Mathematics and Music
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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, knowledge and science is based on evolving metaphors that get better and better but never perfect. But what does this mean for mathematics which claims to be perfectly logical in spite of irrational numbers? I do like Carl's response to David. Paul ************** Get the scoop on last night's hottest shows and the live music scene in your area - Check out TourTracker.com! (http://www.tourtracker.com?NCID=aolmus00050000000112) ============================================================ 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 |
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In reply to this post by Marcus G. Daniels
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 want in a natural language and what the computer can 'hear' with its mathematical 'ears.' davew On Fri, 11 Jul 2008 15:30:47 -0600, "Marcus G. Daniels" <[hidden email]> said: > 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 Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > lectures, archives, unsubscribe, maps at http://www.friam.org ============================================================ 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 |
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In reply to this post by Carl Tollander
On Fri, 11 Jul 2008 14:39:40 -0600, "Carl Tollander" <[hidden email]> 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 itself? > > Prof David West wrote: > > > > 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 Fri, 11 Jul 2008 14:23:50 EDT, [hidden email] said: > >> 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! > >> > >> (http://www.tourtracker.com?NCID=aolmus00050000000112) > > > > ============================================================ > > 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 > > > > > ============================================================ > 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 ============================================================ 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 |
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In reply to this post by Günther Greindl
> > > > 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 culture. Such predictions are not based on mathematics (a mathematics of culture is pragmatically impossible at the moment). Predictive models do not a science make. davew ============================================================ 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 |
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In reply to this post by Prof David West
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 want and > can say about what I want in a natural language and what the computer > can 'hear' with its mathematical 'ears.' > I think the challenge is not to just facilitate use of natural language. Natural language has the benefit of tolerating ambiguity and thus making it possible to communicate half of an idea while continuing a conversation. But I doubt that it is language issue per se. In describing a problem to, say, a skilled computer programmer, the programmer often models the intent in more operational and precise way than the speaker delivers it. She has the benefit of sharing a lot of common knowledge with the speaker, the challenge of acquiring domain relevant knowledge which she does not share, and also having to keep track of inconsistencies in the story, teasing apart things that are clearly unspecified from those that come from her lack of knowledge of the domain (things that are nailed down but not obviously so). What we don't have now are programming systems that can take a vague set of propositions and instantiate possible candidate computer programs for evaluation. I think the answer is not magical automatic computer programming that can cope with the most muddled of thoughts, but many computer aided analysis and synthesis tools that help communicate back to the user what is not resolved in their idea and the consequences of that, i.e. I think humans have to change too. I would further argue that computer programs are a good way to move from coarse to refined science. A computer program is more expressive than the mathematical toolbox can handle, but with it can also move in that direction. It's a good staging ground for formalization. Marcus ============================================================ 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 |
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In reply to this post by Prof David West
...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 given at Boot Time. Prof David West wrote: > On Fri, 11 Jul 2008 14:39:40 -0600, "Carl Tollander" <[hidden email]> > 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 itself? > > > >> Prof David West wrote: >> >>> 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 Fri, 11 Jul 2008 14:23:50 EDT, [hidden email] said: >>> >>>> 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! >>>> >>>> (http://www.tourtracker.com?NCID=aolmus00050000000112) >>>> >>> ============================================================ >>> 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 >>> >>> >> ============================================================ >> 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 >> > > ============================================================ > 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 > > ============================================================ 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 |
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In reply to this post by Günther Greindl
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 > verbalized/symbolized. He is probably not even aware of the mathamtics > his brain embodies. Excellent point! But, I'm not sure it's right to call that wet-ware "mathematics". It is certainly correct to call it a model, though. More specifically, the physician's brain (in that mode) is an analog of the patient. (By "analog", I mean one extant object that mimics or is largely similar -- by some similarity measure -- some other extant object.) It would be closer to say that the physician's wet-ware brain is an implementation of a (implicit) mathematical model. Or, perhaps it would be better to say that the wet-ware _could_ be mathematically described but isn't. 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, then it's well taken! I find such an extreme limit case degenerate, though, because it obviates the need for one of the two words. If all reality is math and all math is reality, then we don't need both terms and we shouldn't use both terms. We could just say stuff like: "Bobby, go and do your reality homework!" [grin] > When you go mathematical, you make it explicit. Knowledge can be > transferred exactly. You can even mechanize it, meaning that you do not > rely on neural weighting of the brain to which you communicate (drawing > on the other person's experience of living in the same world as you > actually). I can't argue with that! I'd like to; but I can't. Since I'm obstinate, however, if I were able to argue against it, I'd have to go back to the distinction between a real object versus a representation/description of an object. a.k.a. an implementation vs. a specification. A construct in math, being a story/description/specification would then be _less_ particular than an implementation that was described by that story. If the story were so very explicit as to permit only 1 implementation, _then_ we might be able to claim what you claim ... that knowledge can be transferred exactly with math. But if the mapping from the set of constructs to the set of real things is not injective, then that leaves open the chance that any one story defines an equivalence class of implementations. And that means that the implementations are _more_ exact than the story. -- glen e. p. ropella, 971-219-3846, http://tempusdictum.com ============================================================ 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 |
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In reply to this post by Marcus G. Daniels
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 comment on invention vs discovery). As an example, I have recently taken up Taiko. Each dojo has its own set of teachings, how the drums are positioned, what kinds of drums are used, what kinds of stands, how music is played, what music is played, how much to emphasize choreography, pedagogy, how to practice, overall philosophy, and so on. Teachers and students from other places occasionally come by with other ways of going about it, maybe there are different lineages, maybe they are exploring some relatively new way of playing. And they say, ya know, you guys are doing things differently from the way I do it, but I will respect your way and try to show what I know in that context. And everybody learns a bit and gets a bit better as a result of that. But the dojo refines itself in that process, it's not a compromise. Sometimes a guy comes by and sez, no no, you're not playing it right, my way is the way, or worse, you guys do what you want, I'm gonna play it my way, and maybe you should all come study with me. I mention this example, because it seems to me that (1) it reflects the T&G conversations between working mathematicians I personally read online (which, admittedly, is not the same as actual experience), and (2) it highlights the desirability for inquiry of parallel tracks among a set of local foci that occasionally communicate - consolidating dojos (or mathematical centers) would not result in as much progress (moving the exploration and invention along) as the current system. It seems more of a jazz ethic than an academic ethic. CT Marcus G. Daniels wrote: > 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 >> no motivation or handy mechanism to do so. >> > Yet the Will to Power is served by discovery and invention, as well as > by criticism. A risk for the T guy is that the `intellectuals' in his > community are not acting in good faith and not trying to do more than > just refine a self-consistent story, which can then be passed on as the > canon. So it could be the reverse, the T guys are the subtractive or > inhibitory player. > > Imagine optimizing a function of many variables using hillclimbing. In > a bumpy landscape, the single trajectory (the community) will soon get > stuck at a local optimum, even though up to that point progress was > being made. Better not to follow any search rules and just randomly > pick points for a while (multiple trajectories/communities/individuals). > Put another way, there are countless questions to ask, and certain > communities may serve just to create a comfortable consensus reality > which then fails to explore a problem thoroughly enough. > > Marcus > > > > ============================================================ > 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 > > ============================================================ 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 |
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In reply to this post by Prof David West
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, Jul 12, 2008 at 11:16 AM, Prof David West <[hidden email]> wrote:
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In reply to this post by Nick Thompson
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" <[hidden email]> 07/12/08 5:31 PM >>> 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, Jul 12, 2008 at 11:16 AM, Prof David West <[hidden email]> wrote: > > > As a human being, and as an anthropologist, I can make predictions and > create predictive models based on a largely non-conscious understanding > of culture. Such predictions are not based on mathematics (a > mathematics of culture is pragmatically impossible at the moment). > Predictive models do not a science make. > > davew > > > ============================================================ > 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 > ============================================================ 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 |
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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. > > Mike > > >>>> "Robert Holmes" <[hidden email]> 07/12/08 5:31 PM >>> >>>> > 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, Jul 12, 2008 at 11:16 AM, Prof David West <[hidden email]> > wrote: > > >> As a human being, and as an anthropologist, I can make predictions and >> create predictive models based on a largely non-conscious understanding >> of culture. Such predictions are not based on mathematics (a >> mathematics of culture is pragmatically impossible at the moment). >> Predictive models do not a science make. >> >> davew >> >> >> ============================================================ >> 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 >> >> > > > ============================================================ > 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 > > ============================================================ 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 |
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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 things that make for an interesting ABM. I dunno, I just work here. Mike On Jul 13, 2008, at 9:47 AM, Carl Tollander wrote: > 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. >> >> Mike >> >> >>>>> "Robert Holmes" <[hidden email]> 07/12/08 5:31 PM >>> >>>>> >> 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, Jul 12, 2008 at 11:16 AM, Prof David West >> <[hidden email]> >> wrote: >> >> >>> As a human being, and as an anthropologist, I can make >>> predictions and >>> create predictive models based on a largely non-conscious >>> understanding >>> of culture. Such predictions are not based on mathematics (a >>> mathematics of culture is pragmatically impossible at the moment). >>> Predictive models do not a science make. >>> >>> davew >>> >>> >>> ============================================================ >>> 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 >>> >>> >> >> >> ============================================================ >> 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 >> >> > > ============================================================ > 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 ============================================================ 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 |
Re: Mathematics and Music - missed opportunity
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In reply to this post by glen ep ropella
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 interesting and inspiring than anything we can invent. Using a physical systems model the process now bringing about our whole system collapse was seen coming a long way off and it could have inspired the math to demonstrate the turn onto another path instead too. Live and learn I guess. The 2006 paper by Bettencourt is easily generalized to reach this implication, acknowledging that for the physical growth system he considered "achieving major innovation cycles must be generated at continually accelerating rates"( http://www.pnas.org/content/104/17/7301.abstract). That's remarkably close to the basis of proof for the general principle I offered in my "Infinite Society" paper in 1979 (http://www.synapse9.com/UnhidPatt-theInfiniteSoc.pdf). The general principle being the theorem that I've been using ever since with excellent forecasting results. In physical systems "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 Message----- > From: [hidden email] [mailto:[hidden email]] On > 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 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 > better / > > superior / privileged / real language compared to all other languages > > used by humans to think and therefore we cannot really think properly > or > > rigorously unless we are thinking mathematically." > > I don't think that inference is implied by that sentence. I so believe > math is a better language with which to describe reality than, say, > English. But, that's not what the sentence above says. The sentence > above states that a _lack_ of math rigor is a barrier to one particular > domain: plectics. > > Your inference goes quite a bit further than the David's sentence. > > > this annoying attitude is expressed / believed by a majority of > > intellectuals and academicians - not just mathematicians. We cannot > be > > "scientists" unless we 'mathematize' our field of enquiry. > > And although I believe that math is the best known language for > describing reality, I don't believe that one must mathematize every > scientific field or that one cannot be a scientist without > mathematizing > their field. > > Science is the search for truth. And truth can be sought using any > language... any language at all. Some domains, particularly the ones > resistant to rigor are best studied with languages that have a high > tolerance for ambiguity... e.g. English. > > Some domains that are not so resistant to rigor are best studied with > math. Often, it takes a great deal of work using ambiguity tolerant > languages like English before an ambiguity intolerant language like > math > can be effectively used. > > If and when less ambiguous languages can be used, _then_ those > languages > become more effective than the more ambiguous languages. > > From 50,000 metaphorical feet, this can be seen as a simple case of > specialization. A generalist uses coarse tools and a specialist uses > fine tools. Math is a fine tool that can only be used after the > generalists have done their upstream work in the domain. Neither is > really "better", of course, when taking a synoptic view of the whole > evolution of the domain. But math is definitely more refined... more > special. > > > 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. > > I agree. Likewise, the tendency to stick with a coarse language when a > more refined language is called for is also a real barrier to > progress... "progress" defined as: the evolution of a domain from > general to special, coarse to fine. > > -- > glen e. p. ropella, 971-219-3846, http://tempusdictum.com > > > ============================================================ > 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 ============================================================ 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 |
Re: Mathematics and Music - missed opportunity
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Holding ourselves apart from nature,
We are surprised when nature pays our work no mind. Were our methods unsound? Phil Henshaw wrote: > 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 interesting and inspiring than anything > we can invent. > > Using a physical systems model the process now bringing about our whole > system collapse was seen coming a long way off and it could have inspired > the math to demonstrate the turn onto another path instead too. Live and > learn I guess. > > The 2006 paper by Bettencourt is easily generalized to reach this > implication, acknowledging that for the physical growth system he considered > "achieving major innovation cycles must be generated at continually > accelerating rates"( http://www.pnas.org/content/104/17/7301.abstract). > That's remarkably close to the basis of proof for the general principle I > offered in my "Infinite Society" paper in 1979 > (http://www.synapse9.com/UnhidPatt-theInfiniteSoc.pdf). The general > principle being the theorem that I've been using ever since with excellent > forecasting results. In physical systems "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 Message----- >> From: [hidden email] [mailto:[hidden email]] On >> 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 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 >>> >> better / >> >>> superior / privileged / real language compared to all other languages >>> used by humans to think and therefore we cannot really think properly >>> >> or >> >>> rigorously unless we are thinking mathematically." >>> >> I don't think that inference is implied by that sentence. I so believe >> math is a better language with which to describe reality than, say, >> English. But, that's not what the sentence above says. The sentence >> above states that a _lack_ of math rigor is a barrier to one particular >> domain: plectics. >> >> Your inference goes quite a bit further than the David's sentence. >> >> >>> this annoying attitude is expressed / believed by a majority of >>> intellectuals and academicians - not just mathematicians. We cannot >>> >> be >> >>> "scientists" unless we 'mathematize' our field of enquiry. >>> >> And although I believe that math is the best known language for >> describing reality, I don't believe that one must mathematize every >> scientific field or that one cannot be a scientist without >> mathematizing >> their field. >> >> Science is the search for truth. And truth can be sought using any >> language... any language at all. Some domains, particularly the ones >> resistant to rigor are best studied with languages that have a high >> tolerance for ambiguity... e.g. English. >> >> Some domains that are not so resistant to rigor are best studied with >> math. Often, it takes a great deal of work using ambiguity tolerant >> languages like English before an ambiguity intolerant language like >> math >> can be effectively used. >> >> If and when less ambiguous languages can be used, _then_ those >> languages >> become more effective than the more ambiguous languages. >> >> From 50,000 metaphorical feet, this can be seen as a simple case of >> specialization. A generalist uses coarse tools and a specialist uses >> fine tools. Math is a fine tool that can only be used after the >> generalists have done their upstream work in the domain. Neither is >> really "better", of course, when taking a synoptic view of the whole >> evolution of the domain. But math is definitely more refined... more >> special. >> >> >>> 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. >>> >> I agree. Likewise, the tendency to stick with a coarse language when a >> more refined language is called for is also a real barrier to >> progress... "progress" defined as: the evolution of a domain from >> general to special, coarse to fine. >> >> -- >> glen e. p. ropella, 971-219-3846, http://tempusdictum.com >> >> >> ============================================================ >> 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 >> > > > > ============================================================ > 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 > > ============================================================ 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 |
Haiku-ified was: Mathematics and Music - missed opportunity
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Held apart from nature Nature pays our work no mind Were methods unsound? > Holding ourselves apart from nature, > We are surprised when nature pays our work no mind. > Were our methods unsound? > > ============================================================ 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 |
Re: Mathematics and Music - missed opportunity
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In reply to this post by Phil Henshaw-2
Phil, I totally agree with
it: >>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 interesting and inspiring than anything we can invent.<< And
perhaps first we need to
understand quantum mechanic. I think Chaitin and maybe Wolfram are close to
it.
--Mikhail
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Re: Haiku-ified was: Mathematics and Music - missed opportunity
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In reply to this post by Steve Smith
Is this a model?
Enjoy the moment, We will clean it up in post. Steve Smith wrote: > Held apart from nature > Nature pays our work no mind > Were methods unsound? > >> Holding ourselves apart from nature, >> We are surprised when nature pays our work no mind. >> Were our methods unsound? >> >> >> > > > ============================================================ > 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 > > ============================================================ 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 |
Re: Mathematics and Music - missed opportunity
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In reply to this post by Mikhail Gorelkin
And new math should be more like Computational Intelligence than Lie groups and algebras. --Mikhail
============================================================ 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 |
Re: Haiku-ified was: Mathematics and Music - missed opportunity
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In reply to this post by Carl Tollander
Useless words. Excess.
Will they never end? Not in this world, I'm afraid. -- Doug Roberts, RTI International [hidden email] [hidden email] 505-455-7333 - Office 505-670-8195 - Cell On Sun, Jul 13, 2008 at 10:03 PM, Carl Tollander <[hidden email]> wrote: Is this a model? ============================================================ 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 |
Re: Haiku-ified was: Mathematics and Music - missed opportunity
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When words fail,
Seventeen syllables may suffice. Our gumbo simmers. Douglas Roberts wrote: > Useless words. Excess. > Will they never end? > Not in this world, I'm afraid. > > -- > Doug Roberts, RTI International > [hidden email] <mailto:[hidden email]> > [hidden email] <mailto:[hidden email]> > 505-455-7333 - Office > 505-670-8195 - Cell > > On Sun, Jul 13, 2008 at 10:03 PM, Carl Tollander <[hidden email] > <mailto:[hidden email]>> wrote: > > Is this a model? > Enjoy the moment, > We will clean it up in post. > > Steve Smith wrote: > > Held apart from nature > > Nature pays our work no mind > > Were methods unsound? > > > >> Holding ourselves apart from nature, > >> We are surprised when nature pays our work no mind. > >> Were our methods unsound? > >> > >> > >> > > > > > > ============================================================ > > 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 > > > > > > ============================================================ > 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 > > > > > > ------------------------------------------------------------------------ > > ============================================================ > 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 ============================================================ 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 |
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