Theory that really DOES apply: Security.

I recently read and wrote a review of

                               Math for Security by Daniel Reilly.

(For the review see here. It will appear in SIGACT News at some later point. For the amazon link see here. Disclosure: Lance and I are Amazon Affiliates.)

The book had great example of using THEORY for PRACTICAL problems of security (NOT what you think as you will see later). Since I am always surprised (possibly because of my ignorance) when theory REALLY applied to PRACTICE I asked the author some questions which he answered. Our conversation is below.

BILL: I was surprised that a book called Math for Security didn't have crypto in it. Why was that?

DANIEL:
There's a plethora of excellent material that already covers the topic very well. Cracking codes and analyzing ciphers is the first thing most people think of when they think of the relationship between math and security. There are so many other topics where a little creativity and math can open up new avenues and approaches to unique problems we face in security. As an analyst and consultant, a very small percentage of my time goes into cryptographic systems, but I'm regularly asked other questions.  I'm hoping to show that anyone can apply a little math to start making better (or at least more informed) decisions in many of these areas, not just cryptography.

BILL: Many theorists dream of the day when someone comes along to REALLY use their stuff. For example---

DANIEL: (Cuts Bill off) That's funny. As an analyst I'm always hoping to define a theory which explains some system I've been analyzing. Something like Kim Rossmo's formula in Forensics
(see here). Understanding what your data is telling you is good, but discovering why, that's the pinnacle of accomplishment! I guess the grass is always greener on the other side of the fence!

BILL: The first time I saw the problem of determining the Betweeness Centrality of a node is, it was in a paper showing that it was APSP-hard (so likely not in subcubic time).  Hence I was AMAZED that you use it FOR REAL. How hard was it to take the THEORY that you found in the literature and APPLY it.

DANIEL: For the graph theory in the book, and in general, I think it comes down to some basic statistics and understanding the underlying system being modeled. Betweenness centrality is a great example. It's really easy to calculate, but what it means in practice is wholly dependent on what generated the data. A high Betweenness score in a social network is the result of a different underlying structure than in a computer network. This is one reason graph theory made sense as the place to start. There are so many problems that can be represented as a graph with very little change to the methodology needed, but it does show the need to be flexible in your interpretation of theory.
For the programming side, NetworkX is really well designed so I didn't have to do much to implement the algorithms. That made it easy to focus on showing off how the library could be used when analyzing a real data set. Of course, whenever you're taking a general theory and applying it to a specific problem, you'll always have some pieces you need to build. The pieces that glue the theory
and the data together in a useful way. For me, that is the fun part. The art behind the science. You can give 5 analysts the same problem and get back 10 possible approaches!

BILL: I recently looked at the Complexity of the Art Gallery Problem- it is ER-Complete (see Wikipedia entry on Existential Theory of the Reals) which is between NP and PSPACE. Hence I was AMAZED that you use it for REAL. How hard was it to take the THEORY that you found in the literature and APPLY it. For example, the Guards, unlike the Who (see here) cannot see for miles and miles and miles and miles and miles.  (NOTE: Spell check thinks that NP is a word, but PSPACE is not a word. Odd!)

DANIEL: You sound like a broken record. But still a good question. The Art Gallery Project was the one that kicked off the idea to write the book in the first place. I was looking for a method to analyze physical security layouts and I came across a paper describing the problem as it related to security camera placement. That led me to the original paper and then Fisk's paper using the greedy coloring algorithm. I think I read one or two more pieces about how greedy coloring is implemented in NetworkX, but that was it. Once you understand the basic problem formulation, and Fisk's method of solving for n-vertex polygons, you quickly move out of what the theory was designed for. The Art Gallery project therefore represents what I think is a more typical scenario. I'll often start with a
theoretical solution that makes a lot of simplifying assumptions and then remove the simplifications a little at a time by adding in other theoretical bits (such as adding a function to compute a more realistic guess at what area a guard can protect). Sometimes I will find complimentary research on modeling something like walking speed. Other times I rely on my experiences and best guess (like assigning the space for people at an event). At it's core though, the algorithm solving the layout is the same one suggested by Fisk and implemented in NetworkX.

BILL: Anything else you want to add?

DANIEL: There is a quote I love that gets thrown around in System Dynamics a lot It's better for a model to be useful, than accurate I think that idea applies really well when you're building proof-of-concept systems. For example, a model that is very accurate at predicting an adversary's behavior may not be very useful if it is too complex and expensive to use. Ultimately, the best model is the one that is most useful for solving the problem at hand. This means that it is important to consider other factors than accuracy, such as interpretability, cost, and ease of use, when developing your proofs. It's important to remember the goal is not to perfectly model the system your studying, but to model enough of the key components to get a useful response.

Saving Grace

The Grace Hopper Conference has grown to one of the largest in computer science, pushing past 25,000 attendees. Most women in computing, whether a student, faculty or working in industry, are usually in a minority. Grace Hopper gives them the chance to see and be part of a strong community of woman in our field in a safe and comforting environment.

Or so it was supposed to be. At the Expo part of last month's conference, where many companies come to recruit, men made up about 40% of the attendees according to an NPR report. Now Grace Hopper welcomes male allyship but these were no allies. Rather they acted, often aggressively, to reach recruiters and making the experience uncomfortable for the attendees who came for the conference's purpose.

The conference organizers released a statement and a blog post noting they can't legally limit registration based on gender but will work on other approaches to ensure a good conference in the future.

I know there are, in particular, graduating international students desperate to find a job so they can remain in the country. And I've argued that CS needs a full annual meeting, which like Grace Hopper exists to bring people together not to focus on research but to focus on each other. But none of this justifies ruining the experience of those who attend a conference for what it is. 

If you don't have respect, don't come to the party.

When did Math Get So Hard- Part 2

Click here for When did Math Get so Hard-Part 1, though it was not called Part 1 at the time. 

This post is not so much about WHEN math got so hard but an example of math BEING hard. The main issue is that so much is known that the PREREQUISITE knowledge can be overwhelming.

My interest in Hilbert's tenth problem (see here) and an email from Timothy Chow (reproduced in that article) lead me to the book

                               Rational Points on Varieties 

                                  by Bjorn Poonen

(see here for amazon link. Disclosure: Lance and I are amazon affiliates).

Here is the prerequisite for the book as stated in the preface: 

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

A person interesting in reading this book should have the following background:

1) Algebraic Geometry (e.g. [Har77]: up to Chapter II, Section 8 as a minimum, but familiarity with later chapters is also needed at time)--- this is not needed so much in our Chapter 1. 

2) Algebraic Number Theory (e.g., [Cas67], Fro67] or [Lan94, Part One] or [Neu99 Chapters I and II).

3) Some Group Co-homology (e.g. [AW67] or [Mil13], Chaper 2]). 

[AW67] M.F. Atiyah and I.G. Macdonald. Introduction to Commutative  Algebra, Addison-Wesley, 1969

[Cas67] J.W.S Cassels. Global Fields, Algebraic Number Theory (Proc. Instructional  Conf, Brighton), 1965), 1967, 42-84

[Fro67] A. Frolich, Local Fields, Algebraic Number Theory ((Proc. Instructional Conf, Brighton, 1965), 1967, 1-41.

[Har77] Robin Hartshore, Algebraic Geometry, Springer-Verlag, 1977, Graduate Texts in Mathematics, No. 52

[Lan94] Serge Lang, Algebraic Number Theory, 2nd ed. Grad Texts in Mathematics, Springer-Verlag. , 1994.

[Mil13] J.S. Milne, Class field theory (v4.02), March 23, 2013. Available at here

[Neu99] Jurgen Neukirch. Algebraic Number Theory,  Fundamental Principles of Mathematical Sciences Vol 332. 1999.

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

This seems like quite steep prerequisites. I don't have them so perhaps they are easier than they look. 

But in any case, Some parts of math are hard because, over time, so much math is known that builds on earlier math, that just getting through the background material is hard. Comp Sci hasn't been around as long, but its been around in the 20th and 21st century when more was being produces, so its also gotten hard, as I discussed here. Note also that computer science uses some of that hard math, and is also an inspiration for some hard math.

Fall Jobs Post 2023

In the 2022 Fall Jobs Post I talked about the effect of generative AI and that was two weeks before Open AI released ChatGPT to the public. A year later, how will AI change CS faculty hiring? Not much this year but change will come soon enough.

CS enrollment remains strong and computer science departments have not been able to keep up with the demand. Many see programming, rightly or wrongly, as one of the first careers that AI will displace, which may reduce enrollment in the future, as offshoring fears drove CS enrollment down 20 years ago. There will be newish majors, whether Data Science, Artificial Intelligence, Machine Learning or something else that will draw students away from traditional CS degrees. But for now many CS departments still need to grow their faculty. 

Having some knowledge and being willing to teach ML will definitely help in the job search but I expect we'll see demand in all areas, including theoretical computer science. There will also be more people on the market, especially as the major tech leaders aren't yet brought back hiring in CS to its previous levels.

Should you use AI to help you apply? I wouldn't use AI to write your personal statement or other materials--it's style is just too recognizable. But do use AI to read over what you wrote and give suggestions. You might be surprised on what it recommends.

CS departments are not yet using AI to screen faculty job applications. So you are writing for humans. There are many applicants so focus on what makes you stand out.

As always, have a well-designed web page with all your job materials. Make sure your Google Scholar and LinkedIn pages are accurate and up to date. Add yourself you the CRA's CV Database.

Some departments are starting the search earlier, so don't delay your applications.

Most CS faculty jobs are posted to the CRA and ACM. The CRA focuses on jobs for PhDs, the ACM mixes it up with general industry jobs. For theorists, check out TCS Jobs and Theory Announcements. 

If you have a job to announce, please post to the above and/or feel free to leave a comment on this post. 

Paper is a tech-free way to preserve writing. Is there a tech-free way to preserve sound (e.g., music)

I blogged about ACM going mostly paper-free, and had some PROS and CONS about paper-free, in this blog here. One of my many astute readers named Abigail pointed out that paper does not go obsolete: we can still read books written many years ago without having to use some technology. (The first paper in Harry Lewis's book Ideas that Created the Future: Classic Papers in Computer Science was by Aristotle. See here for amazon link to the book and here for my review of the book). By contrast, there are stories of material being lost forever since they are on floppy disks. I wonder if pdf will suffer the same fate. 

However, that is not the theme of this post (do my posts have coherent themes?)

The point is 

PAPER is TECH-FREE and is good at preserving WRITING.

What about SOUND? Is there a Tech-Free way to preserve sound? I am thinking about music, though one can also wonder how old poetry was supposed to sound when read out loud. But back to music:

1) The Bible Psalms- we know the words, but not the medley. Psalms 45 has the following right before it: For the director of music. To the Tune of ``Lilies'' Of the Sons of Korah. A maskit. A wedding song. In my bible there is a footnote saying that maskit is Probably a literary or music term. Not helpful to a 21st century singer.

2) The first Rap Song is from the Bible, in 1 Samuel 18:7. The words are

Saul has slain his thousands and David his tens of thousands.

And again, we don't know the melody or the cadence or the rhythm. I have done a rendition of it for my Bible study group but they complained it was not authentic. They also told me to not quit my day job. 

3) When music went from 

Wax Cylinder to Vinyl and audio cassettes to CD to MP3 to Spotify (and similar systems)

some music was lost in each transition. Indeed, the inspiration for this post is the following personal story:

One of my hobbies is collecting and listening to  novelty songs (this has been mentioned in the following posts: here, here, here,,  here, here, here, here, here) Some are audio tape, some are CDs. A subgenre of novelty songs is Filk Music, which are folk songs with a science fiction (its been expanded to science) theme. They are often  sung at science fiction conventions. It is filklore that an early science fiction convention mistyped folk as filk and they decided to keep it.

I was thinking of a GREAT  filk song titled

Carl Sagan Ronald Reagan San Diegan Pagan (lyrics are here)

and I wondered

a) Do I have it in my collection? (Almost surely yes.)

b) If so can I listen to it? (If on CD then yes. If on audio tape, not sure.)  

c) In any case is it on Spotify or YouTube or...I have found obscure things on both  Spotify and YouTube  so this was plausible. Spellcheck insists I spell it YouTube not Youtube and I will of course obey the Spellcheck God.

ANSWERS

a) It is on Bayfilk Crazies, an AUDIO TAPE that I have. YEAH!

b) I have one audio tape player in my house that I had not used in years. It didn't work. BOO!

(ADDED LATER- I found at Tape Recorder where PLAY worked, though neither FF or REWIND worked. So I got to hear my song! And I was ``forced'' to hear other songs I had not heard for a while. Some were excellent gems I had forgotten about. Others... not so much. But I am happy for now.)

(ADDED MUCH LATER (July 1, 2024) I FOUND Bayfilk Crazies on mp3, here. Yeah!) 

c) So far I cannot find it to listen to ANYWHERE on the web. BOO!

(If you find such a place please leave a comment!)

d) It does not appear to be on CD. BOO! (Again, if you can find a place to buy it on CD let me know.) 

SO, is this great song LOST TO HUMANITY? I know the tune, so I could sing it on YouTube, but there are enough badly sung songs on YouTube and I do not want to add to that. 

But my more important point is MANY SONGS ARE BEING LOST TO HUMANITY!

4) For many old songs we DO have sheet music and lyrics so someone COULD reproduce it. That's great. Is it important to have the authentic real Elvis recordings, or is a really good 21nd century Elvis Impersonator good enough? That depends what you want. And if the sheet music is only online we may have the same problem we are pondering about paper. 

 Famous songs are re-recorded a lot (To see what the most recorded song of all time is, see here. Its not my version of Muffin Math, see here.) But for songs that are not quite famous, or only appeal to certain tastes, we are losing songs!

5) For the written word there is PAPER which does not go obsolete with technology (though there are fires, see the burning of the library at Alexandria). For music there seems to be NO such analog.

6) Video has the same problem. I blogged about that here. 

Measuring Quantum Progress

In August the Google Quantum AI Team posted a blog post How to compare a noisy quantum processor to a classical computer to measure progress in building quantum computers. 

So far quantum advantage (a term that has thankfully seem to replace quantum supremacy) has focused on approximating quantum distributions like Boson Sampling or random quantum circuits as described in the blog post. These results are messy, it's hard to measure success, hard to know the classical complexity of these problems, hard to explain to the public and seem to have little to no practical value.

The poster child for quantum computing has always been integer factoring. Factoring has lots of great properties.

1. Factoring is theoretically easy to solve on a quantum computer via Shor's algorithm.
2. While we don't know the classical hardness of factoring, considerable efforts over decades have yet to produce any even subexponential-time algorithms.
3. It is classically easy to check the factors.
4. It is classically easy to generate hard to factor numbers.
5. You can explain factoring to anyone with even a moderate interest in mathematics.
6. Factoring is critical to a number of cryptographic protocols most notably RSA.

We will achieve true quantum advantage when a quantum machine can factor numbers we cannot then factor on traditional computers alone.

So why don't we measure the progress towards quantum advantage by the size of the numbers that quantum machines can factor? More precisely factoring via Shor's algorithm for order finding followed by some classical computations to get the factors. 

Likely because we don't do very well. As far as I can tell, the largest number factored on a quantum computing via Shor's algorithm is 21. Shor's algorithm just requires a level of entanglement beyond what today's quantum machines can handle even using error-correcting techniques.

It doesn't mean factoring is the wrong measure of the success of physical quantum computers, we're just not ready to do so. 

Young Sheldon gets two things spot-on/Am I more famous than.../Might YS become TS?

 Young Sheldon  is a TV show that I used to only watch on airplanes, but then i got into it and am now up to date. The wonders of technology! Note that catching up on a show would have been harder when I was a kid. (This is NOT a we had it rough in my day thing.)

1) There is an episode where Sheldon, his professor, and his Meemaw (grandmother) collaborate. When its done Meemaw is disappointed to here that all they have is a prototype and the real experiment will need a machine as big as the building they are in and won't be done for 30 years. Contrast  this to when a TV show shows people proving P=NP on a Monday and using it to do stuff on Tuesday (I blogged about this here). And there are other examples where a basic science discovery is useful in far less time then it would be in the real world. 

2) A young Sheldon Cooper has the idea for bitcoin and explains it to his brother. His brother is not as smart as Sheldon in math and science but DOES understand business. As such, he gave the best description of bitcoin I ever heard here.

(ADDED LATER: A commenter left a link to a blog post about why bitcoin is NOT a scam. The link is the text of the link and clickable. Here is a clickable version: HERE

3) I looked up the actress who plays Missy (Sheldon's twin sister) on Young Sheldon. I got the name off of the Young Sheldon page but she does not have a Wikipedia entry. I do have a Wikipedia page. That doesn't seem right since  I am sure that more people say

I want to know more about the actress who plays Missy on Young Sheldon.

then say

I want to know more about that guy who coblogs with Lance.

The set of people who have Wikipedia page seems somewhat arbitrary.

4)  Iain Armitage plays young Sheldon.

In Season 6 Sheldon is 13. See timeline of Young Sheldon

In Season 6 Iain A is 15. See Wikipedia Page for Iain A


If the actors strike goes on for 2 more years then Iain  will be a 17 year old playing a 14 year old. That might not work. They may need to change the name of the show to Teen Sheldon.

The show itself joked about this (intentionally?). When Sheldon is watching Beverly Hills 90210 he asks his father George do you know why this character is depressed ? George answers because he's a teenage who looks 30 years old.

But the real question is- might the strike really affect Child Actors who age-out faster than they would have? I know this is a minor problem compared to the other problems  actors have, but I thought it was worth noting.

The Lyadov Lesson

I've seen many brilliant students, those who flew though high school and undergrad with great grades and little effort. As PhD students, they often feel they still don't need to try, that success will continue to come to them easily. They would be wrong. Some figure it out, others don't live up to their potential.

Igor Stravinksy

I went to a Chicago Symphony concert last week where the first two pieces were "The Enchanted Lake", a short piece by Anatoly Lyadov, followed by Igor Stravinsky's "The Firebird". You likely never heard of Lyadov. There's a reason for that. 

From the program book 

Anatoly Lyadov is often mentioned in music histories, not primarily for his own beautifully crafted orchestral pieces like "The Enchanted Lake," but as the man who missed the opportunity to compose "The Firebird." This ballet, which Igor Stravinsky eventually wrote, became a cornerstone of his career and is frequently featured in programs, often following Lyadov's own works.

The common but unverified narrative is that Lyadov had been so slow to start the project that he had only just bought his manuscript paper when the first part of the score was due. This led Sergei Diaghilev, who was in charge of staging the ballet, to dismiss him. Lyadov had developed a reputation for laziness early in his career. He was known to skip classes at the Saint Petersburg Conservatory, earning the ire of his teacher, Rimsky-Korsakov, who called him "irresponsible." Even Sergei Prokofiev, who studied with Lyadov and held him in high regard, noted in his memoirs that Lyadov's "most remarkable feature" was his laziness.

Anatoly Lyadov

Yet despite these shortcomings, Lyadov had always attracted attention for the audacity and brilliance of his orchestral work. As far back as 1873, when he published his first songs as his opus 1, Mussorgsky described his talent as "new, unmistakable, original." Stravinsky, who benefited from Lyadov's withdrawal from "The Firebird" project, later remarked that although he enjoyed Lyadov's music, he couldn't imagine Lyadov composing a ballet as long and raucous as "The Firebird."

Half-Exponential No More

I've mentioned Kannan's proof that \(\Sigma_2^p\) does not have \(n^2\) size-circuits before. A similar proof shows that \(\Sigma_2^E = \mathrm{NTIME}^\mathrm{NP}(2^{O(n)})\) does not have polynomial-size circuits in general. You can create a language in the third-level of the exponential-time hierarchy that has maximum circuit complexity. Now if SAT doesn't have poly-size circuits you are done. Otherwise the polynomial-time hierarchy collapses to \(\Sigma_2^p\) which means the exponential-time hierarchy collapse to \(\Sigma_2^E\).

Can you show \(\Sigma_2^E\) has near exponential-size circuit complexity? The above proof doesn't quite work. The problem is that while a polynomial of a polynomial is polynomial, a subexponential function of a subexponential function could be superexponential. You can only make the proof work for circuit-size half-exponential, i.e., function \(f\) such that \(f(f(n)) = 2^{o(n)}\). I don't know of any natural half-exponential functions, but they are much larger than quasi-polynomial and much smaller than exponentials. 

The best known smallest class with an exponential circuit lower bound is for \(\Delta_2^E=E^{\Sigma_2^P}\) due to Miltersen, Vinodchandran and Watanabe from the last millennium. 

Lijie Chen, Shuichi Hirahara and Hanlin Ren have a new paper showing that in fact \(\Sigma_2^E\) does require exponential-size circuits. They have the same bound for smaller classes if you allow a bit of advice. 

You've seen these authors names before in this blog. The future of computational complexity is in good hands.

We Must Be Doing Something Right

The Chicago Tribune ran an editorial Monday that started

What’s the best four-year college in Illinois? Not the University of Chicago, Northwestern University or the University of Illinois at Urbana-Champaign.

No, the best college in the state is the Illinois Institute of Technology, of course!

The editorial was referring to the Wall Street Journal that ranked Illinois Tech 23rd in the nation, tops in Illinois, up from 117 last year. Illinois Tech also cracked the top 100 in the latest US News rankings, up from 127. 

Did we just get that much better? Yes, yes we did! 

Or maybe it had to do with changes in methodology. The Wall Street Journal's rankings this year puts a heavy emphasis on "how much will it improve the salaries they earn after receiving their diplomas". As Illinois Tech caters to students who often are the first in their families to go to college, and focuses on technical degrees, we can really raise up students who might not have otherwise had such an education. It's one of the things that brought me to the university in the first place.

US News also "increased the emphasis on how often schools' students from all socioeconomic backgrounds earned degrees and took advantage of information on graduate outcomes that was not available until recently". 

All rankings should be taken with a grain of salt, and universities will always tout rankings where do they well while conveniently ignoring others. It's impossible to linearly order colleges--there are just too many different factors that make different schools better for different people. 

But as people start to question the value of college the rankings are starting to address their concerns. And if that bumps up my university, so be it.

ACM to go paper-free! Good? Bad?

The ACM (Association of Computing Machinery) will soon stop having print versions of most its publications. Rather than list which ones are going paper free, I list all those that are not going paper free:

Communications of the ACM

ACM Inroads

Interactions

XRDS: Crossroads

What are the PROS and CONS of this? What are the PROS and CONS of any publication or book being paper free?

1) I like getting SIGACT News on paper since 

a) It reminds me to read it

b) Reading on the screen is either on my phone which is awkward (especially for math) or my desktop (so I have to be AT my desktop). 

I DO NOT think this is my inner-Luddite talking. 

 

2) QUESTION:  Will SIGACT News and JACM and other ACM publications continue to have  page limit for articles? When I was SIGACT News Book Rev Col editor, and now as Open Problems Col editor, I have often had to ask the editor Can I have X pages this time? The answer was always yes,  so perhaps there never really was a page limit. But is having no page limit good? Not necessarily. Having a limit may force you to only write down the important parts.

3)  PRO: Its good for the ecology to not make so much paper.  While this is certainly true, I think the world  needs to rethink our entire consumer society to really make a difference for the ecology. In fact, I wonder if e-cars, carbon-offsets,  and paper free products make us feel good without really helping much.

4) CON but good timing: I recently had an open problems column with two co-authors. One of them is not in the ACM and is not in the community, but wanted to see a copy of the article. I have arranged to have a paper copy of that one issue sent to him.  If I had published this column in 2024, I could not do this. And saying Just go to link BLAH' does not have the same impact as PAPER. I could have printed it out for him, but that just does not seem like the same as having an official copy. 

I DO think this is my inner-Luddite talking. Or his.

5) For quite some time computer science  conference proceedings have not been on paper (there have been a variety of ways this is done). Before that time the following happened a lot: I am in Dave Mounts office talking about something (e.g., who should teach what). He gets a phone call but motions that it will be short so I should still hang out. While hanging out I pick up a RANDOM proceedings of the conference RANDOM  and find the one or two article in it about Ramsey Theory and read them, or at least note them and read them later. That kind of RANDOM knowledge SEEMS less common  in a paper-free age. But maybe not.  I HAVE clicked around the web and accidentally learned things. Like the facts I learned for my post on simulation theory here.

6) Similar to point 5- I used to go to the math library and RANDOMLY look at a volume of the American Math Monthly or some other similar journal and look at some articles in it.  But now that's harder since they have stopped getting journals on papers and only get them electronically. To be fair, paper versions of the journals are EXPENSIVE. 

7) In the year 1999 my grad student Evan Golub got his PhD and he had to bring a PAPER copy of it to some office where they measured margins and stuff of EVERY PAGE to make sure it was within university specs.  Why? Because in an earlier era this was important for when the thesis was put on microfilm.  Were they doing that in 1999? I doubt it.  Some of my younger readers are thinking OH, they didn't have LaTeX packages that take care of margins for you.  Actually they DID have such packages but, to be fair, the requirement that the university literally measures margins on EVERY PAGE was completely idiotic. I am  happy to say that in 2007 when my student Carl Anderson  got his PhD nobody needed a paper version. I do not know when the rules changed but I am glad they did. 

8) The ACM should promote this paper free change by doing a rap song like Progressive Insurance did here. 

9) Recently I had a paper with 3 co-authors that all three of us, and some others, proofread (I thought) very carefully. The referee accepted it but with a somewhat nebulous this paper needs a better proofreading. I then PRINTED IT OUT and read it AWAY FROM MY COMPUTER (the paper is on overleaf) with a RED PEN and I found LOTS of stuff to fix that we all missed before. So there are some advantages to getting OFF of the computer, though that may require PRINTING. (I also blogged about this topic here.) 

Mr. Jaeger and The Scroll

There were three major influencers in my educational journey: Mike Sipser, my PhD advisor at Berkeley and MIT, Juris Hartmanis who founded the field of computational complexity and led me to it at Cornell, and Philip Jaeger, a math teacher at Millburn High School in New Jersey.

Perhaps your "scroll" will outlast both of us.

I took two math courses with Philip Jaeger, Algebra II and Probability. Mr. Jaeger (I still can't call him Phil) also ran the computer room, a narrow room of three teletype machines where we saved programs on paper tape, where we would do simulations of poker hands for probability class among various other programming. He truly set me up for my future career. 

Mr. Jaeger was also the advisor of the computer club when I was president. 

That's me in the middle of the first photo, with Mr. Jaeger on my right.

Sometime during my high school years I took one of the rolls used in the teletype machine and wrote down a lengthy formula. According to Mr. Jaeger, the formula is for the area of a random triangle. I'm sure it made sense to me in high school.

The Scroll

The Scroll partially unscrolled

Another student Cheryl took the entire formula and put it entirely on an index card. Mr. Jaeger saved both the roll and the card.

The index card (actual size is 3x5 in)

Fast forward to 2023. Mr. Jaeger finds the roll and the card. His son, an academic in his own right, suggested that they track Cheryl and me down. I'm not hard to find. After some emails, they invited me to visit to pick up the roll. Last weekend I was in New Jersey visiting family so I did just that.

What great fun to talk to my old teacher, reminiscing about the high school people and times, and catching up after four decades. It was Mr. Jaeger who showed me the computer dating form that had me create a version for our high school.

I gave Mr. Jaeger a copy of my book and he gave me the scroll and the index card. (Cheryl, now a lawyer, wasn't interested in it). I safely brought it all home to Chicago along with all the memories. I dug up my old yearbook for first two photos above. The scroll will indeed outlast the both of us.

Mr. Jaeger, myself and the scroll.

Asymptotics of R(4,k)- a new result!

 At the workshop 

Ramsey Theory: Yesterday, Today, and Tomorrow, Edited by Alexander Soifer, 2011. (There is a printed proceedings that you can find.)

 I saw Joel Spencer give a great talk titled 

                               80 years of R(3,k).

( Recall that  R(a,b) is the least n such that for all 2-colorings of the edges of K_n there is either a red K_a or a blue K_b).

 The talk was about improvements on both the upper and lower bound on R(3,k) and finally:

                                  R(3,k) = \(\Theta\biggl (\frac{k^2}{\ln k}\biggr )\).

The obvious question was raised: What about R(4,k). The general sense I got was that this would be a much harder problem. However, there has been some progress. A recent paper, here, improved the best known lower bound, so it now stands at

                                   \( c_1\frac{k^3}{\log^4 k} \le r(4,k) \le c_2\frac{k^3}{\log^2 k} \)

How long before we see matching upper and lower bounds?

1) How long did it take to get matching upper and lower bounds for R(3,k). The name of the talk would make one think 80 years, but I would start at a paper of Erdos from 1961 which had the first non-trivial lower bounds. And it was solved in 1995, so that's 34 years. (Note, the talk of Spencer was also on later algorithmic aspects of the problem). 

2) Argument for why matching bounds on R(4,k)  will be found  in \(\le 10\) years: There are more people using more sophisticated tools then were known for the R(3,k) search.

3) Argument for why matching bounds on R(4,k) will take (\ge 20\) years: This problem is dang hard! Triangles are much easier to deal with then  4-cliques.

This is a general problem math has: If a problem is not been solved, is it just dang hard, or are people one or two (or some small finite number) steps away from solving it?

Books to Inspire Math

Two of my colleagues and co-authors from my early days at the University of Chicago have released books over the past few months designed to excite people with math, Howard Karloff's Mathematical Thinking: Why Everyone Should Study Math and Lide Li's Math Outside the Classroom. Karloff was a fellow professor and Li was my PhD student. Neither are currently in academia but both still found the need to inspire young people in mathematics.

Both books aim to make math fun, away from the rote problem solving from high school and early calculus courses to concepts like prime and irrational numbers (Karloff) and sequences and geometric shapes (Li). The books have some overlap, both cover deriving e from interest rates and probability including the Monty Hall problem. Both books have lots of problems to work on. 

Between the two I would suggest Karloff's book for junior high/high school age kids and Li's book for older high school and early college students given the topics covered.

At a time that math plays a larger role in our society, especially dealing with data, finding ways to get more young people interested in mathematics is important. These books fill an important niche for the mathematically curious students to dive in topics they won't likely see in their math classes. Great to see my former colleagues taking the time to reach these students through these books. 

The CONTRADICTION of Margaritaville and other songs

Jimmy Buffett passed away on Sept 1, 2023. His Wikipedia entry (see here) says his death was peaceful and he was surrounded by friends, family, and his dog, so it was likely expected and of natural causes. I later saw a report that he had a serious skin cancer. He was 76. 

He is not related to Warren Buffett--- they actually took a DNA test to find out, see here. They are friends. Buffett isn't that common a name, see here, so it was plausible they were related, but, alas, they are not.

His signature song is Margaritaville (My spellcheck thinks that I misspelled Margaritaville   but I checked it and it looks fine. OR it's one of those things where I keep misreading it.) It wasn't just his signature song---he made a career of it outside of music, see here.

Jimmy Buffett fans are called parrot heads.

There are songs where the lyrics are misheard. Margaritaville is not one of them. Instead, its lyrics are misunderstood. This raised the question:

There are  other songs whose LYRICS and WHAT PEOPLE THINK ABOUT THEM are in CONTRADICTION. What caused the contradiction? Could I make this into a HW assignment the next time I teach logic? Not if my students are looking for their lost shaker of salt.

This link here has 25 songs with misunderstood lyrics. Margaritaville comes in at the 24th. I think it should rank higher (lower index, higher ranking) but I can't complain since I am not an expert and they put in the work (unlike my ranking of satires of Bob Dylan, here, where I am an expert and I put in the work).

I list a few of the songs, plus two more,  and WHY the contradiction. I also listened to them with the following question: ONCE you know what the song is supposed to be about and you listen to it, do you say OF COURSE THAT'S WHAT ITS ABOUT or REALLY? I STILL DON"T SEE IT. This is similar to reading a math proof knowing where it is going so perhaps you say OF COURSE. Of course, you might also say REALLY? I STILL DON"T SEE IT.

 The name of the song in the list below is also a pointer to a video of it.

Imagine by John Lennon. People think it's about peace and love. The writer John Lennon (not be be confused with Vladimr Lenin) says it's a Communist manifesto.  I just listened to it and OF COURSE it's  a Communist Manifesto- but its sung with such an optimistic loving tone that one could miss that. This is John Lennon's best known post-beatles song. 

Total Eclipse of the Heart by Bonnie Tyler. People think it's a power ballad- about love and such. Its actually a vampire love song. REALLY? I STILL DON"T SEE IT. A love song is a love song. It could be about humans, vampires, or, in the case of The Klein Four, Math, but unless they put something Vampire-ish  into it, you can't tell its about Vampires. Two notes: (1) Its Bonnie Tyler's biggest hit, and
(2) it was released in 1983 but also had a large number of sales in 2017. Why? Either guess or see here.

Blackbird by the Beatles. People think its just about a blackbird with a broken wing. Its about civil rights for blacks (or all countries- so I can't use the term African American) REALLY? I STILL DON"T SEE IT. I believe the Beatles intended that meaning.  They also would not play to audiences that had rules about Whites only, or were segregated. So YEAH for them, but I still don't see it. Or hear it. Why the contradiction? Perhaps if I heard it in 1968 I would have understood what it was about. Perhaps they really weren't that clear about it. Perhaps they had to avoid it being censored.

Born in the USA by Bruce Springsteen. This is a well-known misunderstood song, so better to say People USED TO think it was a Pride-in-America song but it was really about the plight of lower class Americans, especially Vietnam War Veterans, after the war. OF COURSE ITS ABOUT THAT. Why was there the contradiction? (1) the chorus is loud and understandable and belts out BORN IN THE USA! as if that's a good thing, (2) the other lyrics are somewhat mumbled (I had to listen to it on a you tube video with closed caption to understand the song), (3) People hear what they want to hear. 

Notes: I was GOING to look up what The Boss's top hit ever was, expecting it to be Born to Run, but that's only his 18th biggest hit. Born in the USA is 8th, and Secret Garden is 1st. Even so, I think of Born to Run as his best known song. Why? (1) It was sung as the opening number of the 2010 Emmy awards (not by him, but done really well- Jimmy Fallon does a GREAT Bruce Springsteen), see here (2) there are several parodies of it, see born to Run (COVID), Born to Run (Bridgegate), Meant To Be (a best man's song), Jedi are Done. Having went to the effort to find parodies of Born to Run I then found parodies of Born in the USA: Bored in the USA (COVID), Touched by the TSA,  Conned in the USA, Borune'D in the USA (cryptocurr) And there are more. Upshot: trying to find out what someone's best-known song is can be a quagmire, but at least I  got to find some cool parodies.

Who Let the Dogs Out by the Bah  Men. People thought this song was about ... Hmmm, I don't know what people thought. Perhaps it was about someone who let the dogs out. Its actually about how BAD it is when men cat-call women. OF COURSE ITS ABOUT THAT once you see the lyrics.  Why the contradiction? Its really hard to understand anything except the chorus. Their biggest hit.

The Macarena by Los Del Rio. People tend to not listen to music that they dance to. So people really did not think it had a meaning. Also some of it is in Spanish. I can't write what it's about here since I may violate community standards as we did with a prior post (see here). See here for what the lyrics mean OR the list I pointed to above. If you listen to it or read the lyrics OF COURSE IT MEANS THAT! HOW DID I MISS IT? TOO BUSY DANCING! Why the contradiction- as I said above, its really a dance song. Their biggest hit. 

Note: Dance Songs usually don't have that many words. Knuth (see here for the original article and  here for the Wikipedia page about it which has later results) noted that the complexity of  That's the way uh-uh I like it is O(1).

Margaritaville by Jimmy Buffett (I'd be curious to see a version by Warren Buffett). This is a well-known misunderstood song, so better to say that people USED TO think it celebrated a relaxed lifestyle but its actually a sad son about a drunk. OF COURSE THE SONG IS ABOUT BEING DRUNK AND DEPRESSED. So why the contradiction? The tune is so happy-go-lucky, and Jimmy Buffett (and others) talk POSITIVELY about The Margaritaville lifestyle. Whats really odd is that the real meaning of the song IS WELL KNOWN, yet is ignored.

Note: A more realistic take on this topic, to the same tune, is  here.  A Marijuana version of the song is here. A crystal meth version  of the song is here. There are FOUR parodies that are NOT about being drunk, high, or on Crystal-meth, but about... COVID: here, here, here, and here. 

99 Red Balloons or  99 Luft ballons (the original German Version) To quote the original link: Whether in its original German language or in English, the happy-pop New Wave jam is easily the most danceable  song about a nuclear holocaust caused by balloons. When I listened to it and read the lyrics OF COURSE ITS ABOUT A NUCLEAR HOLOCAUST CAUSED BY BALLOONS. Why the contradiction?  The more popular version is in German, the English version is a bit mumbled (but not much), but most importantly, if there is going to be a nuclear holocaust caused by balloons  I will get up and dance!

Note:  I knew of one parody 99 Dead Baboons, but through the wonders of search and you tube I found more: the social media song, 99 90s shows, 99 unused balloons, 99 Steins of Beer 

For two more, though they are not on the list, see  'The Pina Colada' Song is Really Messed up and Why the Beastie Boys Hate `Fight for your right to Party'

TO SUM UP: songs that get misunderstood may (1) have some  hard to understand lyrics, (2) be dance songs, (3) have the melody and instruments be at odds with the lyrics, (4) have lyrics that people want to hear and others that they don't, (5) be partly or wholly in a foreign language.  I am sure there are other reasons.  

Jimmy Buffett: You will be missed!

What Makes a Constructive Proof?

In this weblog, we've used constructive in different ways. Often we talk about constructive as something we can create in polynomial time, like an expander. But how about constructive as in logic, when you don't get to assume the "excluded middle" where you get to assume some statement is either true or false?

The simplest well-known example is the theorem: There exists irrational \(a\) and \(b\) such that \(a^b\) is rational. 

1. \(\sqrt{2}^\sqrt{2}\) is rational. Let \(a = b = \sqrt{2}\).
2. \(\sqrt{2}^\sqrt{2}\) is irrational. Let \(a = \sqrt{2}^\sqrt{2}\) and \(b = \sqrt{2}\).

You don't know which \(a\) is correct. You just know it exists. (A far more complicated argument shows \(\sqrt{2}^\sqrt{2}\) is in fact irrational.) 

When I teach intro theory, my first proof that there are non-computable sets is by claiming the computable sets are countable but their are an uncountable number of sets over \(\Sigma^*\) so there must be an non-computable sets. I claim this is a non-constructive proof because I didn't give you the set and do an aside on constructive proofs using the example above. But that's not correct--the proof that there are uncountable number of sets over \(\Sigma^*\) is a constructive diagonalization. Give me an enumeration of the computable sets and I can easily construct a set not on that list.

In complexity, a well-known non-constructive theorem is by Kannan, showing that \(\Sigma^P_2\) does not have \(n^2\)-size circuits.

1. SAT doesn't have n²-size circuits. Since SAT is in Σ₂ we are done.
2. SAT has n²-size circuits. Then by Karp-Lipton Σ₄ = Σ₂ so L is in Σ₂ and we are done.

Jin-Yi Cai and Osamu Watanabe, and independently Sunny Daniels, gave a constructive \(\Sigma^2_P\) machine and thus a single language in \(\Sigma^P_2\) that doesn't have \(n^2\)-size circuits. But it is not a constructive proof, as the argument the machine works requires the two cases as to whether SAT has small circuits. As far as I know, a true constructive proof of Kannan's theorem remains open.

I have no problem with non-constructive proofs—I'm in a firm believer in \(P\vee\neg P\). But if you do talk about constructivity be sure and use it appropriately. 

Theorems and Lemmas and Proofs, Oh My!

I was recently asked by a non-mathematician about the difference between the terms Theorem, Lemma, etc. My first reaction was I probably have a blog post on that. Actually, I looked and I don't seem to. Since I have, according to Ken Reagan, over 1000 posts (see here and here) I can easily confuse things I meant to write a post on with things I wrote a post on. My next thought was Lance probably has a post on that. I asked him, and he also thought he had, but also had not. So now I will!

Open Question: A well defined question that you don't know the answer to and may not even have a guess as to which way it goes. The above is not quite right: sometimes an open question is not that well defined (e.g., Hilbert's 6th problem: Makes Physics Rigorous) and sometimes you have some idea, or a rooting interest, in how it goes. I tried to find some open questions in Mathematics where people in the know don't have a consensus opinion.  I can think of two off hand: Is Graph Isom in P? and is Factoring in P. Maybe the Unique Game Conjecture, though I think people in the know think it's true. Here is a website of open questions, but I think for all of them people in the know  think we know how they go: here.

Conjecture: A statement that you think is true, and may even have some evidence that its true, but have not proven yet. I am used to using this term in math, and hence I hope someone will PROVE the conjecture. Are there conjectures in empirical sciences? If so, then how do they finally decide it's true? Also note- I blogged about conjectures and how once they are proven the conjecturer is forgotten here. EXAMPLES OF CONJECTURES: The same link as in open problems above. 

True story but I will leave out names: There was a conjecture which I will call B's Conjecture. C & S solved it AS WRITTEN but clearly NOT AS INTENDED.  Even so, C & S got a published paper out of it. This paper made M so mad that he wrote a GREAT paper that solved the conjecture as intended (and in the opposite direction). That paper also got published. So one conjecture lead to two opposite solutions and two papers. 

Wild-Ass Guess: You can take a wild-ass guess what this is. 

Hypothesis: An assumption that you may not think is true but are curious what may be derived from it. The Continuum Hypothesis is one. For some reason Riemann's problem is called The Riemann Hypothesis even thought it's really a conjecture.  So is my notion of Hypothesis wrong? In any case, if you know other things that are called Hypothesis then please leave a comment. 

Lemma: A statement that is proven but only of interest in the service of proving a theorem. There are exceptions where a Lemma ends up being very important, see here. The word is also used in English, see here, but I've never heard of the word being used that way.

Theorem: A statement that has been proven. Usually it is somewhat general. There are a few exceptions: Fermat's Last Theorem was called that before it was a Theorem. If you know other things that were called theorems but weren't,  please comment.  EXAMPLES OF THEOREMS: The Fundamental Theorem of X (fill in the X), Ramsey's Theorem, VDW's theorem, Cook-Levin Theorem, The Governor's theorem (see here). There are many more theorems that have names and many that do not. 

Corollary: A statement that follows directly from a Theorem. Perhaps an interesting subcase of a Theorem. Often this is what you really care about. When trying to find a famous corollary I instead found The Roosevelt Corollary to the Monroe Doctrine,  Corollaries of the Pythagorean theorem, and Uses of the word Corollary in English. Are there any famous corollaries in mathematics that have names?

Claim: I do the following though I do not know if its common: During a proof I have something that I need for it, but it is  tied-to-the-proof-of-the-theorem so it would be hard to make a lemma. So I prove it inside the proof of the theorem and call it a claim. I use Claim, Proof of Claim, End of Proof of Claim to delimit it. 

Porism: A statement that you can get from a theorem by a minor adjustment of the proof. I've also heard the phrase Corollary of the proof of Theorem X. I first saw this in Jefferey Hirst's Phd Thesis which is here, on Reverse Mathematics. I liked the notion so much I've used it a few times. It does not seem to have caught on; however,  there is a Wikipedia entry for the term here which also gives two examples of its use, which are not from Hirst's  thesis or my papers. 

Proposition: I see this so rarely that I looked up what the difference is between a Proposition and a Theorem. From what I read a Proposition is either of lesser importance, or is easy enough to not need to give a prove, as opposed to a Theorem which is important and needs a proof.

Axiom: A statement that one assume is true and usually they are self-evident and true. Exceptions are The Axiom of Choice which some people reject since it is non-constructive. Also some people do not thing The Axiom of Determinacy is self-evident. Same for Large Cardinal Axioms. But really, most axioms are self-evident. Note that all branches of math use Axioms.

Postulate: Euclid used the term Postulate instead of Axiom. Actually, Euclid wrote in Ancient Greek so to say he used the term Postulate is probably not quite right. However, the term Postulate seems to mean an axiom of Euclid's, or perhaps an axiom in Geometry. One exception: Bertrand's Postulate which was a conjecture but is now a theorem. The link is to a math-stacks where there is some explanation for the weird name. 

Paradox:  A Paradox is a statement that is  paradoxical. Hmmm. that last sentence is self-referential, so its not enlightening. A paradox is supposed to be a statement that seems absurd or self contradictory, though under closer examination may make sense. Russell's Paradox shows that Frege's definition of a set does not work. The Monty Hall paradox, and the Banach-Tarski Paradox are just theorems that at first glance seem to be absurd. The Monty Hall Paradox is not absurd. Darling thinks the BT-paradox means that math is broken, see this post here for more on that.

Transcripts for the 21st Century

When I start a new academic job, I need to prove that I actually have a PhD. I have to log in my MIT alumni page, pay my $10 and they email my graduate transcript to whomever, all to verify that one bit of information. Why don't I just have a digitally signed certificate I can just hand over?

Our CS department spends an inordinate amount of time looking through transcripts of accepted Masters students to determine if they the right prerequisites for various classes. Great if could automate this process but the transcript come in PDF or JPEG and don't have a standardized format, especially from foreign countries. Also a course name does not give enough information to know what it covers. 

The Chronicle of Higher Education did a forum on The Transcript of the Future, and maybe some solutions to these problems on the horizon. Here are three potential future trends and an elephant in the room.

Modality

Since I went to school, transcripts have moved from paper to PDF. PDFs work for humans to look at, but don't work well to feed into computers to allow for better analysis. Transcripts should move to a structure format, perhaps JSON, to make them readable to machines. It's easy to go from JSON to PDF but less easy in the other direction. 

To make this work you need a standards so each university's transcript doesn't use a different format. Some standards are in the works but this doesn't seem quite settled yet, as best I can figure out from Internet searching.

Content

Once you go digital you can add much more information. You can add a syllabus, the topics a course covers, not just its title. You can add competencies, credentials, certificates, projects and skills achieved. You can add student's activities such as internships, athletics, clubs, leadership roles. You can give grad schools and companies a much fuller picture of a student beyond the grades.

The more stuff we stick into a transcript, the more standards you need to make sense of it. 

Provenance

Who owns the transcript? Right now it is the university, that's why I have to pay $10 for MIT to send it out. But why not in some common database, or on a blockchain, or a file owned by an individual with all the proper technology so it can't be forged. There are privacy and security issues that we would need to figure out. You don't want a student to lose access to a transcript because they lost a password, the way many have lost cryptocurrency. 

Artificial Intelligence

If we do have access to standardized digital transcripts, there will be the temptation to outsource to AI decision making related to them, such as job interviews (already happening) and grad admissions. We can use AI responsibly to help in the process but we need to remember that all these students are individuals and we need people to judge the people behind them.

Why I have some sympathy for the Simulation Theory (We are all characters in a video game.)

There are some people who believe that we are all characters in a video game written by Abisola (this is sometimes called The Simulation Hypothesis). I first dismissed this as nonsense. Then I read about it in the great  book But What if We're Wrong by Chuck Klosterman. He had  some reasons why The Simulation Hypothesis  is plausible. I thought about some more examples of his reasons. I still DO NOT believe it, but the reasons TO believe it do raise some questions.

There is one word that describes all of the reasons: Glitches!  That is Abisola, who wrote the code, made some mistakes that sometimes show through. Actually some might not be mistakes, perhaps Abisola, planned it. She has the bug/feature issue as do we. 

Here are some of those glitches: 

1) Real people who, from an accident, gained an ability that they did not have before.

a) Jason Padget: After being attacked and getting a concussion, woke up and was a math genius. 

b) Derek Amato: After a head injury became a brilliant composer.

c) McMahon: After a head injury woke up speaking fluent mandarin. I could not find a Wikipedia Entry for him.

d) Tony Cicero: After being struck my lightening was an excellent musician. I read this on a Quora entry but could not find it anywhere else. If you have more evidence on this one, please leave a comment and I will add it here later.

2) While I dismiss most accounts of ghosts, ESP, miracles, etc, there are so many of them that perhaps some are real and caused by glitches. Or features. 

3) This happens a lot to me and I am sure others (or analogs of it): I have a LaTeX bug. I delete a line.  The  bug goes away.   I put the line back. Now the bug is gone. 

4) What color is the dress?

5) Neil Degrasse Tyson and Elon Musk are fans of the Simulation Hypothesis.Not sure if this is any kind of justification for the Simulation Hypothesis or if Abisola coded them up to be that way.

6) All of a sudden the spell-check mechanism this blogger uses stops working AND when I leave a comment it does not automatically put my name on it, nor does it automatically bypass moderation (which is how it used to work).  Lance and I try to fix it, to no avail. The staff here tries to fix it, to no avail. a week later it works again. And YES the first thing I did was turn everything off and on again and that didn't work. (Update: this problem seems to come and go.) 

7) A watched pot never boils. Lost socks in the laundry. Etc.

8) On a more positive side, The Unreasonable Effectiveness of Mathematics in the Natural Sciences and The unreasonable effectiveness of Physics in the Mathematical Sciences. You can google to find more unreasonable effectiveness's. Thanks Abisola, though I wish you made Physics and Math easier. 

9) I emailed a HIGH-TECH colleague. My system says that YES I send that mail. He remembers READING that email when it came. Later on he can't find it- not in is normal files, not in trash, not in spam. gmail search can't find it anywhere. (My spell check thinks gmail is not a word. Nor Gmail. Really?)

10) The speed by which humans went from PONG to DWARF FORTRESS is not plausible. Maybe Abisola  found a way to speed up her program.  (This observation has been made by others.)

11) A relative got Eye Surgery recently. (a) The technology for the surgery was fantastic- outpatient, able to drive in 3 days, drive at night in 7 days, totally painless. (b) Still waiting for the paperwork that will allow him to drive without glasses. Gee- eye surgery should be hard, and paperwork should be easy. I think Abisola  found switching the two to be amusing. 

12) Aaronson's law of dark irony, see here.

13) The possibility of  Elon Musk and Mark Zuckerberg having an actual physical fight (see here), makes no sense. Whatever they disagree on (e.g., how a social network should be run, who is wealthier, who has the biggest....) will NOT be settled by a fight. If M wins then we know that M can beat Z in a fight. That is all that will be established. If Z wins then we know that Z can beat M in a fight. That is all that will be established. In both cases a fight will not settle whatever they disagree on. So why might they fight? Ask Abisloa if it is a bug or a feature. 

14) I am sure you can add your own reasons. 

Turning Sixty

I turn sixty today, spending my birthday reviewing a computer science department in Asia. Sixty is a good time to look back and reflect in a rambling way.

I started grad school in 1985. The P v NP problem was only 14 years old when I started. 38 years later we are no closer to solving it.

Nevertheless the field of computational complexity has remained strong, producing exciting research nearly every year. We're not seeing the surprising results that we saw through the early 90s but we've gained a much better understanding of pseudorandomness, coding theory, proof complexity, communication complexity, quantum complexity and circuit complexity (to an extent). The hard problems remain hard but that hasn't hampered progress in the field.

The field hasn't grown as dramatically as some others in theoretical computer science but neither has it shrunk. We have many great young researchers coming up in the field and its future is secure for decades to come.

I have some regrets for the field. Computational complexity has moved more towards mathematics with a focus on technical difficulty over conceptual novelty. We were quick to pick up on probabilistic, parallel and quantum computing, much slower on the cloud and machine learning. Combinatorial optimization has gotten extremely good, we can solve many NP-complete problems in practice, a point we rarely acknowledge.

For myself, I had an active research career for a good two decades. But then the field moved, away from my strength in the structure of complexity classes and more towards more combinatorial, algebraic and analytic techniques. A field should evolve but I found it difficult to keep up. So I focused on this blog, wrote a book, took on larger leadership and administrative roles. I try to follow what's going on in the field, but I'm happy to leave the research to the next generations, especially to my former students, several of whom have become leaders in the field themselves.

Someone recently asked me if I have regrets in my research career. I said that I’ve lived through some incredible advances in computing, but my research has played no significant role in any of it. 

Nevertheless as the computing world, if not the world as a whole, continually gets more complex, computational complexity has a continual mission to make sense of it. And so we shall.