I’ve been asked this question before so I decided to tackle it. Are we alone in the Universe? What are the odds? Can we even know that? The answer is yes, yes we can. And I am going to show you how. But first, I’m going to divert to define carefully what I mean by “life”. Then it gets weird … really weird.
Mars Opportunity deorbit debris
I’m going to use the term “advanced” life to mean any life form that possesses an arbitrary command of energy and power. By an “arbitrary” command I mean life that utilizes energy and power; that is, life that dispenses energy at given power rates into its environment in amounts exceeding that possible by its own metabolic or life sustaining function. And by “life” I mean any natural phenomenon that self-replicates with a fidelity of greater than 10% per iteration. The 10% is a bit arbitrary so we can substitute any variable we like, call it α, to denote that value since it won’t have any bearing on the basic premise of our argument. Thus, life, which we’ll denote as ψ, is defined as:
ψ = Any natural process that self-replicates at any non-zero rate with a fidelity of α per iteration or greater.
Notice that it does not depend on any a priori knowledge or principles of biology. It is a fundamental definition. It is, in effect, a statement grounded in physics and math alone. Now, this leads us to a refinement of our other definitions as well.
An “advanced” life case is any life ψ that generates a causal train resulting in a release of energy into its environment, as measured over its duration of existence as such, greater than the total energy released by the causal train it generates in the release of energy into its environment as a sole consequence of the energy expended to self-replicate as by definition.
Thus, there is some total energy Eψ over the duration of a case existence, ψ, required to self-replicate. It is important to note that this energy includes all energy expenditures consequent to a design to self-replicate, not just the minimum required. In other words, if a microbe expends x amount of energy in an ocean swimming 5 miles this is considered a design expenditure because, from its inherent design, this expenditure follows. It thus does not necessarily follow from a design to expend additional energy as a self-replication strategy that is not “hard wired” in that design. But that proportion of energy expended, should it exist, that is expended outside any identifiable, hard-coded design distinguishes ψ into two different categories; “advanced” and “primitive”. Thus, an additional energy, Eµ, is released into the environment of and by an “advanced“ life case. Thus, we can define “primitive” life as satisfying the relation:
Et = Eψ
Where Et is the total energy released into the environment in a causal origin to which ψ is entrained; from the point in time following ψ to the terminus of its duration as such. And advanced life can be defined as any ψ satisfying:
Et = Eψ + Eµ
So, we can now operationally define what we mean by “advanced” life.
Water vapor clouds over Tharsis. Olympus Mountain is upper left.
We posit that a very large, robust experiment has already been conducted to determine if advanced life exists in this universe, with some space-time limitation. To explain this, we first imagine a region of space and time extending spherically around Earth, but a region beginning only about 1000 miles above Earth and extending to 30,000 miles above Earth. This is mostly empty space. But the point is that for some 100 years since various forms of energetic capture and analysis has existed on Earth, say, for example the existence of radio receivers, we know that no exobiological creatrure … no ψ, has existed in that region in the last 100 years (assuming for discussion that is how long we have been “listening”). Thus, there exists a “light cone” of discovery that excludes the presence of exobiological life in the context provided. This is not a certainty, but exclusion is highly probable since any release of Eµ in that context is unlikely to have occured without detection. And the greater the value of Eµ, the greater our confidence can be. But this is like saying the more “advanced” the hypotheisized life is, the more confident we can be that it is excluded. Now, if we extend that sphere out to, say, a distance of 20 light minutes the light cone becomes a 20 minute light cone. This just means that, because energy propagation is limited to the speed of light we know that, at least 20 minutes prior to our measurement, we can exclude advanced life from the surface of the sphere. Now, if we extend that sphere to 100 light years we see the problem. We only began measuring this 100 years ago. Therefore, unless we do in fact detected a “signal” (what would almost certainly have to be a very loud, noisy one at that) on day one of our observations, we can still exclude the surface of this sphere. But we cannot exclude the space beyond that sphere … regardless of how sophisticated our equipment may be. But there are two subtle things going on here.
1.) Distance to exclusion has increased in this example
2.) Time to exclusion has increased in this example
Therefore, this is a strong case for arguing that assessments of the odds of advanced life existing in the universe are limited by this fundamental relation. For we can extend this sphere arbitrarily far into space but if we do so, we are necessarily forcing our understanding of “now” back into the past, making it impossible to state what any probability regarding the “true now” actually is for that extended region. Thus, we can speak of a probability per unit volume of space per unit time as a fundamental limit on any other construction of odds given the following axiom:
- We exist … right here and right now.
- We have existed at some time right here (Earth’s reference frame) in the last 10 billion years.
The Voyager space probe just before departure in the late 70s. It is now the most distant human-made object ever and is just now entering interstellar space. It will likely last over 100 million years before the erosion of interstellar particles dissolves it completely.
Ceteris paribus, for any arbitrarily chosen volume of space equal to ½ s, the probability of an advanced life existing there is ½. Of course, all is not equal, but it is a fair way to approximate a probability defined only in terms of what we can know. But again, this only covers a time interval of 100 years. The odds are reduced when we factor in the available time over which we can evaluate this. And notice that once again we will make no biological assumptions about evolution or the time it takes for advanced life to present. Thus we are being generous in terms of what can occur in some biolgoical sense and we are examining this only in terms of the limits of nature alone. We will be conservative inasmuch as we will only consider the last 100 years as the time that human beings have existed as an advanced life, at least in terms of this life’s ability to propagate.
We’ll pick a gross estimate for a time interval over which stars have existed, say, 10 billion years. Then,
100 / 10*109 = 1 * 10-8
The volume of a sphere with radius 100 LY is:
R = 2.81 * 106 LY3
The Milky Way Galaxy has a radius of Rmw of about 50,000 LY. It’s thickness is, on average, about 1000 LY. Therefore, the area of the Milky Way Galaxy disk is:
And its volume is:
314159 LY2 * 1000 = 3.14*108 LY3
therefore, the ratio of volumes of the Milky Way Galaxy and our 100 LY sphere is:
3.14*108 / 2.81 * 106 LY3 = 112 yielding a probability adjustment of:
1 * 10-8 * 112 = 1.12 * 10-6. But the probability of any “like” space containing life is only ½ based solely on what we know. Therefore, the probability is:
0.5 * 1.12 * 10-6 = 5.6 * 10-7
1 in 1.79 million against that life at least advanced as “us” has existed in the Milky Way Galaxy in the last 100 years. Ouch. We can adjust these odds to take things like empty space into account, but if you do you’ll see that the odds only get worse, not to mention the fact that you have to start assuming things. But let’s not be totally banal. Might it be better to ask, has an advanced life existed in the Milky Way since some time in the past that might strongly suggest ipso facto that they still exist now? We have to ask this question because the way we framed the odds we did not take longevity of an advanced civilization into account (at least not beyond 100 LY). Let’s do that now. Let’s give them some credit within the bounds of what we already know. Again, it isn’t a certainty because we cannot assume we are “equal” to some other, arbitrary, advanced folks out there. But, to be reasonable, let’s give them 10,000 years before they destory themselves. That means that our odds will change:
100 * 5.6 * 10-7 = 5.6 * 10-5; still far from being likely. That’s 1 in 17857 against there being more than one advanced life in the Milky Way.
Now, here’s the “skeawy pot”. What about ancient ruins of folks that just didn’t work out for mother nature? Very different numbers indeed. Let’s assume that we won’t likely find archaelogical remains more than, say, 100 million years old. Just for kicks. Then:
1000000 * 5.6 * 10-7 = 0.56, about 1 in 2. We have a winner. If we consider other galaxies like Andromeda, we’re certain to find them … lots of them. Now, you see where I’m going with this? The pattern of research we’re seeing on Mars where it is becoming more and more likely that “primitive” life (a slightly different bunch of assumptions, but still) once existed but the odds of finding it in our day and age is slim is a pattern we could have easily predicted using basic logic. We’re not likely going to find ET, but we damn well might find lots of their space probes, old cities and other remnants. Witchy, huh?
Looking at what we now know about Mars (long story, but microbial life was there), a curious pattern seems to be present. From one star system to the next, beginning with the nearest and going outward, we seem to find a similar probability to finding “primitive” life as we do to finding “advanced” life when, from one galaxy to the next, we proceed outward.