Say there are two lottery urns, one containing 1000 balls each numbered from 1 to 1000, and the other containing 10 balls each also numbered from 1 to 10. We have two individuals, one Alice the other Bob. Alice will reach into one of the lottery urns, out of sight of Bob, and present the ball to Bob who must infer from whence the ball came.
Now Alice picks out the ball “3” and presents it to Bob. What shall Bob infer? Based on probability Bob will infer that the ball “3” came from the urn with only 10 balls. That’s because ball “3” in that urn is but one of 10 balls. However, by far most of the balls in the first urn are numbered greater than 10.
From this analogy the philosopher John Leslie has presented a version of the doomsday argument or Carter’s catastrophe, first articulated by Brandon Carter, a relativist of Australian providence, but also later, and independently it must be said, by another relativist, J Richard Gott III. Essentially, the doomsday argument is an argument for lowering our probabilistic estimate for the indefinite continued survival of the species Homo sapiens.
As Leslie puts it in his popularisation of the doomsday argument in his The End of the World
We ought to have some reluctance to believe that we are very exceptionally early, for instance in the earliest 0.001 per cent, among all humans who will ever have lived.
If the human species were to have a rosy future well, well, well into the future then we would be among the earliest humans to have ever lived. We would be quite special. However, if for some reason humanity were to go extinct tomorrow then, because of population growth, we wouldn’t be in a terribly special place on the historical timeline of all humans.
That is because some 10% of all humans that have ever lived are alive now. So, as with the lottery urn, what would be more likely; that we are among the first 0.001% of all humans or among 10% of all humans? Leslie argues, along with Carter and Gott, that we should infer the latter in which case we need to revise our common, quite optimistic, biases regarding the prospects of the species.
Doom soon is more likely than doom later.
Notice this is a version of the Copernican Principle, something that intrigues me greatly. I will leave that aside here.
Now consider the same argument, but with respect to economic growth which is measured by Gross Domestic Product or GDP. Throughout most of human history there has been little economic growth, with takeoff usually associated with the industrial revolution. However, most of the economic growth in the modern era has really occurred from 1950 onward, which is appropriate as that coincides with what geologists increasingly refer to as the Anthropocene. I have always regarded the second industrial revolution as more impactful than the first.
In 2014 global GDP was 77,860 billion US$. From 2013 to 1,000,000 BC combined all of GDP has estimated to have been 313,854 US$. One can take these figures from Wikipedia. There exists the view that, like the future prospects for humanity, economic growth will continue forever. Certainly, that’s one of the main conclusions of endogenous or new growth theory. If so, that means we have been, and are, in a very special spot on the timeline of economic growth say much like the proverbial first 0.001% of all GDP.
However, because of rapid increases in global GDP, the 2014 global GDP figure, 77,860 billion US$ represents just under 25% of all GDP for all time. When, based on the Carter-Leslie-Gott reasoning, would we expect our GDP to fit into the total timeline of all GDP; 0.001% or 25%?
It seems to me that the same doomsday reasoning applies to economic growth. We should revise our estimates, assuming doomsday reasoning is correct which remains unchallenged in this expository post, regarding the longevity of the economic growth experience that so underpins the era of the Anthropocene. The reader will note that this argument with respect to economic growth does not refer to ecological arguments made for limits to economic growth. It is a purely analytical or mathematical argument, but it is something we should be mindful of when thinking about the global ecological crisis.
I suppose that the same applies to information. The graph below depicts information growth over human history.
It is estimated that by 2020 the stock of information will double every 73 days. Say that, I haven’t calculated just assumed for purposes of exposition, this year humans produce 10% of all the information that humans have ever produced throughout all of history. Should humans continue to generate information indefinitely well, well, into the future than we would be, again, at a very special place on the timeline of all information production something akin to the first 0.001% of all humanly produced bits. But, if 10% or some such of all bits produced by humans were produced this year, then we should infer that the era of information growth will also end sooner rather than later.
That’s not an argument that would please exponents of quantum computation.
Perhaps this point generalises. Say we reduce every human being into bits of information. The Carter-Leslie-Gott argument can then be formulated in informational terms. We might also be able to think of economic output not in terms of GDP but in terms of bits of information and assuming so means we can reduce the limits to growth argument in informational terms.
We may have here special cases of a more generalised argument regarding the limits to informational complexity. Certainly, population growth and economic growth are bound together.
Say we develop a similar argument, but this time of an epistemic type. The scientific revolution has seen a continued explosion in the growth of human knowledge. It has often been said that the day when a “renaissance man” like figure such as a Leibniz or a Hume could be across human knowledge has long since passed. Nowadays mathematicians, physicists, biologists, and the like must specialise within niche areas of their own disciplines as discipline wide knowledge is no longer possible let alone human wide knowledge.
Many suppose that human knowledge will continue to advance in leaps and bounds ever, ever into the future. That would mean, again given the proximity of the scientific revolution, that our store of knowledge would be something akin to the first 0.001% of all knowledge generated. Let us assume, for the sake of argument, that due to the explosion of knowledge that in 2017 something akin to 10% of all knowledge created by all humans in all of history was generated.
That being the case, based on Carter-Leslie-Gott reasoning, a looming dark age where knowledge production has collapsed would be more likely than the continued indefinite enlightened generation of new knowledge. The interesting thing about the epistemic version is that it neatly fits into the first two, human survival and economic growth, but especially the first via Ernst Mayr’s, a noted evolutionary biologist, famous argument against the existence of extraterrestrial intelligence.
Mayr argued that evolutionary history suggests that high order intelligence is an evolutionary dead end, as it has only evolved once in all of known biological history. If it were favoured by natural selection intelligence, Mayr surmised, ought to have evolved numerous times. Mayr concluded that it is better to be stupid than smart.The epistemic version of the argument might also suggest so.
A link can be drawn connecting the economic and the epistemic versions, assuming that, following both exogenous and endogenous growth theory in economics, it is knowledge and innovation that drives economic growth. The consistency of different versions and that with application to empirical matters is striking. Consistency of argument does not, of course, imply validity of argument.