Complexification

==========================================================

Everyone knows Simplification: it is the deliberate effort to make complex things simple.

I define Complexification as its precise antonym: a deliberate effort to make simple things complex.

It is the business of every Physics Teacher to simplify a new concept so that it is understood and absorbed by his pupils by citing example after example, telling story after story and showing demo after demo till it weaves itself snugly into the tapestry of concepts already familiar to them.

Wow!!!

Take for example: Simple Harmonic Motion. Some British texts of our time used to define this as the "motion of the foot of the perpendicular dropped from a point on a circle on its diameter as that point goes around the circle uniformly".

My Foot!

Where is the Spring-Mass System Boss? Or at least a Simple Pendulum? Can't Circular Polarization wait?

Complexification is Glorified Obfuscation. Physics Teachers dare not do it to their IIT students (lest they be booed and shooed).

However they sometimes indulge in it for fun to browbeat colleagues, seniors, and interviewers; and impress them.

In one instance a smart third year student tried it on me too.

The other day Saswat mailed me a hilarious account of how he happened to flummox a dour Investment Bank interviewer who was unimpressed by simple well-known statistical Business jargon. Apparently the name of the popular : "VASICEK MODEL" eluded Saswat for the moment and so he mentioned in its stead the Nuclear Physics thing: "ORSTEIN-UHLENBECK MODEL".

The term was new to the Majordomo and he was all over Saswat trying to squeeze the lowdown on what he thought was this latest and greatest Business Model that would perhaps feather his nest for good.

****************************************************************************

For fun DB occasionally used this Complexification Technique to impress and silence our senior colleagues in the Physics Department at KGP.

One day Prof ABC entered our Office (C-239) when DB was away and narrated to me the question posed by a B Tech student of his QM class (ABC happened to have co-written a text-book on QM printed by Thackers like my own blessed Lecture Notes).

The question was routine: "Sir, you say that all Hermitian Operators have real eigenvalues, but the momentum operator has an imaginary eigenvalue for its eigenfunction: exp(-kx)".

ABC was perplexed by this counterexample and apparently approached DB who replied (naughtily): "It goes out of the Hilbert Space" and went out for Tea.

ABC asked me what DB meant and what would be my answer.

I said as usual that the trial wave function cited by the student is not a 'good' one since it explodes at 'minus infinity' instead of dying down.

ABC's eyes lit up but he wanted to know where the blessed Hilbert Space enters this business. I had to refer him to his own book where it is stated that good wave functions must be more or less square-integrable so that they can be given a proper probability interpretation; and that the set of all such 'good and well-behaved' things is called Hilbert Space, in brief.

ABC perhaps never forgave DB.

****************************************************************************

One evening Prof RGC wanted the solution of a very beautiful problem in JEE Mechanics that goes something like this:

"Take a smooth thin rod. Hold it in an inclined position so that it touches a smooth wall and a smooth floor at right angles to the wall. Leave it so that it slides down the wall along the floor. Show that as it slides down and drops to the floor, it loses contact with the wall at a point 2/3 high from where it was left" (or was it 1/3?...it is a good 30 years ago).

He entered our Office and gave this problem to DB and asked him to please give him the solution by next evening.

DB that day was busy writing perhaps one of his papers for JMP and so dumped it in my lap. I went home and did the kitchen-sink experiment with a shaved pencil held leaning against our white-washed wall and mosaic floor to convince myself that the problem was correct (no point banging heads and wasting time on a wrong problem).

It was correct!

Then it took me probably half an hour or so to apply the Newtonian principles of energy and angular momentum and losing contact means vanishing of Normal Reaction.

Which I wrote it up and gave it to DB.

DB was happy but he told me he would like to have some fun with Ramda, and so he recast my Newtonian Solution into one involving (1) the Lagrangian and (2) the Hamiltonian formulations.

And handed it to RGC; who was back in our Office an hour later when I was alone.

He heaved a sigh of relief when I gave him my simplified Newtonian solution; but knowing how naughty Ramda himself was, I guess he gave the student the Complexified DB Solution rather than mine!

Ramda told me he performed the demo at his home too to his great delight.

******************************************************************************

And then there was this 3rd year student AVM (future Ph D Princeton) who challenged Prof VS on his grading, of which I talked in my earlier blog: "Elephant & the Monkey":

http://gpsastry.blogspot.com/2010/05/elephant-monkey.html

When I told him that the set of all classical orbits would have exactly "zero" energy and asked him to verify it, AVM brought his solution next morning: To browbeat me he used the Hamilton-Jacobi Equation instead of Newton's centripetal force law.

No wonder he became the favorite Graduate Student of Phil Anderson at Princeton!

Of course our paper, which apparently is now given out as a Problem to students at Princeton, has only the simpler version.....I like simplification and not complexification:

http://www.physics.princeton.edu/~mcdonald/examples/EM/sastry_ejp_17_275_96.pdf

*************************************************************************

SDM was simplicity itself with DB and me; but he did revel in its opposite with Referees of Journals later in his career.

While giving me the go-ahead for writing up my Ph D Thesis, however, he did caution me:

"Don't use Vector Notation: the Examiner will have a low opinion. Always use Tensor Notation".

He was scared, and that perhaps was ok.

By the way, what is wrong with Vector Notation?

**it stinks the same in Tensor Notation too, no?


===========================================================