The Unreasonable Effectiveness of Mathematics in the Natural Sciences
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The Unreasonable Effectiveness of Mathematics in the Natural Sciences
 
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Nick: I thought you might like this:
http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences The References section at the end of the article are Wigner's and Hamming's papers. Lovely title, I think -- sorta poetic. I'm completely of Tegmark's ilk: A different response, advocated by Physicist Max Tegmark (2007), is that physics is so successfully described by mathematics because the physical world is completely mathematical, isomorphic to a mathematical structure, and that we are simply uncovering this bit by bit. In this interpretation, the various approximations that constitute our current physics theories are successful because simple mathematical structures can provide good approximations of certain aspects of more complex mathematical structures. In other words, our successful theories are not mathematics approximating physics, but mathematics approximating mathematics. -- Owen ============================================================ 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: The Unreasonable Effectiveness of Mathematics in theNatural Sciences
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That's true. Interesting observation.
-J. ----- Original Message ----- From: "Owen Densmore" <[hidden email]> To: "Nicholas Thompson" <[hidden email]> Cc: "The Friday Morning Applied Complexity Coffee Group" <[hidden email]> Sent: Sunday, April 26, 2009 5:13 AM Subject: [FRIAM] The Unreasonable Effectiveness of Mathematics in theNatural Sciences > > I'm completely of Tegmark's ilk: > A different response, advocated by Physicist Max Tegmark (2007), is > that physics is so successfully described by mathematics because the > physical world is completely mathematical, isomorphic to a mathematical > structure, and that we are simply uncovering this bit by bit. In this > interpretation, the various approximations that constitute our current > physics theories are successful because simple mathematical structures > can provide good approximations of certain aspects of more complex > mathematical structures. In other words, our successful theories are not > mathematics approximating physics, but mathematics approximating > mathematics. > > -- Owen > ============================================================ 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: The Unreasonable Effectiveness of Mathematics in the Natural Sciences
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In reply to this post by Owen Densmore
On Sat, 25 Apr 2009 21:13 -0600, "Owen Densmore" <[hidden email]> wrote: > I'm completely of Tegmark's ilk: I assume that means you would also adhere to the sentiment attributed to Einstein: "How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?" Which contains the fallacy, "independent of experience." Thought - and mathematics! - is but a refined metaphor of experience. (following Lakoff) davew > A different response, advocated by Physicist Max Tegmark (2007), is > that physics is so successfully described by mathematics because the > physical world is completely mathematical, isomorphic to a > mathematical structure, and that we are simply uncovering this bit by > bit. In this interpretation, the various approximations that > constitute our current physics theories are successful because simple > mathematical structures can provide good approximations of certain > aspects of more complex mathematical structures. In other words, our > successful theories are not mathematics approximating physics, but > mathematics approximating mathematics. > > -- Owen > > > > ============================================================ > 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: The Unreasonable Effectiveness of Mathematics in the Natural Sciences
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Well said/observed David, I too am a Lakoff/Johnson/Nunez fan in this
matter.
While I am quite enamored of mathematics and it's fortuitous application to all sorts of phenomenology, Physics being somehow the most "pure" in an ideological sense, I've always been suspicious of the conclusion that "the Universe *is* Mathematics". This discussion also begs the age-old question of whether we are "inventing" or "discovering" mathematics. Similarly, it revisits the question of whether discoveries in mathematics portend discoveries in Physics (or other, "messier" phenomenological observations). - Steve Prof David West wrote:
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Re: The Unreasonable Effectiveness of Mathematics in theNatural Sciences
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In reply to this post by Jochen Fromm-4
Owen, et al,
Well, isn't this part of the broader mystery of why logic should get you anywhere in the study of nature?
Isn't logic just a language trick?
Why should nature give a fig for the tricks we play with our words?
This is all reminding me, for some reason, of the "discovery" of the fact that the differential of the integral is just the original function. There seem to be two sorts of "discovery" in our discourse: One is the discovery of something in nature that we did not already know. The other is the discovery of a new implication in what we have already said that we did not anticipate when we said it. I can see why mathematics can help with the latter sort of "discovery", but have no idea why it should help with the former.
In the emergence literature appears the endearing phrase "natural reverence". The early philosophical emergentists believed that one had to accept emergent properties with "natural reverence," since such properties could not be reduced to the properties of their parts. I am deeply ambivalent about natural reverence: one the one hand, I believe that there is no point in being a scientist if you are not prepared to experience some natural reverence. On the other hand, I also believe that natural reverence is the enemy of discovery. Perhaps "natural reverence" is a fleeting pleasure one gets before one gets down to the dirty business of figuring out how things work: too little of it and one would never be inspired; too much of it, and one would never be curious.
Nick
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([hidden email])
============================================================ 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: The Unreasonable Effectiveness of Mathematics in the Natural Sciences
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In reply to this post by Prof David West
On Apr 26, 2009, at 9:57 AM, Prof David West wrote:
> On Sat, 25 Apr 2009 21:13 -0600, "Owen Densmore" <[hidden email]> > wrote: > >> I'm completely of Tegmark's ilk: > > I assume that means you would also adhere to the sentiment > attributed to > Einstein: > "How can it be that mathematics, being after all a product of > human > thought which is independent of experience, is so admirably > appropriate to the objects of reality?" Which contains the > fallacy, "independent of experience." Well, if Al agrees, I'm OK being in his camp! Phooey on your fallacy. > Thought - and mathematics! - is but a refined metaphor of experience. > (following Lakoff) Fine. But none the less, why is it that the subject line is so enigmatically true? .. why do we observe: The Unreasonable Effectiveness of Mathematics in the Natural Sciences? I presume you'd say that experience weld Science and Math together. So? That does not negate the wonder of The Unreasonable Effectiveness. My friend Nick to whom I addressed all this (we spar over the importance of math) might claim that Math is not particularly effective. Do you? -- Owen ============================================================ 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: The Unreasonable Effectiveness of Mathematics in the Natural Sciences
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In reply to this post by Steve Smith
On Apr 26, 2009, at 10:16 AM, Steve Smith wrote:
> Well said/observed David, I too am a Lakoff/Johnson/Nunez fan in > this matter. > > While I am quite enamored of mathematics and it's fortuitous > application to all sorts of phenomenology, Physics being somehow the > most "pure" in an ideological sense, I've always been suspicious of > the conclusion that "the Universe *is* Mathematics". OK: Show how it is not, then. > This discussion also begs the age-old question of whether we are > "inventing" or "discovering" mathematics. No it doesn't. We are discovering it. We are slowly becoming wise. We are uncovering the Structure of Everything. We are peaking under the Rug. God is one smart dude. > Similarly, it revisits the question of whether discoveries in > mathematics portend discoveries in Physics (or other, "messier" > phenomenological observations). They are independent. That's the wonder to which the subject refers. -- Owen ============================================================ 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: The Unreasonable Effectiveness of Mathematics in the Natural Sciences
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Mathematics is effective because there are regularities in nature. (Is that tautological/true/trivial?)
Assuming it's at least true, it seems to me that the real question is why there are regularities in nature? Once one grants that there are, then it would seem obvious that a language that can describe them will be effective. Also, assuming it's at least true, another question is how do those regularities come about? That's a primary concern of my "Reductionist blind spot" paper. -- Russ On Sun, Apr 26, 2009 at 12:41 PM, Owen Densmore <[hidden email]> wrote: On Apr 26, 2009, at 10:16 AM, Steve Smith wrote: ============================================================ 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: The Unreasonable Effectiveness of Mathematics in theNatural Sciences
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In reply to this post by Jochen Fromm-4
Owen Densmore (to his shame) said:
My friend Nick to whom I addressed all this (we spar over the importance of math) might claim that Math is not particularly effective. Do you? You slander me! I have NEVER NEVER NEVER CLAIMED that math is ineffective. Nor have we EVER sparred over the importance of math, because I have always been a flagrant math groupy. . I ===>have<=== vigorously defended philosophy against your claims that it never gets anywhere, but I dont see how that defense constitutes an attack on math since I have also tended to believe that math is a formalization and extension of the methods of philosophy. They stand or fall together. You have --with just cause -- complained about the manner in which I treat mathematical texts: I gnaw at them like a rat denied access to a food cupboard. I nest in them like a mouse, first marking, then tearing their pages into a paper froth of my own construction. I have no "natural reverence." But, as you know, I read everything that way. The only way I know to respect a text is to treat each word as thoroughly MEANT by the author and demand of him and her that the words are consistantly used. What is most tempting about mathematicians is their apparent committment to that same very high standard. As I indicated in my previous post, I share your amazement concerning the discoveries of mathematics, but am less certain than you are, what sort of discoveries they are. All the best, Nick Nicholas S. Thompson Emeritus Professor of Psychology and Ethology, Clark University ([hidden email]) http://home.earthlink.net/~nickthompson/naturaldesigns/ > [Original Message] > From: Owen Densmore <[hidden email]> > To: The Friday Morning Applied Complexity Coffee Group <[hidden email]> > Date: 4/26/2009 1:32:35 PM > Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics in theNatural Sciences > > On Apr 26, 2009, at 9:57 AM, Prof David West wrote: > > > On Sat, 25 Apr 2009 21:13 -0600, "Owen Densmore" <[hidden email]> > > wrote: > > > >> I'm completely of Tegmark's ilk: > > > > I assume that means you would also adhere to the sentiment > > attributed to > > Einstein: > > "How can it be that mathematics, being after all a product of > > human > > thought which is independent of experience, is so admirably > > appropriate to the objects of reality?" Which contains the > > fallacy, "independent of experience." > > Well, if Al agrees, I'm OK being in his camp! Phooey on your fallacy. > > > Thought - and mathematics! - is but a refined metaphor of experience. > > (following Lakoff) > > Fine. But none the less, why is it that the subject line is so > enigmatically true? .. why do we observe: The Unreasonable > Effectiveness of Mathematics in the Natural Sciences? > > I presume you'd say that experience weld Science and Math together. > So? That does not negate the wonder of The Unreasonable Effectiveness. > > My friend Nick to whom I addressed all this (we spar over the > importance of math) might claim that Math is not particularly > effective. Do you? > > -- Owen > > > ============================================================ > 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: The Unreasonable Effectiveness of Mathematics in the Natural Sciences
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In reply to this post by Owen Densmore
On Sun, 26 Apr 2009 13:32 -0600, "Owen Densmore" <[hidden email]> wrote: > > Fine. But none the less, why is it that the subject line is so > enigmatically true? .. why do we observe: The Unreasonable > Effectiveness of Mathematics in the Natural Sciences? Maybe because of a purely coincidental congruence. The "unreasonable" part is a function of of an unstated assumption - that the natural sciences comprise the majority (if not the totality) of "things to be explained / known / understood." In my experience, math helps explain and/or is congruent with about 10% of what I would like to know/understand. There is an equally large set of things that I would like to know/understand that math not only does not help, it actually hinders. Given that experience, there is absolutely no surprise that math (a formal system) can explain large chunks of physics (those parts that are themselves formal systems). The congruency is not anywhere near being "unreasonable." Using programming as an example, I am not at all surprised by the fact that math describes and is useful for about 1% of the programming problems we might encounter. Experience shows that math is not of much help in most of the problems - and certainly not in the design of solutions to the problems - that I have encountered over several decades. And, I am frequently annoyed when mathematics is used as a bludgeon to force adoption of programming solutions - relational databases being my pet peeve - that are actually harmful. If and when someone can show that Reality, and not just scientific reality, is mathematical I will be surprised. > My friend Nick to whom I addressed all this (we spar over the > importance of math) might claim that Math is not particularly > effective. Do you? In a later email, Nick claims slander on this point. But, as you can see in my answer above, I would assert that math is not particularly effective outside a small domain where it is. 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 |
Re: The Unreasonable Effectiveness of Mathematics in the Natural Sciences
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In reply to this post by Owen Densmore
Owen Densmore wrote:
On Apr 26, 2009, at 10:16 AM, Steve Smith wrote:Tricky, tricky! ... that always turns out well, trying to prove a negative! ;) I'll raise your conceptual Jui Jitsu and raise you a bit of conceptual Aikido. < extra-Large work-gloves-encrusted-with-manure coming off now! > My claim is *not* that the Universe is *not* Mathematics, but rather that I am suspicious of any such claim. I *do* think there is a strong relation, but I don't think it is an *identity*. This discussion also begs the age-old question of whether we are "inventing" or "discovering" mathematics. I contend that Mathematics is a (special) subset of Language and I do not know what it would mean (philosophically) to claim that we are *discovering* Language. That said, I think the closest one could come to claiming that we *discover* Mathematics would be one of two (or both) arguments: 1) Given that we have have developed a subset of Mathematics (and therefore Language) known as Mathematical Logic, it is to say that we *discover* elaborations and extens based in it; 2) We *invent* Mathematics (Mathematical Language) to describe the phenomenological patterns which we *discover*. I agree that the "Effectiveness of Mathematics" is fabulously amazing... but I'd ascribe an anthropic explanation of this before I would *insist* that this means that *the Universe IS Mathematics*. Science has a long history of ignoring phenomenology that it doesn't (yet) have the mathematics to describe. Think of the pre-nonlinear-science era (roughly pre-1980) and the consequent *explosion* that came with the development (application and elaboration really) of nonlinear mathematics. We suddenly *discovered* all kinds of things which we had been observing for millenia, but for which we had no concise language for thinking. Similarly with Newton/Leibniz Infinitesimal Calculus. And in the contrapositive: What of Mathematics which has no connection to any known phenomonology? When it appears that we are *inventing* or *discovering* patterns in the language of mathematics, are we discovering patterns about the physical world? Does this mean that we simply haven't looked long enough, or under enough rugs? Can we depend on any new mathematics we might "invent" actually to be a new understanding about the (physical) universe itself? I'm sure there are plenty of positive examples of this, and naturally any negative examples are just waiting for a positive one to negate them. It *does not* surprise me that the preponderance of the Mathematics we have developed is *highly useful* for understanding or explaining the elaborate collection of phenomenology we have recorded in human history. Mathematics *is* the language we use to describe such phenomenology (precisely and unambiguously). That said, you may also remember that I am a big fan of the likes of David Bohm and his Holographic Theories of the Universe and Ed Fredking and his Digital Information Mechanics, which have a vaguely similar odor to "The Universe IS Mathematics". On the other hand, I have to admit to arguing with myself (and Lakoff/Johnson/Nunez) here to some degree... I think they would insist that *all* Mathematics (and Thinking?) is Embodied and therefore must ground out (somewhere) in some experience We are slowly becoming wise.I'd be hard pressed to claim Wisdom(human_race) is a monotonic increasing function. And I have to question whether more understanding of phenomenology is equal to wisdom. It is not clear to me that after Hari Seldon develops Psychohistory, that we will be significantly more wise about what it means to be human. We might be able to predict human behaviour at various levels to varying degrees of granularity and accuracy, but *as always*, is prediction equal to understanding? We are uncovering the Structure of Everything.If you are a strict materialist, then I agree that this is a consequence of your argument... if you are not, then I think it is likely that you will have to agree that one can make formal mathematical statements that do not relate in any way to the physical world? That there might be wisdom and beauty which cannot be described mathematically? Methinks Godel is on my side on this one. We are peaking under the Rug.Whilst sweeping more things under it? <grin> God is one smart dude.Expect some backlash from the Athiests and the Feminists (and Polytheists and Animists, and ...)! <grin> I just read Dave West's "rebuttal" and while I am more generous in quantity to the value/utility/applicability of Mathematics to Phenomenology and more generally, it's relation to Epistimology, I agree with his intuitive assessment that there is plenty human knowledge and experience left that Mathematics *doesn't* provide any traction against. Oddly, those with *more* Math than I (BS Mathematics/Physics + 30 years of random graduate courses/studies) would simply claim that my Mathematics is wanting, while those with *less* would join me in noticing that those with *too much* Mathematics have a tendency to ignore/dismiss/negate anything they cannot describe Mathematically (a tautological argument at best). An Astrophysicist colleague calls the latter type of Mathematicians (many of them good friends of his) "MathHoles"... I won't tell you what *they* call *him*. - Steve ============================================================ 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 |
The Unreasonable Reverence of The Unreasonable Effectiveness of Mathematics in theNatural Sciences
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In reply to this post by Nick Thompson
Nicholas Thompson wrote:
Ah yes... *this* would be the larger and more interesting question. But then, why would we have ever "invented" and "developed" Logic (very far) if it had no real-world use? I suppose that is a good question for Theoretical Mathematicians and Logicians. And Mathematics a "mere" extension of logic. The Anthropic Principle might have a play in this. Any Universe that Linguistic Consciousness would evolve in would "naturally" have some patterns (follow some laws) that are tractable via such tools.
I *do* believe that there have been significant examples of the former... where a bit of heretofore esoteric Mathematics is suddenly found to be *useful* in predicting/understanding a bit of heretofore unknown (or intractable) phenomenology. For Owen's *Identity* "The Universe *is* Mathematics" (or rather, his defense against *my* derisive statement to that effect), we would have to prove that not only is *all* Phenomenology describable by Mathematics, but that *all* Mathematics ultimately describes some Phenomenology. This seems to open the door nicely for the mystics. Enter stage left, Rupert Sheldrake and the Intelligent Designers. Yes, it is a sticky wicket isn't it? I look forward to more elaboration on this topic (given the title/identity of this mail list/group). Or perhaps one would not bother to be a Scientist w/o enjoying the brain chemistry induced by said "natural reverence". It is also surprising/not that we have such brain chemistry... the love of an interesting problem well-solved! I think your first impulse was the most applicable... that somehow "natural reverence" is the reward for understanding the science (and mathematics) well enough to actually *feel* the reverence. Like our Greek and Norse forebearers were wont to go up against their gods, *we* are inclined to go up against our own "natural reverence". I don't know if the accounts of Kurt Godel's run up to kicking the stool out from under Russell and Whitehead included some of his own "natural reverence" of the *completeness* of Principia Mathematica, but I suspect it might have. We create our god(desse)s in our own image so that we can go up against them (or make demi-gods and through unholy unions with them?) Perhaps this is the point of of this thread in the first place, that we *do* find Mathematics amazingly (if not unreasonably) effective at predicting/describing/understanding phenomenology in the Natural Sciences. This "natural reverence" seems to be a good point of departure, suggesting that we are compelled to question it and seek to debunk it. - Steve ============================================================ 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: The Unreasonable Effectiveness of Mathematics in theNatural Sciences
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In reply to this post by Nick Thompson
Nick et al, This is a great question, with, I think, two parts. The first part is why is logic valid. I am almost certainly a platonist or worse on this point --it's validity simply seems to be obvious. Can the proposition that logic is valid be supported by any argument that doesn't implicitly use logic? (Okay, even "implicitly" assumes logic). The argument that we evolved to be convinced by logical implications because it is useful for survival suggests that logic is, at least, approximately valid, which is a lot less of a conclusion than what I would want, and which doesn't explain why logic works in modern physics. The other part of the original question is, even if we grant that logic is valid (or at least approximately valid) why is it useful to put together long strings of logical implications? Believing that logical implications are trivially true, I wonder how can long chains of such implications be anything but trivial. (And if we believe that logic is at best approximately true, wouldn't long chains of implications stop being good approximations if each link in the chain is a little inaccurate.) Perhaps Physics somehow restricts itself to a domain where logic works very well. And maybe things like consciousness are simply outside that domain (but I hope not). I wonder if there is there a domain where logic is a useful approximation, but long chains of implications are not useful? Perhaps social analysis? Perhaps philosophy? Perhaps the humanities? Nick, and others,--I'd be curious about what you think on this issue. ---John ________________________________________ From: Nicholas Thompson [[hidden email]] Sent: Sunday, April 26, 2009 1:40 PM To: [hidden email] Cc: John Kennison; Sean Moody Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics in theNatural Sciences Owen, et al, Well, isn't this part of the broader mystery of why logic should get you anywhere in the study of nature? Isn't logic just a language trick? Why should nature give a fig for the tricks we play with our words? This is all reminding me, for some reason, of the "discovery" of the fact that the differential of the integral is just the original function. There seem to be two sorts of "discovery" in our discourse: One is the discovery of something in nature that we did not already know. The other is the discovery of a new implication in what we have already said that we did not anticipate when we said it. I can see why mathematics can help with the latter sort of "discovery", but have no idea why it should help with the former. In the emergence literature appears the endearing phrase "natural reverence". The early philosophical emergentists believed that one had to accept emergent properties with "natural reverence," since such properties could not be reduced to the properties of their parts. I am deeply ambivalent about natural reverence: one the one hand, I believe that there is no point in being a scientist if you are not prepared to experience some natural reverence. On the other hand, I also believe that natural reverence is the enemy of discovery. Perhaps "natural reverence" is a fleeting pleasure one gets before one gets down to the dirty business of figuring out how things work: too little of it and one would never be inspired; too much of it, and one would never be curious. Nick Nicholas S. Thompson Emeritus Professor of Psychology and Ethology, Clark University ([hidden email]<mailto:[hidden email]>) http://home.earthlink.net/~nickthompson/naturaldesigns/ ----- Original Message ----- From: Steve Smith<mailto:[hidden email]> To: The Friday Morning Applied Complexity Coffee Group<mailto:[hidden email]> Sent: 4/26/2009 10:17:16 AM Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics in theNatural Sciences Well said/observed David, I too am a Lakoff/Johnson/Nunez fan in this matter. While I am quite enamored of mathematics and it's fortuitous application to all sorts of phenomenology, Physics being somehow the most "pure" in an ideological sense, I've always been suspicious of the conclusion that "the Universe *is* Mathematics". This discussion also begs the age-old question of whether we are "inventing" or "discovering" mathematics. Similarly, it revisits the question of whether discoveries in mathematics portend discoveries in Physics (or other, "messier" phenomenological observations). - Steve Prof David West wrote: I'm completely of Tegmark's ilk: I assume that means you would also adhere to the sentiment attributed to Einstein: "How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?" Which contains the fallacy, "independent of experience." Thought - and mathematics! - is but a refined metaphor of experience. (following Lakoff) davew A different response, advocated by Physicist Max Tegmark (2007), is that physics is so successfully described by mathematics because the physical world is completely mathematical, isomorphic to a mathematical structure, and that we are simply uncovering this bit by bit. In this interpretation, the various approximations that constitute our current physics theories are successful because simple mathematical structures can provide good approximations of certain aspects of more complex mathematical structures. In other words, our successful theories are not mathematics approximating physics, but mathematics approximating mathematics. -- Owen ============================================================ 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: The Unreasonable Effectiveness of Mathematics in theNatural Sciences
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John: Why is logic valid?
For the same reason the rules of chess are valid: by definition. Its validity is presupposed. If you don't like chess, don't play. If you do then you have to play by the agreed rules. Else don't call it chess (or logic). Make a new name for your game. In logic, one begins with a rule that a proposition has exactly one of two values: true or false. Other games, like fuzzy logic, have additional "maybe" values, but we use the adjective "fuzzy" to distinguish these games (or rule sets). Other rules are added to define ways to relate (or compose) propositions in the form of conjunctions, disjunctions, etc; to build up structures. All players agree to the rules and knowledge and science progress. Some people don't like these games, so they don't play. Some people play badly and aren't much fun. Some make mistakes (called fallacies) that are hard to see by other players. Some prefer other rules, like "the highest authority is always right" or "there is no truth; only love". More great technical innovations result from playing the game of logic than playing these other games. John: Why is it useful to put together long strings of logical implications? This is probably a result of trivial observation; nature puts together long strings of related events of cause and effects; e.g. chemical reactions and planetary motions. We are merely recording what we see in the formal language of cause and effect, namely logic. In this case, logic is more of a historian's tool. --Rob Howard -----Original Message----- From: [hidden email] [mailto:[hidden email]] On Behalf Of John Kennison Sent: Monday, April 27, 2009 5:15 AM To: ForwNThompson; [hidden email] Cc: Sean Moody Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics in theNatural Sciences Nick et al, This is a great question, with, I think, two parts. The first part is why is logic valid. I am almost certainly a platonist or worse on this point --it's validity simply seems to be obvious. Can the proposition that logic is valid be supported by any argument that doesn't implicitly use logic? (Okay, even "implicitly" assumes logic). The argument that we evolved to be convinced by logical implications because it is useful for survival suggests that logic is, at least, approximately valid, which is a lot less of a conclusion than what I would want, and which doesn't explain why logic works in modern physics. The other part of the original question is, even if we grant that logic is valid (or at least approximately valid) why is it useful to put together long strings of logical implications? Believing that logical implications are trivially true, I wonder how can long chains of such implications be anything but trivial. (And if we believe that logic is at best approximately true, wouldn't long chains of implications stop being good approximations if each link in the chain is a little inaccurate.) Perhaps Physics somehow restricts itself to a domain where logic works very well. And maybe things like consciousness are simply outside that domain (but I hope not). I wonder if there is there a domain where logic is a useful approximation, but long chains of implications are not useful? Perhaps social analysis? Perhaps philosophy? Perhaps the humanities? Nick, and others,--I'd be curious about what you think on this issue. ---John ________________________________________ From: Nicholas Thompson [[hidden email]] Sent: Sunday, April 26, 2009 1:40 PM To: [hidden email] Cc: John Kennison; Sean Moody Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics in theNatural Sciences Owen, et al, Well, isn't this part of the broader mystery of why logic should get you anywhere in the study of nature? Isn't logic just a language trick? Why should nature give a fig for the tricks we play with our words? This is all reminding me, for some reason, of the "discovery" of the fact that the differential of the integral is just the original function. There seem to be two sorts of "discovery" in our discourse: One is the discovery of something in nature that we did not already know. The other is the discovery of a new implication in what we have already said that we did not anticipate when we said it. I can see why mathematics can help with the latter sort of "discovery", but have no idea why it should help with the former. In the emergence literature appears the endearing phrase "natural reverence". The early philosophical emergentists believed that one had to accept emergent properties with "natural reverence," since such properties could not be reduced to the properties of their parts. I am deeply ambivalent about natural reverence: one the one hand, I believe that there is no point in being a scientist if you are not prepared to experience some natural reverence. On the other hand, I also believe that natural reverence is the enemy of discovery. Perhaps "natural reverence" is a fleeting pleasure one gets before one gets down to the dirty business of figuring out how things work: too little of it and one would never be inspired; too much of it, and one would never be curious. Nick Nicholas S. Thompson Emeritus Professor of Psychology and Ethology, Clark University ([hidden email]<mailto:[hidden email]>) http://home.earthlink.net/~nickthompson/naturaldesigns/ ----- Original Message ----- From: Steve Smith<mailto:[hidden email]> To: The Friday Morning Applied Complexity Coffee Group<mailto:[hidden email]> Sent: 4/26/2009 10:17:16 AM Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics in theNatural Sciences Well said/observed David, I too am a Lakoff/Johnson/Nunez fan in this matter. While I am quite enamored of mathematics and it's fortuitous application to all sorts of phenomenology, Physics being somehow the most "pure" in an ideological sense, I've always been suspicious of the conclusion that "the Universe *is* Mathematics". This discussion also begs the age-old question of whether we are "inventing" or "discovering" mathematics. Similarly, it revisits the question of whether discoveries in mathematics portend discoveries in Physics (or other, "messier" phenomenological observations). - Steve Prof David West wrote: I'm completely of Tegmark's ilk: I assume that means you would also adhere to the sentiment attributed to Einstein: "How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?" Which contains the fallacy, "independent of experience." Thought - and mathematics! - is but a refined metaphor of experience. (following Lakoff) davew A different response, advocated by Physicist Max Tegmark (2007), is that physics is so successfully described by mathematics because the physical world is completely mathematical, isomorphic to a mathematical structure, and that we are simply uncovering this bit by bit. In this interpretation, the various approximations that constitute our current physics theories are successful because simple mathematical structures can provide good approximations of certain aspects of more complex mathematical structures. In other words, our successful theories are not mathematics approximating physics, but mathematics approximating mathematics. -- Owen ============================================================ 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: The Unreasonable Effectiveness of Mathematics in the Natural Sciences
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Administrator
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In reply to this post by Owen Densmore
Just to clarify .. the reason I found the article compelling is due to
my tendency towards mathematical formalism. As an example, we spent quite a while looking at formalizing ABM and Steve's wonderful "Complexity Babble". We took two different paths in our wandering. One was to try to nail down good definitions for the various terms in english sentences. The other was a set-theoretic definition, reminiscent of Machine & Grammars in computer science. I append some notes, not sure if they're the latest. We seemed to be getting a bit more traction with the latter, at least in my opinion. For example, both initial conditions, constraints, and boundary conditions were more easily defined set-theoretically than in words. This could easily be a bias amongst the participants. -- Owen A Agent Based Model (ABM) is a four-tuple (A,e,s0,S) - A: set of "agent", which in turn consists of - AV: a finite set of variables, which in turn have a bounded range of values they can take on. - AS: the Step Function for this agent - E: an enumeration function which can visit, and optionally modify, each agent. - s0: the initial state of all agent variables - S: the Step Function which uses E to call each Agent's AS step function. Notes on the above: 0 - We agreed to discontinue, for the present, use of concept names that are easily confused with the same name in other sciences/ domains. If the name is compelling enough, preceding it with the work Agent or Model would be OK. Ex: Agent or Model space to describe the allowed values of the set of variables within an entity. 1 - We agreed on a simple definition of the modeling environment, even removing the notion of patches I proposed earlier. An agent (or entity) simply contains a set of variables, each of which has a set of possible values. And there is a list which lets an enumeration of the agents. Thus we've reduced the scope to: - An agent has a set of variables, and each variable has a set of allowed values. - A way to enumerate the agents is provided. A list is fine. - A procedure runs across the agents periodically. - There apparently is no need for patches yet. - Ditto for global variables This minimalist definition will be extended only when it is necessary to do so. (Thus we could have a model hierarchy similar to computing: Finite State Automata, Push Down Automata, and Turing Machines, with the parallel languages they recognize: Regular Expressions, Context Free Languages, and Lambda Calculus.) 2 - The cartesian product of the set of agent variables forms the Agent Space (or any other name we'd like). We may need to distinguish between the full cartesian product, and a reduction of that set due to the model's rules. This brought up the discussion of two reductions: - Reductions brought about by the initial conditions of the model (i.e. all agents at 0,0 or spread out with a uniform random distribution over the range of x,y values.) These may create a set of values within the full cartesian product that can not occur. - Reductions brought about by boundary conditions. These may not be an issue, they can simply be a reduction of the scope of one or more variables, but this needs to be decided upon. This gives us a reasonable set theoretic starting point: a set of agents with a set of variables with a restricted set of allowed values, along with a procedure that can enumerate over the agents to step the agents forward in time. ============================================================ 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: The Unreasonable Effectiveness of Mathematics in theNatural Sciences
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In reply to this post by Robert Howard-2-3
Robert: As you say, logic can be viewed as a game, like chess. You also say that "More great technical innovations result from playing the game of logic than playing these other games." The question then is what is it about logic that leads to more great technical innovations than other games. --John ________________________________________ From: [hidden email] [[hidden email]] On Behalf Of Robert Howard [[hidden email]] Sent: Monday, April 27, 2009 2:13 PM To: 'The Friday Morning Applied Complexity Coffee Group' Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics in theNatural Sciences John: Why is logic valid? For the same reason the rules of chess are valid: by definition. Its validity is presupposed. If you don't like chess, don't play. If you do then you have to play by the agreed rules. Else don't call it chess (or logic). Make a new name for your game. In logic, one begins with a rule that a proposition has exactly one of two values: true or false. Other games, like fuzzy logic, have additional "maybe" values, but we use the adjective "fuzzy" to distinguish these games (or rule sets). Other rules are added to define ways to relate (or compose) propositions in the form of conjunctions, disjunctions, etc; to build up structures. All players agree to the rules and knowledge and science progress. Some people don't like these games, so they don't play. Some people play badly and aren't much fun. Some make mistakes (called fallacies) that are hard to see by other players. Some prefer other rules, like "the highest authority is always right" or "there is no truth; only love". More great technical innovations result from playing the game of logic than playing these other games. John: Why is it useful to put together long strings of logical implications? This is probably a result of trivial observation; nature puts together long strings of related events of cause and effects; e.g. chemical reactions and planetary motions. We are merely recording what we see in the formal language of cause and effect, namely logic. In this case, logic is more of a historian's tool. --Rob Howard -----Original Message----- From: [hidden email] [mailto:[hidden email]] On Behalf Of John Kennison Sent: Monday, April 27, 2009 5:15 AM To: ForwNThompson; [hidden email] Cc: Sean Moody Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics in theNatural Sciences Nick et al, This is a great question, with, I think, two parts. The first part is why is logic valid. I am almost certainly a platonist or worse on this point --it's validity simply seems to be obvious. Can the proposition that logic is valid be supported by any argument that doesn't implicitly use logic? (Okay, even "implicitly" assumes logic). The argument that we evolved to be convinced by logical implications because it is useful for survival suggests that logic is, at least, approximately valid, which is a lot less of a conclusion than what I would want, and which doesn't explain why logic works in modern physics. The other part of the original question is, even if we grant that logic is valid (or at least approximately valid) why is it useful to put together long strings of logical implications? Believing that logical implications are trivially true, I wonder how can long chains of such implications be anything but trivial. (And if we believe that logic is at best approximately true, wouldn't long chains of implications stop being good approximations if each link in the chain is a little inaccurate.) Perhaps Physics somehow restricts itself to a domain where logic works very well. And maybe things like consciousness are simply outside that domain (but I hope not). I wonder if there is there a domain where logic is a useful approximation, but long chains of implications are not useful? Perhaps social analysis? Perhaps philosophy? Perhaps the humanities? Nick, and others,--I'd be curious about what you think on this issue. ---John ________________________________________ From: Nicholas Thompson [[hidden email]] Sent: Sunday, April 26, 2009 1:40 PM To: [hidden email] Cc: John Kennison; Sean Moody Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics in theNatural Sciences Owen, et al, Well, isn't this part of the broader mystery of why logic should get you anywhere in the study of nature? Isn't logic just a language trick? Why should nature give a fig for the tricks we play with our words? This is all reminding me, for some reason, of the "discovery" of the fact that the differential of the integral is just the original function. There seem to be two sorts of "discovery" in our discourse: One is the discovery of something in nature that we did not already know. The other is the discovery of a new implication in what we have already said that we did not anticipate when we said it. I can see why mathematics can help with the latter sort of "discovery", but have no idea why it should help with the former. In the emergence literature appears the endearing phrase "natural reverence". The early philosophical emergentists believed that one had to accept emergent properties with "natural reverence," since such properties could not be reduced to the properties of their parts. I am deeply ambivalent about natural reverence: one the one hand, I believe that there is no point in being a scientist if you are not prepared to experience some natural reverence. On the other hand, I also believe that natural reverence is the enemy of discovery. Perhaps "natural reverence" is a fleeting pleasure one gets before one gets down to the dirty business of figuring out how things work: too little of it and one would never be inspired; too much of it, and one would never be curious. Nick Nicholas S. Thompson Emeritus Professor of Psychology and Ethology, Clark University ([hidden email]<mailto:[hidden email]>) http://home.earthlink.net/~nickthompson/naturaldesigns/ ----- Original Message ----- From: Steve Smith<mailto:[hidden email]> To: The Friday Morning Applied Complexity Coffee Group<mailto:[hidden email]> Sent: 4/26/2009 10:17:16 AM Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics in theNatural Sciences Well said/observed David, I too am a Lakoff/Johnson/Nunez fan in this matter. While I am quite enamored of mathematics and it's fortuitous application to all sorts of phenomenology, Physics being somehow the most "pure" in an ideological sense, I've always been suspicious of the conclusion that "the Universe *is* Mathematics". This discussion also begs the age-old question of whether we are "inventing" or "discovering" mathematics. Similarly, it revisits the question of whether discoveries in mathematics portend discoveries in Physics (or other, "messier" phenomenological observations). - Steve Prof David West wrote: I'm completely of Tegmark's ilk: I assume that means you would also adhere to the sentiment attributed to Einstein: "How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?" Which contains the fallacy, "independent of experience." Thought - and mathematics! - is but a refined metaphor of experience. (following Lakoff) davew A different response, advocated by Physicist Max Tegmark (2007), is that physics is so successfully described by mathematics because the physical world is completely mathematical, isomorphic to a mathematical structure, and that we are simply uncovering this bit by bit. In this interpretation, the various approximations that constitute our current physics theories are successful because simple mathematical structures can provide good approximations of certain aspects of more complex mathematical structures. In other words, our successful theories are not mathematics approximating physics, but mathematics approximating mathematics. -- Owen ============================================================ 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 ============================================================ 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: The Unreasonable Reverence of The Unreasonable Effectiveness of Mathematics in theNatural Sciences
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In reply to this post by Steve Smith
Thus spake Steve Smith circa 04/26/2009 06:06 PM:
> Nicholas Thompson wrote: >> >> Why should nature give a fig for the tricks we play with our words? > > The Anthropic Principle might have a play in this. I think this is the fundamental reason for the unreasonableness. Math, like any other language, helps us be goal-oriented. And anything that helps us be goal-oriented will _seem_ true to us, regardless of whether it is true or not. This is the situation for just about any method: burning witches, hunting Communists, making marijuana illegal, worshiping mythical beings, meditating surrounded by crystals and incense, voodoo dolls, murdering people in foreign lands, torturing enemy combatants, etc. If it focuses our attention and allows us to maintain focus on some objective, then, as a tool, it _is_ useful and will _seem_ true. When it ceases to be useful, we will be surprised, sit back, and wonder why we were so enamored with it before... and many of us will even poke fun of and deride those people who still find it useful. -- glen e. p. ropella, 971-222-9095, http://agent-based-modeling.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 |
Re: The Unreasonable Effectiveness of Mathematicsin theNatural Sciences
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In reply to this post by John Kennison
John: "...what is it about logic that leads to more great
technical innovations than other games." Aren't those fun questions? I look at the logic operators as
a starting point. As operators, they have two inputs, A and B, which invoke 16
possible operators. The IMPLIES operator seems to be the most interesting one. It
typically interprets A to be the “before” state and B to be the “after”
state. And that’s just what we see in nature: related spatial states that
have lifetime; e.g. “the orange was on the table” and “the
orange is now on the floor”. Each state (or observation) is a static or
unchanging perception that lasts for a period of time. They are lines in
spacetime where each point on the line is the “same” as the others –
if you like that analogy. It’s more of a mental picture than actual
physics. It allows one person to say “lion!” and another to recognize
it. We all objectively see the same spatial static boundaries because we’re
mostly all copies of the same stuff. As soon as some point changes in some significant way, we call it the
end of the first state and the beginning of the second state. We observe that
these line segments are often and predictably close to each other. For example,
one line segment might be two balls rolling toward each other. The segment
represents the “the rolling toward each other” and not any one ball
rolling. A second segment (or observation) is the two colliding. A third is a
big crashing sound. Each of the three segments have the same spatial values and are
contiguous in time. That is, they all were observed “on the table” one
temporally after the other. So we use propositions to model the line segments
and IMPLIES to join them temporally or group them. The “composing”
operators (AND, OR, XOR, ...) are used to create complex propositions from
simpler ones. They build the statics. IMPLIES builds the dynamics. Together, we
describe observations in spacetime by noticing (1) where things do not change; sometimes
called statics, classes, noun phrases, or symmetries; and (2) where things do
change; sometimes called the dynamics, objects, or verb phrases. So logic is a formal system (having no ambiguities) that can be functional
composed (the results of an operator is a proposition) to convey one person’s
observations and rules to another person in a manner that convinces the first
person that the second person understood. When a person understands his or her own observations, or when people
understand each other’s observations, great technical innovations just
have to happen. It’s economics! A technical innovation is really judged
by its ability to manipulate nature to make lots of people happy. This means
understanding nature by understanding one’s observations (or drawing upon
historical observations of others); by understanding other people’s
problems and desires via statistics, marketing trends, and polls; and by
understanding the constraints of producing and delivering the innovation to
these customers. Logic does this most efficiently by eliminating contradiction
and ambiguity early in the process; hence it’s more efficient and faster
than other games in the context of technical innovations. My thoughts, Rob -----Original Message----- Robert: As you say, logic can be viewed as a game, like chess. You also say
that "More great technical innovations result from playing the game of
logic than playing these other games." The question then is what is it
about logic that leads to more great technical innovations than other games. --John ________________________________________ From: [hidden email] [[hidden email]] On Behalf
Of Robert Howard [[hidden email]] Sent: Monday, April 27, 2009 2:13 PM To: ' Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics
in theNatural Sciences John: Why is logic valid? For the same reason the rules of chess are valid: by definition. Its validity is presupposed. If you don't like chess, don't play. If you do
then you have to play by the agreed rules. Else don't call it chess (or
logic). Make a new name for your game. In logic, one begins with a rule that a proposition has exactly one of
two values: true or false. Other games, like fuzzy logic, have additional "maybe" values, but we use the adjective "fuzzy" to
distinguish these games (or rule sets). Other rules are added to define ways to relate (or
compose) propositions in the form of conjunctions, disjunctions, etc; to build
up structures. All players agree to the rules and knowledge and science progress. Some people don't like these games, so they don't play. Some people play badly and aren't much fun. Some make mistakes (called
fallacies) that are hard to see by other players. Some prefer other rules, like
"the highest authority is always right" or "there is no truth;
only love". More great technical innovations result from playing the game of logic
than playing these other games. John: Why is it useful to put together long strings of logical
implications? This is probably a result of trivial observation; nature puts together
long strings of related events of cause and effects; e.g. chemical reactions
and planetary motions. We are merely recording what we see in the formal language of cause and effect, namely logic. In this case, logic is more
of a historian's tool. --Rob Howard -----Original Message----- From: [hidden email] [mailto:[hidden email]] On
Behalf Of John Kennison Sent: Monday, April 27, 2009 5:15 AM To: ForwNThompson; [hidden email] Cc: Sean Moody Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics in theNatural Sciences Nick et al, This is a great question, with, I think, two parts. The first
part is why is logic valid. I am almost certainly a platonist or worse on this
point --it's validity simply seems to be obvious. Can the proposition that
logic is valid be supported by any argument that doesn't implicitly use
logic? (Okay, even "implicitly" assumes logic). The argument that we
evolved to be convinced by logical implications because it is useful for survival
suggests that logic is, at least, approximately valid, which is a lot less of a conclusion than what I would want, and which doesn't explain why logic
works in modern physics. The other part of the original question is, even if we grant that logic
is valid (or at least approximately valid) why is it useful to put
together long strings of logical implications? Believing that logical
implications are trivially true, I wonder how can long chains of such implications
be anything but trivial. (And if we believe that logic is at best
approximately true, wouldn't long chains of implications stop being good
approximations if each link in the chain is a little inaccurate.) Perhaps Physics somehow restricts itself to a domain where logic works
very well. And maybe things like consciousness are simply outside that
domain (but I hope not). I wonder if there is there a domain where logic is a useful
approximation, but long chains of implications are not useful? Perhaps social
analysis? Perhaps philosophy? Perhaps the humanities? Nick, and others,--I'd be curious about what you think on this issue. ---John ________________________________________ From: Nicholas Thompson [ Sent: Sunday, April 26, 2009 1:40 PM To: [hidden email] Cc: John Kennison; Sean Moody Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics in theNatural Sciences Owen, et al, Well, isn't this part of the broader mystery of why logic should get
you anywhere in the study of nature? Isn't logic just a language trick? Why should nature give a fig for the tricks we play with our words? This is all reminding me, for some reason, of the "discovery"
of the fact that the differential of the integral is just the original
function. There seem to be two sorts of "discovery" in our discourse:
One is the discovery of something in nature that we did not already know. The other is
the discovery of a new implication in what we have already said that we did
not anticipate when we said it. I can see why mathematics can help
with the latter sort of "discovery", but have no idea why it should
help with the former. In the emergence literature appears the endearing phrase "natural reverence". The early philosophical emergentists believed
that one had to accept emergent properties with "natural reverence," since
such properties could not be reduced to the properties of their parts. I am
deeply ambivalent about natural reverence: one the one hand, I believe
that there is no point in being a scientist if you are not prepared to experience
some natural reverence. On the other hand, I also believe that natural
reverence is the enemy of discovery. Perhaps "natural reverence"
is a fleeting pleasure one gets before one gets down to the dirty business of
figuring out how things work: too little of it and one would never be inspired; too
much of it, and one would never be curious. Nick Nicholas S. Thompson Emeritus Professor of Psychology and Ethology, http://home.earthlink.net/~nickthompson/naturaldesigns/ ----- Original Message ----- From: Steve Smith<mailto:[hidden email]> To: The Friday Morning Applied Complexity Coffee Group<mailto:[hidden email]> Sent: 4/26/2009 10:17:16 AM Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics in theNatural Sciences Well said/observed David, I too am a Lakoff/Johnson/Nunez fan in
this matter. While I am quite enamored of mathematics and it's fortuitous
application to all sorts of phenomenology, Physics being somehow the most
"pure" in an ideological sense, I've always been suspicious of the conclusion that
"the Universe *is* Mathematics". This discussion also begs the age-old question of whether we are
"inventing" or "discovering" mathematics. Similarly, it revisits the
question of whether discoveries in mathematics portend discoveries in Physics (or other, "messier" phenomenological observations). - Steve Prof David West wrote: I'm completely of Tegmark's ilk: I assume that means you would also adhere to the sentiment attributed
to Einstein: "How can it be that mathematics, being
after all a product of human thought which is independent of experience, is
so admirably appropriate to the objects of
reality?" Which contains the fallacy, "independent of
experience." Thought - and mathematics! - is but a refined metaphor of experience. (following Lakoff) davew A different response, advocated by Physicist Max Tegmark
(2007), is that physics is so successfully described by mathematics because the physical world is completely mathematical, isomorphic to a mathematical structure, and that we are simply uncovering this bit by bit. In this interpretation, the various approximations that constitute our current physics theories are successful because simple mathematical structures can provide good approximations of certain aspects of more complex mathematical structures. In other words, our successful theories are not mathematics approximating physics, but mathematics approximating mathematics. -- Owen ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at lectures, archives, unsubscribe, maps at http://www.friam.org ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at lectures, archives, unsubscribe, maps at http://www.friam.org ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at lectures, archives, unsubscribe, maps at http://www.friam.org ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at lectures, archives, unsubscribe, maps at http://www.friam.org ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at 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: The Unreasonable Reverence of The Unreasonable Effectiveness of Mathematics in theNatural Sciences
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In reply to this post by glen e. p. ropella-2
Very well said, methinks.
An approach needn't even lose it's utility to poke fun at it, it merely has to lose "Universal Utility". I believe many folk remedies, crafts, knowledge fall into that category. They become "vestigal" knowledge for entire generations until circumstances drift far enough (or abruptly enough) that they become the only or best (known) answer to a given problem (again). Come the revolution, we'll all be chewing willow bark and slippery elm to relieve what ails us, and laughing at our forefathers who thought all medicine had to be manufactured and shipped in a bottle. In the meantime, such remedies seem somewhere between "quaint" and "absurd". glen e. p. ropella wroteth circa early c21: Thus spake Steve Smith circa 04/26/2009 06:06 PM: ============================================================ 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: The Unreasonable Reverence of The Unreasonable Effectiveness of Mathematics in theNatural Sciences
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Awhile ago on this thread I said that mathematics is effective because there are regularities in nature. No one commented on that. There have been many comments discussing whether what goes on in our minds matters, but very little about what goes on outside our minds. It's amusing to poke fun at the way some people think, but I'm not sure it gets us anywhere.
Are there regularities in nature? If so, then why is it surprising that mathematics is useful for describing them? On the other hand, one might claim that even asking that question is imposing our (perhaps foolish) mental model of what we mean by regularities on nature. But taking that stance suggests that we can't get out of our minds at all and there is no point in having this discussion. So which side are you on? Is it useful to share with each other what goes on in our (separate) minds? Is it possible that what goes on in our minds can be mapped onto what goes on in nature? Or is there no point in attempting to exchange thoughts since they are all just internal foolishness? Evolution suggests that it is not all just internal foolishness. If it were we wouldn't have evolved to have these thoughts. One could argue that that thought itself is just as much internal foolishness as any other. But then why bother to write it down and send it to this list? -- Russ On Tue, Apr 28, 2009 at 11:16 AM, Steve Smith <[hidden email]> wrote:
============================================================ 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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