R2's Day:Marshall Savage's Really Big Numbers

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There's a book that I enjoy thoroughly, even though in some respects it never quite panned out the way it wanted to- called The Millennial Project: Colonizing the Galaxy in Eight Easy Steps  by Marshall T. Savage.  Kevin and I have been trading this book around for about a quarter century.  

The engineering is interesting (and occasionally dated), the science is fascinating (same caveat)- but you've gotta admire his goals. He does think big.In any case, part of his rationale for colonizing the galaxy is that we are very much alone.  Here's his reasoning-

Let's presume that all that is required for the evolution of life is the formation of a single self-replicating chain of DNA. (A great deal more than just this chemical accident is of course required to produce single celled organisms, and then a complete biosphere, and finally intelligent beings.  but for the sake of argument, let's assume that a minimal chemical precondition is all that is required to set the chain of causality in motion that will eventually evolve you and me out of the mud.)  As it turns out, the minimum chain length for self-replicating DNA is around 600 nucleotides.  (Nucleotides are the building blocks of DNA, consisting of the base pairs of adenine-thymine or guanine-cytosine that form the rungs , and the phosphates which form the backbone of the ladder in the double helix.)  Six hundred links is an exceedingly short DNA chain.  Consider that a very simple virus contains 170,000 links, and a bacterium seven million; your own DNA chain is six billion links long.

How likely is it that the primordial soup, given enough time, will cook up a strand of "Genesis DNA"?  To calculate the odds of such an event occurring at random, we need to turn to 'information theory'.  This is an arcane branch of statistics developed to aid in the design of computers and telecommunications networks.  Essentially, information-theory reduces the nebulous concept of 'information' to exact mathematical quantities relating to message length and content.  According to information-theory, a message with meaning can be interpreted as a level of probability.  In other words: how likely is it that the message will be generated at random?   This probability is dependent on the number of bits of information required to encode the message.   The number of bits is then the exponent (base 2) of the number of random trials it would take to generate that message.  In plain English, this means that generating even a relatively short message by random trial and error takes an enormous number of tries.Words, like those you're reading now, contain meaning-- at least that's the intent.  In theory, the same message content could be generated randomly (perhaps it would make more sense if it was).  Using information-theory, we can find out what the odds are of a given message being generated by chance. 

Let's use a very simple message, one I'm sure we're all familiar with from our earliest attempts to decode these alphabetic hieroglyphics:"See Spot Run."  This minimal message contains just thirteen elements: ten letters, two spaces, and a punctuation mark.  Written English requires only about 50 symbols to convey any message: 26 letters, 10 figures, 13 punctuation marks, and blank spaces.  The first position in our message has one chance in fifty of being an "S".  The odds of generating a particular message one symbol long are 50 to 1.  The second position has the same odds, so the chances of a message two symbols long turning up as "Se", are 50x50,  or 502 to one.  Every time a symbol is added to the sequence, the odds against that sequence go up by one multiple: three symbols -- 50x50x50, or 50^3 to one; four symbols--50^4 to one, etc.  It is very easy to calculate the odds of any message being generated at random: the number of possible symbols is the base and the base number is raised to an exponential power equal to the number of symbols in the message.  The odds of generating "See Spot run." at random are 50^13 to 1.  To create this rudimentary message by accident would require 610,000,000,000,000,000,000,000 (six hundred billion trillion) trials.  If a computer wre programmed to generate a 13 character string at random and created 10 million new strings every second, it would take the computer two billion years to come up with "See Spot run." 

Information theory shows why generating a 600 nucleotide chain through random chemistry is--to put it mildly--unlikely.  The genetic alphabet is much shorter, containing only four symbols: A-G, G-A, C-T, T-C; but this doesn't help matters very much.  The same rules of chance apply.  The odds of generating a particular string of nucleotides 600 base pairs long are 4^600, or 10^360 to 1.  If these are the odds against the bob-tail nag, you'd better bet on the bay.

 To generate a strand of "Genesis DNA" would take 10^360 chemical reactions.  That is a completely ridiculous number.  Writing out such a number is an exercise in futility; it requires hundreds of zeroes.  Describing it with words is just about as hopeless; a million billion trillion quadrillion quintillion sextillion septillion octillion nonillion decillion doesn't even touch it.  The only way to describe it is as ten nonillion nonillion googol googol googol.  You can't even talk about such numbers without sounding like your brain has been fused into molten goo.  If you persist in thinking about them it certainly will be.Surely, there must be numbers of equal magnitude available to rescue us from such overwhelming odds.  After all, DNA is just a large molecule.  So we must be dealing with atomic numbers, and those are always mind boggling--right?When Life arose, the Earth's ocean's were, as Carl Sagan suggests, one giant bowl of primordial soup.  The number of chemical reactions going on in that stew must have been incredible.  Over billions of years, any possible combination of DNA could have been cooked up-- couldn't it?  Well, let's take a look; the bottom line is always in the numbers.

 The oceans of the early Earth contained, at most, 10^44 carbon atoms.   This sets the upper limit on the possible number of nucleic acid molecules at 10^43. (Assuming every atom of carbon in the ocean was locked up in a nucleic acid molecule--an unlikely state of affairs.)  The oceans could therefore contain no more than about 10^42 nucleotide chains, with an average length of ten base pairs.  If all these nucleotides interacted with each other 100 times per second for ten billion years, they would undergo 3x10^61 reactions.   This should still leave them woefully short of the sample needed to generate a strand of Genesis DNA.  To get a self replicating strand of DNA out of the global ocean, even if it was thick with a broth of nucleotides, would take ten billion googol googol googol years.  Makes your eyes spin counter-clockwise, doesn't it?But there are billions of stars in the galaxy and billions of galaxies in the universe.  Over time, the right combination would come up somewhere--wouldn't it?  Assume every star in every galaxy in the entire universe has an Earth-like planet in orbit around it; and assume every one of those planets is endowed with a global ocean thick with organic gumbo.  This would give us 40,000 billion billion oceanic cauldrons in which to brew up the elixir of life. Now we're getting somewhere--aren't we?  In such a universe, where the conditions for the creation of life are absolutely ideal, it will still take a hundred quadrillion nonillion nonillion googol googol years for the magic strand to appear.  Sheesh!Assuming some radically different form of life, independent of DNA, doesn't really help.  By definition, life forms will always be complex arrangements of matter and/or energy.  This complexity has to arise out of chaos.  Therefore, some initial degree of order must first just happen.  Whatever the form of life, its creation is dependent on the same sort of chance event that created our first strand of Genesis DNA.  It doesn't matter what sort of coincidence is involved: the matching of base pairs, alignment of liquid crystals, or nesting of ammonia vortices; whatever the form of order, it will be subject to the same laws of probability.  Consequently, any form of highly complex, self replicating material is just as unlikely to occur as our form.  Simply put, living is an unlikely state of affairs.

 When all of the fundamental constants underlying the bare existence of the universe are also taken into account, it becomes all too obvious that life is a sheer impossibility.  How can  glop of mud like me possibly be walking around, wondering why it exists?


-- Marshall T. Savage, The Millenial Project: Colonizing the Galaxy in Eight Easy Steps