Galactic civs limited by inability to grow exponentially

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Galactic civs limited by inability to grow exponentially

Postby The Reaper » Thu Jun 25, 2009 12:13 am UTC

http://www.physorg.com/news164986606.html
Galactic Colonization Limited By The Inability To Expand Exponentially

(PhysOrg.com) -- For more than 50 years, many have taken the so-called Fermi Paradox to indicate that the existence of intelligent alien civilizations is an impossibility. However, a recent re-examination of the paradox points out that, rather than discounting the spread of an intelligent civilization, the Fermi Paradox merely points out that advanced civilizations with exponential growth are unlikely to exist.

Enrico Fermi speculated (during a lunch break) that the age of the universe, as well as its size, meant that there should be a number of advanced societies keeping Earth company, in a galactic sense. Growth of these civilizations would be exponential, Fermi implied, and therefore if they existed, we would have encountered them already. Ergo, advanced alien societies must not exist, since their expansion hasn't brought them into the range of our detection.

A new take on the Fermi Paradox, though, changes the equation a bit. At Pennsylvania State University, two scientists suggest that the key to the paradox is the assumption that civilizations would colonize the universe at an exponential rate. Jacob Haqq-Misra and Seth Baum point out that finite resources preclude exponential expansion. Technology Review offers a look at the problem of exponential growth:

"The problem is that this kind of growth may not be possible, and they look at Earth as an example. For any expansion to be sustainable, the growth in resource consumption cannot exceed the growth in resource production. And since Earth's resources are finite, and it has a finite mass and receives solar radiation at a constant rate, human civilization cannot sustain an indefinite, exponential growth."

This means that, if we decide to colonize our galaxy, Earth's civilization will be unable to do so at an exponential rate. If you apply the realities of Earth to possible alien civilizations, then it becomes much more likely that there are other advanced societies out there. Like Earth, though, they are limited in their expansionary capabilities. Perhaps there are thousands of alien societies out there, just trying to effectively colonize their moons or settle on planets in their solar systems. It is possible that, if that is the case, the question of existence of intelligent alien life may not be answered in our life times.
This popped up on my sciencey news site, and I figured it was interesting, but I wasn't sure if this should go here, or in Science.

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Re: Galactic civs limited by inability to grow exponentially

Postby Sharlos » Thu Jun 25, 2009 12:31 am UTC

It seems to be a flawed argument to me, if a civilisation is advanced enough to leave their solar system, unsustainable needless growth would hardly be an overarching goal.

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Re: Galactic civs limited by inability to grow exponentially

Postby Diadem » Thu Jun 25, 2009 12:44 am UTC

But exponentional growth is not needed at all for the Fermi paradox.

The galaxy is about a hundred thousand lightyears across. Even if expansion is as slow as 1% of the speed of light, then an alien civilization will fill it in 10 million years. Which is a very short timespan, compared to evolutionary times.

Also, can you get a publication for something so obvious these days? Has physics fallen that low? Of course growth can not be forever exponentional in a universe where travel is limited by the speed of light. The best you can do is a third power, since that is how fast your reachable volume of space goes up. This is trivial.
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Re: Galactic civs limited by inability to grow exponentially

Postby i » Thu Jun 25, 2009 12:51 am UTC

I read the OP's quote and immediately thought it was stupid. So I went to the blog and this is what it said in the comments section:
I don't think this is the argument in the paper. Earth's resources are finite, but a multi-planetary civilization has by definition access to more than one Earth, so as long as they don't consume more resources per planet than there are available, there is no constraint to the total size of the civilization.

The paper's argument is a bit subtler (although possibly made more confusing than necessary by the references to our single-planet civilization, which doesn't translate well to the more unconstrained general case). It simply states that the Fermi Paradox assumes exponential growth in a civilization, and thus failure to observe extraterrestrial intelligences is only an argument against exponential growth civilizations. While it is true that an Earth-bound civilization might find exponential growth unsustainable because of resource constraints, they don't claim that such resource constraints will make the exponential growth of other civilizations unsustainable, only that some mechanism might be impeding exponential growth, and thus make current observations consistent with the existence of extraterrestrial intelligence.


so..... it's crappy journalism.

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Re: Galactic civs limited by inability to grow exponentially

Postby Sharlos » Thu Jun 25, 2009 12:56 am UTC

Diadem wrote:But exponentional growth is not needed at all for the Fermi paradox.

The galaxy is about a hundred thousand lightyears across. Even if expansion is as slow as 1% of the speed of light, then an alien civilization will fill it in 10 million years. Which is a very short timespan, compared to evolutionary times.

Also, can you get a publication for something so obvious these days? Has physics fallen that low? Of course growth can not be forever exponentional in a universe where travel is limited by the speed of light. The best you can do is a third power, since that is how fast your reachable volume of space goes up. This is trivial.

But why are you assuming that there will be any expansion at all? That is the fundamental flaw I see with this premise.

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Re: Galactic civs limited by inability to grow exponentially

Postby Diadem » Thu Jun 25, 2009 1:18 am UTC

Sharlos wrote:But why are you assuming that there will be any expansion at all? That is the fundamental flaw I see with this premise.

I'm not. I'm merely stating that lack of exponentional growth does not solve Fermi's paradox.

We do not see the aliens. Something must be preventing them from comming to us. Lack of exponentional growth is not it. So it must be something else.
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Re: Galactic civs limited by inability to grow exponentially

Postby The Reaper » Thu Jun 25, 2009 1:20 am UTC

Diadem wrote:
Sharlos wrote:But why are you assuming that there will be any expansion at all? That is the fundamental flaw I see with this premise.

I'm not. I'm merely stating that lack of exponentional growth does not solve Fermi's paradox.

We do not see the aliens. Something must be preventing them from comming to us. Lack of exponentional growth is not it. So it must be something else.
How bout the fact that its a really big place? Or that we've only really been noticable for the past... 100 years? sooooo anything within 100 light years might find us, but things on the other side of the galactic disc probably wont, even if they are spreading like wildfire.

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Re: Galactic civs limited by inability to grow exponentially

Postby i » Thu Jun 25, 2009 1:35 am UTC

The Reaper wrote:
Diadem wrote:
Sharlos wrote:But why are you assuming that there will be any expansion at all? That is the fundamental flaw I see with this premise.

I'm not. I'm merely stating that lack of exponentional growth does not solve Fermi's paradox.

We do not see the aliens. Something must be preventing them from comming to us. Lack of exponentional growth is not it. So it must be something else.
How bout the fact that its a really big place? Or that we've only really been noticable for the past... 100 years? sooooo anything within 100 light years might find us, but things on the other side of the galactic disc probably wont, even if they are spreading like wildfire.

Earth radio signals become undetectable at one lightyear away.

Also, extraterrestrial life doesn't exist.

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Re: Galactic civs limited by inability to grow exponentially

Postby The Reaper » Thu Jun 25, 2009 1:41 am UTC

i wrote:Also, extraterrestrial life doesn't exist.

And the earth was made 6k years ago. :\ And it's flat.

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Re: Galactic civs limited by inability to grow exponentially

Postby i » Thu Jun 25, 2009 1:49 am UTC

The Reaper wrote:
i wrote:Also, extraterrestrial life doesn't exist.

And the earth was made 6k years ago. :\ And it's flat.


Do you have evidence for any of those claims?

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Re: Galactic civs limited by inability to grow exponentially

Postby Princess Marzipan » Thu Jun 25, 2009 2:15 am UTC

i wrote:
The Reaper wrote:
i wrote:Also, extraterrestrial life doesn't exist.

And the earth was made 6k years ago. :\ And it's flat.


Do you have evidence for any of those claims?

I'm willing to bet he has as much for his as you do for yours.
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Re: Galactic civs limited by inability to grow exponentially

Postby The Reaper » Thu Jun 25, 2009 2:26 am UTC

Princess Marzipan wrote:
i wrote:
The Reaper wrote:
i wrote:Also, extraterrestrial life doesn't exist.

And the earth was made 6k years ago. :\ And it's flat.


Do you have evidence for any of those claims?

I'm willing to bet he has as much for his as you do for yours.

I have photographic evidence that the earth is flat and circular, as well as having literature / historical proof that the earth was made 6k years ago. NEVERMIND THE QUALITY OF MY EVIDENCE. I HAVE IT SO IT MUST BE TRUE!

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Re: Galactic civs limited by inability to grow exponentially

Postby BlackSails » Thu Jun 25, 2009 2:37 am UTC

Well, obviously long term growth is logistic, not exponential.

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Re: Galactic civs limited by inability to grow exponentially

Postby i » Thu Jun 25, 2009 2:41 am UTC

The Reaper wrote:
Princess Marzipan wrote:
i wrote:
The Reaper wrote:
i wrote:Also, extraterrestrial life doesn't exist.

And the earth was made 6k years ago. :\ And it's flat.


Do you have evidence for any of those claims?

I'm willing to bet he has as much for his as you do for yours.

I have photographic evidence that the earth is flat and circular, as well as having literature / historical proof that the earth was made 6k years ago. NEVERMIND THE QUALITY OF MY EVIDENCE. I HAVE IT SO IT MUST BE TRUE!


DAMN YOUR CREATIONIST INTELLECT! But rest assured the minions of satanic evilution will have the last laugh! Mwuahaha!

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Re: Galactic civs limited by inability to grow exponentially

Postby Bright Shadows » Thu Jun 25, 2009 3:25 am UTC

i wrote:
The Reaper wrote:
Princess Marzipan wrote:
i wrote:
The Reaper wrote:
i wrote:Also, extraterrestrial life doesn't exist.

And the earth was made 6k years ago. :\ And it's flat.


Do you have evidence for any of those claims?

I'm willing to bet he has as much for his as you do for yours.

I have photographic evidence that the earth is flat and circular, as well as having literature / historical proof that the earth was made 6k years ago. NEVERMIND THE QUALITY OF MY EVIDENCE. I HAVE IT SO IT MUST BE TRUE!


DAMN YOUR CREATIONIST INTELLECT! But rest assured the minions of satanic evilution will have the last laugh! Mwuahaha!

Meh, the pope doesn't care, so I won't.
:p

Anyway, 1% the speed of light is really fast.
The whole paradox is silly. Why would a civilization want to expand past an area they could well inhabit for a very long time? Filling up each planet before expanding further seems the more likely stepwise system, which would be much slower than dropping off some people and continuing on. Add in the likelihood of complex life capable of moving between solar systems... Yeah.
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Re: Galactic civs limited by inability to grow exponentially

Postby Kain » Thu Jun 25, 2009 4:15 am UTC

The Reaper wrote:
Princess Marzipan wrote:
i wrote:
The Reaper wrote:
i wrote:Also, extraterrestrial life doesn't exist.

And the earth was made 6k years ago. :\ And it's flat.


Do you have evidence for any of those claims?

I'm willing to bet he has as much for his as you do for yours.

I have photographic evidence that the earth is flat and circular, as well as having literature / historical proof that the earth was made 6k years ago. NEVERMIND THE QUALITY OF MY EVIDENCE. I HAVE IT SO IT MUST BE TRUE!


The Earth is most definately NOT flat. It is a hollowed out sphere, with humans living only on the interior surface, with the sun inside it, orbiting a shiny starlike thing we call space. I have this on the really good authority of some peyote using people out in New Mexico! They have a really clear sky! Clearly their analysis is best!
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Re: Galactic civs limited by inability to grow exponentially

Postby The Reaper » Thu Jun 25, 2009 6:58 am UTC

Kain wrote:
The Reaper wrote:
Princess Marzipan wrote:
i wrote:
The Reaper wrote:
i wrote:Also, extraterrestrial life doesn't exist.

And the earth was made 6k years ago. :\ And it's flat.


Do you have evidence for any of those claims?

I'm willing to bet he has as much for his as you do for yours.

I have photographic evidence that the earth is flat and circular, as well as having literature / historical proof that the earth was made 6k years ago. NEVERMIND THE QUALITY OF MY EVIDENCE. I HAVE IT SO IT MUST BE TRUE!


The Earth is most definately NOT flat. It is a hollowed out sphere, with humans living only on the interior surface, with the sun inside it, orbiting a shiny starlike thing we call space. I have this on the really good authority of some peyote using people out in New Mexico! They have a really clear sky! Clearly their analysis is best!

I stand defeated. Hopefully the infinite singularity inside our planet will forgive me.


On an interesting note, this sounds like the plain of fire may well be inhabited by non-fire creatures living inside giant bubbles floating around in the fire around small singularities...... o_O

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Re: Galactic civs limited by inability to grow exponentially

Postby Freakish » Thu Jun 25, 2009 9:30 am UTC

I don't understand what Earth's resources have to do with space travel... Once you get to another planet with it's own resources doesn't Earth become moot?
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Re: Galactic civs limited by inability to grow exponentially

Postby Plasma Man » Thu Jun 25, 2009 9:42 am UTC

Not entirely, Earth would still be your main base. Also, being able to access more planets does not equal infinite resources. Your resources increase, but are still finite: If finite resources preclude growing exponentially, that limits your growth to below an exponential rate.

I'd be like to see more work done on this, it's an interesting idea.
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Re: Galactic civs limited by inability to grow exponentially

Postby Zamfir » Thu Jun 25, 2009 11:36 am UTC

Plasma Man wrote:If finite resources preclude growing exponentially, that limits your growth to below an exponential rate.


But a finite total resource base is not an impediment to exponential growth, it is an impediment to infinitely during exponential growth, and of course to any infinite growth.

But that's hardly relevant: by the time finite resources are limiting your growth, you must already be using most of them, including presumably our solar system, and Fermi's paradox is back.

For the argument from the paper to work, you do not need a stop to exponential growth, but to all (spatial) growth.

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Re: Galactic civs limited by inability to grow exponentially

Postby Sharlos » Thu Jun 25, 2009 12:03 pm UTC

My problem with this paradox is that it assumes intelligent life will have gone searching for us (and unless your closer than a hundred light years of Earth, we'd be very hard to find). And that it assumes intelligent life is capable of travelling to discover us, after all, we aren't spreading our probes throughout the galaxy in search of life.

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Re: Galactic civs limited by inability to grow exponentially

Postby Heisenberg » Thu Jun 25, 2009 1:24 pm UTC

Sharlos wrote:My problem with this paradox is that it assumes intelligent life will have gone searching for us (and unless your closer than a hundred light years of Earth, we'd be very hard to find). And that it assumes intelligent life is capable of travelling to discover us, after all, we aren't spreading our probes throughout the galaxy in search of life.

Not really, it just assumes that a civilization will expand to all the good planets (Earth is a good planet). And it's not assuming that all aliens are expansionist, just that some of them are (and looking at our history, it's important to point out that we do not all still live in Africa, so expansionist life does exist). And as far as probing the galaxy for life, the Voyager left our system many years ago in search of friends, and we're just getting started.

Plasma Man wrote:Not entirely, Earth would still be your main base.

Not if we were smart. I can think of a planet right now that is close by, has a wealth of untapped resources, is habitable, and is 9 times easier to take off and land from than Earth. And I bet there's one within a hundred light years that's even better.

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Re: Galactic civs limited by inability to grow exponentially

Postby Kain » Fri Jun 26, 2009 2:04 am UTC

Heisenberg, which planet/moon are you thinking of? Europa, Enceladeus (sp?), Titan, some other one? The problem with using any planet/moon/etc other than Earth as a base of the species is our attachement to the familiar. I sincerly doubt that an expanding human empire would abandon Earth as its cultural and political center, unless some catastrophe dictated otherwise.

On to the paradox: We are assuming that a civilization capable of expanding exponentially would want to. What if every civilization that operates on the idea of exponential expansion somehow manages to destroy itself before it can spread out of its home stellar system? After all, we can see that uninhibited growth on Earth can have extremely detrimental consequences.
Perhaps then the only civilizations that make it to the interstellar arena are those that by nature or ideology have adapted a linear growth model or the like. Should that be the case, the resources or lack thereof would not be the issue, but instead the vastness of space seperating us from them. Just a thought...
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Re: Galactic civs limited by inability to grow exponentially

Postby gmalivuk » Fri Jun 26, 2009 4:26 am UTC

Sharlos wrote:My problem with this paradox is that it assumes intelligent life will have gone searching for us (and unless your closer than a hundred light years of Earth, we'd be very hard to find).

We can already detect planets farther away than that and we only just started looking. While it's (probably) true that you wouldn't know there was technological civilization on Earth until you were fairly close, you'd know its size and temperature and distance from the sun from a lot farther off, and you'd know some of the elements it was made of. That'd be enough to know that Earth is a potentially excellent planet for anything that lives in something like our own sort of environment.

If we were going through the galaxy, with the intent to find a place to live, and found a planet where those characteristics matched Earth's, you're damn right we'd go in for a closer look.
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Re: Galactic civs limited by inability to grow exponentially

Postby Bakemaster » Fri Jun 26, 2009 4:42 am UTC

Diadem wrote:Of course growth can not be forever exponentional in a universe where travel is limited by the speed of light. The best you can do is a third power, since that is how fast your reachable volume of space goes up.

You keep using this word. I do not think it means what you think it means.
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Re: Galactic civs limited by inability to grow exponentially

Postby gmalivuk » Fri Jun 26, 2009 4:46 am UTC

Um... you sure he's the one misunderstanding the precise mathematical meaning of exponential growth...?
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Re: Galactic civs limited by inability to grow exponentially

Postby The Reaper » Fri Jun 26, 2009 7:36 am UTC

gmalivuk wrote:Um... you sure he's the one misunderstanding the precise mathematical meaning of exponential growth...?

I thought I knew, but now I'm not so sure....

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Re: Galactic civs limited by inability to grow exponentially

Postby Diadem » Fri Jun 26, 2009 12:42 pm UTC

The thing is that you'd expect earth's biological signature to attract alien civiliations flies to a pot of honey. An oxygen atmosphere screams "LIFE!", and any advanced alien civilization should be able to read that message from pretty much the other side of the galaxy.

It's possible that all the aliens out there are enlightened, and think "Ok that planet's taken, we'll leave it alone". But some sort of explanation of why all alien civilizations out there are peaceful is then required. I suppose "because they do not exist" would be a good explanation.

Even so you'd expect them to be curious, and come say hello. Maybe star trek is true after all, and the aliens have a prime directive forbidding interference with primitive lifeforms. But that does not explain why we can not see them. Spaceships capable of travelling interstellar distances should be detected over huge distances. So should alien settlements. Maybe they are giving us a very wide berth or maybe they are using camouflage techniques near us. But that implies a lot of assumptions about the nature of those aliens. So without some sort of explanation why all alien races would do that, this explanation fails.

Space is vast. And interstellar travel is slow. That is a serious obstacle towards meeting aliens. But the timescales involved are also huge. And curiosity is most likely a biological imperative for any intelligence. So if alien lifeforms are out there, they must be expanding. And they will with overwhelming probability been doing that for a very long time.

So I can see only two explanations for lack of aliens in our every day life.
1) They do not exist.
2) They are for some incapable of reaching / contacting us.
3) They purposefully leave us alone

No serious scientist believes 1. All the laws of nature seem to imply that life should be common. And for nearly a thousand years science has been downgrading humanity, from God's creation at the centre of the universe to just some slightly-more-intelligent ape on some backwater planet somewhere in a corner of a run-of-the-mill galaxy. Suddenly promoting humanity again to a central and unique role in all the 'verse... would be shocking.

Number 2 is a real possibility. A sad one. Maybe sci-fi will never be more than sci-fi. Maybe it will turn out that there just isn't much more to science then we have right now, and we'll never develop the technology to expand around the galaxy, because such technology is just a theoretical impossibility.

The best explanation would be 3. That would be awesome, since that would imply we life in the star trek universe. So cool.
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Re: Galactic civs limited by inability to grow exponentially

Postby Belial » Fri Jun 26, 2009 12:56 pm UTC

4. Something kills nearly all civilizations when they reach the point of being capable of interestellar travel. The "something" in question might be themselves (ie, any civilization that advanced has a high rate of self-destruction), some obscure law of the universe ("who knew that turning on our warp drive would cause our planet to blip out of existence?"), or some inscrutable but mostly-dormant alien force bent on suppressing or destroying all interstellar powers ("When we tested our warp drive, something out past the solar system rim, that we previously assumed was an asteroid, woke up and started moving toward homeworld. I wonder if they're friendly....").

It's been done as a sci-fi trope in grimmer universes a lot. The videogame "Freespace" and the book series "Revelation Space" jump readily to mind.
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Re: Galactic civs limited by inability to grow exponentially

Postby gmalivuk » Fri Jun 26, 2009 1:32 pm UTC

The Reaper wrote:
gmalivuk wrote:Um... you sure he's the one misunderstanding the precise mathematical meaning of exponential growth...?

I thought I knew, but now I'm not so sure....

My point was, Diadem's analysis is correct, so Bakemaster thinking there's something wrong with it was probably incorrect, though I'm not sure what problem he saw.

Exponential growth means like 2t, whereas light speed limits us to something like t3, which is much, much slower after the exponential growth really gets going.
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Re: Galactic civs limited by inability to grow exponentially

Postby MartianInvader » Fri Jun 26, 2009 1:38 pm UTC

Why is everyone assuming that aliens would want an oxygen-rich atmosphere (or anything else that we have on earth)? For all we know an alien species might breathe gaseous silicon and talk by emitting high-intensity gamma rays. To them the earth would look like a frigid wasteland incapable of supporting life.

...also, I gotta mention that one of my big pet peeves is people using "exponential" as a synonym for "very fast." POLYNOMIAL GROWTH CAN BE PRETTY FAST TOO, FOLKS! :oops:
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Re: Galactic civs limited by inability to grow exponentially

Postby gmalivuk » Fri Jun 26, 2009 3:05 pm UTC

People here are using "exponential" to mean "exponential", in a mathematical sense. I haven't seen any of the misuse you describe anywhere in this thread, so I'm not sure what your point is.

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Re: Galactic civs limited by inability to grow exponentially

Postby BlackSails » Fri Jun 26, 2009 4:37 pm UTC

Belial wrote:It's been done as a sci-fi trope in grimmer universes a lot. The videogame "Freespace" and the book series "Revelation Space" jump readily to mind.


Also homeworld. You jump back to your home planet after completing the first hyperspace test to find the atmosphere boiled away and everyone dead because you just violated a 10,000 year old peace treaty.

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Re: Galactic civs limited by inability to grow exponentially

Postby Bakemaster » Fri Jun 26, 2009 4:44 pm UTC

gmalivuk wrote:My point was, Diadem's analysis is correct, so Mr. Bakerstein thinking there's something wrong with it was probably incorrect, though I'm not sure what problem he saw.

Diadem wrote:exponentional

These are the jokes, people.

(Though in the interest of full disclosure, I also do not really understand what Greg is talking about.)
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Re: Galactic civs limited by inability to grow exponentially

Postby i » Fri Jun 26, 2009 4:51 pm UTC

Diadem wrote:No serious scientist believes 1. All the laws of nature seem to imply that life should be common. And for nearly a thousand years science has been downgrading humanity, from God's creation at the centre of the universe to just some slightly-more-intelligent ape on some backwater planet somewhere in a corner of a run-of-the-mill galaxy. Suddenly promoting humanity again to a central and unique role in all the 'verse... would be shocking.


You're using a philosophical concept to support a question of science.

MartianInvader wrote:Why is everyone assuming that aliens would want an oxygen-rich atmosphere (or anything else that we have on earth)? For all we know an alien species might breathe gaseous silicon and talk by emitting high-intensity gamma rays. To them the earth would look like a frigid wasteland incapable of supporting life.


Carbon and oxygen tend to be either more abundant in the universe or more reactive than any other element that life could theoretically sustain itself on.

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Re: Galactic civs limited by inability to grow exponentially

Postby artifex » Fri Jun 26, 2009 6:07 pm UTC

The Fermi paradox doesn't take into account the exponential rate of change in a civilization due to advancing technology. Curiosity and expansion may be biological imperatives, but are they imperatives of post-biological life? What happens when biological life can change it's imperatives? I'm not sure it's reasonable to draw conclusions from the assumption that a million year old civilization would share the motivations of a ten thousand year old one.

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Re: Galactic civs limited by inability to grow exponentially

Postby Yakk » Fri Jun 26, 2009 6:41 pm UTC

So what if you need something as complex as a biosphere to build a self-replicating industrial civilisation.

And what if it takes ~1-10 billion years to take a rock in a good spot in space, and build up such a biosphere.

And it a given solar system only has, on average, enough resources to pump out 2 seed colonies, each with a 60% survival rate to getting to the same stage.

Then you'd send out seed colonies to nearby stars (young ones with what looks like planets in the right orbit), have them seed life, and wait a few billion years.

This is an exponential curve that is limited by both the speed of light, and by the heat-death of the universe. If the 'seed to interstellar probe' took an average of 3 billion years, and each such colony pumped out an average of 10 new successful seeds per cycle, the curve of the number of seeded planets would be:

K * e^( t / 3 billion * ln 10 )
Assuming this got started ~3 billion years after the universe started at 100 different locations in our galaxy, we'd have:
K e^( ln 10 ) = 100
K = 10

Plugging in 15 billion years, we get:
10 e^(5 ln 10) = 1,000,000 colonies every 'active' (many of which would have died out).

If they are visible to radio waves, at our current level of technology, within 10 light years, that generates a total volume of about 10^50 m^3 of "you can hear life on the radio".

The galaxy's volume is about 10^51 cubic miles. Which would indicate that life is thin on the ground.

The above assumes that the best a civilisation can pull off is to send 'seeds of life' to a planet around another star, and wait billions of years for technological civilisation to develop there and do the same.
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Re: Galactic civs limited by inability to grow exponentially

Postby Woofsie » Fri Jun 26, 2009 8:52 pm UTC

Yakk wrote:The above assumes that the best a civilisation can pull off is to send 'seeds of life' to a planet around another star, and wait billions of years for technological civilisation to develop there and do the same.


That's.. one hell of a huge assumption. I know interstellar travel is slow, but one would think that at least some civilizations would want to actually send out colonists to other planets.

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Re: Galactic civs limited by inability to grow exponentially

Postby Yakk » Fri Jun 26, 2009 9:08 pm UTC

Interstellar space is both long and barren.

Earth is ridiculously comfortable -- even the most remote and deserted parts of the surface -- than anywhere in space. Living in space makes living at the south pole look like it was designed for humans. And if you are colonising another star, you need to be able to live in space (or equally harsh environments) indefinitely without resupply from a terraformed planet closer than light years away. Let alone the journey.

This might not be at all practical.

I ran those numbers with the presumption "what if the amount of time it took earth to go from life to civilisation was actually the time it takes for a civilisation to reproduce in another star system". If that is the case, then looking into the stars and seeing absolutely nothing is what you would expect.

Now this strategy isn't ridiculous. After a few more billion years, more and more of the galaxy will have terraformed planets on them. And spreading over such planets is easier than bootstrapping from barren rocks.

Well, marginally. :) Of course, this kind of process would take billions upon billions of years. And we would be only partially the way along it.

At an assumed rate of 10x colony growth every 3 billion years, it would take a mere 30 billion more years to saturate the galaxy to a point where adjacent intelligent species are decently likely to hear each other on the radio at our level of technology. The entire time, growing colonising the galaxy exponentially. But today, our chances of hearing such a radio would be 1 in 10^10 or so.
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Re: Galactic civs limited by inability to grow exponentially

Postby Sharlos » Fri Jun 26, 2009 9:31 pm UTC

But the fact that humanity isn't out colonising the galaxy seems to suggest that other life also isn't doing the same.

Life is likely fairly common, intelligent life might be harder to come by. The fact that life on earth didn't produce an intelligent species the first time round back with the dinosaurs suggests its not too easy.

But hell, alien life could have visited earth already, saw a bunch of roaming dinosaurs and moved on. But making the assumption that life should have already visited us when we, also life, havn't gotten around to leaving earth yet let alone looking for other lifeforms just seems silly.


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