We don’t know where is the tipping point, so uninformed prior gives equal chances for any T between 0 and, say, 20 C additional temperature increase. In that case 2C is 2 times more likely.
But the idea of anthorpic shadow tells us that tipining point is likely to be 10 per cent of the whole interval. And for 40C before moisture greenhouse it is 4C. But, interestingly, anthropic shadow tells us that smaller intervals are increasingly unlikely. So 1C increase is orders of magnitude less likely to cause a catastrophe than 4 C increase.
I will illustrate this as following example:
Imagine you are buying a used car which had run 300K miles. It is a unique survivor for its age.
If the car had 1 in 1000 chance to survive until its age, then doubling period of the probability of death (aka half-life) for it is 30K miles (10 doublings); if it had 1 in 1 000 000 chances to survive until current age, it has 20 doubling or 15K miles. The 1000 times growth of anthropic shadow lower car’s life expectancy only 2 times.
Future survival declines very slowly:
Anthropic shadow power 1 in 1000 = survival 10 per cent more
Anthropic shadow power 1 in 1000 000 = survival 5 per cent more.
Your calculations apply to an exponential distribution. Do we have reasons to choose an exponential prior over a uniform/loguniform prior for the location of the existential tipping point? I guess one possible disadvantage of the exponential prior is the lack of a maximum (which should arguably be assumed given our knowledge about moisture greenhouse), but this could be solved by using a truncated exponential.
I use exponential prior to illustrate the example with a car. For other catastrophes, I take the tail of normal distribution, there the probability declines very quickly, even hyperexponentially. The math there is more complicated. But it does not affect the main result: if we have anthropic shadow, the expected survival time is around 0.1 of the past time in the wide range of initial parameters.
And in the situation of anthropic shadow we have very limited information about the type of distribution. Exponential and normal seems to be two most plausible types for catastrophes. There is also semi-periodic ones, but they could be described as a sum of periodic plus normal.
We don’t know where is the tipping point, so uninformed prior gives equal chances for any T between 0 and, say, 20 C additional temperature increase. In that case 2C is 2 times more likely.
But the idea of anthorpic shadow tells us that tipining point is likely to be 10 per cent of the whole interval. And for 40C before moisture greenhouse it is 4C. But, interestingly, anthropic shadow tells us that smaller intervals are increasingly unlikely. So 1C increase is orders of magnitude less likely to cause a catastrophe than 4 C increase.
I will illustrate this as following example:
Imagine you are buying a used car which had run 300K miles. It is a unique survivor for its age.
If the car had 1 in 1000 chance to survive until its age, then doubling period of the probability of death (aka half-life) for it is 30K miles (10 doublings); if it had 1 in 1 000 000 chances to survive until current age, it has 20 doubling or 15K miles. The 1000 times growth of anthropic shadow lower car’s life expectancy only 2 times.
Future survival declines very slowly:
Anthropic shadow power 1 in 1000 = survival 10 per cent more
Anthropic shadow power 1 in 1000 000 = survival 5 per cent more.
Thanks for the reply!
Your calculations apply to an exponential distribution. Do we have reasons to choose an exponential prior over a uniform/loguniform prior for the location of the existential tipping point? I guess one possible disadvantage of the exponential prior is the lack of a maximum (which should arguably be assumed given our knowledge about moisture greenhouse), but this could be solved by using a truncated exponential.
I use exponential prior to illustrate the example with a car. For other catastrophes, I take the tail of normal distribution, there the probability declines very quickly, even hyperexponentially. The math there is more complicated. But it does not affect the main result: if we have anthropic shadow, the expected survival time is around 0.1 of the past time in the wide range of initial parameters.
And in the situation of anthropic shadow we have very limited information about the type of distribution. Exponential and normal seems to be two most plausible types for catastrophes. There is also semi-periodic ones, but they could be described as a sum of periodic plus normal.
But obviously there is more to dig here.