Re: Wittgenstein
Posted by
Kenneth Lloyd on
Oct 02, 2008; 3:04pm
URL: http://friam.383.s1.nabble.com/Wittgenstein-tp1133169p1134109.html
Phil,
There are many solutions* to the problem as written.
By focusing on A solution, we lose sight of alternative, perhaps equally valid
solutions - which was the point of my post. For example, d may be a complex
number (say, representing day.ergs), not the assumed
integer.
I have just finished writing a book on modeling complex
systems. In it I cite Dennett and Kinsbourne's** studies of perception
between what they call the Cartesian Theater model and the Multiple Drafts
model. When one views a model, or when one views a mathematical
relationship, there are resonances caused by consonance and dissonance in the
understanding of the symbology. These resonces are the source of emergent
concepts from the Multiple Drafts. You speak of divergence. I see
this more as a process of entanglement - leading to what Prigogine refers to as
a dissipative system, or Large Poincare System. Until the model is
realized, the temporal symmetry is not broken and you can have "do-overs" or
reversibility. Once the model has been physically realized, having been
realized in time, it cannot be totally reversed in configuration space-time -
so-called Arrow of Time.
*Possibly infinitely
many.
Ken
Ken,
To
make that divergent math work, your 2 + 2
= n + d is just the kind of dilemma with modeling the emerging divergent
systems of nature that not studying divergent sequences distracts us
from. There’s a solution. Can you
guess?
Phil
From:
[hidden email] [mailto:[hidden email]] On Behalf Of
Kenneth Lloyd
Sent: Thursday, October 02, 2008 10:12
AM
To: [hidden email]; 'The Friday Morning Applied
Complexity Coffee Group'
Subject: Re: [FRIAM]
Wittgenstein
Nick,
First,
2 + 2 does not equal 4 in base 3. Second, equality only works in
equilibrium. What if our mathematics rule stated for every day d that
passed, 2 + 2 = n + d? The mathematics would be linearly dynamic.
There
are subtle cultural assumptions being imbued upon mathematics that may not
hold. Mathematics is designed to communicated the least false concept
with the least information content at some maximum entropy. Thus 2 apples + 2
oranges does not equal 4 orapples, but 1 fruit basket, yet generally 2 + 2 = 4
(in equilibrium).
Ken
From:
[hidden email] [mailto:[hidden email]] On Behalf Of
Nicholas Thompson
Sent: Wednesday, October 01, 2008 11:18
PM
To: [hidden email]
Subject: [FRIAM]
Wittgenstein
I have
put the following material in an email message because is suspect it would
fascinate some of you., and given that you are mostly people with real jobs
and given that the information comes from the guts of a 700 page book, I
suspect that many of you would be unlikely to stumble on it on your
own.
I have, as I
have said, been reading Monk's biography of W. In it we learn many
weird things, for instance, that W. turned up at Russell's door in Cambridge
in 1911 or so, an callow Austrian lad, who had graduated from a
technical school and got a job making kites in Manchester. Within a
year, Russell was ruminating about whether he should turn his entire
project in the foundations of mathematics over to W. and do something else
himself.
By 1937, W. had
developed enormous contempt for the whole foundationalist project. As
luck would have it, both he and Turing were giving relevant lectures at
Cambridge and Turing came to hear W. talk. W. (never a
particularly nice man) took the occasion to beat on Turing about the
absurdity of the foundationalist project
Here is a quote
from Monk, p. 418.
"Wittgensteins technique
was not to reinterpret certain particular proofs, but, rather, to redescribe
the whole of mathematics in such a way that mathematical logic would appear
as the philosophical aberration he believed it to be, and in a way that
dissolved entirely the picture of mathematics as a science which discovers
facts about mathematical objects . I shall try again and
again, he said, to show that what is called a mathematical discovery had
much better be called a mathematical invention. There was, on his
view, nothing for the mathematician to discover. A proof in
mathematics does not establish the truth of a conclusion; if fixes, rather,
the meaning of certain signs. The inexorability of mathematics, therefore,
does not consist in certain knowledge of mathematical truths, but in the
fact that mathematical propositions are grammatical. To deny, for
example, that two plus two equals four is not to disagree with a widely held
view about a matter of fact; it is to show ignorance of the meanings
of the terms involved. Wittgenstein presumably thought that if he
could persuade Turing to see mathematics in this light, he could
persuade anybody."
Turing apparently gave up on W. a few lectures
later.
I have
to admit the distinction that W. is making here does not move me
particularly. It seems to me as much of a discovery to find out what
is implied by the premises of a logical system as to find out how many
electrons there are in an iron atom, and since logic is always at work
behind empirical work, I cannot get very excited about the difference.
Perhaps because I am dim witted.
No response necessary.
Nick
Emeritus
Professor of Psychology and Ethology,
============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at
http://www.friam.org