All,
One of the running arguments I have with one of my favorite colleagues here in
Santa Fe is about whether Mathematics is (or isn't) different from all other
intellectual enterprises, such as psychology or philosophy. in that, unlike
them, mathematics "adds up," in the long run. Contrary to
I would like to return to that Chaitin lesson: it seems that a full and correct
definition of mathematics is *impossible*... like a
full axiomatization of arithmetic. Mathematics is so complex that an accurate
definition of it is equal to doing math (no
compression in Chaitin's terminology). It
Nick,
Concerning the following quote from your email one could easily replace
musical style with painting style or writing style or clothing style
or style.
Orlando
*"Mathematical style is far more important than it usually seems. It is
intimately connected to the essence of m
Psychology and Ethology,
Clark University ([EMAIL PROTECTED])
- Original Message -
From: Orlando Leibovitz
To: [EMAIL PROTECTED];The Friday Morning Applied Complexity Coffee Group
Sent: 7/10/2008 10:24:05 PM
Subject: Re: [FRIAM] Mathematics and Music
Nick,
Concerning the following
A tract on how the history might work, again, *sigh*:
http://www.dcorfield.pwp.blueyonder.co.uk/HowMathematicians.pdf
The point being, that mathematics, like Cluetrain products, are
conversations, and that those that coalesce and progress don't get made
without some awareness of the continuity
A larger question might be (perhaps indicating my own ignorance) : is
mathematics inherent in the universe or a rational construct of the human mind?
Paul
**
Get the scoop on last night's hottest shows and the live
music scene in your area - Check out TourTracker.com!
(ht
To: [EMAIL PROTECTED];[EMAIL PROTECTED];friam@redfish.com
Sent: 7/11/2008 12:24:00 PM
Subject: Re: [FRIAM] Mathematics and Music
A larger question might be (perhaps indicating my own ignorance) : is
mathematics inherent in the universe or a rational construct of the human mind?
Paul
Glenn, I personally agree with your analysis of what mathematics is
either in large part or wholly.
But there are others who do not. The field of mathematical philosophy
has many branches of opposing belief.
None of which has been proven for the most part and the subject has
mostly languis
Mathematicians have asserted both positions - some believing that math
is a process of "discovery" of the intrinsic nature of the universe (or
the mind of God) while others believe it is a process of "invention" and
isomorphism between the invention and the universe is serendipitous.
davew
On F
>
> We have also talked about the lack of rigorous mathematical
> representation of complexity and that being a barrier to progress
> in the science.
the idea of magic raised your hackles - the above sentence raises mine.
implicit in the sentence is some variation of "mathematics is a bet
Perhaps the invention is intrinsic? The either/or conundrum seems
artificial, unless one buys into a narrower definition of mathematician.
C.
Prof David West wrote:
>
> Mathematicians have asserted both positions - some believing that math
> is a process of "discovery" of the intrinsic nature
> Interestingly enough, all advances in science stem from the uses of
> metaphor - not mathematics. (see Quine) The premature rush to abandon
> the language of metaphor and publish using arcane squiggles is the real
> - in my not very humble opinion - barrier to progress.
Well, depends on what
Michael Agar wrote:
> Is a computer program a mathematization?
>
Proof is that Mathematica is in large part written in the functional
programming language Mathematica, and Macsyma/Maxima written in Lisp.
Marcus
FRIAM Applied Com
David Mirly wrote:
> One of the more opposite views, however, is the Platonist view (I
> think I have that right) where mathematical concepts
> are a set of universal truths and we just discover them as opposed to
> creating them.
Well, I don't want to object to the idea that Platonism opposes
Prof David West wrote:
>
>> We have also talked about the lack of rigorous mathematical
>> representation of complexity and that being a barrier to progress
>> in the science.
>
>
> the idea of magic raised your hackles - the above sentence raises mine.
>
> implicit in the sentence is some
Carl wrote:
> A tract on how the history might work, again, *sigh*:
>
> http://www.dcorfield.pwp.blueyonder.co.uk/HowMathematicians.pdf
Given a master with power and an apprentice without, don't see why the
genealogical view is necessarily at odds with tradition-constituted
enquiry -- such that o
Sent: Friday, July 11, 2008 6:10 PM
Subject: Re: [FRIAM] Mathematics and Music
Prof David West wrote:
>
>> We have also talked about the lack of rigorous mathematical
>> representation of complexity and that being a barrier to progress
>> in the science.
>
&
Well, the geneological enquiry (as described) seemed more adversarial
than the traditional - the G guy is trying to discredit the other guy by
showing that he is just on a power trip of some sort. I tend to look at
them as subtractive (G) and additive (T) sculpture - complementary if
some comm
Günther Greindl wrote:
> Well, depends on what you want to do - developing _new_ theories is best
> done via metaphor; to get a qualitative feel for the stuff; speculative
> philosophy, if you like (that is indeed what I like to do :-))
>
> But to make it into science, which means that you can ma
Carl Tollander wrote:
> the G guy is trying to discredit the other guy by
> showing that he is just on a power trip of some sort. I tend to look at
> them as subtractive (G) and additive (T) sculpture - complementary if
> some common goal is in mind, but the G guy never gets there, as he has
>
Glen,
> I agree with your gist but not your specific words. [grin]
:-)
> All pursuit
> of truth is science, regardless of the language. So, developing new
> theories with metaphor _is_ science (as long as the theories are testable).
Ok, I agree. I like your distinction (below) between coars
Carl et al,
Yes, perhaps mathematics is built into our brains which seem (again speaking
out of innocent ignorance) function somewhat as a binary electrical system.
And perhaps our nervous system reflects the "nature" of the universe.
As many philosophers, e.g., Whitehead, have postulated, kn
A computer program, currently, is an attempt to mathematize; and the
goal of traditional computer science is to refine the process of
creating a computer program to the purely formal / mathematical. It is
still an attempt, because a huge gulf remains between what I want and
can say about what I
On Fri, 11 Jul 2008 14:39:40 -0600, "Carl Tollander" <[EMAIL PROTECTED]>
said:
> Perhaps the invention is intrinsic? The either/or conundrum seems
> artificial, unless one buys into a narrower definition of mathematician.
>
> C.
the mathematician is channeling the universe as it expresses its
> >
> > But to make it into science, which means that you can make predictive
> > models certainly means mathematizing the theory.
> >
>
As a human being, and as an anthropologist, I can make predictions and
create predictive models based on a largely non-conscious understanding
of cultur
Prof David West wrote:
> A computer program, currently, is an attempt to mathematize; and the
> goal of traditional computer science is to refine the process of
> creating a computer program to the purely formal / mathematical. It is
> still an attempt, because a huge gulf remains between what I w
...or vice-versa, depending on which sort of mathematician you are
today...I think I would be more content with a universe that continually
reinvents itself rather than one that waits patiently to be discovered.
The former seems more happily complex. Pi would be more conserved over
time than
Günther Greindl wrote:
> Hmm - in the background he will have hypotheses; knowledge which is
> implicit in the neural weigthing in his brain (representing the evidence
> he has seen and categorized). So the physician has a mathematical
> (probabilistic) model of the situation, albeit maybe not
So maybe simulated annealing is another way of looking at it. But...
In the tradition-orientation that Corfield is describing, the "hill
climbers" would be talking to each other, and refining their ears. In
any case, I don't view this as necessarily an optimization problem (see
the companion
Let me see if I've followed David's argument... science doesn't need math
and it doesn't need to possess any predictive power and - given the
cultural/individual specificity of metaphors - reproducibility seems kinda
optional. So exactly what does something need to make it science?
Robert
On Sat,
Damned if I know. Clarity of an assertion about how the world works with intent
to revise against subsequent experience?
Probably spent too much time in Vienna.
Mike
>>> "Robert Holmes" <[EMAIL PROTECTED]> 07/12/08 5:31 PM >>>
Let me see if I've followed David's argument... science doesn't need
Coherent is good, but an epithet we usually reserve for scientific
theories more than science per se.
Michael Agar wrote:
> Damned if I know. Clarity of an assertion about how the world works with
> intent to revise against subsequent experience?
>
> Probably spent too much time in Vienna.
>
> M
Hola Carlos. (I'm in Buenos Aires)
I don't want to separate theory from practice like that. And
"coherent" in the Euclidean sense of consistent axioms isn't what I
meant by "clarity." Clarity can be about where in the assertion
contradictions and contingencies are made explicit, the sorts of
Glen,
> So, I agree with you that it's a model; but I disagree that it's a
> mathematical model except in the pathological limit-case where all of
> reality is somehow defined as "mathematics". A strong Platonist might
> well say that all reality is mathematics. And if that's your point,
> t
Mikhail Gorelkin wrote:
> I would like to return to that Chaitin lesson:
Well, the problem with focusing on the Chaitin talk is that there were
many things said in the talk, not all of which point in the same
direction. So, it would be better if you would single out a specific
aspect of the ta
ginal Message -
From: glen e. p. ropella
To: The Friday Morning Applied Complexity Coffee Group
Sent: Monday, July 14, 2008 5:08 PM
Subject: Re: [FRIAM] Mathematics and Music
Mikhail Gorelkin wrote:
> I would like to return to that Chaitin lesson:
Well, the problem with foc
Mikhail Gorelkin wrote:
>>> Glen between brackets<<
>
> 1) >>I maintain my claim that math is a living language by which we
> describe aspects of reality.<< and >>But I disagree that an accurate
> definition of math is equal to doing math.<<
>
> I don't know a better definition of math than: it i
glen e. p. ropella wrote:
> This general sensory-motor category (I'll call it SMI) is the _only_
> evidence we have that an external reality even exists.
Those characters you think you see on your computer screen. Those
sounds you think you hear coming from your speakers. That us. The
voice
Morning Applied Complexity Coffee Group
Sent: Monday, July 14, 2008 9:45 PM
Subject: Re: [FRIAM] Mathematics and Music
Mikhail Gorelkin wrote:
>>> Glen between brackets<<
>
> 1) >>I maintain my claim that math is a living language by which we
> describe
Lie Groups are fancy?
Simple, elegant, perhaps. Not fancy.
Ken
_
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf
Of Mikhail Gorelkin
Sent: Monday, July 14, 2008 11:02 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Mathematics and Music
Mikhail Gorelkin wrote:
> We all have *two* me: the one is indefinable "I am"
> (who thinks, the real one) and the another is the product of thinking
> of the first one (me as I think about me).
Well, OK. I kindasorta agree. But, one has to realize that the latter
me is just as "real" as the fo
pretations and comments or make (invent) them after all. --Mikhail
- Original Message -
From: glen e. p. ropella
To: The Friday Morning Applied Complexity Coffee Group
Sent: Tuesday, July 15, 2008 1:15 PM
Subject: Re: [FRIAM] Mathematics and Music
Mikhail Gorelkin wrote:
>
Mikhail Gorelkin wrote:
> >>Glen<<
>
> 1) >>But, one has to realize that the latter me is just as
> "real" as the former me.<<
>
> Probably, from a point of view of an
> authentic self, a degree of such "real-ness" is not very significant
> - zero probability - and may be ignored almost complet
the
one that has.. to see / experience this difference :-) (this is an axiomatic
level) --Mikhail
- Original Message -
From: glen e. p. ropella
To: The Friday Morning Applied Complexity Coffee Group
Sent: Tuesday, July 15, 2008 7:11 PM
Subject: Re: [FRIAM] Mathematics and Music
Mikhail Gorelkin wrote:
> >>Glen<<
> >>Going back to the original point, I maintain that both the
> act of creation and the act of making occur within what I call
> sensory-motor interactions, not somehow "beyond" or behind them.<<
> No, *nobody* can convince you. He/she can show you but you're t
nce")
because it's prior any proof, even any
language. --Mikhail
- Original Message -
From: glen e. p. ropella
To: The Friday Morning Applied Complexity Coffee Group
Sent: Wednesday, July 16, 2008 12:41 PM
Subject: Re: [FRIAM] Mathematics and Music
Mikhail Gorelki
Mikhail Gorelkin wrote:
> Glen, from my 4th part, where I was talking about Feynman's saying
> and a difference between *our makes* and *creations of our Geniuses*,
> I thought that it was clear that two "me" are actually: me and my
> invisible Genius (or esoterically - ye, I know that you hate
w (instinctive,
animal) self, and some African artists represent a man with three faces: his
low-, rational-, and higher selves. --Mikhail
- Original Message -
From: glen e. p. ropella
To: The Friday Morning Applied Complexity Coffee Group
Sent: Wednesday, July 16, 2008 4:56 PM
S
We can *refer* to mathematics as seeking (by God) the universal language and a
set of the universal rules to express the essence of
the world and write the universal program to get "correctly" the rest as its
output (like in Wolfram's A New Kind of
Science). --Mikhail
Sorry, instead of "as its output", it should be "as it's running" --Mikhail
- Original Message -
From: Mikhail Gorelkin
To: The Friday Morning Applied Complexity Coffee Group
Sent: Friday, July 18, 2008 6:33 PM
Subject: Re: [FRIAM] Mathematics and Mu
athematics and Music
Sorry, instead of "as its output", it should be "as it's running" --Mikhail
- Original Message -
From: Mikhail Gorelkin
To: The Friday Morning Applied Complexity Coffee Group
Sent: Friday, July 18, 2008 6:33 PM
Subject
day Morning Applied Complexity Coffee Group
> Subject: Re: [FRIAM] Mathematics and Music
>
> Prof David West wrote:
> >
> >> We have also talked about the lack of rigorous mathematical
> >> representation of complexity and that being a barrier to progress
> &g
'voila', cool new science at every turn!
>
> Phil
>
>
>> -Original Message-
>> From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On
>> Behalf Of glen e. p. ropella
>> Sent: Friday, July 11, 2008 6:10 PM
>> To: The Friday Morning Applied Com
Behalf Of glen e. p. ropella
> Sent: Friday, July 11, 2008 6:10 PM
> To: The Friday Morning Applied Complexity Coffee Group
> Subject: Re: [FRIAM] Mathematics and Music
>
> Prof David West wrote:
> >
> >> We have also talked about the lack of rigor
nday, July 13, 2008 10:21 PM
Subject: Re: [FRIAM] Mathematics and Music - missed opportunity
I think what may be holding back the math is our failure to go to the next
level and consider change as a physical process. When you do that you find
what nature actually does much more int
quot;growth runs into
> complications"
> > and nature does a lot of creative stuff with it. You just look for
> the
> > complications coming and then 'voila', cool new science at every
> turn!
> >
> > Phil
> >
> >
> >> -Original Messa
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