A few years ago I was walking through the parking lot of JPL in Pasadena when a license plate caught my eye. It took me a few seconds to figure it out, but it had to be a vanity plate and one I wouldn't mind having. I pointed and exclaimed something like 'how brilliant' to a rather perplexed friend. Just a few days ago someone set a rather amazing Internet ad. It had an easter egg that grabbed my eye for the same reason, although this was much more explicit. There is a connection between the license plate and the ad. I'll get to that, but first I need to talk about some playful tools that physics and astrophysics types use.

Any sort of creative work needs a playful component. Its how you develop your intuition. I'm sure many fields have their own power tools for play and you may want to think about yours as mostly they are so natural that they become part of how we think. You need to try and discard a large number of ideas without fear of failure. Some of these can be rather silly. Often you build toy models in your head or at the blackboard. Typically they aren't practical .. if someone were to ask how many cattle are required to provide shoes for New York City you might say to yourself 'consider a spherical cow'.. Physics problems tend to exclude much of the real world so you can focus on just the bit of interest. Mental or blackboard math rules. You aren't worried about exact answer. I love the power of computer simulations but anything you have to type into would just slow you down and break the flow during the play stage. You want to create little visual models that seem like an extension of your mind so you can dance with them. People develop a certain affinity for numbers and you carry around a few rough rules of thumb. Things like π^{2} ≈ 10 to about 1.3% .. when you're only worried about 10% errors the arithmetic is easy. Some bits of Nature are stored in this fashion:

° there are π × 10^{7} seconds in a year to better than a half percent

° the speed of light in a vacuum is close to 3 × 10^{8} meters/second. An interesting coincidence is the original definition of a meter was 1/10,000,000 of the distance from the pole to a point on the equator. Distances can be measured in the time light takes to travel the distance. We're used to light days and light years, but light goes about a foot in a billionth of a second or a nanosecond. A very tall friend sometimes gives her height as six and two thirds nanoseconds .. about the time light takes to traverse her length.^{1 }

° a light foot is sort of practical when thinking about connecting parts of a computer. If modules are separated by 10 feet, a delay of at least 10 nanoseconds is introduced. This gets interesting when you're using a lot of fiber optics or physical wire as the speed of light is slower.^{2} The speed of light in the fiber is about 2/3s that of in a vacuum or air. A signal will traverse 1000 km in about 5 thousandths of a second, while a radio wave going through the air only requires 3.3 thousandths of a second. A very long time for a computer. The difference was large enough to justify the construction of a specialized microwave network between Chicago and New York City to give some traders an advantage based on the difference between the index of refraction of air and optical fiber.

° the acceleration caused by Earth's gravity is denoted by g and is roughly 10 meters per second^{2}. It varies depending where you are on the surface, but unless you want to weigh a pound less or more, the rough figure works for quick calculations.

° the diameter of the Sun divided by the height of a person is roughly the same as the height of a person divided by the diameter of a hydrogen atom.

° it takes about 500 seconds for light to travel from the surface of the Sun to the Earth

° photosynthesis in crops and trees is usually under 0.5% efficient

° a cow requires about 10 times as much energy as the plants it eats to produce the same amount of energy

° ...

There are hundreds of little relations like this and a few curious numbers too. One of the most famous is the fine structure constant which describes the strength of electromagnetic interactions between charged particles. It is close to 1/137 and appears in enough calculations that every physicist knows it. If you want to flag one down in a stream of people (airports for example), just write 137 or 1/137 on a piece of paper and hold it in view. I've experimentally found this to be remarkably effective.

Some of the relationships aren't directly connected with Nature, but are just fun and sometimes are even useful. There are too many to list, but here are two..

° e is the base of the natural logarithms and is of fundamental importance to economics and science. It happens to be irrational and transcendental, but the first few digits are easy to remember: 2.7 1828 1828 45 90 45 (1828 repeats twice, and the angles in a right angled isosceles triangle)

° of course there is Hardy–Ramanujan number. The story goes that G. H. Hardy was visiting his friend and colleague Srinivasa Ramanujan in the hospital. He had ridden in cab number 1729 and remarked that it was such a boring number. Ramanujan counted, pointing out that it was the smallest number you can express by cubes in two ways: 1^{3} + 12^{3} and 9^{3} + 10^{3}. This has slipped into popular culture and has appeared in both the Simpsons and Futurama in the form of easter eggs. But then again some of the principals of those shows are mathematicians.

And number on a taxi brings us back to the number on a vanity plate. My eye was probably caught by the initial 23, which happens to be my favorite prime, but it looked suspicious - something close to 20 plus π ... I remembered e^{π} - π is just a bit less than 20. The number on the plate had to be an approximation of e^{π}. The connection with the ad is perhaps the most beautiful relation in mathematics : ^{3}

e^{iπ} + 1 = 0

While e^{π} isn't the real thing, it is suggestive enough to bring a smile. Of course there is the possibility the owner just considered e^{π} cool without thinking of e^{iπ}, but this **was** the JPL parking lot.

If only vanity plates allowed superscripts...

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^{ 1} again an approximation. If you want to do this more exactly the speed is about 0.984 ft/ns ..

^{2} the speed of light in a material is c/n, where n is the index of refraction. n is close to 1.0 for air, but about 1.5 for optical fiber

In physics experiments signals are delayed with respect others to make logic gates work properly. You develop a sense that 8 inches or 20 centimeters is about a nanosecond in coax.

^{3} It links the two most important irrational numerical constants e and π, number i which is the base of the imaginary numbers which gives us complex numbers, the additive identity 0 and the multiplicative identity 1. It also answers the question "how many mathematicians does it take to change a light bulb?" Then answer, of course, is -e^{iπ}...

If it seems strange that the exponential of a complex number could be equal to 1, consider what the number e is. It is closely related to compound interest ... e^{z} is the limit of (1 + z/N)^{N} as N goes to ∞. If you set z = iπ and do the math you get -1 + 0i or just -1. Here's an animated gif:

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Recipe Corner

**Caramelized Carrots**

**Ingredients**

° 3 pounds of carrots - go for the fancy colored ones if you want it to look good

° salt and freshly ground pepper

° 2 clementines or one large orange

° 1 tbl red wine vinegar

° 3 tbl butter or vegan margarine

° half a bunch of fresh thyme

**Technique**

° peel the carrots. you can quarter of halve them, but if they're pretty whole carrots with a bit of the tops on are beautiful

° put carrots in a large pan and just cover with water. Add a bit of salt and ground pepper and the clementine juice, the vinegar and butter

° bring to a boil and cook until nearly all the liquid has evaporated

° add the thyme sprigs, reduce heat to low and cook for about 5 minutes to caramelize

## placetime

trees are the poems nature writes to the heavensI 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 skyWe fell them down and turn them into paperThat they may record our emptinessSeveral 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 skyI realize poetry often doesn't translate, but consider Jheri's inspired variation much better and have been using it.

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^{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.Posted at 12:16 PM in building insight, critical thinking, general comments, play | Permalink | Comments (1)

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