So in particular

and I'm summarizing
Montrell's argument here

what he says is the following

The way to explain this
feature of the data

is that the company as a whole

has this goal of keeping the
log prices to a constant spread

Now why keep log prices
to a constant spread?

Well there is potentially a
psychological explanation

that says

we tend to perceive things on

a multiplicative or logarithmic scale

we perceive things as being

twice as expensive or half as expensive

we don't perceive things as being

10 dollars more, 10 dollars less

this is a psychological feature

that we see not only on our perception

of social goods

like the cost of something

but also things like light

our perception of whether

something is brighter than another thing

we tend to perceive those multiplicatively

as opposed to additively

we are able to sense the difference

between one paperclip and two paperclips

in a way that we can't
sense the difference between

a brick, and a brick and a paperclip

even though

the additive amount is the same

the multiplicative amount in

the second case is much smaller

So, the idea is that the strategy

that Sears-Roebucks pursues

whether or not is conscious

is certainly a beneficial one

for the corporation as a whole

it makes it potentially, for example

easier to sell goods by keeping the range

not too large and not too small

and what happens

as we grow as a nation over time

and as people cycle through
the system of Sears-Roebucks

as they cycle trough the pricing system

and we go from, you know

selling dresses that look like this

to selling dresses that look like this

or women's cloths that look like this

people try all sorts of strategies

if they where trying
one particular strategy

if they had some really clever method

then you would not expect

the distribution to be so easily
described by two parameters

remember, the two parameters
for a log distribution

is the mean and the variance

the log normal distribution is

the mean and the variance

and in fact

if you believe Montrell's original claim

that the price distribution

is well represented

by this log normal distribution

what you're implicitly agreeing to

is the system is maximally disorganized

is maximally disorganized subject
to only two constraints

the mean and the variance

obviously the mean is gonna be constraint

because Sears is trying to target
a certain market

the idea is that the 
variance is also constraint

because Sears is trying to maintain

a psychologically plausible
distribution of prices

something that is able to market well

but the most interesting step

I think that gets made

is not just that observation

but the observation that

the maximum entropy says

that that's all that's happening

thats' the only structure
left in the system

all other kinds

of decision making patterns

so, for example

presumably, if you look in that data

and look at the pricing

and in fact Montrell brings it up

if you look at the pricing of guitars

you know there is a couple of guitars

priced here, maybe a couple out here

and may be there is two
right in the center

if you look at the pricing of dresses

maybe it looks like this

but overall, all this different
decisions that people make

add together incoherently

and what you're left with in the end

despite the fact

that there's billions of dollars

in getting the Sears catalogue right

despite the fact

that one of the mayor
corporations in the country

is obsessed with this particular question

all of the different
strategies that pursues

and all the different strategies

within each division that are pursued

add in some way incoherently

they add in some way so that all structure

all pattern that may have been left

by somebody having a great idea

about how to sell women dresses

or somebody having a great idea

about how to sell guitars

all those patterns wash out

and what's left behind is

a thermodynamic system

a system with a very small
number of constraints

so out of great complexity

comes great simplicity

and that's part of the reason why

max entropy methods have such a appeal

is a kind of paradox

that you should be able to describe

for example

a jungle the way John Hart does

by simply constraining two things, right?

the average abundance of the species

and the average energy
consumption of the species

if the open source
ecosystem argument is right

it seems remarkable that a system

that's politically froth
and socially froth

a system involving students and faculty

you know, billionaires at google, right?

and 12 year olds

and some guy in Finland

it seems remarkable that

you would even be able to describe

all of the outcomes of
those complex decisions

by such simple model

but that's exactly what
Max. Ent. allows you

at least, test the hypothesis

this brings me to a quote that I love

and I'm gonna read this to you

because I encounter this quote

in fact, before I came across
maximum entropy models

is a quote from a novel by C.P. Snow

so, Snow was an interesting man himself

he wrote a famous book
called "Two Cultures"

about the clash between art and science

but he was also a novelist

in addition to being a scientist

in addition to being a public intelectual

and in his book, "The Light And The Dark"

he focuses on a particular character

and this is the narrator talking

about what happens the hero
of the "The Light And The Dark"

he says

"Usually, decisions built
themselves from a thousand small

arrangements, ideas, compromises,
bits of give and take"

and what's he's talking about here

is he's talking about decision making
by the British government in world war two

"there is not much which has
decisively changed by human will

just has a plan for a military campaign

does not spring fully grown
from some master general

it arises from a sort of
brownian movement

of colonels, and majors and captains,

and the most the general can do is
rationalize it afterwards"

and I think that's at the heart
of the kinds of arguments

you can make using
maximum entropy methods

the arguments he make say essentially like

'you constraint a very small
number of quantities

and you can explain potentially an
enormous amount of richness in the system'

a system that seems like its
imposible to model from the ground up

how would you begin to build a model
of an open source community?

how many different kinds
of agents would you need?

how many different internal parameters
for the agents would you need?

would you need to sort of

would an agent be defined
by his education level?

His income, his amount of free time

and whether or not he's single?

or would an agent in the
Sears-Roebuck pricing scheme

would a CEO of Sears-Roebuck

would she need to be defined by

her experience within the fields?

and the amount of time she put in

and whether or not she
had training as a psychologist?

if you would have tried
to build from the ground up

agent based models of this systems

I think you would stall out

but instead by looking at
this aggregate quantities

by looking for example

the distribution of prices

or by looking at the distribution
of language abundances

you start to realize that

maybe a lot of those details don't matter

a lot of those details wash out

the particular dynamics

are not necessarily what you need to know

in oder to unterstand
the system a larger scale

you may be able to describe

the choice of languages in
the open source movement

by reference to maybe one or two

quantities

and you don't even have
to know those quantities

for any particular language

all you have to know is

their average abundance is fixed

and their average programmer
time investment is fixed.