[extropy-chat] sjbrain calcs with figures

[Spike]

Please open the enclosure.

It is said a picture is worth a thousand words, and 
in my case more than that, having scored a few dB down
on the old verbal SATs, but having more than made it
up on the math section.

I made some Matlab 3D plots, but then realized most
extropians do not have Matlab at home.  Most do
have microsloth Excel however.  Of course excel sucks 
at 3D graphing, so I set up some 2D views.

Hit the tab "1".  Those two graphs show 36 nodes of one
ring of an MBrain, a top view and a side view, if you
want to think of it that way.  Imagine the points as
nodes in a circular orbit around a star.

Now hit tab "2".  This is the same ring rotated thru
an angle of 45 degrees.  Change the value theta1 to
some other values and see what happens to the ring.

OK hit tab "3" and witness two nested rings of radius
5 and 4.  Change the values of theta1 and theta2.  The
angles can be anything and the radii can be anything so
long as they are not equal to each other.  Imagine the
rings as particles in a circular orbit.  The smaller ring
orbits faster but it doesn't matter: there are no collisions
because the two rings do not intersect.  Change the values
of theta1 and theta2.

Now hit tab "4" and see 5 rings, all different angles and
different radii.  Is it clear that there are no intersecting
orbits?  Is it equally clear that there are no possible
collisions between particles in different orbits, so long
as the radii differ?  Change the angles and radii and see
that you could have a trillion nodes per ring and few billion 
rings, with the relative angle between adjacent rings a 
microradian, thus forming a sphere, all with no intersecting 
orbits, no colliding nodes and no gravitational instability.

This is a traditional Bradburian MBrain.

OK now as a thought experiment, think of this MBrain being
formed around a rocky planet instead of a star.  Continue
removing material from the planet and adding it to the rings
until there is no planet left, all of it being in the rings,
and there you have it: an SBrain.  If Jupiter were rocky and 
metally instead of gas, and this process were used to form a 
sphere a minute in diameter, then from the point of view of 
earth, it would look like a full moon, only more than twice the
apparent size of luna.

Merrrrry Newtonmas everyone!  See you in a week.  spike
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