Hideaki Akaiwa, real-life superhero
I've been to the town of Ishinomaki, once, on my way to visit the famous temple on the island of Kinkazan. It's a small, not particularly exciting town best known for being the birthplace of Ishinomori Shotaro, manga artist who drew Cyborg 009 and Kamen Rider. They've got a whole museum devoted to his works.
Ishinomaki has pretty much been turned into a lake by the tsunami. Eek.
This one guy, named Hideaki Akaiwa, escaped from the tsunami, but he couldn't contact his wife. So seeing his neighborhood consumed by the tsunami, he decided to grab a SCUBA suit and dive in, swim through the freezing, murky, black currents and riptides and the cars and jagged metal chunks getting tossed around, and find the apartment building where his wife was trapped on the top floor. He rescued her and somehow brought her back out to safety. He and his wife were both surfers, so I guess he had some relevant experience for this kind of thing.
And that's not all! Hideaki Akaiwa couldn't contact his mother either. So a couple days later he went in to the tsunami again, find where his mother was trapped, and rescue her too.
Now he goes back into the flooded city every day looking for more survivors.
This guy is a real-life superhero.
Article from the LA times. A somewhat more colorful retelling at "Badass of the Week".
Oh my god Bret Victor is SO SMART. He's one of the smartest humans I've ever met.
In 2006 he wrote Magic Ink, a paper that changed the way I thought about UI design forever.
We tried to get him to work for us at Humanized, and then later at Mozilla, but a guy like that can work anywhere he wants. He worked at Apple for a while but has recently gone freelance again.
You sad about the death of last generation's computer pioneers? Well, here's a guy in our generation who is going to be world-famous for doing something amazing. I'm not sure what it is, yet, but it might be this:
He doesn't really mean to kill math, of course. He means to kill the user interface of math.
Which is to say: you know that activity where you represent a problem by writing some squiggles on a piece of paper... and then you pick one of several arcane rules that you know, and apply the rule to the squiggles, to come up with a slightly different set of squiggles, and you write that set beneath the first set... and you keep doing this until you either somehow produce an answer or you give up?
Yeah, that activity is not math. That activity is math's user interface, and it's a terrible one.
Bret points out that in the Roman empire people thought multiplication was this incredibly arcane and difficult task that only a very few initiates would ever understand. But it turned out this wasn't because multiplication was conceptually difficult, it's just because Roman numerals totally suck for multiplying. Once people switched to Arabic numerals, multiplication became something we could teach to second graders.
So maybe the squiggles on paper are holding us back in the same way. I know that I was often frustrated by the arbitrariness of the notation when I was doing higher math in college. More than the notation, what was frustrating was what they didn't teach us.
For instance they walked us through lots of famous proofs, but they never taught us how mathematicians came up with those proofs, or how to invent one ourselves (other than for trivial and contrived textbook problems.) Sure there are a few well-known tricks like induction and contradiction, but mostly I remember a feeling of blind groping as I tried one random technique after another, never knowing whether I was getting closer or farther away. Same thing for doing integrals: there's no general method other than "try to think of a function that has a derivative similar to what you're looking at". So mostly integration is a matter of repeated guess-and-derive, or of applying rules at random looking for anything that works. A lot of higher math (and therefore physics) always had this flavor for me. Whatever real mathematicians and physicists were doing, it was apparent that most of the work was in the gap between one step of the derivation and the next, the gap where they had some mysterious flash of insight that told them what to do next. But since that flash of insight never made it onto the paper, none of the teachers ever talked about it.
(I think this is why so many people learn to hate math: in math you rise as far as your innate mathematical intuition can take you, then you get stuck because everything past that is a black art that nobody knows how to teach you.)
Bret doesn't have the answer yet about what a new user interface for math would look like, but he's asking some verrrrry interesting questions. His writings include some cool interactive visualizations, which you can play with to help yourself gain that oh-so-vital intuition about how systems behave.
A lot of people have apparently looked at these and said, "So this is to help people understand the equations?" but Bret is like "no, you're missing the point, this REPLACES the equations". A set of equations is an abstraction to describe the behavior of a system; an interactive drawing is also an abstraction to describe the behavior of a system, but it's a better one because you can poke it and it moves, and the human brain is evolved to be really good at figuring out what something is based on how it moves when we poke it. It's not evolved to manipulate squiggles on paper.
Moving from squiggle manipulation to interactive visualization forces us to reconsider what math is for. Is the goal always to "solve" something and get a number or equation which we call an "answer"? Or do we just fall into thinking that way because looking for an "answer" gives us a convenient stopping-point for the squiggle-manipulation method? With an interactive drawing, finding the point that makes some quantity equal some other quantity -- "solving" -- is a trivial matter of swiping around until something matches up the way you want. But there's so much more you can do beyond just "solving"; you can keep exploring, discovering new questions to ask; what happens if I do this? Oh did you see what happened when I cranked this input all the way up and the other one all the way down? Why was that?
Relatedly, does it matter if we can't solve the gravitational three-body problem in closed form, if we can have an arbitrarily accurate computer simulation based on iterative methods, that any child can play with and gain a delightful intuition of how a three-body gravitational system behaves?
If we could create a new UI for math, what would people do with it? Well, maybe it's nothing beyond a curiosity. Maybe people already know all the math they have any use for in daily life. How often do you say "if only I had a way to solve a differential equation right now?"
But maybe not. The Romans probably thought that the plebians would never have a use for multiplication. But it turns out that if you understand multiplication then you find uses for it every day. IBM famously didn't think anybody would have a use for a computer in their home, until Apple proved otherwise. When tools get cheaper and easier, people find whole new uses for them. They apply them not just to different problems but to different types of problems.
The basic concept of a system of differential equations isn't hard to grasp at all. "This jet is burning fuel to accelerate. But the faster it goes, the more air resistance it runs into, which slows it down. The amount it speeds up or slows down also depends on how much it weighs, which decreases as it burns fuel." Differential equations are a way of describing scenarios where several interrelated variables are changing over time and the value of one variable at any instant affects the rate of change of another variable. The concept is easy, but answering questions like "how much fuel does the jet have to burn to reach Mach 1" turns out to require some astoundingly difficult squiggle-manipulation.
But situations with variable, interdependent rates of change are everywhere. If you were really good at differential equations -- or whatever the post-Kill-Math replacement is for them -- you might find reasons to use them every day. You would instinctively see them under the surface of the physical, ecological, and economic systems you interact with every day. You'd feed them (somehow) into your interactive visualizer, or whatever it is, and play with the simulation until you understood how to subtly prod the real system to elicit the results you want.
You would, in short, have what would seem like superhuman intelligence to the people of today. You'd do things we could barely dream of.
Imagine if we could use computers to make that level of understanding accessible to people of merely average brainpower.
Man. That's the kind of thing Silicon Valley should be working on. Not "how do we get users to report everything they do to us through their cell phones so we can sell behaviorally targeted advertising".