3 ms·
A half-life of 10,000 years means the fraction (0 to 1) of healthy bonds at year t can be modeled by (1/2)^(t/10000). To have 1% bonds broken, it would take an
by ReaLNero 5y ago
A half-life of 10,000 years means the fraction (0 to 1) of healthy bonds at year t can be modeled by (1/2)^(t/10000). To have 1% bonds broken, it would take an expected 145 years.
EDIT: Fixed the numbers, my bad!
- vient 5y ago>>> log(0.99, (1/2)**(1/10000)) 144.99569695122509
- jdmoreira 5y agoI don't understand this. Does half-life even say anything else about the probability distribution? aren't you assuming specific distribution here?
- dekhn 5y agohalf lives (specifically, the "decay" of any individual thing is stochastic but the aggregate of many molecules models exponential decay (in radioactivity. I have no idea what happens in a complex mash of DNA)
- sannee 5y agoIt's not a terrible assumption to make. We just need to assume[1] that the decay events are independent, that is, every bond flips a coin every 500 years and if it comes up heads, it breaks, independent of what the other bonds do. That is, the process is inherently "local", individual bonds having no way of knowing what the other bonds are doing. [1] It may be a bit worse in the long run, since if many bonds break, the higher order DNA structure gets damaged and that may change the rate of decay experienced by individual bonds (?).
- cochne 5y agoYour 15 years number is for 0.1%
- stocknoob 5y agoThis shows the importance of mental gut checks. If indeed 1% break after 15 years, then 10% (ignoring compounding) break after 150 years, and 50% after 750 years. That doesn’t square with a half life of 10,000.
- ReaLNero 5y agoI always forget Bernoulli's inequality. Your gut isn't as clever as mine :)