Emerson's Zero-One Law
 


"Subhuti, suppose there were as many Ganges Rivers as there are grains of sand in the Ganges River. What do you think, would the grains of sand in all those Ganges Rivers be many?" Subhuti said, "Very many World Honored One.That many Ganges rivers alone would be uncountable, how much the more so the grains of sands contained in them." "Subhuti, I am speaking truthfully. Suppose a good man or good woman had filled with the Seven Kinds of Precious Gems as many Threefold Great Thousand World Systems as there are grains of sand in all those Ganges Rivers and gave them as an offering. Would that person obtain many blessings? Subhuti said, "Very many, World Honored One."


It is commonly said that in fundamental physics, since time is merely a dimension of space, certain events (e.g. time reversal, or the air suddenly rushing out of an open container to leave a vacuum) are not impossible, but merely very improbable. For example:


But the temporal asymmetry case is trickier. First of all there is the fact that a later state of even an isolated system can very well be one of lower entropy than an earlier state.

Lawrence Sklar, "Up and Down, Right and Left, "Past and Future" in The Philosophy of Time, Poidevin and MacBeath, eds., Oxford, 1993, p. 111


However, Sklar's phrase "very well" is wrong here. Except for tiny transient fluctuations, lower-entropy states are only purely formal possibilities. As Eddington says says of one version of the sudden-vacuum case:

 

The reason why we ignore this chance may be seen by a rather classical illustration.... If an army of monkeys were strumming on typewriters they might write all the books in the British Museum. The chance of their doing so is decidedly more favorable than the chance of the molecules returning to one half of the vessel

 

Eddington, Arthur, The Nature of the Physical World, Gifford Lectures, 1928, p. 72.

 

The monkey-typewriter-Shakespeare probability has been calculated:


More soberingly still, a physics professor at Yale, William R. Bennett, has calculated that if a trillion monkeys typed ten random characters a second, it would still take a trillion times longer than the universe has been in existence just to produce the sentence, “To be or not to be, that is the question.” Moving from calculation to experiment, The Monkey Shakespeare Simulator, in existence since 2003 with a hundred monkeys typing at a vastly accelerated speed, has produced just nineteen letters from The Two Gentlemen of Verona after 42,162,500,000 billion monkey years: “Valentine. Cease to 1dor:eFLPoFRjWK78aXz."


http://goldenrulejones.com/?p=990; see also: http://www.thevalve.org/go/valve/article/now_god_help_thee_poor_monkey/;
http://www.thevalve.org/go/valve/article/form_function_intention/.

 

(It might be noted that, once the monkeys had succeeded in banging out the plays of Shakespeare or some variant edition of them (along with many cubic light years of incoherent, non-Shakespearean or pre-Shakespearean typescript), finding Shakespeare in that mess would be more or less as time-consuming as producing the Shakespeare had been in the first place. You might just as well have said that Shakespeare is all right there on the keyboard -- which is, in fact, true. In other words, the works of Shakespeare would be there only in the sense that they are a mathematically-possible combination of letters. In the same way, there's a half-billion dollars worth of gold in a cubic mile of seawater, but it would cost much more than half a billion dollars to extract it.)


Now, Kolmogorov's zero-one law goes like this:


In probability theory, Kolmogorov's zero-one law, named in honor of Andrey Nikolaevich Kolmogorov, specifies that a certain type of event, called a tail event, will either almost surely happen or almost surely not happen; that is, the probability of such an event occurring is zero or one.

http://en.wikipedia.org/wiki/Kolmogorov%27s_zero-one_law


Emerson's zero-one law shares the Kolmogorov law's demented binarism: everything is either impossible or inevitable. What I have done is to set the limits differently. Provisionally, Monkey-Typewriter-Shakespeare (and by extension, everything less likely than that) will be defined as impossible. (At some point it may be decided to set the limit more restrictively -- e.g., the Monkey-Typewriter-Hamlet: a trillion monkeys typing during the lifetime of a trillion universes to produce "To be or not to be".) By the Zero-One principle, then, everything else will be defined as inevitable (or MTS-inevitable). "One chance in a million billion trillion" would become just one of the ways of saying "inevitable".

Alternatively, whenever someone choosed to make a thermodynamically-impossible (but not formally impossible) conjecture -- the old "not impossible, but merely very unlikely" dodge -- they should be required to repeat the word "very" a thousand times, so that the reader has some intuition of how bogglingly unlikely it is. Boggling improbability could be even quantified in terms of Monkey-Typewriter-Shakespeare units, so people would know whether a given event were merely MTS-impossible, or (for example) MTS-squared-impossible.

 

(Note also that the supposedly improbable events of evolution are not at all MTS-impossible. In fact, the vaunted impossibilities anti-evolutionists talk about are, on the MTS scale, inevitable.)


 

I am emersonj at gmail dot com.

Original materials copyright John J Emerson

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