🚀 go-pugleaf

In article <1990Feb5.193530.13545@Neon.Stanford.EDU> gilham@Neon.Stanford.EDU (Fred Gilham) writes:
>No!  Mathematica does not know algebra or mathematics.  To see why
>this is so, we just have to look at the human analogy of Mathematica,
>namely "cookbook" math. Mathematica is a sophisticated system for
>doing cookbook math.  Many people can do calculus from the integral
>tables without really knowing calculus.  I remember taking a class
>where I was taught just that.
>
>Someone who knows calculus can go outside the cookbook.  Such a person
>can apply his knowledge to problems that are not covered by any of the
>rules he already knows.  Besides this, such a person can see
>applications for the rules that are not immediately obvious.
>
>To use a simpler example, take long division.  Most of us know the
>standard algorithm for long division.  I taught it to kids in
>elementary school.  But I could tell that some of these kids were
>following the rules without knowing why they worked, or really, what
>the use of it all was.  Yet they could do the algorithm reliably.  I
>would say that they did not know division, even though they could
>execute the steps of the algorithm so as to produce the result.  If
>I had asked them to think of some other algorithm for doing long
>division, they would have looked at me as if I were crazy.  They
>probably would have thought "This IS long division."
>
>The "book", then, contains the steps of the algorithm.  It is at least
>two steps removed from knowledge, in that something needs to execute
>the algorithm and some mind needs to interpret the results..  The
>whole trick behind the Chinese Room argument is that it is possible to
>handle symbols in two ways, mechanically and semantically.  The
>Chinese Room argument claims that a mind can assign meaning to symbols
>that are produced by an entity to which the symbols have no meaning.
>Making the entity very complicated does not change this.
>
>-Fred Gilham   gilham@csl.sri.com

Does one have to be aware of a fact to know it?  It is clear that we know
how to breathe.  We are rarely aware of our breathing (though we would
surely be aware if we stopped).  We know how to talk, to speak in coherent
sentences.  But do we know the rules by which thought is produced?  Planets
circle the Sun according to the laws of physics.  But do the planets know
physics?

The fact is that knowledge can exist without human awareness.  Even if all
people were to die, the Earth wouldn't stop revolving about the Sun.  Even
if you remove human knowledge from the human, the knowledge is still there.
This is how we can store knowledge in history books, encyclopedias, and
Mathematica programs.

As for "a mind interpreting the results,"  this is in no way part of
knowing "math."  It is part of knowing how to interpret results.  The two
are very separable.  Knowing how to interpret results, escaping the system,
or "consciousness" is an act we can apply to any intellectual discipline.
But that doesn't make it an intrinsic part of those areas, including math.  
Once again, it is possible to know something and not be aware of it, thus
being unable to interpret it.  This is something that Sartre called
"transcendence."  We can reflect on ideas that we are aware of, but most
ideas we have are our "axioms," things we take for granted.

So for a computer to do math as well as a human, yes, it will need
"consciousness" of the math, or an ability to escape the system.  But this
is not the issue.  This fact is already pre-supposed by the Chinese Room
puzzle, stating that there is a book which can give responses just like a
native Chinese speaker.  This would require awareness.  

I feel, though, that my analogy still stands.  Awareness is not a
requirement of knowing.  So knowing math doesn't imply being able to escape
the system.

Cliff Chaput
Mneme Project -- Northwestern University Psychology Dept.
cliff@mneme.psych.nwu.edu, cliff@eecs.nwu.edu