High Dynamic Range

I’m impressed with the new “high dynamic range” (HDR) photography feature in iOS 4.1 for iPhone 4. The feature basically takes three versions of the image in quick succession, each using a different light setting. Software then combines the three photos using image processing algorithms. The goal is to avoid washed-out bright areas and dark, almost-black shadowed areas.

I took the picture below with HDR turned on. I did not use a tripod, did not set anything manually, and did no post-processing other than cropping. (Click it to see full resolution.)

Seattle skyline using iPhone with HDR

The plain, non-HDR version of the image looked pretty good too, but everything was more washed out, especially the buildings and sky. The trees were a bit brighter but didn’t look as rich. I think the HDR version looks astonishingly professional.

Math in Ancient India

I just checked my web server statistics and found that part of my high school research paper on the history of mathematics is getting well over a thousand requests a month.

The topic of that paper is “the usually unrecognized achievements of Vedic and Hindu mathematicians from 2000-300 B.C.” When writing it, I was surprised at how hard it was to find good research on the topic:

In Mathematical Thought from Ancient to Modern Times, [a “comprehensive” summary of] the history of mathematics, [author Morris Kline] included only half a chapter (out of 50 chapters total) on Indian math. Everything he said seemed to sneer at them, put them down, and belittle their accomplishments.

Despite this dearth of understanding, the facts were clear:

Besides using simple arithmetic operations like addition, subtraction, etc., Indians invented the decimal system and the idea of positional notation, both of which are still in use today. They also used the “Pythagorean” theorem and “Pascal’s” triangle long before either of those men were born!

Today, it turns out that if you google “Sulva Sutras” (the title of the web page getting most of the visits), my research paper is the first result, above Wikipedia and everything else! If you search for “mathematics in vedas”, I’m the third result.

True, this seeming popularity may have something to do with spelling inconsistencies — the Wikipedia article uses “Shulba Sutras” and is the first result if you search with that spelling. It’s also true that my paper was written in 1999 and has been on the web since 2003, so has had time to gather links from other websites (which influence Google’s ranking).

But we’re talking about the founding documents of mathematics! The origin of zero! The “Pythagorean” theorem, recorded hundreds of years before Pythagoras! And the most relevant article was written by a fifteen-year-old?

In my research paper’s conclusion (which is mostly too embarrassing to quote), I wrote, “I find it unbelievable how little work has been done in the field…. The vast majority of the work has been done only by Indians. Most of the books on the subject are written in Sanskrit or Hindi [and are ignored by] eurocentric scholars.”

Ten years later, my incredulity lives on.

Steve Jobs’ fifth revolution

I think one of the most significant announcements at Apple’s media event today was that the iPod touch now has over 50% market share in the worldwide portable gaming industry — the iPod touch outsells the portable game consoles from Nintendo, Sony, and all other manufacturers, combined. Steve Jobs also said over 1.5 billion games have been downloaded so far to iPod touches alone. “It has become by far the most popular game player in the world.”

Steve Jobs discusses the iPod touch as a gaming platform

It’s widely recognized that Jobs has already revolutionized four industries: personal computers (Mac), digital music (iPod and iTunes), animated films (Pixar), and smartphones (iPhone). I think it’s now safe to add a fifth to that list: portable gaming.

His impact is a revolution both in terms of the new multi-touch user interface for gaming and the App Store platform for game distribution and payment. The major products involved are not just the iPod touch but also the iPhone and iPad.

So what will be number six?

Apple is making some progress on movies and TV shows. However, the studios and cable companies have all the power, and they are terrified about what happened to the music industry. It’s hard to find a path that transitions the industry from cable TV “channels” to browsing and paying for individual shows.

Another possibility for revolution is in textbooks and online education, where iTunes already carries recorded lectures and the iPad has started to inspire a new class of interactive educational content.

7″ iPad

I continue to see rumors that Apple will release a 7-inch iPad. The idea is that it would be closer in size to a paperback or Kindle; lighter and less expensive than the current iPad; and easier to fit in a purse.

I’m a bit scared of this vision because it means all of our apps would have to be redesigned for yet another screen size. iPhone apps already do run on the iPad, but they are awkward to use. Scaled-down iPad apps are not really an option because the touch targets would be too small. Apple could use a screen with the same number of pixels as the iPhone 4 (but bigger in size); that way, all retina-display-compatible apps would fit pixel-by-pixel on the device. Still, graphics would look too big and some interactions would still be awkward. In short, redesigning our apps would be necessary for a good user experience.

This redesign will be a lot easier than porting apps from the Mac to the iPad. Still, for the sake of my own sanity, I hope Apple waits a while before introducing the next screen size.


Update: On the other hand, most of our existing Mac apps have to be designed to work well at any screen resolution between the 13″ MacBook and the 30″ Cinema Display. From this point of view, having to support just two discrete iPad sizes should be comparatively easy.


Update 2: Steve Jobs just criticized the 7-inch form factor.


Conversation

“Conversation… is one of the most important ways of establishing equality.”

-Theodore Zeldin

Humanizing math

I used to think that math was the perfect subject to teach via computer software (instead of lectures). My rationale was that computers are already good at math; and software-driven customization for each student is most useful for topics that require a solid knowledge of previous topics (e.g. algebra builds on multiplication and fractions).

This TED talk by Dan Meyer challenges those assumptions. He suggests that good math education starts with good discussions. It uses open-ended questions whose answers may be as unpredictable as responses to works of literature. It emphasizes how math relates to intuition and the real world, and deemphasizes arithmetic and equation solving. In other words, it humanizes math, a notion which makes a lot of sense in a world where computers not only compute sums but can easily solve, graph, and symbolically manipulate indefinite integrals. (On a cell phone. For free.)

Indeed, a lot (most?) of cutting-edge science today involves calculations so complicated that it would never even occur to the scientists to complete the math by hand.

So why bother teaching students in detail how to do the things that computers will always be better at? Meyer’s approach focuses on the human side — understanding when and why to apply mathematical tools. It’s not immediately clear how computers themselves will figure into this educational mission.

Instinct

“Instinct… is largely memory in disguise. It works quite well when it is trained, and poorly otherwise.”

-Robert Bringhurst (The Elements of Typographic Style)