Obsessing About Selection
I’m currently trying to solve a fun problem that’s captured my attention and refuses to relent. Here’s the basic setup:
- A collection of k devices arrive at a shared channel. Each device has a message to send.
- Time proceeds in synchronized rounds. If more than one device tries to send a message on the channel during the same round, there’s a collision and all devices receive a collision notification instead of a message.
- The devices do not know k.
In this setup, a classic problem (sometimes called k-selection) is devising a distributed algorithm that allows all k devices to successfully broadcast in a minimum number of rounds. The best known randomized solutions to this problem require a*k rounds (plus some lower order factors), for a small constant a > 2.
What I am trying to show is that such a constant is necessary. That is: all distributed algorithms require at least b*k rounds for some constant b bounded away from 1 (and hopefully close to 2).
The Dash Method
What I’ve noticed in my thinking about this problem over the past week or two is that at the beginning of each deep work session, I’ll typically come up with a novel approach to attempt. As I persist in the session, however, the rate of novelty decreases. After thirty minutes or so of work I tend to devolve into a cycle where I’m rehashing the same old ideas again and again.
I’m starting to wonder, therefore, if this specific type of deep work, where you’re trying to find a creative insight needed to unlock a problem, is best served by multiple small dashes of deep work as oppose to a small number of longer sessions.
That is, given five free hours during a given week, it might be better to do ten 30-minute dashes as oppose to one 5 hour slog.
My Experiment
So I’m going to try this. For the next week or so, I am going to limit my thinking on this problem to under 30 minutes at a stretch, and try to sprinkle such dashes throughout my week.
Of course, if I make a breakthrough in one of these sessions, I will then default to the more standard long stretches required to work through the tricky details of any such proof. (In other words, I want to make clear that the brevity I am pitching in the dash method is really only well-suited to this quite specific type of work.)
I must admit that I approach this technique with some trepidation. My main concern is that once the dash gets too short I’ll start to leverage the impending termination to excuse my tendency to sidestep the annoying math that is sometimes necessary to verify whether or not an idea works. (My mind much prefers “eureka solutions” in which the applicability is self-evident, to the point where it will sometimes ignore potentially good but hard solutions in hopes of a eureka lurking around the neuronal corner.)
We’ll see.
In the meantime, if you have a solution to the above problem, let me know.
(Photo by Kacper Gunia)
I tend to come up with creative solutions to starting tackling a problem when I’m waiting for the bus or something or reading someone else’s article on a related topic and not when sitting at a desk trying to solve the problem. The latter is more conducive to working out the logical details – like writing the program to estimate the model. I can’t schedule and plan creativity. You can schedule and plan productivity. But I think this will vary by personality type.
I’m dealing with a similar problem on a surgical technique I’m not quite sure why it’s getting the results it gets. I am needing to use information I haven’t thought about in years and sometimes pull out undergrad physics books.
Anyway, this methods works well, except I need to clearly document my work and then summarize my thinking in a sentence or two and read it before the next session.
For instance, I recently had a 2am epiphany, not uncommon, and got up and doodled for an hour and and went back to bed. A few days later I was thinking of the topic and ended up re-work in through my previous thoughts. It would have been nice to have summary of conclusions and still open questions from my last “dash”
I think this method also works better for planning. Having 5hrs to work on a project is nice, unless I get mentally jammed or need to step away and come back from a different angle.
Why not both? For creative work I think my pyramid works well:
Monday: 3x20min sessions (“dashes”)
Tuesday: 3x35min sessions
Wednesday: 2×1.5h sessions
Thursday: off
Friday: a 4h session
Saturday: off or 45min review or 2x20min sessions
Sunday: off
Cal, first I want to say thank you for you book “So Good They Can’t Ignore You. It honestly was one of the most influencial books in my life. I only regret that I wish I could have read it as a sophmore in college instead of well into my career. I also really appreciate your blog and thoughts on deep practice. My thought on a problem like this goes back to a theme in your book. When trying to come up with a creative solution to a difficult problem remember to get to the adjacent possible. Review the relevant material and ideas and make sure you have examined all of the existing material related to the situation and then very often you are able to take the next step. Good luck and thank you again
For creative (divergant) thinking I do short, ad-hoc sessions as well. This process can’t be forced or stretched. Only straightforward, well-defined tasks, which use convergant thinking, can you grind through. Attempting to grind a creative task can be counterproductive.
Hi Cal,
Robert Boice advises academic writers to work in “Brief Daily Sessions” (BDS) based on research he did on academic writers and productivity. I see a few advantages to this tactic: (1) the work gets “touched” every day and is mentally foregrounded; (2) the writer doesn’t binge out, get exhausted and then find the work too aversive to return to it; (3) when a long session is possible, the writer is prepared and ready to take advantage of it.
This might not translate to the types of problems you work on, but for me, doing serial BDS’s gives my mind time to work on a problem. I tend to come up with new and more creative solutions doing it this way.
–Kathryn Temple
I realize the idea is to work in short dashes, but in my experience thirty minutes is not long enough. When working on complex problems, it usually takes about 15 minutes to get relevant information set up in my brain. Any deep thinking would proceed afterward, so a thirty minute dash would only leave fifteen minutes for deep thought.
Though I am getting better at it, I must say this state is sometimes quite fragile and all the prerequisites can be lost in an instant. There again, sometimes I can maintain this state across getting snacks, etc. Talking (aside from to myself or to pets) seems a sure way to lose the state.
I think Seth Godin’s concept of “The Dip” might apply here. The basic idea is that when you begin a new activity, you’ll keep going for a while simply because it’s something new, and therefore interesting. But there comes a point where difficulties arise, and you have to power through to reach a level of mastery. Most people quit when the going gets tough.
Paradoxically, though, Seth says that quitting is a good thing, and people should do more of it. The reason is that the “dip” may, in fact, be a “cul-de-sac”, a dead end that no amount of persistence is going to break through. So his message is to quit early and often, and reserve your persistence for things that are going to pay off.
The trick, of course, is to know which is which. As you move from one 30-minute session to the next, do you take an entirely different tack? Or do you try to move forward with the approach you were using in a previous session? Perhaps your experiment will give you some new insight into these questions. Good luck!
I’m glad you’re experimenting with this and I think working in shorter, well-spaced increments aligns perfectly well with your previous advice to study in shorter, well-spaced increments.
Not sure if you’re going to try to come at this from multiple angles, but I’d love to read whether you find any value in working for 30 minutes, breaking for long enough to relax or move around, but not so long as to lose your train of thought or the context you’ve built up, and then doing another 30-minute dash.
I personally love doing back-to-back dashes on a specific problem, but I think I fail to make them occur enough on important problems because I don’t organize enough or set clear enough goals.
Your situation seems more or less equivalent with trying to solve “minor but persistent bugs in large software projects”: also puzzles for which many have already put in some effort and require creative entries or methods to solve them.
My method to solve them is not to fix time, but just devote to a single novel method each time and see how far it goes. Sometimes, I’m back in familiar waters after 10 minutes, sometimes it takes me several hours before I’m truly convinced the solution will not be in that direction.
My point is: I don’t know in advance how much time I will need before I consider a method to be exhausted. I prefer to use the enthusiasm that trying it (for the first time) generates to pull through and find out in a single session whether the method is worth to continue. So, I don’t like to fix time. However, not fixing a time limit means that I have have to be honest with myself, and admit to myself that when the method is exhausted I should (take a break) and start working on a different task/problem (unless during the break a novel method came up, which happens actually quite a lot — those breaks are generally very productive)
With certain computer problems that I have at work, I find if I “sleep on them” rather than trying to grind out a solution, I’m suddenly able to come up with a quick, more elegant solution on the next day. That would imply “dashes work.” But in writing I feel that it’s possible to loose your train of thought between one day and the next, so you loose efficiency by breaking it up too much.
Hey Cal,
In Cognitive Psychology there is this concept of memory availability and accessibility. Availability is total sum of all your memories that could potentially recall. While accessibility is the memories that yo can actually recall.
What studies have consistently found is that location, emotional state, and even colors of the room you are in can dramatically effect what is and what is not accessible. For example, in one study they found that taking a test in the same place you studied could increase recall from 60% to 85%.
I believe that the same principle of accessibility applies to solving hard problems like the k-selection problem. Often when we sit down in the same place day after day, the psychological cues are so strong that they often force us down habitual ways of thinking. That is one of the reasons people love traveling by themselves. People enjoy the novelty, but at the same time being a new place with new people opens your freedom of action. You’re range of free-will expands and so does the range of thoughts you can have.
I started a Coursera class taught up Dr. Terrence Sejnowski and Dr. Barbara Oakley, Learning how to Learn.
Interestingly enough in the first video they mention the difference between focused learning, which seems to be deep focused though, and diffuse learning, which seems something more like day dreaming. They mention that Salvador Dali and Thomas Edision used a combination of both to come up with new ideas, starting with diffuse to get to an idea state, and then using focused to build upon it.
Perhaps this partially answers your questions as Dr, Barbra Oakley mentions that trying to stay in focused thinking is not an efficient way to learn.
This is my five minute summary though and it may be wrong so if interested you should check out the lecture personally to base your own conclusions. The class is linked below
https://class.coursera.org/learning-001/lecture
Great Post Cal!
30-40 mins of intense sessions are genereally quite enervating. Any advise on how to rejuvenate after each session?
Hey Cal — I see this in my strategic planning work all the time! Usually, I end up doing some sort of deeper dive into the same conceptual ideas.
Recently, a team member and I did a 2 day retreat to plan the next two years (including a MAJOR rebrand & strategic shift). We very successfully broke it down like into two longer work periods (day 1) and 6 short bursts (day 2).
Day one was mostly:
1) Identify current state and low hanging choices
2) Questions — what assumptions were built into this? What would we need to do to double our revenue? 10x it? What kind of timelines would we look at for this?
Day two was all about the short sprints of novel ideas — we took the questions and assumptions that we had identified and ran in different directions each sprint. Between them, we got up, went outside and took a real mental break. We sat in different chairs upon return and often changed the way we were talking (white board centric versus paper versus no writing).
This was the most successful structure for such a meeting I’ve ever used.
Thanks for helping me codify it in my brain!