Despite the fun title and the apparent sense that somehow the material is digestible by a kindergartener, this paper is really only accessible and relevant if you’re already well versed in the language of quantum computation and you’re interested in different ways to construct, represent, and manipulate quantum circuits using a mathematical formalism called the ZX calculus.
As I read through it I was asking myself whether the author had ever met many kindergarteners. Just saying that something is "like a lego block" doesn't make it so. At best, the lego block can be used to illustrate a concept just as ping-pong balls might be used to diagram DNA. That doesn't mean that anyone who can play pingpong understands genetic drift.
> somehow the material is digestible by a kindergartener, this paper is really only accessible and relevant if
When suggesting a novel science education conceptualization, there are two sides. Science side, showing correctness and fruitfulness. These research papers. And education side, showing accessibility and effectiveness. The long unavailable book. Though I fuzzily recall fragments or draft being available somewhere.
Say I were exploring how getting the color of the Sun right in K-13, might then be used to help teach other things better, like color. Which I just might get around to. And maybe, beyond a correctly colored circle, I wanted realistic limb darkening and tint. Science side would be python color code, and spectra from papers. Or perhaps now simply python exoplanet library code. Education side is a white circle. Maybe a radial gradient for easily drawing it with a slightly darkened and red tinted edge. And perhaps a "no, not yellow, not at all - that's a pervasively common misconception - sorry all the adults and textbooks in your life are wrong - collectively we suck and don't care". :/ One side is color theory and code, browser limitations and image standards. On the other, a white circle.
In the pipeline from science research to education content, I suggest the bottleneck failure is at the science end. In using deep domain understanding to explore for fruitful and accessible conceptualizations. Whether string diagrams for quantum works out as educational content seems an open question. But it seems to me a good question.
This work has context in speculation that string diagrams might provide a useful representation across a variety of domains. With its ties to category theory. One nice aspect of string diagrams is that transformation correctness is more transparent than with equations. And one can easily imagine interactive editors making it a plaything. Scratch 2040, but vastly more general and powerful. But fleshing out how it might be used to represent various domains is IIRC a work in progress. As is demonstrating that it's a compelling cross-domain representation. Then there will be minor matters of pedagogy, and finding a foothold ahead of large scale curriculum change. But first task is finding something usefully worth attempting to teach.
Conventional math notation coevolved with prevailing display technologies, from cold type to early serial computer interactions. It took a generation for people to learn to chat on a phone, and a generation for the shift from typewriters to word processors to change how people compose text. It will take a similar generation drawing on a digital tablet to change how people compose mathematical thought. However, teaching through a pandemic, this evolution has been radically accelerated.
Apps like Notability fluidly replace blackboards for teaching on Zoom. They however are primitive drawing editors. One outgrows them like a beginner windsurfing board. Apps pioneered by digital artists such as architects support much more advanced algorithmic drawing. Concepts is my current favorite; an example of math notes in Concepts is here: https://www.math.columbia.edu/~bayer/S21/Combinatorics/Week7...
Still, these are closed editors. Unlike Emacs, they can't be used to modify themselves. One longs here for Lisp-universe live drawings, a break from the misconception that a static final visually appealing canvas is the objective. Rather, how much thought can we externalize and reify as live doodles? What notion of space will replace artboards and layers, for supporting drawings as live computation, completely accessible as if one had a time-traveling functional programming debugger?
When software supports this, crosses that threshold like a general purpose programming language where users can create arbitrary modifications and extensions in this visual medium, then we'll see more papers like the present.
I don't see how the ability to automate drawings of the figures in your Concepts example makes either a student's or teacher's life easier. If anything it just overwhelms a reader with excessive visual information.
Typing on a smartphone, using a word processor, or drawing on a digital tablet hasn't produce better communicators, typists or artists. People today can accomplish tasks faster, but not necessarily better. If you and I were having this conversation 100 years ago, I'd be typing these words on a mechanical typewriter, on a piece of paper which would reach you in a couple of weeks. If anything, the quality of my writing would probably have been better in that scenario. Same goes for tablets: there are lots of "learn to draw" apps on my iPad - but do they make it easier to learn how to draw? I'm not sure. The things I need to learn don't change significantly whether I draw on a tablet or on paper. The apps can certainly help me draw something, or even draw something for me, just like a human teacher would. And that's great, but it does not lead to any significant changes in how I learn or how I think.
If you want to change how people think, you should focus on that, on the thinking part, not on the tools. When you succeed in that, you end up with something like this: http://worrydream.com/LadderOfAbstraction/ To me, the visualizations there is an ornament that makes the ideas a little more entertaining, a lubricant that makes the material a little easier to follow. However, if you remove all those diagrams and animations you don't really lose much - everything in that essay is described in words well enough to get the idea across. In fact, if you try to read it carefully while deliberately ignoring any visual information, you might actually get more out of it! That is not to say visualization are useless. Sometimes a picture is indeed worth a thousand words. Sometimes it does make learning dramatically easier. This has been true for thousands of years, and the recent technology you mentioned does not really change much in this regard.
> Typing on a smartphone, using a word processor, or drawing on a digital tablet hasn't produce better communicators, typists or artists. People today can accomplish tasks faster, but not necessarily better. If you and I were having this conversation 100 years ago, I'd be typing these words on a mechanical typewriter [...]
"If you and I were having this conversation 1000 years ago, I'd be a scribe in a royal court writing these words with a quill. If anything, the quality of my writing would probably have been better in that scenario. [...] but it does not lead to any significant changes in how I learn or how I think."
Though I think it fun that someone in 1500's Spain might be rumored to have made a deal with Devil, based on being able to read not only silently, but, gasp, without moving their lips!
How to put this. I suggest you are vastly underestimating the importance of environment to accomplishment. The technology version of a wealthy kid's "growing up in poverty wouldn't have made any difference - I'm just naturally good at things".
> but do they make it easier to learn how to draw?
iPad, drawing apps, and an ecosystem of artist youtube videos, versus... let's say, a snail-mail booklet from scam "Learn to Draw!" advertisements in the back classifieds of 1960's Popular Mechanics? Um, yes.
> However, if you remove all those diagrams and animations you don't really lose much - everything in that essay is described in words well enough to get the idea across.
One bit of progress in teaching over recent years, has been the slow realization that "get[ting] the idea across" isn't the hard part. But rather pruning misconceptions and firming understanding.
Students and their teachers remain steeped in misconceptions. A main lesson of physics education research has been that if you think you're teaching successfully, then you're also not testing successfully. worrydream's work is an attempt at being less badly unsuccessful.
Revisiting this the next day, perhaps it might be usefully thought of as like a customer acquisition funnel? One with lots of friction/leaks. Say a bad landing page, broken install instructions, no examples, poor documentation, no community, and unreadable source. Given that, still, some visitors will survive the gauntlet, to become minor and major customers. And customers will spend far more time working the product, than working around these not-critically-significant-for-customers frictions. And no amount of fixing, will make most visitors into minor customers, nor most minor into major. And yet. You'll have more visitors, and more visitors will become minor customers, and more minor customers will become major ones, if these frictions are improved. Perhaps similarly, for tool quality and people's skill?
When Newton wrote his Principia, he had to turn all of his algebraic calculations into geometric manipulations, so that people would actually believe his results. Now we are faced with the reverse: graphical calculi manipulations are having to be rewritten into algebraic notation in order for papers to be published [1].
Regarding modifiable, fluid, math notation editor - I heard of this post through a friend and would like to bring your attention to the Graspable Math Canvas with embedded Desmos graphing features: https://graspablemath.com/canvas?load=_607afeebfb63a5be
(Sorry if my formatting is weird, I've never used this platform before).
13 comments
[ 309 ms ] story [ 1046 ms ] threadWhen suggesting a novel science education conceptualization, there are two sides. Science side, showing correctness and fruitfulness. These research papers. And education side, showing accessibility and effectiveness. The long unavailable book. Though I fuzzily recall fragments or draft being available somewhere.
Say I were exploring how getting the color of the Sun right in K-13, might then be used to help teach other things better, like color. Which I just might get around to. And maybe, beyond a correctly colored circle, I wanted realistic limb darkening and tint. Science side would be python color code, and spectra from papers. Or perhaps now simply python exoplanet library code. Education side is a white circle. Maybe a radial gradient for easily drawing it with a slightly darkened and red tinted edge. And perhaps a "no, not yellow, not at all - that's a pervasively common misconception - sorry all the adults and textbooks in your life are wrong - collectively we suck and don't care". :/ One side is color theory and code, browser limitations and image standards. On the other, a white circle.
In the pipeline from science research to education content, I suggest the bottleneck failure is at the science end. In using deep domain understanding to explore for fruitful and accessible conceptualizations. Whether string diagrams for quantum works out as educational content seems an open question. But it seems to me a good question.
This work has context in speculation that string diagrams might provide a useful representation across a variety of domains. With its ties to category theory. One nice aspect of string diagrams is that transformation correctness is more transparent than with equations. And one can easily imagine interactive editors making it a plaything. Scratch 2040, but vastly more general and powerful. But fleshing out how it might be used to represent various domains is IIRC a work in progress. As is demonstrating that it's a compelling cross-domain representation. Then there will be minor matters of pedagogy, and finding a foothold ahead of large scale curriculum change. But first task is finding something usefully worth attempting to teach.
Conventional math notation coevolved with prevailing display technologies, from cold type to early serial computer interactions. It took a generation for people to learn to chat on a phone, and a generation for the shift from typewriters to word processors to change how people compose text. It will take a similar generation drawing on a digital tablet to change how people compose mathematical thought. However, teaching through a pandemic, this evolution has been radically accelerated.
Apps like Notability fluidly replace blackboards for teaching on Zoom. They however are primitive drawing editors. One outgrows them like a beginner windsurfing board. Apps pioneered by digital artists such as architects support much more advanced algorithmic drawing. Concepts is my current favorite; an example of math notes in Concepts is here: https://www.math.columbia.edu/~bayer/S21/Combinatorics/Week7...
Still, these are closed editors. Unlike Emacs, they can't be used to modify themselves. One longs here for Lisp-universe live drawings, a break from the misconception that a static final visually appealing canvas is the objective. Rather, how much thought can we externalize and reify as live doodles? What notion of space will replace artboards and layers, for supporting drawings as live computation, completely accessible as if one had a time-traveling functional programming debugger?
When software supports this, crosses that threshold like a general purpose programming language where users can create arbitrary modifications and extensions in this visual medium, then we'll see more papers like the present.
Typing on a smartphone, using a word processor, or drawing on a digital tablet hasn't produce better communicators, typists or artists. People today can accomplish tasks faster, but not necessarily better. If you and I were having this conversation 100 years ago, I'd be typing these words on a mechanical typewriter, on a piece of paper which would reach you in a couple of weeks. If anything, the quality of my writing would probably have been better in that scenario. Same goes for tablets: there are lots of "learn to draw" apps on my iPad - but do they make it easier to learn how to draw? I'm not sure. The things I need to learn don't change significantly whether I draw on a tablet or on paper. The apps can certainly help me draw something, or even draw something for me, just like a human teacher would. And that's great, but it does not lead to any significant changes in how I learn or how I think.
If you want to change how people think, you should focus on that, on the thinking part, not on the tools. When you succeed in that, you end up with something like this: http://worrydream.com/LadderOfAbstraction/ To me, the visualizations there is an ornament that makes the ideas a little more entertaining, a lubricant that makes the material a little easier to follow. However, if you remove all those diagrams and animations you don't really lose much - everything in that essay is described in words well enough to get the idea across. In fact, if you try to read it carefully while deliberately ignoring any visual information, you might actually get more out of it! That is not to say visualization are useless. Sometimes a picture is indeed worth a thousand words. Sometimes it does make learning dramatically easier. This has been true for thousands of years, and the recent technology you mentioned does not really change much in this regard.
"If you and I were having this conversation 1000 years ago, I'd be a scribe in a royal court writing these words with a quill. If anything, the quality of my writing would probably have been better in that scenario. [...] but it does not lead to any significant changes in how I learn or how I think."
Though I think it fun that someone in 1500's Spain might be rumored to have made a deal with Devil, based on being able to read not only silently, but, gasp, without moving their lips!
How to put this. I suggest you are vastly underestimating the importance of environment to accomplishment. The technology version of a wealthy kid's "growing up in poverty wouldn't have made any difference - I'm just naturally good at things".
> but do they make it easier to learn how to draw?
iPad, drawing apps, and an ecosystem of artist youtube videos, versus... let's say, a snail-mail booklet from scam "Learn to Draw!" advertisements in the back classifieds of 1960's Popular Mechanics? Um, yes.
> However, if you remove all those diagrams and animations you don't really lose much - everything in that essay is described in words well enough to get the idea across.
One bit of progress in teaching over recent years, has been the slow realization that "get[ting] the idea across" isn't the hard part. But rather pruning misconceptions and firming understanding.
Students and their teachers remain steeped in misconceptions. A main lesson of physics education research has been that if you think you're teaching successfully, then you're also not testing successfully. worrydream's work is an attempt at being less badly unsuccessful.
Revisiting this the next day, perhaps it might be usefully thought of as like a customer acquisition funnel? One with lots of friction/leaks. Say a bad landing page, broken install instructions, no examples, poor documentation, no community, and unreadable source. Given that, still, some visitors will survive the gauntlet, to become minor and major customers. And customers will spend far more time working the product, than working around these not-critically-significant-for-customers frictions. And no amount of fixing, will make most visitors into minor customers, nor most minor into major. And yet. You'll have more visitors, and more visitors will become minor customers, and more minor customers will become major ones, if these frictions are improved. Perhaps similarly, for tool quality and people's skill?
What does this even mean?
If it means that only children born by parents who had a phone can chat using them, it is a false claim, seeing that even the Queen has a phone and uses it to chat. https://www.cheatsheet.com/entertainment/queen-elizabeth-ii-...
When Newton wrote his Principia, he had to turn all of his algebraic calculations into geometric manipulations, so that people would actually believe his results. Now we are faced with the reverse: graphical calculi manipulations are having to be rewritten into algebraic notation in order for papers to be published [1].
[1] https://twitter.com/coecke/status/1362800194895642631
A lot of what you said has resonated deeply with me. Is there any way I can get in touch to discuss further?
https://www.cs.ox.ac.uk/ss2014/programme/Bob.pdf