Monday, May 30, 2022

Discussions I wish we were having

1) Democrats think the best way to avoid school shootings (and other problems with guns) is to have regulations on Guns. They have proposed legislation. The Republicans think its a mental health issue. They have proposed legislation for this. NO THEY HAVEN"T. I would respect the its a mental health issue argument if the people saying this  respected it. They do not. See here. Idea: Politico should leak a (false) memo  by Gov Abbott where he says 

We have a serious mental health crisis in Texas which caused the recent event. I am not just saying this to deflect from the gun issue. I have drawn up a bill to fund mental health care, providing more money, for care and for studies. I call on Republicans and Democrats to pass it ASAP.

I wonder- if this false memo was leaked, would he deny it and say 

I didn't write that. I am using mental health only as a way to deflect from the gun issue. How dare they say that I am reasonable and am proposing actual solutions. 

Or would he be forced to follow through?

2) Democrats think Biden won the election. Some Republicans think Trump won the election. One issue was Arizona. So some republicans organized a recount of Arizona. And when they found out that Biden really did win it they said, as the good Popperian scientists they are, we had a falsifiable hypothesis and it was shown to be false, so now we acknowledge the original hypothesis was wrong. NO THEY DIDN"T. They seem to point to the Arizona audit as proof that they were right, even though it proves the opposite. (Same for all the court cases they lost.)

3) At one time I read some books that challenged evolution (Darwin on Trial by Phillip Johnson was one of them). Some of them DID raise some good points about how science is done (I am NOT being sarcastic). Some of them DID raise some questions like the gap in the fossil record and Michael Behe's notion of irreducible complexity.  (In hindsight these were window dressing and not what they cared about.) MY thought at the time was its good to have people view a branch of science with a different viewpoint. Perhaps the scientists at the Discovery Institute will find something interesting. (The Discovery institute is a think tank and one of their interests is Int. Design.) Alas, the ID people seem to spend their time either challenging the teaching of Evolution in school OR doing really bad science. Could intelligent people who think Evolution is not correct look at it in a different way than scientists do, and do good science, or at least raise good questions,  and come up with something interesting? I used to think so. Now I am not so sure.

4) I wish the debate was what to do about global warming and not is global warming happening? Conjecture: there will come a time when environmentalists finally come around to nuclear power being part of the answer. At that point, Republicans will be against Nuclear power just because the Democrats are for it. 

5) I sometimes get email discussions like the following (I will call the emailer Mel for no good reason.)


MEL: Dr. Gasarch, I have shown that R(5)=45.

BILL: Great! Can you email me your 2-coloring of K_{44} that has no mono K_5?

MEL: You are just being stubborn. Look at my proof!


Clyde has asked me what if Mel had a nonconstructive proof?

FINE- then MEL can tell me that. But Mel doesn't know math well enough to make that

kind of argument. Here is the discussion I wish we had


MEL: Dr. Gasarch, I have shown that R(5)=45.

BILL: Great! Can you email me your coloring of K_{44} that has no mono K_5?

MEL: The proof is non-constructive.

BILL: Is it a probabilistic proof? If so then often the prob is not just nonzero but close to 1. Perhaps you could write a program that does the coin flipping and finds the coloring.

MEL: The proof uses the Local Lovasz Lemma so the probe is not close to 1.

BILL: Even so, that can be coded up.



Maybe Mel really did prove R(5)=44, or maybe not, but the above conversation would lead to


Sunday, May 22, 2022

In the 1960's students protested the Vietnam war!/In 1830 students protested... Math?

 I was at SUNY Stonybrook for college 1976-1980. 

I remember one student protest about a change to the calendar that (I think) would have us go home for winter break and then come back for finals.  I don't recall how that turned out. 

However I had heard about the protests in the 1960's over the Vietnam war. Recall that there was a draft back then so college students were directly affected. 

I was reading a book `Everything you know is wrong' which noted that some people thought the first time there were student protests was in the 1960's but this is not true. (Not quite as startling as finding out that a ships captain cannot perform weddings.) 

It pointed to The 1830 Conic Section Rebellion. I quote Wikipedia (full entry is here)

Prior to the introduction of blackboards, Yale students had been allowed to consult diagrams in their textbooks when solving geometry problems pertaining to conic sections – even on exams. When the students were no longer allowed to consult the text, but were instead required to draw their own diagrams on the blackboard, they refused to take the final exam. As a result forty-three of the ninety-six students – among them, Alfred Stille, and Andrew Calhoun, the son of John C. Calhoun (Vice Pres a the time) – were summarily expelled, and Yale authorities warned neighboring universities against admitting them.

Random Thoughts

1) From my 21st century prospective I am on the students side. It seems analogous to allowing students to use calculators-- which I do allow. 

2) From my 21st century prospective the punishment seems unfair. 

3) The notion of a school telling other schools to not admit student- I do not think this would happen now, and might even be illegal (anti-trust).

4) I am assuming  the students wanted to be able to consult their text out of some principle: we want to learn concepts not busy work.  And again, from my prospective I agree that it was busy work. 

5) Since all of my thoughts are from a 21st century prospective, they may be incorrect, or at least not as transferable to the 1830 as I think. (Paradox: My ideas may not be as true as I think. But if I think that...) 

6) I try to avoid giving busy work. When I teach Decidability and Undecidability I NEVER have the students actually write a Turing Machine that does something. In other cases I also try to make sure they never have to do drudge work.  And I might not even be right in the 21st century- some of my colleagues tell me its good for the students to get their hands dirty (perhaps just a little) with real TM to get a feel for the fact that they can do anything. 

7) The only student protests I hear about nowadays are on political issues. Do you know of any student protests on issues of how they are tested or what the course requirements are, or something of that ilk? I can imagine my discrete math students marching with signs that say: 


Sunday, May 15, 2022

Is Kamala Harris our first female PREZ? No. Do I have a theorem named after me. No. But in both cases...

On Nov 19, 2021 Joe Biden got a colonoscopy and hence the 25th amendment was used to make Kamala Harris the president temporarily (this source: here says 85 minutes, though I thought I heard a few hours from other sources). 

Does this make Kamala Harris our first female president?

I would say NO and I suspect you agree. A friend of mine suggested the phrasing Kamala Harris is the first women to assume the powers of the president under the 25th amendment.  True.  I don't think it means much. She tacked on the under the 25th amendment since Edith Wilson was essentially president when Woodrow Wilson had a stroke (see here).

A student asked me Is there a theorem that is referred to as Gasarch's Theorem or something like that?

I will answer YES and NO, but really the answer is NO.

YES: In 1999 Gasarch and Kruskal had a paper in Mathematics Magazine: 

When can one load of Dice so that the sum is uniformly distributed?

In that paper we have a theorem that gives an exact condition on

(n_1,...,n_k) for when there is a loaded n_1-sided dice, n_2-sided dice,...,n_k-sided dice so that 

the sums are all equally likely.

In 2018 Ian Morrison published a paper in the American Math Monthly:

Sacks of dice with fair totals

which used our work and referred to our main theorem as The Gasarch-Kruskal Theorem.

Hence there is a theorem with my name on it!

NO: The Gasarch-Kruskal paper has only 8 citations (according to Google Scholar). This is more than I would have thought, but its not a lot. The fact that ONE person calls the main theorem THE GASARCH-KRUSKAL THEOREM hardly makes it a named theorem. 

QUESTION: So what criteria can one use?

We could say that X has a theorem with their name on it if there is a Wikipedia entry about the theorem, using that name. That works to a point, but might fun afoul of Goodhart's law (if a measure becomes a target it stops being a measure) in that, for example, I could write a Wikipedia entry on The Gasarch-Kruskal Theorem. 

We could say that 10 people need to refer to the theorem by the name of its authors. Why 10? Any number seems arbitrary. 

CAVEAT: If someone asked Clyde Kruskal is there a theorem that bears your name that is trickier, since The Kruskal Tree Theorem bears his name.... but its not his theorem. Reminds me of the (fictional) scenario where a Alice steals  a Field's medal and tells Bob I have a Field's Medal! and Bob  thinks Alice is a world-class mathematician since she has a fields medal, rather than thinking Alice is a world class thief. See here for my post on that. 

(I originally had Kruskal Three Theorem instead of Tree Theorem. I have corrected this but I hope it inspires Clyde to prove a theorem about the number Three so he can have a named theorem. And if he is lucky, over time, people will confuse it with the Kruskal Tree Theorem!) 

Tuesday, May 10, 2022

Queen Elizabeth is the 3rd longest reigning monarch; The problem with definitions

 A few days ago Queen Elizabeth passed Johann II of Liechtenstein to be the third longest reigning monarch (see here). 

A summary of the top 4:

4) Johann II, Liechtenstein ruled from Nov 12 1858 until his death on Feb 11, 1929. When he became King he was 18. He was king for 70 years, 91 days. 

3) Queen Elizabeth II (thats a two, not an eleven) ruled from Feb 2, 1952 until now. When she became Queen she was  25. I am writing this on May 10 at which time she ruled 70 years, 94 days. 

2) Bhumibol Adulyadej (Thailand) ruled from June 9, 1946 until Oct 13, 2016. When he became King he was 19. He was king for 70 years, 126 days. 

1) Louis XIV ruled from May 14, 1643 until Sept 1, 1715. When he became King he was 4 years and 8 months. He was king for 72 years, 110 days. 

Johann, Elizabeth, and Bhumibol started their reigns a bit young (they would have to to have ruled so long) but their first day of their reign they knew what the job was, what they are supposed to do etc. 

Here is my complaint: Louis XIV being king at the age of 4 years 8 months should not count (someone who proofread this post wondered if 4 years 9 months would count. No.) Shouldn't we define the reign of a king as the point at which he can make real decisions as king? Or something like that. 

For the record of the longest marriage there is a similar problem. The three longest marriages are legit in that the people got married at a reasonable age (I think all were married after they were 17). The fourth longest marriage of all time involved two people that were married when they were 5. That should not count (see here).

Is there a way to define monarch's reigns and also marriage length so that it corresponds to our intuitions? 

In Math we can use rigorous definitions but in English its harder. 

Wednesday, May 04, 2022

The (R)evolution of Steve Jobs

I don't mention it that often in this blog, but I fell in love with opera in the 90's and watch as much as I can, often fitting opera into my travels or vice-versa. Rarely do the tech world and operas collide but they did so this weekend in visit to Atlanta, I saw the (R)evolution of Steve Jobs, yes an opera about the iconic Apple founder that was first performed in Santa Fe five years ago. This production played in Austin and Kansas City earlier this year.

The story focused on relationships, Steve Wozniak, his wife Laurene, his guru Kōbun Chino Otogawa and Chrisann Brennan, the mother of Job's daughter Lisa, and on Steve Jobs focus on perfection and his company, as he often shunned others and even his own health. The music worked and the singers were generally strong. There were about 20 large monitors on the set which were used to enhance the story in pretty clever ways. The opera bounced around in time from when Steve Jobs father bought him a worktable to his memorial service. 

100 minutes is short for an opera, especially one on a person as complicated as Jobs, and some of the story lines and characters could have benefited by a longer exposition, or perhaps a more focused story could have had a larger emotional punch.

Laurene had a message at the memorial service but really meant for the audience in the opera.
And after this is over,
The very second this is over,
For better or worse,
Everyone will
Reach in their pockets,
Or purses,
And — guess what? —
Look at their phones,
Their “one device.”
I’m not sure Version 2.0 of Steve
Would want that.
Version 2.0 might say:
“Look up, look out, look around.
Look at the stars,
Look at the sky,
Take in the light,
Take another sip,
Take another bite,
Steal another kiss,
Dance another dance,
Glance at the smile
Of the person right there next to you.”
The (R)evolution of Steve Jobs has a couple of more performances in Atlanta this weekend, including a livestream, and heads to Calgary and other venues in the future.

Next year, The Life and Death(s) of Alan Turing at Chicago Opera Theater. 

Sunday, May 01, 2022

Elon Musk To Buy Complexityblog

Elon Musk has offered to buy out Complexityblog. The money is too good to turn down. As part of the contract we can't say how much or in what cryptocurrency, but suffice to say it will be more than the royalties from our books. Or not.

Readers be aware of the following changes to the blog:

1) We can no longer send Donald's Trump comments into our spam folder.

2) All of our posts will be written by Tesla autopilot.

3) Complete free speech in the comments. Or not. Depends on Elon's mood that day

4) Purchases made through this blog can be in bitcoin or other cryptocurrencies. Or not. Depends on Elon's mood that day.

5) Switch the business model (Lance- we have a business model?) from advertisements to a subscription service. How much will people pay per year to access complexity blog? 

6) Lance and I have been invited to fly to orbit on a SpaceX rocket so we can post from space. Or was it posting from the backseat of a Tesla? Depends on how you read the contract.

7)  April Fools day posts will henceforth be on May 1.