This is a mathematical formula I came up with.
The Probability of Life in the Universe = 0.64
The proof is as follows:
Imagine looking at our sun. The probability of finding life near our sun is 1, since we know we are here.
Next, extend our scope to a nearby star, like P.Centauri. Assuming there is no life near that star, the probability of life is now 0.5, since out of the two systems only ours have life.
The probability of NOT finding life = 1 - 0.5 = 0.5
Now lets extend our scope to another star system. Assuming the new star system is also barren:
Probability of finding life = 1/3
Probability of NOT finding life = 1 - 1/3
Continuing to an arbitrarily large number of star systems, assuming all but ours are devoid of life:
Probability of finding life = 1/x
Probability of NOT finding life = 1 - 1/x
where x is the number of star systems under consideration.
Now, transfer our attention to an area of space far away from the group of stars we are considering. Assuming the probability of finding life in any star system is the same as the probability of finding life in the area we just left, and extending our scope now to a large number of star systems,
probability of NOT finding life = ( 1 - 1/x )^x
Here's the kicker: the equation approaches a value of about 0.36 if we limit x to a very large number. Means the probability of finding life = 1-0.36 = 0.64.
Now, you may ask: Since the probability of finding life is so high, where the hell is ET?? Remember, this equation gives a value for the probability of 1 form of life (us) happening in the ENTIRE universe.
But don't fret. One of the assumptions in the proof is that the probability of finding life over a large number of star systems is the same as the probability of finding life within a star system. 0.64 is a large number. Our own solar system is not fully explored yet. Who knows there may be life on Europa.
Comments?
Mathematical Proof: Probability of Life = 0.64
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ChaosKnight
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zong
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Hi ChaosKnight... I wanna point out a few flaws in your proof.
First you're assuming that any star around our size MUST have life (thus your probability = 1?). However, given measurements so far (although the star wobble detection method is until now still not precise. For assumption let's take that it is precise enough) even many stars our size have confirmed no life.
Next, no matter what the star type or star size, as long as there is a rock planet far enough (or near enough for smaller stars) there can be a possibility of life.
Your probability is also faulty. You cannot use the probability of not finding life and adding ^x to it. Taking your measurements are correct (ie. 1 local star system only 1 planet with life) you should take probability of finding life = (1/x)^x instead. For a large x, this gives you a superbly small value. Sorry, but your theory actually proves that life is hard to find in the universe...
For me, I do HOPE there will be intelligent life elsewhere... But statistically nothing so far has given me proof to back it up...
First you're assuming that any star around our size MUST have life (thus your probability = 1?). However, given measurements so far (although the star wobble detection method is until now still not precise. For assumption let's take that it is precise enough) even many stars our size have confirmed no life.
Next, no matter what the star type or star size, as long as there is a rock planet far enough (or near enough for smaller stars) there can be a possibility of life.
Your probability is also faulty. You cannot use the probability of not finding life and adding ^x to it. Taking your measurements are correct (ie. 1 local star system only 1 planet with life) you should take probability of finding life = (1/x)^x instead. For a large x, this gives you a superbly small value. Sorry, but your theory actually proves that life is hard to find in the universe...
For me, I do HOPE there will be intelligent life elsewhere... But statistically nothing so far has given me proof to back it up...
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zong
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Maybe I will try my own statistical theory for suggestions? Here's what's been giving me faith enough:
Take star-wobble planet predictions to have an accuracy of 0.1. Assume we have monitored 1% of the stars in the universe. Thus, (0.1 * 0.01)% of the stars are confirmed without life.
By the VERY (and i do mean VERY) optimistic view, 1 out of every 10 stars we have checked but not confirmed have life. that gives 0.0001% of the stars. Also, take that 1 in 5 stars we have not checked have life. that means another 19.8%. Totalling up, it is 19.8001%. Take a generous error margin of 15%. That leaves us 19.8% (+-) 15% which, at the lousiest, is 4.5%. That gives us 1 in 20 chance!
I assumed a lot of things though... But this is the best I can give myself for the assurance...
Take star-wobble planet predictions to have an accuracy of 0.1. Assume we have monitored 1% of the stars in the universe. Thus, (0.1 * 0.01)% of the stars are confirmed without life.
By the VERY (and i do mean VERY) optimistic view, 1 out of every 10 stars we have checked but not confirmed have life. that gives 0.0001% of the stars. Also, take that 1 in 5 stars we have not checked have life. that means another 19.8%. Totalling up, it is 19.8001%. Take a generous error margin of 15%. That leaves us 19.8% (+-) 15% which, at the lousiest, is 4.5%. That gives us 1 in 20 chance!
I assumed a lot of things though... But this is the best I can give myself for the assurance...
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ChaosKnight
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I am not assuming any star similar to ours have life. I am assuming ours is the only star with life in the entire universe.zong wrote:Hi ChaosKnight... I wanna point out a few flaws in your proof.
First you're assuming that any star around our size MUST have life (thus your probability = 1?). However, given measurements so far (although the star wobble detection method is until now still not precise. For assumption let's take that it is precise enough) even many stars our size have confirmed no life.
Next, no matter what the star type or star size, as long as there is a rock planet far enough (or near enough for smaller stars) there can be a possibility of life.
Your probability is also faulty. You cannot use the probability of not finding life and adding ^x to it. Taking your measurements are correct (ie. 1 local star system only 1 planet with life) you should take probability of finding life = (1/x)^x instead. For a large x, this gives you a superbly small value. Sorry, but your theory actually proves that life is hard to find in the universe...
For me, I do HOPE there will be intelligent life elsewhere... But statistically nothing so far has given me proof to back it up...
And I realise there is something wrong with the mathematical logic. But not the way you described. The error is in defining the event.
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ChaosKnight
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The troublesome thing about Drake's equation is that for some terms it is not so straightforward to obtain reasonable estimates. Like the lifespan of a species, or the probability it will try to make communication.
One interesting thing about this problem that has been bugging me is this: at it's worst case the incidence of life is very improbable. But the universe is a huge place. So, which factor outweighs the other?? Many people think because the universe is so huge, the probability of life somewhere else is a sure thing. On the other hand there are people who think life is so improbable it can't exist anywhere else other than here on Earth. For either case nobody has been able to come up with any conclusive evidence.
One interesting thing about this problem that has been bugging me is this: at it's worst case the incidence of life is very improbable. But the universe is a huge place. So, which factor outweighs the other?? Many people think because the universe is so huge, the probability of life somewhere else is a sure thing. On the other hand there are people who think life is so improbable it can't exist anywhere else other than here on Earth. For either case nobody has been able to come up with any conclusive evidence.