Probability of Intelligent Life in the Universe.

[ChaosKnight]

Probability of Intelligent Life in the Universe

Introduction

We have often wondered if we are alone in this universe. Are we the only intelligent lifeforms around, or are there other extraterrestial civilizations out there, waiting to make contact?
Here is a simple mathematical model seeking to offer a partial answer to that question. The derivation of the proof is presented, as well as a brief discussion on the interpretation of the results.

Derivation of the Sample Space

Suppose there is an imaginary boundary around our solar system. Enclosed within is our planet, which has intelligent life(us). Now, we allow this imaginary boundary to expand outwards to nearby star systems and beyond. As the boundary expands, we encompass more and more star systems.

At any time, the number of star systems within the boundary is x.

Assuming all this while, ours is the only system with intelligent life,

p(star forms that eventually will have intelligent life) = 1/x.

p(star forms that eventually will not have intelligent life) = (x-1)/x.

And following, within the sample space:

p(all stars eventually do not have intelligent life) = [(x-1)/x]^x.

p(there is one system with intelligent life) = x(1/x)[(x-1)/x]^(x-1).

Therefore,

p(at least 2 intelligent lifeforms) = 1 - [(x-1)/x]^x - x(1/x)[(x-1)/x]^(x-1).

As we let x tend to a very large value (infinity) the probability of at least 2 intelligent lifeforms in the universe tend toward a value of 0.264. There is a 0.264 chance we are not alone in the universe.

Discussion of the Results

We have assumed as our sample space x extends, we are, at all times, the only intelligent lifeforms around. This assumption may not be true. Perhaps, in a nearby star system, there are already intelligent life there. As such, the value of 0.264 is a lower bound. The probability we are not alone can be higher, but not lower.

One of the questions that concerns us is: will we make contact with the intelligent extraterrestials? We are likely to make contact if, firstly, we are in close proximity to them, and secondly, they are able to communicate.

To answer the first part, lets modify the equations a little. Assuming there are 1 billion stars in our galaxy,

p(at least 1 other intelligent lifeform in our galaxy) = 1 - [(x-1)/x]^1e11 - (1e11/x)[(x-1)/x]^(1e11-1).

If we graph p against x, the value of p falls very quickly to zero. This indicates that the probability there is another intelligent lifeform within our galaxy is very small. However, the implicit assumption here is that the probability of a star system having life eventually is 1/x, and tends to zero as x (the number of systems) tend towards infinity. This may not be true. The probability of intelligent life forming around a star should not be dependent on the number of star systems in the universe. Likely it will level off into some finite value. This probability (1/x) is true only if, as we assumed, we are the only intelligent life around in the entire universe.

If we pick the closest 5000 stars, this probability will tend to zero even faster. In other words, it becomes increasingly unlikely to have an intelligent civilization close to us. But remember, this probability is also a lower bound.

To answer the second part, unfortunately this mathematical model does not say if the intelligent life has communication capabilities. The initial sample space is based on us being the only intelligent life around. We certainly do not have long range communication capabilities. In all fairness, following the assumptions strictly, neither will the intelligent extraterrestials.

[Airconvent]

HI Chaoknight,
I did not go into the gruesome details behind your derivations but unless I am mistaken, astronomers have estimated that there are 100 billion stars in the Milky Way..

rich

[gwenyi]

that's the drake equation eh ?

[ChaosKnight]

HI Chaoknight,
I did not go into the gruesome details behind your derivations but unless I am mistaken, astronomers have estimated that there are 100 billion stars in the Milky Way..

rich

Damn...mistake on my part......yes you are right.
Thanks for pointing it out.

[ChaosKnight]

The Drake Equation is N = N* fp ne fl fi fc fL
Information can be found here: http://www.activemind.com/Mysterious/To ... ation.html

[Guest]

Probability of Intelligent Life in the Universe

Intelligent life in the universe......now THAT would be a first....it surely cannot be us the way we humans behave

[ChaosKnight]

Probability of Intelligent Life in the Universe

Intelligent life in the universe......now THAT would be a first....it surely cannot be us the way we humans behave

And how do we behave?

[Kamikazer]

did you factor in the fact that there is near infinite number of galaxies in the universe and that each galaxy has a hell lot of stars?

[ChaosKnight]

Yes.