"You're a card player?"
"Yes. I mean, I play online."
"So if you take a deck of cards that
are shuffled into a particular order, you never know what order the deck of
cards is in unless you look. By simple combinatorial analysis, a deck of cards
has 52 factorial[i]
distinct orderings. That's such a big number[ii],
it might exceed the number of atoms in the universe[iii].
"Imagine a deck that is in initial
order, inside a sealed box. Let's call that deck number one. We label some
hydrogen atom deep inside the Sun with the number 1 to keep track of it. Then
we swap the top card, the ace of spaces, with the next card, the deuce of
spades.
"We'll call that deck number two, and
likewise we label another atom somewhere inside the Sun as number 2 and keep
track of that deck there. Keep in mind the hydrogen atoms inside the sun are
not really atoms because the Sun is made of plasma[iv],
but you get the idea."
"I follow."
"Now, keep rearranging the deck and
numbering them as I've described in my example until you've run out of atoms in
the Sun. Then keep doing that for each star in the Milky Way galaxy. You'd
still have plenty of decks to arrange and there are billions of galaxies, but
let's stop there."
"Uh huh."
"Imagine you hold a single deck of cards
in a single arrangement such that you could point to a specific atom of the Sun
and say, 'This is deck number whatever and it corresponds to this atom.' Now imagine
that you peel off several of the top cards and see what order the first few
cards are arranged."
"Okay."
"Now, of the remaining order of cards
you could say that all of the other atoms, or nuclei, really, in the Sun around
and next to your atom are all the remaining possibilities of decks that have
the same starting arrangement as yours."
"I don't follow."
"It's like the street address of a
building and the floor number and office number. The first few cards determin
which galaxy in the universe to choose. The next few cards determine which star
to look in. The rest of the deck could point to any single nucleus in the plasma
soup inside the Sun.
"Imagine each star in the Milky Way
being named after a unique group of a deck of cards whose first few cards are
in the same order. Now the Sun has billions and billions of decks mapped to
each atom, or nuclius, and your deck is just the one deck of cards you've
shuffled and hold in your hand."
"Yeah," said Mark grinning at the
stupefying image.
"So this unique deck that you've
shuffled and hold in your hand is as unique deck among all shuffled decks as
the Sun is unique from all other stars in the Milky Way, indeed as unique as
any atom in our universe."
"I like it."
"But I'll repeat again that this deck
of cards is set in a particular sequence. It doesn't change. It is not 52
factorial number of decks simultaneously held in one hand, like a universe of
atoms in your palm. It is only one deck and no other deck. This particular deck
is set in one unique ordering and it is not a trillion trillion trillion decks
at once.
"If I look inside the deck to identify
it, as I peel off each card and show you which one is next, the deck is
revealed card by card. The deck order does not change in any way, it is fixed
in advance. You don't know what order it's in, but that doesn't mean it could
be all possible orders at the same time. Do you see the difference?"
"Sort of," said Mark. "I
really like the idea of the galaxy in my palm, like the galaxy on Orion the
cat's belt in Men in Black."
Samantha rolled her eyes. "I don't
even know what you're talking about," she said. "I assume it's the
Will Ferrel movie."
"No, Will Smith."
"Oh," said Sam.
"No, but I get it," said Mark.
"There are no multiverses. Only one universe with the present state. The
superposition is possibility but only because we haven't observed all the
information available yet."
[i] "In mathematics,
the factorial of a non-negative integer n, denoted by n!, is the product of all
positive integers less than or equal to n. For example,
"5! = 5 * 4 *
3 * 2 * 1 = 120.
"The value
of 0! is 1, according to the convention for an empty product.
"The
factorial operation is encountered in many areas of mathematics, notably in
combinatorics, algebra, and mathematical analysis. Its most basic occurrence is
the fact that there are n! ways to arrange n distinct objects into a sequence
(i.e., permutations of the set of objects)."
Ibid.
[iii] "Assuming the
mass of ordinary matter is about 1.45×1053 kg ... and assuming all
atoms are hydrogen atoms (which in reality make up about 74% of all atoms in
our galaxy by mass, see Abundance of the chemical elements), calculating the
estimated total number of atoms in the universe is straightforward. Divide the
mass of ordinary matter by the mass of a hydrogen atom (1.45×1053 kg
divided by 1.67×10−27 kg). The result is approximately 1080
hydrogen atoms."
(Samantha is off
by perhaps 20% with her statement.)
[iv] "Plasma ...,
according to natural science, is one of the four fundamental states of matter
(the others being solid, liquid, and gas). ... Plasma comprises the major state
of matter of the Sun."
