Notes on the EHT black hole image

Following on to the recent post on the other blog about the imaging of a black hole in a nearby galaxy, here are my lightly cleaned up notes from watching Katie Bouman's lecture on how the images were captured using the Event Horizon Telescope (EHT), which is actually a collection of several radio telescopes whose individual data sets are combined using very sophisticated image processing techniques to emulate a single Earth-sized telescope.

I have no great insights to offer, but there are some pretty interesting details in the original lecture.  I've thrown in some commentary here and there, without taking any real care to distinguish it from the source material. The full lecture is on Caltech's YouTube channel.  As always, any errors or distortions are mine.



Technically, the image gathered by the telescopes working in combination is in spatial frequency, basically how quickly bright changes to dark as you scan over the actual image.  For example, a square divided into a white rectangle and a black rectangle has a lower spatial frequency than one divided into thin black and white stripes.  It's possible to reconstruct a visual image from information about the spatial frequency, and the more information you have, the better the reconstruction.  This sort of reconstruction is widely used in many fields, including astronomy, medical imaging and the image compression that lets us stream video over the internet.

The exact spatial frequencies being measured depend on the distance (baseline) between the telescopes.  When the telescopes are spread across distant locations on the Earth, the image technique is called Very Long Baseline Interferometry (VLBI).  Interferometry refers to measuring how the signals from different telescopes interfere with each other, that is, whether they reinforce each other or cancel each other out when combined.  Very Long Baseline refers to, um ...

In this case there were eight radio telescopes at six different sites, taking data together on four different nights, scanning for a few minutes at a stretch.  This provides 21 different pairs of telescopes, which would mean 21 different baselines, that is, 21 different spatial frequencies to combine, except that the baselines change as the Earth rotates.  This is good, because it provides samples of more frequencies.  There is at least some talk of adding telescopes in low Earth orbit at some later stage, which would not only provide more raw data but more varied baselines, since satellites move faster than the Earth rotates.

As mentioned in the other post, each scope collected hundreds of terabytes (hundreds of trillions of bytes), enough data that it was easier to fly the drives with the data to the site where it would be processed, rather than try to send it over the internet (and the South Pole data had to be flown out in any case).

The actual signal, coming from about 50 million light-years away, is quite weak, and noisy.  There is a lot of matter at the center of a galaxy, radiating at various frequencies and blocking various frequencies.  The radio band was chosen to minimize these effects, but there is still noise to contend with, along with noise from a variety of other sources, including atmospheric noise and imperfections in the telescopes themselves.

The various telescopes are looking through different amounts of atmosphere, depending on whether the black hole is overhead from their location or on the horizon, and this also affects how long it takes the signal to arrive at each telescope.  It takes about 20 milliseconds longer for the signal to reach a scope that has the black hole on the horizon that it does for one where it's overhead.  For a 1GHz signal, that means a difference of 20 million cycles -- and again, this is varying as the earth rotates.

All this means there is a lot of calibration to be done to make sure you're lining up the right data from the various telescopes and accounting for all the various sources of noise and distortion.  In all, there were hundreds of thousands of calibration parameters to work with, though the team ended up using (only) ten thousand or so.

The reconstructed image is meant to represent what an Earth-sized telescope would see, if one could be built, but there are actually infinitely many such images that would match up with the limited data that was collected from a few scattered points on Earth.

Fortunately, having multiple telescopes means you can cross-check and isolate errors.  There are also "closure quantities" that should be the same regardless of the exact details of calibration.  I didn't really understand the details of closure quantities, but the idea of looking for quantities that don't depend on hard-to-control parameters is a powerful one.  It's sort of similar to checking arithmetic by adding up digits.

The team used two different methods of calibration, and they split into four subteams, two for each method.  The subteams worked independently for several weeks to reconstruct an image from the raw data.  Bouman's own work involved getting the human-tuned method (CLEAN) to work without human tuning.

In addition to the work by the subteams, there was a lot of work done up front to try to make sure that the image processing algorithms they were tuning were robust.  Much of this involved taking test images, calculating what signals the telescopes would get and then reconstructing the test images from the calculated signals.  They did this not only with images of discs and rings that one would typically expect in astronomical images, but also with a variety of non-astronomical images.

The team actively tried to break the image processing algorithms, for example by tuning the parameters to favor a solid disc rather than a ring, and verifying that a ring still came out as a ring.  Python fans will be glad to know that at least some of the code involved was written in Python.

The publicly distributed image is a combination of the images from the subteams.  Since it's meant to represent only what we can be confident about regarding the actual black hole, it's deliberately a bit blurry.  Even still, there are some significant results [I haven't yet re-checked the details here, so what follows may be garbled]:

• There is, in fact, a ring as would be expected from a supermassive black hole.
• The same ring was observable night after night.
• Previously there had been two separate estimates of the mass of the black hole, one from the motions of stars around it (stellar dynamics) and one from the appearance of the gas flowing into the accretion disc.  The size of the ring in the image supports the first mass estimate.
• One portion of the ring is brighter than the rest, due to the doppler shift of matter orbiting around the black hole.  This is to be expected, and the position of the bright spot matches up with other observations.
• The position of the bright spot is shifting over time, consistent with a rotation period on the order of weeks (I think this implies that the black hole's axis of rotation is not on the line of sight).  Since the black hole in the Milky Way (Sgr A*) is much smaller, its rotation period is expected to be on the order of minutes.  Since the observation scans are also on the order of minutes, the image processing for Sgr A* will have to take this into account.

It's also possible to analyze the raw data directly as a cross-check.  A disk of such-and-such size should result in such-and-such radio signals arriving at the various telescopes, independent of any reconstructions produced from that data.  The raw signals are consistent with a ring of the size found in the visual reconstructions.  This is not a surprise, given how the reconstructions were done, but still good to know.

Despite the whole effort taking years and requiring expensive radio telescopes at widely dispersed locations, and employing dozens of people at various stages, the movie Interstellar still cost a lot more to make.  While its image of a black hole may be prettier (and, as I understand it, one of the parts of the movie where the science was actually plausible), the EHT image was both cheaper and more informative.

Again, really good stuff.

Detectability and the Drake Equation

I've argued in posts on the Drake Equation (really more a framework for trying to work out the odds of finding extraterrestrial life), that the L factor, representing the amount of time for which an intelligent civilization is detectable on a planet, is both underappreciated and overestimated.  That is, it's not just important whether a planet can develop life -- which is were a lot of attention is -- but just how long a planet with intelligent life is detectable as such.  If that time span is not very long, then there might well be intelligent civilizations out there that we don't know about, or have much hope of ever knowing about.

Radio transmissions are often used as a proxy for intelligent life.  Clearly, if we detect a radio signal coming from planet X with a structure we can't explain by natural means, we have to seriously consider the possibility that some intelligent life form sent the signal.  Artificial-looking radio signals strongly imply intelligent life, but lack of them doesn't imply lack of intelligent life.

Radio isn't the only way to go looking for intelligent life.  We're already able to get some idea of the atmospheres of exoplanets based on their effect on light from the parent star as they transit between us and that star, provided everything is in a favorable alignment.  That ability is liable to improve over time, to the point where we'll be able to detect whether a planet has a chemical composition that's likely to be produced by something like life as we know it.  That's pretty impressive, if you think about what it entails, and we're just getting started.  Astronomy has gotten really good at gleaning ridiculously faint signals from vast fields of noise, and while there are some fundamental limits to what we can gather, there's clearly a lot more we can do within those limits.

Likewise, if we can detect some signal related to a planet's surface, and we can observe the same planet from different angles (which is often possible since planets rotate) we can get some idea of any changes in the surface as seen from different angles.  Similar techniques were used to get a very rough map of Pluto's surface prior to the New Horizons mission.  It may also be possible to detect the polarization of light coming from a planet, and there are probably other sources of data.  Put together enough such hints and we may be able to measure whether a planet has anomalously dull or shiny or hot or cold regions or similar that might indicate ... something, maybe enough to say that there's probably a civilization something like ours on a given planet, and not just an odd configuration of protoplanetary dust.


So suppose that some twin Earth in the general vicinity -- say a few dozen or a few hundred light-years -- develops along similar lines to ours.  Suppose that some time after a species like ours arises it discovers radio, but not long after that it finds more efficient ways of communicating than blasting radio waves in all directions (including a tiny fraction headed towards us).  In my previous posts I argued that that's probably about it.  We won't be able to detect any signs of intelligent life (life, yes, civilization no) except for a tiny portion of the planet's existence, and so the odds are very low that we happen to be listening at the same time they're broadcasting.

But surely twin Earth will have cities and other large artifacts for longer than it has detectable radio emissions, and have them both before and after their radio era.  Our ability to detect such artifacts will only improve over time.  Suppose our techniques get to the point where we could detect the analog of a city of, say, 100,000 people by way of its structures and overall impact on the surrounding environment.  There are thousands of those on Earth now and, more to the point, there have been for quite a while.  Thousands of years, versus decades for radio transmission.  It's at least possible that there will continue to be cities for thousands of years more.  This is a couple of orders of magnitude longer than our detectable radio era might end up being, not something easy to write off.

Nonetheless, I don't know that it changes the picture much.  On the one hand, even this larger time window is still pretty small on a planetary time scale.  On the other hand, it's not at all clear to me that detecting a signature consistent with cities means that there are cities there.  I'd want to see a lot of work to rule out natural formations that we haven't thought of, and even then city-like collections of life don't necessarily mean intelligent civilization.  We are not the only life forms on Earth that can gather in numbers or have a significant environmental effect.

It's also entirely possible that we'd see the same effect with cities on Earth as with radio, just on a slower scale.  That is, we or our counterparts might have cities for a long time, but not have detectable cities for very long.  I'm not going to predict that humanity will necessarily lessen its overall impact on the environment over time, but it's possible.  If we become cleaner and (much the same thing) more efficient, we become harder to spot, and likewise for a hypothetical alien civilization.

Nonetheless, it seems dangerous to assume that whatever impact we do have, or an alien civilization has, will be undetectable from interstellar distances.  It will probably be detectable as an overall signature.  The question is what could we make of such a signature.  We'd probably be able to associate it with life, but what kind of life?

[ Re-reading an earlier post I see I already took this point into account, although in a more abstract way -- D.H.]

Science on a shoestring

On the other blog I would occasionally put out short notices of neat hacks (as always, "hack" in the "solving problems ingeniously" sense).  I recently ran across one that didn't have much to do with the web, so I thought I'd carry that tradition over to this blog.


Muons are subatomic particles similar to electrons but much heavier.  They are generally produced in high-energy interactions in particle accelerators or from cosmic rays slamming into the atmosphere.  Muons at rest take about 2 microseconds to decay, actually a pretty long time for an unstable particle.  Muons from cosmic ray collisions are moving fast enough that they take measurably longer to decay (in our reference frame), which is one of the many pieces of supporting evidence for special relativity.

The GRAPES-3 detector at Ooty in Tamil Nadu, India detects just such decays using an array of detectors set into a hill 2200m (7200 ft) above sea level.  The detectors themselves are made largely from recycled materials, particularly square metal pipes formerly used in construction projects in Japan.  The total annual budget for the project is under $400,000, but the team has already produced significant results.  Auntie has more details on the construction of the instruments here.

There are a couple of narratives that are often spun around stories like this.  One is a sort of condescending "Isn't that cute?" with maybe a reference to the Professor on Gilligan's Island building a radio out of coconuts.  Another is "Look what people can do without huge budgets.  Why do we need all these multi-billion-dollar projects anyway?"

I'd rather not tell either of those.  What I see here is highly skilled scientists making use of the resources they have available to produce significant results.  Their counterparts at CERN or whatever are making use of different resources to produce different significant results.  Both are moving the ball forward.  There have been plenty of neat hacks at CERN, including something called "HTTP",  but today I wanted to call out GRAPES-3, mainly because it's just plain cool.

Reworking the Drake equation

In speculating about life on other worlds (here and here for example) the Drake Equation provides a useful framework.  This equation multiplies a number of factors to arrive at the number of civilizations in the Milky Way that would be technologically capable of communicating with us.

When it was first formulated, most if not all of the factors had such wide error bars that it's hard to argue that any meaningful number could come out of it.  An answer of the form "2.5 million, but maybe zero and maybe several billion or anything in between", while honest, is not a particularly useful result.  For much of the time the Drake Equation has been around, it's been useful more as a  framework for reasoning about the possibility of alien civilizations (and, in my opinion, a reasonable one) than as a way of producing a meaningful number.

Recently, though, a couple of the error ranges have tightened considerably.  Let's look at the factors in question:

• the average rate of star formation in our galaxy.  This is currently estimated at 1.5 - 3 stars per year
• the fraction of formed stars that have planets. This is quite likely near 100%
• the average number of planets per star that can potentially support life.  There is some dispute over this.  You can find numbers from 0.5 to 4 or 5, and even outside that range.  My personal guess is toward the high end. 
• the fraction of those planets that actually develop life.  At this point we can only extrapolate from life on Earth, a minimal and biased sample.  It's noteworthy that life now seems to have begun shortly (in geological terms) after suitable conditions arose.
• the fraction of planets bearing life on which intelligent, civilized life has developed.  Developing intelligent life as we understand it took considerably longer: billions of years.  Again extrapolating from our one known example, this implies that a large fraction of life-bearing planets haven't been around long enough to develop intelligent life.
• the fraction of these civilizations that have developed technologies that release detectable signals into space.  Still extrapolating, this fraction may be pretty high.   On geological scales, humanity developed radio pretty much instantaneously, suggesting it was nearly inevitable.
• the length of time, L, over which such civilizations release detectable signals.  I've argued that this is probably quite short (see the links above and the discussion below for a bit more detail).

Looking at the units in those factors, we have

• civilizations = (stars/time) * (a bunch of fractions that amount to civilizations/star) * time

which is perfectly valid.  However, I'm not sure it's the best match for the problem that we're trying to solve.  I've argued previously that timing is important.  The last factor (length of time a civilization produces detectable signals) takes that into account, but the other time factor, in the rate of star formation, seems less relevant.  There are billions of stars in the galaxy.  At a rate of a couple of stars per year that's not going to change meaningfully over human timescales.

So let's try the same general idea but with different units:

• expected signal = planets * (expected signal / planet)

First, shift the focus from stars to planets.  For our purposes here that includes objects like planet-sized moons of gas giants.  This cuts out the estimation of star formation and planets per star, since we can now observe planets (in some cases even directly) and get a pretty good count of them.  Or at least we're now guessing about planets directly, instead of guessing about stars and planets.

Then, let's pull back a bit from the details of how a planet would produce a signal of intelligent life, and focus on the signal itself, by estimating how strong a signal we can expect from a given planet.   This consolidates the estimates of life evolving, civilization evolving, civilization developing technology and the duration of any signal into a single factor.

The "expected" means we're looking at weighted probabilities.  To take a familiar example, if you roll a six-sided die and I pay you $10 per pip that comes up, you should expect to get $35 on average and you shouldn't pay more than that to play the game.  This really only holds up if you expect to play the game a number of times.  If you only roll the dice once, you could always just get a bad roll (or a good one).

Likewise, if we say that a planet is producing a signal of a given expected strength, we're saying that's the average strength over all the possibilities for that planet -- maybe it's young with only one-celled life, maybe it's harboring a civilization that's producing radio signals, etc.  We're not claiming that it's actually producing a signal of that strength.  We can get away with this, more or less, because we'll be adding up expectations over a reasonably large number of planets.

Looking at expected signal accounts for a couple of factors.  What a planet emits in the radio spectrum will vary over time.  The raw strength will vary.  Earth has gone from watts to at least gigawatts in the past century or so.  The signal to noise ratio will also vary.  As we make better use of encryption, compression and such, our signal looks more like noise.  Signal strength also accounts for distance.  A radio signal falls off as the square of the distance. 

A given planet will have a particular profile of signal strength over time.  Ours is zero for most of our history, rises significantly as humans develop radio and (I've argued), will drop off significantly as we come to use radio more efficiently and use broadcast less and less.

There are two sources of uncertainty in what strength of signal we would expect to detect, knowing how far away a planet is and how much background noise there is:  We don't know what the signal strength profile for a given planet is, and we don't know where we are in that profile, that is, just how old the planet is at the moment.

For the first uncertainty, the best we can currently do is compare to our experience on earth.  My best guess is that we should expect a very brief blip (brief on planetary scales).  If we expect a blip on the order of hundred years and a planetary age on the order of billions of years, this reduces the expected signal -- again, "expected" in the probabilistic sense -- at any given time to a very low level.  This would be true even if planets occasionally send out strong, targeted transmissions, as ours does.

In the absence of anything better, we can account for the second uncertainty by averaging the signal strength over the expected age of the planet.  That is, we assume the planet could be at any point in its history with equal probability.  In real life, we may be able to do better by looking at factors like the age of the star and the amount of dust around it.

Strictly speaking we should be talking about intervals rather than instants, since listening for a million years is more likely to turn something up than listening for a hundred, but human timescales are tiny enough that this doesn't really affect our calculations of what we should expect with current or near-future technology over our lifetimes.  Either way, we can still define expected signal.

We also need to account for the distribution of planets in space.  If stars were uniformly distributed in space and background noise didn't matter, this would cancel out the effect of decreasing signal strength, since the number of stars at a given distance would increase as the square of the distance.

But they're not.  If they were then the nighttime sky would also be uniformly bright in all directions.  The Milky way is only about a thousand light years thick.  After about half that distance the number of stars increases much more slowly than the square of the distance.  This means we're really looking at a weighted sum of expectations rather than just multiplying planets by expectation per planet, but that doesn't greatly change the overall analysis.

Finally, we should take background noise into account.  As the strength of a signal (actual, not expected strength) drops toward zero, our ability to detect it doesn't drop in tandem.  Once the signal becomes weaker than the general background noise in that part of the sky, our chances of detecting it are already very near zero.  This correction should be applied to the signal profile before averaging over time.

My engineering intuition tells me that the upshot is that we can neglect planets more than a relatively short distance away, say tens of light-years.  At some point background noise will wash everything out.  That's more or less the limit for having a meaningful conversation anyway, since it takes a year for a radio signal to travel a light-year.

So where does that leave us?

Estimating the probability of a detectable signal from a planet requires knowing

• The distribution of planets as a function of distance.  Our knowledge of this has sharpened dramatically over the past couple of decades.
• The effect of distance on the strength of a signal we detect.  This is fairly well understood.
• The background noise for any particular location in the sky.  This is directly observable.
• The expected strength of the signal emitted by a planet, averaged over its lifetime.  This is where the uncertainty is concentrated.

Essentially we've consolidated all the various fractions of the Drake equation into a single factor and characterized it in terms of signal strength over time (which we then average over time unless we can think of something better).

When searching for life, "signal" doesn't necessarily mean "radio signal".  Soon we will be able to search for signatures such as high levels of oxygen in the atmosphere, which suggest that there is life of a similar form to ours, though not necessarily intelligent, technological or whatever.  This signal would have a much different profile from radio.  In our case it would rapidly jump from zero to full strength relatively early in our history and stay there for billions of years.  It may also be a stronger signal than radio leakage in the sense that we can feasibly detect it from further away.

If we take our experience on earth as a basis, this implies it's quite likely that we'll detect life on other planets, but unlikely that we'll detect radio signals (and probably other smoking-gun signs of civilization as we know it).  Looking for signatures of life in general is probably going to be more informative in any case.  If we don't find any radio signals from other planets, which seems more and more likely, it could just be because even planets with intelligent life don't tend to emit high signal-to-noise radio signals for long.  If we find chemical signatures indicating life on X% of planets with detectable atmospheres, that gives a strong estimate on the probability of life arising in general.  This is true whether X is 0, 100 or something in between.

[Technical note: Somewhat ironically, since I started out talking about unit analysis, the units here are less clear than they might be.  If we're talking about radio, then at any given moment a planet is emitting radio signals at a given power, say X Watts.  Power is energy per unit time.  Probably the most natural way of expressing what we actually detect over time is an amount of energy, say Y Joules -- power times time is energy.  We'd like that to stay the same whether we're talking about an actual measurement or a probabilistic estimate.  So the quantity we're trying to estimate for a given planet is power.

If we assume a particular profile of power over time, and we average it, we're summing up power over time to get total energy, then dividing by the total time span over which we think we might be looking -- the age of the planet -- to get power again.  Accounting for distance still gives power, that is energy we expect to receive per unit time.  Using units of power also accounts for the amount of time we spend looking.  If we look for 100 years we expect to detect 10 times as much signal (energy) as if we look for 10 years.  I tried to gloss over that in the main article on the grounds that the numbers are all likely to be too small to matter.  But it's better to think of a minuscule amount of power over a shorter or longer time than to try to assume everything's an instant.

I've made a few edits to the main article, mainly changing "signal strength" to "signal" in several places to try to reflect this.]

[And having gone through all that, and thought it over a bit more ... the really natural units to use here are bits and bits per second.  At the end of the day, we're trying to glean information from listening to the skies, and information is measured in bits.  This accounts for several troublesome factors:

• We're trying to estimate detectable information from other planets.  This starts by estimating what information they transmit over time, as measured by an observer in the near vicinity (say, in low Earth orbit or on the Moon in our case)
• I've argued that as we use compression and encryption more, our signal looks more like noise.  This is quantifiable in terms of bits and bit rates.
• If a planet is far away or in a noisy area of the sky, we're less likely to detect a signal from it.  There are well-established formulas relating signal power, bandwidth and signal/noise ratios that can be used to translate an estimate of what radio signals a planet emits to an estimate of bits/second we could detect.
• As above, integrating bits/time over time spent listening gives us the total information we would expect to detect, which is arguably the quantity of interest in the whole exercise.
• So
• bits detected = sum over time of the sum over planets of bits per second we expect to detect from each planet
• leaving out the sums, which don't change the units: bits = (bits/second)/planet * planets * seconds

]

Not in our lifetime vs. never in a million years

The great physicist Enrico Fermi once asked "Where is everybody?", by which he meant "It seems quite likely that there are other civilizations in the universe, so why haven't we seen convincing evidence?"

Without going into detail, I agree with Fermi that there's no convincing evidence that there are other civilizations in the universe.  However, despite the lack of smoking-gun evidence, I'm pretty well convinced there is life elsewhere in the universe, even in our own galaxy.  It seems reasonably likely that there is life within our neighborhood, and not out of the question that there is some form of life elsewhere in our solar system.

I also think it's pretty likely that there are intelligent civilizations (leaving aside exactly what that means) in our galaxy, and almost inevitable that there are such civilizations somewhere in the universe besides here.  So again, why haven't we heard from them?

When we use terms like "in our neighborhood", it's easy to forget that, when talking about astronomy, "neighborhood" is a very relative concept.  Here, I'll use "in our neighborhood" to mean "within 50 light-years, give or take a few percent".  That's close enough that we could send a signal and get a response in something on the order of a human lifetime.  It's also vastly farther than we have ever travelled, or could hope to travel with any kind of technology we know.  Within this 50 light-year radius there are about 2,000 stars.

Compared to our galaxy, this is a pretty cozy little corner.  Our galaxy is much bigger, on the order of 100,000 light-years with hundreds of billions of stars.  The observable universe is much, much bigger still, with some hundreds of billions of galaxies, depending on how you define "galaxy" and "the universe", each with a huge number of stars.

Summarizing: If you talk about "the galaxy", you are talking about on the order of a hundred million times more stars than our neighborhood, and if you're talking about "the universe" you're talking about on the order of a hundred billion times more stars than the galaxy, or on the order of ten quintillion times more stars than our neighborhood.  If only one in a million stars harbors an intelligent civilization, then there are almost certainly no others in our neighborhood, but some hundreds in the galaxy, and tens of trillions in the universe.

That one in a million figure is just for the sake of illustration.  At this point, we really don't know how likely or unlikely life is, if only because we don't have a lot of data points to go on.  We know for sure there's life on Earth.  It looks pretty unlikely that there's life on the Moon, or Mercury.  If there's life on the surface of Venus, it's got to be pretty bad-ass, but the best guess is probably not.  The jury's still out on Mars; we're pretty sure it had liquid water, but not at all sure either way about the life part.  Quite possibly there used to be but isn't any more.

There are a couple of other possibilities.  Jupiter's moon Europa probably has considerably more liquid water than we do, Saturn's moon Enceladus appears to have a large subsurface ocean, and Saturn's moon Titan has a dense atmosphere and pools of liquid.  Methane and ethane, that is, at a temperature of about -180C (-292F).  Could life develop in either of those environments?  We really don't know, but, maybe.  Certainly not a definite "no way", particularly since we've discovered life on earth in all kinds of extremely harsh environments where we used to think life had no business being.

It's also possible that there is some form of life in the clouds of the gas giants or floating in Venus's thick atmosphere, or on some less likely-looking moon than Enceladus, Europa or Titan, but at this point, Mars, Enceladus, Europa and Titan look like the best bets.

By that reckoning we have, in our solar system, one place that definitely has life and four others that plausibly might have, or might have had.  From what we know, our sun is not a particularly unusual star for our purposes here.  There are plenty of other main sequence stars of similar mass and age, and from recent discoveries, it looks like there are plenty of planets outside our solar system.  There are also plenty of stars not like our sun, but still with planets that might plausibly hold life.

Again, we don't know what the real odds are, but we can try to break things down more finely.  We might consider that any planet or moon with a large amount of liquid water is "favorable to life".  In our solar system, that would mean us, Europa or Enceladus (so far ... the jury is still out on Jupiter's moons Ganymede and Callisto).  Before too long we might have a good guess at how common such situations are.  For the sake of the argument, let's say that one in ten stars has such places.  Likewise, we could guess that there's a 50% chance that a place favorable to life actually develops life.  So that's one star in 50, or about 40 in our neighborhood.   And so forth.

This exercise of taking wild guesses at probabilities and multiplying them together goes by the formal name of the Drake equation (though it probably originates with Fermi).  Writing a formal equation doesn't reduce the wide error bars on our guesses about, say, how likely life is to develop or what portion of planets have favorable conditions, but it does give a well-defined framework for talking about such things.   That's helpful, but if you hear a statement like "According to the Drake equation there are N other technological civilizations in our galaxy," whether N is zero or a million ... um, no.  All that means is that under someone's particular set of guesses, there would be N technological civilizations.

You could make a reasonable argument that we're not just guessing at the numbers to plug into the Drake equation, we're guessing about what some of the terms even mean.  What is life, after all?  Does "technology" mean essentially the same thing for all possible kinds of life?

I suppose at some point I should explain the title of this post.  Why not start now?

Suppose that there's a planet fifty light-years away orbiting a star identical to the sun and with the exact same history and technology as us.  Could we detect signs of intelligent life from it?

The Earth (and so, therefore, Twin Earth) has been pumping out radio signals for about a century.  This means it's at least physically possible that we could pick up Twin Earth's broadcast signals from fifty light-years away.  Right now we would be picking up Twin Earth radio and TV shows from the early 1960s.

Before getting too excited about that, keep in mind that Twin Earth's radio signal is going to be very, very faint at that distance and right next to a much brighter radio source, namely Twin Sun (which is still pretty faint compared to most things we can pick up with radio telescopes).  Radio telescopes, even the really big lots-of-dishes-hooked-together kind, have considerably lower resolution than optical telescopes, and as far as I know we're not even close to being able to distinguish Twin Earth from Twin Sun in the radio frequencies, even if they were similarly bright.

Maybe we could, with a few more advances in technology and after careful observations, figure out that something unusual was going on around Twin Sun, but we're not just going to point a radio dish at Twin Earth and tune in to The Beverly Hillbillies.  Which may be just as well.

At this stage in our development, we are at the beginning of being able to contemplate detecting something like a civilization similar to ours orbiting a star in our immediate neighborhood.  Our telescopes (optical and radio) will doubtless improve, and we'll figure out ways of squeezing more and more information of of the signals they provide, but at the same time something else is going on: Earth, and therefore Twin Earth, is liable to go dark.

I'm not talking about civilization ending in the near future, or humanity morphing into some sort of cyber-species with no need for physical bodies.  Whatever you think the odds of those things may be, we're probably not going to spend too much more time spewing radio waves into empty space simply because it's wasteful.  Ultimately, it reduces bandwidth.  Even now, we can listen to the radio and watch TV over land-based connections.  That's probably just going to get more and more prevalent.  There's a good chance that through sheer technological progress we'll stop sending out whatever faint signal we've been sending.

So say that we, and thus Twin Earth, spend about 200 years sending out a radio signal indicating intelligence.  There are other ways we might detect Twin Earth and deduce that it has life, but only through a structured signal like our radio transmissions would it be clear that it was intelligent life -- OK, we could also look for Dyson spheres and such, but let's not go there just now.  It's also possible that Twin Earth could decide to deliberately send out a signal, permanently, to every star in its neighborhood, after it stops using high-powered radio broadcasts.  But "permanently" to creatures such as us is "momentarily" on planetary time scales.

To get a feel for what that last statement means, suppose that Twin Earth is like us in every way, except that it formed just a little bit earlier or later.  Say a tenth of a percent earlier or later.  Earth is about 4.54 billion years old.  A tenth of a percent of that is 4.54 million years.  If Twin Earth formed a tenth of a percent earlier than us, then we're several million years too late to pick up the brief flash of detectable signals of intelligent life it put out.  If it formed a tenth of a percent later, we won't have a chance to detect its hairless, tool-making social primates for millions of years yet.

This is why Drake's equation has a factor for how long we guess that an intelligent civilization would put out a detectable signal.  Obviously, the Twin Earth scenario is a gross simplification compared to the possibilities of life in the universe, but I think it sheds some light on the Fermi paradox.  There's a decent chance that everybody's out there, or will be at some point in the future, but we just plain missed them or they're not even here yet.



Electromagnetic radiation, which is all we currently know how to detect from other star systems, follows the inverse square law.  Twice as far away, a signal is four times fainter, three times farther away, nine times fainter, and so on.  That means that a star system 20 light-years away would have to produce a signal four times as strong as one 10 light-years away in order to be equally detectable.

Earth has has broadcast some sort of radio signal into space for the past hundred years or so, but at first that signal was very weak -- just a single small transmitter.  Eventually it grew, and quite likely it will eventually fade out.  The amount of time we've spent transmitting our brightest signal is shorter than the time we've spent broadcasting half that signal, and so forth.

Just so, the amount of time that a given civilization spends putting out a signal that we could detect decreases with distance.  At some point, probably well within our galaxy, it becomes effectively zero.  There could be civilizations 1,000 light-years away (again, the Milky Way is about 100,000 light-years across) that never have and never will put out a signal bright enough for us to detect.

In short, the search for extraterrestrial intelligent life probably boils down to watching a few thousand star systems in our immediate neighborhood for signatures of intelligence.  It seems quite plausible that some number of those planets harbor life, and that of those, a not-too-much smaller number of those have developed or will develop intelligent life and at some point in their histories, and for a brief time, put out something we could detect.

If that's the case, then some portion of them have already passed their detectable phase.  Maybe there are a dozen out there that have yet to announce themselves.  As always, a wild guess.  There might be none at all.  There might be hundreds, but probably not much more -- there are only so many stars close enough.  If there are such a dozen, and we can keep listening, we'll eventually spot one.  But "eventually" here likely means millions of years, not decades.

Are we likely to detect signals from civilizations around other stars?  Not in our lifetime, I'd say.  But some time in the next million years?  Maybe.



Postscript: I forget where I saw this mentioned, but another problem is that as our radio communications get more and more efficient, the signal we put out gets hard and harder to tell from noise.  Faint as it may be, a morse code radiotelegraph signal is clearly non-random and statistically unlike anything known to be naturally produced.  A compressed digital television signal looks much like random noise, which can come from any number of sources.  Mix together all the digital television signals currently broadcast on earth and you get something even more like noise.  Probably the only way we could detect a signal from Twin Earth and tell that it was a signal from something intelligent, would be for them to be sending a signal directly at us.  But if they're like us, they're only beaming signals to a few stars, and for relatively short periods of time.

Post-postscript: Randall Munroe's What If makes most of the same points as here, with a lot fewer words (and a couple of pictures).