If Loud Aliens Explain Human Earliness, Quiet Aliens Are Also Rare
https://arxiv.org/pdf/2102.01522.pdf
Hard Step Model
- Carter (not sure where yet) posits that a sequence of steps each of which are acheived at some rate per unit time.
- The average time to complete a step is .
- How does it imply a power law of time?
Power Law
”A power law is a functional relationship between two quantities where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the size of the initial quantities”
If we have some observable thing A that’s related to another observable thing B by a power law. If A increased by 50%, then B would increase by x1.5 that is some constant times 50%.
How do I model A increasing as an exponential.
In a linear system, there is a constant relationship between A and B. It doesn’t change through time.
What if the relationship was further characterised by what B became for a given A? Fundamentally, the relationship is changing through time. The constant between the too is growing.