I’m wondering whether anyone has attempted to compute the value of the whole Universe, in dollars.
This strikes me as a crazy idea—a kind of reductio ad absurdum of the economist’s worldview. But people have come pretty close, so I figure it’s just a matter of time. We might as well try it now.
Let me explain.
The price of the Earth
There’s a trend toward trying to estimate the value of ‘ecosystem services’, which means ‘the benefits of nature to households, communities, and economies’. There’s a practical reason to do this. Governments are starting to offer money to farmers and landowners in exchange for managing their land in a way that provides some sort of ecological service. So, they want to know how much these services are worth. You can read about this trend here:
• Wikipedia, Payment for ecosystem services.
It’s a booming field in economics. So, it’s perhaps inevitable that eventually someone would try to estimate the value of ecosystem services that the whole Earth provides to humanity each year:
• Robert Costanza et al, The value of the world’s ecosystem services and natural capital, Nature 387 (1997), 253–260.
They came up with an estimate of $33 trillion per year, which was almost twice the global GDP at the time. More precisely:
Abstract. The services of ecological systems and the natural capital stocks that produce them are critical to the functioning of the Earth’s life-support system. They contribute to human welfare, both directly and indirectly, and therefore represent part of the total economic value of the planet. We have estimated the current economic value of 17 ecosystem services for 16 biomes, based on published studies and a few original calculations. For the entire biosphere, the value (most of which is outside the market) is estimated to be in the range of US $16–54 trillion (1012) per year, with an average of US $33 trillion per year. Because of the nature of the uncertainties, this must be considered a minimum estimate. Global gross national product total is around US $18 trillion per year.
You can read the paper if you’re interested in the methodology.
In 2014, some of the authors of this paper redid the assessment—using a slightly modified methodology but with more detailed 2011 data—and increased their estimate to between $125–145 trillion a year:
• Robert Costanza, Changes in the global value of ecosystem services, Global Environmental Change 26 (2014), 152–158.
They also estimated a $4.3–20.2 trillion loss of ecosystem services due to land use change during the period from 1997 to 2011. While still difficult to define, this loss per year could be more meaningful than the total value of ecosystem services. Sometimes a change in some quantity can be measured even when the quantity itself cannot: a famous example is the electrostatic potential!
The price of humanity
Back in 1984, before he became the famous guru of string theory, the physicist Ed Witten did a rough calculation and got a surprising result:
• Edward Witten, Cosmic separation of phases, Phys. Rev. D 30 (1984), 272–285.
Protons and neutrons are made of up and down quarks held together by gluons. Strange quarks are more massive and thus only show up in more short-lived particles. However, at high pressures, when nuclear matter becomes a quark-gluon plasma, a mix of up, down and strange quarks could have less energy than just ups and downs!
The reason is the Pauli exclusion principle. You can only fit one up and one down in each energy level (or two, if you count their spin), so as you pack in more the energy has to increase. But adding strange quarks to the mix means you can pack 3 quarks into each energy level (or 6, counting spin). So, you can have more quarks at low energies. At high pressures, this effect will become more important than the fact that strange quarks have more mass.
For this reason, astronomers have become interested in the possibility of ‘strange stars’, more dense than ordinary neutron stars:
• Fridolin Weber, Strange quark matter and compact stars, Progress in Particle and Nuclear Physics 54 (2005), 193–288.
Unfortunately, nobody has seen evidence for them, as far as I can tell.
But the really weird part is that Witten’s calculations suggested that ‘strange matter’, containing a mix of up, down and strange quarks, could even be more stable than normal matter at ordinary temperatures and pressures! His calculation was very rough, so I wouldn’t take this too seriously. The fact that we don’t actually see strange matter is a very good sign that it’s not more stable than ordinary matter. In principle ordinary matter could be just ‘metastable’, waiting to turn into strange matter under the right conditions—sort of like how water turned into ice-9 in Kurt Vonnegut’s novel Cat’s Cradle. But it seems implausible.
Nonetheless, when the Relativistic Heavy Ion Collider or RHIC was getting ready to start colliding nuclei at high speeds at the Brookhaven National Laboratory, some people got worried that the resulting quark-gluon plasma could turn into strange matter—and then catalyze a reaction in which the whole Earth was quickly transformed into strange matter!
This is interesting example of a disaster that would have huge consequences, that is very improbable, but for which it’s hard to estimate the precise probability—or the precise cost.
So, a debate started!
Needless to say, not all the participants behaved rationally. Frank Close, professor of physics at the University of Oxford, said:
the chance of this happening is like you winning the major prize on the lottery 3 weeks in succession; the problem is that people believe it is possible to win the lottery 3 weeks in succession.
Eventually John Marburger, the director of the Brookhaven National Laboratory, commissioned a risk assessment by a committee of physicists before authorizing RHIC to begin operating:
• R.L. Jaffe, W. Busza, J.Sandweiss and F. Wilczek, Review of speculative “disaster scenarios” at RHIC, 1999.
In 2000, a lawyer and former physics lab technician named Walter L. Wagner tried to stop experiments at RHIC by filing federal lawsuits in San Francisco and New York. Both suits were dismissed. The experiment went ahead, nuclei of gold were collided to form a quark-gluon plasma with a temperature of 4 trillion kelvin, and we lucked out: nothing bad happened.
This is very interesting, but what matters to me now is this book:
• Richard A. Posner, Catastrophe: Risk and Response, Oxford U. Press, Oxford, 2004.
in which a distinguished US judge attempted to do a cost-benefit analysis of the Relativistic Heavy Ion Collider.
He estimated a $600 million cost for constructing the device and a $1.1 billion cost for operating it for ten years (discounted at a rate of 3% per year). He guessed at a potential total benefit of $2.1 billion—which he said was probably a huge overestimate. This gave a net benefit of $400 million.
Then he took into account the risk that the experiment would destroy the Earth! He very conservatively estimated the price of a human life at $50,000. He multiplied this by the number of people now living, and doubled the result to include the value of all people who might live in the future, getting $600 trillion.
This may seem odd, but discounting the value of future goods can make even an endless stream of future human lives have a finite total value. More annoying to me is that he only took humans into account: as far as I can tell, he did not assign any value to any other organisms on the Earth!
But let’s not make fun of Posner: he freely admitted that this result was very rough and perhaps meaningless! He was clearly just trying to start a discussion. His book tries to examine both sides of every issue.
Anyway: his estimate of the cost of human extinction was $600 trillion. He then multiplied this by the probability that RHIC could wipe out the human race. He estimated that probability at 1 in 10 million per year, or 1 in a million for a ten-year-long experiment. So, he got $600 million as the extra cost of RHIC due to the possibility that it could make the human race go extinct.
Taking the net benefit of $400 million and subtracting this $600 million cost of our possible extinction, he got a negative number. So, he argued, we should not turn on RHIC.
Clearly there are lots of problems with this idea. I don’t believe the entire human race has a well-defined monetary value. I’m inclined to believe that monetary value only makes sense for things that you can buy and sell. But it’s not so easy to figure out the ‘correct’ way to make decisions that involve small probabilities of huge disasters.
The price of the Universe
Suppose, just for fun, that we accept Posner’s $600 trillion estimate for the value of the Earth. What then is the value of the Universe?
I think it’s a stupid question, but I feel sure someone is going to answer it someday, so it might as well be me. Maybe someone has already done it: if so, let me know. But let me give it a try.
I’ll be very relaxed about this, so it won’t take long.
We could try to calculate the value of the Universe by estimating the number of planets with intelligent life and multiplying that by $600 trillion. It’s very hard to guess the number of such planets per cubic megaparsec. But since the Universe seems to extend indefinitely, the result is infinite.
That’s my best estimate: infinity!
But that’s not very satisfying. What if we limit ourselves to the observable Universe?
No matter what I say, I’ll get in trouble, but let me estimate that there’s one intelligent civilization per galaxy.
A conservative estimate is that there are 100 billion galaxies in the observable universe. There might be twice as many, but perhaps a lot of them are small or less likely to support life for various other reasons.
So, I get $600 trillion times 100 billion, or
as my estimate of the value of the observable Universe. That’s $6 × 1025, or $60 septillion.
The price of everything
The title of the article is taken from a line in Oscar Wilde’s play Lady Windermere’s Fan:
Cecil Graham: What is a cynic?
Lord Darlington: A man who knows the price of everything, and the value of nothing.