Our Achilles Heel

From xkcd*:

(Click image for larger view over at the source.)

-cvj

*Thanks Jude!

10 Responses to “Our Achilles Heel”

• spyder

I believe in the 60s we called this game “mindtag.” More points were awarded for tagging a person (accomplished by completely derailing their line of thinking or reasoning particularly when they were speaking or lecturing) who was not under the influence of whatever (usually in academic or professional work settings), and points were deducted for taking unfair advantage of friends who were too high to track any thoughts past the first verb phrase. I see it has now under gone a comix-reduction reaction when combined with the bizarre (but oddly entertaining) cult-film DeathRace 2000.

• Steve

Whoosh!! Off I went on the internet to find this: http://arxiv.org/PS_cache/cond-mat/pdf/9909/9909120v4.pdf. Equation (32) is what you need.

Whoosh!! Out came my trusty Mathematica:

R[m_,m_]/;m>=2:=-(((-1+2 (-1+m)) R[-2+m,-2+m])/(1+2 (-1+m)))+(4 (-1+m) R[-1+m,-1+m])/(1+2 (-1+m));
R[m1_,m_]/;m1==m+1&&m>=1:=2R[m,m]-R[m,m-1];
R[m_,0]/;m>=2:=-R[-2+m,0]+4 R[-1+m,0]-2 R[-1+m,1];
R[m_,p_]/;0=2:=-R[-2+m,p]-R[-1+m,-1+p]+4 R[-1+m,p]-R[-1+m,1+p];
R[0,0]=0;
R[1,0]=1/2;
R[1,1]=2/\[Pi];

whence

In[8]:= R[2,1]
Out[8]= -(1/2)+4/\[Pi]

• Ha HA! Excellent! And you did not get hit by a truck either!

Thanks…

-cvj

• Steve

It seems that some of my Mathematica code got “eaten” by your commenting system, but luckily the code that got through can still compute R[2,1] correctly.

• Steve…. maybe use LaTeX… See sidebar.

Cheers,

-cvj

• Hi Steve,

thanks for the reference – that’s a cool paper!

Happy New Year!

Stefan

• Carl Brannen

Here here on the paper and calc! When I was in grad school, R(0,1) was assigned as a problem on the PhD qualifying exam some years before, and so was studied by students. I’m adding a link back to here on the page I wrote up complaining about the uselessness of the calculation.

Seeing the Brillouin zone problem with the elegant discrete Laplacian solution makes me feel better about the problem in general, but I still think that the R(0,1) problem is a stupid one to put on a qualifier. Uh, I guess I should mention that I got my MS in physics by passing the PhD qualifier but didn’t go on to write a thesis.

• Carl Brannen

Clifford, the more I think about that elegant paper Steve linked above, the more I think that this would make an excellent subject for a full blown blog post, if not by you then perhaps by someone more interested in condensed matter or solid state quantum mechanics. If nothing appears for a couple of months, I’ll write one up myself.

• As a non-physicist librarian, I thought it was funny enough when they said, “See that physicist crossing the road?” I’m glad it proved more meaningful than that.

• Carl, it is indeed interesting. I cannot promise a blog post, however. Too many things on my plate at present.

-cvj