Tech Transforming Art: Maths Lessons from Photography
For a book about transforming maths education, the topic of photography appears surprisingly often in Conrad Wolfram’s The Math(s) Fix. At first glance, maths and photography may seem largely unrelated, but the fundamental shift from analogue to digital photography is still fresh in the minds of anyone not born this side of the millennium. Maths, Wolfram argues, is about to go the same way.
One of the core tenets of The Math(s) Fix is that our education system is stuck: stuck using old methods to teach students how to use old tools that help them solve old problems. At the end of it all, we’re left with students who aren’t adequately prepared for the real world, a problem that’s only going to get worse as we enter the AI age.
“But Hand Calculating Is the Essence of Maths!”
The trouble is, after years of learning traditional maths, it can be difficult to see how antiquated the subject — with its overarching focus on hand calculation — has become.
Proponents of our existing maths curricula argue that “Hand-calculating procedures teach understanding” or “Students need to understand the basics first” or even “Today’s maths trains your mind”. Wolfram addresses each of these ideas in The Math(s) Fix, but they all seem to trend towards the same problem: a misunderstanding of what the essence of maths actually is.
Wolfram jokes that if photography were a mainstream school subject, the first lesson today would still be how you load a film into a camera. But is understanding the mechanics of an analogue camera the essence of photography? Is understanding the how to do long division by hand the essence of maths?
An Excerpt from “The Math(s) Fix”
As a child, I used 35mm film in a single-lens reflex camera. There was a necessary ritual around loading in a new 36 exposure film, advancing the film by hand, storing, processing and printing it (all of which I’d put some effort into learning). […] The envelope of what photos I took was controlled by the cost and difficulty of dealing with film, my experience tempered by not immediately seeing the results of taking a picture as I awaited its processing and then tried to construct what settings of exposure, aperture and focus had led to which results. Eventually I had some system of noting these values for post-development comparison, but it was cumbersome.
Digital photography has completely changed the mechanism of capturing images. Gone are those constraints. In are some new issues — including huge numbers of new options to optimise alongside new automation to help. A far larger number of people can capture images with less knowledge of the mechanics. Many new styles, uses and forms of photography are opened up, both in absolute terms and for a given user of photography. For example I can now take a huge number of photos at low cost and throw most of them out. With film, few people other than professionals, like press photographers, would do so.
In the transition from film there were many arguments put forward that film would never be replaced by digital for serious photographers — that this replacement would cause photography’s essence to be lost. This seems eerily similar to some of the arguments used around maths education for not using computers. Of course, the early digital cameras weren’t anything like as good at capturing images as film, by then so carefully engineered over decades. But this wasn’t fundamental, just a reason not to adopt then. There will always be differences too, and some people may not like those. But the idea that never would digital capture meet or surpass film technically for almost all uses now correctly looks ludicrous.
As does the idea that digital loses photography’s essence… or that calculation by computer loses maths’ essence. The ritual of loading film into a camera or, indeed, before that of coating a glass plate in chemicals was not the essence of still photography… in much the same way as the finery of writing odd maths symbols doesn’t seem to me to be the essence of maths. Rather I might describe that photography essence as a way to capture and present a view of life, crystalise an observation… or of maths, deploying the most powerful of problem-solving systems.
It’s certainly the case that many more people can trivially produce very uninteresting photos now, but so is it the case that vastly more people produce interesting, well-crafted, technically good photos too. Crucially, almost everyone now has a rather good camera available to them almost all the time. New photography, instantly beamed around by anyone to anyone. Or you just take a photo as a record in case you need it: where you parked your car, what something looked like before you took it to pieces and so forth.
From a somewhat niche field, photography has become massively mainstream. The mechanics have changed everything, including broadening and changing the essence. Imagine what could occur now with mainstream computational thinking, if not held back by mismatched education.
Now, as someone who enjoys a spot of traditional analogue photography, I would argue that there is something about the format that just can’t be replicated by its digital counterpart. But does that mean I would advocate it be the basis of photography for the billions of people around the world with cameras in their pockets? Of course not!
Likewise, if hand-calculating techniques are the foundation of your enjoyment or specialisation in maths, that is not threatened by shifting mainstream maths education to a computer-based approach. Just as analogue film is having a resurgence through people finding joy in the process and the format, so too will there be people who enjoy the process and format of hand calculating.
By reducing that barrier of entry to discover the true potential of maths as the world’s most powerful problem-solving tool, more people can discover their own favourite specialisms within, rather than being put off by rote learning for exams and becoming disengaged as the maths they’re taught fails to reflect the world they live in.
About the blogger:
Craig Cowley
Craig Cowley is a marketer with a background in software and computer networking and a degree in business and marketing. As a musician and a fan of photography, he is perpetually interested in both the cutting edge of the intersection of arts and technology and the history of the tools that got us to where we are today.
