BTW Camille, since you're such an intellectual with a great grasp of science and technology- I was wondering...

I'm trying to converge a Taylor-series expansion of the electrostatic field around a molecule out to a width of about 1 Angstrom- but no matter what order I go up to in the expansion the radius of convergence appears to fall short of that distance.

What do you think? Could it be a numerical problem? After all- I am calculating the higher order gradients by finite displacements over a mesh- and once you get past the fourth order- it all gets a bit tricky to converge the gradients with respect to the displacement size.

Maybe it's an inherent property of Taylor series expansions on non analytic smooth functions- that the radius of convergence is always finite- because past a certain distance you can't tell what's going on in the function by a local analysis at the origin. I'm not sure.

I should explain- I'm trying to use the field gradients in a three-body wave-function calculation in order to solve for the nuclear quantum dynamics of protons in a bg field. I'm also interested in the quantum momentum distribution- because after all- reproduction of infrared vibrational spectroscopy is not the only game in town.

Would you suggest Taylor expanding the field across distributed sites within the molecule- or is it better to keep the expansion to a single site? I'm not sure. One problem is whether I can treat the fields across two molecular sites as independent quantities or not. It's probably more elegant to carry out a multi-center expansion- but it would be so much easier if I could get the one-site expansion to converge.

Anyway Camille- you're an intellectual master of science. Please let me know your thoughts on my little problems.

Thanks Camille for defending Limbaugh for us. I was under the impression that he's a draft-dodging chickenhawk who is only too happy to see young kids die in foreign lands as long as he can hind behind phony patriotism.

I see now that it's just my stupid liberal prejudices. I wish I were as intellectual as you so that I too could interpret black as white and war as peace.

Even as a Harry Potter fan and a listener to rock music, I have zero interest in reading this article.

Remember when Salon used to be relevant?

Never thought I'd agree with the spiritual/religious nuts who post to Salon, but...

I don't even have to read this article (which I haven't) to know that there's nothing new that I haven't seen 100 times on Salon's pages before. This debate has been played to death already. Nobody's got anything new or interesting to say.

Call me when you find some actual evidence of a God- even Thor's hammer would do. Also, drop me an email if an atheist finally breaks through and convinces religionists that they're living a fantasy.

Actually- scratch that. I'd even settle for an article exposing Richard Dawkins as a closet Hindu, or revealing that Pat Robertson does covert research into genetics.

See- I'm not so hard to please.

Testing the waters here to see if this type of speech is still allowed on Salon!

There's a difference between Catholicism and scientific consensus.

In Catholicism, a geriatric makes pronouncements based on no evidence whatsoever- and his loyal followers obey, or at least pretend to obey.

A scientific consensus on the other hand arises from reasoned argument about available data using sophisticated 21st century models and analysis.

Another difference is that some scientists are female, whereas all popes have been male.

I'm glad that Camille is a lapsed Catholic, but has she learnt anything if she can't distinguish the relative plausibility of Catholicism versus scientific consensus?

Can't Camille at least learn some humility, or is she pretending that we should take her scientific opinions more seriously than actual scientists who get their papers published in the peer-reviewed literature?

The word mouse is not a mouse. A computer simulation of a mouse down to the level of interacting atomic wave-function may well be a mouse. If its behavior would be indistinguishable from that of the aforementioned rodent then one would have to grant it a great deal of 'mouseness'.

Likewise, if the solution of the equations of Newtonian dynamics gives a trajectory completely indistinguishable from that of a real ball- then one should grant it the status of 'ball-ness'.

The fact that we don't yet have (and maybe never will) obtain the complete equations for the universe- and the fact that even if we did obtain them we would presumably never be able to simulate more than a few elementary particles doesn't mean that this analogy is useless.

A universe simulator which could produce behavior indistinguishable from that of the real universe would also contain simulated sentient beings. On one level the simulator is just churning through 1's and 0's- but on another level the simulated sentient beings would perceive themselves in a real universe. Even though they're simulated sentient beings- their sentience is 100% real and not simulated.

Now the point is that one doesn't even have to run the computer simulation to solve the equations. The solution already exists in 'mathematical space' whether or not we solve it or not. The simulated beings don't know or care whether we're running the computer program or not- they still exist as part of the solution to the equations.

There's no need to explain where the universe came from. It just exists. An extraordinary piece of mathematics- a simulation with no simulator.

There's no God making sure that 1+1=2 or that PI holds to a zillion decimal places. Mathematics takes care of that by itself. It doesn't even need mathematicians to work.