Which is a more correct representation of a beloved member of your life—an audio recording, a photograph, a video recording, a pencil sketch, a realist portrait painting, or an abstract painting?  That’s the question I keep asking myself every time I think about analogies, metaphors, and representations in physics.

The classic example of a representation challenge in physics is wave-particle duality:  do particles act like little billiard balls?  Or like waves moving through a non-existent medium?  The answer is they act like both.  The challenge is, as realities, they feel mutually exclusive.  But, as representations, the act as complements.  Each representation, either wave-like or particle-like, gives a framework for describing how a fundamental object, like a photon or an electron or a neutrino, will behave under certain circumstances.  Both representations are right in the sense that they will produce precise, numerical results that can be calculated and will match observed values.

In the same way, if I gave you a photograph of a close family member in my life to try and describe their behavior—how they interact with the world—you would gain one kind of understanding.  If, on the other hand, I gave you an audio recording of that same family member, the information would be complementary to what you learned from the photograph, but completely different.  Obviously though, we don’t cry foul and say, but how can the person be invisible voice waves and a static two-dimensional color object at the same time, and what does this have to do with their behavior?

That’s because we understand that they are representations of a thing and not the thing itself.  Of course, from an intellectual standpoint this argument is partly philosophical and psychological and has had volumes written about it.  But from a practitioner standpoint there’s no challenge: both representations are valid, and the combination gives a better understanding than either one representation alone.  In fact, in the close family member’s behavior analogy it’s easy to see that having more representations is better, because each added representation layers our perspective with additional understanding.

If I were trying to discover something new about someone else’s family member it might even help to force me to use different representations: an audio recording might tell me about how that person speaks or interacts with others, a photograph might show me that person’s physical characteristics and the kinds of events they participate in, an abstract painting might tell me what about that person most captures someone else’s perception.

In physics, having multiple representations of the same physical system can do the same thing, especially since most of our studies want to know about the behavior of something (its dynamics), but most representations are static (don’t move).  Words and math sit on a page.  Photographs sit frozen in a flat plane.  Videos sit in a flat plane and replay a sequence of still shots at high speed over and over.

At least with a living family member we can go meet them in person.  We can set aside the photograph.  We can ignore the voicemail.  We can turn off text and video messaging and go get all that experience in real-time, face-to-face.  Not so in physics.  The simulated photographs, the recordings, and the equations are as close as we will ever come to some members of nature’s family, especially in particle physics.  Biology, geology, and the social sciences, to name a few, have the advantage over particle physics, in that respect.  Though any investigations into the past are equally handicapped by lack of direct access.

So, it seems to me we need to accumulate as many representations and models as we can get our hands on.  Aim for a collage, not a pixel.  No one representation will ever be all things to all situations.  Because no representation will ever be the real thing.  By narrowing down representations to “the right picture” instead of generating representations to get “the right mix” we cut off a route to discovering something new.  After all, when we allowed both the wave and particle representations into physics we opened the door to countless previously inconceivable and undiscovered phenomena, like neutrino oscillations (the ability for a neutrino particle to spontaneously change particle type as it travels, which relies on quantum mechanical wave interference between its constituent parts).  When it comes to conceiving of the inconceivable, representation, not rightness, rules.

It occasionally strikes me of just how many mythical notions I had about how researching discovery, fusing it with my own neutrino research, and putting it on “The Insightful Scientist” site would work.  Perhaps “pre-conceptions” or “ideas” would be a better word.  Which has me thinking about ideas.

I’m currently part of what is known as “the Hive” in my institution, a tribute to the symbol of the city we’re in—the Manchester bee.  But on the ground floor of our building is something known as the “Ideas Mill”.  It’s a place for lectures, break-out groups, conferences, students to study and lounge, etc.  And its name honors another Mancunian legacy–industrial mills.

When it comes to scientific discovery I think we too often have an image of the mind as a vessel that gets filled up.  If you are an “average person” then that liquid is just water—necessary, but uninspiring, and on really long days the vessel can get a bit leaky.  If you are one of the “gifted ones”, like good old Albert (Einstein of course), then the liquid is a bit more like fuel and your vessel an engine that runs like a honed machine churning out “something new” at an astonishing rate.

But watching my own ideas evolve, in writing and thinking about the meeting of the minds down in the Ideas Mill and expressions like “grist for the mill”, I think a more helpful picture might be to see the “discovery mind” as a mill.

Raw material is taken in (content, like knowledge and experience).  The materials are prepared for production in some way (distilling, sorting, accepting and rejecting content).  Then the materials are worked upon to create something new (refining, fusing, categorizing mental content).  And at last the final product is packaged for sharing and consumption (articulating mental content).

Each step, as the grist moves through the mill of the discovery mind, could become better known so that discovery-friendly tactics could be applied at key points throughout production.  This matches somewhat with aspects to the three-phase picture of discovery in parts of the philosophy of science.  My own view of the “discovery cycle” has already evolved to now include six phases that I think are suited to theoretical physics.  The main point is to perceive ideas and discovery as a process that can be built up and refined in the mind.  In this picture, how productive we are at discovery will depend on how much care we have taken with our internal mode of manufacture.

In any case, three phases, six phases, or other, it’s something to think about. In other words, grist for the mill.

When I first started reading and thinking about how to actively, meaningfully, and systematically foster the frequency and pace of discovery in my own work I was of two minds.

In psychology there is a line of thought which compares a child with a scientist, albeit with different degrees of content knowledge.  In this picture, the scientist’s capacity for discovery is taken to be part of an innate skill set, evidenced by the learning and daily discovery capacity of children, necessary for human development.  At the same time, sociology studies talk about institutional and field norms inhibiting discovery.  Using this mindset, I rationalized that achieving discovery more often might be about eliminating inhibitors to discovery. It’s as if we start out with the necessary tools, but access to the toolbox gets restricted over time and the tools get rusty.  Here the goal would be to identify these discovery inhibiting factors and strive to experience less of them, less often.

But upon reading the philosophy and cognitive psychology literature I generated an alternative mindset: here the emphasis is often on the individual and on mental strategies acquired by the individual over time that make discovery more likely.  Particularly fascinating, and resonant for a physicist, were the computational psychology studies reproducing famous discoveries.  Out of these investigations, into human discovery processes and computer artificial intelligence, grew techniques and algorithms much beloved by physicists today: machine learning approaches.  Using this mindset, I rationalized that achieving discovery more often might be about cultivating enablers to discovery. It’s as if we start out with a small set of tools and then add-on a toolbox and new tools over time, keeping them in pristine condition through care and attention.  Here the goal would be to identify these discovery fostering factors and strive to experience more of them, more often.

Of course, this is actually a continuum, between doing more discovery cultivating and doing less discovery inhibiting.  But which way to move toward first?  Especially in tough times, i.e., in a “limited resources scenario” where your time, your money, your patience, your motivation, and even the data available might be limited to the bare minimum.  What’s a discoverer to do then?

I found one possible answer to this question in something I read a few months earlier.  I was reading a book on evidence-based approaches to mindful meditation for pain management, by a pair of British practitioners and academics, when I came across a fictionalization they devised regarding the pull between positive and negative tendencies.  I think it stuck in my memory since, being an American from the East Coast, I used to visit the Blue Ridge mountains, connected to the Great Smoky Mountains in the story’s opener:

“It was a crisp autumn day in the Great Smoky Mountains.  A group of Cherokee children had gathered around their grandfather and they were filled with intense curiosity and excitement.  A few hours earlier, a fight had broken out between men and the village elder was called upon to settle the dispute.  The children were keen to know what the elder had to say about it.

‘Why do people fight?’ asked the youngest child.

‘Well,’ the elder replied.  ‘We all have two wolves inside us and they constantly do battle with each other.’

‘Inside us too?’ asked another child.

‘Yes, inside us all,’ he replied.  ‘There is a white wolf and a grey wolf.  The grey wolf is filled with anger, fear, bitterness, envy, jealousy, greed, and arrogance.  The white wolf is filled with love, peace, hope, courage, humility, compassion, and faith.  And the two wolves fight constantly.’

‘But which wolf wins?’ asked another child.

‘The one that we feed,’ replied the elder.”

[Vidyamala Burch and Danny Penman, Mindfulness for Health, published by Piatkus (2013), p.177-178.]

It came back to me in the context of scientific discovery because it feels like it sums up the issue in another way.  To me the wolf metaphor says, if you only have two bones, give one to yourself and one to the white wolf.  In other words, we could spend a lot of time trying to remove all the obstacles to discovery (i.e., chasing away the grey wolf).  But even if we are wildly successful, if we haven’t cultivated what fosters discovery, then all we’ll have is the most lovely, discovery-friendly environment in the world where precisely nothing happens because we didn’t actually build the capacity to discover anything yet (i.e., feed the white wolf).

So focusing on fostering seems like one promising approach.  Some old narratives of scientific discovery and high achievement  tended to liken discovery to a battle between two competing forces, a kind of assault of the intellect on the hidden aspects of Nature embodied in “ignorance”.  But, perhaps, the war is part of the problem, part of what occasionally misdirects our discovery aspirations and saps our limited resources.

Perhaps another discovery paradigm might be more effective.  Just feed the white wolf of scientific discovery and discovery may become your companion more often than you think.

For a long time, I’ve been drawn to the idea of a “spark.”  I know where this began.  My long-time love and fascination with the Walt Disney World character Figment, as in “a figment of your imagination”.  Only in the Disney story, a man by the name of Dreamfinder makes Figment real.  More to the point, there is a song that used to play during the original iteration of the 1983-1998 ride in Walt Disney World, which I first saw at the age of 3 years old (and still remember it being love and adoration at first sight):

“We all have sparks, imaginations

That’s how our minds create creations

Right at the start of everything that’s new

One little spark lights up for you.”

(Lyrics from “One Little Spark”, Walt Disney World Ride “Journey Into Imagination”, Composed by the Sherman Brothers, Performed by Chuck McGann and Billy Barty)

The ride and song also featured something about electron beams (I got my Ph.D. in physics), the famous writer Edgar Allan Poe (I got an M.A. degree in creative writing), and even tap dancing (I remember tap dancing to the song “The Good Ship Lollipop” at around age 4 for a brief stint in dance lessons).  So, no doubt, I’m now living the Figment dream, albeit with a little bit of Freud thrown in (I got a B.S. in Psychology too—you can never have too many sparks).

But what stuck most was the word “spark” and it resonated even louder as I was reading the Stanford Encyclopedia entry on scientific discovery about the moment of discovery conception where the authors have a “happy thought” or the “Eureka” moment.  For me it is the “spark point”, when you become aware of the presence of an idea or option which then goes on to become a bona fide discovery.  So what are these spark points?  And can discovery be cultivated by fostering these spark points?

Good questions to craft into scientific hypotheses for testing, maybe in cognitive psychology.  But strictly speaking my own current work remains hypotheses in physics.  So I will have to approach this more as a matter of trial and error, unless I can find a discovery-friendly adventuresome collaborator from another field who might want to investigate the issue, or happily find a body of research has been done that, as of this writing, I just haven’t read yet.  Until then, I will make a sort of ramshackle working hypothesis to guide my trial and error in that direction.

What then is a spark point?  The one-line phrase that pops in to my mind is “an unseen cluster in the network of the mind.”

It’s as if a discovery path were a bridge leading from the known to the unknown.  The bridge exists, always there, but the trick is to find it.  Perhaps there are in fact many roads that lead to this bridge, either directly or indirectly, but even though you may take and re-trace a route you might not happen upon the bridge.  Or upon seeing the bridge you might not recognize it as a route to somewhere new.  So here lie all these links and the route to discovery, but it goes unrecognized.  It’s a key intersection, a crossroads, hiding in plain sight.

It’s similar to the mind perhaps.  We have neural connections linking to the key point from which a discovery idea could be made.  In fact, we re-use and add on to these neural connections with new learning, associations, and experiences daily.  But we don’t see that they are forming a cluster around a key point, a spark point, which provides the neural bridge between known and unknown.  It’s as if the discovery just sits there on a quiet neural pathway that never lights up because it never gets ignited by a spark.

I think maybe discovery strategies help by uncovering these spark points or allowing us to build up connections to them by re-visioning what is known.  Discovery strategies and approaches make the search active, dynamic, explicit, and unfamiliar, causing us to pay attention to what otherwise might go unnoticed.

In my personal experience these spark points often feel like they “resonate” somehow with one’s thinking, because the connections are there, even if as yet unnoticed, in the network of the mind.  The trick would be to lay down new roads through experience or shine a new light on old roads.  A good part of a discovery process search will look for ways to illuminate these hidden clusters and learn how to cultivate them.  This is an area I will definitely have to investigate more deeply.  For indeed, where there’s spark, there’s fire.