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.