The Apple and the Universe

[Prologue of the book
Programming the Universe
A quantum computer scientist takes on the cosmos
Seth Lloyd
A Borzoi Book
Published by Alfred A. Knopf
A Division of Random House, Inc.
(New York, 2006)]
 
«In the beginning was the bit,» I began.
 
The chapel in the seventeenth-century convent
that housed the Santa Fe Institute
for the study of complex systems
was filled with the usual collection
of physicists, biologists,
economists, and mathematicians,
with a leaving of Nobel laureates.
 
The grand old man of astrophysics and quantum gravity,
John Archibald Wheeler, had challenged me
to give a talk on the subject «It from Bit.»
 
I had accepted the challenge.
 
I was beginning to wonder
if that had been a good idea,
but it was too late to back down now.
 
I held an apple in my hand.
 
«Things, or 'its,' arise out of information, or 'bits,'»
I continued, nervously tossing the apple in the air.
 
«This apple is a good 'it.'
 
Apples have long been associated with information.
 
First of all, the apple is the fruit of knowledge
'whose mortal taste brought death into the world, and all our woe.'
 
It conveys information about good and evil.
 
Down the line, it was in the trajectory of the falling apple
that Newton traced the universal laws of gravitation,
and the curved surface of the apple
is a metaphor for Einstein's curved spacetime.
 
More directly, the genetic code
locked in the seeds of an apple
programs the structure of future apple trees.
 
And last, but not least,
an apple contains free energy
-the calories of bit-rich energy
that our bodies need to function.»
 
I took a bite of the apple.
 
«Clearly, there are
many types of information
contained in this apple.
 
But how much information does the apple embody?
 
How many bits are there in an apple?»
 
I placed the apple on the table
and turned to the board
to perform a short calculation.
 
«Interestingly,
the number of bits in an apple
has been known since the beginning
of the twentieth century,
since before the word 'bit'.
 
At first, one might think that an apple
embodies an infinite number of bits,
but this is not so.
 
In fact, the laws of quantum mechanics,
which governs all physical systems,
make finite the number of bits required
to specify the microscopic state
of the apple and its atoms.
 
Each atom,
by its position and velocity,
registers only a few bits;
each nuclear spin in an atom's core
register but a single bit.
 
As a result, the apple contains
only a few times more bits than atoms
-a few millon billion billion zeros and ones.» (10ˆ24)
 
I turned back to face the audience.
 
The apple was gone. Not good.
Who had taken it?
 
I glanced at the benign face of Wheeler
and the impassive expression of Murray Gell-Mann,
Nobel laureate, inventor of the quark and wearer
of one of the world's physics heavyweight title belts.
 
«I can't continue without the apple.
No it, no bit,» I declared, and sat down.
 
The hunger strike lasted only a few moments
before an impish engineer from Bell Labs produced the apple.
 
I took it from him and held it on high,
issuing a challenge to anyone
who might attempt another theft.
 
This was a mistake.
 
For the moment, though, all seemed well.
 
I continued:
 
«All bits are equal in terms
of the amount of information they can register.
 
A bit, short for 'binary digit,'
is registered by two distinguishable states
-0 or 1, yes or no, head or tails.
 
Any physical system
with two such states
registers exactly one bit.
 
A system with more states registers more bits.
 
A system with four states
-for example, 00, 01, 10, 11-
registers two bits;
a system with eight states
-for example, 000, 001,
010, 011, 100, 101, 110, 111-
register three bits, and so on.
 
As mentioned before,
quantum mechanics guarantees
that any physical system with finite energy
confined to a finite volume of space
has a finite number of distinguishable states
and therefore will register a finite number of bits.
 
All physical systems register information.
 
In the words of IBM's Rolf Landauer,
'Information is physical.'»
 
Here Gell-Mann interrupted:
 
«But are all bits truly equal?
 
What about the bits that tells us
whether some famous unsolved
mathematical conjecture is true or not?
 
Compare that with a bit derived
from a random coin toss.
 
Some bits are more important than others.»
 
True, I agreed.
 
Different bits play different roles in the universe.
 
All bits can register
the same amount of information,
but the quality and importance
of that information varies from bit to bit.
 
The significance of «yes»
depends on the question asked.
 
The two bits of information
that determine the identity
of a base pair in the apple's DNA
are far more important
for generations of future apples
than the bits of information
registered by the thermal jiggling
of a carbon atom
in one of the apple's molecules.
 
Only a few molecules and their attendant bits
are required to convey the smell of the apple,
whereas billions and billions of bits are needed
to provide the apple with its nutritional value.
 
«But,» Gell-Mann interjected,
«is there a mathematically precise way
of quantifying the significance of a bit?»
 
I did not have
a complete answer to this question,
I replied, still holding the apple.
 
The significance of a bit of information
depends on how that information is processed.
 
All physical systems register information
and when they evolve dynamically in time,
they transform and process that information.
 
If an electron «here» registers a 0
and an electron «there» registers a 1,
then when the electron goes
from here to there, it flips its bit.
 
The natural dynamics of a physical system
can be thought of as a computation
in which a bit not only registers a 0 or 1
but acts as an instruction:
0 can mean «do this»
and 1 can mean «do that.»
 
The significance of a bit
depends not just on its value
but on how that value
affects other bits over time,
as part of the continued information processing
that makes up the dynamical evolution of the universe.
 
I continued to identify the bits
from which the apple arises
and to elaborate the roles
those bits play in the processes
that make up the apple characteristics.
 
Things were going well.
 
I had addressed the problem
of «it from bit»
and had survived the questioning.
 
Or so I thought.
 
As I finished the talk
and stepped away from the board,
someone tackled me from behind.
 
One of the audience members
had taken seriously
my challenge to steal the apple.
 
Doyne Farmer was one
of the founders of chaos theory
-a tall, athletic man.
 
He grabbed my arms
to make me drop the apple.
 
To break his grasp,
I slammed him
back against the wall.
 
Pictures of fractals
and photos of pueblo fell.
 
But before I could wriggle free,
Farmer wrestled me to the ground.
 
We rolled around the floor, overturning chairs.
 
By now, the apple was gone.
 
It had been reduced to bits...