Troll Math

I hate these kinds of problems.

Movies and Vidya

[some language towards the end]

I was thinking about the plots of movies I've seen v. the plots of videogames I've played.

...

I've been thinking about the plots of movies v. the plots of ANYTHING ELSE.

Is it just me...or does nearly every single movie plot either suck or is a repeat of some rehashed plot?  And, whenever Hollywood 'gets it', and creates an original plot (a.k.a., steals an original plot from a book), everybody loves it and it gets raves reviews.  So, what happens next year?  A focus on originality and none of the same mass produced T.V. drama shit? No.  Fuck that.  Sequels off of the good stuff.

I'm going to describe some archetypes over the next few posts, and you're going to know exactly what I mean.  First up is the "Old Team Reunion".  This is me copypasta'ing stuff I've wrote before to fill up the blog--BUT I DON'T CARE:

The Soviet scientists that made the unmanned Luna rovers were later called upon in their retirement to help out during the Chernobyl crisis.  They retrofitted a bunch of bulldozers as unmanned machines to help with the clean-up.

You know those "Old Team Reunion" movies?  The kind where, some disaster strikes, and the government sets out to recruit the leading experts in the field, of which there are only 4 or 5 and they're all in retirement now?  And they have a short recruitment montage for each of the experts, and of course one of the experts has fallen to the wayside over the past few years, and it takes their old leader to give him a pep-talk to join the team?  Then the rest of the movie is Apollo 13-ish drama?

But I'd like to see a good old cheesy "Old Time Reunion" movie with the scientists from the Lunakhod program building bulldozers for the Chernobyl crisis.  The KGB would go to the leader first, and he'd say something like, "I'm sorry comrades, but those glory days are long behind me.  I've completely forgotten how to build a Luna rover."  And then the KGB agent would reveal himself as the former leader of the Soviet space program, pull out a picture of his dead wife, and say, "Are you going to live in her shadow forever?"  They leave him with the picture, and the next day he calls up the director and says, "I'm in."

The rest of the montage would show the former Lunakhod leader going to all of his former teammates.  Of course the first one he goes to is the 'buddy'-stereotype.  The guy he used to be good friends with but lost contact.  And of course, this usually happens with the 'buddy' stereotype, he's also a danger-junkie.  And he's now no longer doing radio telemetry; but doing something insane like base-jumping.  And the old leader catches him in the act.  They start having small talk and catching up, until the 'buddy' finally says, "Alright, spit it out, why are you here?"  And after the old Lunakhod leader says that he's trying to recruit the old team members to clean up the Chernobyl radiation, the 'buddy' spins his back to him with a disgusted look on his face, starts to walk away...before he dramatically (and cheesily) spins around and says, "You bet I'm in!"

The rest of the recruitment goes fine until they (of course, man, so many cliches with this kind of movie) meet the team member who has fallen by the way side, but has some obscure knowledge that no one else has that makes him absolutely necessary.  He has started drinking and let himself go.  Eventually, the old team leader pins him up against the wall and says, "Dammit Breznokovsky!  Are you just going to let it end like this?  Living alone in some little tenement in Moscow, decaying until the end of your days?!  I know you've still got the brains, and you still got the guts!"  He looks away sullenly before saying that he'll do it...for old times sake.

Then they actually get to work, meeting up at the site, and start requisitioning supplies.  Only, they find that the supplies are either non-existent or will get there too late.  At a late night meeting they start to get frustrated, someone mentions something about the old leader's dead wife, which causes him to blow up in front of everyone and storm out.  The old 'buddy' goes out to talk to him and help him face his past.  After this they start walking about, thinking about what they can do without any equipment, when they notice a bunch of unused bulldozers used for the construction of the radio tower next to Privayt.  They rush back to the meeting room, where almost everyone else has fallen asleep and after waking them up begin talking about whether they can retrofit the bulldozers.

Someone brings up a crucial technical question that makes everyone second-guess whether the idea is even possible.  They all look at the obscure expert since only he has the knowledge that would make it possible to overcome such a technicality.  Everyone stares at him as he dramatically pauses and rubs his chin, mulling it over.  The camera scans over the sweat-stained faces of the other men in the room.  Breznokovsky stands up and beings to pace around, talking to himself.  Then, he stops, and falls silent.  After a long pause the leader tentatively questions him again on whether or not it's possible, in a much softer and less confident voice.  Breznokovsky then dramatically turns around and says, "Yes.  Yes I think it just might work."  Everyone looks at each other, smiles and high-fives abound.

Then starts the construction montage.  Complete with 80's music.  Add in some laugh track clip of someone holding a blueprint upsidedown.

Finally, they begin using the machines to enter the worksite.  There is some tension as they get closer to the reactor as the technicality earlier mentioned is brought up again.  They ask Brez. whether or not he wants to stop, "Dammit!  It's too late to turn back now!"  The entire team is on edge.  Suddenly, there's a collapse in the reactor wall that damages some of the relay equipment on the bulldozer.  If they can't move it, then the bulldozer has effectively blocked a crucial entrance and threatens to let out a large radioactive pocket for some reason.  The team starts to break down as everyone begins yelling at each other and blaming each other for various parts in the project.  Then, Brez. yells, "Switch the rotor to AUX" (a reference to an obscure command that someone in Mission Control during Apollo 12 yelled out that saved the mission).  At first, no one even knows what this means, and after Brez. explains the 'buddy' immediately mentions how risky this is.  The room goes silent as leader and Brez. look at each other with cold glances.  Brez. gives the leader a steely nod, to which he replies in kind and then gives the order to switch to AUX.

There is a long, tense pause as the camera pans over each of the team members during the long radio silence after the switch.  The bulldozer is able to complete its mission.

Fade to credits.  Bring up more 80's music.

Likewise, every action movie follows along the same premise:

• Bad guy is a stereotypical drug dealer (or some criminal) who
• Kidnaps the guy's family (or threatens them, or he's fighting to see his family again, or has the girl of his dreams)
• Guy goes on a fucking rampage
• Tough guy kisses his wife/wife-to-be while explosions/ruins lie in the background

For example:

There are so many fucking movies like this I don't even know where to begin.  I don't think it'd be an exaggeration to say half of all movies are this one action movie.

Let's compare to some videogames.

Hell, let's compare these movies to SOME GODDAM CARTOONS.

Shit, how about some goddam T.V. DRAMAS.

MOVIES HAVE BILLION DOLLAR BUDGETS!

THEY SPEND YEARS IN PRODUCTION!

WHY THE FUCK CAN'T THEY COMPARE TO THIS SHIT?!

GAAAAAAAAAAAAAAAAAAAAAAAAAAAAA!!!!!!!!!!!!!!!!!!!!!!!

I know every once in a while they do, but for all the resources involved you'd think it'd be better than the piss-shot they have now-a-days!

'Trivial' trivialities

I am slowly coming to the conclusion that...mathematicians should really stop saying that things are 'trivial'.

As a cultural phenomena, it typically engenders some pretty bad actions--namely, continually negative self-talk and derision.  It is really more a source of punishment, although most people in mathematics, including myself, do it with good intentions by hoping that we are really conveying the message, "Don't worry, this isn't too bad."  If you constantly berate yourself and others that stuff is simple, then when you do find a beautiful--elegant--proof, it will initially be a source of great displeasure.

It also encourages fairly one-sided thinking.  I.e., the slick proofs are typically the proofs that show something in a few lines.  If someone mathematically matures with such proofs, and creating such proofs, they tend to think more like every other mathematician (i.e., it creates a lack of creativity), and the harder, longer proofs will be less frequently come by.

Think, for example, of Posa's Soup Proof.

That proof is absolutely trivial!  Why didn't the mathematical community do this?!  How could we be so stupid?!

^Tl;dr, the above is not helpful.

Mathematical notation....and mathematical NOTAAAAAAAAAAAAAAAAAAAAAAAATION

There's mathematical notation.

And then there's mathematical notaaaaaaaaaaaaaaaaaaaation.

'Mathematical notation' includes all kinds of notation.  '+' is a symbol to denote addition, or 'e_i' refers to basis vectors, or even the picky stuff like 'capital letters refer to matrices and lower case letters refer to scalars'.  And, unfortunately as I'll get into, the VAST vast VAST VAST...vast?...VAST VAST VAST majority of 'mathematical notation' is what kind of letters stand for what (f,g,h are typically reserved for function, x,y,z for variables, etc.).

But then...then there's notaaaaaaaaaaaaaaaaaaaaaation.

Notaaaaaaaaaaation is the really big, fundamental stuff.  It's when some mathematician realizes that when you write something in a different way, it completely changes your conception of the world.

Here is an example:

'x+y'

This is a standard, basic, operation.  But the point is that if this is the notation you have, while analysts can use it quite well and all, it is really suited more for algebraists.  However, rewrite the above as:

'+(x,y)'

And now just writing it so differently has changed the conception completely.  Now instead of thinking of it as an operator, it is a function.  It certainly made sense before to think of '+' as a function and to say it is continuous.  However, simply writing it in this form greatly pedagogically clarifies the matter.  The notation is reflecting the paradigm of thought.

When notation can do that, then it's notaaaaaaaaaaation.

But, then there's even bigger notaaaaaaaaaaation.  This is stuff like...the guy who first thought of writing:

A->>B

Meaning A maps surjectively into B.  Modern module theory would not have been possible had someone not thought of making these arrow-chasing diagrams of modules, with each arrow representing a different kind of map (surjective, injective, etc.).  Notaaaaaaaaaaaaaation also involves a way of just being able to even represent certain things.

To a certain extent, I suppose this is time dependent.  Whereas now-a-days saying 'x' stands for a variable is just notation, when the first mathematician thought of representing algebraic equations by x's and y's, that was first class notaaaaaaaaaation; although now-a-days it's rather taken for granted.

Often, I think now that mathematicians have a few stages:

-Average mathematicians slightly generalize a result, or show a certain, VERY specific counterexample.
-Good mathematicians create new results, or completely pathological counterexamples.
-Great mathematicians develop amazing notation and definitions.
(FWIW, I'm a bad mathematician :P)

I suppose for possibly this reason, I might controversially say that Leibnitz was a better mathematician than Newton.  He developed first-rate notation that enabled calculus to really get going.  (nonetheless, Newton was a great mathematician as well by this criteria, as he did invent some notation that caught on at least in physics (the dot notation)).

FWIW, I remember talking to Charles Von Loan, and he very much thought of tensors and tensor product as notaaaaaaaaaaation for the upcoming generation.

Halmos is Batman

I suppose you can find me saying something similar to this at amazon, but either way....

PRAISE FOR HALMOS.

Something I like about Halmos is that he actually details his FAILURES (gasp!).  He detailed when he failed from graduate school in philosophy, his hardship in becoming an assistant or getting a job. I certainly learned a lot from Halmos' successes, but I felt I learned a lot more in his detailing of his failures.
The reason I am pointing this out in such detail is because if you read other biographies of other famous scientists, you get the feeling that you have to have been doing hardcore science since you were 15, have excelled in every path you came across, and finished your PhD by your 21st birthday; and if you don't you're a miserable failure of a human being. Halmos is the antithesis of these stories. Halmos story shows that you can do math if you thunk around everywhere, so long as you keep your nose to the grindstone and like what you're doing, and gives valuable advice about HOW to do this. Halmos wasn't born with some superhero genetics or superpowers.

Halmos is the Batman.

Siesta

Argentina has this tradition of siestas.  The town closes down and everyone goes to bed in the middle of the day.

I love siestas.

The "Let's Have Fun" Urge

One more thought.

Connected with the experience of boredom, is a reaction to this experience--something which I like to call the "Let's Have Fun Urge".  Whereas boredom, in my experience, always comes before LHF, there are instances in which one can be bored and not have LHF.  Also, although a Behaviorist would/should argue that LHF will eventually die out, in my experience it does not.  It can continue for endless hours or even days if you let it.  Really, psychologically, it is very similar to the physical pain of, say, a canker sore.  It will remain omnipresent and constantly grate at your attention until you do something about it.

I very much like the analogy to a canker sore, it seems to suit the emotion very well...

However, while with boredom there might be a possibility of a cognitive shift of such an emotion to something more akin to 'mono no aware' or something similar...I have not found a similar strategy for LHF.  It is constant, annoying, and does not go away.  Now, the common response to this is, typically, to not let it go away.  And, instead, to succumb to it.  I really dislike this response.  I like to think that I'm not an automaton, that I'm not a slave to my desires.  And, at the very least, personal freedom is the most immediate aspect of one's self that remains readily amenable to be worked upon.