A few more notes about Tom L

Tom Lehrer passed away on July 26, 2025, at the age of 97. I wrote a blog-obit here. One of my readers read the post and went down a rabbit hole (or did he?), which lead to a blog post about rabbit holes here. 

A few more notes about Tom L.

1) When someone of interest to our readers dies, Lance calls me (he seems to always know before I do) to discuss who should do the obit (me, him, someone else, or perhaps no obit needed). This was a case where there was no need for a discussion.  To say I am a fan of novelty songs would be an understatement---I've been a fan of novelty songs before I was a fan of mathematics. A link to my website of novelty songs by topic, including Math, is here

2) Whenever Lance calls I answer with Who Died? 

3) Who was the oldest novelty song singer to die in the Summer of 2025? The summer is not over yet but I think the answer is known. And it's NOT Tom L!

Jane Morgan, a singer, died on August 4, 2025, at the age of 101.  She recorded a parody of  Johnny Cash's A Boy Named Sue titled A Girl Named Johnny Cash 

A boy named sue:  here

A girl named Johnny Cash: here

Wikipedia Page for Jane Morgan: here

To my knowledge, Jane Morgan only had one novelty song  (she had many non-novelty songs) so calling her a novelty singer is a stretch, but its a great song, so I will call her a novelty singer.  (I checked if the flipside of that song was a novely song. It was Charley, a love song, not a novelty song. Ask your grandparents what a flipside is.) 

4) Tom Lehrer and Jim Lehrer (news anchor on PBS, deceased) are not related.

I googled how many people have last name Lehrer

Google-AI:  FamilySearch.org estimates there are 211,503 records for the surname.

But this website says approximately 5982 bear this surname.

I'm surprised by the large gap there.

5) There have been more elements found since Tom L did The Elements. I wondered whether someone updated it. Of course they did:

The Original by Tom L: here

Updated version by Leonard  Lehrman that has the latest element, Number 118, Oganesson: here

I've heard that 118 is natural barrier- we probably won't create 119 or higher. Elements that high are created, not discovered. They also don't last long. 

6) There are many elements, so a list-song made sense. There are a lot of complexity classes, so a list-song makes sense for those as well. 

Dave Barrington sings Song of the Complexity Classes: here

7) How many people emailed me to tell me that Tom L passed away? R(5).

8) One of my favorite and less known Tom L songs, whose advice he did not take: Selling Out

9) Tom L wrote a paper with R.E. Fagen (Not Ronald Fagin) for the NSA. It's a real math paper, but note the third reference in the bibliography, the paper is here.

Total Pixel Space

Last month the New York Times highlighted some AI generated short movies, including Total Pixel Space, by Jacob Adler that gets philosophical about information, à la infinite monkeys. It imagines the finite number of images and video that contain all human history, both real and fake, along with all possible creatures, and even the rise and fall of alien civilizations.

Let's talk about the math. According to the video there are roughly 7.8 x 10^7,575,667 possible 1024x1024 images, and 9.3 x 10^{1,309,075,411,322} possible two hour films, incomprehensibly large numbers. The narrator acknowledges that most of the images are random noise.

But within this ocean of pixel possibility, natural images are but a drop. Recognizable scenes, faces and objects are extremely rare islands in a vast sea of noise.

So how do we capture which images actually matter? Let's visit our friend Kolmogorov Complexity, which measures information by the amount we can compress. A JPEG image typically compresses (lossily) to about 200 KB, which reduces the number of images to 8.7 x 10^1,061,650. Still enormous.

All the images and videos were generated by short prompts. JPEG compression reduces raw pixel space by discarding details our eyes don’t notice. Prompts do something similar at a higher level: they compress ideas, not pixels.

Consider prompts of length 100 over a 10,000 word alphabet typically used in prompting and we're down to 10⁴⁰⁰ possibilities, a mere quintic of the number of atoms in the universe. And you could cut that down by considering grammatical structure.

Now from a prompt you won't get the same image each time, based on the randomness of machine learning. But that's the whole power of AI, the randomness just gives us examples of the structure embedded in the prompt. It's the structure that matters.

And perhaps those monkeys would be more efficient if they entered prompts into AI, instead of generating random text. What images they could produce!

My Tom L post inspired a mathematical definition of Rabbithole

NICK: I read and enjoyed your blog post on Tom L (see here). I then spent 40 minutes down a rabbithole listening to his music on YouTube.

BILL: You call that a rabbit hole?!  A while back I spent 3 hours reading questions and answers on quora ranging from is Michelle Obama actually a man? to Is Donald Trump the Anti-Christ? (The answer to both is no.) THATS a rabbithole. Listening to Tom L is not.

NICK: SO... what is and isn't a rabbit hole? Also, is it rabbithole or rabbit hole?

BILL: Spellcheck is happy with rabbithole, hence so am I. As to your question,  we need a function \(f\) and a threshold \(T\) such that

if you spend \(x\) minutes on A, and 

you get y enjoyment out of it, where \(0\le y\le 10\), and

 \(f(x,y)\ge T\)  

then A is a  rabbithole.

(Note- I was kidding. There can't possibly be a function f that works.)

ONE DAY LATER

NICK: I asked Gemini  what \(f\) and \(T\) are  and it told me:

 \(f(x,y) = \frac{x}{y+1} \) and  

\(T=20\).

  It also gave me some examples:

1) The Tom L. Example: 40 mins, 8/10 enjoyment. Score 4.44. NOT a Rabbit Hole!

2) Doomscrolling: 90 mins, 1/10 enjoyment. Score  45. Rabbit Hole!

3) Binge-Watching Mediocre TV: 3 hours (180 mins), 4/10 enjoyment. Score = 36. Rabbit Hole!

4) Incredible Documentary: 3 hours (180 mins), 9/10 enjoyment.  18. Worthwhile but its close.

Gemini also output a heatmap, see here.

BILL: Uh- I was only kidding.

NICK: Well, the jokes on you. 

AI and ...

AI and Vacation

I'm back from my German vacation. This was my first AI vacation, by which I mean how I used AI to navigate a foreign country. Taking a picture of a hand-written menu board, not just to translate the dishes, but to get a description of each. Visiting a palace with a German-speaking tour guide and translating in real time. Even the more mundane taking pictures of buildings to learn about them.

On the TV I saw something about Künstliche Intelligenz, and Chatty told me it was German for Artificial Intelligence. The Germans use KI instead of AI partly because AI can be confused with Ei (egg). At least that's what AI tells me, so it must be true.

AI and Math

At the beginning of my vacation, Google announced that they achieved gold medal status in the International Mathematical Olympiad. An impressive achievement though Terry Tao makes a good point that comparing an AI system to a time-constrained high-school students is not an apples-to-apples comparison.

I already find talking to AI about math topics quite useful, though it's like talking to an early PhD student. Sometimes they just say things that aren't correct, but usually they are. The reasoning models are particularly good at finding holes in P v NP proofs. For example here's the conclusion of ChatGPT o3-pro's review of the paper from Eric's guest post.

The paper is a reminder that lower‑bound proofs live or die on the exact breadth of the algorithmic model they exclude—too narrow and the result is unsurprising, too broad and the proof tends to break. At present this work sits in the first category.

What I want to see is AI come up with a solution to an open math problem, a true new insight beyond just some optimized search. I'm not looking for P ≠ NP, just some result that would be publishable in a respectable conference or journal, even just a new completeness result. We haven't really seen that yet, but I suspect we will soon and then we can figure out where math goes from there.

AI and Bill

In his presidents question and solution, Bill states that AI had failed to find the right answer to his problem. Back in June, I saw Bill's draft post and tried AI to solve it.

AI initially failed the test but for a good reason. Bill's initial draft post had Ford and Dole in Group Two because they received LLBs instead of JDs. In the past the LLB was the professional law degree. Yale didn't change to JD until 1971. Ford got his LLB from Yale in 1941.

When I removed Ford and Dole, ChatGPT o3-pro correctly gave the reason for the partition, though it did take over 13 minutes.

Every name in Group One spent time in a law school—most completed a J.D. or LL.B., and the two exceptions (Al Gore and, in some accounts, Lloyd Bentsen) still enrolled in law studies.

• examples – Walter Mondale (University of Minnesota Law) en.wikipedia.org,
  JD Vance (Yale Law) en.wikipedia.org,
  Al Gore (attended Vanderbilt Law) en.wikipedia.org.

No one in Group Two ever attended a law school; their highest formal education is in fields such as engineering (Jimmy Carter), economics (George H. W. Bush), business (Donald Trump), political science (Paul Ryan), or acting (Ronald Reagan) en.wikipedia.orgen.wikipedia.org.

So the distinguishing property is legal education: every Group One figure went to law school, while none in Group Two did.

Another commentor got a similar result for ChatGPT o4-mini-high. I just tried it on Gemini 2.5-Pro and it also gave the correct response, this time in seconds.

On the other hand, E tried several base models and none of them succeeded. The lesson: You want to solve a tricky problem, pony up the $20/month and use a reasoning model.

Some thoughts on journals, refereeing, and the P vs NP problem

A guest post by Eric Allender prompted by an (incorrect) P ≠ NP proof recently published in Springer Nature's Frontiers of Computer Science.

For a time, I served as Editor-in-Chief of ACM Transactions on Computation Theory, and in this role I had to deal regularly with submissions that claimed to resolve the P vs NP problem. Finding referees for these papers was sometimes challenging, so I frequently ended up reviewing them myself.  Dealing with such submissions involves enough overhead that ToCT, J.ACM and ACM Transactions on Algorithms limit the frequency with which authors can submit work of this sort.  But for every submission, on any topic, the overall process was the same: Find someone on the Editorial Board who has sufficient expertise to find referees and make knowledgeable use of their recommendations.  If there was no such person on the Editorial Board, then it was always the case that the submission was out of scope for the journal.

These thoughts are brought to mind by a recent case, where it seems to me that the editorial process broke down.

Springer publishes several high-quality academic journals that deal with Theoretical Computer Science.  One Springer journal, Frontiers of Computer Science, recently published an article entitled SAT Requires Exhaustive Search, where one of the authors is a Deputy Editor-in-Chief of the journal.  The abstract of the article states that it proves a result that is stronger than P not equal to NP.  The Editorial Board of the journal has some members who are expert in computational complexity theory.  However, all the ones whom I know personally have asserted that they had no knowledge of this paper, and that they were not involved at all in handling the paper.

When Ryan Williams and I learned about the publication of this article, we drafted a comment, which we sent to the Editor-in-Chief.  We recommended that the paper be retracted, in which case there would be no need to publish our comment.  However, the Editor-in-Chief declined to retract the article, saying that he could find no evidence of misconduct, and thus we have been assured that an edited version of our comment will appear in the journal.

Our comment calls attention to some shortcomings in the proof of the main theorem (similar to shortcomings in several other failed attempts to separate P from NP).  But we were able to say more.  Often, when one is looking for bugs in a purported proof, one has to deal with the situation where the claimed theorem is probably true, and the only problem is that the proof is not convincing.  However, the main theorem in their paper (Theorem 3.2) states that a particular constraint satisfaction problem requires time more than \(d^{cn}\) for any constant \(c<1\) (where \(d\) is the domain size, and \(n\) is the number of variables).  In particular, their purported proof claims that this holds even when \(k=2\) (meaning that each constraint has at most 2 variables).  However, Ryan Williams presented an algorithm more than two decades ago that runs in time \(O(d^{(0.8)n})\) in this special case, contradicting the lower bound claimed in the article.

The article contains an appendix, with glowing testimonies from various researchers; the lead-in to the appendix also contains enthusiastic comments from Gregory Chaitin.  I contacted Gregory Chaitin, and he asserts that he did not read the paper, and that he was quoted out of context.

The edited version of the comment that Ryan Williams and I wrote, which will supposedly appear in Frontiers of Computer Science soon, differs from the version linked here (our original submission) primarily in one respect:  Our closing paragraph was removed.  Here is that paragraph:

Finally, it is our opinion that the publication of this article is a complete embarrassment to this journal and its publisher. We believe that, at the very least, the paper should be withdrawn, and Springer should conduct an investigation to understand how such a paper could have made it through the peer review process.

Update (Lance, 8/5/25): The authors of the paper in question have asked me to link to their reply to the Allender-Williams comment. I do so with no endorsement. 

Eric Allender asked me to note that their claim about Ryan’s algorithm requiring exponential space is misleading; the amount of space is not more than the runtime of the algorithm, which is less than the lower bound that they claim. (Their theorem does not state that \(d^{cn}\) time is required under the additional assumption that the algorithm use only \(n^{O(1)}\) space.)

Tom Lehrer Passed Away at the Age of 97

Tom Lehrer passed away on Saturday July 26 at the age of 97. (For other obits see this collection of ten obits here.)

He worked in both of my fields of interest: Parody Songs and Mathematics. 

1)  He got a BA in Mathematics from Harvard, magna cum laude, in 1946. (Spell check thinks magna  and laude are not words). 

2) While he was an undergraduate he wrote and performed the song Fight Fiercely Harvard which was a gentle football fight song. IDEA: Use the melody to write a song about Harvard's current fight with the Trump Administration.

3) He wrote some political songs. Some were performed by Nancy Ames on the British satirical Show That was the week That Was. Tom L didn't like that probably because they cut some of the more controversial lyrics. He later wrote and performed songs for another political satire show, The Frost Report. Here are some of his political songs and comments on them:

 Who's Next -- about which countries have or will have nuclear weapons. IDEA: Update it.

Vatican Rag--About the Catholic Church- controversial then, rather tame now. If you heard it now you won't understand why it was ever controversial. Such is the nature of biting satire. I noticed this in my blog-obit for Tommy Smothers  here.  As such, I view old political novelty songs as entertaining history. 

4) He went to graduate school for Math at Harvard. He worked on it on-and-off and had other jobs but left Harvard in 1965 (see his Wikipedia entry here for the full story).

5) One of the things he was doing while he was at Harvard was compose, sing, and record songs. Here are the some of particular interest to my readers:

New Math - -I was actually a victim or beneficiary of the new math. 

Lobachevsky-- Historically inaccurate but funny.

The Elements-- This might be Tom L's best known song. It's to the tune of  I am the very model of a  Modern Major General; however, some of the songs that use that Tune seem to be parodies of The Elements. I have a website of parodies of Modern Major General here. Unfortunately the song that is most clearly a parody of  The Elements, Dr Jane's The Muscles of the Kitty Cat, seems to have disappeared from YouTube. It is not on Spotify. (Spellcheck thinks that YouTube is a word but that Spotify is not a word.) I can't find it anywhere on the web. I DO have it on CD.

 The Decimal Song--About using base 10. This was on The Frost Report. Not on any album so you might not know this one, though it is on YouTube.

 That's Mathematics--Originally written to be the theme song for a PBS math show now titled Square One Television. They did not use it. He later added a lyric about Andrew Wiles. Square One Television often features math songs. Here are my favorites: The Mathematics of Love,  8% of my love,That's Combinatorics, Polka Patterns (by Weird Al).

 That's Mathematics sung by Mathematicians-- A nice tribute to him. It was done a few years ago. Tom L knew about it and was delighted. 

Derivative song (indexed to where it is within a longer segment)

 6) A few years ago Tom L put his songs in the public domain, see here. That website also includes lyrics for songs that were never recorded. IDEA: Record them! ADED LATER- a few have been recorded, though by other people. I found a website of that has lots of science novelty songs including some by him here. Much of it is not available on any record and not even on YouTube.

7) Tom L claims to have invented Jello Shots as a way to get around alcohol-free requirements. The Great Luke Ski wrote a song about Tom L in the style of Tom L. It's not on YouTube but it is at FUMP (FUnny Music project) here (click on play on second song) 

8)  His singing career was fairly short. Three albums, a few tours, a few other songs. Weird Al has 14 albums. Alan Sherman has 10 albums (Alan Sherman was born four years earlier than Tom L but died in 1973). However, the percent of great song on Tom L's albums is around 90%, whereas for Weird Al and Alan Sherman it's around 60% (this is just my opinion).  Also, Tom L had a day job. He has said he never really retired from singing, he wrote when he felt like it, and over time didn't feel like it. For what he said about retiring from singing, see his Wikipedia page here.

9)  There are two  stories about Tom L I bring up - one seems to be TRUE though I thought it was FALSE, and the other IS FALSE.

a) He stopped political satire because:

Political satire became obsolete when Henry Kissinger won the Nobel Peace Prize. 

I have the following (possibly false) memory: 

Tom L has denied this and points out that he had pretty much stopped many years earlier. And I'll point out that he wrote non-political novelty songs as well (that is Tom L did, not Henry K). 

BUT- Wikipedia and other sources say that it's true. Who am to  disagree with the Google Gods?

b) He was sued by Wernher von Braun's family for his song about Wernher. This is false and the web says that it is false. Tom L denied it in a 2003 interview. I have a (possibly false) memory of reading that he wished it was true because it would mean people are still listening to his music. 

9) On Jan 1, 2025 he became one of the rare people who:

-- Lived during two square years (1936 and 2025).

-- Was of age and mental ability to appreciate that they had done this

I had a blog on people who lived through two square years here.

10) I end with what might have been his last song

 I'm spending Hanukkah in Santa Monica 

Answer to my GROUP ONE/GROUP TWO Prez question

In a prior post I asked what criteria I used to place Prez and VP nominees since 1976 into two groups. 

In the book Abundance I read that since 1984 all of the Democratic nominees for Prez and VP except Tim Walz had gone to law school.  I decided to get data on that, along with Republicans, and also go back to 1976 since leaving out 1980 (Jimmy Carter did not go to law school) seemed like a cheat. So GROUP ONE all went to law school, and GROUP TWO did not. I restate the groups and note which law school and a few other fun facts. There are a few glitches along the way. And then I have comments on the problem and AI (when was the last time there was a blog post that did not mention AI?) 

GROUP ONE:

VP-1976 and 1980. Prez-1984
Walter Mondale. University of Minnesota Law School. 1956.

Prez-1976
Gerald Ford. Has an LLB from Yale. 1941. What is an LLB? Some law degrees were called LLBs in an earlier time. This is a glitch. Some places on the web call it an undergraduate degree in Law (the B stands  for Bachelors) but some say it's equivalent to a JD. Fords's seems to be equivalent to a JD. 

VP-1976. Prez-1996
Bob Dole. Has an LLB from Washburn University in Topeka Kansas in 1952 . See entry on Ford for what an LLB is. From the Wikipedia entry on Bob Dole it seems like the LLB was an undergraduate degree, but its hard to tell. 

VP-1984
Geraldine Ferraro. Fordham University School of Law. 1960.

Prez-1988
Michael Dukakis. Harvard Law School. 1960.

VP-1988
Lloyd Bentsen. LLB from the  University of Texas Law School. 1942. See Entry on Ford for what an LLB is. From the Wikipedia entry I cannot tell if it was the equivalent of a JD. 

VP-1988 and 1992
Dan Quayle. Indiana University Robert H. McKinney School of Law. 1974.

Prez-1992 and 1996
Bill Clinton. Yale Law. 1973.

VP-1992 and  1996. Prez-2000
Al Gore.  Vanderbilt University Law School. He quit to run for the House of Representatives. I still count this but it's a glitch. 

VP-2000
Joe Lieberman.  Yale Law School. 1967.

Prez-2004
John Kerry.  Boston College 1976.

VP-2004
John Edwards.  University of North Carolina School of Law. 1977.

Prez-2008 and 2012
Barack Obama.  Harvard Law School. 1991.

Prez-2012
Mitt Romney.  MBA/JD (a joint program) from Harvard. 1975. (This surprised me.)

VP-2008 and 2012. Prez-2020
Joe Biden.  Syracuse University College of Law. 1968.

Prez-2016
Hillary Clinton.  Yale Law School. 1973.

VP-2016
Tim Kaine. Harvard Law School. 1983.

VP-2016 and 2020
Mike Pence. Indiana University Robert H. McKinney School of Law. 1986.

VP-2020. Prez-2024
Kamala Harris. University of California, Hastings College of the Law. 1989.

VP-2024
J.D Vance. Yale Law School. 2013.

The only names that were flagged for being misspelled are Dukakis, Bentsen, and Kamala.) 

--------------------------------------
GROUP TWO

Prez-1976 and 1980
Jimmy Carter

Prez-1980 and 1984
Ronald Reagan

VP-1980 and 1984, Prez-1988 and 1992.
George H.W. Bush 

(The only people who were nominated for VP twice and Prez twice are John Adams and George H.W. Bush. Richard Nixon was nominated for VP twice and for Prez three times.) 

VP-1996
Jack Kemp

Prez-2000 and 2004
George W. Bush

VP-2000 and 2004
Dick Cheney

Prez-2008
John McCain

VP-2008
Sarah Palin

VP-2012
Paul Ryan (This surprised me.) 

Prez-2016 and 2020 and 2024
Donald Trump

VP-2024
Tim Walz

(The only name flagged for being misspelled was Walz.) 

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

Some notes

In these notes I treat Bentsen, Dole, Ford, who all got LLB's,  as having gone to law school and finished it.

1) Of the 16 Democrats, 14 went to law school and 13 finished law school.

2) Of the 14 Republicans, 6 went to law school (all finished).

3) The LLB's and the fact that Al Gore started but did not finish law school are examples of edge cases which are cases that are odd outliers which an AI might not have been trained on or know to look for. Over time will these diminish or will we always need humans to help with that? 

4) I was surprised that Mitt Romney had a double-degree MBA/JD since (a) I didn't know there were such things and (b) since he worked at Bain Capital I thought of him as a business person--- MBA--- which is correct but incomplete. 

5) I was surprised that Ford, Dole, and Bentsen had LLBs since I never heard of that before.

6) I was surprised that Paul Ryan does not have a law degree. Seems like the type that would have one. 

7) Let LL mean Prez and VP both went to law school. Let LN mean prez went, VP didn't go. NL and NN are obvious. We considered 13 elections. Dems: 10 LL, 2 NL, 1 LN. Reps: 5 NN, 5 NL, 2 LN, 1 LL. Since I was surprised that Romeny went to law school AND I was surprised that Ryan did not, I would have thought 2012 for Reps was NL but it was really LN. 

8) One of the commenters used several AI programs on the question and NONE solved it. Some humans DID solve it. 

a) Some comments suggested that an AI should be able to list several ways the lists differ, and have probabilities of which ones are sensible.  My take: maybe in the future but not now.

b) Is this kind of question fair to ask an AI (or for that matter a person). They have to guess what I have in mind. Be that as it may, the AIs tried on the program.

DID NOT list out a different criteria that was right

but

INSTEAD gave criteria that were just wrong. 

 c) A commenter wrote  that the study was not rigorous. That's correct. So view this blog post as the starting point: study how AI's do on this question and others like it, keeping track of which AI and how the question is posed. Then we will have a better sense. 

9) Is this a sign that AI is not as good as people think OR is it just a hiccup?

Trevisan Prize- Deadline July 31 for Notification Intent, Aug 31 for nomination.

A new prize:

The Trevisan Prize, in honor of Luca Trevisan, who died in 2024 (blog obit is here, open problems column in his honor is here), has been announced. 

 The link is  here.

 

The deadline for notification of intent is July 31 which is soon.

 The deadline for the nomination is Aug 31. 

 

 

A Prez Question: Can AI do it? Can you? Can I?

 I am curious how AI or humans can do on the following question.

I have listed out the nominees for Prez and VP (Vice Prez) since 1976 and put them in two categories.

What criteria did I use?

The criteria is about their lives. So it's not going to be something like

The ones in GROUP ONE have last names with at most 3 vowels.

A few notes before the lists:

1) You may come up with  criteria I didn't come up with.  It may even be outside of my rules- for example about vowels. Fine- I will be curious if some criteria like that happen to be equivalent to my criteria.

2) You can use whatever you want- Wikipedia, ChatGPT, your friend who knows a lot about presidents.

3) Leave comments with your proposed answer AND HOW YOU GOT IT, though be warned to NOT go to the comments if you want to work on it yourself, since the right answer might be there.

4) There are people who were the nominees for Prez or VP several times.
I want the list to be in chronological order. I list everyone only once.
What to do about (say) the fact
that Bob Dole ran for VP in 1976 and for Prez in 1996?
I list people in order of the FIRST time they were the nominee.
So I have:

VP 1976. Prez-1996
Bob Dole

5) I added some misc information for fun. That information is NOT relevant to the solution. 

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

GROUP ONE:

VP-1976 and 1980. Prez-1984
Walter Mondale

Prez-1976
Gerald Ford

VP-1976. Prez-1996
Bob Dole

VP-1984
Geraldine Ferraro

Prez-1988
Michael Dukakis

VP-1988
Lloyd Bentsen

VP-1988 and 1992
Dan Quayle

Prez-1992 and 1996
Bill Clinton

VP-1992 and  1996. Prez-2000
Al Gore

VP-2000
Joe Lieberman

Prez-2004
John Kerry

VP-2004
John Edwards

Prez-2008 and 2012
Barack Obama

Prez-2012
Mitt Romney

VP-2008 and 2012. Prez-2020
Joe Biden

Prez-2016
Hillary Clinton

VP-2016
Tim Kaine

VP-2016 and 2020
Mike Pence

VP-2020. Prez-2024
Kamala Harris

VP-2024
J.D Vance

(The only names that were flagged for being misspelled are Dukakis, Bentsen, Kamala.)

--------------------------------------
GROUP TWO

Prez-1976 and 1980
Jimmy Carter

Prez-1980 and 1984
Ronald Reagan

VP-1980 and 1984, Prez-1988 and 1992.
George H.W. Bush
(Not counting the early elections which had different rules,
I think the only other person who got the nomination twice for VP
and twice for president is Richard Nixon. If I am wrong, let me know.)

VP-1996
Jack Kemp

Prez-2000 and 2004
George W Bush

VP-2000 and 2004
Dick Cheney

Prez-2008
John McCain

VP-2008
Sarah Palin

VP-2012
Paul Ryan

Prez-2016 and 2020 and 2024
Donald Trump

VP-2024
Tim Walz

(The only name that was flagged for being misspelled was Walz.) 

Turing, Wagner, Ruth

Douglas Hofstadter first published Gödel, Escher, Bach: an Eternal Golden Braid in 1979 and my then high school self tried, and failed, to read though the entire book. It focused on the contradictions, with Kurt Gödel's incompleteness theorems, M. C. Escher's Drawing Hands and Johann Sebastian Bach's Canon a 2 per tonos, a piece that keeps rising until it ends a whole tone higher than it started.

I'd prefer to focus less on the paradoxes and self-reference to the true beauty and complexity of computation. So now having had a long career in the field, who would I call on to capture the power and beauty of computing?

It has to start with Alan Turing. His seminal paper On Computable Numbers, with an Application to the Entscheidungsproblem gives a clean model for computation and still the best argument (Section 9) for why this simple model captures everything computable. The Entscheidungsproblem, that you can't mechanize all of mathematics, comes as a consequence, not as a goal of the paper. In a much later paper, The Chemical Basis of Morphogenesis, he shows how the beauty of nature can emerge naturally from computation, which of course we now know much better arises from discrete DNA sequences.

For music, instead of Bach's abstract works, I prefer to focus on the emotional power of music that still arises from a musical score that is not unlike a computer program in the way it lays out the composition. Take for example Richard Wagner's Prelude and Liebestod (the beginning and the end of his opera Tristan and Isolde). It captures the tension of the two lovers from the very first notes and keeps that tension going until it resolves at the very end.

While soccer and basketball have mostly continuous play, I prefer that great American game of baseball that after each pitch has a very discrete state space that stadiums would capture with a few light bulbs (strikes, balls, outs), and yet could keep the excitement and tension on every one of those pitches. No one dominated the game more in his time than George Herman "Babe" Ruth, who I might have admittedly also chose to keep the same syllable cadence as Hofstadter.

So let's thank Turing, Wagner, Ruth, and the many others that showed we can show how incredible complexity and beauty can arise in the simplicity of computation. So many stories to tell. 

How much money did Francis Scott Key give to have a building named after him?

UMCP has a building named 

The Francis Scott Key Building

STUDENT: How much money did Francis Scott Key give to have a building named after him?

BILL: He didn't give money. He wrote The Star Spangled Banner.

STUDENT: I get it! He left the royalties! That would be a lot since Major League Baseball plays that song before every game!

BILL: The song is in the public domain.

STUDENT: That's too bad. Well, at least UMCP got some money out of it before it was in the public domain.

BILL: Francis Scott Key did not give UMCP the royalties from his song.

STUDENT: Well then what did he give UMCP?

BILL: He didn't give UMCP anything. He died in 1843 and UMCP was founded in 1856.

STUDENT: Oh. So his descendants gave money to have a building named after him.

BILL: No, that didn't happen either.

STUDENT: Then why is there a building named after him?

BILL: To honor him.

STUDENT: What does that mean? The only reason to name a building after someone is if they give money to the school. The notion of "honoring someone" sounds so odd--in fact I honestly don't know what it means. OH, I get it, they are just using that name as a placeholder until they find someone who gives the school money for a building.

BILL: I doubt that. Once a building is named to honor someone, it won't change the name for money. That's just too crass.

LANCE: Don't be so sure. When I started undergrad at Cornell in 1981, Benjamin Franklin hall, the site of the country's first Electrical Engineering Department, was just renamed to Olive Tjaden hall. One of my professors made fun of the change, "Why should we name it after Ben Franklin—he never donated to Cornell".

During an alumni weekend, we had a visit from a former alum and his wife, Olive Tjaden, to my fraternity, Kappa Delta Rho (Yes, I was a frat boy in college). She was not shy about bragging that the building was named after her. For some reason Mr. Franklin never showed up to defend the old name. 

Cornell still has a Lincoln Hall named after the former president. 

BILL: Does any campus name buildings to honor people anymore? 

LANCE: At this point I wouldn't be surprised if some university names a building "Donald J Trump Hall" as part of a settlement.

But really, these days, you need money to build buildings, so they get named after donors—or after someone the donor wants to honor. Even if a building is built on state funds, it's usually given a generic name to leave open a naming opportunity later. 

BILL: What happens if you name a building after someone because they gave money but later if they found out that they are an X (you can fill it in with some type of person you would not want to honor)? If you had named the building to honor them, you can change the name. If you named it because they gave money you may have a contractual obligation to keep the name. (This was almost a problem with Enron Field, see here).

LANCE: In 2017, Yale renamed Calhoun College, named for a white supremacist, to honor Grace Murray Hopper. 

BILL: I hope they got all the bugs out first.

I conjecture very few (any?) colleges name buildings anymore to honor people. It is purely transactional. 

1) Am I right? ADDED LATER: Some comments pointed out that I a wrong. See the comments and also these pointer:

Univ of MD at College Park: Pyon-Chen Hall here, 

Univ of MD at College Park: Johnson-Whittle Hall (same pointer as Pyon-Chen) here, 

Univ of MD at College Park: Thurgood Mashall Hall here.

Princeton: (Toni) Morrison Hall: here

Univ of CA at Irvine: (F. Shewood) Rowland Hall here

Univ of CA at Irvine: (Fredrick) Reines Hall here

UT Austin: Anna Hiss Gym. here

 Readers- if you have other examples of BUILDINGS named after people do honor thos people, please leave a comment about it that provides enough information so I can get a pointer.

2) If so, is this a bad thing?

3) And when will Grace Murray Hopper College be renamed again after a donor?

The Customers of the Academy

I had an epiphany reading an article in the Trenton Times when I lived in New Jersey at the turn of the century. The article interviewed companies along a certain street lobbying for a new bus route so their employees could more easily get to work. The customers for mass transit are not its riders but the employers who need workers to get to them. Maybe that's why mass transit trains and buses offer a functional but not particularly comfortable ride.

So who are the customers for universities? Before I go there, let's look at newspapers. Until the early 2000s, newspapers were primarily driven by advertising revenue. Readers were the product. While newspapers needed readers to sell, they could get them by offering cheap subscriptions by focusing on quality coverage that focused on news and analysis from a broad range of views. But since then, the few newspapers that thrive now do so mostly on subscription revenue, print and digital, and the readers have become the customers. They also have more competition from other sources like social media. So newspapers now tailor their coverage and their brand for the paying subscriber, and while most still focus on accuracy, they'll stick to narrower views in their analysis which often overshadows the pure news.

Universities have a mission beyond just serving students, providing them with knowledge in exchange for tuition. They have a societal mission. The Morrill Land-Grant Act of 1862, which helped establish and grow a number of public universities, wanted to educate students to improve the productivity of American agriculture and industry. The GI Bill in 1944 brought the masses of returning soldiers into higher education. The Higher Education Act of 1965, brought in resources for students through Pell Grants and federally-guaranteed student Loans to further the competitiveness of America through the Cold War. Most universities have non-profit status because of their broader mission.

In other words, society as a whole was our customer. Our role is to educate and prepare students to help push our society forward. Many universities also have a research mission, also mostly government funded, both to recruit expert professors to educate our students, but also to produce important knowledge to manage the complexities of the world. Students participated willingly for future intellectual and financial gain and our role was to ensure the students got a strong education, for the betterment of not just themselves but the workforce and society they would later join.

Our viewpoint has changed as college costs increased and universities became more dependent on tuition and governmental financial aid. Institutions started treating the students as the customer, to ensure they came to the university and stayed there. More amenities, grade inflation, much more student support and tolerance. The relationship became transactional, a student comes, pays their tuition and their time, gets a degree and gets a job. The focus becomes more on degrees that prepare you for the workplace, a focus more on immediate skill and credential building than producing students who have the critical thinking skills to build a strong career. 

And now in a time of changing demographics, less government support and AI heading towards performing many of the skills universities teach, how does the story continue? How do universities focus back on producing students who can not just live in our society but improve it? How do they focus on the right customers while ensuring educational quality? Universities need to get it right, or they won't have customers at all. 

The New Lower Bound on Busy Beaver of 6.

 We denote the busy beaver function by BB.

BB(n) is the max time a Turing machine of size n takes to halt on the empty string.

(A particular model of TM and a notion of size has become standardized.)

BB(n) grows faster than any computable function. That is obviously interesting. What is less obvious (and  some of my co-bloggers disagree) the pursuit of actual values of BB is interesting. For an excellent overview of the BB numbers, written in 2020 (that is relevant) by Scott Aaronson, see here. (Computable and Aaronson are flagged by my spell check but I think they are spelled correctly.) 

When Scott's article appeared, BB(5) was not known. In June 2024 the value of BB(5) was discovered.  See Scott's blog on this, here. The value of BB(5) isn't even that big- its just 47,176,870. That's one of those numbers that is SMALL now but would have been LARGE in (say) 1964 (see my blog about a different number of that type here). 

What about BB(6)?

No, I am not going to announce that Scott announced it is now known. 

I am going to announced that Scott announced better lower bounds for BB(6) are now known. 

I won't restate the lower bounds since (a) Scott already has (see here) and (b) typesetting the bounds is hard (for me). 

SO, what to make of all this?

1) At the time of Scott's article it looked like BB(6) was large. How large was hard to say. Intuitions about how large BB(6) would be are hard to come by, so the new result is neither surprising nor unsurprising. 

2) We will never know BB(6). Shucky Darns!

3) Many of the results on BB are not published in refereed journals. However, the ones mentioned in the context of BB(5) and BB(6) were verified in Coq.  I doubt other parts of math could take this approach;  however, it is interesting that results can be verified via computer in this field. Indeed- I doubt a referee could verify the results without a computer aid. 

4) Why the interest in BB? Some speculation:

a) Computing power is such that one can actually get out some results (read Scott's blog on BB(5) for more on that).

b) The internet: there are not that many people working on BB but those that are can easily communicate with each other. 

c) Scott's article and his blog posts on it helped generate interest. Since I asked Scott to write the article for my open problems column, I get some credit here also (very little).

d) Results generate interest, and interest generates results.

e) Items a,b,c,d,e all help to reinforce each other. 

A Professor Again

A new dean has taken my place, and I have returned to the professoriate at Illinois Tech, ending thirteen years in administration, six as dean and seven as department chair at Georgia Tech. I won't rule out more administrative roles in the future, but only if the right role presents itself.

I'll teach intro theory in the fall, my first course since 2018, and take a sabbatical in the spring, mostly at Oxford. I plan to focus on writing, hoping to get out another book or books and other projects. It will be hard to go back to traditional computational complexity research, the field has changed considerably. I plan to spend some time understanding how AI changes the way we think about computation. Particularly why we see many of the benefits of P = NP while cryptography remains secure.

Also for the first time in 13 years I don't have a "boss". Technically I report to the department chair, who until a few days ago reported to me. But tenure protects my job, I choose my own research agenda, and teaching and service assignments are more of a negotiation than a top-down decision. Freedom!

For the blog, I have held back talking about the inner workings of universities while I had administrative roles. I'll now be more open in giving my thoughts, at least in general terms.

The next chapter begins...

Two high school students have a new proof of the Pythagorean Theorem / Pythag theorem older than thought

(I wrote this post a while back so its no longer NEW. More important--- if there has been a follow-up to the story that is not in my post, let me know.)  

 We have something NEW and something OLD about the Pythagorean Theorem. Now all we need is something BORROWED and something BLUE.

NEW

Two high school students have a new proof of the Pythagorean Theorem, see here. (An anonymous commenter provides a pointer to their published article in the American Math Monthly.)

They used trigonometry. Oh wait, that sounds circular since Trig is based on the Pythagorean Theorem. While this is a fair question to ask about the theorem, it has recently been accepted for publication and looked at carefully (those two are not equivalent) so it seems to be correct. 

The Pythagorean Theorem is an often-proved-theorem. Often an often-proved-theorem has proofs that use hard math (e.g., proofs that primes are infinite using Ramsey Theory, see my post on that here). However, the new proof of PT seems to be elementary. 

Kudos to them!

OLD:

Pythagorean theorem found on clay tablets 1000 years earlier than Pythagoras: see here.

My students would ask me

 How come Pythagoras didn't go to arXiv to see if someone already had the theorem? 

The Distribution of Prime Numbers: A Geometrical Perspective

Alberto Fraile and Daniel Fernández guest post on random walks generated by the distribution of prime numbers.

In our recent papers, we explored the sequence of prime numbers by defining "random walks" governed by simple algorithms applied to their sequence.

We introduced a prime number visualization called Jacob’s Ladder. The algorithm plots numbers on a 2D graph that oscillates up and down based on the presence of prime numbers, creating a ladder-like structure. The path ascends or descends based on the primality of subsequent numbers. When a prime number is encountered, the path alters direction, leading to a zig-zag pattern. Number 2 is prime, so it flips and goes down. Now 3 is prime, so the next step changes direction and goes up again, so we move up. But 4 is not a prime, so it continues up, and on it goes.

Jacob’s Ladder from 1 to 100,000 (Top) and from 1 to 1,000,000 (Bottom).
The blue line represents y=0, or sea level.

The x-axis can be imagined as sea level, the zig-zag above it as mountains, and those below as ocean chasms. Our intrepid navigator sails eastward, occasionally discovering new lands—sometimes tiny islands, other times vast continents.

As we chart this new world, it is natural to wonder about the location of the next continent (if any), the height of its highest mountain, or the depth of its deepest ocean. One thing we know for sure is that gaps between primes can become arbitrarily large. This suggests there may be no upper bound on the mountains’ heights or the chasms’ depths.

A natural question arises: if the voyage continues into infinity, would this world contain equal amounts of land and sea? Or, more formally, does the construction exhibit symmetry in the limit, with equal numbers of positive and negative points? The beauty of Jacob’s Ladder lies in its simplicity, yet it raises many questions that are surprisingly difficult to answer.

Prime Walk

In our second study, we examined the behavior of a 2D "random walk" determined by the sequence of prime numbers, known as the prime walk (PW), choosing a direction based on the last digit of the next prime (1 down, 3 up, 7 right, 9 left) ignoring the primes 2 and 5.

Graphical representation of three different PWs up to N=108. Color coding represents step progression.

Observing the PW in action raises numerous questions.

For instance, will this PW eventually cover the entire plane as N → ∞? Will the area explored continue expanding indefinitely, or will it reach a limit? Initially, we conjectured the area would be unbounded.

We thought this conjecture might remain unanswered indefinitely, so we challenged the community with a modest prize for anyone who could prove it within two years of publication. Surprisingly, we found the solution ourselves, detailed in our recent work.

Moreover, within the explored region, certain points remain unvisited—small regions or isolated spots. Could some points remain unreachable forever? These straightforward questions, intriguingly, remain remarkably difficult to answer.

If you do well in the UMCP HS Math Competition you may win $1,000,000

The Univ of  MD at College Park holds a HS Math Competition every year. At the reception for the winners Professor Larry Washington points to many past people who did well on the exam. Two stand out for different reasons:

1) Serge Brin did well on the UMCP HS competition and went on to be a Stanford Math Grad Student Drop Out. Oh well. (I originally had Standard instead of Stanford. That sentence will makes sense.) 

2) Sarah Manchester did well on the UMCP HS competition  and went on to win $1,000,000 on Wheel of Fortune. 

Is there a connection between doing well on the UMCP Math Competition and winning $1,000,000 on Wheel of  Fortune? 

Only 4 people have won the $1,000,000. Worse, if you don't win the $1,000,000 you will probably win less than $50,000. An article about those 4 is here. This is so few that while I am sure Sarah is good at Wheel of Fortune (a) she had to also be very lucky, and (b) I doubt being good at Math had much affect on her winning. 

While we are here, lets look at two other game shows.

14 people have won $1,000,000 or more on Who wants to be a Millionaire?, see here. That show has the advantage that even if you don't win $1,000,000 it's not so unusual to get over $100,000.

(What kind of people do not want to be millionaires? I give two answers later.) 

Deal or No Deal has different versions in different countries so it gets more complicated:

UK: 9 big winners, Turkey: 1 big winner, Australia: 4 big winners, America: 2 big winners. 

ANYWAY back to Sarah and Wheel of Fortune: The statement

Sarah did well on the UMCP HS Math Competition and went on to win $1,000,000 on Wheel of Fortune

is technically true but conveys a causality that is not true. 

Who does not want to be a millionaire? 

Would be a terrible name for a quiz show. However, taking it as a question the answer is with one caveat: I define Millionaire as someone who has AROUND $1,000,000. 

a) Billionaires. Actually, anyone who has much more than  $1,000,000 would not want to come down to only $1,000,000.

b) People who think it would change their life in ways they don't want. 

Fulbright Memories

As the entire Fulbright board resigned last week and as the program that promotes international visits for US researchers, and vice-versa, may not survive the Trump administration, I thought I would recount some memories from my Fulbright scholarship to the Netherlands in 1996-97.

The program had considerable paperwork for a relatively small stipend, but it went beyond the compensation. I went to a meeting in Amsterdam with the other fellows, mostly grad students and postdocs. I was the old one as a recently tenured associate professor. The others had strong reasons for being in the Netherlands: An historian who wanted to research the Dutch army, and a piano player with hands too small who came to study with the world's leading teacher on a specialized narrow-keyboard grand.

And so they asked me why I would go to the Netherlands from the US to study computer science. But I spent the sabbatical year at the Centrum Wiskunde & Informatica (Center for Mathematics and Computer Science) in Amsterdam working with Harry Buhrman, Leen Torenvliet, Paul Vitányi and others. I also made several trips to universities in Germany, England, France and Israel, and had one of my best research years.

My coolest Fulbright experience was having Thanksgiving dinner at the US ambassador's house in The Hague, perhaps the most American thing I did during the year.

I also participated in celebrations marking the fiftieth anniversary of the Fulbright program, established in 1946 to encourage international educational and research collaborations, alongside the Marshall Plan and NATO, to draw the US closer to Europe and later the rest of the world. Too bad we seem to be moving away from those ideals today. 

Lance never thought he would see a Pope who roots for the same team as him. And now...

 A year ago if I showed you a picture of The Pope wearing a Baseball cap for the Chicago White Sox  (or any Amercan team) you would assume it was computer-generated.  And you would likely be right. 

Are there any real pictures of any Pope before Pope Leo XIV with a baseball cap on? 

I doubt it 

A real picture of Pope Leo wearing a Chicago White Sox baseball cap is here.

1) Having an American Pope is so incongruent with how we think of Popes that pictures like Pope Leo XIV in a baseball cap look very odd.

2) Pope Francis was a soccer fan (see here).  Is there a real  pictures of him wearing a soccer jersey?

3) Before the web we didn't know much about the personal lives of leaders. I don't just mean we didn't know about (say) their affairs; we didn't even know about non-controversial things like what sports team they root for. 

4) Lance has tweeted that he never thought he would see the day where he and The Pope rooted for the same baseball team. I want to see a picture of The Pope and Lance together at a game, both wearing Chicago White Sox caps. A real picture may be hard to do, but I suspect that once The Pope  sees this post he will create such a picture. 

5) I hope the next Pope is a fan of the San Diego Padres for two reasons

a) The name of the team.

b) They have never won a World Series. They need all the help they can get.

Defending Theory

In the June CACM, Micah Beck writes an opinion piece Accept the Consequences where he is quite skeptical of the role of theory in real-world software development, concluding

It is important that we teach practical computer engineering as a field separate from formal computer science. The latter can help in the understanding and analysis of the former, but may never model it well enough to be predictive in the way the physical sciences are.

I certainly agree that theoretical results can't perfectly predict how algorithms work in practice, but neither does physics. The world is much more complex, both computationally and physically, to perfectly model. Physics gives us an approximation to reality that can help guide engineering decisions and theory can do the same for computation.

You need a basis to reason about computation, lest you are just flying blind. Theory gives you that basis.

Let's consider sorting. Beck complains that Quicksort runs in \(O(n^2)\) time in the worst case even though it is used commonly in practice, while the little-used Insertion sort runs in worst-case \(O(n\log n)\). Let's assume Beck meant an algorithm like heapsort that actually has \(O(n\log n)\) worst-case performance. But theorists do more than fixate on worst-case performance, Quicksort runs in \(O(n\log n)\) on average, and on worst-case if you use a random pivot, or a more complex deterministic pivoting algorithm. Introsort combines Quicksort efficiency and worst-case guarantees and is used in some standard libraries.

Beck worries about secondary storage and communication limitations but theorists have studied sorting in those regimes as well. 

The other example he talks about is about a theoretical result that one cannot use an unreliable network to implement one that is completely reliable while textbooks consider TCP to be reliable. But in fact TCP was designed to allow failure because it took account of the theoretical result, not in spite of it.

Beck ends the article talking about Generative AI where theory hasn't kept up with practice at all. Beck calls for using classical AI tools based on formal logic as guardrails for generative AI. However, the lack of theoretical understanding suggests that such guardrails may significantly weaken generative AI's expressive power. Without adequate theory, we must instead rely more heavily on extensive testing, particularly for critical systems.

There are stronger examples Beck could have used, such as algorithms that solve many NP-complete problems efficiently in practice despite their theoretical intractability. Even here, understanding the theoretical limitations helps us focus on developing better heuristics and recognizing when problems might be computationally difficult.

I agree with Beck that relying solely on the theoretical models can cause some challenges but rather than have the students "unlearn" the theory, encourage them to use the theory appropriately to help guide the design of new systems.

Beck's call to separate software development from theory only underscores how important we need to keep them intertwined. Students should know the theoretical foundations, for they shape problem solving, but they should also understand the limitations of these models.

The New Godel Prize Winner Tastes Great and is Less Filling

David Zuckerman

The 2025 Gödel Prize has been awarded to Eshan Chattopadhyay and David Zuckerman for their paper

Explicit two-source extractors and resilient functions

which was in STOC 2016 and in the Annals of Math in 2019. 

We (Bill and Lance) care about this result for two different reasons.

BILL: The result has applications to constructive Ramsey---

LANCE: Ramsey Theory? Really? This is a great result about

Eshan Chattopadhyay

pseudorandomness! In fact the only interesting thing to come out of Ramsey Theory is the Probabilistic Method (see our discussion of this here). 

BILL: Can't it be BOTH a great result in derandomization AND have an application to Ramsey Theory. Like Miller Lite: Less Filling AND Tastes Great (see here)

LANCE: But you don't drink!

BILL: Which means I can give a sober description of their application to Ramsey Theory.

All statements are asymptotic.

Let \(R(k)\) be the least \(n\) so that for all 2-colorings of \(K_n\) there is a homog set of size \(k\).

Known and easy: \(R(k)\le 2^{2k}/\sqrt{k} \)

Known and hard: \(R(k) \le 3.993^k \). How do I know this is true? Either I believe the survey papers on these kinds of results (see here) or a former student of mine emailed me a picture of a T-shirt that has the result (see here) from (of course) Hungary.

Known and Easy and Non-Constructive: \(R(k)\ge k2^{k/2}\)

Can we get a constructive proof? There were some over the years; however, the paper by Eshan Chattopadhyay and David Zuckerman improves the constructive bound to exponential in \(  2^{(\log k)^\epsilon}.\) 

SO Lance, why do you care?

LANCE: First of all when I chose this paper as one of my favorite theorems (a far bigger honor than the so-called Gödel Prize) I gave the post the clever title Extracting Ramsey Graphs that captures both the pseudorandomness and the Ramsey graphs. But of course the Ramsey result is just a minor corollary, the ability to get a near perfect random bit out of two independent sources of low min-entropy is the true beauty of this paper. 

BILL: You have no sense of good taste.

LANCE: Well at least I'm not less filling.

Rules vs Standards

You can write laws that are very specific, like the US tax code, or open to interpretation like the first amendment. In the literature these are known as rules and standards respectively. 

In computational complexity, we generally think of complexity as bad. We want to solve problems quickly and simply. Sometimes complexity is good, if you want to hide information, generate randomness or need some friction. But mostly we want simplicity. How does simplicity guide us in setting guidance, either through rules or standards?

 

Rules are like a computer program. Feed in the input and get an output. Predictable and easy to compute. So why not always have tight rules?

Nobody ever gets a computer program right the first time, and the same goes for rules. Rules can be overly restrictive or have loopholes, leading to feelings of unfairness. Rules can require hoops to jump through to get things done. Rules don't engender trust to the ones the rules apply to, like very tight requirements on how grant funds can be spent. We know that in general we can't predict anything about how a computer program behaves, so why do we trust the rules? 

A good example of a standard is that a PhD dissertation requires significant original research. Rules are things like the exact formatting requirements of a thesis, or statements like a CS thesis must contain three papers published in a specific given set of conferences. 

As an administrator I like to focus on making decisions based on what's best for my unit, as opposed to ensuring I followed every letter of every rule. Because if you live by the rules, you'll die by the rules.  People will try to use their interpretation of the rules to force your hand.

Sometimes we do need strict rules, like safety standards, especially for people unfamiliar with the equipment. Structured rules do give a complete clarity of when an action is allowed. But it also gives an excuse. Have you ever been satisfied by someone who did something you didn't like but said "I was just following the rules"?

Even strict rules tend to have an out, like a petition to take a set of courses that don't exactly match the requirements of a major. The petition is a standard, open to interpretation to capture what the rules don't. 

As a complexity theorist I know what programs can't achieve, and as an administrator I see the same with rules. I prefer standards, principles over policies. Set your expectations, live by example, and trust the people, faculty, staff and students, to do the right thing and push back when they don't. People don't want strict rules, but they mostly act properly when they believe they are trusted and have wide latitude in their work. 

Complexity theory of hand-calculations

 (Thanks to David Marcus who sent me the video I point to in point 4 of this post. Tip for young bloggers (if there are any) you can have a half-baked idea for a post and then someone sends you something OR you later have an idea to make it a full-baked idea for a post. That's what happened here. So keep track of your half-baked ideas.)

1) When I was 10 years old I wanted to find out how many seconds were in a century. I didn't have a calculator (I might not have known what they were). I spend a few hours doing it and I got AN ANSWER. Was it correct? I didn't account for leap years. Oh well.

(An astute reader pointed to a website that does the centuries-to-seconds conversion as well as many other conversions. It is here. If such was around when I was a kid, what affect would it have on my interest in math? Impossible to know.) 

2) Fast forward to 2024: I wanted to find the longest sequence of composites all \( \le 1000\). One long sequence I found by hand is the following (I also include the least prime factor):

114-2, 115-5, 116-2, 117-3, 118-2, 119-7, 120-2, 121-11, 122-2, 123-3, 124-2 , 125-5, 126-2

length 13.

I wanted to find the answer WITHOUT using a computer program or looking at list of primes online (though I do allow a calculator just for division and multiplication). 

Of more interest mathematically is trying to prove that there is no sequence of length 14. (If there is, then perhaps the attempt will lead us to it.) 

Assume there was a sequence of consecutive composites \(\le 1000\) of length 14.

Map each one to the least prime that divides it. 

At most 7 of them map to 2

At most 3 of them map to 3

At most 2 of them  map to 5

At most 1 of them  map to 7.

At most 1 maps to 11. (Can look at 11*p for all primes \(11\le p \le 89\) and see any of them are in a sequence of length 14.) 

I'll stop here. This is getting tedious and might be wrong. So I asked Claude. It gave me a  sequence of composites of length 19. Here it is (I include the least prime factor):

888-2, 889-7, 890-2, 891-3, 892-2, 893-19, 894-2, 895-5, 896-2, 897-3, 898-2, 899-29, 900-2, 901-17, 902-2, 903-3, 904-2, 905-5, 906-2.

Can one show by hand that there is no sequence of length 20? 

3) The more general question: what is the complexity of finding the longest string of composites all \( \le n\) . This is actually many questions:

a) By hand: by which I mean only allowing multiplication and division and only of numbers \(\le n.\)

b) Theoretically. Use whatever fancy algorithms you want.

c) Theoretically but can assume some Number theory Conjectures that are widely believed. The Wikipedia page on prime gaps is here. (ADDED LATER- an astude commenter pointed out that we want LARGE gaps between primes, but the wikipedia article is about SHORT gaps between primes.) 

d) Do a,b,c for the set version which is as follows:  Given \(n\) and\( L\) determine if there a sequence of consecutive composites of length L that are all \(\le n\).  

4) Does anyone else care about calculation-by-hand? Yes! There are people who want to compute\(\ pi\) to many places JUST BY HAND. Here is a video about them here. Spoiler alert: they did very well. 

The Hilltop Story

 

On Route 1 in Saugus, Massachusetts, about a twenty minute drive from Cambridge, stood the Hilltop Steak House. When I went to graduate school in the late 80's, Hilltop led all restaurants in the United States by sales (about $30 million in annual revenue) and volume (about 2.5 million customers).

I went there several times during graduate school. Despite the size, about 1500 seats, always a long wait but worth it to get a good steak at a price a grad student could afford. 

But in 1994, Hilltop was bought by an investment company from the original Giuffrida family. The cost of labor went up and to keep costs reasonable, the new owners cut the quality of the meat. No longer a place to get good steak at a good price and with changing tastes, they lost customers and would finally close in 2013.

Computer Science as an academic discipline has had its Hilltop moment with tremendous growth pretty consistently from 2010 through about 2023. But with the growth of AI and an uncertain job market, if we don't maintain quality and adjust to the new needs and interests of our students, CS may become just a road sign on Route 1.

Some are Mathematicians, some are Carpenters' Wives, Some are Popes.

 (Trivia: What song has the lyric Some are Mathematicians, some are Carpenters's wives ? It's not a parody song, though sometimes it's hard to tell a  parody song from a so-called real song.)

In my post about Pope Leo XIV I made the following comments in different parts of the post:

Pope Leo XIV has a degree in Mathematics.

Prevost [his pre-Pope name] has a degree in mathematics from Villanova. 

He is not the first Pope to know some mathematics.

I also wrote:

Since Pope Leo XIV was a mathematician, as Pope he won't only know about sin but also about cos.

Someone emailed me about this line, not to say it was a bad joke or even a good joke, but to say 

Since Pope Leo XIV was a mathematician: What qualifies one to be considered a mathematician?

A few thoughts on this question.

1) I blogged about this topic here. Hence today I will discuss issues I did not discuss then. 

2) Robert W  Prevost wrote a book that (just from the title) seems to use some math:

Probability and Theistic Explanations, see here.

that was published in print in 1990 and online in 2023.  I wonder if it will sell more copies now.  I am tempted to ask for a free copy to read and do a review of, but I'm not sure I really want to read it. 

One would think that if someone named Robert Prevost wrote a book that seems to use math and theology then it would be the Robert Prevost who is now called Pope Leo XIV. I thought that. A commenter on my blog thought that. But Lance read an earlier version of this post and pointed out that 

Robert W Prevost NE Robert  F Prevost AND

Robert F  Prevost = Pope Leo XIV.

Hence, alas, the author of the book is NOT Pope Leo XIV. It's striking how plausible it would be that Pope Leo IS the author.  The book STILL might sell more copies since people may think it's by the Pope. 

Robert W Prevost's Wikipedia page is here.

Robert F Prevost's Wikipedia page is here.

3) If someone keeps LEARNING math but doesn't DO math I WOULD consider them a mathematician.

4) If someone is a math crank then the question of are they a mathematician will depend on how cranky they are.

5) If one KNOWS a lot of math but is neither learning anymore or doing any more (perhaps myself when I retire) can you consider them a mathematician?

6) If someone gets a PhD from MIT in Pure math but then goes to industry and programs would you consider them to be a mathematician?

7) If X is NOT a math crank and X considers themselves a mathematician, are they a mathematician?

8) I WOULD consider applied math to be math. This should not need to be said but there may be some pure-math-snobs reading this post. Computer scientists, statisticians, are more of a borderline case that, without being a snob, I might not consider mathematicians.

9)  Someone posted on the blog where this came up Does Lance consider himself a mathematician? I asked Lance and he said:

For the next 37 days I consider myself a Dean. After that, who knows?

The Blog of Record

On Saturday, I had my last Illinois Tech graduation as dean before I step down at the end of June. The College of Computing had nearly 1600 graduates and I shook many, many hands that morning.

After graduation I caught a plane to Washington, DC to attend the wedding of my daughter's college friend. We were invited because we became good friends with the bride's parents when we lived in Atlanta. My last trip before Covid was to DC for an NSF panel and this was my first trip to Washington since. 

The out-of-town guests were housed at the Hyatt Regency Bethesda, coincidentally the same hotel that hosted STOC 2009. My favorite STOC talk of all time took place in that building. But I remembered nothing about the venue except for the jogging path near the hotel.

No trip to the DMV would be complete without seeing my co-blogger Bill Gasarch in person for the first time in years. We chatted about many things, most notably his last few posts where he joked about the new pope's undergraduate math thesis, taken seriously by both our readers and ChatGPT. I reminded Bill that we are the blog of record, often used by wikipedia as a primary source for much in and out of complexity. Later Bill took out the fake thesis titles.

With graduation behind me, not much more for me to do as dean before my term ends. On the plane ride home, I thought about the question everyone asks me: What's next? I have no idea, but it's going to be fun.

Is Satire Dangerous in the AI-Age?

There have been times when satire has been mistaken for reality. A list of Onion stories that were mistaken for reality (or was it a mistake?) is here. When I say mistaken for reality I mean that a large set of people were fooled.

My own Ramsey-History-Hoax (blog here, latest version of the paper here) has fooled some people; however the number of people is small since the number of people who know the underlying math is small. 

In my last blog (see here) I said that the Pope Leo XIV majored in math (that is true) and then I gave a false title for his thesis (I HAVE SINCE REMOVED THE ENTIRE PASSAGE). 

 Later in the post I said that his ugrad thesis was not on that topic, but  gave another false title (I HAVE RMEOVED THAT AS WELL.) 

I thought the reader would know that it was false, but one comment inquired about it so I left a comment admitting it was false.

This is all very minor: Not that many people read this blog and very few non-math people would care about what the topic of the  Pope's undergraduate thesis.

The last part of the last sentence is false. Its the POPE! People Do care about his background. 

But surely my blog post isn't so well read so as to make the fictional  title of his thesis a hoax that fools a lot of people. 

Even so, I left a comment wondering if LLM's might learn the incorrect title of the Pope's ugrad thesis. 

A reader named E posted the following:

 It might be too late. I did this search this evening:

E: Did Pope Leo XIV study Ramsey Theory?

Gemini: Pope Leo XIV, whose given name is Robert Francis Prevost,
earned a Bachelor of Science degree in mathematics from Villanova
University in 1977. His undergraduate thesis focused on Rado's Theorem
for Nonlinear Equations.

0) This may not be too bad- one would have to ask about The Pope and Ramsey Theory to get that answer. But in the future this answer might pop up on the question`What did the Pope Study as an Undergraduate' or similar questions.

1) Might future satires or April Fool's Day jokes be mistaken for reality in the future by AI and hence reach a much larger audience than this blog does?

2) If so, should we be careful with what we post (not sure how to do that)?

3) What about people who have a much larger following than complexityblog  (yes, there are such people)?

4) In the past one had to be a celebrity or similar to change peoples perception of reality (see Stephen Colbert and Wikipedia here). Now a complexity blogger may be able to change people's perception of reality. Hence I ask

Is Satire Dangerous in the AI-Age?

 

 

 

 

 

A Bittersweet Anniversary

The National Science Foundation was founded on May 10, 1950, 75 years ago last Saturday. No doubt the NSF has seen better days, but first let's take a look back.

At the end of World War II, Vannevar Bush, Director of the Office of Scientific Development, wrote Science, The Endless Frontier, where he laid out the importance of scientific research and the need for the US government to foster that research. 

A new agency should be established, therefore, by the Congress for the purpose. Such an agency, moreover, should be an independent agency devoted to the support of scientific research and advanced scientific education alone. Industry learned many years ago that basic research cannot often be fruitfully conducted as an adjunct to or a subdivision of an operating agency or department. Operating agencies have immediate operating goals and are under constant pressure to produce in a tangible way, for that is the test of their value. None of these conditions is favorable to basic research. Research is the exploration of the unknown and is necessarily speculative. It is inhibited by conventional approaches, traditions, and standards. It cannot be satisfactorily conducted in an atmosphere where it is gauged and tested by operating or production standards. Basic scientific research should not, therefore, be placed under an operating agency whose paramount concern is anything other than research. Research will always suffer when put in competition with operations.

The report laid out the National Research Foundation that would actually spread across three agencies, DARPA, NIH, and the NSF.

While Bush didn't significantly mention computing, given the time, Computing would become a central part of NSF's mission with the establishment of the Computing and Information Science and Engineering (CISE) directorate in 1986, placing Computing at the same level as the Math and Physical Sciences Directorate and the Engineering Directorate.

In 1999, the President’s Information Technology Advisory Committee (PITAC) issued a report that led to the NSF Information Technology Research (ITR) program, which became one of the largest NSF research initiatives of the early 2000s. The report helped reframe computing not just as infrastructure but as a scientific discipline in its own right, deserving of the same kind of basic science funding as physics or biology.

CISE has led many initiatives through the years, for example the TRIPODS program established several centers devoted to the theoretical study of data science.

In recent weeks, the NSF director stepped down, hundreds of grants were canceled, new grants were put indefinitely on hold, indirect costs on new grants will be capped at 15%, and many staff members were pushed out. Divisions below the directorates are slated for elimination, advisory committees have been disbanded, and Trump's proposed budget cuts NSF’s allocation by about half. The CISE AD (Assistant to the NSF Director, or head of CISE), Greg Hager, stepped down last week and through the CRA sent a message to the community.

Under these circumstances, my ability to carry out my vision, to provide a voice for computing research, and to provide authentic leadership to the community are diminished to the point that I can have more impact outside NSF than within it. Echoing Dr. Nelson’s powerful article, leaving “allows me to speak more clearly in my own language,” and, in doing so, even more effectively amplify the work of the incredible, dedicated CISE leadership and staff who continue to strive to fulfill NSF’s mission. 

As I move beyond NSF, I will continue to make the case for computing research. Computing is central to so much in today’s world and computing advances are now core assets to the Nation’s research enterprise. NSF’s support for the past 75 years has forcefully demonstrated the value of computing research for advancing national health, prosperity and welfare; enhancing national economic competitiveness; securing the national defense and helping promote all of science and engineering. NSF-funded work has continually catalyzed new innovations, created new industries, and made us the envy of the world.  

We all need to join Greg in continuing the fight to ensure that Vannevar Bush's vision continues to survive another 75 years and beyond.