Syzygies

I believe that these "groupoid" ideas lead into higher category theory, and the supporting mathematics for theorem provers such as Lean.

> Galois connections may be used to describe many forms of abstraction in the theory of abstract interpretation of programming languages.

https://en.wikipedia.org/wiki/Galois_connection

My father Bryce Bayer studied this question fifty years ago at Eastman Kodak; his approach is known as ordered dithering:

https://en.wikipedia.org/wiki/Ordered_dithering

One is effectively posterizing a grayscale image, and his primary goal was to reduce artifacts drawing unwanted attention to the borders between poster levels.

With improvements in hardware other approaches to dithering took over. The last time I saw my father's pattern was on a DEC box logo. He moved to the color group at Kodak, and designed the "Bayer filter" used in digital cameras.

Thank you. I suppose I was downvoted, hiding your careful response, because I appeared to be pitching a product. I was attempting a precise analogy, I had nothing to gain from the promotion. I was robbed on BART recently, and my judgment is off.

I've relied heavily on spaced practice for learning languages for travel. There are two phases to that experience: Study, where one takes in as much as possible, then real world practice without further study. I find myself wishing I'd memorized a play for the first phase, to access faster than a phrase book on the ground, with lots of pathway shortening while I travel. Learning models tend to assume learning is single-phased, though even more academic learning is two phased: acquire, then later apply.

I'm a math professor who has lost years to this question. I've met various authors involved in successful proofs. My 1976 grad school application from the University of Illinois came postmarked "Four Colors Suffice" (Appel, Haken). I've also been inundated with well-intended crank proofs of every tar pit like this. One can tell the difference without focusing one's eyes.

These authors have long, established careers, with 2,000 MathSciNet citations between them. Waterloo is a hotbed of combinatorics; I doubt that they posted this before passing the paper around a bit.

Graph theory as a branch of mathematics is like photography as an art form: Anyone can point a camera, and one sees a lot of incredibly weak graph theory if one digs deep enough into the regional conference circuit.

This work is deep, relying on an understanding of generating functions that many casual practitioners don't possess. If the proof has a flaw, the issue will be technical and difficult to uncover. I love how people take the obvious bet that this is likely wrong because so many proof attempts have failed. In a prediction market, I'd bet on this proof being right.

Your credit card company is the entity you can expect to apply basic logic.

In the short term, that logic will be to refund your money to keep your annual spend, but not to bother Uber. In the long term, this could raise the fees Uber pays for credit card services.

Long before Uber, a JAX airport auto rental was improperly tacking an $8 fee onto every "paid in full" Hotwire reservation. This can add up over a year. When challenged, they lied and claimed it was an upgrade. American Express of course made no effort to protest this, they just refunded my $8. Not very satisfying, but still my best course of action.

The "Honey Souk" in Morocco's Marakech medina sells the best and most diverse selection of honey I've ever seen. If I could travel one hour at a time, I'd go get Shirunashi Tantanmen ramen noodles at King-ken in Hiroshima, then go honey shopping at the Honey Souk in Marakech.

This ramen is a reason to visit Hiroshima, it's that good. This honey is a reason to visit Marakech, it's that good. (Otherwise, if one visits one medina, it should be Fes.)

There are too many people missing legs in Morocco from diabetes for me to easily accept this study.

Thanks! When we put in solar twenty years ago they kept patching me through to engineers they normally protect from customers, because I'd learned more than any customer-facing staff.

You're saying, same drill here.

I was blown away years ago, visiting the Anchor brewery in San Francisco. They approximated traditional steam beer in an enormous shallow pool. To improve consistency the whole room was at positive pressure, using state-of-the-art hospital air filtering.

Aside from the smell of beer, it was like stepping out into the Swiss Alps. I've never understood why rich people will spend $40K on audiophile equipment yet put up with crappy phones; I did a BBC interview remote in their NY studio using a $10K mic and the difference was staggering. Here, I swore if I ever got rich I'd want good indoor air.

It turns out I can afford to redo my house in California with a heat exchanger. I'm certain the hardest part will be finding a contractor who will exceed standards. Standards are why I have 1/2" pipes under my house. I want the bleeding edge of what's possible in my lifetime.

When I can, I run a pair of box fans exhausting through the windows in one room, letting the air in through the windows in the other room. This feels roughly like living on a houseboat, and is how I can read 450ppm.

I'm now at 728ppm after cooking lunch, windows closed. There's a good kitchen exhaust to a roof fan, so I can get that number down a fair ways by cracking a window.

Returning to college teaching mid-pandemic, I bought an SAF Aranet4 Home CO2 meter for measuring my classrooms. It mostly lives in my apartment, waiting to alert me in case I didn't realized I was using my gas range.

There's good evidence predating the pandemic that sufficient air exchange can nearly eliminate respiratory disease transmission. Just as they learned long ago in London that one could eliminate cholera by not drinking sewage water, we understand that the air quality and rate of exchange of indoor air should approximate that of outdoor air. We're however too cheap to do anything about this; it will take more deadly pandemics to drive the needed infrastructure changes.

Do you wince at the idea of people in London drinking sewage water? Those ignorant savages? Yeah, that's how people in the future will look back at us, getting colds and worse all the time in indoor air cesspools.

As we breath out CO2, it makes a great way to measure whether we're changing the air in a room fast enough to keep up with occupant breathing. Wilderness air passed 400ppm as part of global warming. My Manhattan apartment is above the Henry Hudson Parkway, and I can tell the time of day and day of week from the effect of traffic on my CO2 meter. I'm lucky to ever get below 450ppm.

The Aranet works far better than a $30 meter at the measurements a $30 meter will make, such as humidity. By appearance and build quality it's in a different league. CO2 is a bonus.

Dunno whether I'm having more fun watching the Musk bonfire, or the FTX collapse.

My digital timestamping paper is cited by the original bitcoin paper, so people assume I appreciate cryptocurrencies. They're an environmental crime and a Ponzi scheme. Many people have tried to explain to me why cryptocurrencies aren't a Ponzi scheme. The poker player / oral examiner in me kicks in: They may not realize they don't understand or believe what they're saying, but they don't make sense.

Denial is powerful. People want to believe this is their moment.

A high school friend's older brother did PhD research in short-acting drugs that were legal because they were so obscure. We got banned from my high school chem lab after an after-hours session left a uniform white residue on all surfaces. My friend said we were mopping up water with an eraser. The VP found this explanation wanting.

I switched to math.

Yes, I'd take this as Level arrogance.

For another data point, I never managed to pick locks in my twenties, but something aligned for me in an evening lock picking course in my sixties, and I picked everything in the room. One wants a training set of locks to learn on, one pin, two pins, three pins, ... then one learns easily. It also helps that with age one's brain quiets down. To pick a lock, you need to listen to it.

I asked the organizers, surely they had something that would stump me. They handed me an American padlock identical to one I'd been buying for years. It stumped me.

It took LPL more than one pass to pick a basic American. He made it look easy, still reassuring me there was some skill involved:

https://www.youtube.com/watch?v=oaP1nFZ9AXE

Videos by others describe more advanced American locks that took several months to overcome. American takes basic countermeasures, that Level could have easily adopted.

Yes, surely they would have told you had they lost. Instead, silence and a change in spending habits.

I don't know here that "not easily verifiable" is deliberate, but it could be.

In the case of the Fields Medalist, one can read in major publications that they engaged a PR firm. Those articles don't specifically spell out sanitizing the web. If one already knows every detail of the event in question (in my case, confirmation includes overhearing him express concerns about a wrongful death lawsuit), an internet search finds many accounts relaying a cover story, and a single forum comment that correctly describes the event. That comment was apparently beyond the PR firm's reach.

> Stephen Wolfram would die before he gave up control, the entire thing is his precious child.

I understand that Wolfram made unrealistic agreements with the original programmers, incompatible with growing a large organization to support his evolving vision for Mathematica. Rather than renegotiating, he attempted a maneuver that did not survive a court challenge. The original programmers are now rich.

I cannot find any account of this on the web. There's an unrelated "Fields medalist car accident" that I again know from first-hand accounts, that also has no trace on the web. Huh.

I too thought about becoming a "code shrink".

I helped my department found a "Mathematics of Finance" masters program, teaching numerical methods for the first three years. Three guys were trying to combine all their courses for an omnibus project that would get them dream jobs. They were coding a never-implemented research paper in C++. Sensing my finance background was thin but I was good at programming, they arrived at my office hours to describe their failing code.

I didn't understand a word they were saying. Keeping a poker face, I was sinking into depression. "They pay so much to be here, and I don't know what I'm doing. I've got to think of something to say so they'll just leave. Happy, but please, just leave."

Then I heard a catch in their voices, as they described inserting a fractional time step between program phases. I jumped up, "No! You don't have to do that!" I proposed an alternative, asserting this could be their bug.

I got an effusive email message that evening, and they came back two more days. Now I knew the drill.

Ever notice how one is aware of cooking mistakes as one makes them? Code is the same way, one often hears the mistake as one makes it. And it's easier to hear in others.

Belt buckles taught me that conventional behavior can have unwanted consequences. Using Windows is conventional behavior.

Conventional and unconventional behavior can both have unwanted consequences. We each pick our poison.

Another senior here.

As a child I scratched my father's guitar with a belt buckle I had been told to wear. I learned to distrust adult judgment, I still don't wear belts half a century later, and I have a successful research career for which I partly thank this errant belt buckle. I lost a potential life as a rock God, but I've been protected from ever buying Microsoft products. This story horrifies me but it doesn't surprise me; I made a fair trade.

Carpentry is a great analogy. Half of all woodworkers have no concept of the properties of wood grain; they'll mix up edge and end grains on decorative cutting boards.

I wish I understood the "grain" in programming better. It's a lifelong search.

The Fibonacci sequence is characterized by satisfying the simplest recurrence relation, just as the exponential function is characterized by satisfying the simplest differential equation.

It's hard to think clearly about anything when there's enough cultural static in the way. Did you first learn of Bruce Springsteen after his Time and Newsweek covers? Here, Fibonacci numbers and the Golden Ratio enjoy a cult status that many including myself find repellent. To have original thoughts I want to avoid group think.

Nevertheless, Fibonacci numbers are like the prime "2". Life depends on properties of the element carbon, and other elements don't enjoy the same evolutionary success. I ask myself why a simple sensor pattern for digital photography that my father came up with half a century ago is still in use? The game "Core Wars" ended when a virus kept winning. Simplest answers often have an uncanny effectiveness.

Here, as an aging mathematician, I believe that this article could be reporting on an effect that's real.

Ha! Erdős–Bacon numbers originated in a 2002 Telegraph article by Simon Singh, referenced by Wikipedia as [1]:

https://web.archive.org/web/20121112081753/http://www.telegr...

I came up with this game after realizing I had an Erdős–Bacon number. He credits me, but spun the article to make this sound like a "thing" other people cared about.

I was written out of that Wikipedia page long ago. Very little of what survives on that page stands up to close scrutiny.

Combining these numbers is an obscure amusement, but people take the separate numbers seriously. For Erdős numbers, should one count posthumous papers? My "2" via Persi Diaconis goes to "3" if one doesn't.

The original intent of the Bacon number game was to count actors in fictional speaking roles. My "2" here is from a speaking role in "A Beautiful Mind". The "Oracle of Bacon" replaced this intent with whatever their database could easily report. Appearing as oneself in a documentary on Erdős had the obvious hilarious effect.

One understand these links better by studying IMBD credits. Daniel Kleitman's "2" depends on a "Thanks" credit from "Good Will Hunting", and few of the other low Bacon numbers on the Erdős–Bacon Wikipedia page can be confirmed at all.

"Never attribute to malice what can be explained by incompetence."

I fly American between JFK and SFO regularly, including today. They have the best prices these days for an "international" business class on this route. The food is good, the flight attendants are friendly and good at their jobs...

Automobile manufacturers offer pathetic "center console" software compared to Apple, Google. American's in-flight entertainment system makes auto makers look like geniuses. They just don't understand software.

My name is Dave, and I'm an addict.

Charlie Watts wasn't just into jazz, he was into all music. George Harrison understood that jazz could deepen him as a musician, but found Indian music.

If one wants to write a language that is truly original, that might actually influence the future, not just smearing around familiar weightings for features found useful "in the trades", then one wants to have some grasp of languages representative of every language in use. Then, only proceed with a compelling vision of what's missing.

For the rest of us, being a language junkie can be a problem. Without being judgmental, it is possible for a person to be too promiscuous. Same with languages. I wish I could just stick to Haskell and get work done.

When I gained access to an APL terminal in 1975 I was coming from FORTRAN punched cards on an IBM 1130 (think Apple ][ but dumber and half a room, shared by my entire college). APL blew my mind. I worked one summer as a commercial APL programmer, and we ran circles around our client's in-house FORTRAN shop.

Languages like Haskell scratch that itch now.

We're at danger of losing the patient, extraordinary measures are welcome. I for one embrace any experiment at saving APL.

I read the first edition of K&R when it came out, and switched to C for a computer algebra system that got me tenure as a math professor. K&R is a religious scripture, and remains the benchmark against which I measure all other programming books. It's in the same league as the aspirational SICP, and a far easier read.

In college I'd programmed Fortran on punched cards. APL was like dropping acid, and I worked one summer as a commercial APL programmer, but it wasn't appropriate for what I needed. Pascal didn't quite fit either. C was in that context mind-blowing. The future had arrived! I had full access to the machine!

If one is learning to become a plumber, one might not be so interested in how plumbing worked in 1840. If however, one is a herding dog, and needs serious work to avoid getting bored and destructive, reading K&R would put C in historical context.

Later, as I depended on C, I bought each edition of C: A Reference Manual by Harbison and Steele, and read it as if I were studying to be a lawyer.

I now program in Haskell, and wish I was equally versed in Clojure and Rust. If I were returning to C, I'd instead choose Rust. For my work, I have a free choice.

Yes. I'm missing an unusual screw from the armrest of my office Ekornes Stressless chair, and the closest Amazon length didn't work. I've seen the Mcmaster website before, but thanks for the reminder! I jumped on it, found the right screw in seconds.

My copy, found somewhere once on the web, is a complete 416 page scan of a book.

As a Harvard math PhD student around 1980, Fridays were amusing. In the math department was "wine and cheese" and inebriation levels were high by modern standards.

Over in the bio labs, they preferred cannabis. The sessions were intellectually stimulating, with a reverence for when Timothy Leary ran his "seminars". That's where I first saw this book, and it made a lasting impression.

Haskell can be a beautiful small language. One can enjoy it like a walk in the woods, without worrying about which typeclass models our light cone in the universe.

My first functional language was APL; I later moved from C to Standard ML. I loved Scheme till I realized I was camping, it was getting late, and I needed to build a shelter from Y-shaped twigs. Somehow OCaml never took for me, but reading a few of its source code modules was an efficient crash course for coding in a functional language.

What is the dream that these languages and Haskell aspires to realize? We want to slice computations in arbitrary ways and manipulate the parts as algebra. This dream of many since the first Lisp meets resistance from those who don't love algebra, but one cannot fault the aspiration: Find a way we can all code with more leverage, less effort.

Pretend Haskell is as small as APL or Scheme. Ignore those who scoff at your primitive avoidance of an emerging Haskell pattern.

I highly recommend Simon Marlow's "Parallel and Concurrent Programming in Haskell". I don't know any language that handles parallel as gracefully, and one can read this book without ever seeing an >=> or <=<.

>> With the danger of hurting HN Rust hipsters

They engaged in a rewrite, and they chose a modern language. These are orthogonal.

Even in academia, one sees a prevailing view that language choice is picking a brand of toilet seat. Others see language as one of the central questions of our evolving identity as a species. There are those in the middle, just trying to get work done, considering their language choices but not seeing that as fashion.

"hipsters" certainly tips one's hand.