[extropy-chat] NEF tensor (was Psychogenic Fields)

[Anders Sandberg]

The Avantguardian wrote:
> Sorry. This is why I wish I had more formal physics-
> math background than I do. I think you may be over
> complicating things. In this case by tensor field I
> mean simply a position specific "bundle of vectors"
> namely E(x,y,z) and B(x,y,z).

That is a vector field. A vector field consists of a vector at every point
in space.

Tensors are a bit more abstract, a bit like generalised matrices (a number
or a vector is a particular kind of simple tensor). The important thing
with these mathematical objects is that they change in predictable ways
when you change the coordinate systems, so that an equation written in
tensors (or vectors) remains true regardless of the coordinates (which are
after arbitrary conventions). Very practical.

> Correct. Now at any given instant in time, the
> elements of the above matrix will take on a unique set
> of specific numerical values at different points in
> space around the brain. Now if we could measure those
> specific values at each point for thousands of such
> points in parallel (e.g with a "helmet" consisting of
> thousands of miniture SQUIDs shielded from external
> magnetic sources ) and store them on a hard-drive,
> then we would have a high resolution map of my
> unfortunately named psychogenic field.

Think of it like this: each neuron is surrounded by a little NEF, and they
all sum together. But the high frequency components decay over distance.
The shape and information of the NEF from a single neuron gets blurred out
a few micrometers away, and similarly a group of neurons also blend
together if measured more than about their diameter or so. When measuring
from outside the skull, about a centimeter away from the brain, you will
only get information about activity patterns larger than one centimeter.
Which leaves out all the interesting stuff.

[Technically: the multipole fields decay as 1/r^3 or faster. And I'm
fairly certain a Dirichlet boundary condition isn't enough to specify the
source/sink distribution inside the skull. E.g.
http://www.ipp.mpg.de/de/for/bereiche/stellarator/Comp_sci/CompScience/csep/csep1.phy.ornl.gov/bf/node3.html
]

OK, if we could get all the field at a high resolution many researchers
and doctors would be very happy, since there is much medically useful data
here. Current EEG and MEG are still rather crude.

> I have no equations to offer you and I am not
> suggesting that non-trivial analytic solutions to the
> NEF tensor exist. Although as a trivial solution, I
> would expect for a dead person, the tensor matrix will
> be filled with zeros.

Or some somple electrical potential.


-- 
Anders Sandberg,
Oxford Uehiro Centre for Practical Ethics
Philosophy Faculty of Oxford University