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 a particular type
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 reasoned 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 allows our existence.
He realized that we 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 in that universe.
Weinberg calculated that the density of dark energy should most typically be observed to be around 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 they are more
likely to find themselves in that type.
This sort of reasoning seems useful - it enabled a decent guess at the cosmological constant.
So, 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.
And 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 the 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?
Well, 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 both 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
that your current self exists 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
one is a 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 name 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.
Our Patreon contributors make a huge difference - ensuring we'll be able to keep making and
expanding Space Time until doomsday - whether it's soon or late.
And today I wanted to give a huge shoutout thank you to John S, who's one of our Big
Bang contibutors.
John, you are in a reference class of your own: reference class supremely awesome.
As a special thanks we pulled a few strings and got you moved over to the doom-never box
. If anyone wishes to join John S in reference class awesome, any level of contribution is
a big help.
And any level - even $2 - also gets you access to our new Space Time discord channel, where
at this very moment brilliant and curious individuals are discussing the future of humanity,
the nature of space and time, the weirdness of quantum mechanics - you name it.
And don't forget with the holidays coming up, to check out our merch store.
OK, so our last episode was a journal club looking at a study that claimed to have evidence
that the universe is not infinite after all.
Let's start with a question from the discord: Habunelahack asks if it's ever be possible
to measure the curvature of space to get an estimate on the size of the entire universe.
Well, the answer is maybe: if the universe is closed and has positive curvature then measuring
that curvature absolutely will give us the total volume of the universe.
If it turns out to the universe is negatively curved then well it's infinite.
On the other hand, if we keep finding geometric flatness we'll never actually know whether
it's finite or infinite because it may be that there's a slight positive or negative
curvature just beyond the sensitivity of our measurement.
Daniel M. and Sam Harper ask whether a universe can transition between different geometries.
In a universe like ours where matter and energy is evenly distributed on the largest scales
the curvature does changes but the global geometry does not.
A flat or hyperbolic universe remains flat or hyperbolic respectively and so remains
infinite, while a positively curved universe remains positively curved and therefore finite.
That said, patchs of the universe CAN change in curvature depending on the behavior of
matter in those patches.
The most obvious example is that regular gravitational fields around stars and galaxies can be positively
curved patches in a flat or hyperbolic universe.
That means it's also possible to produce a closed, positively curved bubble universe
within an infinite inflating multiverse.
One commenter, O.N., pointed out that an infinite universe is technically possible within a
bubble that otherwise looks finite from the outside.
Well, that's something I need to dig into deeper before I comment on it - but it sounded legit
in a deeply, abstractly theoretical sort of way.
Rei Spring points out that there are flat geometries that are not infinite, but rather
closed - for example the 3-torus embedded which is like a donut, but with more dimensions.
Now the non-brain-breaking analogy is a 2-torus like in the game Asteroids, or PacMan
where opposite walls connect to each other.
These are basically flat mappings of a donut. And there are weirder, multiply connected finite space times that are also flat.
Now while these are valid geometries for spacetimes that can be constructed within Einstein's
general relativity, it's not clear
how such a universe would form, and certainly forming a 3-torus
as a bubble out of eternal inflation might not be possible.
Ni999 dropped some wisdom from Ethan Seigel, whose excellent Forbes article on this closed universe
paper emphasized a point that we mentioned only in passing that is worth repeating:
that is that the baryon acoustic oscillation signatures seen in galaxy clusters
are an independent measure of curvature, and
these point to a much flatter universe than implied by this new result from the CMB gravitational lensing.
In short, there's still significantly more evidence in favour of flatness than positive curvature.
Last time in an attempt to be "funny" I dissed english weather.
Shaun Humphreys kindly took the time to pen an extensive treatise on why the British climate
is really optimal for humans.
I stand thoroughly corrected, Shaun.
Coming from Australia, where it swings between 5000 degree heat and raining ... spiders,
I do envy the consistency of your 17 different types of drizzle.
Also, thank you for Douglas Adams - and thank god most people got the hitchhikers reference in that last
episode - you really are the hoopiest froods on the internet.