( --> Dick Henry's web page )

      ... has discovered (and has now caused to be corrected) a serious deficiency in Mathematica!

You can, if you like, review the history of my work on this.

2008 December 06

As a beta-tester of Mathematica 7, I knew that the problem had finally been fixed.
When I got the public-release version on November 19, I ran my entire Zachary & Macintosh program.
Here is the 198-page-long result.

What to look for? Go to page 54.
The top half of the page (and all the previous pages) are in bold,
and they are the script for Mathematica that is produced by my fortran program.

The bottom half of page 54 (and all the remaining pages) are produced by Mathematica from my script.

What is evaluated are all 17 Zachary & Macintosh Black Hole invariants (and more).
The metric is the Kerr-Newman metric,
and it appears as the last two lines of page 54, and the first four lines of page 55.
That is the entire input to the program!

Highlights to look for in the output:

page 63, the Riemann Tensor Rαβ&gammaδ

page 83, the components of the Ricci Tensor Rα&beta. (These are not all zero unless the electric charge Q is zero.)

page 86, zm05 (effectively the Gaussian Curvature) which is zero. The Gaussian Curvature of Spacetime near, and in, a Black Hole is ... zero!

page 118 (for example). This is Cαβγδ, which Mathematica 7 unfortunately reports with bizarre parentheses.
The problem is that Mathematic does not fully distinguish between superscripts and powers
which of course are totally unrelated things.
I reported this bug as a beta tester, but got no reply.
I have reported it again, and I am told that a bug report has been generated.

page 191, this is the remanant of the problem that I found.
But the correct result for zm15 is produced nonetheless.

page 192, zm16. This takes 56.51 minutes.
It was the fact that Mathematica 3.0 (which came out in 1996)
could not do zm16 at all (although Mathematica 2.2.2 could—and indeed still does)
that set me out on this twelve year odyssey.

page 194, the Kretchmann scalar! I published this in 2000.

page 198, the total time taken: 203.47 minutes, which is 3.39 hours.

OK, so how does that compare with the speed of Mathematica 2.2.2?

Well, in 1993 Mathematica 2.2.2 took 5.78 days to do the same thing that 7.0 now does in 3.39 hours.

And re-running 2.2.2 a few days ago on my IBM-chip Mac (system 9.2) the whole thing took 24.9 hours.

We conclude that both computers, and Mathematica, have improved a lot in 12 years!

Note added 2008 Dec 27: I just installed 7 on the old IBM and ran the identical script. It took 443.03 minutes = 7 hours 23 minutes.

So there is a factor 3.37 improvement in speed of 7 over 2.2.2

And a factor 2.18 improvement, Intel desktop Mac over IBM desktop Mac.

updated 2008 December 27     by our Webmaster