Sarah H

Study the following 2 pictures, both of which are published on the official NASA/JPL Spirit Rover site:

http://marsrovers.jpl.nasa.gov/gallery/all/2/n/183...

http://marsrovers.jpl.nasa.gov/gallery/all/2/n/184...

There seems to be an anomaly in the upper centre-left of the second picture - a black mass behind one of the boulders, which is not present on the first picture. As the shape is evidently behind the boulder, it does not appear to be a picture or processing defect.

I would be very much interested in understanding whether anybody has a scientific or technical (i.e. non-idiotic) explanation for this, as this has me totally perplexed.

The standard “Schwarzschild’s solution” is usually given as:

ds² = (1-2m/r)dt² - (1-2m/r)^-1.dr² - r²(dθ²+sin²θdφ²)

The standard interpretation is that 'r' is the distance from the center of the gravitating mass, m. With sufficient mass that is sufficiently compacted, the gravitational force will be stronger than all forces that oppose it, and the mass will become infinite as r goes to zero - a singularity/black hole. But this entails dividing by zero, a forbidden move. Schwarzschild’s actual solution was:

ds² = (1-α/R)dt² - (1-α/R)^-1.dR² - R²(dθ²+sin²θdφ²)

R = (r^3 + α^3)^(1/3), 0 < r < ∞

R is the distance from the center of the gravitational field and r is a parameter of the curvature of the space. In Euclidian space, R=r. However the space of General Relativity, and of black holes, is non-Euclidian. In Schwarzschild’s actual solution, as r goes to zero, R (the actual distance variable) goes to α, a non-zero number. There can be no point mass and therefore no black hole. I suggest that Black holes are figments of the imagination.

Given the apparent simplicity of the above, has anyone got any robust mathematical arguments to contradict this basic proposition?

Does human (or animal) conciousness arise entirely primarily as a result of biological processes in the brain, or is the brain partially a kind of 'receiver' that modulates a separate conciousness that exists in another place, outside the observable universe and known spatial dimensions?