The Technium

Where the Linear Crosses the Exponential

[Translations: Japanese]

Freeman Dyson is my favorite big picture thinker. He tackles the world with both his heart and his calculator. He enjoys entertaining suspect heresies just to see if he can learn anything from them. He’ll take an unusual position and then calculate what would happen if it were true. Do the rough numbers match with what else we know?

Dyson has just written one of the best analysis of the conundrum of global warming I’ve seen — disguised as a book review in the New York Review of Books. Using his unique ability to tease out new perspectives by estimating the physics of a phenomenon, his “review” offers three novel perspectives.

1) A speculative solution to global warming. He suggests bioengineering “deep carbon eating plants” because his calculations based on the famous Keeling chart show that plants could absorbed the extra carbon in one decade. I think this biotechnology is feasible. But I have doubts we would be able to implant them in wild species “covering one quarter” of the earth’s landmass as he figures we need to do, because these altered species would not (by design) behave or interact in the way their wild ancestors do. They would be markedly different by the very fact they are precipitating much more carbon. Maybe these deep carbon plants would work if planted at large scale in agricultural products. But to arrive at this speculation, Dyson’s summary of the problem is refreshing.

2) More interesting, Dyson has penned the best description of the new global religion, an emergent religion few others have noticed. I think he is 100% correct about this:

There is a worldwide secular religion which we may call environmentalism, holding that we are stewards of the earth, that despoiling the planet with waste products of our luxurious living is a sin, and that the path of righteousness is to live as frugally as possible. The ethics of environmentalism are being taught to children in kindergartens, schools, and colleges all over the world. Environmentalism has replaced socialism as the leading secular religion. And the ethics of environmentalism are fundamentally sound. Scientists and economists can agree with Buddhist monks and Christian activists that ruthless destruction of natural habitats is evil and careful preservation of birds and butterflies is good. The worldwide community of environmentalists—most of whom are not scientists—holds the moral high ground, and is guiding human societies toward a hopeful future. Environmentalism, as a religion of hope and respect for nature, is here to stay. This is a religion that we can all share, whether or not we believe that global warming is harmful.

3) But most importantly, and the reason why his essay is noteworthy for long term thinking, Dyson explains in brilliant clarity one of the key riddles for generational thinking: how much of a “penalty” today should this generation pay in order to ensure prosperity in the future?  Here’s Dyson on the riddle:

If we can save M dollars of damage caused by climate change in the year 2110 by spending one dollar on reducing emissions in the year 2010, how large must M be to make the spending worthwhile? Or, as economists might put it, how much can future losses from climate change be diminished or “discounted” by money invested in reducing emissions now?

This is called the “future discount.” Any long-term project must confront this calculation.

The conventional answer given by economists to this question is to say that M must be larger than the expected return in 2110 if the 2010 dollar were invested in the world economy for a hundred years at an average rate of compound interest. For example, the value of one dollar invested at an average interest rate of 4 percent for a period of one hundred years would be 54 dollars; this would be the future value of one dollar in one hundred years’ time. Therefore, for every dollar spent now on a particular strategy to fight global warming, the investment must reduce the damage caused by warming by an amount that exceeds 54 dollars in one hundred years’ time to accrue a positive economic benefit to society. If a strategy of a tax on carbon emissions results in a return of only 44 dollars per dollar invested, the benefits of adopting the strategy will be outweighed by the costs of paying for it. But if the strategy produces a return of 64 dollars per dollar invested, the advantages are clear. The question then is how well different strategies of dealing with global warming succeed in producing long-term benefits that outweigh their present costs.

The choice of discount rate for the future is the most important decision for anyone making long-range plans. The discount rate is the assumed annual percentage loss in present value of a future dollar as it moves further into the future.

Dyson then returns to the riddle of global warming. The two opposing views of the future discount rate in the books he is reviewing are Stern and Nordhaus.

In Stern’s view, discounting is unethical because it discriminates between present and future generations. That is, Stern believes that discounting imposes excessive burdens on future generations. In Nordhaus’s view, discounting is fair because a dollar saved by the present generation becomes fifty-four dollars to be spent by our descendants a hundred years later.

There are a number of ways to recast the same quandary. Is it okay to burn a lot of coal right now if it will lift millions out of poverty today, instead of burning less coal now and postponing poverty alleviation for later?  Will prosperity/pollution today deliver more to future generations or will environmental health/poverty today deliver more? If you were to be born of a future generation, what would you want? To be born into poverty or to be born into a clean world?

Shouldn’t we pass on both, prosperity and health? Sure, that is the goal. But what Dyson’s explanation of the future discount makes clear, there will always be a tradeoff. Almost by definition we cannot absolutely satisfy both the present generation and future generations. The needs of each — present and future — may overlap but they don’t coincide.

There is a very definite time preference for individuals. Almost without exception a person would prefer to have $1,000 today rather than $1,000 in fifty years from now.  But if you make the choice between $1,000 today and $30,000 fifty years from now, the two vie for preference. That difference between those two amounts — present and future — drives what we call interest — the amount of money someone will pay to have something now.  Some people will pay too much for current rewards, and may get stuck in a position of never being able to pay off their interest. So the rate of interest and the discount rate for the future need to be set wisely.

Societies also seem to have a time preference. All things being equal they would like to have prosperity now rather than later. How much are they willing to pay to have their reward now? Would they pay the price of dirty air, and climate change, and long-term debt in order to gain prosperity right now? They may, and they may also be willing to pay too much. The “interest” rate for immediate prosperity might be something that no future generation could every repay.

Furthermore, the push of technology accentuates the weirdness of the future discount. In some projects delay vastly increases the cost in the future. Waiting to maintain infrastructure such as roads and bridges means it requires ever more money to upgrade them as decay breeds decay. Neglect can be self-accelerating so it becomes almost impossibly expensive to repair what is seriously neglected. On the other hand, take Moore’s Law. If computers are half as cheap and twice as fast every year into the future, then it makes sense to delay some very computational challenges. Many biologists suggested it made the most economical sense to delay sequencing the human genome.  You could wait a few years for the technology to evolve and then once it was cheap it would overtake the quick start as the efficiency and speed doubled each year. Thus it would be cheaper and faster to wait.

All extropic  systems — economy, nature and technology — are governed by self-accelerating feedback cycles. Like compounding interest, or virtuous circles, they are powered by increasing returns. Success breeds success. There is a long tail of incremental build up and then as they keep doubling every cycle, they explode out of invisibility into significance. Extropic systems can also collapse in the same self-accelerating way, one subtraction triggering many other subtractions, so in a vicious cycle the whole system implodes. Our view of the future is warped and blinded by these exponential curves.


But while progress runs on exponential curves, our individual lives proceed in a linear fashion. We live day by day by day. While we might think time flies as we age, it really trickles out steadily. Today will always be more valuable than some day in the future, in large part because we have no guarantee we’ll get that extra day. Ditto for civilizations. In linear time, the future is a loss. But because human minds and societies can improve things over time, and compound that improvement in virtuous circles, the future in this dimension is a gain. Therefore long-term thinking entails the confluence of the linear and the exponential. The linear march of our time intersects the cascading rise and fall of numerous self-amplifying exponential forces. Generations, too, proceed in a linear sequence. They advance steadily one after another while pushed by the compounding cycles of exponential change.

Balancing that point where the linear crosses the exponential is what long-term thinking should be about. For each generation and for each issue that equation of intersection will be different. Sometimes the immediate needs of the now will dominate, and the discount rate will favor the present. For example, the chronic use of childhood vaccines and antibiotics may prove to have long-term downsides, but their value to present generations is so great that we agree to send the cost to the future. Descending generations will have to pay the price — or to solve the problem by inventing better medicines using exponentially better knowledge and resources. Other times future generations will be so enhanced by the later exponential growth begun in a small immediate gain that we raise the discount rate. For example the yield in educating girls in any society is so great, so amplified and compounded in so many ways, over so many generations, that it is worth an awful lot to pay its costs now — even stiff costs in the face of cultural resistance and low immediate yields. Here the cost point is shifted to the present.

A timeline of where we expect these cost/benefit/risk-thresholds to fall in each sector of our civilization, or a field map of places we can see where our linear lives cross exponential change — either would be very handy to have.


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