omenti

brain power

your brain runs a 5k every day

 

let me explain:

On a walk a few days ago I found myself thinking about the power people need to live.  A ballpark figure is about one hundred watts of power or, over the course of a day, 2.4 kilowatt-hrs of energy.   A remarkable feature of people is that our brain requires a good deal of this - something like fifteen to twenty percent.

Thinking about at the energy requirements for a few physical activities it struck me that the amount of energy your brain uses in a day is roughly the same as an average person running a 5k.  

I mentioned this to Charlie who asked  the right question.  What is the difference between concentrated and unconcentrated thought?  Some time ago I came across some work that suggested there's little to no difference - at least within the accuracy of measurement.   I checked with a neurology researcher who was aware of more current work.  Serious amateur chess players playing against a computer program where the program was set to play a bit beyond their level represented hard thought.  The same people not focusing was the baseline.  There was a small difference - hard thinking would require a couple of regular (not peanut) M&Ms over an eight hour period.  Mediation appears to be the same as normal thinking.    

(Note:  energy is power times time.  Power is the rate of energy use.)

 

the fundamentals

mini-post

The Standard Model of Physics dates back to the mid 70s and is far and away the most complete and accurate description of three of the four forces of Nature.  Add General Relativity for gravity you have the basis to  answer fundamental questions like what we're made of and the forces. That's the bedrock of physics.    (the Standard Model with General Relativity tacked on is sometimes called Core Theory)  It's something that almost every physicist wants to see fail as there are hints of something deeper.

It's very elegant physics with beautiful mathematics, but good enough non-technical descriptions aren't easy.  Here's the best short discussion I've seen.  

 

I should note that while physics can describe all of these interactions, there's a problem with calculation.  Our mathematical techniques are often too weak so we have to resort to clever and not so clever approximations.  A lot of physics turns out to be applied mathematics.

 

playing with dimensions

Many occupations develop tricks to get "good enough" answers question.  These range from rules of thumb to shortcuts that are based on some insight.  In physics dimensional analysis - checking to see the technique or answer has the right dimensions - is important. After all - you don't want to measure someone's height and come out with an answer in pounds.   

 

The common shorthand is to use square brackets to denote the dimension of a physical quantity.   For a distance r [r] = L, velocity [v]  = L/T, g (the acceleration of gravity) [g] = L/T².  Generally M is the dimension for mass, L for length, and T for time. 

 

With a bit of additional information you can make quick estimates and even gain some insight.  Consider two athletes of similar build and physicality, but different heights.  One is six feet tall, the other five feet.  If you want to compare the power to weight ratio all you need to know is the power a muscle generates is proportional to its cross sectional area.  Their weights scale as the cube of their height, so  [power/weight] = L²/L³ or 1/L.  The shorter athlete has a twenty percent power to weight advantage.   You can use this type of analysis and freshman level physics to sort out why different sports dictate very specific body types at the elite levels of sport.  

 

Techniques like these are used during the early and very playful part of asking questions.  They can tell you if your approach is plausible or if it's going to be wrong.  Plausible doesn't mean right, but it's very useful to recognize what can't work so you can try something else.  It's a lovely way to learn by failing gently.  With time and experience you develop an intuition for what might work. 

 

One of these quick calculations is legendary.  A series of photos of the Trinity after the end of WWII.   Four stages of the explosion with a length and time indicators.  Details like yield were classified.  A British physicist didn't realize calculations were classified and did his own back of the envelope calculation in a few minutes.  His estimate was published and caused a kerfuffle worrying that secret information had been leaked.  

 

There wasn't a leak. The truth is many of the physicists involved made quick estimates that were good enough - enough to tell them the device's yield was about what they thought it would be.  They just didn't publish for obvious reasons. 

 

Here's my ten minute estimate using dimensional analysis and a bit of physical intuition. I'm avoiding a very difficult set of differential equations with some very messy boundary conditions - not to mention some quantities I have no way of knowing as an outsider.  To make it as simple as possible consider a spherical blast. The ground will have a minimal on the radius of the blast in the atmosphere, so ignore it.  The blast creates an expanding bubble that has to push against air outside the bubble. The most important terms in any expression will include the radius of the blast, the density of the air outside the blast, and the energy of the device.  There are many other things going on - this is just an attempt to see if a very simple high level relation of the relevant variables can be found in a few minutes.

 

Basically rearrange these terms dimensionally to see if you can find radius as a function of time after the device was set off.   Remarkably a simple relationship emerges.  So why not plug some numbers in?   The time and radius can be found in the photos and the density of air is well-known.    My radius measurement is crude - I know the device was on a tower and found a point that looked like the center.. draw some lines on a piece of paper, put it up to the picture and estimate 90 meters... perhaps a bit less.  A bit of arithmetic and a yield of equivalent to fifty thousand tons of TNT falls out.   

 

(pardon the handwriting, but it's much quicker and more natural than trying to typeset it)

 

 

The estimate isn't that far off - it gives you a good sense how the radius scales as the one fifth power of the blast's energy and to the two fifths power of time.  Those relationships are more illuminating than the estimated yield.  Since there are four images you could do something a bit more elaborate measuring all of the photos and making a plot of the growth of the fireball. 

 

 

 

diving into boiling stones

The air you breathe is about 21% oxygen and 78% nitrogen by volume.  People suffering from serious Covid-19 need much higher oxygen concentrations to hopefully buy some time.  Hospitals need to keep local stocks of liquid oxygen or high pressure oxygen tanks filled to provide treatment.   Patients can be treated at home with a portable oxygen supply and lower the burden on the hospital.  Often this means oxygen concentrators.

 

Around 1800 a mineralogist noticed heating stilbite produced steam. The class of materials was called zeolites from the Greek for "to boil" is zeo and lite is a mineralogy shorthand for lithos or stone.  There are a few hundred such materials each with a similar internal structure or framework.  The framework creates tiny pores - pores that can absorb substances and even be used as molecular sieves.  Wikipedia shows a structure for a common zeolite called mordenite.  It's based on a silicate (SiO₄) building block - I show it as this framework is common to zeolites and there's a nice public domain image.

 

 

Now back to oxygen concentrators.  Rather than getting bogged down in their operation just note regular air is passed through a molecular sieve made out of a different zeolite that traps nitrogen and allows oxygen to pass.  Relatively inexpensive machines for home use can produce about 10 liters per minute of enriched air that is 80 to 90 percent pure oxygen.   These are regularly used by people who need oxygen therapy and have kept a lot of people out of the hospital during the pandemic.

 

A wonderful invention, but there's something extremely beautiful about zeolite.

 

Chemists and physicists have their own way of looking at its repeating framework - the one called the secondary building unit.  Mathematicians have their own interesting way.  To get there a bit of a digression is warranted. 

 

Take a deck of cards.  Assuming it's well shuffled (say a dozen shuffles or so) I guarantee the order of the cards has appeared only once and will never appear again.  The reason comes from the fact there are an enormous number of possible combinations of cards: 52!  (52*51*50 ...  *3*2*1) or something over 8 *10⁶⁷ unique orderings!  One way of thinking about it a mathematician might consider each possibility a point in a 52 dimension space.  It's a bit abstract as we are only used to three physical dimensions, so here's a way to think about these configuration spaces.

 

A mathematician looks at a cube and says "that's a three dimension cube..."  A square is a 2 dimension cube, a line is a 1 dimension cube and a point is a cube of 0 dimensions.  She can go in the other direction too..  4 dimension cubes and up.   OK - now back to the cards.  Take three cards labeled 1, 2 and 3.  There are six (3! = 6) possible orderings:    {(1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), (3,2,1)}  Make yourself a 3d grid with an x, y and z axis and plot the six points.²  Now connect them up - pretend you have a rubber band to snap around them.³ 

 

Sweet!  You get a hexagon.  Shine a light on it at the right angle and it will cast a hexagon shadow.  The combinations of the three cards are linked to a shape!  

 

Now take four cards labeled 1,2,3 and 4.  There are 4! = 24 possible ways to order them.  Plotting them on a 4 dimension grid doesn't work for our spatially limited brains, but if you do the same trick of connecting them up you get a 3 dimensioned gem-like shape .. the exact shape of zeolite's framework (the secondary building unit).  If we lived in a place with four physical dimensions the shape of that object would cast a three dimensioned shadow..  

 

Thinking about the structure of an important molecular sieve with four playing cards..  math can be a curious playground.

 

__________

¹ The repeating unit is fairly complex: (Ca, Na₂, K₂)Al₂Si₁₀O₂₄·7H₂O

² you can also do it with two 2d grids..  say x,y and z,y and see the pattern  

³ the convex hull

mother's day

She enjoyed having to wait.  People around her would become characters in stories she'd make up.  Story making was a hobby of hers.  Often she'd invite you to join in.  As you gained experience, she'd take greater leaps.  Simple things on the street would develop complex plot twists and even find themselves in other eras or places.  

 

She was a bit on the quirky creative side and some of that may have rubbed off on me and my sister.  Here are a few lessons I learned:

° It's good to have some boredom in your life. It encourages you to try something new.

° It's fine to not be great at something if you enjoy it.

° You need several very different interests because they'll have conversations with each other if you just listen.

° Don't worry about names and dates in school. "How" and "why" are better.

° chocolate is good, pie is good, ice cream is good.

° Your friends may turn out to be at least as important as your family.  Find the good ones.

 

We were never pushed to do homework school. My parents were busy enough that our upbringing was more semi-supervised free range.  There were a lot of books and trips to the library.  The reward for a good report card we'd get an ice cream cone from Dairy Queen.  Perfect marks scored a banana split or milk shake.  And even if she didn't understand our interests, she'd support us how best she could. 

 

When I was about fifteen I read Edwin A. Abbott's Flatland - probably the book that had the biggest impact on me until I went to college.  As I  described the world Abbott created, Mom ran with it and developed a richer story and asked some "how" questions.  Those questions started me down a path  that taught me a little engineering - subjects she was unfamiliar with.  I began to see the value of story telling - particularly those visual stories.

 

Besides stories she enjoyed drawing and painting.  She wasn't very artistic, but spent a lot of her free time playing with projects.  I wondered why as my sister's art was much better.   Then I went off to college and found myself drawn to sketching.   I was and still am terrible, but it's a form of play that can take me to a state of flow.  I realized she was probably doing the same thing.  My sister became an accomplished artist - some her pieces have been described as snapshots of quirky short stories.   She picked up a lot from Mom too.

 

We celebrate those important ones through memories and  recognition of how they helped us become who we are.  Even now I find myself watching people and imaging stories when I'm waiting and everyone else is studying their phone.  She would have laughed at how unimaginative smartphones are.

 

Happy Mother's Day Mom.

 

objects and friction

Randall Munroe's xkcd is a necessary visit for anyone doing science, math, or engineering.   Artistically simple, he often sums things up with an almost poetic simplicity. Some have suggested topic ideas - he's taken two of mine and created beautifully distilled views of the underlying concepts that make me envious of his talent.  And he does it about three times a week.   Every now and again he creates something that resonates across a community.    It happened again last week:

 

 

Anyone who reads a lot of scientific papers recognizes this. Dozens of variations emerged overnight.  Some were very specialized - at least three relevant to astrophysics alone and I only know that because I know the community.    Here's one Abeba Birhane posted.¹

 

 

Serious truth!  A good deal of the community is this clueless.

It made me think of friction and objects.

 

One of the most remarkable features of physics is its simplicity.  While it may be non-intuitive and sometimes requires a bit of tricky math, you can remove complexity and discover underlying bedrock.  Once you understand the simple basics you can restore the complicating bits a piece at a time and describe a vast set of physical processes.  The fact that you can deconstruct and reconstruct so effortlessly is unique among the sciences.  It's why a physicist will tell you physics is the simplest science.  

 

Beyond physics complexity and emergent properties become important.  It turns out that asking "what is life?" is one of the most difficult questions. Working backwards from biology to biochemistry to chemistry to physics breaks down along the way.

But back to simplicity 

Students learning about motion and collisions start with a statement like "assume a frictionless surface."  Concepts become clear and it's easy to describe interactions where everything is understood.  Two blocks colliding elastically for example.  Later on you can restore friction.  Mechanical engineers, working in the real world,  are forced to deal with it.  In some of their systems - say a chain and gear bicycle transmission - it's possible to have efficiencies that exceed 99%.  Frictionless is the ideal here.  On the other hand you don't want frictionless tires or brakes - you'd never start and, if somehow put in motion, you couldn't stop.  The bicycle and road system is complicated enough that friction is good in places.  Fortunately good engineers know how to deal with such things.

 

The concept of "frictionless" has extended to interactions between computational objects and people.  In fact people are often treated as objects that contain a long series of properties.  Constructions like these lack the meaningful emergence that social creatures have. Serendipity and insight are often the result of social "frictions" in our interactions with other people.   We can have simple low friction interactions.  Sometimes they're great as we're not looking for much, but they're generally shallow.  A worry is large scale machine learning can create a faux sense that interactions with machines are deeper than they really are.  And many of these interactions are with other parties who make decisions about and for us. 

 

A few who build large scale social platforms have deep backgrounds in the social sciences and the humanities and think deeply about underlying social issues, but much of it is done without much clue by coders who build things quickly and then iterate to make them better - often more frictionless.  

 

Separately I had two wonderful reports from people at a very creative company.  Fully vaccinated people are back at the office with some precaution and maskless outside.  One reported she's had more insight and exciting ideas in the last week than in the last six months - largely through random talks with coworkers where they could "read" each other.  I hope all of you find the light at the end of the tunnel soon.

__________

¹ She's a cognitive scientist from Ethiopia who specializes in critical race theory - a rather important intersection these days.

 

 

 

when subtraction beats addition

The hammer and feather were released at the same time as a few million people watched back on Earth.  Absent air resistance, both objects fell to the lunar surface at the same rate.  David Scott had performed a version of the experiment Galileo Galilei is known for - the one your high school physics teacher said was true if you could ignore the air.

 

It turns out Galileo never dropped anything from the Leaning Tower of Pisa.   Instead he rolledballs of different masses down inclined planes.  The balls accelerated uniformly independent of their mass, but at a rate related to the angle of the plane.  He recognized their acceleration on a 90° ramp would be the same as dropping them from a tower.  One of his insights was if you get rid of friction and air resistance, the problem becomes simple.   This is one of the deepest insights in all of physics - that you can make seemingly ridiculous simplifications and get useful results. And once you know the idealized solution you can add in the fiddly bits that kept you from seeing things clearly at first. 

 

Physicists are trained to simplify wherever possible - (paraphrasing Einstein) just not too much. It's part of the art of the sport. It's so deeply engrained you find yourself using the approach in unrelated areas.  With this background I was struck by a piece in Nature showing people tend to add rather than subtract when solving problems.  It's very common.  Software can get overloaded with features in a hurry consider Microsoft Office.  It's fine to add some functionality over time.  The hard part is understanding something enough to subtract features to improve it's functionality takes serious creativity - in some areas it might be called taste.

 

Once the core ideas are understood it becomes possible to go much further. Before the scientific revolution of the 16^th and 17^th centuries Aristotle's teleological view of the world dominated Western thought.   An object's motion was determined by its nature and all processes were determined by goals.  It's a crude handwavy explanation that sort of makes sense if you don't ask too many questions.   Place a coffee cup around on your desk and give it a shove.  It moves for awhile and comes to a stop.   Everything in motion must constantly be moved by something. Galileo shattered this way of thinking and others built on it.  Newton came up with a good model for motion and gravity that still works well for most of what you and I do - you can and a probe on Mars and fly a helicopter there with it. .  About one hundred years ago Einstein, motivated by some foundational flaws in Newton's work, created "simple, but not too simple" theories that gave a much deeper view that solves a few thorny issues.  That helped to explode our view of the universe.  It also made global positioning systems work. 

 

With this deeper understanding of Nature our minds can travel to the most exotic places. Recently a visualization of a binary black hole system was released.  While the calculations are difficult, requiring a lot of supercomputer time, the core ideas are straightforward.  Enjoy the lightshow as the massive black holes warp nearby spacetime  (the notes are a good explainer)

 

There's much to be learned talking with people in very different fields.  Some are motivated by simplicity, but their approaches are often different and enlightening. .  These people have a lot of skill and experience playing with their kind of simplification.  I'm thankful for conversations I've had with some of you where you've been open enough to let me learn a bit from you.  It's sharpened my approach.

 

 

getting down to the bedrock

Some areas are built on foundations of fundamental principals that can be built upon.  For example many of the world's religions have a form of the golden rule in their bedrock.  Physics has a few of these cornerstones that are so deep they're considered beautiful and have become guides.  I've been thinking about one of them - complementarity -  a lot recently.  Particularly as it appears outside of physics in many areas probably including some you're used to thinking about.

 

Neils Bohr and Albert Einstein were contemporaries - peers actually.  Both were great sources of quotes.  Einstein's fame is such that it's difficult to figure out exactly what he did say without original sources. Bohr's lack of fame outside of physics makes it easier. Here are a few:

 

“We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct. My own feeling is that it is not crazy enough.”

“Never express yourself more clearly than you are able to think”

“A physicist is just an atom's way of looking at itself.”

“There are trivial truths and there are great truths. The opposite of a trivial truth is plainly false. The opposite of a great truth is also true.”

 

None were meant to be flippant and the last one is one of the richest quotes I know.  Really deep ideas have meanings that go beyond the surface.   As an example consider this question

 "is light a particle or a wave?"

 It turns out it's both, but sometimes it's most useful to describe it as a wave while other times you treat it as a particle.  It's impossible to apply both descriptions at the same time.   The essence of complementarity is there are different ways of looking at the world and each can have its own language and domain where it's true. 

 

You can step back a bit and look at a satellite in orbit.   Physics developed by Newton are good enough to put it there and predicting where it is to good precision, but if you're worried about the accuracy of its clock you need to bring in relativity.  Einstein and Newton offer very different theories that describe orbital motion and how clocks keep time.  Relatively turns out to be richer, but Newton's ideas are good enough for almost everything people normally do - that and I'd hate to describe the motion of a volleyball using special and general relativity.  

 

I won't go into quantum mechanics, but complementarity is at the core how you think about things.  That and like Newton and Einstein's models, there are boundaries where one is more useful than the other.  The trick is knowing both and where the boundary lies.  It's for another discussion, but I think complementarity is a good basis for talking about the concept of free will. 

 

Bohr was so taken with the idea of complementarity that he made it part of his coat of arms with a nod to Eastern religious philosophies and the Order of the Elephant.  (how's that for clickbait?)

 

Light offers another example. Newton used a prism to break whiteish sunlight into a spectrum of colors.  Later Keats objected to the beauty of science claiming Newton unwove the rainbow.  

Do not all charms fly/at the mere touch of cold philosophy?/There was an awful Rainbow once in heaven. 

 In reality something deeper is afoot.

 

 Consider a yellow light on your desk.  The wavelength of the light makes it look yellow, but if you are moving towards at a constant velocity you observe a shorter wavelength.  If you're moving fast enough it looks blue.  Faster still and it's ultraviolet.  If you're moving away the wavelength lengthens and it shifts towards the red.  In fact by selecting your velocity with respect to the light, the wavelength can be anything you want.   In this view of nature the color of light only depends on your velocity relative to it.   It may not seem useful, but it turns out to be one of the most important tools for measuring the size and age of the Universe. 

 

Complementarity appears all over physics and turns out to be a useful way of thinking about new phenomena.   Over time I've come to think of it in areas outside of physics.  The spoken word and a television show can both get across their own versions of something.  Neither is complete and understanding both can lead to a deeper appreciation.  Picasso and Rembrandt had very different portrait styles and both tell us something deep about their subjects in very different ways.  Mix different forms of art - a piece of music might describe the feeling of Winter quite differently from a painting, but both can offer deep if incomplete views of the feeling of the season.   Sports are offer many examples.  Movement in a sport can make statements that added with the emotion of the crowd give a more complete picture.

 

You can't use a flat Earth, geocentric universe, or being able to turn off gravity for an hour tomorrow.  The descriptions have to be valid in some domain  in the first place.  But having two good but very different representations of something in your head at the same time may just lead to a deeper understanding.  Usually you're not thinking about deep truths, but that's fine.  This doesn't come easily, at least not to me, but it's a lot of fun once you get the hang of it. 

 

 

good tide-ings

Jheri asked a good question about the tides.  First you need to watch Henry Reich's piece on the subject.  (His goal is to move quickly so you might have to stop every now and again and rewatch a segment.)

Basically differential gravity - the water on the side of the Earth closest to the Moon is attracted to the Moon. So is the Earth, but the Earth acts as a solid body so you can abstract it as a mass at it's center.  Since the center of the rigid Earth is farther from the Moon than the near-side water, the whole Earth moves a bit less towards the Moon than the near-side water. In other words the water level closest to the Moon rises.   The water away from the Moon is even further away than the center of the Earth, so the Earth is effective moved closer to the Moon than the water.  This gives the tidal bulges on either side.   Henry goes on with some other things including the tidal effect of a black hole (known as in the trade as spaghettification:) 

 

Jheri's question gets at something deeper.  "Why aren't there tides on ponds and lakes? Or in my coffee cup?"

 

That's a great observation  - one that never occurred to me until I was working on a homework problem in college.  There were three parts - describe the effect in simple terms, derive a formula for the tidal gravitational potential, and finally calculate the average high tide in the center of the ocean.  I answered the first part like Henry did.  The second part wasn't difficult - it was just Newtonian physics and I thought I did it properly.  Then the third part..  the numbers just didn't make sense.  I was getting sub-millimeter sized tides, but I couldn't find the flaw.  

 

Finally the answer came. The expression I derived was correct, but the my model wasn't.  Jheri is right..  If the Earth is rigid why wasn't the coffee in a cup rising?  Why wasn't I rising?  I'm not going to do the model here, but the trick is considering each point on the oceans and integrating the vector components of the forces.

 

 Imagine the Earth covered with water and the Moon orbiting over the equator.  A glob of water at the poles would be attracted to the center of the Moon.  Draw lines from the center of the Moon to these globs and you see they form an angle.  If you work out the vector components every glob of water not on the equator would have a small force pointed towards the equator.   If you add up all of these forces - do the integral - the total force is substantial.  Since water is fluid it is getting squeezed a bit.  Although each bit is small, the oceans are huge and all of those little bits add up to the tides we observe.

 

The same squeezing happens on the solid Earth, but our planet is rigid enough that the effect is small.  A tide exists in the coffee in a cup, but the total force is small enough to make them microscopic.  A large lake like Lake Michigan might build a few centimeters of tide, but you don't notice it with normal waves and wind.

 

The example in the video is sort of right - there really is differential gravity. The problem is it's about ten million times weaker than the surface gravity on Earth.  It's also an example of failure when a model is too simple and seems to be good enough.  Fortunately people like Jheri notice something's wrong which means you need a better model. 

 

claw your way to insight

Over the weekend I caught a segment on wallaby sightings in Britain.  It seems they've been zoos and private collections since the 1930s.  They're talented escape artists and many were turned out to the countryside during WWII.  Over the years there would be sightings for a year or two and then the individual would vanish.  In recent years a change has taken place and sightings are more common.  An attempt to make a census suggests there may be two breeding populations.  Momma wallabies with joeys in their pouches... 

 

In the past twenty years Britain's climate taken a major shift.   Indeed the South of England is climatically similar to wallaby-rich Tasmania.  British wallabies have few natural predators and Brits tend to love cute furry animals. It looks like they have a shot at success. 

 

Climate change.  The impact has been making marks in places we haven't thought about as well as the obvious ones we have. This one isn't too big, but it's an easy to understand example.  There are millions of others that quickly get to wicked complexity.  Mass migration, pandemics (loss of habitat is probably partly responsible for some epidemics and clearly pandemics are possible), the list of possibilities is huge.   So how do you begin to think about this class of problem?

 

The underlying physics is straightforward and known at a coarse level for about fifty years.  Thirty years ago it became clear global warming was a serious threat although it was difficult to gauge the impact.  Since then the science has become much more refined - essentially settled - and many of us became alarmed.  My conversion was about twenty years ago.  At the time I thought education would be a powerful tool and titled at those windmills for about eight years.  I didn't realize how interconnected  and nonlinear social and economic issues were. How do you communicate, how do you change minds, what is important to people?  Next regions are all different. Mix in how our brains are wired and an existential problem candidate becomes difficult to make meaningful headway on.   

 

How do you work on fundamentally difficult problems - those that are complex and non-linear?  People in my field deal with problems that tend to be much simpler, but are often too difficult to approach directly.  Early on you try to make the problem as simple as possible.  Very rough calculations often done mostly in your head or maybe a few scribbles with a stick of chalk.  The idea is to throw out a lot of bad approaches and find a few that make sense. It's playful and even exhilarating with the right people. Then you see if you can break the problem in components. It only works if the problem is decomposable with weakly interacting components.   Many problems aren't like that - the whole is much greater than the sum of the parts.   There are Nobel Prizes that have been awarded to people who have figured out clever hacks so you know how and when simple approximations can be made.  

 

Moving up to the next level of difficulty often makes careful study prone to error or even impossible.  Sometimes a way forward is possible.  A rough out of focus answer may give you the information you need to move forward. This type of integrated thinking, Murray Gell-Mann called it a coarse look at the whole or CLAW, is rare.  I've been part of three studies that used the approach.  Getting a diverse mix of people who are known to have the ability to listen to each other is important.  You need a few core experts and a mixture of generalists who recognize and build connections.  One group had a historian, psychologist, two sociologists, mathematician, two climate experts, a meteorologist, a rabbi, two computer scientists, a forestry expert, two oceanographers, a poet  and a few others including myself. (we needed a musician and chef :-) The project required two days a week face to face for two months with lots of homework. I think we had some important insights even if they were fuzzier than most of us were accustomed to.

 

There aren't many places with the structure to do this kind of coarsely focused work.  Those that do may not be as diverse as they need to be.   That said I think this can be done on a smaller scale - even with just two or three people.  Perhaps companies, government organizations and NGOs might think about tapping the power of internal diversity.  The warning is that you don't want to build internal think tanks (or even hire external ones) as that has problems of it's own. (lots of horror stories from a couple of companies I know.) 

 

A few notes from the groups I've been part of.  Counterfactuals are extremely important.  Looking at low probability, but desirable outcomes may give some insight into how to make them happen.  They can also reveal landmines you hadn't considered.   The diversity of metrics used by others can help inform your own work later on.   Picking the right people is difficult.  The success of the effort depends on it as much as anything. Understanding a bit of history can be very important. And finally a comment on simplification - the coarse graining. It needs to be discovered than imposed and that takes awhile.  A few days of conventional "brainstorming" isn't going to cut it.