Emerging from the Pandemic

The City of Chicago yesterday agreed with the latest CDC guidelines that those of us fully vaccinated no longer have to wear masks in most settings. Lollapalooza, the big Chicago music festival, will be held in full capacity this summer. There are still some restrictions but barring any surprise setbacks should be mostly gone by the Fourth of July.

It's not appropriate to call the pandemic over. Too many countries are suffering and lack good access to vaccines or strong health care. But in most of the US vaccinations are readily available and it really feels like we are putting the pandemic in the past.

Variants that beat the vaccines could emerge. Vaccines could become ineffective over time. Too many still need to be vaccinated and too many don't want to do so. Typically problems start small and quickly get big by exponential growth but likely with enough warning if we need boosters or extra precautions. And all those who cut in line to get shots early are now my canaries for the effects wearing off.

What will this post-pandemic world look like? Continued virtual meetings from people who don't want to spend the 10-15 minutes to get across campus or to come to campus at all. A bigger move to casual dress, even in the corporate world. No more snow days. Changes in ways we won't expect. 

We all have our different attitudes but I'm ready to move on. Time to start the "after times".

Why do countries and companies invest their own money (or is it?) in Quantum Computing (Non-Rhetorical)

 There have been some recent blog posts by Scott (see here) and Lance (see here)  about the hype for SHORT TERM APPLICATIONS of Quantum Computing, which they both object to. 

I have a question that has been touched on but I want to get it more out there.

PREAMBLE TO QUESTION:  The following scenarios, while distasteful, do make sense: 

a) A researcher on their grants exaggerates or even out-right lies about the applications of their work. 

b) A journalist in their articles exaggerates or even out-right lies about the applications of the science they are covering.

c) A company exaggerates or even out-right lies about the applications of their project to a venture capitalist or other kind of investor. 

QUESTION: 

Why does a company or country invest THEIR OWN MONEY into Quantum Computing which is unlikely to have a short term profit or benefit? Presumably they hire honest scientists to tell them the limits of the applications in the short term. 

ANSWERS I HAVE GOTTEN FROM ASKING THIS

1) QC might be able to do something cool and profitable, like factoring, or simulating physics quantum experiments or something else, in the short term. Quantum Crypto is already happening, and that's a close cousin of Quantum Computing. 

2) QC might be able to do something cool and profitable (like in (1)) in the long term, and both companies and countries think they will be around for a long time. (For a list of America's 10 oldest companies see here.) 

3) The company or country is in this for the long term, not for a practical project, but because they realize that doing GOOD SCIENCE is of a general benefit (this might make more sense for a country than a company). And funding Quantum Computing is great for science. 

4) Bait and Switch: The company claims they are doing Quantum to attract very smart people to work with them, and then have those smart people do something else.

5) (this is a variant of 1) While Quantum Computing may not have any short term applications, there will be classical applications INSPIRED by it (this has already happened, see here).

6) Some of these companies make money by applying for GRANTS to do QC, so its NOT their money. In fact, they are using QC to  GET money.

7) For a country its not the leaders money, its that Taxpayer's money- though that still leaves the question of why spend Taxpayer money on this and not on something else.

8) For a company its not their money- its Venture Capitalists  and others (though for a big company like Google I would think it IS their money). 

9) The scientists advising the company or country are giving them bad (or at least self-serving) advice so that those scientists can profit- and do good science. So this is a variant of (3) but without the company or country knowing it. 

10) In some countries and companies group-think sets in, so if the leader (who perhaps is not a scientist) thinks intuitively that QC is good, the scientists who work for them, who know better, choose to not speak up, or else they would lose their jobs...or worse. 

11) For countries this could be like going to the moon: Country A wants to beat Country B to the moon for bragging rights. Scientists get to do good research even if they don't care about bragging rights. 

12) (similar to 11 but for a company) If a company does great work on QC then it is good publicity for that company. 

13) Some variant of the greater fool theory. If so, will there be a bubble? A bail-out? 

Cryptocurrency, Blockchains and NFTs

 I first wrote about bitcoin in this blog ten years ago after I gave a lecture in a cryptography class I taught at Northwestern. Two years later I had a follow-up post, noting the price moved from $3 to $1000 with a market cap of about $11 Billion. My brother who thought they were a scam back then has since become a cryptocurrency convert. The bitcoin market cap is now over a trillion dollars and other cryptocurrencies are not far behind. No longer can we view cryptocurrencies as simply a neat exercise in applied cryptography now that it has serious value.

The main uses of cryptocurrencies are for speculation or illegal activities, such as drug sales, ransoms, money laundering and tax evasion. Sure you can buy a Tesla with bitcoins but that's more of a gimmick. Cryptocurrency spending is simply too slow, expensive and volatile right now to replace other methods of electronic payment. 

Non-fungible tokens (NFTs) truly puzzle me. They are just a digital certificate of authentication. What could you do with them you couldn't do with docusign? Collectibles of publicly available digital goods is a fad already fading.

I'm not a fan of a fiat currency governed by strict rules not under governmental control. Bad things could happen. However thinking of cryptocurrencies and the blockchain technology that underlies them have brought up real needs for our digital world.

• An easy way to pay online without significant fees, expenses or energy consumption.
• An easy and cheap way to transfer money between different countries.
• A distributed database to allow tracking of supply chains, credentials and financial transactions for example. I see less a need to make these databases decentralized.
• A need, for some, to have a digital replacement for the anonymity of cash.
• People need something to believe in once they have given up believing in religion and a functioning democracy. 

Don't change your investing habits based on anything I write in this post. Speculation and illegal activities are powerful forces. Or it could all collapse. Make your bets, or don't.

Note: Since I wrote this post yesterday, Elon Musk tweeted that Tesla will no longer accept bitcoins, and the bitcoin market cap has dropped below a trillion.

Trump, Facebook, and ComplexityBlog

 I care about the Facebook decision to ban Trump, but I do not have a strong opinion about it. I have heard arguments on both sides now, from up and down, and still somehow... I don't know how I feel. So instead of posting my opinion I post other opinions and my opinion of them.

1) Facebook is a private company. If they want to have liberal bias or a free for all or whatever then  it is not the governments place to interfere. If enough people don't like what they see then they will lose customers. The invisible hand of the market will regulate it enough. Libertarians and honest small-gov republicans might believe this. On a personal level, I don't want someone else telling Lance and I that we can't block some comment; however, for now, more people use Facebook then read Complexity Blog. 

2) Facebook is a private company but they need to follow standard business practices of having their uses sign an agreement and stick to it. Since the user signed the agreement, Facebook need only stick to that agreement. This is problematic in that (1) if the agreement is not that rigorous then Facebook can be arbitrary and capricious, but (2) if the agreement is to rigorous then people can game the system. Imagine if Lance and me had  rule that you could not use profanity in the comments. Then someone could comment 

People who think P vs NP is ind of ZFC can go Fortnow themselves. They are so full of Gasarch.

 (Something like this was the subplot of an episode of The Good Fight)

3) Facebook is so big that it has an obligation to let many voices be heard, within reason. This could lead to contradictions and confusions:

a) Facebook cannot ban political actors. What is a political actor? (Jon Voight is pro-trump and Dwayne ``The Rock'' Johnson is anti-trump, but that's not what I mean.) High level people in the two main parties qualify (how high level?). IMHO third parties (Libertarian and Green come to mind) need the most protection since they don't have as many other ways to get out their message and they are serious. (I wonder if Libertarians would object to the Government  forcing Facebook to not ban them). What about the Surprise Party or the Birthday Party (which did have a platform see here). And what about people running for Mayors of small towns (much easier to do now with Facebook)? Should just running be enough to ban banning? 

b) Facebook can ban posts that are a threat to public health and safety. I am thinking of anti-vaxers and insurrectionists, though I am always wary of making them free speech martyrs. 

c) Fortunately a and b above have never conflicted. But they could. I can imagine a president who has lost an election urging his followers to storm the capitol. Then what should Facebook do?  (ADDED LATER- A commenter points to a case where a and b conflicted that is not the obvious case.) 

4) Facebook is so big that it has an obligation to block posts that put people in danger. This may have some of the same problems as point 3---who decides? 

5)  Facebook is so big and controls so much of the discourse that it should be heavily regulated (perhaps like a utility).  This has some of the same problems as above- who decides how to regulate it and how?

6) As a country we want to encourage free speech and a diversity of viewpoints. There are times when blocking someone from posting may be better for free speech then letting them talk. When? When that person is advocating nonsensical views that stifle the public discussion. But I am talking about what the country should want. What do they want? What does Facebook want? Does either entity even know what they want? These are all ill defined questions. 

7) Facebook is a monopoly so use Anti-Trust laws on it. Anti-Trust was originally intended to protect the consumer from price-gouging. Since Facebook is free this would require a new interpretation of antitrust. Judicial activism? The Justices solving a problem that the elected branches of government are currently unable to solve? Is that a bad precedent? What does it mean to break up Facebook anyway--- its a network and hence breaking it up probably doesn't make sense (maybe use MaxCut). 

(ADDED LATER- a commenter pointed out that anti-trust is NOT just for consumer protection, but also about market manipulation to kill small innovators.) 

8) Lets say that Facebook and Society and the Government and... whoever, finally agree on some sort of standards. Then we're done! Not so fast. Facebook is so vast that it would be hard to monitor everything. 

9) As a side note- because Facebook and Twitter have banned or tagged some kinds of speech or even some people, there have been some alternative platforms set up. They always claim that they are PRO FREE SPEECH. Do liberals post on those sites? Do those sights  ban anyone? Do they have SOME rules of discourse? I ask non rhetorically. 

Negotiations

So you got an offer to be an assistant professor in the computer science department at Prestigious U. Congratulations! 

Time to negotiate your offer with the chair. Don't be nervous. This shouldn't be adversarial. Both of you have the same goal in mind--for you to come to Prestigious and be successful. 

Let's discuss the different aspects of each package.

Research 

Funds for supporting your research such as equipment, graduate student support, travel and postdocs. Here you should explain what you need to be successful. This will vary by subdiscipline, a systems researcher will need more equipment and students than a theorist. Keep in mind the university is giving you funds for 2-4 years to start your research, after which you are expected to fund your own research via grants.

I don't recommend taking on a postdoc right at the start of your first academic appointment. Postdocs require good mentoring while you need to spend the first year getting your research up and running. If you do ask for postdoc money, ask to have a flexible start time.

Many departments give course reductions to get your research going. I'd suggest asking to spend your first semester teaching a graduate topics course based on your thesis research to pick up some PhD students followed by a semester with no classes to get you research program going.

Salary

This includes actual salary, which is also the base for future raises, and summer salary in the first couple of years. Feel free to ask for more salary, but often these numbers are fixed for new assistant professors. There is more give if you take an academic job later in your career. You could also say something like, "Well if you can't give me more salary maybe you could give me another semester of grad student support?"

Partner

It seems 80% of the time, a job candidate has a partner that needs accommodating. Don't wait until the end of negotiations, bring it up early. The more time we have, the better we can help. Doesn't matter what job they want--we know people and we know people who know people.

Thesis

Many schools won't hire you as an assistant professor if you haven't finished your thesis. Has to do with college rankings work. Don't worry--they will generally give you some other role with the same package until you finish. This might delay your tenure clock though.

Delayed start time

A January start is usually fine with good reason but if you weren't planning to start until the fall of 2022 why are you on the market this year? If you do get the department to hold a position for you, remember you are also making a commitment--this is not an opportunity to try again for something better.

Overall

You may not get all that you want after a negotiation--don't take it personally. You shouldn't necessarily choose the place that gives you the biggest package. It's far more important in the long run that you pick a place where you can best succeed both professionally and personally, and the package is just a small piece of that puzzle.

The Mythical Man-Month, Hen-Day, and Cat-Minute (Fred Brooks Turned 90)

 (Added later: Fred Brooks passed away on November 7, 2022, at the age of 90.)

The Mythical Man-Month is a great book which talks about the (obvious in retrospect) fact that putting more people on a project may slow it down. It was by Fred Brooks who turned 90 in April (he is still alive). It's a good read. I actually read it many years ago when I exchanged books with a Software Engineer I was dating- She lent me The Mythical Man Month which I found interesting, and I lent her What is the name of this book by Smullyan which she found amusing. Did this exchange of books help our relationship? We have now been married for many years, though its not clear if we can trace this to the exchange of books OR to the fact that she had KNUTH Volumes 1 and 3, and I had KNUTH Volume 2. 

 Fred Brooks: You have my thanks and of course Happy Birthday!

When I read The Mythical Man-Month  I was reminded of a math problem I heard as a kid: 

If a hen-and-half lays an egg-and-a-half in a day-and-a-half then how many eggs can seven hen lay in seven days? 

My answer: if (3/2) hens lay (3/2) eggs in (3/2) days then that's 2/3 of an egg per hen-day, so the answer is 

49* 2/3 = 32 and 2/3 eggs.

It did not bother me one whit that (1) you can't have 2/3 of an egg, and (2) Just like adding more people might slow down a project, adding more hens might end up being a bad idea-- especially if they are all crowded into the same chicken-coop and hence don't feel much like laying eggs.

Who was the first person to note that adding more people or hens might be a bad idea? I do not know, but here is an amusing, yet realistic, article by Mark Twain on what I would call The mythical cat-minute. My advisor Harry Lewis send it to me in the midst of an email exchange about The Mythical Man-Month. He got it from a student of his, Larry Denenberg. Here it is: 

CATS AND RATS

The following piece first appeared in ``The Monthly Packet'' of February
1880 and is reprinted in _The_Magic_of_Lewis_Carroll_, edited by John
Fisher, Bramhall House, 1973.


   If 6 cats kill 6 rats in 6 minutes, how many will be needed to kill
   100 rats in 50 minutes?

   This is a good example of a phenomenon that often occurs in working
   problems in double proportion; the answer looks all right at first, but,
   when we come to test it, we find that, owing to peculiar circumstances in
   the case, the solution is either impossible or else indefinite, and needing
   further data.  The 'peculiar circumstance' here is that fractional cats or
   rats are excluded from consideration, and in consequence of this the
   solution is, as we shall see, indefinite.

   The solution, by the ordinary rules of Double Proportion, is 12 cats.
   [Steps of Carroll's solution, in the notation of his time, omitted.]

   But when we come to trace the history of this sanguinary scene through all
   its horrid details, we find that at the end of 48 minutes 96 rats are dead,
   and that there remain 4 live rats and 2 minutes to kill them in: the
   question is, can this be done?

   Now there are at least *four* different ways in which the original feat,
   of 6 cats killing 6 rats in 6 minutes, may be achieved.  For the sake of
   clearness let us tabulate them:
      A.  All 6 cats are needed to kill a rat; and this they do in one minute,
          the other rats standing meekly by, waiting for their turn.
      B.  3 cats are needed to kill a rat, and they do it in 2 minutes.
      C.  2 cats are needed, and do it in 3 minutes.
      D.  Each cat kills a rat all by itself, and takes 6 minutes to do it.

   In cases A and B it is clear that the 12 cats (who are assumed to come
   quite fresh from their 48 minutes of slaughter) can finish the affair in
   the required time; but, in case C, it can only be done by supposing that 2
   cats could kill two-thirds of a rat in 2 minutes; and in case D, by
   supposing that a cat could kill one-third of a rat in two minutes.  Neither
   supposition is warranted by the data; nor could the fractional rats (even
   if endowed with equal vitality) be fairly assigned to the different cats.
   For my part, if I were a cat in case D, and did not find my claws in good
   working order, I should certainly prefer to have my one-third-rat cut off
   from the tail end.

   In cases C and D, then, it is clear that we must provide extra cat-power.
   In case C *less* than 2 extra cats would be of no use.  If 2 were supplied,
   and if they began killing their 4 rats at the beginning of the time, they
   would finish them in 12 minutes, and have 36 minutes to spare, during which
   they might weep, like Alexander, because there were not 12 more rats to
   kill.  In case D, one extra cat would suffice; it would kill its 4 rats in
   24 minutes, and have 26 minutes to spare, during which it could have killed
   another 4.  But in neither case could any use be made of the last 2
   minutes, except to half-kill rats---a barbarity we need not take into
   consideration.

   To sum up our results.  If the 6 cats kill the 6 rats by method A or B,
   the answer is 12; if by method C, 14; if by method D, 13.

   This, then, is an instance of a solution made `indefinite' by the
   circumstances of the case.  If an instance of the `impossible' be desired,
   take the following: `If a cat can kill a rat in a minute, how many would be
   needed to kill it in the thousandth part of a second?'  The *mathematical*
   answer, of course, is `60,000,' and no doubt less than this would *not*
   suffice; but would 60,000 suffice?  I doubt it very much.  I fancy that at
   least 50,000 of the cats would never even see the rat, or have any idea of
   what was going on.

   Or take this: `If a cat can kill a rat in a minute, how long would it be
   killing 60,000 rats?'  Ah, how long, indeed!  My private opinion is that
   the rats would kill the cat.

Ferrer's Diagrams can be used to prove X theorems about partitions. What is X?

1978: I took an excellent  ugrad course in combinatorics from James C Frauenthal (he sometimes wrote his name as the biniomial cofficient (J choose F))  and he covered Ferrer's diagrams. They are a nice way to prove equalities about types of partitions.   See here for a definition and a few examples. I have this (possibly false) memory that there were LOTS of partition theorems proven nicely with Ferrer's diagrams.

Fast forward to 2021:

2021: My TA Emily  needs a topic to cover in Honors Discrete Math. I have this memory that there were LOTS of theorems about partitions proven with Ferrer's diagrams. We look at many websites on Ferrer diagrams  and  find only TWO examples:

The numb of partitions of n into k parts is the numb of partitions of n into parts the largest of which is k.

The numb of partitions of n into \le k parts is the numb of partitions of n into parts the largest of which is \le k

We DO find many theorems about partitions such as this corollary to the Rogers-Ramanujan theorem:

The numb of partitions of n such that adjacent parts differ by at least 2 is the numb of partitions of n such that each partition is either \equiv 1 mod 5 or \equiv 4 mod 5.

This is a HARD theorem and there is no Ferrer-diagram or other elementary proof. 

SO, I have one MEMORY but the reality seems different. Possibilities:

1) My memory is wrong. There really are only 2 examples (or some very small number).

2) There are other examples but I can't find them on the web. I HOPE this is true--- if someone knows of other ways to use Ferrer diagrams to get partition results, please comment. 

The Million Dollar Sermon

Illinois Tech has one of the greatest origin stories for a university. In 1890 Frank Gunsaulus, a pastor on the south side of Chicago, gave a sermon where he said "If I had a million dollars I would build a school to provide students from all backgrounds meaningful roles in a changing industrial society". Philip Armour, a wealthy industrialist in the congregation, went up to Gunsaulus after the sermon and said, "if you give me five years for this school, I'll give you the million dollars". Thus started the Armour Institute of Technology which after some mergers became the Illinois Institute of Technology.

The "million dollar sermon" really happened, though the exact wording and even the exact year are lost to posterity or, as speculated, hidden in a cornerstone of one of the original campus buildings. 

In 1890 we were in the beginnings of the second industrial revolution, a revolution of communication, transportation, electrification and soon the assembly line. The first revolution happened a century earlier with mechanization and the steam engine. The third revolution was computers and automation, and we are now in the early parts of the fourth industrial revolution, one based on data and information. 

There are many parallels between 1890 and today. Like 1890, the private economy is dominated by a small number of large companies that have an outsized influence in our society. Like 1890, technology is changing faster than we can manage it. Like 1890, many workers are finding their skills quickly outdated.

Today Gunsaulus's words ring truer than ever. We more than ever need to provide students of all backgrounds meaningful roles in a changing technological society. 

An investment puzzle and speculation as to why some think its hard

 This is a Guest Post by David Marcus. He gives a puzzle and its solution, which is interesting, and then speculates as to why some people get it wrong. 

---------------------------------------------------------------------------

THE PROBLEM:

Investing Puzzle or Arithmetic Can Be Useful

The following is an example of investment results that I saw in an

investment newsletter. There are two portfolios that use different

strategies. Both portfolios start with $1 million twenty years ago and

withdraw 5% each year. The idea is that you are retired and withdrawing

money to spend. Not all years are shown in the tables.

Portfolio A

Year   Return  Withdrawal    Balance

2000   15.31%      57,655  1,095,445

2005    1.81%      59,962  1,139,273

2008  -12.65%      51,000    969,004

2009   34.26%      65,049  1,235,936

2010   11.94%      69,175  1,314,331

2015   -2.48%      64,935  1,233,764

2020   10.27%      66,935  1,271,765

Total Withdrawal: 1,685,190

Change in Balance: 27.18%

======

Portfolio B

Year   Return  Withdrawal    Balance

2000   -0.95%      49,524    940,956

2005    3.80%      44,534    846,154

2008  -20.11%      35,922    682,523

2009   18.27%      40,360    766,833

2010   11.57%      42,777    812,764

2015    0.99%      50,767    964,567

2020   13.35%      65,602  1,246,433

Total Withdrawal: 1,425,573

Change in Balance: 24.64%

Portfolio A has a final balance that is 25,000 more than Portfolio B's and

had about 260,000 more in withdrawals. Does the example lend credence to

the Portfolio A strategy being better than the Portfolio B strategy?

---------------------------------------------------------------------------

THE ANSWER:

Investing Puzzle or Arithmetic Can Be Useful: Analysis

Summary: The two portfolios have about the same performance over the 20

years. The difference is mainly due to Portfolio A having a good year or

years near the beginning before much money was withdrawn. The example

merely shows that it is better to withdraw money after a gain rather than

before.

Detailed Analysis:

The scenario is: Start with X = $1 million. Withdraw 5% a year.

Define "gain factor" to be 1 plus the percentage return. For example, if a

portfolio returns 5%, then the gain factor is 1.05.

Let A_j, j = 1, ..., 20, be the gain factors each year for portfolio A.

Let B_j, j = 1, ..., 20 be the gain factors each year for portfolio B.

The final amount in portfolio A is

   F = X * A_1 * 0.95 * A_2 * 0.95 * ... * A_20 * 0.95 .

The final amount in portfolio B is

   G = X * B_1 * 0.95 * B_2 * 0.95 * ... * B_20 * 0.95 .

From the "Change in Balance" values or the balances for year 2020, we see

that F and G are almost the same:

   F = 1.271865 * X,

   G = 1.246433 * X.

But, as we learned in elementary school, multiplication is commutative, so

   F = X * 0.95^20 * \prod_{j=1}^20 A_j,

   G = X * 0.95^20 * \prod_{j=1}^20 B_j.

Since F and G are almost the same, the total gains (product of the gain

factors) for the two portfolios are almost the same, i.e.,

   \prod_{j=1}^20 A_j \approx \prod_{j=1}^20 B_j.

Then what accounts for the big difference in the amounts withdrawn?

Portfolio A must have had some good years near the beginning. (We see in

the tables that Portfolio A did better in 2000 than Portfolio B.) So, all

the example shows is that it is better to withdraw your money after your

gains rather than before.

To take an extreme example, suppose an investment is going to go up 100%

this year. It is better to take your money out at the end of the year

(after the gain) than at the beginning of the year (before the gain). This

is a triviality.

The example tells us nothing useful about the two strategies.

Note: The total gains aren't exactly the same, but the timing of the yearly

gains is what is driving the results. We have (rounding off)

   ( F - G ) / 0.95^20 = 70942.81 .

So, if there had been no withdrawals, the difference in the portfolio

balances would have been about $71,000, much less than the $260,000 +

$25,000 difference with the withdrawals.

---------------------------------------------------------

WHY IS THIS HARD FOR PEOPLE?

Many people have trouble with this puzzle. The difficulty may be that such

people don't make a mental model (or a written model) of the process that

is producing the balance. If you write down (or have in your head) a

formula for the balance, then you see that the gain factors are independent

of the withdrawal factors. That is, we could withdraw more or less money,

or even deposit money, without affecting the gain factors we would use in

the model. This then leads us to consider the gain factors on their own,

and to recognize that the gain factors are the true measures of how the

strategies perform.

Ordering Beauty

First, congratulations to fellow complexity theorist and blogger Scott Aaronson for receiving the 2020 ACM Prize in Computing for "groundbreaking contributions to quantum computing". The prize is ACM's highest honor for mid-career researchers. Well deserved! 

Now back to our regularly scheduled post...

Every freshman at Cornell back in 1981 had to take two seminar courses, basically one-shot courses in an usually humanities area which required no prerequisites but lots of writing. I took my first course in philosophy. The instructor, a PhD student, at one point described his research, a philosophical argument that there is an intrinsic total ordering of beauty, say that Beethoven would always sit above the Beatles, no matter the beholder. I didn't believe him then and still don't today. A few months ago the Washington Post ran a story with the same theme entitled Maradona was great, and maybe the greatest. Can we make similar claims about artists?

Somehow we have this belief when it comes to conference submissions, that there is some perfect ordering of the submissions and a good PC can suss it out. That's not really how it works. Let's say a conference has an accept rate of 30%. Typically 10% of the submissions are strong and will be accepted by any committee. About half the submissions are just okay or worse and would be rejected. The other 40% of the submissions will be chosen seemingly randomly based on the tastes of the specific members of the program committee. Experiments in the NeurIPS and ESA conferences have bourn this out. 

Why not make the randomness explicit instead of implicit? Have the PC divide the papers into three piles, definite accepts, definite rejects and the middle. Take the third group and randomly choose which ones to accept. It will create a more interesting program. Also randomness removes biases, randomness doesn't care about gender, race and nationality or whether the authors are at senior professors at MIT or first year grad students at Southern North Dakota. 

We put far too much weight on getting accepted into a conference given the implicit randomness of a PC. If we make the randomness explicit that would devalue that weight. We would have to judge researchers on the quality of their research instead of their luck in conferences.

Given that conferences, especially the virtual ones, have no real limits on the number of papers and talks, you might say why not just accept all the papers in the middle. Works for me.

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. 

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.

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. 

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.

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,…,x_n 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 x_i > 0 for each i. These are n orthogonal hyperplanes.
• The hyperplanes x₁+…+x_n > 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(n^0.5) fraction of the edges (sharp by the hyperplane x₁+…+x_n > n/2). Thus you need at least O(n^0.5) hyperplanes which for 50 years was the best known bound.

Gil Yehuda and Amir Yehudayoff have given a new lower bound of O(n^0.57). The paper gives a O(n^0.51) 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 n^1.57 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.

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 be 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? 

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. 

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?

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?

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. 

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. 

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. 

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.

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. 

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

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?

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.

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.

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.

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. 

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 Σ₂^P-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 Σ₂^P, a bit surprising as MA is in Σ₂^P.

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.

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? 

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.

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.) 

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.