In the great science fiction novel,

**, by Arthur C. Clarke, an armada of benevolent alien Overlords arrives at Earth and cultivates the growth - maturity of humanity. Only very late in the novel do the Overlords finally reveal their physiognomy - looking just like assorted depictions of "Satan" through antiquity.**

*Childhood's End*But one wonders what would have transpired if the visiting aliens foolishly revealed themselves first. It doesn't take a lot of imagination to project all the human armies of the world would likely have attacked the invaders but the results would have been radically different from

*'Independence Day'*. The two scenarios provide different cautionary tales on how humans may have to process any future alien landings.

"Aw, that's the stuff of fantasy! Never happen! Not in a billion years!"

Don't be so sure! As Carl Sagan observed in his own Cosmos series (and Neil de Grasse Tyson does at the end of his), from deep space Earth appears as an un-twinkling

**(also the title of another Sagan book). The actual image-photograph of this pale blue dot exists (shown in the last Cosmos episode) and was accomplished at the behest of Sagan when he requested NASA have the Voyager spacecraft turn its cameras back toward Earth as it ventured beyond Jupiter on its way out of the solar system.**

*pale, blue dot*Make no mistake that to any transiting alien craft this would provide an inviting target or destination. What would come next depends on the intent and the nature of the aliens at the helm, Would they be beneficent? Possibly. But it would be foolish to make the assumption that all such visitors would have our interests at heart.

Indeed, in an article I wrote in 1978,

*'We Are Not Alone'*, e.g.

_{}

^{}

_{}

^{}

**." He predicted that it would be**

*like a malignant, technological cancer spreading across the galaxy” and we’d "do well not to wish for any meeting*__the most aggressive species__we'd be most likely to encounter first.

Tragically for us and our kind, for whatever reason this alien species would have discovered the engineering basis for practical interstellar travel long before their aggressive and conquistadore dispositions were bred out of them. No surprise then, that no less a luminary than Stephen Hawking has also warned about allowing our hubris to get the better of us, e.g.

http://www.nbcnews.com/id/36769422/ns/technology_and_science-space/t/hawking-aliens-may-pose-risks-earth/#.U5xq6JVOXzA

This is not mere bunkum and the odds for meeting such beings should not be under-estimated. In the paper ‘

*Galactic Civilizations: Population Dynamics and Interstellar Diffusion’*by William Newman and Carl Sagan, in

*Icarus*, Vol. 46, June 1981, we get a wake-up call.

The authors began with a standard diffusion equation, treating the spread of any colonizing civilization similarly to any medium that diffuses – for example, viruses, or general infections, or even human populations (say in the early colonizations of the New World).. The basic diffusion equation used was (p. 301, eqn.12):

d(r )/dt = DIV(D(x,t,r ) x grad r (x,t)

where, r (x,t) describes the population density at time t, and position x, and D is the diffusion coefficient in terms of x, t and r . The preceding equation is then tweaked and used as the basis for future refinements.

Rather than weary the reader with the dozens and dozens of equations leading to the

*Results*section (page 314), I will simply commence at that section and then go from there.

The authors' first major computation is of N’, the steady state number of extant advanced civilizations in the Milky Way. This is essential to obtain because it is one of the key variables used to compute the mean distance between advanced civilizations in the Milky Way:

L

**= (2.5 x 10**

_{m}^{11}/N’)

^{1/3}

Where the numerator refers to the

*number of stars estimated in the galaxy*. The result is in parsecs, assuming the mean separation between stars in the galaxy is 1pc = 3.26 light years. (Bear in mind while our region near the outer rim is sparse with stars, the interior third of the Milky Way is teeming with them, very densely packed)

Based on a star –planet formation factor, f *~ 1, and a mean lifetime for an advanced civilization of 10

^{6}years, the authors obtain: N’ = f(10

^{6}) = 10

^{6}, or one million advanced civilizations in the Milky Way alone.

Then, the mean distance between advanced civilizations in the Galaxy is:

L

**={ (2.5 x 10**

_{m}^{11}/ (10

^{6})}

^{1/3}= [2.5 x 10

^{5}]

^{1/3}= 63 pc = 205 Light years

Readers may well not appreciate this, but this is literally “next door neighbors” in terms of the galaxy!

The authors’ next task is to obtain the velocity of the colonization wavefront which they give as (Eqn. (79), page 316):

V = (v

**)(D g)**

_{k}^{1/2}

Here, (v

**) is a dimensionless constant of order unity(1), and g ~ 0.1 (based on the rate of migration of human populations today (Newman and Sagan estimated 0.01 /yr, but that was nearly 30 years ago before the age of globalization). The diffusion coefficient, D, is (very) conservatively estimated at: D ~ (2 x 10**

_{k}^{-8}pc

^{2}/yr).

Thus, the colonization wave velocity would be:

V = (1)[ (2 x 10

^{-8}pc

^{2}/yr)(0.1 /yr)]

^{1/2}= 4.4 x 10

^{-5}pc/ yr

Which would imply 1.4 x 10

^{6}or 1.4 million years before the colonization wave reached Earth, assuming a 63 pc distance to the nearest advanced colonizers.

Now, before anyone gets too ecstatic, bear in mind:

1) Sagan and Newman based their diffusion coefficient on relatively low travel speeds (v much less than c) since anything near v ~ c would be enormously expensive in terms of shielding, propulsion (page 312). They opted then for speeds far below relativistic (e.g. ~ 40,000 km/h).

2)They deliberately assumed a “random walk” diffusion with directional bias “away from population centers".

Personally, I believe the first is way too conservative and ignores the sort of ingenuity and enterprise that may well apply to a truly advanced civilization which is also space faring. And again, just because we can’t imagine humans attaining relativistic speeds, doesn’t mean advanced aliens couldn’t. So, just a shift (reduction) of the base travel time to about one ten thousandth of what the authors use enhances the diffusion wave speed, V to 0.004 pc/yr.

This reduces the time to encounter to 1.57 x 10

^{4}yrs. or just over 15,700 years. A blink of an eye.

Thus, if the alien colonizers commenced a journey in our general direction (the next thing I will deal with in (2)) from about 3ky before the Holocene geological era, then they’d be roughly 700 years away from finding us. (Give or take 1000 years in terms of uncertainties). This means the colonizers may well be “right around the corner”.

As for the authors’ assumption (2) that the directional bias is away from population centers, or populated planets, I suspect this is based on their beneficent view of colonizing aliens. Their take is that a true spacefaring civilization would have had to oust its aggressive tendencies for the most part, otherwise they'd not be able to have their civilization reach the stage of interstellar travel. They’d have destroyed themselves long before.

We better hope Newman and Sagan are right and any aggressor aliens have done that before they access the technological wherewithal to head for the "pale blue dot'!

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