Wouldn’t trade places

Last week at the Heidelberg Laureate Forum, I was surrounded by the most successful researchers in math and computer science. The laureates had all won the Fields Medal, Abel Prize, Nevanlinna Prize, or Turing Award. Some had even won two of these awards.

I thought about my short academic career [1]. If I had been wildly successful, the most I could hope for would be to be one of these laureates. And yet I wouldn’t trade places with any of them. I’d rather do what I’m doing now than have an endowed chair at some university. Consulting suits me very well. I could see teaching again someday, maybe in semi-retirement, but I hope to never see another grant proposal.

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[1] I either left academia once or twice, depending on whether you count my stint at MD Anderson as academic. I’d call my position there, and even the institution as a whole, quasi-academic. I did research and some teaching there, but I also did software development and project management. The institution is a hospital, a university, a business, and a state agency; it can be confusing to navigate.

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Proof maintenance

Leslie Lamport coined the phrase “proof maintenance” to describe the process of producing variations of a proof over time.

It’s well known that software needs to be maintained; most of the work on a program occurs after it is “finished.” Proof maintenance is common as well, but it is usually very informal.

Proofs of any significant length have an implicit hierarchical structure of sub-proofs and sub-sub-proofs etc. Sub-proofs may be labeled as lemmas, but that’s usually the extent of the organization. Also, the requirements of a lemma may not be precisely stated, and the propositions used to prove the lemma may not be explicitly referenced. Lamport recommends making the hierarchical structure more formal and fine-grained, extending the sub-divisions of the proof down to propositions that take only two or three lines to prove. See his paper How to write a 21st century proof.

When proofs have this structure, you can see which parts of a proof need to be modified in order to produce a proof of a new related theorem. Software could help you identify these parts, just as software tools can show you the impact of changing one part of a large program.

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Love locks

If you walk across the Seine in Paris on the Pont des Arts you’ll see thousands and thousands of love locks. I saw this morning that Heidelberg has its own modest collection of love locks on the Old Bridge across the Neckar.

love locks on Old Bridge across Neckar

These may be new. If they were here last year, I didn’t notice them.

There are several other points along the Old Bridge that have locks but nowhere are there very many.

love locks on Pont des Arts across Seine

Photo credit: Disdero via Wikimedia Commons

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Steep learning curves you wish you’d climbed sooner

I asked on Twitter today “What steep learning curves do you wish you’d climbed sooner?” Here’s a summary of the replies:

  • R
  • Version control
  • Linear algebra
  • Advanced math
  • Bayesian statistics
  • Category theory
  • Foreign languages
  • How to not waste time
  • Women

IgorCarron‘s response didn’t fit into the list above. He said “I wish I had known that sensing all the way to machine learning is about approximating the identity” and gave a link to this post.

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Radiation equipment

John Tukey said that the best thing about being a statistician is that you get to play in everyone’s backyard. This morning I got to play in IsoTherapeutics‘ backyard. The most photogenic thing on the tour they gave me was their box for working with highly radioactive material with robotic arms. (There was nothing hot inside at the time.)

 

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Twitter news

Starting next week, @MedVocab will post two tweets a day, once in the morning and once in the afternoon (CDT).

I’ve stopped posting to @DailySymbol. It was a fun experiment, but it was time to wrap it up.

My most popular account, @CompSciFact, now has over 100,000 followers. It’s interesting how some Twitter accounts take off and some don’t. CompSciFact has done quite well but I’ve shut down several other accounts that never gained much of a following.

You can find a list of my accounts here with a very brief description of each. Some of the accounts are a little broader than the name implies.

 

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Engineering a waterpark

This weekend my family went to Schlitterbahn, a waterpark in New Braunfels, Texas. (The German-sounding name of the park and the city are evidence of the large number of Germans that settled in this part of Texas.) I thought about several engineering questions while we were there.

Most of the rides involve sitting in an inner tube and floating down a course with rapids, waterfalls, swells, etc. At many points there are back currents. You could be headed toward a fall but then find yourself reversing direction. It’s surprising to have to work to make yourself go downhill. At most if not all these points there are employees standing in the water to grab hold of rafts and pull people in the right direction who need a little help.

One question I had is what causes the back currents. Ultimately you could solve Navier-Stokes equations, but it would be nice to understand at a more rule-of-thumb level how these currents work. It would also be interesting to see whether a park could reduce the number of guides while keeping the rides as fun. The guides also serve as lifeguards, so the park may need to position people in all the same spots even if they didn’t need as many guides.

The slowest person in the family was consistently yours truly. I’d start out in front and inevitably end up bringing up the rear. I was curious how I could be so inept at a mostly passive activity.

I was also curious how they designed the rapids to be so safe. You’re repeatedly tossed straight toward rocks — perfectly smooth artificial rocks, but still not not things you want to hit your head on — at a fairly high speed, and yet you never hit one. It has something to do with how they position jets to push you away from the rocks, but that would be interesting to understand in more detail.

Another thing I was curious about is what the park does with its water in the off-season. Schlitterbahn in New Braunfels is actually two parks, an older park that uses untreated water from the Comal river, and a newer park that uses treated water. When the parks close for the season, the older park must just let its water return to the river. (At least one of the rides ends in the river, so they’re already returning water to the river.)

The question of what to do with the treated water in the new park is more interesting. I assume they cannot just dump a huge volume of chlorinated water into the river. Aside from ecological consequences, I wonder whether they’d even want to dump the water. Is it economical to store the water somewhere when the park closes for the year? If not, do they store it anyway because they have no way to dispose of it, or do they treat it so that they can dispose it? I suppose they could circulate the water occasionally while the park is closed, though that seems expensive. I wonder whether different waterparks solve this problem different ways.

If I could propose a new ride for Schiltterbahn, it would be a video presentation about how the park was designed followed by Q&A with a couple engineers. This would be a terrible business decision, but a few visitors would love it.

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Pi and The Raven

Michael Keith rewrote Edgar Allen Poe’s poem The Raven to turn it into a mnemonic for pi. Keith’s version follows the original quite well considering his severe constraints. The full poem has 18 stanzas. Here I include only the first and last. The full version can be found here.

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Poe, E.
Near a Raven

Midnights so dreary, tired and weary,
Silently pondering volumes extolling all by-now obsolete lore,
During my rather long nap — the weirdest tap!
An ominous vibrating sound disturbing my chamber’s antedoor.
“This,” I whispered quietly, “I ignore.”

So he sitteth, observing always, perching ominously on these doorways.
Squatting on the stony bust so untroubled, O therefore.
Suffering stark raven’s conversings, I am so condemned, subserving,
To a nightmare cursed, containing miseries galore.
Thus henceforth, I’ll rise (from a darkness, a grave) — nevermore!

***

The number of letters in most words encodes a digit of pi. Words with 10 letters encode a zero. Words with more than 10 letters encode two consecutive digits of pi. The poem encodes the first 740 digits of pi.

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Every exercise in the book

When I did an independent study course with Ted Odell, he told me to get a copy of De Vito’s Functional Analysis and work every exercise. I don’t recall whether I actually worked every problem, though I believe I at least did most of them. I heard of someone who learned algebraic geometry by working every problem in Hartshorne.

Doing all the exercises in a book isn’t a bad way to learn something, though it depends on the book, what you’re trying to accomplish, and on the quality and quantity of the exercises.

Have you ever gone through a book working every exercise? If so, what book? How was your experience?

 

 

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