So now what Montroll does is He goes trough and looks at the value of this two expectation values He looks at the value, in particular, of the average, alright? this one here, one of the two maximal entropy constraints and the he also looks at the value of this constraint right here how that changes over time So let's look at the average of the Log of the price This is the first that's constraint, because remember it's a gaussian distribution N(x), where x is Log(P) Logarithm of the price So, this are the two quantities that are being fixed if we wanna work in price space as opposed to Log of price space. So the first thing he points out, is that the average of the Log of the prices is a slowly increasing function of time except for a funny little 'blip' here, ok? So this is something you would expect, over time the average Log price, and in fact, the average price as well, is going to increase, and is going to increase solely because of inflation a good that costed a dollar ten years ago, would generally cost more than a dollar today. Inflation is a multiplicative process but what he draws your attention to is this column here this is the variance of the Log price over time and what you can see in the variance of Log of the Price is that over 75 years of the Sears-Roebuck catalogue and, it's important to say, both world wars, enormous social change, so, here they are selling buggy whips, and here they are selling cassette tapes enormous economic change, so certainly the overall prices have gone up, they go from 0.1 in Log price space to 4 in other words, prices increase by a factor of 2,4,8... 16, by a factor of 16 the variance of the Log of the prices stays almost constant is roughly a factor of 2, the deviation, in other words, from the average price, or the average Log price the square deviation from the average Log price is constant at around 2, over 75 years and Montroll sees "this is worthy of explanation" this here we already understand, we understand why prices grow but we don't understand why their variance stays constant why is it the case that the Sears-Roebuck catalogue presumably the stability in the catalogue here, and the catalogue here, an entirely different group why is it the case that that they where able to, or somehow ended up doing the following? keeping this variance constant and one of the things he notes is the following that lets say, in 1900 the Log price had a certain distribution and indeed a certain variance, sigma, in 1975 if every single good in the Sears Roebuck was still in the catalogue in 1975, and every single good inflated at the same rate then ok, yes, the mean would go up, the mean would go up but all this goods, all this columns here, would all grow by the same amount so if every price P was multiplied by the same factor alpha then of course every Log price Log P is simply added to Log alpha so ok, you would spect the variance to stay constant in that very particular case, other wise allowing for the natural drift of goods and in particular, allowing for different rates of inflation allowing for alpha, in particular, to be a random variable just has it was previously on our model of language growth once alpha becomes a random variable then generically speaking what's gonna happen is that the variance will rise because some goods will multiplicatively over time, just randomly accrue lots of really large multiplications they become expensive really quickly sort of like, let's say, college education, apparently and other goods, deflate, even though, become cheaper so one of the things you see in the Sears Roebuck catalogue is that women dresses become cheaper, because the materials to make them become synthetic, and then become better and better at making synthetic dresses so other goods, in fact, deflate quickly another good that deflates quickly, although is not presumably a dominant feature of the Sears Roebuck catalogue in the early years is computers, so the cost of a device with the same computing power something 10 years ago, is minuscule compared to the price it was then, even in absolute terms so there is some goods deflate enormously, some goods inflate enormously, in the organic larger scale consumer culture but what we find is, in the data, the deviations, the square deviations from the mean in Log space stay constant that's against the spectations that we have and the problem is to explain it.