Advanced Arithmancy is not mentioned in the books (as far as
I’m aware), but it does show up in the movie adaptation of Harry Potter and the Prisoner of Azkaban. In a couple of previous posts I tried to make a case of why Hogwarts or some other school of magic
should hire a chemistry professor – namely me. As someone who teaches Physical
Chemistry I would like to make a case of why I would be suitable for Advanced
Arithmancy.
Let’s start with basic Arithmancy. The term comes from the
Greek words arithmos and manteia, meaning number and divination
respectively. So says Wikipedia. “Arithmancy is thus the study of
divination through numbers.” Numerology remains quite popular today as it did
in times past. Even Hermione, who rejected Divination class with Trelawney as
being “wooly”, seems to think there is something more concrete in Arithmancy
class with Professor Vector. But can you really divine the future with numbers?
In Newtonian mechanics, if you know the
positions and velocities of all particles in a system at any instant, you can
predict the future behavior of all those particles. The caveat is that they
must obey Newton’s laws. There are three problems: (1) Knowing all the
positions and velocities is a tall order but possible, at least in theory, (2)
particles at the level of atoms are governed by quantum mechanics, and (3) for
any “real” system of interest, there are likely to be external influences that
must be taken into account.
This is where Physical Chemistry, or
P-Chem, comes in. It turns out that for an ensemble of particles, you can make
good predictions using the “laws” of quantum mechanics. The field of
statistical mechanics then allows you to derive thermodynamic quantities. Why
is thermodynamics important? It tells you, at least for equilibrium
thermodynamics, where things are headed given where you are now. And you don’t
need to know the individual details of all particles. The thermodynamic
quantities allow you to make macro-scale future predictions without needing to
know everything that’s going on at the micro- or nano-scopic level. That, in
principle, helps overcome the first two problems. A year of P-Chem (required of
Chemistry majors) should give students a headstart in this area. Now, it’s not
going to be easy – but it will be very interesting. And at the end of the
course, students can even get the famous bumper sticker that says “Honk if you
passed P-Chem”. These were quite popular some years ago but I haven’t seen many
recently. The third problem is more complicated but a follow-up class, perhaps
Double Advanced Arithmancy, could cover the fundamentals of non-equilibrium
thermodynamics.
So can numbers predict the future? This
is what scientists are attempting in many areas. Probably the most familiar are
large-scale simulations of the earth and its environment – that show up
non-stop on the Weather Channel. Closer to my field, simulations are run to
predict the properties of new catalysts, advanced materials, and biochemical
evolution. We build mathematical models, estimate the “present” conditions, and
using the “laws” of quantum and/or classical mechanics we can predict the
future of something not yet physically seen or built.
But what most of us care about from a
Divination point of view is “what is going to happen to me in the future”? That’s
not so easy to tell. Like a single quantum particle, perhaps an individual’s “future
is not set” (I admit to recently watching Terminator Genisys). We seem to do
reasonably in making some macro-level predictions for ensembles of particles
(or individuals), but what if these individuals started to collude in ways that
were not represented in our models. Do we know what all the feedbacks might be?
Maybe that might be the heart of quantum mechanics. (Or at least I’m a quantum
mechanic at heart.) Sounds like another class: Triple Advanced Arithmancy. Is there a Hogwarts College, I wonder? Maybe I could help start one.
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