Chip Kendrick
WCT: Writer as Lawyer,
Writer as Detective

Encoding Ourselves

	In Carl Sagan's Can We Know The Universe? Reflections on a Grain of Salt, 
Sagan presents an optimistic view of the final level of understanding that science can 
achieve.  Examining one of the classic arguments against human knowledge of the 
universe, the idea that even the smallest particle contains more information than the 
human brain can hold, Sagan provides an alternate view.  Essentially Sagan's claim is that 
by examining the patterns of information we can encode huge amounts of information 
into simple formulas that most humans can understand and could make use of to generate 
any of the information thus encoded.  The problem with this argument is the nature of 
what 'encodes' huge amounts of knowledge into such a simple form.
	Often computers make use of encoders to temporarily shrink large amounts of 
information.  Sometimes the idea of encoding prompts the novice to ask how the 
encoders can lop chunks of data from a file and still leave it whole: how can this 
information simply disappear? There are many levels of answers to this question:  I'll 
begin with the simplest.
	The encoding program has a counterpart that decodes the shortened file.  The 
encoding program's job is to look for patterns in a file and replace them with symbols 
that the decoding program can understand.  For instance if a file contained a particular 30 
bit code in around 5000 places ( this is common ), the encoding program might replace 
each occurrence of this 30 bit code with a 4 bit code, and 'leave a note' for the decoding 
program explaining that the 4 bit code stands for the 30 bit code.  The information that 
has disappeared, then, is contained in the dialog between the encoding and decoding 
algorithms.
	Similarly, Sagan's 10 bit equation capable of describing an entire crystal is an 
encoded form of the immense amount of information describing the crystal.  Just as a 
computer encoding program replaces a reoccurring pattern with symbols to be translated 
by the decoder, so the equation replaces spatial coordinates with symbols to be 
interpreted by a physicist.  At some point in the past, another physicist made an 
intellectual leap that allowed him to encode the pattern of the crystal into an equation 
that he could explain to a fellow physicist.
	So the analogy becomes encoders talking to decoders just as the discoverer of the 
crystal equation talks to a fellow physicist.  What is the medium of this communication, 
the meta-language being used?  In the case of the physicists, the crystal can be expressed 
by a mathematical equation written in the language of mathematics.  In the case of the 
pair of computer programs, the medium of translation is an algorithm, written in a 
language that machines 'understand'.  Does the analogy end here?  Or more specifically, 
what do these two languages, mathematics and machine code, have in common?
	Each language, and all languages, have their origin in human thought: in logic.  It 
is logic that creates the algorithm capable of distilling binary information into an encoded 
form, it is logic that created mathematics and physics capable of distilling information 
about the physical world into an equation.
	What this means is that we cannot happily claim that the grain of salt has 
magically become 10 bits of independent information: somewhere in the brain, the logic 
that translates that 10 bits of information into a crystal lattice resides and is taking up 
space just as encoding and decoding programs take up space on a computer disk.  As 
with a computer, the total amount of space that the encoding and decoding programs take 
up is less than the amount of room they have saved by encoding many different files.
	Here a fundamental misconception springs up: that our understanding of the 
universe is somehow separate from the universe itself.  Knowledge, like memory, is 
encoded in the brain, which is definitely a part of the universe whether our 'minds' are 
something disassociated or not.  Therefore to understand the universe we must 
understand our understanding of the universe.  Our understanding of our understanding of 
the universe then becomes knowledge itself, so that we must understand our 
understanding of our understanding of the universe.  Here, if no where else, the chain of 
knowledge becomes infinite and cannot be distilled in an equation.  We might argue that 
we have now understood the infinite of the chain of understanding, but this starts the 
infinite chain again, since we must understand this further understanding.
	To return to the computer metaphor, in trying to understand our understanding we 
must encode the encoder, and encode the encoded version of the encoder, and so on.  We 
quickly reach a point at which the encoder cannot further encode itself.  This is 
analogous to the point at which we see the infinitude of trying to understand our 
understanding.
	Finally, in order to fully describe the encoder, we look not at the encoder itself 
but at its effect on each and every file.  In order to define and understand logic, we must 
look at the way in which we understand all things in the universe, which is the equivalent 
of describing every phenomenon in the universe without using patterns: the very thing we 
thought logic was helping us to avoid!  We can try to understand the universe with logic, 
but we will finally see that logic, a part of the universe and therefore a part of what we 
are trying to understand, is defined in terms of the universe itself.
	What Sagan has missed is that he is a part of a larger whole: that his every 
characteristic and his identity itself are a part of the universe he is trying to examine and 
know.  Sagan's misconception is implicit in every sentence of his parting paragraph.  The 
idea of expressing a preference for one kind of universe or another is ridiculous since 
Sagan's identity is defined by the universe.  Sagan apparently thinks the idea of a static 
heaven to be the product of a 'weakminded theologian', saying that an entirely known 
existence would be too dull for a thinking being.  This reveals an assumption by Sagan 
that he would be the same or similar thinking being if transferred to somewhere outside 
of the universe.  Sagan follows this with two more similar sentences before finally 
seeming to allude to very idea that makes the rest of his paragraph fall apart.  In his last 
sentence Sagan 'guess'es that the match between ourselves and our universe may not be a 
'coincidence', suggesting either a match orchestrated by some kind of creator or the 
founding thought of the ideas given above.  Either way, Sagan's final sentence is a 
stepping stone to a much larger concept.