Abstraction and Standardization

What is the future of art? What media will it use? Computers, obviously. Information technology is very good at imitating old media: drawing programs, music programs, word processors designed for playwrights or authors. But none of these tap into the intrinsic strengths of the computer, able to do something no other medium can: simulate. Bret Victor, the man so demanding of user interfaces he left Apple, is dissatisfied with the tools available to artists that allow them to simulate. So he made his own, and gave a one-hour talk on it.

Those interested should definitely take the time to watch it, but to summarize, he demonstrates the power of simulation in creating art that is part animation and part performance, with the human and computer reacting to one another. He then lifts the curtain and show us the tools he used to simulate the characters in the scene, and it’s not code. Instead, it’s a drawing program, with lines and shapes, that he uses to define behavior. Code, he points out, is based on algebra, but his system is based on geometry. Finally, he concludes with a short performance that he built with these tools. Higher is the story of earth, from the stars to cells to civilization to space travel back to the stars.

What blew my mind about Higher is that a few years ago, I had independently created a short film on exactly that topic, with exactly the same background music (Kyle Gabler’s Best Of Times from World of Goo). Victor’s piece was far more polished, but we had both been inspired by the same music to express the same idea, the journey of life to the stars. Remember when I complained about not finding people who shared my narrative? So this is what that feels like.

What drove Victor to create his tools was the belief that art is an attempt to communicate that which cannot be put into words. By binding simulation to lingual code, we make it inaccessible and unsuitable for art and artists. Direct manipulation of the art, which is how art has been created going back to cave paintings, allows the artist to interact with and lend emotion to the art in ways not possible through code’s layer of indirection, of abstraction.

The reason artists’ needs have been neglected by developers is that, for the rest of the world, code works just fine. As I’ve previously blogged, language is one of humankind’s most powerful inventions. The direct manipulation that is liberating to the artist is confining to the engineer. Language is how we manage many layers of abstraction at once; without it we are reduced to pointing and grunting. It’s harder to communicate with a computer in code than a well-designed direct manipulation interface, but code is more powerful. In the sciences, a good result is consistent with what is already known; in art, a good piece is unexpected and shakes our established worldview. More fundamentally, the sciences observe and record some objective outside truth; art looks inward to offer one of many interpretations of the subjective human experience.

This tension that we see between science and art also shows up in schools. In a recent TED talk, Sir Ken Robinson extols diversity as a fundamental human trait, which schools attempt to erase and replace with standardization. We agree that standardization has its place, but I personally think he downplays its importance. Standardization is writing, is language; those things can’t happen without common ways of thinking. At first, children need to explore concepts and use their own terms, without a top-down lesson plan imposed by school administrators. Nevertheless, the capstone is always learning what the rest of the world calls it. That isn’t smashing creativity, but rather empowering the child to learn more about the topic from others and from reference sources. It’s creating a minimum level of knowledge common every adult member of society, which is assumed by all media. Being able to communicate  facts with others isn’t just the result of education, it’s what makes education possible in the first place. With language, groups of people can unambiguously refer to things not present, a shared imagination. Verbalization is a form of abstraction.

Let’s get back to the role of diversity in school. Students should be able to explore what interests them, but the converse is not true: some topics must be taught to everyone, even if some people do not find them interesting. This is especially true before high school. I know you’re not passionate about fractions, Little Johnny, but you need to learn them. Society expects everyone to have a minimum level of competence in every subject. Additionally, passion for a field isn’t always “love at first sight”. The future mathematician isn’t always the first in the class to get basic arithmetic.

Although the curriculum needs to be largely standardized, the pedagogy does not. The neglect of diversity in schools is most heavily felt not in what kids are or are not learning, but how they are learning it. The inflexibility imposed on lesson plans is degrading to teachers and failing our kids. Teachers should be trusted to adapt lessons to their class, and empowered with testing results they find useful, early enough to use it. Standardized testing as it exists today does not fit the bill. Every student needs to achieve the same core competencies, but the paths to doing so will be as diverse as the children themselves. A broad exposure to both methods and topics promotes the development not just of knowledge, but of personality and identity. The reason to have art in school isn’t to improve test scores but because it’s part of being human.

To be more precise, we should distinguish between “the arts” and “art”. The arts are how to create with the media classically used for art: paint, music, poetry, drama, dance, and so on. Like any other discipline, the arts require a standardized language to record and transfer this knowledge. Sometimes it’s plain English, sometimes it’s jargon, sometimes it’s symbols, but it’s still an agreed-upon abstraction. Diversity of ideas expressed in the language is inventive and healthy; diversity of the language itself is nonstandard and chaotic. With this in mind, the arts take their place at one end of a spectrum of knowledge: mathematics, natural science, social science, and history. And the arts.

But art is something entirely different. It is the personal and emotional perception of an experience that communicates without words. Art is direct and concrete; it is subjective and sublime. Much of the arts attempt to create art. Victor’s tools advance the arts; what he creates with them is art.

It’s a defensible position to say that art, because it does not rely on language as all the other fields of knowledge do, is not knowledge at all. But I’ll indulge Victor and say that not all knowledge can be verbalized. That doesn’t mean that art is beyond classification; Victor and I saw the same artistic ideas in the same piece of lyricless music. Conversely, just because something is written down doesn’t mean it’s standardized or useful knowledge. Recently, the mathematics community has been bewildered by an inscrutable set of papers which claim to prove a fundamental piece of number theory. No one can decipher them to tell if the proof is valid, and their author has not been forthcoming with an oral explanation. So in extreme cases, the analogy between language and standardization breaks down. The wordless expression is more coherent than words.

For all the knowledge that abstract language has brought us, ineffable art remains part of the human experience. It is important for our children to learn about art to become mature and thoughtful adults. It is equally important for us to provide tools that support the nonverbal side of thought, to engage the visual and auditory parts of our brains in ways words never can. These are the same failure: the refuge in abstraction, the desire to have everything neat and orderly and predictable. Art exists to explore ambiguity and paradox; it does not demand simple answers but asks complex questions.

A lot of futurists imagine a time when technology makes everything easy. There is a faith in technological convergence, where everything speaks the same language and interacts intelligently and flawlessly. But historically we see technologies become incompatible. If there’s an open standard underneath, such as email, you still get dozens of providers and clients; and if there’s not, you get the walled gardens of social media, loosely tied together by third-party “integration”. What’s important to realize is that the path of technology is not fixed. Our gadgets don’t have to make us more productive and connected; they can make us more artistic and provide privacy, if we design them so. We should stop aspiring to a monoculture of technology because, not only will it not happen for technical and economic reasons, it shouldn’t happen. Standardized technology leads to standardized thinking, especially when coupled with standardized social institutions. Creativity is  not only what drives technology further, but art and humanity as well.

Automated Grading Done Right

The Khan Academy dashboard is meant to provide students and teachers with information that can help them target where a student is struggling, and improve. Unfortunately, the data given isn’t what’s useful to teachers, just what’s easy for computers to measure. These metrics include time spent watching and rewinding videos, time spent on different topics (broken up by videos and quizzes), and proficiency levels in exercises. But as one of the teachers I follow on Twitter points out, these programs don’t let him “SEE my students’ work so I can know HOW/WHY they got questions wrong.”

Mathmistakes.org attempts to counteract that. Math teachers send in anonymized samples of student errors that they find telling, common, or inscrutable. Teachers comment as to what they think the student is not understanding and how to fix it. In the process, newer teachers get to see the thought process of their more experienced colleagues. There are patterns to these mistakes, so can a computer be programmed to recognize them?

The most obvious example, which I doubt I’m the first to come up with, is to anticipate patterns of wrong answers. Let’s say you’re testing a physics problem where students need to plug values into an equation. (Yes, this is a naive view of physics but go with it.) Have experienced teachers compile patterns of mistakes students are likely to make: forget to square something, leave off the constant, divide instead of multiply, use a different formula, and so forth. Then the grading software picks new values to plug into the formula, and calculates all the wrong answers for these values (picking numbers so that none of the wrong answer patterns lead to the same numeric answer). Then, if the student gives any of the anticipated wrong answers, the program knows exactly what mistake the student made and can correct them. Hopefully finding a mechanistic error will provide the human teacher with a window into finding and fixing a qualitative misconception.

Let’s take a more complex, real-world example. In some computer science classes at Tufts, the programs written for homework are subjected to a battery of tests, written by both the professor and the students (and their predecessors). In one case, the assignment is to create a programming language interpreter that determines the “type” of pieces of code. For example, it needs to know that true is a boolean, 7 is an integer, and asking if true equals 7 is an error. To clarify, there’s the code the students write (called an interpreter) and then the code that it tries to type, as a test. An interpreter can fail in a number of ways: it can find the wrong type, find a type when it should raise an error, raise and error when it should find a type, stop unexpectedly with an exception, or never stop at all.

I know that’s a bit much to wrap your head around, but (1) that’s the sort of complexity we’re up against and (2) it’s not just an example, it’s a case study. I have a visualization for this data already made, as a class project. My group wanted to take this data and provide actionable reccomendations for the professor, to be able to say, “you’re not handling this properly” or “you don’t understand this very specific detail”. So we hand-built an automated classifier using what we knew about the errors. Here’s part of the visualization we came up with.

Circle errors

The size of each circle represents the number of students who failed at least one test with that error. The vertical position of the circle corresponds to the average number of tests passed by the students who got that error. Colors encode categories, and the horizontal spread means nothing (just a way to prevent overlap). Click on a circle and you’ll get:

Error bars by student

Each bar is a student, identified by an anonymized hash. Their errors are grouped together, with the taller bars being the error we have selected. On the real thing (not these images), you can click on any other bar to jump to that error. Hover over the bar and move around to show each of the tests failed with that error below the circles. This highly-specific information allows the user to look at the individual tests and hypothesize the underlying cause of the error.

You can play with the interactive visualization online here.

Education isn’t a no-computers-allowed clubhouse, but software developers are must be smarter about how we approach these tools. Programmers need to work with educators and fill their needs, not just offer up whatever statistics are easy for them to collect. We have powerful tools like machine learning and visualizations, and teachers with decades of experience. We can make useful automated systems, if we stop acting as if it’s a trivial job.

And yet… all of this takes the views education as a series of questions with right and wrong answers. This is largely true in the STEM fields and even in the humanities, but not in the arts. There really is no good way to automate grading of the arts (or to grade the arts, for that matter). We need to nurture our future artists, but more importantly, we need to teach the skills necessary to appreciate the arts, and to dabble in them. As part of the human condition, we all find ourselves with emotions and ideas that we need to express, through music, painting, or writing (writes the blogger). The fact that very few people will appreciate these works is fine; what matters is the catharsis they give to their creator. That’s something no machine could ever understand.

Activists and Engineers

Tufts is an activist’s college. You can hardly walk across campus or read The Daily without encountering arguments about the Middle East, sexual assault, racial or class privilege, the LGBT movement, or any other social movement. Don’t get me wrong, these are worthwhile causes and injustices worth correcting. But nevertheless it becomes grating. Everyone at Tufts wants to save the world, and it’s tiresome. My housemate summed it up when she said, “there are eight sides to every coin”. My campus doth protest too much.

What if I’m tired of ambiguity? What if I just want to curl up into my own little corner of knowledge marked “Engineering” and make things that work? Unfortunately, I don’t get the choice.

Today was the final project presentations for my Visualizations class. The field straddles art and science. One one hand, we learn about the human visual system, the mathematics of multidimensional data, and the coding techniques behind certain graphics. On the other, there are many subjective design and aesthetic choices to be made. What questions do you ask of the data, and then how do you present them to the user? Success is cruelly defined by whether the target user can navigate and learn from what you produce, which is as definitive as any physical phenomenon but much harder to predict or explain.

Later in the afternoon I attended a colloquium by Mike Eisenberg (computer science and cognitive science, U Colorado). He spoke about education technology that does not involve traditional screens. He asked how we can design physical spaces and materials to be conducive to science and math education. My mind wandered upstairs to the electric engineering lab, where I had been the beneficiary of an obsessively-organized collection of resistors and capacitors in constructing a complex circuit for another final project. I then thought back to the machine shop where I built robots in heigh school, which was called “Chaos Central” for a reason. Tools did have their homes, mostly, but old robot parts hung from the ceiling and it was never truly clean. Much as I would like to fantasize about a large, organized workspace to host my own robot team years down the line, I realized that chaos is part of the equation, even (especially?) for engineering. Eisenberg read my mind, rather literally. He said that although math and science are rational disciplines, the paths into them are anything but. The apex of his talk used language quite similar to what I have previously used on this blog: if only we could find the perfect way to present material, the universal narrative, education would be a solved problem. But we can’t, because it’s idiosyncratic, subjective,  and personal. My head reeling, I wondered: how can we eliminate the stigma and misconception that the sciences are dull and austere? They are anything but.

Then, later that night, I attended a talk given by Daniel May, Director of J Street U. Try this one on for size: a Jew, speaking mostly to Jews, about the right of Palestinians to a state, because it was the right thing to do. (Liberalism defined). Some of the questions he fielded were from even further left. The conflict has been notoriously divisive, even by Tufts standards, so it was pretty jarring to hear reasoned and well-articulated criticism of Israel. The larger point was that this was not a utopian undertaking but rather meant to be merely a more perfect union, an improvement over the status quo.

I have nothing against those who take up advocacy of Cause X, but I realized tonight that it’s not my narrative. Zoom out enough and you get “righting wrongs”, a banner most college students will happy walk under. But zoom in just a bit on Tufts and you get “righting social wrongs,” and that’s not what I’m in to. I want to right intellectual wrongs. I want to change education, to end the stigma over science and math, and stop those who deny the ways in which we have made such tremendous progress. Homeopathy upsets me. The antivaccination movement infuriates me as much as any other activist trying to end the senseless deaths of children. And the fourth-grade “science” quiz that’s been circulating the internet makes me livid.

The secret to life is education. It’s really that simple. Yet I feel that my chosen institution of education, for all that I love about it, has a subtle yet core value not quite aligned with mine. Change doesn’t begin in a foreign country with one of the most intractable conflicts of human history. Luckily, Tufts realizes that engineering and education don’t take place in a vacuum. I can’t treat people as robots or build robots without thinking of people (although many do). On the other hand, I do not want to fight against every injustice every committed. There just isn’t time or energy. The political causes I support have objective grounding: if you can’t get someone to accept a fact, how can you ask them to accept a person? Everyone at Tufts wants to save the world, but maybe the engineers will actually make some headway.

A week without social media

The Jewish holiday of Passover requires adherents to not consume or possess any leaven during its eight days. Leaven symbolically represents excess, to be puffed up and arrogant. As I became increasingly aware of the time I was wasting on social media, I hit upon the mechanism that sites like these use to identify you: cookies. Which are leaven, right? So I decided to spend Passover without Facebook or Twitter.

It started small: I would stare at my phone where the apps had been idly looking to kill a few moments. Instead of needing to be on top of my newsfeeds, I found myself putting my phone away more readily and engaging in what I was doing. I began to notice details in the objects and buildings around me, but human contact proved elusive. Without sifting through other people’s half-baked ideas on an hourly basis, I felt like I had a tremendous amount of free time on my hands. The time I would have spent clicking “refresh” became time I spent walking around campus lost in thought. Unplugging led to a good deal of, not necessarily loneliness, but solitude.

Sometimes details matter, and a focus on trends leads to dangerous generalizations. The problem with social media is that it’s all details, with no underlying story or pattern to cling to. Our brains are taxed by trying to glue these shards together, but no two come from the same whole. Occasionally we manage to create a passable mosaic.

After all this introspection, I came to be more at peace with my religion. There are things that we know to be true, like evolution, and we should promote them. And there are things we know to be patently false, like homeopathy, and we should decry them. But a lot of things fall in the middle, not least of which is the human condition. The most visible parts of religion espouse certainty, but the Passover seder is really about uncertainty. It invites questioning and varying interpretations. Judaism embraces ambiguity and even contradiction. (Especially contradiction.) This is a welcome break from a world of pithy opinions crammed into 140 characters and relationships pigeonholed into a dropdown menu. It’s complicated, indeed.

Is slavery a presence or an absence? On one hand, I still feel that social media distracts us as a society from what really matters. It fragments our thought processes, and our relationships, by prizing efficiency over effort. On the other hand, technology connects and empowers us; without it we regress. Is social media a way to break down the interpersonal walls on campus, or a cause of their existence? Does the spread of information strengthen the spread of knowledge, or short-circuit it?

I have always felt that long-form writing helps me put together my thoughts on factual issues. In writing this piece, I realized that the same is true in the personal realm. True connection means giving people the freedom to think independently and then express themselves to others. Slavery is to uncritically compress and post whatever comes to mind.

Sherlock Holmes and Hard Problems

“With a few simple lines of computer code,” boasts Moriarty in BBC Sherlock, “I can crack any bank, open any door”. (Paraphrased from memory, shh.) Without any spoilers, I can tell you that Sherlock’s nemesis is portrayed as controlling every detail, forseeing every possibility, and manipulating a web of individuals through blackmail, bribery, snipers, and sowing distrust. And, he makes vague claims of having the ultimate computer hack, stronger than any security system.

What kind of software would this be? Most of computer security relies on mathematics that is computationally hard. Consider a traditional padlock. If you know the combination, it takes almost no time to open the lock. If you don’t know the combination, you have to try every possible code. The combination is easy to check, but difficult to discover.

A completely general computer hack of the sorts Moriarty claims to have would be like being able to open a padlock without the combination as fast as you could with the combination. Sherlock operates in much the same way. Anyone can verify his string of deductions after he’s made them; his genius is to devise them in the first place.

So that’s what separates fact from fiction. These portrayals of genius are unrealistic because they take the same amount of time to produce a solution as it takes to verify one. Right?

Not quite. “Can any answer than can be checked quickly also be created quickly?” is one of the great unsolved problems of computer science. We don’t know.

The Diamond Age: An Edtech Reading

I recently reread Neal Stephenson’s The Diamond Age. It’s a work of science fiction that depicts a future infused with nanotechnology, set in Shanghai and the surrounding areas. It offers some great material for a discussion on the role of technology in education and the limits of computers. Its themes are also relevant to edtech, which is pretty impressive for something published in 1995.

As a quick summary, Lord Finkle-McGraw asks engineer John Hackworth to create a computerized book (the Primer) to supplement his granddaughter Elizabeth’s schooling. Hackworth attempts to create a second copy for his own daughter illicitly, but is mugged and the book falls into the hands of the young street urchin Nell. The Primer guides Nell through leaving her abusive domestic situation and educates her using a customized fantasy story. Though the Primer is capable of reacting to voice commands and displaying a wealth of information, its narration is performed by a human actress Miranda whom Nell does not know. Hackworth, charged with intellectual property theft, makes a plea bargain to provide the source code of the Primer so copies may be distributed to tens of thousands of young abandoned Chinese girls. In the process of modifying the Primer to use a computerized voice, Hackworth is finally able to secure a copy for his daughter Fiona, before disappearing to serve his ten-year sentence.

That’s the first act. To do a proper analysis, I’m going to have to drop a few more spoilers from the most memorable parts of the book, so be warned.

Continue reading

Programming our Children

A generation ago, computers only understood text. You would program the computer in English text. You would ask your questions on punchcards encoding text. Your answer would be provided as monospaced, unadorned text. Since the early 1980s we have refined the graphical user interface, or GUI, to allow humans to communicate with computers on more familiar terms. Although a boon for the layperson, GUIs have been troublesome for computer scientists. They are hard to build because they are so open-ended. They are hard to test, because rather than printing a single correct answer there are many paths the user may take to accomplish the same goal.

Computer science still starts with a text editor and a compiler, because programming is better served by text. Text affords programmers absolute control over their programs. Written language is far more expressive than pointing and clicking, allowing for a explicit and precise descriptions. Clean code is a clear explanation of an algorithm directed to a mindless worker. The struggle of a programmer is to achieve sufficient clarity for both the computer and him- or herself. It can be a very enlightening experience, to debug an algorithm and then discover it doesn’t quite do what you wanted it to do, and so adapt it further. That said, the sheer austerity of the task can make it daunting without the right training and motivation on the part of the programmer.

GUIs are quite the opposite. They show many available options, reward experimentation, and make complex actions easy by hiding detail.  GUIs make computing accessible to a wide audience. A user interacts with a GUI as a peer, clicking and dragging and seeing how the interface reacts. Ultimately, convinced the GUI is logical and predictable, they embrace it as a new way of thinking. But GUIs are limited. They make it very difficult to perform analogous actions repeatedly or store a sequence of actions for later use.

There is an analogy to be made with education. Programming is like direct instruction, where knowledge is relayed linguistically and authoritatively. (No wonder Bill Gates and Salman Khan like it.) GUIs are like constructionism, where feedback loops reveal non-arbitrary behavior of a system that the user/student slowly begins to internalize. (So I constructed my own definition. How meta.)

Both methods of interacting with a computer are valid and potentially productive, so it seems both educational philosophies are valid as well. But there is a critical flaw in the analogy. For GUIs, students are analogous to the user and the computer is akin to some representation of the material itself: manipulatives, an experiment, a video, a graph or plot. But for text-based programming, the student is not the programmer; they’re the computer! The teacher is the programmer, the direct instructor, who crafts clear explanations of algorithms for the students to mechanically follow.

Direct instruction is degrading. It robs them of their ability, desire, right to explore and create. Knowledge transfer is not like copying a file, where we wait as it is methodically duplicated. Knowledge is personal, with idiosyncrasies and unique contexts. To insist on teaching children the same way we program a computer is simply wrong. It cuts to the core of what Dethorning STEM is about: our society treats people like computers and computers like people.

On a positive note, this analysis suggests that we should introduce computational thinking as another way for students to interact with the material in a constructionist setting. Having students write their own psuedocode for long division may be a viable way to teach it, if  it needs to be taught at all. Computational literacy will play an increasing role in the next century as computers become more ingrained in out lives. In the future, following an algorithm won’t be good enough — you’ll have to be able to write one.

Unfortunately, the state of computer science education is in shambles. Basic computer classes often teach how to use Microsoft Office by following rote algorithms — truly the blind leading the blind. Computer science itself takes a back seat to all other subjects, and is only sometimes offered as an elective. But I think that computational literacy does not require a computer scientist, a computer lab, or even a computer. It’s not content; it’s a technique. By cleverly inserting the right activities into the existing curriculum, teachers can cover computational thinking alongside any subject. Training teachers how to do that, and getting the administrators to sign on, will prove difficult.

A new, innovate approach is needed. One that breaks from the ossified red tape and small scale of the classroom and equally from the poor pedagogy underlying of most edtech products. The next generation of children deserve no less.

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