Probability of ET's visiting us (modified Drake Equation)

The Drake Equation in its usual form is used to estimate the possible number of extraterrestrial civilizations in our galaxy, but I thought it might be interesting to slightly modify it in order to estimate the chances that a civilization on another planet close enough to detect our radio signals has detected our presence and decided to visit us. Apparently the first radio signal at a frequency high enough to penetrate Earth's ionosphere was the opening ceremony of the 1936 Olympics[1]. Since radio waves travel at the speed of light that means any star system without a radius of 82 light years could potentially detect our signals.

This is a nice number to use for our estimate because it's extremely unlikely that our radio signals would even be detectable amongst the background noise beyond 80 light years and because it's extremely unlikely any species further than 80 light years from us could reach us since it would take 80 years even traveling at the speed of light. In order to make the estimation we can adjust the Drake Equation to take into account only the star systems within range of our radio signals instead of the whole galaxy. The result of this calculation will hopefully provide some insight into the likelihood of ET's detecting our presence and visiting our planet.

So here is the modified equation:

N = Ns · Fp · Ne · Fl · Fi · Fc

Ns = the number of star systems close enough to detect our radio signals
Fp = the fraction of star systems that have planets in stable orbits
Ne = the average number of potentially habitable planets per star
Fl = the fraction of those planets that develop reproducing life forms
Fi = the fraction of those planets on which intelligent life does evolve
Fc = the fraction of those civilizations which detect our signals and travel to us

The number of star systems close enough to detect our radio signals

This is rather easy to calculate since we know the density of stars in our region of the galaxy and we know the volume of space covered by our radio signals. The stellar density near the Sun is estimated as 0.004 stars per cubic light year[2] and using the equation to calculate the volume of a sphere we find that a sphere with a radius of 82 light years has a volume of 2.31×10^6 cubic light years. Multiplying the stellar density by the volume of space filled by our radio signals, we find that there are approximately 9240 star systems within an 82 light year radius of our star system.

The fraction of star systems that have planets in stable orbits

Wikipedia states that "recent analysis of microlensing surveys has found that fp may approach 1 — that is, stars are orbited by planets as a rule, rather than the exception; and that there are one or more bound planets per Milky Way star."[3] This means that the fraction of stars that have planets orbiting them is very high, so for Fp I feel a value of 0.95 is easily justified but still accounts for the fact not quite every star has planets in orbit. In other words we're assuming that 95% of all stars have orbiting planets.

The average number of potentially habitable planets per star

According to the latest space surveys "there could be as many as 40 billion Earth-sized planets orbiting in the habitable zones of sun-like stars" within our galaxy[3]. Since there is around 100 billion stars in our galaxy and virtually all stars have planets this implies the value for Ne is roughly 0.4 but researches have also shown that only about 10% of star systems contain the right elements and suitably low radiation levels to support life, which implies the value for Ne is below 0.1[3]. However I know some people will take issue with a value that low so we'll split the difference and use 0.25, meaning for every 4 star systems there is 1 habitable planet on average.

The fraction of those planets that develop reproducing life forms

The chances of a reproducing organism assembling itself from a random collection of chemicals is extremely small, however biological life arose on Earth shortly after favorable conditions presented themselves, so given billions of years the probability may become substantial. The problem is that the only example we have is our own planet so any estimates of Fl suffer from anthropic bias. Wikipedia states that "From a classical hypothesis testing standpoint, there are zero degrees of freedom, permitting no valid estimates to be made". This means the only logical value we can use for Fl is 0.5 because we're uncertain either way.

The fraction of those planets on which intelligent life does evolve

This is another difficult variable to estimate but out of the 8 million species on Earth we are the only one which developed civilizations with advanced technology, implying the value of Fi is very small. However when millions of species have billions of years to evolve there's more chance at least one of them will evolve into a civilized species with an understanding of science. However in order for that to happen the creatures must avoid extinction and have favorable conditions which last billions of years. There's at most a 1% chance all the right things will occur, but I want the result to be optimistic so we'll use 0.01 for Fi.

The fraction of those civilizations which detect our signals and travel to us

The value of Fc is going to be very small just like Fi because detecting our radio signals from such long distances is very difficult and involves a lot of luck because they have to be looking in the right place, for those at 80 light years it would be an almost impossible challenge. Also the chance they will develop technology for interstellar travel is very small since we know it's a tough problem and a warp drive is required to make it feasible at all, and we're not entirely sure such a drive can even be built. However lets be optimistic and assign Fc a value of 0.1, meaning a 10% chance any given civilization manages to reach us.

So the resulting calculation will look as follows:

N = 9240 · 0.95 · 0.25 · 0.5 · 0.01 · 0.1

N = 1.09725

Well that's rather interesting result, the answer is basically one, meaning we are that one civilized species in our neighborhood of the galaxy, although we obviously haven't developed interstellar travel yet. The only variables which have a substantial impact on the final result are Fi and Fc because they are the only really small fractions and we didn't even use a very small value for Fc. The other variables can be changed within reason without impacting the final result very much. However Fi and Fc are also two of the hardest variables to estimate, which is why I tried to be optimistic.

Even so the result still shows us we are probably the only intelligent species in our region of the galaxy and we almost certainly have not been visited by ET's. If we plug in more realistic values for Fi and Fc we find that there's an exceptionally low probability we have been visited by extraterrestrials. This is an important result because it shows us that if there are indeed advanced crafts moving around our atmosphere then there's very little chance they are controlled by beings who traveled here from another planet using a propulsion mechanism capable of FTL speeds.

1] briankoberlein.com...
2] en.wikipedia.org...
3] en.wikipedia.org...

Just to play devils advocate, what if..... we were not the civilized ones in our neighborhood, and there is another more advanced than us out there. And... what if they've always been here hiding under our noses all this time, not from another star system. Really good thread, you put some work into this one. S&F.

a reply to: ChaoticOrder

I'm thinking that since people have reported seeing landed UFO's with non human occupants, and I have seen them myself, that this modified part that says it's unlikely we have been visited is quite flawed.

It's interesting how there are two completely unique reality viewpoints that both ignore the other, and even socially ignore each other. People who subscribe to one totally ignore the other.

We know nothing.. therefor nothing about how old a potential alien race is.. could be millions of years ahead in tech from us.
We could not even dream of what kind of tech could be in a race like that

a reply to: NoCorruptionAllowed

I'm thinking that since people have reported seeing landed UFO's with non human occupants, and I have seen them myself, that this modified part that says it's unlikely we have been visited is quite flawed.

The result does not say it's unlikely advanced crafts are flying around our atmosphere, it says if they are then they probably are humans. Even if they don't look exactly like us that doesn't prove they are not human, they are humanoid. What I'm alluding to with this thread is the idea they could be humans from the future, as I have been discussing in some of my recent threads.

originally posted by: gunshooter
Just to play devils advocate, what if..... we were not the civilized ones in our neighborhood, and there is another more advanced than us out there. And... what if they've always been here hiding under our noses all this time, not from another star system. Really good thread, you put some work into this one. S&F.

Aliens from another planet in our solar system is also far more likely than aliens from other star systems visiting us, because not only would it be much more plausible for them to reach us but our solar system already contains organic life so it's not very hard for microorganisms to transfer to nearby planets as with Transpermia theories.

originally posted by: Spacespider
We know nothing.. therefor nothing about how old a potential alien race is.. could be millions of years ahead in tech from us.
We could not even dream of what kind of tech could be in a race like that

That is irrelevant, the Fc variable encapsulates the probability they will develop any tech making it possible for them to reach us within a reasonable time. And saying there's a 10% chance any given civilization has achieved that is certainly over-optimistic.

originally posted by: gunshooter
Just to play devils advocate, what if..... we were not the civilized ones in our neighborhood, and there is another more advanced than us out there. And... what if they've always been here hiding under our noses all this time, not from another star system. Really good thread, you put some work into this one. S&F.

You just circumvented the entire point of OP's equation. You can add any "what if" scenario you want, but 1.) intention is not part of the equation, and 2.) Our civilization is, and 3.) if there is another civilization within our star system, we ought to be able to see it. There's nothing wrong with your speculation here. It is perfectly valid, it's just that you've stated OP "put some work" into it, and then you tossed the entire thing out the window.

originally posted by: ChaoticOrder

originally posted by: Spacespider
We know nothing.. therefor nothing about how old a potential alien race is.. could be millions of years ahead in tech from us.
We could not even dream of what kind of tech could be in a race like that

That is irrelevant, the Fc variable encapsulates the probability they will develop any tech making it possible for them to reach us within a reasonable time. And saying there's a 10% chance any given civilization has achieved that is certainly over-optimistic.

And where did you pull that 10% chance from ?

a team of scientists led by Mihran Vardanyan at the University of Oxford did a statistical analysis of all of the results. By using Bayesian model averaging, which focuses on how likely a model is to be correct given the data, rather than asking how well the model itself fits the data. They found that the universe is at least 250 times larger than the observable universe, or at least 7 trillion light-years across.

How can you put a % on something we cannot see

a reply to: Spacespider

And where did you pull that 10% chance from ?

Well we know it requires extremely advanced science which requires a very high level of intelligence. In fact we don't even know if the laws of physics allow for any form of FTL travel to exist because it usually requires exotic forms of matter to make it work. Lets say we detect an intelligent signal from a star system several light years away, do you really think there's more than a 10% chance we'll develop the tech to travel there, and then actually make it happen, and then just sneak around their atmosphere without making contact when we get there?

They found that the universe is at least 250 times larger than the observable universe, or at least 7 trillion light-years across.

The universe is most likely infinite actually: Why the universe is infinite and didn't begin as a singularity. But even at FTL speeds it can take a long time to travel many light years. Also, they couldn't locate us without first detecting our radio signals. They are not going to travel light years without being sure there's something at their destination. So it makes perfect sense to only consider star systems within a certain radius around us.

a reply to: ChaoticOrder

and why again are aliens visiting us? anyone know?

They are already here, and have been for tens of thousands of years, if not longer

originally posted by: visitedbythem
They are already here, and have been for tens of thousands of years, if not longer

Here is a new video of the structures on the moon!

Just wait till you see this! They are all over the place, and earth moving equipment leaving tracks.

After you see this vid, you will never look at the moon the same way again!

I ascribe to the idea so called aliens may very well be humans from the future .
The logic ( assuming cases of abducting people is true then is .
With all the chemicals and pollution the male humans fertility rate is already dropping so like the movie
millennium the Humans need good DNA to help them reproduce thus sending people back to collect DNA ( in teh movie they collected people who were going to die such as plan crashes and what not )

Funny thing about a time machine if it can be built it already exists . Why because a machine like that is out of time and can exists in every time at the same time . All this means is it makes the probability even higher it has been done sometime .Go back to 300 million BC and the machine has existed in every possible time from when earth first got life .

BTW It has been done www.collective-evolution.com... www.iflscience.com...

originally posted by: Spacespider
We know nothing.. therefor nothing about how old a potential alien race is.. could be millions of years ahead in tech from us.
We could not even dream of what kind of tech could be in a race like that

The one breakthrough is either faster-than-light propulsion or teleportation. If we just knew how to disconnect a block of atoms from the local space-time continuum that could be done. It's that quantum foam (gluons, inertia, mass, momentum) that keeps everything connected to everything else. There's enough evidence to suggest that is done with HF alternating magnetic fields.

Everything else like guidance systems, star navigation, crew environments has already been done. Perhaps they have decoded their own genomes and know how to cure cancer and aging. Once that is known, anything is possible.

Call me on my cell phone ..... Oh sorry wrong Drake .

Chances are it's not distant aliens traveling billions of miles in space to visit earth but rather interdimensional beings, it would explain why we don't see any evidence , I.e
No crash sites no fossil records no space debri ( that's not ours ) unless you count the black knight.

You really have to ask yourself why would any technically superior race of advanced aliens be making so much effort to stay cloacked and invisible to us , after all we would be like ants to them , why do they care so much to stay hidden , if they were taking resources like gold or other rare metals you only get on earth we would notice , there would be evidence of mining etc.

The Drake equation is basically saying they are out there but they just don't have the ability or the need yet to contact the human race on earth , imagine staying in a house in America and there was not one other occupied house in the whole of the country but yours , no one else but you.

My theory is the human race is billions of years old and is spread right through out the cosmos where we hop from planet to planet trying to stay keep our species alive, only problem is the gaps are so big between planets we lose all trace or memory of the previous planet.

This could also explain why the aliens are humanoid in form cause after a few generations in space the DNA would change and they would look a lot different after a few thousand years or so.

a reply to: ChaoticOrder
And that is just using the original "test" equation . What most folks do not know , Drake's Equation is really not an official equation . It was only put forward as an example of how the laws of probability and statistics could be used in astronomy. Not meant to be "followed" by so many folks.
The "Theory" behind Drake's Equation has been modified now to include 100s of factors that were never there , yet need to be accounted for.
Results - We may well be unique in the entire Universe.

a reply to: ChaoticOrder

If you really think that the only way extraterrestrials can discover our existence is by detecting our radio signals, then you are assuming that they possess the same level of technology as ours for detecting life and on this account your equation is flawed.

If a premise is wrong, then everything that follows from that premise must be wrong.

a reply to: shambles84

Chances are it's not distant aliens traveling billions of miles in space to visit earth but rather interdimensional beings, it would explain why we don't see any evidence

This is just another way of saying they are capable of moving between time lines.

a reply to: surnamename57

Regardless of what tech they have we are quite certain that no other particle moves faster than the speed of photons so the quickest method of detecting our presence is looking for our radio signals. What other possible way of detecting us could they use? Let me guess they use their psychic powers to remotely view us.