Unbecoming Levity :: Silent Sky - A Thought Experiment

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Silent Sky - A Thought Experiment

by Abacquer on Wed 28 May 2008 12:57 PM EDT | Permanent Link | Cosmos

This is an interesting thought experiment and it involves statistics and some figuring, so I welcome any of my smart friends or anybody who cares to think about it to chime in here.

Assume that sentient civilizations with the ability to transmit some form of radiant communications signals (radio, light, whatever) started appearing in our galaxy as early as 4.5 billion years ago (when the Earth was forming), and assume that they continue to appear (each on its own evolutionary trajectory) for another 4.5 billion years. Further assume that over this timespan of 9 billion years a total of one million different intelligent civilizations begin transmitting radiant communications. After a random time period of 100 to 1000 years each civilization stops transmitting radiant signals, either because they move on to a better technology that does not require radiant communication (pretty much necessary for interstellar communications) or the civilization dies out. Finally given that our galaxy's diameter is about 100,000 light years, assume that any of these civilizations when transmitting would be at some random distance from us which does not exceed 100,000 light years (yes I know that's a little big since we aren't at the very edge of the galaxy, but bear with me.)

Now, here we are, smack-dab in the middle of that timescale, halfway between year 1 and year 9 billion. We turn an array of radio telescopes to the sky and listen in all directions simultaneously, constantly, for a period of 1,000 years.

Is our sky silent? Or is it noisy? With a million civilizations out there at some point or another, all sending signals out at different times, what are the chances we would hear none of them at all even if we listen for 1000 years?

I threw together a crude simulation last night to try and answer this question, and I have a result which you might find surprising, but I'm curious to know what other people think first. Care to venture a guess? Or perhaps create your own sim and see what results you get? I'll post my results tomorrow.

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Comments

Re: Silent Sky - A Thought ...

by vespa rich on Wed 28 May 2008 03:05 PM EDT | Permanent Link

inthought I read recently that our transmissions disapated and were lost in the background noise of space...

Re: Silent Sky - A Thought ...

by Abacquer on Wed 28 May 2008 03:39 PM EDT | Profile | Permanent Link

If by "lost" you mean "very hard to detect" I will grant you that. For the purposes of the experiment, assume you are able to detect any signal no matter how weak even if it has crossed 100,000 LYr of space to reach you.

Re: Silent Sky - A Thought ...

by JPB on Wed 28 May 2008 04:42 PM EDT | Profile | Permanent Link

One million civilizations over 9 billion years in the space of 100,000 light years radius -- it seems to me that you have a low probability of hearing any of them.

That's the most detailed analysis I can muster at the moment.

Re: Silent Sky - A Thought ...

by Pat on Thu 29 May 2008 08:19 AM EDT | Profile | Permanent Link

My thought process on the problem:

One way to look at this is to imagine a large beach ball which would represent the three dimensional volume of our galaxy.

Next, get a handful of ping pong balls. The ping pong balls' walls would represent the three dimensional area that a radio signal would be propagating from each ping pong balls center.

Now, if you could, take a couple or three ping pong balls and toss them in the beach ball (assuming it wouldn't deflate ,that's a whole other though problem). The volume within the beach ball occupied by the ping pong balls' plastic walls (not their centers) would be the area at any given time you could 'detect' the race that 'created' the ping pong ball.

Some things to consider here:

1. The ping pong balls would vary in size up to the size of the beach ball, but their wall thickness would remain the same (over time they would grow).

2. On average, you would have 11 to 12 of these balls in the beach ball at any given time.

3. To represent us listening for a signal, pick a single random point somewhere in the beach ball.

With all of that, it would seem very unlikely we would ever be listening as a ping pong ball grew past us. Looking from the outside of the beach ball it would look noisy, but very little volume of the beach ball is actually occupied by the plastic of the ping pong balls. Unfortunately, to us on our little speck of dust in the beach ball, it would appear we were all alone.

Re: Silent Sky - RESULTS

by Abacquer on Thu 29 May 2008 09:54 AM EDT | Profile | Permanent Link

My brute force approach was to run 10,000 simulations of the scenario described above and keep track of how often the time frame when a civilization's transmission arrived at Earth overlapped with when Earth happened to be listening. If we heard nothing, that was no overlaps. If we received signals from one civilization that was 1 overlap, and so forth. Here are the results:

1672 overlaps in 10000 sims.  Overlaps/sim = 0.17.


Statistics:





0 overlaps --> 8467 sims


1 overlaps --> 1406 sims


2 overlaps --> 115 sims


3 overlaps --> 12 sims


4 overlaps --> 0 sims


5 overlaps --> 0 sims


6 overlaps --> 0 sims


7 overlaps --> 0 sims


8 overlaps --> 0 sims


9 overlaps --> 0 sims

So based on the simulation, there is about an 84.7% chance of hearing nothing at all when you turn your ear to the sky for 1000 years in the above scenario. Your chance of hearing 1 or more civilizations is about 15% (1 chance in 6.5).

As VespaRich notes, this doesn't take into consideration signal loss, nor does it take into consideration stellar motion, stellar noise, or the ability to recognize an alien signal when we see it. Given all that, it seems unlikely even in a galaxy where a million civilizations arise, that we will ever discover one by receiving radiant signals. Space and time are simply too vast for that sort of approach.

Incidentally a member of the AtMoB discussion list came up with a simple statistical way to calculate the odds. He computes the chance for a silent sky at 88.5% if all civs transmit for 1000 years, or 80.1% if all civs transmit for 100 years. My result based on random transmission periods of 100 to 1000 years falls right between these at 84.7% so I suspect his reasoning is sound. Here's what he said:

With uniformly distributed start dates, the calculation is simple
for best and worst cases: we just need to exclude a listening
window. For a 100 year radiator:

((9e9 - 1100)/9e9) ^ 1000000 or ~88.5% chance of silence

For a 1000 year radiator:

((9e9 - 2000)/9e9) ^ 1000000 or ~80.1% chance of silence

Those are the upper and lower bounds. 1000-year case goes to
about 50% at 3.15M civs.

Re: Silent Sky - A Thought ...

by Mike on Thu 29 May 2008 02:50 PM EDT | Profile | Permanent Link

I assume the chances of another intelligent lifeform ever existing in the universe is high. Given the size of the universe, the chances of Earth being within a few thousand light years of a star system where an intelligent civilization once existed, or will someday exist, is very remote. And the chances of being around in the same epoch as any other civilization is probably nil.

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