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.