Fermi’s (Paradox) miscalculation

Wikipedia says this about Fermi’s Paradox:

en.wikipedia.org...

In 1950, while working at Los Alamos National Laboratory, the physicist Enrico Fermi had a casual conversation while walking to lunch with colleagues Emil Konopinski, Edward Teller and Herbert York. The men lightly discussed a recent spate of UFO reports and an Alan Dunn cartoon[9] facetiously blaming the disappearance of municipal trashcans on marauding aliens. They then had a more serious discussion regarding the chances of humans observing faster-than-light travel by some material object within the next ten years, which Teller put at one in a million, but Fermi put closer to one in ten. The conversation shifted to other subjects, until during lunch Fermi suddenly exclaimed, "Where are they?" (alternatively, "Where is everybody?")[10] One participant recollects that Fermi then made a series of rapid calculations using estimated figures (Fermi was known for his ability to make good estimates from first principles and minimal data, see Fermi problem.) According to this account, he then concluded that Earth should have been visited long ago and many times over. But if colonization means it increases the likelihood of finding alien artifacts or alien contact you have to factor in that the earth may not have been habitable to colonize at the time the alien was made aware of the earth.

It also says a lot more. Surprisingly, the article on Fermi’s Paradox is rather accurate. Basically, Fermi calculated that a planet would send out a self-replicating probe to a star. The probe would replicate and become 2. Next, 4, then 8, then… You get the picture.

Fermi calculated that at that rate, it would take a few million years to colonize the whole of the galaxy. Debate has been raging since then; “what if they have been here 3 million years ago?” “If they did come, what makes you think they would want to talk to us?”

Skeptics, of course, say that since they haven’t come here a long time ago, they don’t exist. Fermi’s paradox proves it and you can’t deny the logic nor the mathematics. This is where they make their mistake. The logic and the mathematics don’t work in real life the way the do on paper. And here is the proof:

I am neither a mathematician or a scientist and will not attempt to make complicated calculations. It would be worthless to do so anyway. Let’s keep things simple.

A civilization sends out a self-replicating probe to its closest star. It replicates and both probes go on to 2 other stars and so on.

To make things simple, let’s assume a 2-D galaxy containing 31 stars. Let’s assume an average flight time of 10 years between stars, including the time it takes to study the star system.

Simple mathematics tell the following:

Year 0
The original probe is launched.

Year 10
The probe replicates, there are now 2 probes
1 star has been visited

Year 20
The probes replicate, there are now 4 probes (2 probes, doubled = 4)
3 stars have been visited

Year 30
The probes replicate, there are now 8 probes (4 probes, doubled = 8)
7 stars have been visited

Year 40
The probes replicate, there are now 16 probes (8 probes, doubled = 16)
15 stars have been visited

Year 50
The probes don’t need to replicate
31 stars have been visited

This is all nice and simple on paper, but let’s see what would happen in the real world.

We have to assume that in this galaxy, as in ours, it would be impossible for the people on the original planet to see all the stars in the galaxy; we can’t and even among those we do see, we have no idea where a lot of them actually are. So it’s not possible to program any itinerary ahead of time; the probes will have to discover most of the stars by themselves.

In my charts, I’m using basic logic; the probes will go to the nearest unvisited star. So, first, the original galaxy. I’ve named the stars from A to Z, then AA, BB, CC, DD and EE. The positions are irrelevant as we assume an average flight time of 10 years.

[atsimg]http://files.abovetopsecret.com/images/member/810aea319793.jpg[/atsimg]

As stars are visited, I’ve changed their colours from orange to ice blue. I’ve tried to make the flight paths as clear as possible, but, as you’ll see, it will rapidly become difficult.

Year 0
The original probe (1) is launched

[atsimg]http://files.abovetopsecret.com/images/member/8ca789635a22.jpg[/atsimg]

Year 10
The probe replicates, there are now 2 probes (1) and (2)
1 star has been visited

[atsimg]http://files.abovetopsecret.com/images/member/65c3575f45c7.jpg[/atsimg]

Year 20
The probes replicate, there are now 4 probes (1), (2), (1a) and (2a)
3 stars have been visited

[atsimg]http://files.abovetopsecret.com/images/member/5fe734a8726f.jpg[/atsimg]

Year 30
The probes replicate, there are now 8 probes
7 stars have been visited

[atsimg]http://files.abovetopsecret.com/images/member/0e7aedd0b214.jpg[/atsimg]

Year 40
The probes replicate, there are now 16 probes (8 probes, doubled = 16)
15 stars have been visited

[atsimg]http://files.abovetopsecret.com/images/member/a6e7217a6a93.jpg[/atsimg]

Now this is where it becomes interesting… As you can see, probe (1d) is leaving star E and heading toward star BB, since it is the closest available, even though this star has already been visited. Meanwhile, probe (1g) is leaving star BB and heading toward star E.

This is where Fermi got it wrong. I will explain shortly.

Year 50
The probes still need to replicate as 4 stars have yet to be visited.
27 stars have been visited

[atsimg]http://files.abovetopsecret.com/images/member/bda380cf2b0f.jpg[/atsimg]

In our example, it would take at least 60 years to visit all the stars. The reason is simple:
The probes don’t know where all the others have been or where they are going.

We have an original probe which heads to star B, then clones itself. Probe (1) heads to star C, while probe (2) heads to star O. So far, no problem. At the 20 year mark, still no problem. When you get to the 30 year mark, this is where you can start expecting problems. In this example, we’ve encountered them at year 40, but it could happen earlier. Lets examine the probes at year 40.

Our probes are identified as:
(1), (1a), (1b), (1c), (1d), (1e), (1f), (1g), (2), (2a), (2b), (2c), (2d), (2e), (2f), (2g).

(continued on next post)

[edit on 25/2/2010 by ajmusicmedia]

If you go back to where they split, you realize that all the probes in the group (1) know that the probes in the group (2) have been to stars B and O. But they have no idea where else they have gone. Likewise, all the probes in the group (2) know that the probes in the group (1) have been to stars B and C, but they don’t know where else they’ve gone.

You could break it down even more if you wanted to. Probe (1) knows that probe (1e) has been to stars B, C and AA, but nothing else. I have the whole break down in excel if anyone wants to see it; just U2U me and I’ll send you the file.

What happens is that as a probe discovers a new star, it has no idea if another probe has been to it or not. As probes replicate, more and more of them will be heading toward the same stars, therefore, duplicating, triplicating, etc. the effort.

In this example, 31 stars in a 2-D galaxy, with an average flight time of 10 years, we are adding 10 years to the amount of time it takes to visit each star. Imagine how much more time you’ll be adding in a 3-D galaxy which contains hundreds of millions of stars… And this is without counting on accidents, replication defects, probes maybe destroyed by alien species that have detected them and are unhappy to see them. This will add on even more time.

Devil’s (Skpetic’s) Advocate

Is there a way around this? Partially. If I were sending the original probe, I would start by sending more than one. Hundreds, if not thousands. But I’d add communication to them. Think about it, you don’t want all these probes to roam the galaxy and have to wait for them to come back home to learn of their discoveries.

Once a star system has been explored, and right before replication, I would have the probe send out several beacons in circular orbits around the star (several orbits so that a probe approaching from any direction will detect it). These beacons would send out information about the star system; composition of the star, planetary system, any civilisations or fauna and flora catalogue. This would serve 2 purposes. The home planet, which would probably be equipped with huge listening devices, could get a quick glimpse at the nearest stars; its inhabitants would know where to go first for whatever they would be looking for.

The second purpose would be to advise other probes not to waste their time visiting this star as it has already been done. Of course, probes would not have gigantic listening devices, so they would probably have to get within a few light-years to get the signal from the beacons and be able to properly decipher them. It would keep a probe from visiting a star a second time, but once the probe received this beacon, it would still have to seek out a new star.

This would save a lot of time, but would not bring us anywhere near the timeline that Fermi calculated.

Do we have communication?

I’ve always wondered at the background noise of the galaxy. We are told this is the sound of the explosion of the Big Bang. Let’s assume the Big Bang really did happen. It would have lasted a fraction of a second. So why would the sound still be lingering billions of years later? There may be a reasonable explanation to this, and I am willing to hear it. But then again, maybe they’re the sounds of billions of beacons sending out their messages… I’ve never actually listened to this sound. As a musician, I might be able to find a sequence to it, although I doubt it. Perhaps a brilliant musician with a perfect ear might be able to detect something?

How I found the answer

A problem is easy to solve when you don’t know it exists… Unsolvable mathematical equations have been solved by people who didn’t know there were no solutions. Back in 2000, I wrote a short story which I simply titled “probe”, in which I discuss exactly this situation; a xenophobic species living on a planet near the centre of the Milky Way that sends out these probes. One arrives on Earth. At the time, I had never heard of Fermi or his paradox. Therefore, when I first heard about it, I immediately knew where he had gone wrong.

Eventually the rate of uncontrolled (if there's no adequate & timely communication/verification process) replication would smother the universe with probes would it not?

Interesting theory nonetheless but I think any advanced program would use less a cumbersome approach. Again though, interesting theory as maybe one civilization out of potentially billions might just try it that way.

Originally posted by Atlantican
Eventually the rate of uncontrolled (if there's no adequate & timely communication/verification process) replication would smother the universe with probes would it not?

Eventually, certainly. The problem is that so many of these probes would be heading toward the same destinations. Many stars would be completely missed.

Interesting theory nonetheless but I think any advanced program would use less a cumbersome approach. Again though, interesting theory as maybe one civilization out of potentially billions might just try it that way.

The problem with the advanced program is that you have to know in advance where the stars are located. We can't see the whole galaxy, so it's not possible to calculate all locations.

I like when you say "potentially billions"; I think that civilizations in this galaxy alone probably added up to at least several dozen million.

reply to post by ajmusicmedia


You've already address some of what I'm going to say, but basically this whole scenario nicely illustrates why you have engineers build things instead of mathematicians.

1) There is no reason to assume probes can only double per iteration. If you have a probe capable of landing on a barren world, self-replicating, and then relaunching again, why not allow a probe to make ten copies of itself? 100? Why assume only two?

2) Without the doubling limit, it would be more useful to keep at least one probe in every system that is visited. You would want to do this anyway to create a communcations network amongst your probes back to your civlization.

3) Given even only our current level of technology, it should be possible to map out the stars of this galaxy in advance. You could easily eliminate the problems of knowing which stars had already been visited, simply by creating a "flight-plan" in your original probe such that the destinations of each generation of child probe were already decided.

Fermi approached the situation as a mathematician looking at a simple exponential growth. Not as an engineer trying to solve a problem.

reply to post by LordBucket


I agree with you, Fermi did approach this as a mathematician. The major problem is that skeptics keep throwing this in our faces and other mathematicians keep backing him up. As if only mathematicians would be involved in such an endeavour.

I like your ideas;
-replicating more than once would make sense and make things go much faster
-leaving a probe around every star for communications and to keep an eye on development also makes sense; between the time the original probe arrives and the time the civilization that sent it arrives, a lot of time may have passed

As far as mapping it out, I go back to what I said previously. We can't possibly see every star in the galaxy. We're not even sure of the exact shape of the galaxy. And even if our telescopes see stars, that still doesn't tell us where they are; each one has to be mapped out individually (several hundred million of them).

im not sure if this even counts as an actual paradox, as some simple common sence thinking can solve it..

in this theoretical situation, all the people who build these probes woudl have to do is make sure that if a probe gets to a star and theirs already a probe their, it just goes to the next ... it doesnt even need to communicate with the probe which is already their, as luckily the universe is infinate , as will the potental amount of probes be with self replication ... which means that their would never be an un probed star, but it would probably take a bit longer.

but, the "stars not having probes and doubles at one star" problem most likely would not happen as nowadays we have mapped a hell of alot of the stars in our own galaxy and cooords and a check list could easily (by the people who make these sorts of probes of course)

quote from LordBucket
why not allow a probe to make ten copies of itself? 100? Why assume only two?

personaly, i think that 2 probes from one would be the case, from a payload and cost point of view... The same reason noone has sent a moon base up to the moon on a rocket already.

[edit on 26-2-2010 by boaby_phet]

[edit on 26-2-2010 by boaby_phet]

Originally posted by LordBucket
reply to post by ajmusicmedia

 

3) Given even only our current level of technology, it should be possible to map out the stars of this galaxy in advance. You could easily eliminate the problems of knowing which stars had already been visited, simply by creating a "flight-plan" in your original probe such that the destinations of each generation of child probe were already decided.

What if you completely randomized each flight path as the new probe was created, maybe even having them skip every 3rd, 5th, 105th (yet again random) star in order to help avoid overlapping probes. Even if it where to happen, if it detects a probe already on said star, it will continue downs it randomly generated flight path.

Since the universe is infinite, would it really matter where the probes mapped? Sure there might be areas of interest, but over time (thousands of years?) how relevant would it still be?

reply to post by ajmusicmedia


Interesting post.

Astrophysicist Carl Sagan also makes some good points in this article from 1962:

Prof Says Beings From Outer Space Have Visited Earth

Associated Press, November 26, 1962

LOS ANGELES. (AP) - Some of the best scientific minds in the country were stumped when a slender, dark-haired young man chalked on the blackboard this equation:

N equals R FP NE FL FI FC L.

The speaker was Dr. Carl Sagan, a 28 year-old assistant professor of astronomy at Harvard University.

His audience consisted of several hundred members of the American Rocket Society, gathered for his luncheon address.

The equation was his way of expressing the mathematical probability that intelligent beings from outer space have visited earth.

Sagan soberly explained that in his equation N Stands for the number of advanced technical civilizations in the universe possessing the capability of interstellar communication.

R is the mean rate of star formation averaged over the lifetime of the galaxy.

FP is the fraction of stars with planetary systems.

NE is the mean number of planets in each system with environments favorable for the origin of life.

FL is the fraction of such planets on which life does develop.

FI is the fraction of such inhabited planets on which intelligent life with manipulative abilities rises during the lifetime of the local sun.

FC is the fraction of planets populated by intelligent beings on which advanced technical civilizations rises.

And L is the lifetime of this technical civilization.

Sagan said information in his formula is based on current estimates by astronomers. In making calculations, he assigned each symbol an arbitrary numerical value.

As expressed in numbers, Sagan said, the formula means that at least 1 million of the 100 billion stars in our Milky Way galaxy have planets which have developed civilizations capable of travel between the stars.

"Let's say that each of these civilizations sends out one interstellar expedition per year," he said.

"That means that every star, such as our sun, would be visited at least once every million years. In some systems where these beings found life, they would make more frequent visits. There's a strong probability, then, that they have visited earth every few thousand years.

"It is not out of the question that artifacts of these visits still exist or even that some kind of base is maintained, possibly automatically, within the solar system, to provide continuity for successive expeditions.

"Because of weathering and the possibility of detection and interference by the inhabitants of earth it would be preferable not to erect such a base on the earth's surface. The moon seems one reasonable alternative."

"Forthcoming photographic reconnaissance of the moon from space vehicles - particularly of the back - might bear these possibilities in mind."

At a news conference Sagan predicted man himself would be capable of interstellar flight at close to the speed of light "within a century or two."

Asked if he believed in flying saucers, he said: "I do believe there are objects which have hot be identified."

Link

Cheers.

reply to post by ajmusicmedia

As far as mapping it out, I go back to what I said previously.
We can't possibly see every star in the galaxy.

So far as I know, we also lack the technology to create self-replicating, interstellar probes that average 10 years between stars. It's not unreasonable to suggest that by the time we have the technology to reasonably attempt what we're discussing, doing the mapping may be fairly trivial. As it is, we can certainly see farther than we can travel.

And if not, the communications network created by leaving probes in every system can be used to relay information on which have already been visited. Again...you want communication anyway, since presumably the whole point of this expedition is to find someone or something...not simply to send a piece of metal to every star in the galaxy.

Though...since this is all hypothetical, we're having to make a lot of guesses as to the available technology. We appear to be assuming that these probes can move faster-than-light, or at least close-to-light speed. Do we also have communications technology that can do that? Or is it communication instantaneous? Or is our propulsion faster than our communications?

A lot of this is speculative, so I don't think knowing where stars are to begin with is unreasonable.

reply to post by boaby_phet

i think that 2 probes from one would be the case, from a payload and cost point of view

...but presumably you're not carrying materials to construct the child probes in the initial probe. You're scavenging them either from the systems you visit, or manufacturing them from spare hydrogen atoms you pick up along the way. If you need to bring materials with you, I think the entire premise is broken to begin with.

So if you're landing a probe on a planet, and using the materials from that planet to build more probes...I think your probes would have to be really big if you couldn't be making millions of the things at every star if you really wanted to.

reply to post by ProjectedLogic

Since the universe is infinite, would it really matter where the probes mapped?

The original scenario assumes we're only visiting this galaxy, not the entire universe.



[edit on 26-2-2010 by LordBucket]

Originally posted by LordBucket

Since the universe is infinite, would it really matter where the probes mapped?

The original scenario assumes we're only visiting this galaxy, not the entire universe.

I failed to notice that. With that in mind, I would have to agree that mapping the galaxy does not seem unreasonable.

I find the replies to this thread interesting, however you fail to miss the point. Or perhaps I didn't explain it well enough in the OP; this can happen with a long exposé. If I didn't explain it well, then I humbly apologize and will try again here:

Fermi, over lunch apparently, postulated that if a civilization built a self-replicating probe and sent it to the nearest star, it would take, according to his calculations, only a few million years for them to conquer the galaxy. Now, considering that we are in a relatively "young" part of the galaxy (stars near the center of the galaxy were at the same point as our sun billions of years ago), then they should be here already. So, he exclaimed, "where are they?"

To Fermi, and to many skeptics, that fact that we are not enslaved to an ET civilization means that they do not exist. The Fermi paradox is consistently thrown in by skeptics who say that his equations are pefect, therefore his paradox proves the non-existence of ETs.

I have simply endeavoured to show that although Fermi's calculations are probably right, they do not apply in real life. Theory vs Reality.

I reiterate, because it has come up several times, mapping the galaxy is not possible. We have not mapped a substantial part of the galaxy. Remember, several hundred million stars. We can see part of the center of the galaxy and its general shape is assumed only. Apparently it looks like a flat brick. It was determined last year that our galaxy is not a spiral; it only has 2 arms. Now until last year, it was assumed it had four. This shows how little of it we do know. And physics being what they are, the only way to map the galaxy would be to send ships out there carrying telescopes and infrared and what not equipment to get better vantage points. By the time you would get a map back, you would have had time to send ships all over the galaxy.

Interesting post. I've always loved Fermi's paradox.

I think the problem of double visits can be eliminated with a little bit of logic programming within the probe. Remember that each probe will always have a complete record of how to get back to the original planet because it will store the location of each previous division within its memory. If you think of the original planet as the origin of a spherical area then the probes can use that as their basis for heading off in slightly different directions that do not overlap.

Let me try to give you an example.
The first probe goes to the nearest star and splits. Now the probes programming kicks in. Lets pick something easy for the sake of argument and say that odd numbered splits divide the probe's search area in half left to right and that even number splits divide the probe's search area in half top to bottom. So at the first division, odd, the probe will reference back to the origin point and split its search area into two hemispheres with one probe taking the hemisphere to the left and the other taking the hemisphere to the right. There are now two independent search areas that cannot ever overlap because each new daughter probe will know which hemisphere it is suppose to be in. At the second division, even, each probe will again divide its search area in half, this time vertically with one probe taking the top half of the new section and the other one taking the bottom half. There are now four probes and four quadrants to be searched and again, they will never overlap because they know where the original planet is and which section they are in. The third division, odd, would again split each search area in half left to right. There would now be 8 probes and 8 sections to be searched. Continue this logic pattern for as long as it takes to explore the galaxy.

Since the search pattern is based on the number of divisions and not distance or time the more densely packed areas will automatically get more probes to explore them and the less densely packed areas will get fewer probes. This means you are not wasting time or probes in areas that do not have many stars. This pattern also has the advantage of continually moving the probes away from the home planet and out into the ever expanding search area.

The only difficulty with this setup is that if one of these probes meets a stray asteroid it may well leave a good chunk of the galaxy unexplored. Obviously they would have to have some ability to avoid this but nothing is perfect. The collected data would have to be bounce relayed, probe to probe, back to the home world via radio signals.

Hope everybody is able to follow this.

reply to post by Riddle


Hey Riddle, this makes sense. So, we're stuck with the probability that some probes will be destroyed for a variety of reasons; from impact to simple malfunction. Therefore, communication is key to all of this.

Therefore, let's assume an alien civilization has done this; could we pick up their communications? If a probe at some time in our past has visited us and is still emitting a beacon; how can we pick up its signal?

That reminds me that Tesla thought he had...

Then again, if it's possible, we won't hear about the results. I remember a paper about a scientist explaining how to detect ships in transit between stars; sub-light ships. A lot easier than trying to find a planet around a star and it could be done in a few minutes. He was completely ignored by mainstream science. Just a thought...

reply to post by ajmusicmedia

let's assume an alien civilization has done this;
could we pick up their communications?

I would guess guess probably not. For interstellar communication to be of practical use it would need to be faster than light. So far as I know we mostly scan electromagnetic radiation: visible light, xrays, microwaves, etc. These are simply too slow to be an especially useful interstellar communications medium.

If a probe at some time in our past has visited us and
is still emitting a beacon; how can we pick up its signal?

We would have to be looking at the medium of their communication. I phrase it that way because assuming that a signal is being "sent" is rather arbitrary. With the distances involved, the whole idea of "sending" a message and having it pass the entire length of the distance between two stars via some medium is impractical.

For example...let's say you wanted to send a message from our star to the galactic core. That's a distance of 26,000 light years. Even if you could send the message at a thousand times the speed of light it would still take 26 years for that message to arrive.

To be useful, you would need a means of communication that was instantaneous, or nearly so: fold space to decrease the distance between the points, quantum entanglement, whatever. But these methods would be undetectable by us for two reasons: first, we don't have the technology to do it, or to detect it, so we don't even know how or what to look for. Second, communications via such methods would not necessarily need to pass through all points of space between sender and receiver. Even if we knew to look for it, and even if we're sitting in exactly the middle point between sender and receiver, the message may be arriving without passing through the space we're sitting in.



[edit on 27-2-2010 by LordBucket]

To one starry eyed author Velikovsky referencing Jeans
"Astronomy and Cosmology" allows only one star in 100,000
to form a planetary system.
In a Galaxy of 100 million stars, a planetary systems can form
one in five billion years.
Our Galaxy is 2 Billion years young and going to difficult to find
a population more advanced.
Reality must put a damper on Fermi's world.