Musings on Collaboration

This post last edited January 30th, 2023 - John Halleck. (Addendum added October 6th, 2022)
Rewordings, mostly.

Stylistic note: If you see a noun phrase below, and the words look like they are capitalized for no apparent reason, then the phrase is likely something I view as worth googling if you are not familiar with it.

Fair warning: This post is not really finished. It has, however, gotten quite long. I thought I had better post this draft now before it becomes something book length before I get around to cleaning it up. I am still making edits, and will be for the foreseeable future.

I can read (almost anywhere) many great articles, papers, blogs, and web pages, that show off successful efforts to solve problems, often with incredibly clever techniques. But publishers rarely, if ever, cover any failed projects. So people exploring see that everyone else they read about has brilliant flashes of insight. But their own efforts just seem to be hard work, and their own explorations seem to lead nowhere with little or no real insights. Some folk even give up at that point.

BUT, in fact, every mathematician/logician/scientist I've ever talked to at length, has followed very inviting lines of reasoning that dead ended or proved more work than they thought worth it. The explorations that panned out they publish, and the ones that don't work never see the light of day. And the ones that work they ride as far and wide as they can. That was certainly true back in the days that math (and logic, and science) papers were almost always single author works. Nowadays, more and more math (and logic or science) papers have multiple authors. The mathematical/logical/scientifc culture is now much more collaborative than it was... and the fields are better for it.

I used to have the "Everyone else has brilliant insights... but I work at it and barely get any insights at all, much less good ones" view. But in my case my personal history changed it. I had a brilliant coworker/mentor [LeRoy Eide] with very broad interests. I explored his interests, and he mine, and his insights cleared out many of my dead end projects, I did some help on his dead end projects. Almost all of his observations were good, and some of mine were good... But I didn't realize that they were good until he pointed it out. The longer we collaborated the more I was able to recognize good insights.

We were collaborating, although that's not how I viewed it at the time, since we didn't publish anything. We should have, such as what properties a binary operator needs to admit to a "shift and [operator]" version such as multiply being done with "shift and add". I thought we were just having fun. It was enough fun that it expanded into the "Utah Logic Group", that met regularly and exchanged ideas (some in logic) for many many many years (more than 30). Everyone had different but broad interests, and the regulars were interested in expanding their knowledge. Sadly, the group finally folded a few years ago when most of the older regulars died off over a relatively short period.

My first paper in a refereed journal ("Least Squares Network Adjustment via QR factorization" in the June 2001 issue of Surveying and Land Information Systems) was as a one author paper. Mathematicians, almost univerally at the time, used Orthogonalization methods for such tasks. And I was not aware of them using Normal Equations for the task. I didn't have any great flash of insight on the mathematics, but I did notice that the Land Surveying Field instead used Carl F. Gauss's "Normal Equations" for the task. But most surveyors (other than some surveying instructors) had never heard of anything else for the task, and many of those that had heard assumed that the newer methods were "esoteric trigonometry laden complex impractical theoretical methods". The biggest network adjustment in history up to that point in time, was the National Geodetic Survey's NAD 1984 nation wide adjustment [roughly 400,000 stations, and 1.5 million observations] and it was done with Normal Equations [and some very clever factorizations]. But some people involved worried that the numerical stability problems of Normal Equations might cause the project to fail. But the mathematical literature at that time already had articles about using orthogonalization methods for such tasks. In fairness to NGS, their project was already underway when those came out, and the staffing for that adjustment was much lower than the previous adjustments. Totally rewriting and testing new software using QR factorization instead of Normal Equations was not remotely practical at that time.

When I pointed that out to mathematicians that surveyors were still using Normal Equations, the responses were things like "Really???, Why?". The main reason, in my opinion, is that the mathematics folk and the surveying folk had/have different cultures, and different terminology, and different views of the problem. And I have to admit that Normal Equations have a great deal of intuitive appeal in surveying. I'd talk about Givens Rotations, and they'd try to assume it rotates some part of their survey. They weren't being dense... it was just culture and culture language issues. And there was some inertia involved.

Since I'd been involved in surveying caves for years, I was lucky to have a foot in both cultures. So I decided to write a paper introducing the land surveyers to the results of the Mathematics world. And it was a lot of work, with lots of iterations. And got everyone I could find, in both fields , to look it over... in part because I worried that it wouldn't fly since it had no great or even clever insight. From this I learned how careless my usage of the terminology was.. and I corrected it. And I learned lots and lots of ways to explain this to surveyors that didn't actually work, and I found some that did. So, no earth shattering insights, and lots and lots of work.

Did this make everyone convert over to orthogonalization methods? No. But it did enlighten some folk, and I still get favorable email and questions about it. I didn't realize at the time, but the "get everyone to look at it" step was actually collaboration... Just not the way I had envisioned it worked. "Collaboration? Oh no, I'm the sole author, but I had lots of folk proof reading and making suggestions."

I started my drift into *real* collaboration when I contacted a famous author in logic [Larry Wos], that happened to be a compulsive collaborator, because I saw that something I was working on in my solitary fashion that might feed into one of his passions [shortest possible proofs]. This was the start of a number of very fun little collaborations, including us collaborating on a "shortest possible proofs" study that by the end of that week we started was producing useful work on open questions on the status of alleged single axioms for the BCI logic system. And that got me involved in work by the person that produced the candidates we proved to be single axioms of the system. Larry wrote up articles on what we did and things that happened as a result of what we did, always with at least appropriate credit given. The paper on that first collaboration used to be at http://www.automatedreasoning.net/docs_and_pdfs/fecundity_of_the_bci_logic.pdf but now that he has died, his webpages have vanished. There is still a copy at https://web.archive.org/web/20210509092949/https://automatedreasoning.net/docs_and_pdfs/fecundity_of_the_bci_logic.pdf. And all of his old site is at https://web.archive.org/web/20210509092949/https://automatedreasoning. He was a very good writer, and has had fun with the topics. Larry also kept urging me to write up some of what I was doing by myself. I dragged my feet because I was unsure that anything I had to say was all that deep or interesting to anyone other than me, and I thought I showed no real insight. He once made an argument sort of like "Making yourself feel good by playing with your logic behind closed doors is not as fun as letting others play with it, or even you playing with theirs." [He might have quibbled about the exact wording, and possibly the color of that quote.]

I finally dipped my feet in publishing my own work with a reply (October 2010 Association for Automated Reasoning newsletter) to a challenge Larry Wos offered (June 2010 AARP newsletter). [TODO: the articles link to my web pages for more information, and those don't exist any more, I need to host them somewhere.] This paper introduced the idea of using a certain class of not necessarily valid inferences to efficiently produce a valid proof. A lot of people found the very idea humorous (as did I). It does work, it is valid, and makes proving some very special classes of VERY LARGE alleged theorems practical. [ Another single author work, but there were a broad base of people to talk to about it, and interesting email exchanges where others asked for information and they, in turn brought in others.]

My next refereed paper in the Hawai‘i Journal of Medicine & Public Health was actually multiple authors, in a medical journal. I was second of three authors, and the I was the only one not a doctor. Update: The journal has changed names since then, it is now the 'The Hawaiʻi Journal of Health & Social Welfare".

Since then I've worked with a number of folk, using what I've done to help with what they've done. Lately, I've been finding single axioms for systems of logic where the originator has asked if I could [a number of logic folk have their own "pet" logics.] And I'm really pleased and surprised that some of them were pointed my way by people with names I recognize as authors of work I admire.

I'm still having fun, but I'm not following Larry's advice as often as I should.

My personal advice is:

• Keep broad interests
• Discuss a broad range of topics with people with broad interests
• Listen, study, share
• New folk are a resource, not a burden, get them involved
• Have a thick skin when asking questions, or for opinions
• Ask questions, and for opinions
• Have fun with your interests
• Share your passions
• At least try other's passions
• Follow Larry's advice above, write it down, and SHARE!

Addendum (Oct. 6, 2022): Someone objected to part of the article above, on that grounds that my newsletter articles (mostly caving articles and website postings) aren't even mentioned. The complaint is valid. However, they tend to be soon forgotten, and only relevant (usually) to the conversations going on at the time.

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