Neatly Scattered Papers
In an article in Scientific American* on the possibility of time running backwards, the author states:
Increasing entropy is a cosmic certainty because there are always a great many more disordered states than orderly ones for any given system, similar to how there are many more ways to scatter papers across a desk than to stack them neatly in a single pile.
That sentence contains an implied statement of fact: "there are many more ways to scatter papers across a desk than to stack them neatly in a single pile."
But is it a fact?
Thankfully the grammar police are not equipped with tasers, so having got away with starting three sentences which blatantly ignore prescriptive grammar I shall now split an infinitive.
To neatly scatter where nobody has neatly scattered before.
In the human scale of things there would appear to be an infinite number of ways that all of the sheets of paper in a pile could land on a desk. However, desks and sheets of paper are composed of atoms and so the laws of physics restrain the infinite number of possible arrangements of sheets of paper to a mere astronomically huge number.
Now, when you stack the papers in the "correct" order, that is just one way of creating order out of chaos. In fact, if "neatness" is the sole objective then any permutation of the papers will do. Now, where do you put the stack of papers? On the desk of course - but where on the desk?
If an infinite number of monkeys ever get so fed up with typing the Compleat Workes of William Shakespeare that they scatter the paper infinite times on the desktop they will demonstrate every possible location and orientation of any single sheet of paper as constrained by the fact that objects are made of atoms which interact in subtle ways. Trust me, that is a hugely astromeganomic number and is of the order of magnitude of the number of atoms A in the surface plane of the desk.
For any number S of sheets of paper in the real world it is possible to scatter them in a combination of ways if angular orientation is ignored. And we shall not focus on angular orientation if only because it makes us giddy. The combination is an S-combination of locations (atoms) from A.
Now consider that S sheets of paper can be stacked in any linear order or permutation S! of different orders and placed in any 1 of A different locations.
So, which is the greater -
a scattering, being an S-combination from A ?
a stacking, being an S-permutation multiplied by A ?
Answers on the proverbial $10 bill.
Hint: Lee Billings knows somewhat of that whereof he writes.
What would happen to the laws of physics if time ran backwards?
Just a thought: Newton's anti-first law -
When viewed in an inertial reference frame, an object continues act upon an external force until the object either assumes a state of rest or of continual motion at a constant velocity.
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*
2 Futures Can Explain Time's Mysterious Past
New theories suggest the big bang was not the beginning, and that we may live in the past of a parallel universe
December 8, 2014 |By Lee Billings
