trees are the poems nature writes to the heavens
I need to find a suitable tree in the woods. Sandy caused so much damage as did Irene and the pre-Halloween snowstorm. Finding the right tree has not been easy this time.
but I'm getting ahead of myself...
When I was an undergrad I read Polya and decided to write down some steps on problem solving. This is not meant to be specific to a field and it tries to be serious even though some of the steps may seem trivial. It isn't a checklist - just a rough structure for approaching a problem. I wrote these on a sheet and keep it above my desk.
there are many techniques. Not every problem would have all of these steps and some would have new ones. I've added a bit of annotation (in blue) to the original for clarity, but feel free to skip down. The point is I wanted to impose some structure to make progress.
1. Understand the problem
- do you understand all of the words and equations in the problem?
- can you restate the problem in your own words?
- can you think of a picture or diagram to help understand the problem?
- what do you want to find or show?
- what level of accuracy do you need?
- is there enough information to find a solution?
- is the problem a relevant problem or is it gibberish?
- what is the scale of the problem? can you do it in an hour or will it require unobtainium?
2. Devise a plan
- guess and check
- consider special cases. what are the boundary conditions?
- select your tools
- do you fully understand your tools?
- draw a picture
- solve a simpler version first
- create a model
- use approximations - but understand their impact
- work backwards
- be ingenious … this comes with experience and often with re-thinking the problem in a different context.
This and the next step - connecting the dots are the non-trivial piece!! Remember:
play and your ability to fail with grace are essential
curiosity is your driver - remember informed ignorance rules in science and math! never lose fact that your final job is to expand your ignorance - results are a by-product!!
- connect the dots - this is a subset of being ingenious
serendipity is another driver. remember that serendipity is making discoveries by accident, but you must have enough sagacity to note what holds potential.
dot connecting is best done using averted attention. Don't tool constantly on your problem. Focus hard, but pivot off to equally long period of something completely different. This may even fool others into thinking you have a life.
3. Carry out your plan
- find a quiet place with no interruptions. nature is your friend
- use some care and be a craftsman
- if you get stuck, take some time off and try to forget about what you are doing
- if you fail, use another approach
- know when you have failed
- if you are working with others know where the strengths are and divide appropriately
4. Check with reality
- does your answer make sense?
- can your solution make testable predications?
- ask an expert in your field to examine your work for flaws
- reflect on what you have done and examine what worked and what didn't
This approach helped with physics and math problems, but needed modifications for doing real science - something that I began to taste in grad school. Observation and experiment have their own techniques and learning that answers may not be what you are looking for requires adjustment.1
There are many places to jump from here. Several have been mentioned in earlier posts, but I want to concentrate on how this fits with place and time.
Finding a bit of nature has been important for me - even in city environments. As an undergrad I would spend time in the library listening to music for awhile and then going to "my rock" - a large rock just inside a small wooded area that no one seemed to walk through. Being able to lay on my back and look up through the trees seemed to clear my mind and it was easy to tune out other noises.
You can always build a simple tree platform or even a tree house. These don't have to be elaborate, but they have the feature of purposefully removing you from some of the world. Of course it is important to not have electricity and you need to leave your mobile phone behind, or at least turn it off.
Working mostly out of my home these days I'm finding the woods to be an extremely important place and tool. In addition to spending time working there I take a daily walk around lunch that allows one to mentally shift. There is something constant, but always changing nature about the place that is worth a lot to me.
I was lucky enough to have started in a lab at Bell Labs that strongly believed in some daily private time. Even the phones went dead for incoming calls during the period. You could chose to collaborate, but the choice was yours. When I moved to other organizations that didn't have this policy I found myself coming in very early to get a few uninterrupted hours.
The organization that first used the private time approach evolved a few curious practices that seemed to be organic extentions. There were a variety of small collaboration areas outside the (private) offices. If you wanted to collaborate and could find someone else agreeable (signaling was done with colored flags just outside your office door), you would often meet in one of these areas - somehow that was better than either office. They had nice chairs and a blackboard and were tucked into quiet out-of-the-way parts of the building. Places for special collaboration times.
Intersection and collaboration with others is also critically important. The old Bell Labs Murray Hill installation was something of a maze. Throughout a career your office would move and would find yourself collaborating with people in other parts of the building.2 I don't believe in most forms of brain storming, but I've seen it work in some small and stable groups. These groups were usually attached to place, time and often had some ritual. One of my favorites was unscheduled, but usually took place late on Friday afternoons (three to seven pm was common), invovled a couch, a nice view of some trees, had three or four regular participants who were friends and was fueled by chocolate covered coffee beans.
Collaborations can, of course, be remote. There is a growing understanding of what works and doesn't. Collaborations in place often fail and remote collaborations are sometimes fruitful. It is important to understand for you and your organization what works and what doesn't and why. Much of it comes down to personality and relationship strength, but corporate culture often has a role.
Working on some ideas and projects, one tends to run into walls. Ideas and approached become stale and work slows to a crawl. A good approach is to shift the primary focus to something else - something entirely different. Sometimes a break to an extremely different activity or place is called for. Somehow the mind seems to be considering the original problem and a flash of insight can come.
Proper toolkits help a lot. Perhaps it is the time I'm from, but a real slate blackboard and high quality chalk are important to me. Whiteboards don't cut it. When AT&T Research moved to Florham Park, NJ after the AT&T/Lucent fission, the head of research recognized this and gave everyone a choice of board. The same holds for paper and pencil for sketching - get something that feels wonderful when the pencil is in motion. Sketching can be anything of the moment - sometimes visualization of the problem, sometimes working through equations and sometimes doodling or trying to focus and draw something. The last is a form of meditation to me and a often a path to clearer thinking. The paper has to feel good under a good sharp pencil. Everyone will have something that is important to them - the point is figure out what it is and use it. These are cheap paths that can encourage flow.
These are some of the tools I find useful - time from an earlier post and place and the interaction of time and place. The point is you should find what placetimes and supports to them work for you.
Back to the beginning of the post. Clearly the line is much more beautiful than anything I would pen. Yesterday Om tweeted an Instagram post of his with a somewhat similar line by the poet Kahlil Gibran. I've read quite a bit of his work. This one is famous and, while beautiful, breaks into sadness
Tree are poems the earth writes upon the sky
We fell them down and turn them into paper
That they may record our emptiness
Several years ago one of you had a similar line - the one at the beginning of this post - and I had to ask. It turns out she had rewritten a someone similar line from a much older poem in her native language
God's fingers are the trees painting the sky
I realize poetry often doesn't translate, but consider Jheri's inspired variation much better and have been using it.
1 I can't stress enough how important simple things like wiring are a well as trying to deal with all sources of error. Play is even more important as is the ability to play with others who have different skill sets and views. There is also a realization that hunting for the discovery - that rare eureka moment - is not what science is about, but rather finding new questions is much deeper. But that is a core theme of this blog (hopefully)
2 It is wonderful that cross disciplinary collaboration is "hot" again in some institutions. I've never seen a place that supported it better than the old Bell Labs.