Doing something hard

When on the journey to becoming someone I have never been, I have to do hard things I’ve never done.  I consider earning a PhD to be in this catagory.  In the iconic words of my father:

“A PhD proves that you can do something really hard for a really long time.”

So, as I work 12+ hours days everyday of the week I’d like to say, “I’ve never worked this hard before!”  But I can’t honestly say this. In my previous career I was frequently working more hours and sleeping less.  However, after a year and a half of graduate school, I claim sitting on your butt and thinking can be just as difficult as the most hectic job.

Mathematics is a lesson in frustration.  For you see, mathematicians live for those little (and big) “ah ha!” moments.  This is the proverbial red pill of mathematics.  If you struggle through the confusion, then you can see beautiful logic unfold before you.   Then, the higher up in mathematics you get- the longer the periods of confusion are.  Then you start to relish the challenge more than the completed problem, then you are on your way to becoming a mathematician.  We repeatedly throw ourselves against the things we don’t understand.  We actually feel angry when the professor sets problems which are too easy.  Can you believe that?  We are angry that the problems aren’t complicated enough!  This is how dedicated we are to the idea of hard work.  Later in our careers we go looking for really awful problems and we develop beautiful sayings like:

The problems worthy of attack are the ones that fight you back.

So the next time you are disapointed with your job, just imagine throwing yourself repeatedly agianst a blackboard all day.  And if that image strikes your fancy- you are (or ought to be) a mathematician.

I wanna be a sponge when I grow up.

I’m madly studying for prelim #2.  I learned that I was not a very good sponge on prelim #1.  The professor included many questions that we did in class that I had not fulling absorbed.  A friend later commented it was not an exam on intelligence, but an exam on “how good of a sponge you were.”  I learned I was not a great sponge.  I was okay, but not truly great.

So, when I grow up, I want to be a good sponge.  I’m practicing my sponge skills now as I study for algebra.  The professor who writes this exam is fairly axiomatic about his topics.  Thus, I’m dutifully studying and trying to understand all the concepts.  But it feels like memorization.  Perhaps that is step one to understanding? Perhaps not?  Regardless, I am here memorizing tactic after tactic and proof after proof, hoping that they will appear on the prelim as I expect them too.   Below I have included an image of the sponge I hope to become.  You can almost see the layers of proofs and theorems hidden in the little holes!

Vampire Equilibrium

Whether you were sucked in by the story of Buffy, Edward, or Dracula everyone knows something about the lore of vampires.  Perhaps when you were young you wondered if they could be real.  Perhaps you didn’t. Perhaps it wasn’t until your differential equations class when you professor talked about rabbits and foxes that you wondered about the stability of a vampire/ human interaction.  One of the fundamental questions about whether vampires exist is solving if vampires could exist.   Assuming vampires exist, then could there be a equilibrium where vampires and humans coexist?

Maybe it won’t come as such a surprise to you that people have written papers about this dilemma.   A good friend recently pointed me to a post which references this article and, of course, the original paper by Brian Thomas.  The most impressive part of the whole thing is that after all his calculations, he projects the equilibrium population of Sunnydale to be 36,346 humans and 18 vampire and the show labels the population of Sunnydale at 38,500.  (of course, Brian may have rigged this to work out…) There is not much else to say except to show you a glimpse of the paper to entice you to go read it for yourself.

The most important thing that I have learned from this paper is that Stephenie Meyer’s vampires are less plausible.   That scenario must have a really small b factor to make up for the total lack of predators.  I mean, yes, the vampires in Twilight self-police, but despite my love of the Twilight Series, I think Sunnydale has a more believable scenario.

Regardless of which is more believable, I would have definitley paid more attention in my first differential equations course if they presented the population dynamics with something this extravagent.