The mathematics of opinion formation

Here’s something to drive innumerate spin-doctors wild: a mathematical theory of opinion formation by Fang Wu and Bernardo Huberman of HP Labs. Abstract reads:

We present a dynamical theory of opinion formation that takes explicitly into account the structure of the social network in which individuals are embedded. The theory predicts the evolution of a set of opinions through the social network and establishes the existence of a martingale property, i.e. that the expected weighted fraction of the population that holds a given opinion is constant in time. Most importantly, this weighted fraction is not either zero or one, but corresponds to a non-trivial distribution of opinions in thelong time limit. This coexistence of opinions within a social network is in agreement with the often observed locality effect, in which an opinion or a fad is localized to given groups without infecting the whole society. We verified these predictions, as well as those concerning the fragility of opinions and the importance of highly connected individuals in opinion formation, by performing computer experiments on a number of social networks.

So now you know. The paper has lots of nice equations of the kind that make some people’s eyeballs revolve. But, at heart, it reaches reassuringly obvious conclusions. For example,

Our theory further predicts that a relatively small number of individuals with high social ranks can have a larger effect on opinion formation than individuals with low rank. By high rank we mean people with a large number of social connections. This explains naturally a fragility phenomenon frequently noted within societies, whereby an opinion that seems to be held by a rather large group of people can become nearly extinct in a very short time, a mechanism that is at the heart of fads.

These predictions, which apply to general classes of social networks, including power-law and exponential networks, were verified by computer experiments and extended to the case when some individuals hold fixed opinions throughout the dynamical process. Furthermore, we dealt with the case of information asymmetries, which are characterized by the fact that some individuals are often influenced by other people’s opinions while being unable to reciprocate and change their counterpart’s views.

Gadget wars (contd.)

Bah! Quentin has a new toy.

It’s the Sony PRS – the Portable Reader System – which is a bit like a giant read-only PalmPilot that uses the new e-Paper type display. It’s designed to be a replacement for a paperback – a way of viewing eBooks, and unlike some earlier devices, it’s not limited to DRM-encoded books downloaded from the manufacturer. You can put text files, RTF files, PDF files on it as well, and they look gorgeous.

However, there was a big question-mark over my purchase, which was that there is no official Mac or Linux support for this device. You can use a card reader to plug an SD card into your Mac, copy the files onto it and then plug it into the PRS, but that’s hardly convenient, especially in comparison to the (optional) USB docking station. Sadly, the PRS doesn’t just appear as a USB storage device. You can run the Sony software just fine under Windows using Parallels, but that’s yucky too…

Needless to say, he’s hacked it. He’s found a way to take an arbitrary document on his Mac and make it available as a pdf on the Sony device. See the full post for the grisly details.

Later… And to add insult to injury, he’s put Memex on it!

US generals ‘will quit’ if Bush orders Iran attack

From today’s Times Online

SOME of America’s most senior military commanders are prepared to resign if the White House orders a military strike against Iran, according to highly placed defence and intelligence sources.

Tension in the Gulf region has raised fears that an attack on Iran is becoming increasingly likely before President George Bush leaves office. The Sunday Times has learnt that up to five generals and admirals are willing to resign rather than approve what they consider would be a reckless attack.

“There are four or five generals and admirals we know of who would resign if Bush ordered an attack on Iran,” a source with close ties to British intelligence said. “There is simply no stomach for it in the Pentagon, and a lot of people question whether such an attack would be effective or even possible.”

A British defence source confirmed that there were deep misgivings inside the Pentagon about a military strike. “All the generals are perfectly clear that they don’t have the military capacity to take Iran on in any meaningful fashion. Nobody wants to do it and it would be a matter of conscience for them…

Server power

A new study by the Lawrence Berkeley National Laboratory (pdf available here) finds that:

Aggregate electricity use for servers doubled over the period 2000 to 2005 both in the U.S. and worldwide Almost all of this growth was the result of growth in the number of the least expensive servers, with only a small part of that growth being attributable to growth in the power use per unit.

Total power used by servers represented about 0.6% of total U.S. electricity consumption in 2005. When cooling and auxiliary infrastructure are included, that number grows to 1.2%, an amount comparable to that for color televisions. The total power demand in 2005 (including associated infrastructure) is equivalent (in capacity terms) to about five 1000 MW power plants for the U.S. and 14 such plants for the world. The total electricity bill for operating those servers and associated infrastructure in 2005 was about $2.7 B and $7.2 B for the U.S. and the world, respectively.

Nicholas Carr comments:

The estimate that servers account for 1.2 percent of overall power consumption in the U.S. is, as the San Francisco Chronicle reports, considerably lower than some previous estimates, which put data center power consumption as high as 13 percent of total U.S. consumption. It should be noted that the study, underwritten by AMD, looks only at power consumption attributable to servers, which represents about 60% to 80% of total data center power consumption. Electricity consumed by storage and networking gear is excluded. The study also excludes custom-built servers, such as the ones used by Google. The number of servers Google runs is unknown but is estimated to be in the hundreds of thousands.

It all goes to explain why Sergey Brin & Co are getting so exercised about power consumption.

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