Co.Design
ExApple Designer Creates Teaching UI That "Kills Math" Using Data Viz
We hear a lot of design manifestos around here. But Bret Victor's stuck out: He wants to kill math. He's no Luddite, though  he thinks mathematics is one of the most powerful, transcendent ways humans have for understanding and changing the world. What he wants to kill is math's interface: opaque, abstract, unfamiliar, hard. "The power to understand and predict the quantities of the world should not be restricted to those with a freakish knack for manipulating abstract symbols," he writes. Now he's created a prototype iPad interface that turns differential equations into something that doesn't feel mathey at all: visual, intuitive, and touchable.
Equations and squiggly symbols aren't math at all: They're merely our interface.
Victor's key insight is that what we think of as "math"  equations, numerals, operators, variables, those squiggly symbols filling up millions of blackboards and textbooks  isn't math at all: it's merely the interface. And it sucks. "I hate symbolic abstraction, [because] I think it's a barrier to creativity," he tells Co.Design. "So I don't hate math per se; I hate its current representations. Have you ever tried multiplying roman numerals? It's incredibly, ridiculously difficult. That's why, before the 14th century, everyone thought that multiplication was an incredibly difficult concept, and only for the mathematical elite. Then arabic numerals came along, with their nice place values, and we discovered that even sevenyearolds can handle multiplication just fine. There was nothing difficult about the concept of multiplication  the problem was that numbers, at the time, had a bad user interface."
It may not surprise you, after reading that, to hear that Victor used to be an interface designer at Apple  a company whose founding mission could be restated as "kill computers." Of course Jobs and Co. didn't hate computers  they just hated the technical, limiting abstractions involved in using them. But Victor left Apple because he has "zero interest in helping people look through photos and listen to music," he says. As an interface designer, he wanted to hunt (and "kill") bigger game  the kinds of problems that artists and scientists deal with. "I saw Ali Mazalek's 'Pathways' project, which was an attempt to design a 'tangible interface' for visualizing and exploring biochemical pathways," he says, "Their design was very problematic, and the biology researcher 'clients' were not very enthusiastic about it. But seeing the problem gave me some ideas, and I whipped up a little prototype basically as a way of teaching them how to think about this sort of UI design."
That prototype eventually grew into the interface shown in the video clip at the top of this article. Although it can run on an iPad, Victor isn't planning on releasing "anything resembling the design shown" as an app. "The prototype was intended to teach and inspire tool designers, so that's the metaaudience." It's a variation on the old saw: give a man a fish, and he eats for a day, but teach him to fish, and he eats for a lifetime. If Victor is going to "kill math," a single specific app won't do it  but a set of inspiring examples just might, if they inspire others to think about how they can "kill math" themselves.
Victor left Apple because he has "zero interest in helping people listen to music."
"The dirty little secret is that the greatest mathematicians don't actually think in symbols," Victor explains. Einstein himself said that he "did his thing" with "sensations of a kinesthetic or muscular type." Sure, e=mc² is an equation  a gloriously elegant and simple one. But the point is that the equation isn't the math; it's not the insight, the creativity, that actually happened inside Einstein's head. What if Einstein didn't have to resort to symbolmanipulation to express and communicate the idea that "matter is equivalent to energy in this exact way"? What if the next Einstein doesn't have to do that? If fact, what if "not having to do that" is how we get the next Einstein?
That's the headshot Victor wants to take in his "kill math" project. "When a technology gains an interface that transforms it from a 'technical' subject to an artistic medium, that's when creative magic happens," he says. "The pocket calculator and the spreadsheet both made huge contributions in allowing people to do mathematical explorations without dealing with the crap. I'm hoping to take the next step."
[Read more about Kill Math and Bret Victor's design explorations]
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His overall message is "VISUALIZE DATA". It how our brains work. Our brain just work better when things are represented in a visually stimulating approach rather then just oldage pen and paper. When your taking notes next time, just do a little doodle that represents what your trying to remember. I can assure you that you will retain the information alot better then just writing out notes line after line.

I will wait impatiently to see what comes out of this new interface. But why in the world would this "kill math"? By the author's own prose, math isn't about the symbols at all. He is right in this point. Finding a new way to explore and expose the mathematics is simply finding a new way to "do the math".
Why not just say that? No one "kills" math. It actually hurts the article to try to be so creative as to be deceptive.
Other then that, sounds fun.
Richard Brown  Mathematics Department, Johns Hopkins University

He's using the term in the way that people understand it. To nearly everybody  practitioners and researchers included  math is the symbols and operations etc.
Maybe he should phrase it Kill "Math". At any rate, it's not a big deal to the point of hurting the article. It also serves the point of drawing (unnecessary) controversy which the media is more likely to pick up and then expose this better way of approaching quantitative subjects for the masses in most fields who do not need to learn the rigour of mathematical methods and abstractions to do their jobs.

Graphical solutions of course are actually quite old school; I have fond
memories of one math professor who, on one of his test questions,
presented the option to the student to solve the problem either via
traditional equation proof or graphically. The equation proof was quite
laborious, the graphical proof was 4 measured lines with a ruler,
massively easier, and functionally as accurate. Yet all students solved
the problem via linear equation based proofs, out of habit, or even
worse, fear of disappointing the perceived "established way".That said, modern technology allows for great flexibility of
mathematical perception, especially over time and mixed inputs, as
demonstrated here. I deeply agree that such enhanced abilities to
literally "play" with equations and their outputs can greatly enhance
learning and the desire to learn.Another challenge: Chemical electron orbital clouds. Chemistry students
all memorize the accurate yet arcane and tedious atomic orbital energies
via the model based on "1s, 2s, 2p, 3s, 3p, ...." etc. but I always
hated the abstraction and desperately wanted to understand the shapes
and phase changes and attain an intuitive sense of the differences.
Completely nonexistent in textbooks of the 80s, and I fear even now.
Imagine a virtual environment, say with pressure resistant gloves, where
students could "feel" electron cloud shapes, simulate higher energies
by applying pressure and receiving snaps back and seeing correlating
photon emissions... much more appropriate understanding of nature than
rote linear patterns of "1/s 2s, 2p. etc". A student could snap together
elements to form molecules and see the cloud shapes change, and have a
physically based intuitive sense of the energies involved... much deeper
understanding of nature to be found if that could ever be achieved.Also, expect resistance from some circles. I've found that those who
have mastered a schema representing a specific natural phenomenon can be
instinctively hostile and dismissive to a new different schema,
regardless how accurate the newly arrived schema is, and despite the
fact that the newly arrived schema only represents enhanced
understanding of the target phenomenon. It's sadly a reliable human
phenomenon itself. :( 
I really appreciate the visualization and easytouse interfacing. It's always painful to sit through a lecture where slides are covered in equations with only a brief mention to the physical interpretation.
While Einstein may have thought physically rather than in terms of symbols, his equations have been powerful tools for other physicists & mathematicians who may not have gotten to the same point just going on physical and visual observations. The beauty of equation manipulation is that concepts in one system can be translated to other systems with relative ease.I would really like to see the above software combine mathematical equations with its current interactive visualization capabilities (e.g.  put equations next to the population graphs; highlight coefficients in the equations as you adjust the value sliders; etc). There is a strong case for using this kind of a tool to teach children how to connect physical reality to the nittygritty equations. Being able to look at an equation and visualize what it means is an immensely valuable tool in science & engineering (and beyond: finances...). We should be careful not to sacrifice the value of mathematical symbols and equations in an effort to make math easier. Instead we should look to synergistically combine equational math with visual mathematics. ...You might even call the new field physics :)...

Pretty telling that the example given was a physicist, not a mathematician. Of course, Einstein's theory of the universe was actually inspired by the pure math done by Gauss, Riemann, etc  not the other way around. I'm pretty sure that neither this guy, nor anybody else, is going to come up with software that makes curvature any easier to understand. On the other hand I would love to see an app like this for the field equations.

He gave that one example because it's just that  an example. It was not an exhaustive list. Mathematicians like Grothendieck and Perelman also think this way before manipulating the symbols. If symbol manipulation was all it took to come up with EGA and SGA, then talented mathematicians would not still be struggling to understand the content.
Grothendieck was known to ask himself novel questions (that is, not from instruction) even at a young age:
"Already then, Alexander asked himself a question that showed the uniqueness of his mind: How to accurately measure the length of a curve, area of a surface, or volume of a sold?"
He would later, in college, rediscover alreadyknown methods for solving just such problems, but I think the point to be made here and Bret made in his video "Inventing on Principle" is that creative people (scientists or artists) often have to push their ideas to the back of their minds until such a time as a tool is developed that will enable them to achieve their goals or just give up entirely. In this case, Grothendieck was able, as Feynman was, to develop his own tools and other people have been able to use them to expand the field.
Redesigning math will not solve all the difficulty that exists in math any more than all the tools created thus far have reduced the problems or problem areas in mathematics  on the contrary the problems are more numerous and more intractable. But it would shift the difficulty from the more mechanical and repetitive tasks (a la automation in industries) to more thinking and experimentation and quick prototyping of ideas by any analytical person who otherwise has great ideas but gets scared by greek symbols. More people would be able to take part and expand math into even more disciplines.
The bright side is that more people can now apply their economic ideas and supplant mysterious economic assumptions  such as "utils" and quantification of subjective value  with more realistic models and do so with math that they can "see".

This is available already and for free on the iPad. Just check out http://itunes.apple.com/us/app...

I fail to understand what make this app so innovative over (the dozens of) tools like this:
http://www.awbc.com/ide/idefi...
Interactive! Runs in the browser! Boy, that was already 10 years ago ... :)

It's not an app meant for use; it's a demo app to help explain an idea. The idea is far from realisation as you've noted ("that was already 10 years ago").

Check out the Profiler feature of JMP software. Basically, you can turn a series of related equations into sliders to do precisely what he's talking about. Visualizations like this go a long way toward making math intuitive, rather than confusing.

Very thought provoking. Wonder what would it be like applied to another arcane symbol language: musical notes. The missing link between music and math...

Too cool for words. I'm a big fan...

"By 1944, Einstein had recruited a new assistant at Princeton. His assistants were always talented young mathematicians who could make up for Einstein's selfconfessed weakness in this area."from The Book of Universes, by John D. Barrow, 2011, p. 104

When Bret Victor speaks of "killing math", I don't think he means to eliminate the symbolic systems that we use in doing math. The dynamic visualization of what differential equations are about goes a long way toward building mathematical intuition. Even if we can do differential equations, the visualizations may show us things not yet seen about this area of math.
Ceci n'est pas une pipe.

Awesome article! I currently teach math to high school students that are having a difficult time with passing the state mandated test and I am always trying to show them a new way to look at the concepts to help them understand them. I am definitely going to look into more of Victor's stuff!

I taught math and even how to teach math. I also did research to understand why some people had no problem with learning math while others couldn't deal with the subject. My research showed that people who have good models in their head to understand the topic did well. Strugglers had no models to picture the concepts. Why not use an IPad etc. to help with models and visualization?

Very interesting! I never liked Math (or at least I found I didn't speak the interface's language), now I'm curious!

This is brilliant. I never liked math, but always appreciated its value, especially when applied to things I take more interest in, such as physics and sacred geometry. If your work could be adopted in classrooms, it might make disinterested students (like my former self), more interested. This article also reminded me of the work done by Dan Meyer (http://blog.ted.com/2010/05/13...

I think it's important to maintain a distinction between the syntax needed to actively do math, and that needed to passively visualize it. Of course these types of visualizations are great, but people aren't going to be solving differential equations on their iPads anytime soon...
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