Interactive Exploration of a Dynamical System from Bret Victor on Vimeo.

I recently stumbled upon this amazing article on how an ex-Apple developer is using the iPad to create a better user interface for math.

Better than what?

Better than numbers and symbols and equations.

It’s quite an insight really — symbolic systems as a “user interface” — and it’s absolutely true.

I’ve been noodling on this one for quite some time now. I have always been “good at math” — good enough that I was always a step ahead of my teachers in high school when we were learning calculus or geometry, and I later majored in math in undergrad. However, I’ve always sucked at arithmetic. Give me a bill and it will take me several minutes and a pencil to calculate and add up the tip.

If you ask me why, I’ll tell you that my brain has a bad user interface when it comes to math.

I just don’t think about it the right way. I can add double digits intuitively, and then I have rely on a small set of memorized facts to get me the rest of the way… simple multiplication tables, adding zeros to multiply by 10… Armed with this limited tool box, I try to break down complicated problems into smaller ones and then recombine them. But the process is inefficient and requires a lot of working memory. I keep forgetting where I was and having to start over.

Math needs a better user interface. A visual one.

And we should teach it to kids early in school so that they get into the habit of using it.

Indeed, several people with exceptional arithmetic abilities report interpreting numbers as having visual qualities that might seem strange or foreign to ordinary people like me. A former colleague of mine was like that — he could multiply 3-digit numbers without difficulty. When I asked him how he did that, he said that numbers in his mind were organized in a huge visual grid and that he used it to solve complex calculations.

I wish I carried around a visual math grid in my head at all times.

Some people go even further. Check out the Wikipedia article on Daniel Tammet who has high-functioning autism, synesthesia, and savant-like math abilities:

"Tammet’s unusually vivid and complex synesthesia has been widely reported. In his mind, he says, each positive integer up to 10,000 has its own unique shape, colour, texture and feel. He can intuitively "see" results of calculations as synaesthetic landscapes without using conscious mental effort and can "sense" whether a number is prime or composite. He has described his visual image of 289 as particularly ugly, 333 as particularly attractive, and Pi as beautiful. The number 6 apparently has no distinct image yet what he describes as an almost small nothingness, opposite to the number 9 which he calls large and towering."

How fascinating is that?

Not all of us are gifted with natural synesthesia to supplement our math skills (most synesthetes aren’t either), but how amazing would it be if an outside tool or a piece of software like an iPad app could provide that synesthesia-like interface for us, turning numbers into something that we can instinctively understand and manipulate?

That is an innovation I would love to see happen, and a company I would be thrilled to work for.