Sand Dollar Success!

I figured out what was wrong with my program.  There were two things:

1.  I needed to use the output as the new input, instead of sending a set of predetermined points through the function to generate output.

2.  I was taking the square root of a number that didn't need it.

In the end, the fixes took a grand total of a minute to fix in the program; however, it took many hours to discover what was wrong.

Enjoy my sand dollar.

My MS degree exam questions

1.  Explain the Schodinger's cat paradox.

2.  Consider the Stern-Gerlach (SG) experiment.  If you direct a beam of ions through one SG apparatus, and then place another SG apparatus oriented the same as the first in the path of one of the first split beams, then place a screen on just beyond the second SG apparatus, how will the ions be distributed on the screen?  Follow-up:  how many ions should hit the screen given a beam containing 1000 ions.

3.  A sailor drops a ball from the top of the mast on a sailing ship.  Where will the ball land?

4.  Consider a rod of uniform mass density resting balanced on a cylinder when a puff of wind tilts the rod.  At what angle will the rod slide off of the cylinder?  Note: there is static friction between the rod and cylinder.  Follow-up:  is the rod stable if it tilts by small angles compared with the angle required to slide off?  Follow-up:  will the rod experience harmonic motion at the small tilt angles?

5.  What makes the dynamics of neurons nonlinear?

Do YOU know the answers?  

statistically unique solutions

Is there a mathematical model which statistically predicts a more likely solution over another?  Often times in "real world" physical problems, there is no unique function or solution to determine the evolution of a system.  This occurs in many other sciences and applications.  So, I'm wondering if a statisical prediction of which solutions might work can be found.  In some simple systems, like the kinematic equations for constant acceleration, there are an infinite set of solutions how an object behaves under the influence of a constant acceleration.  All one needs to do to solve the problem is to pick a set of initial conditions for the position and velocity of that object.  However, in some problems like building a three-dimensional image of a brain from magnetoencephalography (MEG), there is no unique image based on the data gathered from the MEG probes.  But there must be some way in which one can determine the most likely image of the many (if not infinite) options...right?

Failed mappings

The ones that look like a play button and a jelly fish should be sanddollars.  The sideways torch is supposed to be a diagonal line.  All are failed attempts at a program I'm working on, but they're still neat.

potential, potential difference, voltage, volts

Voltage means potential difference.  So when someone says, "The voltage of that power line over yonder is at 10kV."  What they mean is that the potential to which the wire itself is set is 10kV ABOVE the potential of the earth or ground.  Typically we take ground to be zero volts, but the 10kV has to be in reference to something standard.  Otherwise, it makes NO SENSE to say something is just at "blah" volts, unless it's in reference to something everyone listening understands what the implied reference is.  Therefore, people who don't REALLY know what they're talking about in say a scientific situation where everyone should be on the same knowledgable page should make sure to include to what their potential is referencing.

ALSO, volts is only the unit of potential and thus potential difference (voltage), SO you cannot interchange the words to hope for the same meaning in what you present.

flame

Instead of laying down to read as I had initially planned about twenty minutes ago, I've been downloading my photos.  While they transferred from camera to computer, I watched my candle light flickering.  No no, I'm not sitting in the dark with the glow of my computer screen and one lit biscotti scented candle as I may have made you imagine.  I've my corner medusa lights on too.  Back to my biscotti light.  

Nope.  

I just went on a net-tangent reading about the earth's magnetosphere...at least it's relevant.

Despite a simple candle flame not truly being a plasma, I still think it exhibits a very similar structure as the auroras.  If you look closely, the tip of the flame sometimes has noticeable cuts jutting into it to make it look like the curtain shape of the auroras.

Maybe that's god's way of giving a little bit of spectacular lights to anyone who can create a flame.

Awww.

Minkowski Space

The title is nothing more than Euclidean space merged with the dimension of time. In other words, your familiar three physical dimensions and one time dimension. I realized something with this space (maybe it's true) just now. You CANNOT have physical degeneracy since the dimension of time lifts any sort of degeneracy you might see in statics. By physical degeneracy I mean one cannot have the same physical value for one instant and another instant.

Consider something traveling on a ring. If we set this ring in Euclidean space (x,y,z), say on the x-y plane and start our something object at (x=R, y=0), where the radius of the ring is R, then if we think about the points in this 3D space where our something will can be, then we are (in this case) stuck on the ring. So, our something can start at (x=R, y=0) and rotate about the ring and be back where it started even after tracing out the shape of the ring. Physically, our something doesn't know the difference between the cylindrical coordinates (an inbreed from Euclidean space, instead of (x,y,z) defining a point in space we use (s,@,z) where z is equivalent to the z in Euclidean space, s is the distance from the z axis, and @ gives us the rotation about the z axis...really @ is denoted by the Greek letter theta, but I don't have a theta key or option) (s=R,@=0,z=0) and (s=R,@=360E,z=0) (E being degrees). With the help of cylindrical coordinates, we can see that we've made a full rotation, but we're in the same spot! This causes the degeneracy of our physical space. But in the Minkowski space, we have time to consider. Our coordinate in this space is denoted by (x,y,z,t). At the beginning of our something's rotation, it's at (x=R,y=0,z=0,t=0), but after making a full rotation, we now have (x=R,y=0,z=0,t=T). Clearly, these two state coordinates are not equivalent, and thus there is no more degeneracy. In other words, our something was someplace, then some time passed. During this time, our something could move or stay put, but it's state is always unique!

This is really somewhat of a trivial bit of information, but it was fun to think about since I just read that Minkowski space is Euclidean space tensored with the time dimension. Also, this degeneracy business is really fascinating when applied to other systems and spaces.