Bill DeRouchey (@billder) was the opening presentation at CyborgCamp and was wonderfully entertaining and informative. Here are some quick notes I took:
- How did the "Play/Pause" button become univerally understood?
- Typewriters choose the winning "letter symbols"
- Symbols evolve.
- Are we losing some types/modes of literacy? Is that such a bad thing?
- @ - commerce symbol "each at", then location, then identity
- # - means a group on twitter "context, topic"
- Mouse pointer ~1984
- Future directions in the evolution of tech languages?
- Splintered groups of tech languages
- Emotional bandwidth
- Gatekeepers of knowledge, screening out less knowledgeable people
is used to measure distances based on a given coordinate system. In terms of the 
where 
is the transpose of the 
is a symmetric matrix for any matrix 
, the metric tensor is always symmetric. (In fancy-pants math lingo this is called a 
to 
is always the same as the distance from 
where 
is a parameter with respect to some coordinate system, then we can write an infintesmal displacement element as 
. The length of this displacement is
and the length of the curve from 
to 
is 
.
where the 
's are a new coordinate system defined in terms of the original coordinate system, the 
's. (Note that we are using subscripts, 
denotes the second element of the 
vector.) The determinant of this matrix ![J=det([J_{mn}])](http://leto.net/x/latex/d0fe757a8cf7ff95400c7c2ffd69af93.png "J=det([J_{mn}])")
is important because this represents the constant of proportionality between volumes in the old coordinates and in the new coordinates. As a simple example polar coordinates is the transformation 
. When we want to perform an integration in cartesian coordinates by transforming into polar coordinates, we write 
, the factor of 
is precisely the Jacobian. So in general, to convert an integral in the 
where 
and 
.
where 
. Because this is a linear system, the solution will always be a linear combination of exponentials 
where 
are the 
are the 
is time, which is positive. Since
, we must have 
for the solution to decay to a steady state. If this is violated for any
then that exponential "blows up" as 
, since it is an exponential with an ever-increasing postive argument. Note that if the eigenvalues are complex then the imaginary part of the eigenvalue is related to the oscillatory part of the solution.
would be called an unstable eigenvalue of the system and also forms part of the vector space called the unstable manifold. Instability is defined as the tendency for a system to shoot away from a certain state when it is slightly disturbed (perturbed) from that state. Stability is the feature of a system to come back to a certain state if it is slightly perturbed from that state.
. This required some heavy hacking on the 
, it's important. 
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