Learning Feels Different

OLYMPUS DIGITAL CAMERAI grew up surrounded by music teachers. My mother was a piano teacher and her father, my grandfather, taught violin, guitar, and piano. They both taught students in their living quarters so my own home and my grandparent-visits were woven through with the sounds and sights of music lessons. The line up of nervous children waiting their turn, the dissonant sound of songs not quite mastered, the ritual tones of fitful tuning, the repetition and nervous laughter. If you’ve ever heard “Tuna Fish” pounded out on the piano keyboard by a well-meaning eight-year-old, well, you’ll know just what I mean.

Though I lacked the native talent of my matriarchal lineage, growing up without learning to play an instrument just wasn’t an option. I started with the piano, but my instrument of choice was guitar. I learned mostly by imitating others and through sporadic lessons. Once I’d left home my guitar stayed with me but it mostly hung out under my bed, collecting dust. Occasionally I’d feel the itch to play, pick it up and quickly put it back when I realized how rusty I’d become and how little I remembered.

Recently I decided to pick up the thread. By luck I found a very good guitar teacher, Wayne Anderson, who is a perfect match to my ambition (gentle, non-intimidating, and relaxed). We meet once a week for 30 minutes.

It didn’t take long for it to feel familiar again – the comfort of the instrument’s wooden swell on my lap, the companionship of working a pattern out in my head, and the dull ache on the fingertips of my left hand.

But what was completely unfamiliar and a delightful surprise is how guitar teaching has changed.  Wayne’s approach to my lessons, as facilitated by digital tools, is a completely different animal to the way my mother and my grandfather taught.

Pitch Lab's tuner screen shot.

Pitch Lab’s tuner screen shot.

The differences begin with the most commonplace of lesson openers – tuning the instrument. Wayne introduced me to a number of apps for my iPhone. After looking them over, I downloaded a free, easy-to-use app from Pitch Labs. Flawless, no-sweat tuning, every time.

Next up, there are no books. Gone are the color-coded Schwann’s piano books, clutched nervously in sweaty fingers with scribbled annotations in the margins as the lesson proceeds. Wayne has a laptop and printer in our small cubicle of a practice room. When we’re working on a new piece, he finds the guitar tabs or sheet music online and prints it out for me. Voila.

As we work together to figure out the piece, assess the timing, and decipher the picking technique he searches for a YouTube video of the song, as played by the songwriter. Bob Dylan, Antje Duvekot, Leonard Cohen, the Avett Brothers, and Joan Baez regularly visit my practice cubicle.

When we’re working on a particularly tricky element we make use of the recording option on my cell phone. Last week, for example, I was struggling with Travis picking. After many failed attempts, I was finally getting it. Wayne gestured to my phone, suggesting I might want to capture this, while the going was good. I propped the phone up on the music stand, pressed record, and did my bit. Back at home, practicing, if I fumbled (which I did regularly), I could just pull out my phone and hear myself picking the right way. I can also recorded Wayne playing and, and in so doing, take my teacher home with me.

On my own I’ve found countless (and I mean thousands and thousands) of excellent instructional videos.  Really good guitar teachers, showing you step-by-step, how to play non-trivial songs on the guitar like Blackbird or Freight Train (seriously, do a search). Often the video production values are so good they’ll show you the right and left hand on a split screen or the musical tabbing along with playing top-to-bottom. Videos are, of course, endlessly patient. I play, stop, rewind, and fast-forward them as needed.

My teacher also makes use of software called Scorch as a teaching device. He bought the software, I have the free plug-in. Wayne will create a scorch file from a piece of sheet music and share it with me. With my plug-in, I can play the song on my laptop and control the speed, slowing it down to match my learner’s pace, and play along with it. Huge.

I haven’t even touched on the various ways to record tracks, edit sound recordings, and write music (I’m so not there yet), but even at my amateur state I can see that teaching and learning music has fundamentally changed.






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Reflections on #FutureEd



Week #6 brings the end of the History and Future of Mostly Higher Education MOOC (#FutureEd). Time for reflection on what I’ve learned as well as the experience of the course itself (since that was part of the mission).

First, a few facts.  This was a free, six-week course, offered on the Coursera platform, requiring 2-4 hours of work per week.  Cathy Davidson, Duke University, was the instructor.  The course was open to anyone interested in the topic to take asynchronously, but there also were three physical locations where the course took place synchronously.  The axis of the course was a series of videos (4 – 6 of them per week) featuring Cathy Davidson, sharing her insights about education, interviewing other experts, and talking with other faculty. In addition to the videos, there were forums for discussion, quizzes, and small (optional) assignments.  There was a “certificate” option for the course, which I did not take.

My participation in the course was fairly typical – I was there for the duration, but didn’t do the assignments.  I kept up with the course’s pace, watched all of the videos, dipped into the forums, but I did not take any of the quizzes nor did I complete the assignments.  I’m sure I would have gotten much more out of the course if I had but, even without that more robust involvement, I still got a lot and I’m very glad for the experience.

The most interesting content insights for me…

  • The importance of knowing and using history purposively (what did we do in the past, and why)
  • Unlearning (our preconceptions about how things “have to happen” and how difficult it is to shake old habits, be open to new ideas and new solutions)
  • Value in alliances with other change makers (innovation is happening all around us – listen, learn and share)
  • The importance of experimentation (the more novel approaches we try, the more likely we are to find ideas that work)
  • There is value in what we count and we count what we value (interesting reflections on assessment)
Coursera Forum for the course.

Coursera Forum for the course.

As for the mechanics of the course, as with other MOOCs I’ve taken, it is a challenge to find community within the great expanse of an asynchronous MOOC.  Although I visited the online forums each week, it felt like looking for a needle in a haystack (no pun intended…).  There was just so much to wade through…and many of the comments and stories just weren’t relevant to me. Stephen Downes and George Siemens make good use of newsletters in their Connectivism MOOCs. They send out daily newsletters (via email) that serve as brief summaries, each with a curated list of things to read or watch. Downes and Siemens aggregate and sift, then share what they deem the most relevant and interesting blog posts, tweets, images, videos, and recordings made by the course participants.

It’s all about harvesting distributed information. To that end, Downes developed gRSShopper (see the “RSS” in the middle there?) to do this. It works to harvest links from given feeds (having established metadata tags in advance) and compile them. This solves the problem of the need for centralization (for sanity’s sake) in a learning environment that hopes to maintain and leverage a distributed network (!). People prefer to write in their own environments (not on a Moodle discussion board or a Coursera Forum), but something like gRSShopper pulls it all together to connect the learners. An idea that #FutureEd could have used. Stephen Downes says it well, “…connectivism is the thesis that knowledge is distributed across a network of connections, and therefore, that learning consists of the ability to construct and traverse those networks.”


FutureEd Meeting in Second Life

One obvious path toward making such a BIG course feel more intimate and personal is to form a small group – a study or discussion group consisting of fellow travelers who share a common interest in the course. A number of small FutureEd groups formed during the run of the course – on Facebook, through Twitter, and a few who were geographically close met in person. Liz Dorland and I formed such a group and blogged about it here. We were a small, but intrepid, group who met weekly in the virtual world of Second Life for an hour to discuss and share. We probably could have done a better job of organizing the group, encouraging the members to come regularly, and perhaps we could have worked together to build artifacts of our learning – but it was a good start.  Liz Dorland said it well when she said, “I’m sure we could do it better the next time we go through the course!” (one more time, Cathy?)

Our group would have benefitted from some guidance and support from FutureEd’s teaching hub. I wonder if, in future versions of the course, Cathy Davidson might recruit a small army of teaching assistant-type volunteers (I’m sure many would be happy to help). With a little advance preparation and training, these volunteers could fan out to provide mentoring for the myriad small groups organically forming in a course like this. As Dan Lynch, founder of Interop and former director of computing facilities at SRI International, wrote, “The most useful impact is the ability to connect people. From that, everything flows.”

Week #5, the most useful week in the course for me, provided an object lesson in getting the most from these online experiences. Innovation in Pedagogy and Assessment was the week-five overarching topic; we took a look at digital badging systems as an example of a novel way to think about assessment.  Interestingly, one of the reasons that this turned out to be my most useful week was due to an unintended accident. Cathy had interviewed Connie Yowell, the Education Director for the MacArthur Foundation (and an expert on digital badging). Some disaster befell that interview video and, as a substitute, the course directed us to an alternate video (of Connie Yowell speaking at a conference) as well as other links and resources on the HASTAC site.  Those directed explorations yielded a rich harvest for me. I watched, read, explored, reflected and then blogged about it.  By far the most rewarding week and all because I invested more time – more of myself – to investigate, read and connect. Duh, right?

It was a terrific course – thoughtfully put together, well-organized, and welcome range of jumping off points to investigate and connect. Thank you, Cathy Davidson, and the whole team “behind the camera”.

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“Badges? We Ain’t Got No Badges…”

"Badges?  ...Badges?"

“Badges? …Badges?”

Unlike the bandits in The Treasure of the Sierra Madre, it looks maybe we do need some badges.

Girl Scout sash.

Girl Scout sash.

Week #5 of the History and Future of (Mostly) Higher Education MOOC focused on innovations in pedagogy and assessment.  As part of our study this week, we learned about the use of badges in education  - and I’ve been thinking about them ever since.  I have very fond memories of the badges I earned as a Brownie and a Girl Scout.  There was a well-worn Girl Scout Manual, listing each of the possible badges one might earn (one badge per page) along with a description of what had to be done to earn them.  Each badge entailed arriving at clear evidence of your mastery and many of the them involved a fairly complex project – building, creating, collaborating.  Once awarded, the small, circular, cloth badges were sown onto your sash (thanks, Mom) so that you could wear them with pride. When meeting a fellow girl scout for the first time you could instantly find points of connection – “oh, so you’re a swimmer…”  or ” you play the piano!” I have a distinct memory of the point at which the number of badges I’d earned meant that my mother had to start sewing them onto the back side of the sash. Some girls had to wear two sashes, like Pancho Villa, to display their collection (I never got there).

But what about badges in education? They’ve been used in gaming and online spaces for awhile now but what if we devised a system of digital badges for learning?  As Connie Yowell, Director of Education at MacArthur Foundation, puts it, digital badges are image files with “stuff” in them. A validated indicator of accomplishment. Tokens of trust. If you earn a digital badge, anyone could open it to find out what you did to deserve it. One could examine the metadata associated with the badge as well as the products and artifacts created by the badge-earner. This suggests a way to clearly and systematically communicate one’s abilities and accomplishments with media-rich, tiled portfolios.

In an educational setting badges could be awarded for knowledge as well as skills. Something you earn along the way of getting better at something larger. Since badges are smaller in scope than a certificate, a badging system gives us an opportunity to break assessment down into smaller (more meaningful? formative?) chunks. Perhaps bringing the assessment closer to actual the learning?

In order to make the badges meaningful, a given education community would have to agree on what’s required to earn a badge.  I could imagine some very interesting decisions coming out of such conversations in school districts and colleges.  What badges could be earned?  How would you break down a general chemistry course into a series of badges?  Who decides when the badge has been earned? What is the relationship between badges and credentials, degrees, grades? How does the definition of the badges alter the way we structure the learning? It would have to be a rigorous system, grounded in the values of the institution and reflection of the learning objectives that drives their curriculum.

As one substantial step in the right direction, the folks at Mozilla have developed Open Badging to provide a shared infrastructure (software and open technical standards) for creating and sharing badges across the web. Earned badges could be displayed on your web page, your social media profile, your cell phone, your online portfolio, your email signature line.

So, where to get more information? The MacArthur Foundation has led the way with careful thought and funding so their site on digital badges is worth a visit.  Cathy Davidson has proposed using a badging system to facilitate peer group feedback in this HASTAC post.  Carla Casilli talks about badge pathways in this post on her blog about badge system design (that’s her image in the figure below). UC Davis has devised a badging system for their new undergraduate major in sustainable agriculture and food. Purdue University has devised the Purdue Passport Program, currently in beta – a way to “show what you know”. Educause recently published one of its helpfully succinct “7 Things You Should Know” documents on Badging.

I am warmed by the implied message here that education happens in many different places and forms; that learning happens in a vast range of places  - after school programs, online, in the home, mentoring programs, internships, study abroad programs, and on the job.  Formal and informal. And isn’t it interesting to consider that the process of earning a badge would give the student a language around their learning, a way to meaningfully talk about what they did, thought, and experienced?

Here’s another intriguing thing to consider –  the concept of the badge as a pathway –  a sort of breadcrumb trail to show others how you got there and, presumably, how to follow you. Badges could work to make learning visible in a way that a diploma or your GPA just doesn’t.  What does an “A” in Geography 101 at Bowling Green State University mean anyway? When you think about it, your diploma or your certificate says more about the institution you attended than it does about you.  A badging system would give you an opportunity to tell the story of your education.

Bade pathways. (Image courtesy of Carla Castilli)

Bade pathways. (Image courtesy of Carla Castilli)


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An Ode to the Talented Folks in the NYTimes Newsgraphics Group

Screen Shot 2014-02-22 at 9.48.34 AM

Opening Shot of the NYT Newsgraphic on Ski Jumping

I don’t know what’s going on in the newsgraphics department at the New York Times these days, but they’ve really hit upon the most wonderful way to create beautifully engaging and effective teaching videos. Have you seen these?

Understanding Short Track Speed Skating

Understanding Giant Slalom

Understanding the Luge

Understanding Ski Jumping

And from 2012….Snowfall at Avalanche Creek  and A Game of Shark and Minnow

There’s so much to love about these gems, it’s hard to know where to begin.  But let me try…

  • Stunning images

    Stunning images

    First and foremost, the clean, elegant look – no intrusion of the interface, the video takes over the whole screen in luscious high-definition.

  • The blend of narration and text to explain (good judgement there about when to use what).
  • I admire the way they control the pace of the learner through the story – you vertically scroll to proceed – with some control –  but at certain key points, the video takes over and just plays.  One caveat to this is that there are no standard video controls available to you.  If you try to imagine (as I’ve done) applying their method to an educational module to explain, say protein synthesis or cell division, you would want to give the learner the ability to “rewind” a scootch, replay, reconsider.
  • The overlay of instructive graphics on top of an image is particularly instructive. Not only does this method skewer our eye to the critical element (in the case of the slalom skier, Ted Ligety, the extreme angle of his body in relationship to the ground), but they guide you through the explanation by drawing the graphic in real-time, John-Madden-style.  Very effective.
  • A generous and smart mix of media types – animation, video, audio, still graphics, text, models, sketches
  • A very clever mix of focus – long-view, close-up, macro, micro – your eye and your brain feel exercised and engaged.   There is no downtime.
  • Numbered steps when you need them to aid the explanation.
  • Often when using digital media to teach, we learners suffer from the “spelunking problem” – that is, it’s a bit like spelunking in a cave, you don’t know where you are in relationship to the whole journey – when will it end?  In the case of these modules, you are given subtle cues about how much information lies ahead of you. Note the small vertical column of dots to the right of the screen that serve as a progress bar – a clear commitment read out.  Knowing that, you can relax and concentrate on the business at hand.

So very, very well done.  Bravo, NY Times, and keep them coming!

You can see all of the NYTimes Olympic graphics here and follow the NYTimes graphics group on Twitter: @nytgraphics


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History and Future of (Mostly) Higher Education



The History and Future of (Mostly) Higher Education MOOC (#FutureEd) has begun.  We’re now in week #2 (of six weeks) and, so far, it’s been a real eye-opener. Cathy Davidson (Duke University, author of Now You See It) is our ring leader, instructor, coach, and provocateur.  The course, like education itself, is made up of many moving parts.  There are the videos – short segments featuring Cathy, so far explaining the historical context for the conversation; the readings; the online forums – lively conversation; the personal assignments – optional, depending on how you are taking the course; and, of course, the myriad other social connections made through Twitter, Facebook, Wordles, and the blogs of the enrolled students.

The goal of the course is to thoroughly explore our American education system, which was primarily designed to prepare workers and leaders for the industrial age, and strategize together, as a community, about how we can change that to fit the era we live in now – the information age.

Until today my pleasure in the course has been mostly private.  I’ve thoroughly enjoyed the readings and the videos, done some exploration in the Forums, wrote a short entry on my favorite teacher (Mrs. Hirschfelder – chemistry) and certainly, I’ve done a lot of mulling and processing.  But today, I was able to take that private mulling to a whole new level with a terrific group of fellow thinkers and FutureEd travelers in the virtual world.  My friend and colleague Liz Dorland (Chimera Cosmos in Second Life; @ldinstl_chimera) organized a group of FutureEd study group to meet and discuss the course as avatars in Second Life.

Our FutureEd study group meeting in Second Life

Our FutureEd study group meeting in Second Life

There were nine of us to join the cozy campfire circle on the Tufts University island, many of us meeting for the first time (here are a few more pictures of the gathering).  We hailed from Pennsylvania, Missouri, California, Washington, Belgium, Scotland, Brazil.  Fellow travelers and adventurers in education.  We talked about our experience thus far in the course, the ideas in the FutureEd videos, other MOOCs we’ve taken (or started, rather), connectivism, immersiveness, the advantages of small group meetings, differences in education traditions between the U.S. and other countries represented by the group, oculus rift, advantages/disadvantages of online learning….in other words, we covered a lot of ground in one hour.

It was a terrific group of smart people, looking to connect and deepen their understanding.  If that sounds like something you’d like to try – join us.  We  plan to meet every Monday at noon SLT (Pacific time).  And here is the SLurl for our starting location (we will take some field trips as well). If you have questions about setting up SL and getting in to join us, comment below and we’ll figure it out together.



Filed under Reflections on Teaching, Virtual Worlds

What Happened to the Passenger Pigeon?

Passenger Pigeons.  Photo by Todd McGrain

Passenger Pigeons. Photo by Todd McGrain

I just picked up Joel Greenberg’s A Feathered River Across the Sky:  The Passenger Pigeon’s Flight to Extinction.  What a terrific read.  I had no idea how abundant this bird was – apparently, the most numerous bird species in North America (and possibly the world) in the 1800′s.  Get this:  In 1813 John Audubon saw a flock that took three days to pass overhead! Witnesses frequently described the birds in quasi-Biblical terms. In their wake, passenger pigeons often left behind ravaged fields, broken limbs (too many of them roosting on one branch), and feet-thick coatings of their droppings.  According to Lake County, Illinois records, “they flew in flocks that darkened the sun.” A single nesting ground in Wisconsin was reported to cover 850 square miles. Such abundance meant for happy hunting. You see where this is going….  By the turn of the century, the species was extinct. There was a captive pair at the Cincinnati zoo – the female of which (the last living member of the species) died in 1914. The publication of Greenberg’s book is timed with the 100 year anniversary.

Greenberg tells the story well. He puts the extinction in its cultural context and writes with great insight about the bird’s natural history (Greenberg is a naturalist and the author of the bird blog, Birdzilla).  The short answer as to why the passenger pigeon went extinct is that it tasted good and was easy to kill.  Of course, Americans got better and better at killing the birds with efficient methods and when you combined that with destruction of the bird’s natural habitat through the logging industry…

One element I loved about the story is the way that, long after the species was extinct, people kept reporting sightings of them and coming up with crazy explanations to explain their reduced numbers – they were in the southwest desert, they migrated to South America, they had all drowned in the Pacific Ocean, or they were hanging out offshore (just out of sight).  As Greenberg suggests, maybe the human role in the pigeon’s extinction was just too much to own (sound familiar?)

The actual pigeon specimen being used for its DNA. Photo by Brian Royal.

The actual pigeon specimen being used for its DNA. Photo by Brian Royal.

Today there is a plan afoot to bring back a genetic recreation of the bird:  The Great Passenger Pigeon ComebackGeorge Church (of the Human Genome Project) is working on this with Stewart Brand‘s (of the Whole Earth Catalog and The WELL fame) foundation Revive & Restore.  Love the combo.  They plan to take passenger pigeon genes from the toe pads of museum specimens ( pictured at the right) and combine them with genes from the band-tailed pigeon.

If reading the book is more than you want to take on, there is a fabulous New Yorker article by Jonathan Rosen that excerpts the story extremely well. And if you want to make the passenger pigeon a part of your travel plans in 2014, there is a memorial to the passenger pigeon at the Grange Insurance Audubon Center in Columbus, Ohio.


Filed under Interesting Science

David Hockney, A Bigger Exhibition

David Hockney at the DeYoung.

David Hockney at the DeYoung.

If you live anywhere in the Bay Area and haven’t yet been to see the David Hockney exhibit, A Bigger Exhibition, currently at San Francisco’s DeYoung Museum, stop reading this right now and go.  It’s absolutely wonderful. And for those of you not fortunate enough to live in the San Francisco Bay Area, there’s plenty here to read about and explore online.

The exhibit includes 400 of his more recent works in many mediums, leveraging many methods – oils, cameras, water colors, charcoal, video, and iPads. Portraits of friends and family, portraits of museum guards, landscapes, and nature scenes from his childhood home in Yorkshire.

His use of multiple digital cameras and iPads is remarkable. Hands-down, my favorite part of the exhibit was a room hung with large iPad replicas. On the screens were various pictures Hockney created using the iPad app, Brushes. On some of the screens you watch as the image emerges (as if on fast forward), layer by layer, color by color.  I watched a bowl of peaches grow from a rough sketch to a fully dimensional, bowl of glowing orangey-yellowey-red orbs, so real I felt I could reach out and eat one.  I must have watched that progression through six times, studying the way the picture progressed – color applied, color removed, color blended or smudged, jumping from one part of the painting to another, testing and retrying, layering.  It was absolutely fascinating. When do you ever get to watch, time-lapse fashion, the creation of art from blank canvas to finished piece? As you can see in this photo, my fellow museum goers were similarly fascinated.  A thick knot of people stood for the longest time – rapt.

Congestion at the iPad display

Congestion at the iPad display

As you gaze at these recorded pictures, it becomes clear that Hockney works very quickly. In this Spencer Michael’s interview with the artist, Hockney says “any draftsman knows about speed, you can see the speed in Rembrandt’s drawings.  I think most painters paint faster than they will tell you.”  He calls the iPad a “terrific new medium – much better than Photoshop or other digital tools.  You can be very fast on an iPad, faster than watercolor.”

I was particularly struck by Hockney’s full command of the technology.  Not only did he master the printing methods of high-resolution imagery, multi-camera videos, and printing (many of the iPad creations were printed out on huge sheets of paper and put together like puzzles), but his full command of the Brushes application.  For instance, in one iPad painting of Yosemite, he seemed to create a stippling effect and then capture (save?) it and re-use it, much like a stamp, thereby creating a forest of pine trees here, here, and here. Quite apart from how impressive and beautiful the paintings were, the 76-year old Hockney dispels any thoughts we might harbor about digital tools being only for younger generations.

The Great Wall

The Great Wall

When you’re there, don’t miss the portion of the exhibit on the main floor (the exhibit is divided in two parts).  Here you’ll find one of the more fascinating artifacts of his research and work – the Great Wall. Created originally in his studio, it’s been recreated here for us to wander and absorb. On the wall, they’ve pinned 100′s of high-resolution, color print outs of classic paintings, hung in order of their creation, from Byzantine art to Van Gogh – a sort of painting timeline. Hockney created the wall in order to sit back, scan and absorb centuries of western painting in one go. To see them juxtaposed and collected. He crafted an order to the collection - Northern European paintings at the top, Southern Europe at the bottom – and looked for patterns. As he studied the timeline, an order began to emerge. He realized that at about 1420, there was a big change in western painting. At that point, it appears that artists could “suddenly” draw better. The images were clearer, more exact, with strong contrasts, more three dimensional. One could even say, the paintings had more of a photographic look. Hockney’s explanation for this sudden change is that artists began to use optic lenses to create their images.

An Unknown Couple, by Lorenzo Lotto

An Unknown Couple, by Lorenzo Lotto

One of the paintings on the Great Wall (by Lorenzo Lotto c.1545 – hanging in The Hermitage), shown here, gave clues to the artist’s use of a lens to create his painting.  Note the elaborate red cloth in the foreground, with a geometric design. When examined closely, Hockney noted an area of the cloth that is out of focus. A physicist friend of Hockney’s, Charles Falco, was able to use the size of the out-of-focus area to confirm that a lens had been used and to calculate the focal length and diameter of that lens. By using a lens to create the realistic looking cloth, the artist has to contend with a problem of geometric optics. When the focus moves from foreground to background, the scale changes.  Placed together, the two halves don’t match and so the artist is forced to paint that area of mismatch out of focus.

Camera Lucida app.

Camera Lucida app.

Hockney used this information to support his speculation that these 15th century painters made use of optics to create more realistic, life-like paintings.  But of course high quality large lenses weren’t available in this period of history. Falco explained that curved mirrors could serve as a lens – and curved mirrors were certainly available.  As you use the mirror to focus the sun’s rays, you form an image.  And if that image is aimed at a surface upon which the artist will draw, the artist will see the scene and the drawing surface simultaneously, allowing them to duplicate the key points of the scene and accurately render the precise perspective and detail. Interestingly, the size of the sweet-spot  image produced by a curved mirror is roughly 30 cm square – and that’s about the size of many of early Netherlands portraits at that inflection point.  This sort of optical device is know more commonly as a camera lucida.  Interestingly, there is now a Camera Lucida app for the iPad and the iPhone (I wonder if Hockney knows about that?).

In 2006, Hockney wrote a book, that later became a BBC television series, called Secret Knowledge in which he delves into this theory in great detail. Of course, the theory is not without controversy.  Some art historians take issue with Hockney’s explanation, claiming that the use of optical lenses has little value in explaining the overall development of western art. But it doesn’t seem that is Hockney’s claim. Using optical lenses of any variety would only be useful aids to someone who already was a skillful artist and would only be one tool in their impressive toolbox, relatively useless without the other skills they would need to render a breathtaking work of art. Besides, isn’t it delightful to contemplate the beautiful union of art and science implied by the idea?

All in all, a thoroughly satisfying exhibit.  Well worth a trip.

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