There are three things that grate me in this review (or, may be, in the book as well, I am yet to read the book). All three have to do with exponentials.
1. The hockey stick chart with world economic growth does not prove that we live in an exceptional time. Indeed, if you take a chart of a simple exponential function y=exp(A*x) between 0 and T, then for any T you can find a value of A such that the chart looks just like that. An yet there is nothing special about that or another value of T.
2. I do not see why economic growth is limited by the number of atoms in the universe. It looks to me similar to thinking in 1800 that economic growth is limited by the number of horses. We are already well past the time when most of economic value was generated by tons of steel and megawatts of electricity. Most (90%) of book value in S&P500 is already intangible, i.e. not coming from any physical objects but from abstract things such as ideas and knowledge. I do not see why the quantity of ideas or their value relative to other ideas would be limited by the number of atoms in the universe. If anything, I could see an argument why it there is growth limit of the number of sets consisting of such atoms, which is much larger (it is 2^[number of atoms]) and, at our paltry rates of economic growth, is large enough to last us until the heat death of the universe.
3. All these pictures with figures of future people are relevant only in the absence of discounting aka the value of time. I do not know if the book ignores this issue but you do not mention it at all in the review. Any calculation comparing payoffs at different times has to make these payoffs somehow commensurate. That's a pretty basic feature of any financial analysis and I am not sure why it would be absent in utility analysis. When we are comparing a benefit of $10 in 10 years time to a current cost of $1, it makes no sense to simply take the difference $10-$1. We should divide the benefit by at least the inflation discount factor exp(-[inflation rate]*10). If we have an option to invest $1 today in some stocks, we should additionally multiply by exp(-[real equity growth rate]*10). When our ability to predict future results of our actions decays with time horizon, we should add another exponential factor. This kind of discounting removes a lot of paradoxes and also kills a lot of long-termist conclusions. This argument gets a bit fuzzier if we deal with utilities and not with actual money, but if the annual increase of uncertainty is higher than the annual population growth rate then the utility of all future generations is actually finite even for an infinite number of exponentially growing generations. So not all small probabilities are Pascalian but ones deriving from events far from the future definitely are! I do not know if this is discussed in the book but any long termism discussion seems to be pretty pointless without it.
There are three things that grate me in this review (or, may be, in the book as well, I am yet to read the book). All three have to do with exponentials.
1. The hockey stick chart with world economic growth does not prove that we live in an exceptional time. Indeed, if you take a chart of a simple exponential function y=exp(A*x) between 0 and T, then for any T you can find a value of A such that the chart looks just like that. An yet there is nothing special about that or another value of T.
2. I do not see why economic growth is limited by the number of atoms in the universe. It looks to me similar to thinking in 1800 that economic growth is limited by the number of horses. We are already well past the time when most of economic value was generated by tons of steel and megawatts of electricity. Most (90%) of book value in S&P500 is already intangible, i.e. not coming from any physical objects but from abstract things such as ideas and knowledge. I do not see why the quantity of ideas or their value relative to other ideas would be limited by the number of atoms in the universe. If anything, I could see an argument why it there is growth limit of the number of sets consisting of such atoms, which is much larger (it is 2^[number of atoms]) and, at our paltry rates of economic growth, is large enough to last us until the heat death of the universe.
3. All these pictures with figures of future people are relevant only in the absence of discounting aka the value of time. I do not know if the book ignores this issue but you do not mention it at all in the review. Any calculation comparing payoffs at different times has to make these payoffs somehow commensurate. That's a pretty basic feature of any financial analysis and I am not sure why it would be absent in utility analysis. When we are comparing a benefit of $10 in 10 years time to a current cost of $1, it makes no sense to simply take the difference $10-$1. We should divide the benefit by at least the inflation discount factor exp(-[inflation rate]*10). If we have an option to invest $1 today in some stocks, we should additionally multiply by exp(-[real equity growth rate]*10). When our ability to predict future results of our actions decays with time horizon, we should add another exponential factor. This kind of discounting removes a lot of paradoxes and also kills a lot of long-termist conclusions. This argument gets a bit fuzzier if we deal with utilities and not with actual money, but if the annual increase of uncertainty is higher than the annual population growth rate then the utility of all future generations is actually finite even for an infinite number of exponentially growing generations. So not all small probabilities are Pascalian but ones deriving from events far from the future definitely are! I do not know if this is discussed in the book but any long termism discussion seems to be pretty pointless without it.