3 ms·
Any study about "criticality" needs to be taken with a huge grain of salt. The standard methodology is that criticality is synonymous with power laws. And power
by knzhou 7y ago
Any study about "criticality" needs to be taken with a huge grain of salt. The standard methodology is that criticality is synonymous with power laws. And power laws are straight lines on log-log plots, with slope equal to the critical exponent.
So when anybody says "we showed X was critical", they actually mean "we plotted a fuzzy cloud of data points on a log-log plot and fitted a line through it", nothing more. But you can fit a line through anything. Even a normal distribution shows up as a line on a log-log plot if your data has a small enough range.
Criticality studies trade on the reputation of physics, where the idea came from, and there it works fantastically. For instance, we can measure critical exponents for liquid/gas phase transitions to three or four significant figures, and even predict those numbers from pure theory. Applications outside of physics usually have barely one significant figure, if they're even measuring power laws at all, and no predictive theory.
- NortySpock 7y ago"6. (Mar's Law) Everything is linear if plotted log-log with a fat magic marker." From "Akin's Laws of Spacecraft Design", https://spacecraft.ssl.umd.edu/akins_laws.html https://spacecraft.ssl.umd.edu/akins_laws.html
- pfdietz 7y agoI'm reminded of a story in Ulam's biography. John von Neumann was at a talk where the presenter had put up a slide with a cloud of points, and had optimistically drawn a line through the cloud. Von Neumann muttered, "at least they lie on a plane."
- hdrujvw-4579 7y agoI've been meaning to read that biography. if anything for its notes about Johnny von Neumann, who strangely doesn't have a biography of his own. https://www.amazon.com/Adventures-Mathematician-S-M-Ulam/dp/0520071549 https://www.amazon.com/Adventures-Mathematician-S-M-Ulam/dp/...
- Florin_Andrei 7y ago> But you can fit a line through anything. Only if the sample size is small enough.
- pixl97 7y agoOr if your spacetime is curved enough
- BlueTemplar 7y agoYou haven't RTFA, have you?
- knzhou 7y agoHuh, I stand corrected. My original complaint still applies to >99% of criticality studies, but the field might be coming around since the last time I looked into it, 3 years ago. Skimming through the papers, I'm still skeptical of how stringent a test their 'exponent relation' really is, but it's an improvement.