The Doomsday Argument (Script) (Patreon)

Since the dawn of humanity around 100 billion people have lived. How many will live in the future of our species? We might hope for a trillion times that if we colonize the galaxy. But a simple statistical argument tells us that the doom of our species is much, much closer. 

In some recent episodes we’ve explored the anthropic principle and seen how it can be used to explain the fact that both our planet and our universe seem very finely tuned to allow the development of life. Our planet and/or universe can be rare and unlikely as long as there are enough other planets and/or universes to stack the odds in favour of our existence. We touched on both the potential power and potential misuse of this principle. Today we’re going to push our luck, and see how this controversial idea can be used to predict the physics of our universe, and also to predict the imminent demise of the human race.

To use the anthropic principle properly we need to use it carefully. We talked about weaving in the Copernican principle which tells us that, all else being equal, we should expect to be in a pretty typical part of the universe. This is seemingly the opposite notion to the Anthropic principle. But together we get something we can use: our existence selects for particular types of potentially-rare observer-supporting environments, but we should expect to find ourselves in the most typical or likely type of environment that is consistent with our existence.

In 1987, physicist Steven Weinberg used this form of anthropic reasoning to estimate the value of the cosmological constant. As a quick refresher: the cosmological constant defines the amount of dark energy, which is the stuff causing the expansion of the universe to accelerate. A number of theories in physics from string theory to eternal inflation predict that the cosmological constant could take on different values in different universes, and its value could be extremely high compared to this universe - up to 120 orders of magnitude higher according to the crudest predictions of quantum field theory. Getting a low cosmological constant is extremely unlikely according to these pictures.

But it’s a good thing ours IS low because otherwise our universe would have blown itself up too quickly for stars and life to ever form. This is a good candidate for the anthropic principle - perhaps we’re just in one of the lucky universes with a low cosmological constant because where else could we be? But if that’s true, then we should be in the most common type of lucky universe.

Under the assumption that lower cosmological constants were less likely than higher ones, Steven Weinberg figured that our universe should have the maximum cosmological constant that would allow galaxies to form - and hence allow our existence. He got a value that was a factor of 10 higher than what would be observed 10 years later when dark energy was discovered.

However before that discovery even happened, Weinberg realized he’d made a mistake. He had assumed that we should be in the most common type of universe that allowed our existence. He realized that he should instead assume that we are the most common type of observer. He refined his estimate of the cosmological constant to be the value that most astronomers across the multiverse would observe, with a few assumptions like that the number of astronomers in a universe is proportional to the amount of mass that ends up forming galaxies.

He calculated that the density of dark energy should most typically be 5-10 times the density of matter. That was in the early to mid 90s, right before dark energy was actually discovered and found to be around three times that of matter. So, off by a factor of 2 - which considering the method, and the fact that dark energy could potentially have spanned many, many orders of magnitude, is pretty amazing.

Weinberg’s refinement of the anthropic principle to talk about observers rather than environments is essentially using the Self-Sampling Assumption, defined by philosopher Nick Bostrom as follows: “All other things equal, an observer should reason as if they are randomly selected from the set of all actually existent observers (past, present and future) in their reference class.” If a type of environment or type of universe produces more observers, then we’re more likely to find ourselves in that type.

This sort of reasoning seems useful - it enabled a decent guess at the cosmological constant. Let’s push our luck and see how far we can take it. Allow me to introduce you to the Doomsday Argument, also known as the Carter Catastrophe, after Brandon Carter who came up with it. That’s the same guy who brought to popular attention and in fact named the anthropic principle to start with.

To start, let’s try a thought experiment. Imagine you have two boxes. Each contains a number of balls which are labeled sequentially from 1 to however many balls are in that box. One box contains 10 balls labeled 1-10 and the other contains a thousand, labeled 1-1000. You don’t know which box is which, but you are allowed to reach in to one box and take the first ball that you touch. The boxes are set up so you can’t tell the number of balls from that action. So you look at your chosen ball at it’s labeled with the number 5. Which box did you choose? The one with 10 or the one with 1000 balls? Probably you drew from the 10-ball box, right? After all, there was a 1-in-10 chance of getting that 5 from that box, versus a 1-in-1000 chance from the 1000-ball box.

OK, let’s try another one. Let’s say there are two possibilities for the future of humanity: in one, we’re destined to spread throughout the Milky Way and forge a galactic civilization that last a million of years across a million star system, and ultimately gives rise to a hundred trillion trillion individual lives - 10^20. In the second scenario, humanity never leaves the Earth and only manages to survive to produce about the same number of people that have already lived - so another 100 billion. or 10^11. We’ll call these the doom-late and doom-soon scenarios respectively.

Let’s apply the self-sampling assumption and imagine that you could have been any one of the past and future humans of our species. We can imagine that the two scenarios are our two boxes - the doom-late box contains 10^20 lives and doom-soon contains 10^11. Think of yourself as the numbered ball pulled from one of these, and the number painted on you is your birth rank, which for you is around 100 billion. So which is more likely - that your birth rank happens to be somewhere around the mid-point of the species lifespan? Or that you in the first 100 billion out of a hundred trillion trillion - or in the first 0.000001%? The same logic that led you to favor the 10-ball box upon drawing a 5 seems to say you should favour the doom-soon box here also. That’s the scenario in which humanity only has about as much time left as has already past.

This is the doomsday argument. In it, our mere observation of our existence suggests we’re already a good fraction of the way through our species existence. In fact we can use statistics to estimate the probability of our species lasting a certain amount of time. Estimates vary, but a simple doomsday calculation give us 50-50 odds of making it through the next couple of centuries. 

If all of this sounds fishy, you’re not alone. There are many proposed refutations of the doomsday argument - more than we can go into - but it’s worth covering some that get at how the anthropic principle is interpreted, in particular through the self-sampling assumption and the definition of your reference class.

Choosing your reference class depends on the question you’re asking. In Steven Weinberg’s case the question was “what sort of cosmological constant is the typical astronomer likely to observe - so reference class was an astronomer - or really any observer capable of measuring the cosmological constant.

In the doomsday argument, the assumption is that our “reference class” is all past and future humans. But is that the right reference class? For example, if you define our reference class as all observers in our past and future evolutionary chain, then we could still be in the middle of that chain but have millions more years ahead of us. Then it all depends on whether you count all living things, or somewhat conscious non-human animals, or things with a prefrontal cortex. It also depends on whether we count all of our descendents as “human”. I for one welcome the doomsday if it means graduating out of our reference class into some sort of cybernetic, gene-spliced ultra-human. In general, it’s the fuzziness of this notion of reference class that makes this idea seem far less mathematically precise - far more fishy - than the question of picking balls from boxes.

Another issue is that the doomsday argument is assigning some sort of reality to the two scenarios - doom-early and doom-late are thought of as existent, so that you can be randomly plucked from one - in the same way the two boxes exist. But presumably only one is true and you weren’t randomly plucked from it - you just are what you are - a being with a mental experience consistent with the 100-billionth entity born into a civilization that may or may not end soon.

Speaking of which, what about this idea that your reference class is exactly you? Or, rather, all that you know is that you’re an entitity that is having your current a mental experience?  This is the definition invoked in the simulation hypothesis and the Boltzmann brain scenarios. We’ve covered both of these, but in short, we can come up with much more common ways for your current self to exist besides evolving on a rare planet in a rare universe. For example, you could be one of countless simulations of yourself in some far-future experiment to recreate the past - an ancestor simulation. Or you could be a momentary entropy fluctuation that caused a brain with exactly your current mental experience and memories to pop into the high-entropy post-heat-death void - that’s a Boltzann brain.

As you can see, anthropic reasoning can lead to powerful predictions, like the value of the cosmological constant, it can lead to dubious but worrying predictions like the doomsday argument, and it can lead to some pretty absurd ideas like the Boltzmann brain.

Let’s try our own little exercise in anthropic reasoning. Here’s a challenge question for you: Your birth rank is 100 billion. Assuming the doomsday argument are valid, what are the chances that humanity will last until the year 3000? Assuming the current rate of population increase slows dramatically so it’s doubling once every hundred years over that period Email your answer to pbsspacetime@gmail.com with the subject line doomsday challenge within 2 weeks of release of this episode. We’ll filter by subject so check your spelling. Best answers get a pick from the space time merch store.

Whether or not doom is coming soon or late, here’s a positive spin on the whole doomsday argument: the chances of us being in the final generation of our civilization are also pretty tiny. Which means you’ll be around for next week’s episode of space time.