Monday, August 13, 2012

We Are Not Alone – A Mathematical Speculation for Alien Life

We Are Not Alone – A Mathematical Speculation for Alien Life:
We are not alone...

To ponder thoughts. To seek answers. To question everything.
It is in the very nature of human beings to be inquisitive. Indeed, some might even argue that our curiosity is the single most important asset that we have.
Speed. Strength. Size. Agility. These are all traits that our species does not have. Yet, humans are the dominant species on this planet. Why? The answer lies within our minds. We are the most intelligent creatures on this planet – but that isn’t enough. We also have the intrinsic drive to create, invent, and innovate – and herein lies our strength. And this innate curiosity (explaining why you’re on this website right now) can be applied to almost any study. The advancements in astronomy have resulted in that curiosity fabricating a single thought that has rested at the back of our thoughts. In fact, it is possibly the greatest question that our species hopes to answer.
Are we alone?
Well I’m here to tell you that we most definitely are not. In fact, I guarantee it. Humans are not the only existing life forms in the universe.  We have actively been looking up towards the skies since the early 1900′s and have not yet found any definitive sign of aliens. Organizations, such as SETI (Search for Extraterrestrial Intelligence), have been set up and millions of dollars have been spent specifically for this one purpose. However, a single confirmation of intelligent activity elsewhere in the universe has not yet been detected. But I still maintain my position. How can I be so sure? Because I put my faith in the simple logic behind mathematical probability.
You have probably seen a similar example in school, but I use this simple problem to demonstrate a concept. Suppose that you have a die. You want to calculate the probability of you rolling a two on the first roll and an even number on the second roll. The answer is obtained fairly simply. The probability of rolling a two is 1/6. The probability of rolling an even number is 3/6. To obtain the probability of these events occurring together, we multiply (1/6) x (3/6) to obtain 3/36. Easy, right?
Let’s see if we can apply this same principle towards determining the probability of life existing within our galaxy. First off, we need to determine the factors that would affect the development of another civilization. As we go along, we’ll assign each one of these factors a variable. This method of determining communicating civilizations is known as the Drake Equation. Read to the end for a surprising revelation (for all those critics)!
The primary factor we need to consider for life is a source of heat, light, and energy. This can be obtained from nearly every star in our galaxy (ex. the Sun). Without a star, a planet would not be able to sustain enough heat or light to form. Assuming that the ecological “food chain” relies on vegetation (as it does on our planet), then life forms would not be possible without this photosynthetic foundation. So the primary factor that should be considered is the number of stars in our galaxy (N*). Since current estimates range anywhere from 200 billion – 400 billion, we’ll use the average and go with 300 billion stars in our galaxy (shown below).
A picture of the Milky Way Galaxy
The next factor we need to consider is how many of those stars  actually have planets around them. Even though the stars provide energy, life requires a stable surface on which it can develop. This can be denoted by F(p), or the fraction of stars with surrounding planets. Current estimates vary wildly from 40% – 100% ! The large variation can be explained by the fact that our current technology doesn’t allow us to spot the smaller planets out there. Using this as basis, some astronomers predict that nearly every star has at least one planet regardless of whether we can detect it or not. We’ll use the average once again and go with 70%.
Now just because planets surround a star doesn’t mean that life can develop there. In our solar system, planets such as Mercury could never develop life because the temperature is either too hot or too cold. For a planet to be able to sustain life, it needs to be located in what is known as the “habitable zone”. This is the zone around a star where a planet, provided it has sufficient atmospheric pressure, can hold liquid water on its surface (since it’s a commonly known fact that water is crucial for life). The number of those planets around a star that  exist in the habitable zone can be denoted as N(e). Scientists predicted this number by examining the distance to Gliese 581 g, an Earth-like planet that has a good chance of being habitable (artist drawing shown below). Combining the distance with the level of detail that they used to find Gliese 581 g, astronomers estimate N(e) to be between 10% – 20%. We’ll go with 15% for our calculations.
An Earth-like habitable exoplanet
However, we must also keep in mind that not every planet in the habitable zone will go on to develop life. This is a tricky one; we need to determine the fraction of those planets in N(e) that will go on to develop life (denoted as F(l) ). Estimates are all over the spectrum, from 0% to 100% ! Those who argue for the former subscribe to the “rare-earth hypothesis” which claims that the existence of life on Earth was  extremely improbable and that the chances of it occurring again are almost nil. The latter side argues that if planets are given the right conditions (such as those in the habitable zone), then life  will develop and it’s just a matter of time. For our purposes, we’ll say that 50% of all planets that can develop life does indeed develop life.
Since we’re looking to communicate with these aliens, we now need to examine the probability that intelligent life will develop – F(i). Looking at the Earth provides a measurement for one end of the spectrum. There are over a billion species on Earth, but only one has gone on to become intelligent. Thus, F(i) is close to zero. Others use the theory of natural selection and state that over the course of time, an intelligent species will develop because of the nature of evolution. According to them, F(i) is 100%. These wide varying ranges make things difficult, but we have to do the best we can ( F(i) = 50%).
While skeptics may find that using averages from these wildly varying guesses seems unreliable, trust me and stay for the ending!
Just because intelligent life exists doesn’t mean it will try to communicate. The life-forms must have the inquisitiveness, like humans, to have the desire to explore the cosmos. Now we need to find the fraction of intelligent life that will make active efforts to communicate – F(c). Once again, the values range from 0% (For the majority of the time, even humans don’t try to send messages into space) to 100% (If given enough time, then other forms of intelligent life will be forced to communicate into space either through travel, radio waves, or other methods). 50% seems to be our closest friend right now.
We’re now at our final factor! We must keep in mind that everything has to come to an end, and this doesn’t exclude civilizations. Just as great civilizations rise, they must one day fall (including alien civilizations). F(L) represents the fraction of the planet’s life for which communicating civilizations existed. Determining this requires us to look at our only data plot (which also happens to be incomplete), the lifetime of the human civilization. The expected lifetime of the Earth is about 10 billion years. So far, humans have been communicating with radio waves for only 100  years. If we assume that our species will die out in the next 1,000 years, then we obtain a fraction of 1/10,000,000 (# years of communication / # years of planet’s lifetime).
So what do we obtain when we multiply all of these numbers together? We get N, the number of communicating civilizations in our galaxy.
N = N* x F(p) x N(e) x F(l) x F(i) x F(c) x F(L).
If we multiply out all of the averages that we deduced above, the result is astonishing. According to our calculations, there are 394 communicating, intelligent, civilizations in our own galaxy! To calculate the value of N for the universe, we simply replace 300 billion stars with the number of stars in the universe (300 Sextillion –  3 followed by 23 zeros). This produces a simply mind-boggling result of 393,750,000,000,000 (“393 trillion, 750 billion) communicating civilizations in our universe! The number would shoot through the roof if we included unintelligent life-forms out there.
Now here’s the part for the skeptics. Many will argue that my results are skewed (and I agree) because I simply used averages. However, I still stand by my original point that we are not alone. Let’s calculate N once more, except we’ll use the lowest possible estimates! For this calculation, I used the lowest value of every single factor we discussed above. The 0% factors have been rounded up to 1% for the sake of simplicity and given assumption that these factors are indeed possible.  (Understand that given even this is still not entirely accurate but provides a strong argument in favor of this stance.) The lifetime of communicating civilizations (F(L)) has been rounded down to 1/1,000,000,000 (which assumes that our species will die off tomorrow, further reducing the number of actively communicating civilizations). This time, the math indicates that, even with all these reductions, there are still 12 million active, communicating civilizations out there! And yes, this doesn’t include the number of species that are unintelligent.
I realize that by no means are these final answers. I do realize that there are many, many other factors which could influence the result. I am not making any definitive claims here, but the sheer probability that we are alone is so little that I refuse to believe it. This is what I mean as the  ”Proof”. The likelihood that we are alone is so improbable that I can say, somewhat certain, that we simply cannot be alone. However, be aware that I am only speculating here, and after all, all great discoveries were made by constant speculation. Maybe I’m missing a crucial detail here. Maybe I made a mistake in my calculations. Maybe this is an innate human instinct being shown in myself – the need for company. Humans are social animals, and the thought that we are alone in the universe is a scary one. Whatever the reason is, I will forever find it hard to believe that we are flying solo through the cosmos.
So if there are so many civilizations out there, why haven’t we made definitive contact with any of them yet? Be on the lookout for another article later today addressing this issue!
For right now though, go outside (or wait until night-time depending on when you’re reading this) and take a look at the skies above (trust me, the feeling is incredible). Realize that somewhere out there, there are just so many life-forms all trying to reach other ones. Realize that we are probably sharing this universe with numerous other beings. And one of these days (assuming that we haven’t already), it is inevitable that we will make contact with them. Perhaps other civilizations have already reached each other and Earth is being left out. Perhaps our planet is simply a lab experiment set-up by other aliens. The possibilities are endless and it’s hard not to be overwhelmed. What we can say though is that only time will tell…
*Update (8/11/2012): Many readers have commented that this post places too much emphasis on assumptions, or that my rounding up to 1% was invalid. I have never said that assumptions were not involved; in fact, I even stated that all of this is speculation. For example, I could go on to state that the universe is infinite which would guarantee the existence of life (no matter what you number you round the percent to). I could further extend this by bringing in the example of the multiverse and an infinite number of universes. All of this would conclude that life exists elsewhere. Yet, what is the basis? The basis relies on pure speculation. Currently, we cannot prove nor disprove these theories. However, speculation of these theories will one day give us an answer. This was the entire goal of the article – not to provide a definite, hard-core scientific answer for alien life (as I have mentioned many times, there are simply too many factors), but to inspire, entertain, and express opinions (with my opinion being that alien life does exist).*