Saturday, October 25, 2014

Jacob's ladder is not the best Biblical metaphor for computational materials science

A more appropriate metaphor is Jacob wrestling with the angel (God).
This point was made in a nice talk that Mike Gillan gave last week at the NORDITA water meeting.

John Perdew has invoked the metaphor of Jacob's ladder to describe his "dreams of a final theory" and the quest for an "exact" exchange correlation functional for Density Functional Theory (DFT).
Perdew's metaphor was earlier reinvoked by Joost VandeVondele in his talk at the meeting.

This painting of Jacob's ladder is by Michael Willmann. In the Biblical account from Genesis 28
Jacob left Beersheba, and went toward Haran. He came to the place and stayed there that night, ....  And he dreamed, and behold, there was a ladder set up on the earth, and the top of it reached to heaven; and behold, the angels of God were ascending and descending on it! And behold, the Lord stood above it [or "beside him"] and said, "I am the Lord, the God of Abraham your father and the God of Isaac; the land on which you lie I will give to you and to your descendants; and your descendants shall be like the dust of the earth, and you shall spread abroad to the west and to the east and to the north and to the south; and by you and your descendants shall all the families of the earth bless themselves. Behold, I am with you and will keep you wherever you go, and will bring you back to this land; for I will not leave you until I have done that of which I have spoken to you." Then Jacob awoke from his sleep and said, "Surely the Lord is in this place; and I did not know it." And he was afraid, and said, "This is none other than the house of God, and this is the gate of heaven.
This was a dream.
The "ladder" of approximations is also a dream because it conveys the idea that with each rung of the ladder one is necessarily getting closer to the correct answer [heaven]. Things are not that simple. For example, Mike Gillan pointed out to me that the generalised gradient approximation (GGA) does worse than the local density approximation (LDA) for the surface energies of solids.   No doubt experts can provide other examples.

Similar issues arise in wave function based computational quantum chemistry. I think Pople first drew a diagram such as the one below (taken from this paper). The idea is that as one increases the size of basis set and the level of theory (i.e. treatment of electron correlation) one moves closer to reality (experiment).

Again, the problem is that the "convergence" to reality is not monotonic or uniform. This is reflected in the existence of Pauling points. Sometimes as one moves down or to the right one on the figure actually gets further away from the experimental value. This is discussed in detail for a specific example in a paper by Seth Olsen.

As Mike Gillan suggested a more appropriate Biblical metaphor than Jacob's ladder is the account in Genesis 32 of Jacob [whose name means deceiver] wrestling with an angel. Afterwards, he is renamed Israel [which means he who wrestles with God].

The painting is by Rembrandt (1659).

Computational materials science is a struggle. Jacob's ladder is a dream.

1 comment:

  1. Hey, I liked this one, and not just because I'm being spruiked (for which I thank you). The best way to fight a colourful metaphor is with another colourful metaphor.