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.