious if Joltin Joe would be sworn in by Joseph or Joe. I was routing for Joe so he would be the second president sworn in by his nickname (Jimmy Carter was the first--his real name is James). When I am sworn in as president I will use Bill and hence join the nickname-club. Lance does not have a nickname, so my veep will be sworn in by his actual name. Would we win? Is  America ready for a 2-Phd ticket? 






Tuesday, January 19, 2021

The Ethics Board

Back in 2014 I recommended a TCS ethics board mainly to deal with plagiarism and who should get credit for a result. It went the way of most suggestions I make in my blog, a quick road to nowhere. Bill asked "Does any other branch of CS have an ethics board? How have they worked?"

The NeurIPS conference created a such a board for the reviewing process, though with a broader mission.

We appointed an ethics advisor and invited a pool of 22 ethics reviewers (listed here) with expertise in fields such as AI policy, fairness and transparency, and ethics and machine learning. Reviewers could flag papers for ethical concerns, such as submissions with undue risk of harm or methods that might increase unfair bias through improper use of data, etc. Papers that received strong technical reviews yet were flagged for ethical reasons were assessed by the pool of ethics reviewers.

Thirteen papers met these criteria and received ethics reviews. Only four papers were rejected because of ethical considerations, after a thorough assessment that included the original technical reviewers, the area chair, the senior area chair and also the program chairs. Seven papers flagged for ethical concerns were conditionally accepted, meaning that the final decision is pending the assessment of the area chair once the camera ready version is submitted. Some of these papers require a thorough revision of the broader impact section to include a clearer discussion of potential risks and mitigations, and others require changes to the submission such as the removal of problematic datasets. Overall, we believe that the ethics review was a successful and important addition to the review process. Though only a small fraction of papers received detailed ethical assessments, the issues they presented were important and complex and deserved the extended consideration. In addition, we were very happy with the high quality of the assessments offered by the ethics reviewers, and the area chairs and senior area chairs also appreciated the additional feedback.

Without seeing the process I cannot say what criteria were used to reject the four papers. There could be legitimate reasons if the authors did violate professional ethics or even inadvertently based their results on biased data sets. But there's a fine line to rejecting papers because you don't like the outcome or the questions they ask. No easy answers here.

Sunday, January 10, 2021

The ACM History Committee call for proposals looks wrong

 In November I (and prob everyone in the ACM) got an email that was a call for proposal from the ACM History committee. Here is a pointer to it. 

One of the passages in it just seems wrong to me:

This fellowship program is designed to support research and/or curatorial projects related to ACM's professional and educational activities and/or to ACM's rich institutional history including its organization, SIG activities, and conferences. 

I will give  examples of history projects that are interesting but do not fit the description. I challenge you to give me a history project that is interesting that does fit the bill. 

1) Compare and contrast how NP-completeness developed in America and in the USSR. For the USSR side it would be an expansion of  Trakhtenbrot's article here. OH, no good, Leonid Levin was not a member of the ACM.

2) Measure how various CS fields have changed by looking at the topics on the CALL FOR PAPERS for a conference. This would be a MASSIVE expansion of my blog post on how CCC call for papers, changed , see here. OH, I could only do ACM conferences. STOC but not FOCS. Okay, it makes perfect sense to study only ACM conference. Oh wait. IT MAKES NO SENSE WHATSOEVER.

3) When did mathematicians begin looking at P vs NP seriously? (e.g.,  In  The Handbook of Mathematical Logic from 1977 only one article mentions P vs NP: Michael Rabin's article on Decidable theories mentioned that even decidable theories may take a long time to decide and noted the importance of the P vs NP problem). How did MATH and CS  interact early on and now? This would need  one to look at math journals. How many of those are ACM? I would guess very few. 

4) When did engineers begin looking at P vs NP seriously, or even notice it? Same issue as the last item. 

5) Looking at how Programming lang design has changed one would have to only look at conference and journals that were ACM. And for those that were ACM but then dropped ACM you might only be able to use them up to the cutoff year. 

6) Which academic studies eventually lead to practical products people can use? This is a really broad topic so one could narrow it down to just academic studies that appeared in ACM journals or conferences. Is that a good way to narrow the focus? Spoiler alert: NO.

7) I recently filled out a survey about the future of theory and if it is insular (the topic of another post surely). Most of the questions were about ``STOC-FOCS'' The people who did the survey clearly do not care that one is ACM and one is IEEE. Does anyone? I ask non-rhetorically. 

Despite the capitol letters, I am not so much mad as puzzled. So I ask non-rhetorically: 

Q1) Did the ACM really mean for people to do history in a way where you can only use ACM materials? 

Q2) If no then please rewrite the Call for Proposals. 

Q3) If yes then give examples of studies that would be interesting. 

I am not asking to be snarky, I really want to know. And I note that interesting is subjective. 

(ADDED LATER- two historians who have worked with this kind of history left comments that indicate the grant is FINE with non-ACM stuff, so Q1 above seems to have the answer NO. Given that they should rewrite the call for proposal next time they do this. ALSO- the historians left pointers to VERY INTERESTING papers they wrote.) 



Tuesday, January 05, 2021

My Survey on Hilbert's 10th for particular (d,n) is ready for you to help me on!

 Hilbert's 10th problem is  (in modern terminology) to find an algorithm that will, given a poly 

p(x1,...,xn) in Z[x1,...,xn], determine if it has a solution in the integers. 

This was shown undecidable by the combined efforts of Davis-Putnam-Robinson and Matiyasevich. 

I posted here about the question of: For which (d,n) is H10 undecidable when restricted to degree d and number of vars n?

I was  invited to make an article out of the blog post and what I learned from the comments  for  the Algorithms column of BEATCS. That first draft is

here


Did I miss an important reference? (Note- I had meant to get out Matiyasevich's book on H10 but have been unable to because of the Pandemic, so if you have it my have stuff I need to know.) 

Did I misspell Matiyasevich? 

Did I say something stupid?

Please leave comments or email me directly if you have suggestions. 

Incidentally I am usually the one who is asking someone else to do an open problems column, a book review, a guest blog. Nice to be the askee instead of the asker for a change of pace.