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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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