Today’s video is sponsored by The Great
Courses Plus, thank-you to ours sponsors. Discovery is the fuel of the scientific progress. But how do discoveries happen? In 2012, the world rejoiced in the announcement
by CERN that the Large Hadron Collider had finally detected the Higgs Boson. It was a momentous day, the crowning achievement
of modern particle physics. The Higgs boson had been predicted half a
century beforehand, and indeed had represented the central goal of the $5 billion LHC. Decades of tedious planning, fundraising,
building and analyzing. But, when the day finally came, there was
also a tinge of disappointment, because this was exactly what we expected, as technically
impressive as the detection was, it didn’t fundamentally alter our view of the universe. In a way, we learned very little that day. But discovery doesn’t always happen that
way. Sometimes, they happen without such long term
planning, or indeed any planning at all - just open minds being in the right place at the
right time. One of the most famous examples happened in
1967, when graduate student Jocelyn Bell was studying the flickering of so-called radio
stars with her advisor Anthony Hewish. To resolve this flickering, they had built
an array of aerials sensitive to variations of a second or faster. And it was in within their data that Bell
discovered unexpected - a series of narrow shaped pulses repeating once every 1.3 seconds. Bell has just discovered the first pulsar,
for which her advisor, but not her, would pickup the Nobel prize seven years later. Pulsars are now understood to be rapidly spinning
neutron stars aligned to our line of sight, like spinning lighthouse beacons scattered
amongst the cosmos. But such stars are very rare, making up just
0.3% of the galactic population. And yet, despite their rarity, Bell’s serendipitous
discovery ushered in monumental insights into how stars live and die. Pulsars teach us that sometimes rare, one-off
events in science can have profound impact. A black swan event. You see black swans, just like pulsars, weren’t
always widely known to exist, as we know today. In the 2nd century AD, the Roman poet Decimus
Junius Juvenalis wrote that a perfect wife is “rara aris in terris nigroque simillima
cycno" - a rare bird in the earth and most similar to a black swan. At that time, black swans were thought to
not exist, and this phrase propagated accordingly into English language, becoming a common saying
in Tudor London as an expression of something being impossible. It wasn’t until 1697 that Europeans first
documented black swans when Dutch explorers encountered them in Western Australia. After this, the term black swan came to take
on a new meaning, generally signifying a rare event with profound consequences. For me, what we might call astronomical black
swans have always held a particular fascination - one that has culminated in a new research
paper on this topic that I’ll discuss today. Research directly supported by many of you
watching right now. You see there’s something captivating about
these events, who knows what we might discover tomorrow if we just keep an open mind? It’s what makes science so exciting, in
any given day, you could stumble across something that might change the world. As a recent example, the 2017 discovery of
Oumuamua, an interstellar asteroid passing through the Solar System, shocked many at
the time. Calculations predicted much lower rates of
such objects, so much so that they generally weren’t expected to be found for another
decade or so. As a result, Oumuamua has catalyzed new thinking
into the formation and transport of asteroids between the stars. Dozens of papers have been triggered to explain
its origins and space agencies are now taking seriously the idea of intercepting the next
interstellar asteroid that comes our way. Perhaps no field embodies the quest for black
swans more than SETI - the search for extraterrestrial intelligence. Here the idea is to monitor the sky continuously
for years, even decades, with persistent, careful patience, on the hope that one day,
in perhaps just one brief moment, an alien radio signal might be detected. Such a discovery would encapsulate a black
swan event, an inherently rare occurrence yet one that would fundamentally transform
our perception of the universe around us. But really, a one-off radio signal isn’t
enough. Because it’s only fair and rational that
the world would have a lot of skepticism about a signal that shows no signs of repeating. There’s an endless list of ways in which
the signal could be spurious or faked. If we’re talking about something as profound
as intelligent life - then one black swan isn’t enough, we need more. Indeed, that philosophy is self-evident in
the astronomical literature. The first hot-Jupiter discovered, 51 Pegasi
b, was met with considerable skepticism amongst the astronomical community at the time - few
predicted Jupiter-sized planets could get so close to their stars. It wasn’t until the analogs rolled in that
skepticism subdued and the exoplanet hypothesis became canonical. Similarly, after Jocelyn Bell’s discovery
of the first pulsar signal, the origin was deeply unclear and appeared at first blush
plausibly artificial. In fact, Bell and Hewish nicknamed it Little
Green Man 1, a term which was used both playfully but also with a profound undertone. Here too, it took a second discovery, dubbed
CP 1919 at the time, to establish that these were natural phenomena scattered across the
sky. So as remarkable as the first black swan was,
in both cases it was the follow-up detections that elevated these detections from mere curiosities
to Nobel-prize winning discoveries. To illustrate this, we’re going to explore
one of the most fascinating counter-examples, a case where no repeats were ever found and
so, not surprisingly, no Nobel prizes were ever awarded. Again, we’re going to turn to SETI here
because of its intimate relationship with black swan events. Let’s talk about the greatest Black Swan
in the SETI literature, indeed perhaps the greatest Black Swan in all of science - the
famous Wow Signal. Before we do, I want to thank the sponsor
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start your free trial today. Wow The so-called Wow signal is the kind of rare
astronomy story that has gone from scientific curiosity to a part of widespread public discourse,
a quick Google and you’ll find dozens of YouTube videos on the topic. One of the best ones is Event Horizon’s
interview with the discoverer Dr Jerry Ehman that I’ll link to down below. Ehman was a SETI volunteer studying computer
print outs from the Big Ear radio telescope in Ohio. In August 1977, one of the prints out he was
looking at showed a highly significant signal, characterized by digits 6EQUJ5, against which
Ehman scribbled Wow. Each digit here represents a signal to noise
measurement taken every 12 seconds, with letters symbolizing numbers greater than 9. What makes the signal exciting is that it
was narrow band, certainly less than 10kHz, suggestive of an artificial transmitter. Yet more, it occurred close to the hydrogen
line, a frequency SETI astronomers expected other civilizations might use for communication. In total the signal lasted 72 seconds but
that’s purely because the telescope was moving across the sky and any given star only
stayed in view for that long. In reality the signal could have persisted
for much longer. But critically the signal wasn’t detected
in real time, it was found by Ehman several days after the observations. To date, there is no accepted natural explanation
for the Wow signal, it’s origin continues to perplex us and it closely resembles the
kind of signal we’d hypothesize by an alien intelligence. The Wow signal is perhaps the ultimate black
swan, but one shrouded in doubt and skepticism since despite many efforts to re-observe it,
no other detections have been recorded. So does the absence of any subsequent detections
allow us to reject the idea that this is an alien transmission? METI president Douglas Vakoch concludes it
has little credibility since any putative SETI signal must be replicated for confirmation. Afterall, this could simply be a classified
spy satellite passing overhead at the time. But an absence of evidence is not evidence
of absence - whilst we might not be able to confirm the Wow signal as alien, does the
lack of repetition allow us to reject it? This is really where my new paper comes in,
for really this is a question of probability theory - a topic we have been fleshing out
into astrobiological domain over the last few years here. Put succinctly, how likely is that our subsequent
observations might have just been unlucky and not caught a second Wow transmission? What this really comes down to is repeatability. At a very basic level, we have to assume that
if the Wow signal does indeed originate from an artificial transmitter outside of the Solar
System, then it repeats on some unknown timescale with some unknown pattern. If that’s not true, we have a kind of bizarre
situation where an alien civilization transmitted a signal towards us once and once only in
their entire lifetime and it just so happened that the Big Ear telescope swept across that
precise patch of the sky at precisely the right moment. It’s a rather contrived scenario, and a
far more reasonable starting point is that this some kind of transmitter that intermittently
sends signals our way. Further, if this transmitter is some kind
of hello beacon, then its transmission pattern and rate are most reasonably stable over time. For example we might imagine some kind pre-programmed
sequence that simply repeats sending signals towards different stars. So that means that rate at which it was sending
our signals our way in 1977 isn’t really any different than today. Using just these assumptions, we can now make
mathematical progress because what we’re describing here is known as a uniform rate
process in statistical parlance. Let’s say that you conduct a survey for
a time t1 and then you get your black swan event. We’ve been thinking a lot about the Wow
signal but really it could be anything, Oumuamua, Boyajian’s star, the first pulsar. And really we can substitute time t1 for a
sample size n1, or effort level e1. We’ll stick to time in what follows, but
the point is the maths is the same and this is a very general formalism for thinking about
black swan events. Ok, so all we know is that it took a time
t1 to get our black swan. Perhaps one of the first questions we might
ask then is how long should we expect until we get a second signal, we can say occurs
at some unknown time t2 To save time, I’m going to skip over the
derivation, as well as other results in my paper like how to infer the repetition rate. I’ll link to the paper below for those who
want the gory details. Instead, let’s just jump right into the
result - how long until the Black Swan repeats, what is t2? It’s turns out t2 follows the highlighted
probability distribution. So we have a steadily decreasing function
as we go out to larger and larger t2 times. At first this might look confusing because
it peaks at zero. But with continuous probability distributions
like this, the y-axis is depicting a density, not an actual probability value. To get a probability out of this, you have
to take the area under the curve between two values. So, for example the probability that t2 is
some number between 0 and t1 is this shaded area, which equals 0.5, a 50% probability. Immediately this seems like great news, if
you observed for 10 days and bagged a Black Swan, just observe for another 10 days and
you have a 50% of getting another. Sounds like a good deal. Now naively, we might think that if double
the observing time, so go out to 2*t1, we should expect the probability to double. So we’d have a 100% chance of detecting
a second black swan. But looking at the curve, we can see that’s
clearly wrong, in fact the probability only goes up to 2/3, 67%. OK, fine, let’s just be more aggressive
and observe for, say, 20 times as long as we did the first time round, 20 t1. Once again though, the shape of the distribution
defies intuition and the probability only goes as far as 95%. Now 95% might seem pretty good to the non-scientist,
but really what it means is that there’s a 1-in-20 chance the Black Swan repeats but
you just didn’t happened to miss it. And when we’re talking about a question
like alien life in the universe, 1-in-20 confidence is hardly conclusive. What this function teaches us is that Black
Swans demand patience - yes you might get lucky and bag a second one pretty quickly,
but its also quite plausibly you have to wait much, much longer than how long it took you
the first time around. So let’s come back to the Wow signal and
see what our formula has to say here. If we add up how long was spent observing
the region after the first detection, how likely is that we just missed a repetition? The Wow signal was initially detected in a
9-day run, where it visited each part of the sky just once. So we can say that t1 = 9 separate attempts. After that, the Big Ear observed it again
somewhere between 50 to 100 times more with the same strategy, but no further detections. Speaking in 2016, Ehman said that considered
these 50 failed attempts enough for him to broadly reject the alien hypothesis [“We
should have seen it again when we looked for it 50 times. Something suggests it was an Earth-sourced
signal that simply got reflected off a piece of space debris.”] But is Ehman right? If t1 = 9 attempts and t2 = 50 attempts, or
5.6 times t1, then the new formula reveals there there’s a 15% chance that Wow is repeating
but Big Ear just missed it. I think Ehman’s conclusion might be a little
a premature then, there is a plausible chance this signal is ongoing. Now you might say perhaps the repeat time
is just really long, maybe many years, but that’s inherently unlikely given the time
it took Big Ear to bag the first detection and is indeed built into this statistical
calculation. But Big Ear isn’t the only telescope to
look for the Wow signal in the years that followed with amateur astronomer Robert Gray
spearheading several campaigns. The most comprehensive study was published
just last year, in which Gray and colleagues used the far more sensitive Allan Telescope
Array. In total, the team collected a staggering
100 hours of observing time monitoring the region and this represents the most comprehensive
search to date. They published their results just last year
and sadly found no repeating signals in that field. Now if we want to use these numbers, it’s
a little bit tricky because Gray’s observing strategy was somewhat different from that
of Big Ear. Let’s start by assuming that the Wow signal
is a sporadic signal that lasts not much more than 72 seconds. Some support for this comes from the fact
that the signal was only detected in one of Big Ear’s two horns, meaning the signal
either abruptly started or ceased in the 3 minute time interval between the two horns
observing the same part of the sky. In this case, we can say that Gray collected
100 hours of data, which is 280 times longer observed than the time it took Big Ear to
obtain their initial detection. Plugging this into our formula, the probability
that Gray could have missed a repeating Wow signal is pretty small, just 0.4%. But another way we can think about the problem,
although somewhat contrived, is that the Wow signal lasts many hours, say a whole day. This is pretty unlikely because it means the
3 minute window the Big Ear looked at it was the exact end-point to this prolonged signal. But if this were true, it’s not so much
the 100 hours of integrated observing time we care about but rather how many unique days
did Gray observe for? From correspondence with Gray, he shared that
they observed on 41 unique days, which when combined with the Big Ear follow-up means
no repeats for 91 days. Here, the odds look much more favorable, giving
a 9% chance that the Allan Telescope Array could have missed it. However, as I said, I think is a pretty contrived
setup and I’d say the 0.4% calculation is the much more reasonable one here. So black swan theory doesn’t prove that
Wow can’t be aliens, but it does put significant pressure on the idea that Wow is a repeating
beacon. Perhaps then, it was, as Ehman suggested,
just a terrestrial radio signal that somehow entered the Big Ear horns. But before we give up on alien signals, you
might have heard that the privately funded Breakthrough Listen team recently found their
own Wow-like signal from a completely different part of the sky. We still don’t have an official report or
paper from the team about their signal, but after I contacted the team directly, they
shared that the source, Proxima Centauri, had been observed for a total of 1550 cumulative
minutes over a span of 1.75 years before their signal was found. Obviously follow-up is ongoing and its unclear
how much has been obtained, but we can use our formula to estimate, how much data would
it take to put pressure on the repeating beacon hypothesis, similar to as we did for Wow? The answer is that to reach 95% confidence,
they’d need to collect 29,450 minutes, which corresponds to 20.5 days of round-the-clock
monitoring. Remember that 95% is not conclusive, but it
means that in just intensive observing season we could at least put pressure on the idea
that this is a repeating beacon. Once again then, this highlights the enormous
patience that Black Swans demand. For those wanting to learn more about this
candidate, be sure to check out our previous video on the topic, as well a live stream
by the Breakthrough team themselves where they cast their own doubts on the reality
of the signal. Black Swans will surely continue to be discovered
from time to time, both within SETI and astronomy more broadly. Louis Pasteur once famously wrote that “Chance
favors the prepared mind” and in this work, we can lay down some of the statistical tools
so that next time we’re ready. Black Swans remind us that often good things
come to those who wait, that through perseverance and patience, extraordinary events can and
will sometimes be found, and those one-offs can often be the most remarkable discoveries
in science. All we have to do is listen, persevere, and
keep an open mind, for in that approach, lies the possibility to unimaginable discoveries. So until next time, stay thoughtful and stay
curious. Thanks so much for watching everybody. This research was supported by donors to the
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