Thursday, November 01, 2007

Groups, Lies, and Assholes

A while ago I was browsing the web for a book on Lie-Groups. I got several hits in the psychology department on lies, group psychology and self-deception, which was the inspiration for this post. Before I go on, a sentence for the pedagogic value of this blog: a Lie Group is maths thingy which underlies our current understanding of the Standard Model. It's named after Marius Sophus Lie, who was Norwegian, so the pronunciation is actually Lee-Group, and it's got nothing to do with lying.

Okay, that was about it with the scientific content of this post.

Now here comes my personal group theory, addressing the question what makes a group work well, such that members get along, act in common interest, are supportive to each other, are able to solve occurring problems within the group, as well as conflicts between the group and others. Most importantly, what is necessary for a group to succeed in working towards its goals?

Here is what Hollywood taught me: No matter what the size of the group, it needs at least sufficient members to fulfil four different tasks.

  1. A Soul
    Most importantly the soul of a group reflects the group identity. He or she typically is the source of encouragement and motivation, the first to stand up after a defeat, the dreamer and the visionary. Though not necessarily a leader, he or she is the person who keeps the group alive by reassuring coherence. There's no working towards a goal without knowing the goal. In movies, the soul is typically the narrator or the hero of the story.

  2. A Brain
    Nothing works without somebody who knows how to make a vision reality. The brain's task is to work out the plan and take care of the details. He or she is usually an efficiently working no-fuzz person, and enables the group to practically get where vision aims at. In movies, the brain is often a scientist with a large nerd-factor, which provides a source for gags and jokes.

  3. A Heart
    The heart listens to concerns, offers comfort and is good with understanding the group member's individual problems. He or she is responsible for the human touch, usually very sensitive to internally occurring trouble, good with negotiation and has a skill for counseling. In movies the heart is often in conflict with #4...

  4. An Asshole
    Or call it an outsider. The asshole's task is to criticize and to question the existence and goals of the group, to try differently, to stumble and fall. He or she typically offends group members with opinions that go against the group identity, but also prevents them from taking their self chosen task too seriously. In movies the asshole is usually responsible for the sarcasm and cynicism.

These functions need not necessarily be fulfilled by four different people. In some cases one person might fulfil several tasks, or one task might be shared among different people. 1 and 2 often need to cooperate when it comes to leadership and organizing group activities.

A nice example are The Fantastic Four

The brain - Mr. Fantastic
The heart - The Thing
The soul - The Invisible Women
The asshole - The Human Torch

And there's Sex and the City

The soul - Carrie
The heart -Charlotte
The brain - Miranda
The asshole - Samantha

Can somebody fill me in whether it works for the A-team (can't recall the details) or the Desperate Housewives (I never saw it)? There are other examples that came into my mind, but few of you will know them (e.g. TKKG).

A common alteration of the theme is to internalize the asshole through self-doubts of the main character, which reduces the core group to three. This works better in books than in movies. Examples for this are Harry Potter (soul + asshole), Hermione (brain) and Ron (heart). Or there is the Lord of the Rings with Frodo (soul + asshole), Gandalf (brain) and Sam (heart).

Another frequently used modification is to export the brain to a mysterious outsider, or to the wisdom of a larger group, like e.g. Star Wars exports the brain to 'The Force', which leaves us with the soul -Luke, the heart - Leia, and the Asshole - Han Solo.

Of course you can have larger groups, but these four core functions are usually present among them, and most other characters are, except for their entertainment value, exchangeable.

What I found most interesting when I thought about it is the relevance of the outsider to the group's functionality. Most often, a plot wouldn't move anywhere without such a person.

Therefore the bottomline is: Never underestimate the asshole-factor.


CapitalistImperialistPig said...

Lemme See:


Rumsfeld = Asshole

Cheney = Asshole

Bush = Asshole

Houston, I think we have a problem.

Anonymous said...

I thought Leia was pretty clearly *also* an asshole in the Star Wars movies?

Arun said...


:) :) :)

But the great state of Texas gave us this problem, so, calling Houston won't help :)

Movie just for you. I'm now wondering whether the beehive follows the same pattern.

Bee said...


:-) Very insightful. Though I think you use the term 'asshole' in a slightly different meaning than I do. If you want to push it, I'd say a group that contains only assholes is dysfunctional because it has no asshole.

Hi Anonymous:

How so? Didn't she always stay behind the mission? Sorry, it's been like ~10 years that I saw the movies last time, so please enlighten me.

Dear Arun:

Thanks for reminding me, I think I mentioned that movie elsewhere let me see ... here, but I had almost forgotten about it (if nothing else then the blog is good to show I had heard of 'it' before, whatever 'it' is). I can't say though it's the kind of movie that I'd call a must see. Do you plan on seeing it? If so, let me know whether it's worth the time.

May the force be with you


Paolo said...

Well, any suggestions for an actual Lie Groups book? As strange as it seems, I'm having trouble finding one for my needs: physical slant (but not too much crystallography), good coverage of the Lorentz group, ... Thanks anyway...

Arun said...

Dear Bee,

It is some of those days for me where, while thankfully nothing goes wrong, nothing goes right either!

So I could use a serious fellow-traveller in the force. But I generously can spare some for you.


Anonymous said...

I think the Perimeter Institute just last month acquired an absolutely gargantuan Official Asshole.....

Arun said...

Sorry for being off-topic, but I thought Stefan might like this one:

"- A hobby historian has discovered the oldest known recipe for German sausage, a list of ingredients for Thuringian bratwurst nearly 600 years old."

CapitalistImperialistPig said...
This comment has been removed by the author.
CapitalistImperialistPig said...

I think any successfull group needs an identity, or zero. It's usually easy to find a zero for a group - but you really can't afford to have more than one. If you add another member, then you will also need an inverse - someone who negates everything the second member does. Fortunately again, it's usually not hard to find someone who is his own inverse, so two element groups are also stable. With three element groups, it never works out unless you can get them to associate, and for four or more you can't even get them all to commute, so committee meetings are a real problem.

Lie Groups pose special problems since you can hardly ever get together enough people (infinitely many, for example) who can do the algebra - oh they all claim they can, but most Lie.

Uncle Al said...

Uncle Al happily assumes the distal and proximal extrema. Clever plus evil is a satisfying synthesis. The really nasty parts are in the middle - in the trenches - where callouses, mud, and panic rule.

Bush the Lesser is stupid, corrupt, and a poltroon. First rate people retain first rate people; second rate people retain third rate people.

Anonymous said...

I have nothing really clever to add, but internalizing the asshole sounds terribly painful.

Anonymous said...

A Group can contain any types of people you want. However, a group tasked to perform work with defined result is more commonly called a Team. A team frequently contains the 4 types mentioned. But a team is doomed to failure without a type called Leader.

QUASAR9 said...

lol CIP, I agree with Bee
if all the orifices (eyes, ears, nostrils, et al) are assholes ...

QUASAR9 said...

I was going to say in the human analogy arseholes are essential.
If not just remember what being constipated feels like.

Actually is there a defining point in biology when 'life' needs an arsehole to get rid of waste and/or excess food (energy intake).

Apologies if that is an asshole question.

PS - So the Torch burns 'crap'
can you fill me in on what is it Samantha does?

The A-Team is like the fantastic four, the brain, the muscle ... and I guess instead of the chic they had 'face' (who gets the chics), and the 'nutter' who hates flying is meant to be like torch?

Anonymous said...

The best groups are finite simple groups of order two.

CapitalistImperialistPig said...

Anon - finite simple group of order two - very cool. Do you know where it was videoed?

Bee said...

Hi Paolo:

Well, yes, this was of course the actual reason for my search. The standard choice is Georgi's book which covers the basics. My problem is that a long time ago I had lecture notes from a Prof in our maths department which were much better, so I am still looking for a book that lives up to this.

Dear Arun:

There's no wrong and no right, and no spoon either ;-)

Hi Anonymous II:

No comment.


Yeah, truth spoken. That's why I don't do well in groups, there's usually no B^-1.

Hi Anonymous III:

Your comment about internalizing assholes was the last I read yesterday evening, I laughed my a** off ;-)

Hi Anonymous IV:

I am not a big believer in top-down approaches. Most often it's too cheap and fails easily. There might be somebody being an 'official' leader, but he needs people behind him. I don't think one person fulfilling all the 4 tasks above works very well. Esp. if you have a group with very intelligent people, leadership can be very difficult.

Hi Quasar:

Well, the torch is the guy who (in the movie) leaves the group and tries to get famous with his abilities. Samantha is the one who is rather cynical about love and relationships altogether (it's all about sex, obviously).

Hi Anonymous V:

Ahrr, Ohr, well, they sing nicely but could need a better songwriter.



Anonymous said...

Hi Bee,

You probably don't remember me
from my e-mail a couple of weeks
ago : I'm the guy with the Phd
in algebra who makes a living as
a petty beaureaucrat for the USDA and studies applications of algebra to physics on his own -- or at least tries to.
So, first some books I've found
helpful --

( 1 ) A Course in Differential
Geometry and Lie Groups
( S. Kumaresan )

For somebody, like me, with not
much background in Diff. Geo. this
was a good start.

( 2 ) Lie Groups, Lie Algebras,
and Representations -
An Elementary Introduction
( Brian C. Hall )

Concentrates on matrix Lie groups,
which is OK for physics applications.

( 3 ) Representations of Compact
Lie Groups
( Brocker - tom Dieck )

( 4 ) Lie Groups - Beyond an
( Anthony Knapp )

Despite the title, I found this
to be quite readable -

( 5 ) Lie Groups and Algebras
with Applications to
Physics, Geometry and
( D.H. Sattinger )

If a pure mathematician asked me
'What's a quark?' , I'd give him
this reference --

( 6 ) Emergence of the Theory
of Lie Groups : An Essay
in the History of Matematics-
( Hawkins )

Well-told history with great period
photos -- and a healthy dose of
mathematics too - Some great anecdotes : Lie loved to hike about
Europe ; to keep his clothes dry
when it rained, he would put his
clothes in his backpack and hike
in the nude !

( 7 ) Supersymmetry for
Mathematicians :
An Introduction
( V.S. Varadarajan )

I was please to find that, since
I already knew something about
graded Lie algebras and Clifford-
Lie algebras, I could read more
of this than I intially expected.

I am not much a part of any
group lately - but not because
I am the habitual 'asshole' --
Would love to find study partners
for applications of Clifford algebras in physics, and SUSY in
particular - I'd try to be the
'soul' of the group ---


p.s. Bee, you and Stephan ROCK!

Diana said...

Star Trek (original series):

Heart: Captain Kirk
Soul: Bones
Brain: Dr. Spock, Sulu (was a physicist), Scotty
Asshole: Everyone except Lt. Uhura!

Anonymous said...

Hi Bee,

we all need an A!

Some 10yrs ago I read Hawking's "brief history of time".

To illustrate the need for 3 dimentions for living creatures to exist there was a drawing of a a 2-dimentional dog.

the poor dog was now separated in two! divided my the tract for food "intake and processing" starting at the mouth and ending at the "A".

I think, that my dachshund would find a way around this problem :-)



stefan said...

Hi Arun,

Sorry for being off-topic, but I thought Stefan might like this one

true :-), that's a cute story, the oldest receipe for Thüringer Bratwurst...

Hi Tim,

thanks for the nice words, and the book suggestions - maybe I can have a look at some of them.

I learned about Lie groups and algebras in a seminar based on the Sattinger/Weaver text - that's really an interesting book, with many examples from very diverse backgrounds. But at times, it's easy to get lost because it touches so many topics.

But I am still looking for "the" book about Lie groups and algebras - those I've seen so far are either mathematical with some add-on physics, but where the connection (say, via a kind of dictionary math-physics) is quite loose, or physics books which are a bit sloppy on the side of maths...

Best, Stefan

Bee said...

Hi Diana:

I tried Star Trek as well, but I'd have made Scotty the asshole? No? Best,


Anonymous said...

This is almost isomorphic to my own concept of 'centers' as illustrated by South Park

Stan - Moral Center - soul
Kyle - Intellectual Center - brain
Cartman - Comic Center - asshole

Not sure where the other one goes.

Paolo said...

Just wanted to thank bee and anonymous for the references... About Georgi's book, the irony is that my "requirement" about the good treatment of the Lorentz group was meant to exclude it ;) Anyway, in the same spirit (I think):

but, as said, I'm really looking for something slightly different... Let's look into anonymous' suggestions... Thanks again.

Alejandro said...

The TV tropes wiki (warning! dangerous time sink!) includes general descriptions with many examples of the Four Temperament Ensemble and of the Four Girl Ensemble. They don't seem to fit exactly with your categories, though.

stefan said...

Hi Paolo,

my "requirement" about the good treatment of the Lorentz group

Do you know "Relativity, Groups, Particles" by Sexl and Urbantke? It's about representation theory of the Rotation, Lorentz, and Poincaré groups.

Best, Stefan

Diana said...

Yes, Scotty may well have been the most consistently assholic, but they all had their moments, except Uhura. She was always a class act, except when under alien mind control.

Pat said...

Nobody's really addressed the A-Team, so let me give it a try:

Soul: Hannibal, no question. Without his leadership, the team wouldn't have lasted a week. He kept them focused on their true role in the world -- helping those in need -- when otherwise they might have focused on making money and evading capture. It's because of Hannibal that the A-Team were heroes instead of merely being mercenaries.

Brain: Also Hannibal. "I love it when a plan comes together." It was almost always his plan. The others were tactically competent, but Hannibal was the one formulating strategy.

Heart: Murdock. Yes, he was crazy, but he was also upbeat and gung-ho, no matter how badly things went wrong. Murdock never gave up, never complained, always pulled his weight. You knew he had your back.

Asshole: B.A. and Face shared this role. Face did it mainly by whining about all the crap he had to put up with. B.A. did it by picking on Murdock and B.A. and doing his best to avoid getting on an airplane. But when all hell broke loose, both of them stopped bickering and charged into battle.

Molon Labe said...

Re South Park

The heart is played by the setting itself...South Park, CO

Anonymous said...

I prefer Trey Parkers' triumvirate of dicks, pussys and assholes (from the closing speech in Team America). It has a simple beauty to it...