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.

Math Linguistics II

Tired.

Math: That feeling you get when you have a qualifying exam on Monday.

Pedestrian:  That feeling you get when you partied to hard the night before.

Brain Dead.

Math: The state of one’s brain when they have spent the last month studying endomorphisms.

Pedestrian: The state of one’s brain when they have watched too much TV.

  I’ll see you next week!  Hopefully with more time and more working brain cells!

Math Linguistics

In general, mathematicians speak in non-normal ways which don’t have simple translations when they project into English grammar.

Allow me to break this down for you:

In general.

• Pedestrian speak: means usually.  In general, I get to work on time, but today I was late.
• Math speak: means always.  It’s always true in a larger sense.  ie: In general, every element in a field has an inverse, not just 2.

normal.

• Pedestrian speak: a property which most things are assumed to posses. ie: It’s normal to hate Mondays.
• Math speak: a nice property most commonly associated with group structures. ie: H is normal in G when gHg^-1 = H.

simple.

• Pedestrian speak: a negative property, sometimes suggesting mental disabilities.  ie: That man is simple.  or That puzzle is too simple for one of my intellect.
• Math speak: a nice property.  If a proof is simple, then we like it better than a complex one.  Also a group theory property for which a group has no subgroups but 1 and itself.

translations.

• Pedestrian speak: the act of interpreting one language into another, requiring alterations in some of the meanings perhaps.  ie: I read a translation of The Iliad because I can’t read Greek.
• Math speak: The act of sliding something on a surface without changing it’s shape.  ie: translate a line to the right by adding 1 to every point.

project.

• Pedestrian speak: To enlarge an image through the use of shaped glass and a light source.  ie: Movie theaters project the movie onto the big screen.
• Math speak: a map which loses some information in order to better understand a multi-dimensional object.  ie: the cube projects a shadow onto the floor.

English.

• Pedestrian speak: the language which normal people speak, except the mathematicians for whom standard English is not good enough.
• Math speak: the language we butcher and redesign to fit our needs.  Also a form of communication we deign to use when we have to include some explanation, but we would rather just use symbols (σψμβoλσ?).

Many people complain about the use of English in the mathematicians world.  But what are they going to say about it?  “This is the sort of utter nonsense, up with which I will not put?”