The Fatal Defect in the Drake Equation

The problem with searching for alien civilizations is that, while there seem to be lots of reasons to suppose that they exist, the evidence, at least the evidence available to the public, the hardest evidence, is feeble.  Indeed, there are those who make a credible case that no such aliens exist at all.

A recent article on Space dot Com states that, “Just 4 in 10,000 galaxies may host intelligent aliens.”  The “rare earth hypothesis” proposes a very similar idea, that only a minuscule portion of planets can sustain life.  If these ideas are correct, the vast size of the universe allows us to assume, nevertheless, that even if alien civilizations are exceedingly rare, they may number in the thousands, even millions.  Is that assumption reasonable?

At first, it seems reasonable enough.  Recent discoveries of exoplanets suggest that planets are common, and therefore, planets capable of hosting life may be abundant on the grand scale of things.  If only one planet in a million has an alien civilization, then with many millions of planets in the galaxy, there could be many alien civilizations.  Right?

But not so fast.  The number of planets in the galaxy (and in the entire universe) is presumably very large, but even so, there is a limit to that number.  The probability of any given planet meeting all the many, many requirements to support life is exceedingly small.  If there are a kazillion planets, but the odds of life are one in a trillion kazillion, then that leaves us with one chance in a trillion, which is statistically zero for most purposes.  Even if you hate math, you can quickly see the point.

Okay, so far, we have established that there may possibly be many alien civilizations, and we have also established that there may not be any.  How do we choose which of those “maybes” is the more reasonable?

Many people employ wishful thinking.  Even skeptics admit that the prospect that there may be aliens is an exciting one (or dreadful, if they are hostile), but the idea that we might possibly encounter them would revolutionize human history (or perhaps end it).  Whether we wish they are there, or wish they are not, however, is not very reliable.

A less fanciful way is to make what we think are reasonable assumptions.  The very famous “Drake Equation” has been, for many years, used as a “starting point” for estimating how many (if any) alien civilizations are “out there.” 

The concept is simple.  Start with the idea that there are many planets.  Then continue with the idea that a certain fraction (of those planets) has water (or some other necessity for advanced life as we know it).  Of those planets that have water, estimate how many have an atmosphere that can sustain life.  Then ask, what fraction of those planets are close enough to their sun (star) to provide life-sustaining warmth.  The series continues, each time reducing the number of planets that can sustain life.  The more requirements there are, the fewer planets that can fulfill all of them.  If there are only ten requirements, one could get a large number of candidate planets.  If there are a hundred requirements, the number diminishes to a tiny amount.  If there are thousands of requirements, the number of planets that can sustain life approaches zero.

Then there are factors that preclude life, even if all the requirements are met.  If the host star explodes, that will surely preclude life.  If the host star emits harmful radioactivity, or has wildly fluctuating temperatures, or the planet is bombarded by meteors and comets—you get the idea.  A lot of things could destroy a civilization before it even gets started.

The question then is, how likely is each factor in the equation?  We do not know.  Even if each factor is fifty-percent, which is large, even then, multiplying all those fifty-percent factors together, soon results in a very tiny chance of an alien civilization existing.

The Drake equation, however, may be making some false assumptions.  For one thing, it assumes that life on any given planet arises (or fails to arise) by chance.  In doing so, it dismisses the idea that life requires something more than the “requirements” of life.  There may be a property of nature that leaves no room for chance when it comes to generating life, or at least for generating intelligent life.  Life may arise, or fail to arise, due to something other than chance.  That “something other” might make life exceedingly common, but it could also limit it to just one planet in the entire universe.

In biology, both evidence and theory have merged into the conclusion that life evolved from nonliving matter, and then without conscious guidance, progressed from the simplest forms, to the most complex forms, including humans.  This paradigm is infused into the assumptions of the Drake Equation.

Yet, there are other merges of evidence and theory that explain the origin and development of life.  One of these holds that life, consciousness and volition (free will) are three fundamental properties of nature.  In this paradigm, there is a life force (élan vital) which acts in a manner loosely analogous to gravity, or even dark matter, to structure atoms into the molecules associated with biochemistry.  This theory eliminates the dependence on chance, that is, on chances that are so small as to approach zero.  Instead, it posits that the universe appears to be the product of intent and purpose because—because it is that product.

If life does not arise by chance, but only by cosmic intent, with a purpose, then the Drake Equation is leading us toward a futile end.  We should not rely on it blindly.

 

Does Infinity Exist?

by Robert Arvay

While infinity is a valid mathematical concept, that is not the same thing as saying that it is real in the physical sense.

Even in the abstract mathematical sense, infinity presents some paradoxes.  For example, in mathematics, it is said that there are an infinite number of positive, finite integers.  That is a paradox, because it implies that there can be an infinite series of finite integers (or anything else).  Why is that a paradox?  If every item in the infinite series is finite, then how can the series be infinite?  Infinity can never be reached, but only approached.  (Even THAT is a paradox, because how can one approach something, yet never get any closer to it?  One is always an infinite distance short of infinity.)  It has no finality.  By definition it has no end.  If one can never get there, is “there” even a “there?”  The semantics are maddening.

How does this apply to the physical world?  In the physical sense, it is speculated, by cosmologists, that the universe may extend forever in all directions.  In the hypothetical, infinitely large universe, we must ask, is that possible?  If the universe is indeed, infinitely large—physically—then infinity has been reached.  It physically exists.  Paradoxically, the endless has been both reached, and yet, can never be reached.

Consider this thought experiment, a test of that principle.  Imagine that you are in a spaceship, traveling in a straight line, in an infinitely large universe.  No matter how far you travel, you will never travel the infinite distance that defines the universe’s reach.  You will never reach the end, because by definition, there is no end.

But wait.  What if you travel at an infinitely fast speed?  What would happen then?

To answer that, let us first look at another, paradoxically infinite universe, one that is both infinite and finite at the same time.  Let us consider a ruler that is twelve inches in length.  Why is this both finite and infinite?  It is infinite, if you measure its length by the number of geometric points along its length.  There are an infinite number of such points.  A geometric point results if one divides the ruler in halves an infinite number of times.  This results in a point having a length of zero.

So, if one begins at one end of the ruler, and begins traveling toward the other end, point by point, then it would take an infinite amount of time to get to the other end.  Indeed, it would take an infinite amount of time to get anywhere along the ruler.  We know this simply by multiplying the speed of movement by zero.  Any amount, any number of points, times zero, is zero.  Since each geometric point is of zero length, then one could never move even as far as one point along the line.  So, one could never move any finite length, if one moves zero length at a time.  To move at all, one would have to move an infinite number of points at a time, all at once;  that is, at infinite speed.

But wait again.  If one moves an infinite number of points all at once, then he has moved a finite distance—but what is that distance?  Is it one foot?  One inch?  One mile?  A billion miles?

Of course, the distance moved would be arbitrary.  One could never specify how far that distance would be.  It could be ANY finite length.

Returning to our spaceship, what would happen if we increased the speed to infinity?  How far would we travel?  If we travel an infinite distance, in an infinitely large universe, then where would we be?  Some random place?  Back where we started?  Outside the universe?  More than one place at one time?  Everywhere?  Where?

What all this tells us is that our intellect is far too limited to understand an infinite reality.

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