The WebGL Shader Language (GLSL) is a very powerful tool for multidimensional vector mathematics. 

Is there any possibility to use that power from JavaScript (running in web browser) for private non-3D calculations? Getting data in is possible, but is there any way to get data out to JavaScript after shader calculations are done?

No actual drawing is necessary, only calculating vectors.
(I am toying with an idea of hardware accelerated gravity simulator written in JavaScript.)

Thank You!

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In the news: Khronos seems to be developing [WebCL](https://www.khronos.org/webcl) which will be a JavaScript accessible version of [OpenCL](http://en.wikipedia.org/wiki/OpenCL). That is exactly what I am looking for, but it will take some time...