six degrees

14 Guests, 0 Users

Humor is the only test of gravity, and gravity of humor; for a subject which will not bear raillery is suspicious, and a jest which will not bear serious examination is false wit. ~ Aristotle

Advanced search

Dilber MulticolorMarley TPSMF Default Theme -

[marshall]

I caught an interesting program on the science channel last night about how the Kevin Bacon six degrees of separation game has inspired a new type of science, network science which has now been applied to many fields as the phenomena appears nearly universal within complex systems. Any one catch wind of that?

[Francis]

No but from what you've said it reminds me of the Kalman filter. Interesting stuff. Does Bacon have a website?

The Kalman filter is an efficient recursive filter that estimates the state of a linear dynamic system from a series of noisy measurements. It is used in a wide range of engineering applications from radar to computer vision, and is an important topic in control theory and control systems engineering. Together with the linear-quadratic regulator (LQR), the Kalman filter solves the linear-quadratic-Gaussian control problem (LQG). The Kalman filter, the linear-quadratic regulator and the linear-quadratic-Gaussian controller are solutions to what probably are the most fundamental problems in control theory.
... Example applications
An example application would be providing accurate, continuously updated information about the position and velocity of an object given only a sequence of observations about its position, each of which includes some error. For example, in a radar application where one is interested in tracking a target, information about the location, speed, and acceleration of the target is measured at each time instant with a great deal of corruption by noise. The Kalman filter exploits the trusted model of the dynamics of the target, which describes the kind of movement possible by the target, to remove the effects of the noise and get a good estimate of the location of the target at the present time (filtering), at a future time (prediction), or at a time in the past (interpolation or smoothing).

Alternatively, consider an old slow car that is known to go from 0 to 60 miles per hour (mph) in no less than 10 seconds. The speedometer on this car however shows very noisy measurements that vary wildly within a 40 mph window around the actual speed of the car. From stop – which is measured with certainty because the wheels are not turning – the driver of the car pushes its gas pedal as far as possible. Five seconds later, the speedometer reads 70 mph. The driver concludes that the slow car cannot be traveling that quickly and uses information about the known speedometer noise to conclude that the car is likely traveling at 30 mph instead. Similarly, a Kalman filter uses information about noise and system dynamics to reduce uncertainty from noisy measurements.

[Francis]

The kalman filter makes use of a recursive algorithm that employs fuzzy logic to find the shortest path to finding a target. The six degrees calculation is a variation on the Travelling Salesman Problem: Given a list of cities and their pairwise distances, the task is to find a shortest possible tour that visits each city exactly once.

http://en.wikipedia.org/wiki/Traveling_salesman_problem

The computation of a Bacon number for actor X is a "shortest path" algorithm:
•   If the lowest Bacon number of any actor with whom X has appeared in a movie is N, X's Bacon number is N + 1.
•   Kevin Bacon himself has a Bacon number of 0.
Here is an example, using Elvis Presley:
•   Elvis Presley was in Change of Habit (1969) with Edward Asner
•   Edward Asner was in JFK (1991) with Kevin Bacon
Therefore Asner has a Bacon number of 1, and Presley (who never appeared in a film with Bacon himself) has a Bacon number of 2.