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The Fermi Paradox

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For those less familiar with this term, this paradox is the apparent contradiction between our expectation of intelligent life throughout our universe and the lack of communication or contact from said intelligent life.  That is, if we are not the only intelligent life in the universe, then why haven’t we received distinguishable radio signals from these other intelligent beings?  In a section of a previous post, I briefly discussed this paradox and I decided it should be addressed in more detail.  That will be the purpose of this post.  Most of the ideas I will be discussing are well-known to those familiar with the topic, but I hope this post will encourage the onset of new ideas from those that haven’t given the topic as much consideration.

Expectation of Extra-Terrestrial Intelligence

Many scientists estimate that our solar system may be but one of many billions in the galaxy, let alone the entire observable universe, let alone the entire unobservable universe.  The estimated number of stars in the observable universe is around 300 sextillion (3 × 1023) which as you may notice is on the same order as Avogadro’s number.  So with all of those solar systems out there, it seems reasonable that a fraction of them may be suitable for supporting life.  The number of civilizations capable of communicating with us can be calculated by what is known as the Drake equation.  While we don’t know which numbers to plug in to this equation, it at least gives us a mathematical view of the variables involved to accomplish such a calculation.

Another factor to look at is the age of our Sun relative to other stars in the universe.  The Sun is relatively young as it was formed a mere 4.6 billion years ago whereas most stars are between 1 and 10 billion years old clocking the average star at around 5.5 billion years old.  Either way, we can see that there are presumably a lot of stars out there that are older than the sun and this means that in many cases, intelligent life could have more time to evolve (and potentially much more time than we’ve had on Earth).  So this means that not only are there a large number of solar systems, but many of them are likely to be a billion or more years older than our own.   If any of those solar systems have supported intelligent life with radio technology, then we may expect to detect some radio signals which have already been traveling toward us for a billion or more years.  This would mean that if a radio transmission had enough energy behind it (enormous amounts of energy at that), it may have already traveled billions of light-years in which case we could detect those signals now — even if they are detected long after the originators have become extinct.  It would support the idea of intelligent life existing (or having once existed) elsewhere.

These reasons basically summarize our expectations for receiving communication from extra-terrestrial intelligent life.  Next, I will discuss several factors compatible with two ideas: intelligent life existing elsewhere in the universe, and the lack of evidence for receiving any communication from said intelligent life.  In other words, I will discuss several ways to resolve the Fermi paradox.

Resolving the Paradox

It seems to me that the paradox can be resolved by examining a number of factors including: the statistically small concentration of intelligent life in the universe, self-destruction by technologically-advanced species, the assumption of extra-terrestrial intelligent life behaving in certain ways based on anthropocentric views (including the assumption of extra-terrestrial life desiring contact with outsiders), human’s relatively short time span with post-radio technology, problems with radio signal propagation, the Hubble constant, and other various reasons.

Small Concentration of Intelligent life in the Universe

Life requires a very narrow range of conditions, and so we’d only expect it to exist if there was a planet at the appropriate distance from a star, and for that planet to contain the correct elemental starting materials (e.g. carbon, hydrogen, oxygen, nitrogen, phosphorous, etc.).  If these conditions are within some range of acceptability, Brownian motion, favorable chemical bonds, and an input of energy from a neighboring star could lead to amino acids, proto-cells, DNA, etc.  Basically, we need particular planetary conditions necessary for abiogenesis (whatever that range of conditions may be).  What this means is that we have at least two variables with opposite effects on the outcome:  a large number of prospective solar systems, and a narrow range of conditions suitable for life.  Thus, one would expect that there are a large number of solar systems that are inhabited by life, but this would constitute a tiny percentage relative to the entire population of solar systems.

On top of this, the conditions needed to support intelligent life are even scarcer, especially after we consider that out of the 3.7 billion years of life on this planet, only in the last several thousand years have we had a form of life capable of developing advanced technology (namely radio technology).  Several factors contributed to intelligent life evolving from simple living systems in order to produce advanced technology.  Among them are: a habitable terrestrial environment, a moon with consequential tidal forces that catalyzed ocean-life’s migration onto land, writing systems & language, opposable thumbs, etc.  If we lacked any of these factors, it’s easy to see how the evolution of intelligent life capable of manipulating its environment in order to develop advanced technologies would be extremely unlikely.

So it is difficult to say how likely it is to have conditions suitable for life, let alone intelligent life.  However, I think it is safe to say that the concentration of intelligent life would be rather small, that is, out of the minute concentration of life-supporting solar systems, we’d have an even smaller concentration of intelligent life-supporting solar systems.  In the next section, I’ll discuss why this minute concentration of intelligent life is also compounded with a limited window of time for the species potentially able to send radio communication (due to the eventual extinction of these intelligent species).

Self-Destruction by Technologically-Advanced Species

If there are indeed many regions in the universe that are presently supporting or have previously supported life, then we must ask ourselves another question:  How long do we expect those species to thrive before they self-destruct?  In other words, if all or most technologically-advanced species inevitably get to a certain point in their evolution whereby they either exhaust all of their resources, succumb to nuclear or biological warfare, lose ecological sustainability (some may call this a Malthusian check/catastrophe), etc. — is it very likely that they will be in existence long enough to design and transmit interstellar radio communication?  Or to ask another follow-up question, if those species are alive long enough to design and transmit interstellar radio communication, how long do they have before they become extinct and their radio communication comes to a screeching halt?  The reason why this is important is because intelligent life able to communicate with us in theory may only have a relatively small window of time before the species becomes extinct.  If this happens after just a few hundred or a few thousand years of developing radio technology, then any radio transmission heading our way would only last for this same time duration.  If we are not in existence to receive it (whether it reached Earth before we evolved into intelligent beings or if it reaches us after we’ve become extinct) then we would have no record of it, even if radio transmission has occurred or will occur one day when we are long gone.  In other words, not only are extra-terrestrials with radio technology a necessary prerequisite for receiving a signal on Earth, but we also have to be alive and able to receive it during a particular relatively narrow window of time.  If the average star is older than ours, than only those solar systems at the appropriate distance would have a window of radio communication capable of reaching us.

Time Span of Radio Technology

In 1879, David Edward Hughes discovered that sparks would generate a radio signal, thus leading to the spark-gap transmitter.  Shortly thereafter in 1888, Heinrich Hertz, utilizing a more rigorous scientific approach than Hughes, was the first person to prove and demonstrate that radio waves could be transmitted (and detected) through free space.  This paved a large path for Marconi,  and after conducting various experiments in the 1890’s, he finally produced a technically and commercially viable form of radio technology.

So we can see that radio technology ultimately surfaced in the last 150 years.  Human civilization as we define it today (e.g. the utilization of agriculture, writing, weapons and other advanced technologies) has been around for about 10,000 years.  This means that only in the latter 1.5% of our time as civilized human beings, did we possess radio technology.  Relative to the 50-100,000 years of Homo sapiens’ existence, this is but the latter 0.1%.  Relative still to the 3.7 billion years of having any form of life on this planet, it is a mere blink of an eye.

So in short, we can see that radio technology wasn’t available to us until very, very recently.  What does this say about the Fermi Paradox?  Well it tells me that once intelligent life has evolved, it can take many tens of thousands of years (or longer) for advanced communicative technologies to exist.  Moreover, it tells me that intelligent life may exist elsewhere in the universe, even if extra-terrestrials have yet to discover radio technology (e.g. electromagnetic wave transmission).  After all, intelligent life seems to require many special conditions in order to develop radio technology, including: writing systems, opposable thumbs (not necessary but it makes it much easier), a terrestrial environment (it’s difficult to fathom how our level of technological progress could be attained in an aqueous environment), etc.  It’s easy enough to see that humans may have never discovered radio technology, as many special conditions were needed in order to do so.  Only very recently were all of those conditions met.

Radio Wave Propagation in Space

Due to the inverse square law (of electromagnetic radiation passing through free space), radio waves tend to become indistinguishable around several light years.  They may be clearly transmitted as far as a few hundred light years (if the signal is amplified and aimed in a specific direction), but radio waves require extremely large amounts of power (on the order of gigawatts) for transmission over distances as short as several light-years.   What this means is that many terawatts of power are most likely needed to send a clear signal over the distances required to reach intelligent life elsewhere in the universe.  So not only must we assume that this extra-terrestrial intelligent life has discovered radio wave technology, but also that it has the energy resources available to propagate radio wave signals over vast interstellar distances of many thousands or even millions of light-years.  The key thing to note here is that the radio wave signal has to be strong enough to overcome the average background noise that we’re already receiving constantly.

Radio waves can also be reflected, refracted, diffracted, absorbed, polarized, scattered, etc., by various materials in between its trajectory and our planet.  So in addition to the energy needed to propagate these radio waves, we must also assume that the waves have a free path so there is little or no information lost during its propagation to Earth.  Now we mustn’t forget that the mean free path of outer space, that is, the average distance a photon can travel without being affected (by matter), is around 10 billion light years.  So I’m willing to admit that the idea of radio waves being absorbed or affected by matter in any significant way is unlikely.  However, there is still bound to be constructive and destructive interference between any radio waves sent and any other electromagnetic radiation it crosses paths with.  If there are radio signals being sent from all over the universe and some were heading in our direction, how many of them have interacted with other waves with varying frequencies, amplitudes, etc.?  I think it is safe to say that regardless of the mean free path in space, the true mean free path, that is, the average distance a photon can travel without being affected (by matter OR electro-magnetic radiation) is probably closer to zero.  The universe is full of radiation moving in every (or just about every) direction.  This ultimately means that any radio transmissions sent from afar would most likely be distorted and changed dramatically.  If this was the case, we may end up receiving radio signals that are comparable to the microwave background radiation we detect now, that is, we may detect signals that don’t appear to carry much (if any) information at all.  So we may just have trouble separating “noise” from potential “information”.  For all we know, any and all radio signals sent in our direction may partially constitute the cosmic microwave background radiation.  If this is the case, then there is little or no hope of receiving any true information.

The Hubble Constant

As it turns out, cosmologists have determined that the observable universe is expanding.  Not only is it expanding, but it is also accelerating.  This rate of expansion is represented by the Hubble constant.  One important thing to realize is that space-time itself is expanding, not just the distance between galaxies within that space-time.  This is important to realize because space-time is actually believed to be expanding faster than the speed of light.  While many may think that this would violate Einstein’s Special Theory of Relativity, it is actually completely compatible.  According to Special Relativity, one consequence is that nothing can travel faster than the speed of light within space-time.  Within the field of cosmology, the general consensus is that space-time itself is expanding faster than the speed of light, thus not violating any physical laws.  Since this cosmic expansion does not allow information to travel faster than light, we are further assured that it adheres to all known physical laws.  This expansion is creating a light cone which incidentally puts a boundary on the observable universe from any point of reference.  That is, due to space-time expanding faster than the speed of light, there is a maximum observable distance from any point in the universe.  Past this distance, electro-magnetic radiation that is being transmitted toward the observer is never able to “outrun” the expansion rate of space-time, and thus it is never able to actually reach that observer.  What this ultimately means is that any potential radio waves that are being transmitted beyond this “observable universe” (i.e. the light cone) will never be able to reach that point of reference (e.g. an observer in the center of that light cone).  It does not matter how much power is used for transmission, it is physically impossible for information to reach us if it is transmitted beyond this point.

If we account for the Hubble constant, it turns out that our observable universe has a radius of approximately 46 billion light-years.  Past this point we can’t see anything (including radio signals).  If we take into account various theories of inflation, it is believed that the true universe (that which our “observable universe” is a constituent of) is many orders of magnitude larger.  So even if the universe had intelligent life distributed at a concentration of only 1 planet per “observable universe”, we would still have billions upon billions of intelligent civilizations in existence and yet there would be no possible way to know about their existence.


So it appears that there are numerous factors that can account for and resolve the Fermi paradox.  Does this mean that there is undoubtedly intelligent life elsewhere in the universe?  Of course not.  It seems clear to me however that the vast size of the universe (especially the unobservable universe) and the degree of homogenization we’ve observed thus far indicates that the probability of extra-terrestrial life is extremely high, regardless of whether or not we have received a radio transmission from them.  So in my opinion, the “Fermi paradox” doesn’t appear to be much of a paradox at all.

Gay Marriage, Sexism, and Simple Algebra

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The social issue of gay marriage gained national importance over this last year.  We heard the reasons behind positions held on both sides of the aisle.  On the one hand, some opponents to gay marriage said that they were interested in keeping marriage “sacred between a man and a woman”.  On the other hand, we had proponents and advocates saying that gay couples should have the same rights as straight couples.  I’d like to address this issue using simple algebra, to show that ultimately allowing gay marriage rights is merely another dissolution of inequality between men and women.  That is, allowing gay marriage to be legalized further illustrates that men and women are equal.  We can say “It’s about gay rights” or “It’s about straight rights”, or even “It’s about religious rights” — but I prefer to say “It’s about equality between men and women”.  Let’s look at the math here:

If a couple is mathematically nothing more than a sum of two variables (we’ll call them A and B, where A represents a female and B represents a male), then marriage can be described by the following:

A + A,   B + B,   or A + B, where the latter is a traditional marriage.

According to gay marriage opponents, neither A + A  nor  B + B can equal A + B, therefore A is not equal to B.

This implies that men and women are not equal.  You will hear a lot less about this issue from a “sexual” discrimination perspective as opposed to a “sexual orientation” discrimination perspective, but clearly opposing gay marriage is also a sexist position.  Just look at the math folks.  The numbers just don’t add up for those opposed to gay marriage, especially if those individuals also claim to promote equality between the sexes (many don’t I’m sure, but I’m also sure that at least some people out there do in fact believe that they are not sexist, yet oppose gay marriage).  I find it surprising that gay marriage rights are still being fought over after we as a society have come as far as we have.  We examine issues like slavery, voting rights, civil rights, etc., and see that the idea of inequality leads to dangerous outcomes.  Haven’t we triumphed over these issues?  Why are we still fighting over rights that seem so obviously inalienable and universal?  Rights that maximize happiness by allowing every unit (be it a single person or a couple) to be treated equally.  Perhaps some people in this country simply need to re-examine their math skills.

Written by Lage

February 4, 2013 at 10:50 pm