**Next message:**ERIC.RAMBERG who-is-at spps.org: "[xmca] cultural effects of and on phylogeny"**Previous message:**Mike Cole: "Re: [xmca] Writing systems"**Next in thread:**Mike Cole: "Re: [xmca] Writing systems"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

Guess I must be really tired. Its all making sense to me in this past few

messages!!

What is the magic spell he weaves

Who Goedel's proof he thus conceives?

mike

On 1/4/07, Ed Wall <ewall@umich.edu> wrote:

*>
*

*> Paul
*

*>
*

*> Godel's Undecidability Theorem is, in a sense, about truth. He
*

*> showed that within a particular system of first order logic that you
*

*> could not with, more or less, the tools of first order logic decide
*

*> the truth or falsity of all statements. However, one need only extend
*

*> these logics. A sort of example is that you cannot, with a ruler and
*

*> a compass, trisect an angle.
*

*>
*

*> Chaitin (and, of course, Turing) has taken all this a bit further
*

*> in a somewhat readable book titled "The Limits of Mathematics"
*

*>
*

*> Thinking about mathematicians as weavers makes a sort of sense if
*

*> somehow reproducibility is factored in. Also mathematics seems to be
*

*> both out there and in there re Debaene.
*

*>
*

*> Ed Wall
*

*>
*

*> Ed
*

*> >Mike,
*

*> > You wrote,
*

*> >
*

*> > "Unless you are going up against Goedel, there IS presumably an
*

*> >answer, a way to figure "it" out."
*

*> >
*

*> > which made me think I might have created a false idea about Godel,
*

*> >maybe not. I don't think Godel was trying to show "there is no
*

*> >answer".
*

*> >
*

*> > My understanding of Godel comes from Newman's book: Godel's Proof,
*

*> >which is written so that anyone who understands arithmetic can get
*

*> >an idea what Godel did. He was basically refuting Russell and
*

*> >Whitehead's attempt to reduce mathematics to logic, that is, to
*

*> >refute the idea that given certain axioms (Peano's basically) that
*

*> >all of math would follow thereon according to the laws of
*

*> >first-order logic--it must be admitted that along the way Russell
*

*> >did develop his theory of types from which Bateson got so much
*

*> >mileage. Godel simply showed that you can't do this. I can't say I
*

*> >have understood Godel's proof, but I did understand the book of the
*

*> >same name. At least I think I did.
*

*> >
*

*> > It really comes down to saying that numbers are "out there", which
*

*> >should be OK for CHAT folk since the mind itself is "out there", not
*

*> >inside the head, from a CHAT perspective, isn't it. Math, as
*

*> >practiced by mathematicians, is really the "theory of math" not the
*

*> >math itself, e.g., weavers perform incredibly complex arithmetical
*

*> >operations in order to produce their designs without having the
*

*> >slightest knowledge of that theory or any formal training in
*

*> >arithmetic
*

*> >
*

*> > Paul Dillon
*

*> >
*

*> > Paul
*

*> >
*

*> >
*

*> >
*

*> >Mike Cole <lchcmike@gmail.com> wrote:
*

*> > Ed-- Sorry-- I needed a quiet enough moment to read your example,
*

*> re-read
*

*> >your
*

*> >initial inquiry, and then come back to your initial example.
*

*> >
*

*> >There are two things you need to know in interpreting my response. First,
*

*> I
*

*> >am TERRIBLE
*

*> >at proofs such as that you give for the infinite number of prime numbers.
*

*> I
*

*> >would have failed
*

*> >at several points, but the essential starting point (suppose the opposite
*

*> is
*

*> >true and show it can't be)
*

*> >would not occur to me never mind I would screw up at some other
*

*> bifurcation
*

*> >point!
*

*> >
*

*> >Second, I am married to a fiction writer.
*

*> >
*

*> >I sometimes get the feeling that maybe what you are saying could be true
*

*> of
*

*> >Dickens, but to describe
*

*> >the experiences and events that constitute one of my wife's books as "the
*

*> >writing writing itself" would
*

*> >simply go against all I have witnessed and been party to. The only way I
*

*> >could get there is if all of the
*

*> >incredibly uneven backs and forths, and getting stuck in blind alleys,
*

*> and
*

*> >then getting distracted by
*

*> >other life exigencies and then returning, reaching "an" end only to have
*

*> a
*

*> >completely different end
*

*> >emerge, if THAT is writing itself, then ok. But what an "itself"!!
*

*> >
*

*> >We sometimes discuss how what I do is different. I, presumably, write
*

*> about
*

*> >"things as they are" such as,
*

*> >for example, the role of culture and biology in ontogenesis. There is a
*

*> >putative, as if reality out there (I
*

*> >naively assume) and I set out to write about it, to describe it, to
*

*> >speculate about, to (ha ha!!) explain it. What
*

*> >I write seems a whole lot easier to do than what my wife does...... and
*

*> what
*

*> >she does seems, in some ways
*

*> >to be "halfway" between what I do and a mathematical proof. Unless you
*

*> are
*

*> >going up against Goedel, there IS
*

*> >presumably an answer, a way to figure "it" out. But what if there is no
*

*> if,
*

*> >if if has to be created from...........
*

*> >
*

*> >So I write fictions that pass as descritions of reality and my wife
*

*> creates
*

*> >descriptions of a reality that pass as
*

*> >fictions.
*

*> >
*

*> >I doubt if that helps you, but it helped me. thanks
*

*> >mike
*

*> >
*

*> >On 1/2/07, Ed Wall wrote:
*

*> >>
*

*> >> Mike
*

*> >>
*

*> >> Here is a sort of expansion (and I am by no means sure about the
*

*> >> authoring business, but the process sounded somehow similar) and
*

*> >> perhaps the best place to begin is with a story. A number of year ago
*

*> >> I was teach a graduate course in mathematics and had, for most of the
*

*> >> period, been working on one or two proofs. At the end of class, a
*

*> >> young woman approached me (she was, my impression, one of the more
*

*> >> knowledgeable students) and said something like "I understood
*

*> >> everything you did, but I didn't understand why you did it. I don't
*

*> >> think I'll ever be able to do proofs." I said the usual dumb thing
*

*> >> something like "It is just a matter of writing down what you were
*

*> >> doing and you'll catch on after doing it for awhile and I've just
*

*> >> been doing it for awhile" and left it at that.
*

*> >> Latter that day and yet still I've been thinking about this. I
*

*> >> tend, I suspect like a lot of others who teach some content, to have
*

*> >> an idea of the direction and a 'feel' for the terrain and then,
*

*> >> depending on where people are at, tend to somewhat improvise. What
*

*> >> makes it difficult is that the young woman was asking me for a
*

*> >> 'formula' for proof and there, in a sense, isn't one. One's beginning
*

*> >> constrains one somewhat, one pulls out of experience some likely
*

*> >> scenarios which have their own affordances and limitations, and one
*

*> >> sort of keeps one's end in sight (sort of what Dewey talks about in
*

*> >> the Theory of Inquiry).
*

*> >>
*

*> >> Perhaps another way to say it is that in a moderately complex
*

*> >> proof there seems to before the 'novice' a huge amount of leeway as
*

*> >> almost every time you write a line you come to a bifurcation point.
*

*> >> However, that is misleading as what has gone before both supports and
*

*> >> simultaneously constrains where you can 'reasonably' go next (holding
*

*> >> that end in sight).
*

*> >>
*

*> >> Let me be more specific and give a very simple example (there is a
*

*> >> lot missing form this so this isn't exactly what I had in mind, but
*

*> >> it perhaps illustrates). Okay, I want to prove there are an infinite
*

*> >> number of prime numbers. The wrong way to do this is write some
*

*> >> formula which gives you an infinite number of primes. There isn't
*

*> >> one. [bifurcation] So a scenario would be to assume the converse -
*

*> >> i.e. there are only a finite number of primes and show this leads to
*

*> >> a contradiction (hence, showing 'logically' that there is indeed an
*

*> >> infinite number of primes). [bifurcation] Now you have an finite
*

*> >> number of something so you write them down (skipping 1 just in case
*

*> >> you want that to be a prime) p1, p2, p3, out to pN and, of course as
*

*> >> you are working with primes (and they are mucked up with
*

*> >> multiplication and division), you write the product p1*p2* out to pN
*

*> >> and set that equal to K. [bifurcation] Then you look at K+1.
*

*> >> [bifurcation] Well, K+1 certainly isn't divisible by p1 or p2 out to
*

*> > > pN so either K+1 is a prime or there is a prime pm less than K+1 that
*

*> >> was not in the original list. Hence a contradiction as was hoped for.
*

*> >>
*

*> >> Okay, I've used some basic knowledge about primes to begin and
*

*> >> that with some arithmetic has both constrained and enabled the proof
*

*> >> at each step. However, there is a sense in which I know that the
*

*> >> appropriate thing to do is multiply the primes and then, of course,
*

*> >> adding 1 is the elegant thing to do (smile).
*

*> >>
*

*> >> Does this help?
*

*> >>
*

*> >> Ed
*

*> >>
*

*> >> >Ed--
*

*> >> >Never mind off topic. We are always shifting topics. And I would be
*

*> happy
*

*> >> to
*

*> >> >respond usefully to your query if I knew how!! The problem is that I
*

*> do
*

*> >> not
*

*> >> >understand
*

*> >> >what you wrote! I am GUESSING that what you are talking about has to
*

*> do
*

*> >> with
*

*> >> >origins and
*

*> >> >change. ("the mathematics one does is both circumscribed and
*

*> supported by
*

*> >> >the math one is
*

*> >> >doing" coupled with expertise-- which I think of as a developmental
*

*> >> >process). But I cannot get
*

*> >> >from that to authoring a novel. And I am not even sure what the math
*

*> > > example
*

*> >> >is about. Can you
*

*> >> >expand?
*

*> >> >
*

*> >> >I am not sure, either, what David is after. My suggestions were
*

*> intended
*

*> >> to
*

*> >> >focus on the origins
*

*> >> >or graphic representations of ....... things.... ideas...... language
*

*> >> (all
*

*> >> >big issues in the history of writing).I picked my
*

*> >> >suggestions for David thinking that what he was interested in the
*

*> origins
*

*> >> of
*

*> >> >scripts of various kinds. Others have gone
*

*> >> >to goody and watt on the consequences of writing, ong, etc. Havelock
*

*> is
*

*> >> an
*

*> >> >interesting "half way" point because he makes
*

*> >> >a big deal of the special properties of the alphabet and hits on
*

*> Chinese
*

*> >> >ideographic writing.
*

*> >> >
*

*> >> >Perhaps you can expand? (And be ready for someone to comment on the
*

*> >> article
*

*> >> >of the month-for-discussion, although who knows!!)
*

*> >> >
*

*> >> >mike
*

*> >> >On 1/2/07, Ed Wall wrote:
*

*> >> >>
*

*> >> >>Mike and all
*

*> >> >>
*

*> >> >> This is not quite on the topic (and, thus, I have held back a
*

*> >> >>bit), but given the amount of expertise that people are bringin I
*

*> ask
*

*> >> >>a question I have asked elsewhere (I apologize for how it is
*

*> phrased,
*

*> >> >>but something like this was appropriate in that particular
*

*> community):
*

*> >> >>
*

*> >> >>> I had a question and wonder if you might point me in a useful
*

*> >> >>>direction(s). The situation is such: It has been argued of late
*

*> that
*

*> >> >>>the work mathematicians do - proof and the such - proceeds within
*

*> the
*

*> >> >>>mathematics being created. That is, without going into a lot of
*

*> >> >>>detail, the mathematics one does is both circumscribed and
*

*> supported
*

*> >> >>>by the mathematics one is doing. This is not exactly a matter of
*

*> >> >>>prior knowledge or the hermeneutic circle per se although it might
*

*> >> >>>have something to do with being an 'expert.'
*

*> >> >>> The reason why I am asking is that, the other day in a somewhat
*

*> >> >>>philosophic discussion around a novel, a participant noted that
*

*> some
*

*> >> >>>authors describe the authoring process as open-ended in the sense
*

*> >> >>>that what finally takes place may differ from what was originally
*

*> >> >>>intended. That is, in a certain sense, the writing writes itself.
*

*> As
*

*> >> >>>this sounded somewhat parallel to the phenomenon I mentioned in
*

*> >> >>>mathematics, I was wondering if you knew of someone(s) who makes
*

*> >> >>>remarks about a similar phenomenon re writing.
*

*> >> >>
*

*> >> >>Ed Wall
*

*> >> >>
*

*> >> >>>Hi David--
*

*> >> >>>
*

*> >> >>>There is a LOT of material on the topic of writing systems.
*

*> >> >>>Two interesting places to start are:
*

*> >> >>>
*

*> >> >>>D. Schmandt-Besserat, Before Writing:. U of Texas Press. 1992 (two
*

*> >> >>volumes)
*

*> >> >>>
*

*> >> >>>R. Harris. The origin of writing. Open Court. 1986.
*

*> >> >>>
*

*> >> >>>David Olson has written extensively on this topic, primarily from
*

*> >> >>secondary
*

*> >> >>>sources.
*

*> >> >>>
*

*> >> >>>I am unsure of best sources that delve into origins of writing in
*

*> China
*

*> >> >>>which were more or less co-incident with
*

*> >> >>>events in Euphrates area.
*

*> >> >>>mike
*

*> >> >>>_______________________________________________
*

*> >> >>>xmca mailing list
*

*> >> >>>xmca@weber.ucsd.edu
*

*> >> >>>http://dss.ucsd.edu/mailman/listinfo/xmca
*

*> >> >>
*

*> >> >>_______________________________________________
*

*> >> >>xmca mailing list
*

*> > > >>xmca@weber.ucsd.edu
*

*> >> >>http://dss.ucsd.edu/mailman/listinfo/xmca
*

*> >> >>
*

*> >> >_______________________________________________
*

*> >> >xmca mailing list
*

*> >> >xmca@weber.ucsd.edu
*

*> >> >http://dss.ucsd.edu/mailman/listinfo/xmca
*

*> >>
*

*> >>
*

*> >_______________________________________________
*

*> >xmca mailing list
*

*> >xmca@weber.ucsd.edu
*

*> >http://dss.ucsd.edu/mailman/listinfo/xmca
*

*> >
*

*> >
*

*> > __________________________________________________
*

*> >Do You Yahoo!?
*

*> >Tired of spam? Yahoo! Mail has the best spam protection around
*

*> >http://mail.yahoo.com
*

*> >_______________________________________________
*

*> >xmca mailing list
*

*> >xmca@weber.ucsd.edu
*

*> >http://dss.ucsd.edu/mailman/listinfo/xmca
*

*>
*

*> _______________________________________________
*

*> xmca mailing list
*

*> xmca@weber.ucsd.edu
*

*> http://dss.ucsd.edu/mailman/listinfo/xmca
*

*>
*

_______________________________________________

xmca mailing list

xmca@weber.ucsd.edu

http://dss.ucsd.edu/mailman/listinfo/xmca

**Next message:**ERIC.RAMBERG who-is-at spps.org: "[xmca] cultural effects of and on phylogeny"**Previous message:**Mike Cole: "Re: [xmca] Writing systems"**Next in thread:**Mike Cole: "Re: [xmca] Writing systems"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

*
This archive was generated by hypermail 2b29
: Thu Feb 01 2007 - 10:11:31 PST
*