I hate the stylus. When I'm using it, I feel I need to "work" with it. The finger is natural and playful. Humans have been using their fingers to paint and draw long before they used brushes or pens.
A stylus is a powerful tool. To require it is folly. You have to create a platform that either ecompasses both inputs or chooses one. Simplicity would dictate the latter, and the finger is just more human.
There are a few apps I use that benefit from styluses, such as Penultimate (and probably Paper, if I could get over their obscene pricing scheme) but the capacitive stylus I have is really lame and I hate using my finger as a pen.
Active styluses pick up and refocus radiation from the screen, powered in a similar way to RFID chips. Maybe instead of providing input through the touchscreen, the stylus could have a tiny digital camera on its tip, detecting which pixel the stylus is on, and sending that info to the phone through Bluetooth or another means?
Perhaps the algorithms that handle touchscreen input are not properly calibrated to styluses, and an app or driver could make them operate more accurately?
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The best stylus experience I've used has been a Wacom dual active/passive screen on an HP tablet/laptop convertible. I had a nearly identical laptop with a passive-only touchscreen, adding the active touchscreen made all of the difference. On Windows 7 in Word, taking notes in economics and college math courses worked pretty well - I could type and take notes, then draw equations and graphs directly with the ink and review tools in Word. The use case was so valuable to me that I'm surprised nobody else did this, and other Office suites don't seem to offer anything even remotely similar.
edit: here's a video with someone using the pen from an HP/Wacom "pen-abled" touchsmart tm2 convertable tablet computer with the Galaxy Note:
Even the pencil tip eraser works.
The stylus looks exactly like the stylus from the HP tx2500 I owned. I don't actually know how large Wacom's technology is nor how much power it draws - I assumed phone manufacturers weren't including the best touchscreen technology for a good reason.
If Samsung's pixelsense technology (CCD built into the LCD) takes off, then you could just have the stylus be a passive IR emitter and the thing would work with a point of any size.
Perhaps the problem comes from the phone functionality. It really is unacceptable having to find a pen to be able to answer the phone. Other than that, people have been carrying around pencils for centuries without too much of a problem.
http://adonit.net/product/jot-pro/
It's fantastic with any iPad notebook app with wrist rejection. (Only downside: write in cursive otherwise it clacks.)