Mandelbrot’s work on phone line errors is more upstream than downstream of fractals, but produced legible economic value by demonstrating that phone companies couldn’t solve errors via their existing path of more and more powerful phone lines. Instead, they needed redundancy to compensate for the errors that would inevitably occur. Again I feel like it doesn’t take a specific mathematical theory to consider redundancy as a solution, but that may be because I grew up in a post-fractal world where the idea was in the water supply. And then I learned the details of TCP/IP where redundancy is baked in.
Huh, I thought all of this was covered by Shannon information theory already.
The paper Gleick was referring to is this one, but it would be a lot of work to discern whether it was causal in getting telephone companies to do anything different. It sounds to me like the paper is saying that the particular telephone error data they were looking at could not be well-modeled as IID, nor could it be well-modeled as a standard Markov chain; instead, it was best modeled as a statistical fractal, which corresponds to a heavy-tailed distribution somehow.
What happened with Approximate Entropy was that Chaos could be useful, it just wasn’t as useful as a pure information theory derived solution. Wouldn’t surprise me if that were true here as well.
Gleick gives Mandelbrot credit for this, but it wouldn’t be the first major misrepresentation I’ve found in the Gleick book.
I know someone’s gonna ask so let me share the most powerful misrepresentation I’ve found so far: Gleick talks about the Chaos Cabal at UC Santa Cruz creating the visualization tools for Chaos all on their own. In The Chaos Avante Garde, Professor Ralph Abraham describes himself as a supporter of the students (could be misleading) and, separately, founding the Visual Math Project. VMP started with tools for undergrads but he claims ownership of chaos work within a few years. I don’t know if the Chaos Cabal literally worked under Abraham, but it sure seems likely the presence of VMP affected their own visualization tools.
Huh, I thought all of this was covered by Shannon information theory already.
Yes, this sounds more like noisy channel coding theorem. But presumably what is meant are these “fractal antennas”.
The paper Gleick was referring to is this one, but it would be a lot of work to discern whether it was causal in getting telephone companies to do anything different. It sounds to me like the paper is saying that the particular telephone error data they were looking at could not be well-modeled as IID, nor could it be well-modeled as a standard Markov chain; instead, it was best modeled as a statistical fractal, which corresponds to a heavy-tailed distribution somehow.
What happened with Approximate Entropy was that Chaos could be useful, it just wasn’t as useful as a pure information theory derived solution. Wouldn’t surprise me if that were true here as well.
Gleick gives Mandelbrot credit for this, but it wouldn’t be the first major misrepresentation I’ve found in the Gleick book.
I know someone’s gonna ask so let me share the most powerful misrepresentation I’ve found so far: Gleick talks about the Chaos Cabal at UC Santa Cruz creating the visualization tools for Chaos all on their own. In The Chaos Avante Garde, Professor Ralph Abraham describes himself as a supporter of the students (could be misleading) and, separately, founding the Visual Math Project. VMP started with tools for undergrads but he claims ownership of chaos work within a few years. I don’t know if the Chaos Cabal literally worked under Abraham, but it sure seems likely the presence of VMP affected their own visualization tools.