Part II

For what companies to go to to get going
on a career in such applied math, I can't
think of any. Mostly people and their
organizations would rather waste money
than get involved with mathematicians
doing work only mathematicians understand.

Again, if want to make math pay, just sell
the results, usually as a vendor outside
the customer.

If are inside the company, then likely no
good work will go unpunished. Basically
to be successful, you will need the strong
personal support of the CEO and hopefully
the Board -- literally. And the CEO will
routinely have to go around and break 2 x
4s over the heads of recalcitrant middle
managers to see if they are just asleep or
really dead -- otherwise those middle
managers can sabotage you with high
determination and creativity.

E.g., twice I saved FedEx from going out
of business and had much more that would
have saved FedEx maybe tens of millions of
dollars a year, but I got flack and push
back and contempt and none of the promised
stock.

Such are some of the challenges in getting
stuff done. But successful people have
been overcoming challenges, some much
worse than I faced at FedEx, for many
centuries.

Now that you know about the possibilities
of some of the absurd challenges, don't be
surprised. Really, one of the best rules
is just to keep your good technical work
essentially a secret until you have a
solution that is just too darned good to
refuse, and then pull back the curtain,
let people see the results and also see
that it's too late to fight with you.

Better still, just provide such results as
a business and own the business. E.g.,
in some cases, just do the work for free,
show the results, and then announce "You
can have this for your real operations for
a fee of only 15% of the savings."

Once there was an in-house research group
that was successful. It was for WestVaco
paper -- think specialty papers, e.g.,
coated papers for milk cartons. So, they
had Ph.D. chem eng guys running their
plants in jungles, etc., that is, where
the trees were, but it was a family owned
business with HQ in NYC.

The research shop was in Maryland, and I
got an explanation from them: Each year
Research went to NYC for their budget.
Always the CEO, family guy, offered much
more money for the Research shop than the
shop was willing to accept (first-cut,
good budget situation!).

Why? The rules: Research picks their own
projects. Projects tend to run from a few
months to a few years. One project in 10
gets to operations. When Research has a
project ready for operations, they
approach the relevant operational
managers. In the first three years,
savings are allocated half to Research and
half to the operational unit. After three
years, all the savings are allocated to
the operational unit. With this
accounting, Research was returning $3 to
the company for each $1 in their budget.
So, sure, HQ wanted to increase the
budget, but Research didn't want to have
to find ways to return $3 for each extra
budget $1 so didn't want a bigger budget!

It is just crucial that the CEO is
supporting such in-house innovation. The
rules are also important.

Ah, while I was in grad school, to make
enough money to support my wife and I
while we both finished our Ph.D.s, I took
a job at a DC area think tank working
for the US Navy.

At one point our problem sponsor group
wanted an analysis of a special, worrisome
scenario of global nuclear war but
limited to sea -- they wanted to know how
long the US SSBN fleet could survive if it
was just held in reserve and didn't shoot
its missiles with nuke warheads. And they
wanted the results in two weeks.

Gee, two weeks to model global nuclear war
limited to sea! How generous! Good that
they were not in a real hurry! Besides it
was good timing since the day after the
due date my wife had already gotten us
reservations for a vacation at Shenandoah!

Well, there was a guy B. Koopman who in
WWII had written a report OEG-56 on
finding things at sea. So, given A and B
wandering around at sea, when might they
have an encounter? Well, Koopman took
the area of the sea, the two velocities,
and the detection radius and came up with
an arrival rate for a Poisson process.
Hmm ....

So, list the Red forces and Blue forces
(the US SSBNs were part of the Blue
forces), that is, list airplanes,
helicopters, destroyers, battleships,
attack submarines, etc., the speed of
each, and the detection radius. Then have
a table with a row for each Blue weapon
type and a column for each Red weapon type
and the detection radius and, if there was
an encounter, the probability that one,
the other, or both died.

Now tap lightly with an independence
assumption (maybe not wildly unjustified),
realize that a sum of independent Poisson
processes is again a Poisson process with
arrival rate the sum of the contributing
arrival rates, and get for the state of
the war a continuous time, discrete state
space (very large from a combinatorial
explosion) Markov process subordinated
to a Poisson process. So, yes, there is a
closed form solution as a matrix
exponential for the transition
probabilities from state to state, but
that matrix exponential is absurdly large.
Instead using Monte Carlo to run off, say,
500 sample paths was easy. I typed in the
code.

Prof J. Keilson did a technical review.
He said, "There's no way you can fathom
that enormous state space.". I said, "At
each point in time, say, 10 days into the
war, the number of SSBNs remaining is a
random variable. Moreover it is bounded
so has finite expectation and finite
variance. So, the law of large numbers
applies. So, run off 500 independent,
identically distributed samples, add them
up, divide by 500, and get the expectation
within a gnat's ass nearly all the time.
Really the Monte Carlo puts the effort
where the action is.". He agreed with me
and passed my work.

The Navy got their results on time, and my
wife got her vacation on time.

Later I was told that my work had been
sold to a leading US intelligence agency.
I could tell you which one, but then I'd
have to ...!

I thought that the whole effort, which
ignored so much maybe crucially important
detail, was close to a joke, but,
surprisingly, the output did look
reasonable. Also, the two weeks was also
so short it made the whole exercise next
to absurd, another joke.

The group I was working for didn't trust
me to get results on time so had another
person working independently. Well, at
the end of the two weeks, the other person
had nothing at all. So, I'd won.

Office politics: One guy said "You write
nice computer programs" and otherwise I
got no thanks but just some jealousy,
contempt, and silence. So, soon afterward
when I'd gotten my Ph.D., I wanted to
leave and did.

Again, no good deed need go unpunished.

Again, own the business, use math as an
internal secret sauce and technological
advantage, and sell just the results.