Upper Bounds

Sergio Meira S.C.O. meira at RUF.RICE.EDU
Sat Jun 27 08:26:16 UTC 1998


Restrictions on 'event complexity' can bear on sentence length-- I recall
from discussions on psychology that there is some limit to the number of
independent entities that we can keep active at the same time in our minds
(seven is the number I remember), which may imply an upper limit to the
number of independent participants that can co-exist in a sentence. So, if
we want to talk about more than seven independent participants, it would
seem that we'd have to use more than one sentence; we'd be forced to stop
a sentence even before its length in sheer number of words became
unbearable. (Colin Harrison at Rice probably has the original references,
I believe, in case you don't).

This is, however, 'event complexity' rather than sheer sentence length. I
agree with Aya and Noel that any real coding system is subject to length
constraints-- e.g. DNA sequences cannot be infinite. But this reflects, as
Noel pointed out, a limit of our universe. The only things  that can be
truly inifinite exist in the realm of abstractions par excellence --
mathematics. It is true that the series of natural numbers is infinite;
but this is a consequence of the fact that Peano's axioms for natural
numbers have 'adding one more' as an operation that can be repeated
forever. There is nothing in the universe, not even subatomic particles,
that you could keep adding to a pile forever. So, Peano's axioms are an
abstraction-- mathematicians assume a world in which 'adding one more
forever' is thinkable. (Incidentally, Quantum Mechanics with wave-particle
dualities and indeterminacies challenges the possibility of 'adding one
more' forever at the subatomic level from another viewpoint-- but this is
a different story).

This shows us what is going on when formalists want to see infinite-length
sentences as a theoretical possibility. It would seem that there are
certain aspects of language that are they way they are because the world
is the way it is-- i.e. limits set by physics, chemistry, biology, etc.,
rather thanm by communication alone. Formalists isolate these aspects of
the real world; they want to see 'language standing alone', so they put it
in a separate world, where only linguistic factors count. The relationship
is not unlike that between mathematics and the real world... You gain the
notion of infinity, for whatever theoretical advantages it might buy you,
but you have to admit that everything else is less important. Formalists
have to say that all of reality, in its entirety, with all its physical,
chemical, biological etc. restrictions is 'contingent', 'less important',
'non-linguistic'-- that 'reality' is 'performance'...

Isn't that an interesting world...

Sergio Meira

P.S. I wondered if anyone knows whether real-world limitations for other
coding systems also have consequences for their functioning and their
structures-- i.e. any consequences of length constraints on DNA sequences
for genetics?



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