Euler Angles And Gimbol Lock

perm url with updates: http://xahlee.org/math/gimbol_lock.html

Euler Angles And Gimbol Lock

Am reading Second Life's doc about rotation (at Source). One interesting thing it mentioned is this:

The main advantage of using quaternions is that they are not susceptible to gimbal lock.

That is interesting. Look at Wikipedia about gimbol lock: Gimbal Lock.

The essence is that, simple gimbols system cannot track motion continuously in some situations. For example, suppose you have a telescope. The base can rotate around freely, and the scope can rotate up and down. If you track some flying object that flew from eastern horizon to directly above your head (noon sun), and then suppose it made a sudden change of direction towards north, then your telescope will have problem to follow it. You'll have to twist the base 90° first before you can move the scope down.

The continuous tracking is important in many applications. Suppose your telescope is a gun turret, and the flying object is a ufo you want to shoot down. Or, suppose you are creating a projection system for Planetarium. You want to be able to project a point in the dome with continuous path, even if its path has sharp turns.

One solution is to provide a extra gimbol. For example, suppose our telescope again. It's base can turn around z-axes. The scope can turn aronud y-axes. But suppose we also make it so that the whole thing can turn around x-axes.

The gimbol lock problem also happens with 3D systems that uses gimbols of 3 axes (e.g. gyroscope).

analogously, this problem occur in abstract math, when you present rotation by 3 angles around x, y, z axes too (e.g. euler angles). If a point you want to trace makes a sharp turn at certain positions, the change in euler angles that track it cannot be continuous.

interestingly, Quaternions solves this, among other advantage and disadvantages.

This is quite interesting. I'm familiar with the gimbol lock problem but never knew there's a name to it. But most importantly, it never occured to me that this mechanical problem has a mathematical abstract meaning, as exhibited in using euler angle to track a point with continuous change requirement. It is interesting to note that quaternions solves this.

fraud in physics; academic review system

Discovered: Jan Hendrik Schoen, “biggest fraud in physics in the last 50 years”.

I discovered this from this blog Three myths about scientific peer review (2009-01-08) by Michael Nielsen Source. Michael Nielsen turns out to be a known writer who was a academic in physics.

Some of the more interesting articles i found in his blog are: Quantum computing for everyone Source, Why the world needs quantum mechanics Source

See also Wikipedia Quantum computer etc.

Avatar movie review

perm url with updates: http://xahlee.org/Periodic_dosage_dir/skina/avatar.html

Avatar (film) Review

Xah Lee, 2010-01-07

Went to watch the movie Avatar (2009 film) in theater today.

Boo. On a scale of 1 to 10, i'd say this is no more than 7. This is totaly predicable, steoreotypical, intellectually shallow. The 3D effect isn't impressive at all, and about the only thing that is positive about this movie is the imaginative floura and fauna.

This movies garnered raving reviews, both by critics as well as being a highly successful money maker. But it's so disappointing to me that i have to think about where to begin.

3D Effect

Ok, lets begin at some easy criticisms, the 3D tech. I recall, back in late 1970s or early 1980s when i was about 10 or so, my mom's mom took me to see one of the first 3D film, in Taiwan, a kung fu film. I vividly recall that i literally dodged when the weapons swung towards me from the screen. Yeah, a lot people did that. That, is the effect of good 3D on you. But now, after 30 years, one'd suppose that the 3D tech has improved vastly, which it has. However, watching Avatar, i hardly get ANY 3D sense at all. In fact, i absouletly don't feel any 3D sense, perhaps a little, if i force my self to feel it, thru its 3D glasses.

What's wrong? I don't know. Perhaps the 3D tech is different. I don't remember which 3D films i've watched back 30 years ago, but am guessing that some 3D tech are designed to have a exaggerated perspectivity, and am guessing the 3D tech used in this movie is designed to be more mellow or wide angle. But over all, i say bah.


Ok, now i might disclose some of this movie's plot, and so here's your “spoiler” warning, but, the movie is so formula driven and stereotypical that it doesn't matter much.

The movie, in one sentence, is about Western powers with high tech wanting to take over gold from some primitive, indigenous people, for their riches in their land. Yeah, that's it. And, yes, there's one hero, who gradually realized that this isn't right, and fell in love with one of the beautiful chick from the indigenous people (right, the daughter of a chieftain!), and saved the tribe, with the help of the animals and nature.

The movies runs 2.5 hours. I didn't particular cry “move on already” at any point, but nor did the long movie had my attention wholly seized.

There's no characters. All are shallow. The bad guys, in this case, the corporation head and the head of marines, are just what they are. The corp head has eyes on the gold, and that's his concern. The marines head has bulky muscles, and is all about toughness. The hero, is just that, with good heart, and handsome to boot, courageous, always miraculously succeeds against all odds, and gets his girl. The heroin, in this case a alien race chick, is of course beautiful as much beauty we can put on a feline humanoid. And what's she like? Well, a beautiful woman, with concerns of loyalty of her man, love of her family, her people, a caring of nature. Actually had sex with the half-human half-alien hero. (inter-species porn anyone?)

Where is the Science in Sci-Fi?

What about the story line? Well, the human animals want this million-dollar land inhabited by primitive tribes. The human animals created what's called a “avatar”, which is a humanoid creature grown from bio-tubes that has mixed dna from humans and the native feline-like humanoid aliens. The avatar is connected and controlled by a sleeping human. When one is awake, the other goes to sleep. Thru the avatars, it is thought that they can persuade the feline humanoids to move out. But the diplomatic way of course didn't work out, and force is resorted to. The hero human/avatar fell in love with the feline-humanoid heroin and felt the sense of US-American Justice, and defended the primitive feline-humanoids with the help of miracle nature.

The Sci-Fi aspect of the avatar concept is all interesting. How does the avatar work? How's it grown? How long it takes? How's the technology to control or connect it? How's the biology of the feline-looking humanoid alien? What they eat? Well, this movie isn't concerned about these things, only that these settings qualify it as Sci-Fi flick.

Another interesting aspect of sci-fi is that the plants and animals on this alien place have some sort bio-wire grown from their body, that allows direct animal-to-animal communication or animal-to-tree. For example, the feline-humanoid can connect her bio-wire grown from her head, with the bio-wire on a 6-legged horse or a flying-saurus, similiar to how you connect 2 electric wires. Also, the plants form some kinda neural network by some bio-chemical means. (see Biocommunication (science)) Again, all this is used as plot-devices, you don't get to whiff them.

The Message?

You can't help but think about American Indians when watching this movie, which the US American Disney proudly showed you in Pocahontas (1995 film). A history of genocide shown as one big, happy tale.

What can we say about that? Is it just a coincidence that this movie made you think of American Indians? The alien race is named “Na'vi”. The tribe is called Omaticaya. They worship their tree deity. They mumble some prayer after killing in hunt, presumably to thank mother nature and bless the deceased prey. They tame wild alien beasts the likes of 6 legged horse and flying-saurus as a warrior's rite of passage. They do their face war-paints. They use bows and arrows...

I'm not sure how much of all these is connected to real American Indian, or pop beliefs in Primitive Culture. What is Primitive culture anyway? Wikipedia doesn't help much except saying it's controversial. One thing for sure, is that the movie isn't shy of perpetuating the primitive people concept.

So is there a message in this movie? Maybe i think too much. Maybe it is simply a visual treat of special effects and explosions. But you can't help thinking how shallow it is, how it reinforces a simplistic picture of Colonization and backwater savages trying to defend it. It would be a insult to anthropology educators.

Enjoyable Parts

I give this movie 6 out of 10. So, it's a bit above average. What i liked is watching the weird-looking, feline-like humanoid alien race. Of course, especially the female heroin. (Yeah, i'd totally do her.) The exotic flora and fauna, based on exotic rain forest things, are enjoyable to look at. The imagined bipedal mech, the vertical take off chopper, are all well done. The final battle, i wouldn't say spectacular, but still, enjoyable.


If you love sci-fi and is a movie-goer, yeah sure by all means to watch it. If you watch movies just 4 times a year, then i'm not sure.

Wikipedia says with references, that the director acknowledged and some critics thought this movie carry some anti-imperialism message. But i think, if anything, it is another black vs white, good vs evil, justice-driven, US-American brainlessness, that is likely to do more harm than good, as far as human animal's moral progress is concerned. Suppose, after watching this movie, viewer came out persuaded by the film and filled with the brainless zeal of JUSTICE. That IS American, and is where the problem is.