tag:blogger.com,1999:blog-1812431336777691886.post305462853605129932..comments2024-02-29T03:57:00.088-05:00Comments on The Mermaid's Tale: The poetry of scienceAnne Buchananhttp://www.blogger.com/profile/09212151396672651221noreply@blogger.comBlogger10125tag:blogger.com,1999:blog-1812431336777691886.post-12848938938845300612010-02-16T11:25:46.906-05:002010-02-16T11:25:46.906-05:00I would say your question is a non-question in the...I would say your question is a non-question in the following sense: mathematics is a way of systematizing logical reasoning and describing things of the world.<br /><br />I think a hard-core mathematophile would say that competitive exclusion could be expressed mathematically within evolutionary or population ecological theory. Whether that gains anything is an open question.<br /><br />Math, to me, often forces things to be more regular and systematic than they may really be, esp. if there is a probabilistic element or the system in question is very complex.<br /><br />So asserting the need for mathematics may be a way of scientist self-congratulation, or a way of hiding unrealism behind intimidating appearance of rigor.<br /><br />But if the rules of logic can legitimately be taken to be true--a debatable point, perhaps--then since mathematics and logic are largely isomorphic, the mathematics above all argument would be relevant.<br /><br />However, we know since Godel that many things in mathematical logic are, like the many body problem in physics, not soluble or knowable.Ken Weisshttps://www.blogger.com/profile/02049713123559138421noreply@blogger.comtag:blogger.com,1999:blog-1812431336777691886.post-65584875662087053822010-02-16T10:39:12.674-05:002010-02-16T10:39:12.674-05:00But must laws necessarily be mathematical?
Take f...But must laws necessarily be mathematical?<br /><br />Take for example Gause's Law, or the competitive exclusion principle, which states that two competing species cannot coexist given that all other ecological factors are held constant. Though predictive models support this conclusion, it was not formulated or expressed in mathematical terms.<br /><br />I would say the same goes for the conservations laws, which CAN be expressed in mathematical terms and which apparently fall out of mathematically-derived physical theorem but which were initially deduced through repeated experiment independently of mathematics.Arjunhttps://www.blogger.com/profile/04388786712611397453noreply@blogger.comtag:blogger.com,1999:blog-1812431336777691886.post-33123382559824891632010-02-16T10:05:32.663-05:002010-02-16T10:05:32.663-05:00I think it was Isaac Newton who said something to ...I think it was Isaac Newton who said something to the effect that if you can't put it in mathematical terms, it isn't science. <br /><br />I don't agree with that, but mathematics is nothing more than attempting to express regularities in nature (or for some pure math, the imagination)<br /><br />Anyone interested in this would enjoy listening to last week's BBC discussion of mathematics and unintended consequences (BBC4, the program called In Our Time), which presents math in just this way--a means of expression regularities in nature.Ken Weisshttps://www.blogger.com/profile/02049713123559138421noreply@blogger.comtag:blogger.com,1999:blog-1812431336777691886.post-18615764499979404022010-02-16T09:45:45.290-05:002010-02-16T09:45:45.290-05:00I've been batting around myself the idea of sc...I've been batting around myself the idea of science as an endeavor to elucidate patterns in nature, preferably in the form of powerful generalizations.<br /><br />Aren't natural 'laws' such patterns summarizing masses of data we've gathered on the world?Arjunhttps://www.blogger.com/profile/04388786712611397453noreply@blogger.comtag:blogger.com,1999:blog-1812431336777691886.post-2969464833134796222010-02-15T13:56:14.578-05:002010-02-15T13:56:14.578-05:00There is probably another element to this, which i...There is probably another element to this, which is probably the same aspects of brain function are involved in many aspects of what seems like 'rigorous' science. Intuition in the sciences is probably similar to that in the arts, and likewise things like pattern recognition, and so onKen Weisshttps://www.blogger.com/profile/02049713123559138421noreply@blogger.comtag:blogger.com,1999:blog-1812431336777691886.post-44520924754992823602010-02-15T12:45:58.415-05:002010-02-15T12:45:58.415-05:00The first episode in the BBC Discovery series was ...The first episode in the BBC Discovery series was an interview with a cardiologist who left the field to become a sculptor, and 10 years later went back into cardiology, equipped with many new skills that he now uses in practice. So, yes, exactly, Arjun. And, thanks for the book reference.Anne Buchananhttps://www.blogger.com/profile/09212151396672651221noreply@blogger.comtag:blogger.com,1999:blog-1812431336777691886.post-15945818084549224772010-02-15T12:40:40.594-05:002010-02-15T12:40:40.594-05:00This entry reminds me of ArtScience, a book I'...This entry reminds me of ArtScience, a book I'm currently reading by David Edwards that investigates how certain individuals have crossed from art into science or vice versa in trying to understand or help the world-- for example, a cell biologist who gained insight into cytoskeletal structure from his experience with 3-D sculpting, or the chemical engineer who saw parallels between mixing paints and the mechanism of fluid mixing in general, or the concert pianist-turned -electrical engineer who uses principles from chaos theory to generate musical variation in original works.Arjunhttps://www.blogger.com/profile/04388786712611397453noreply@blogger.comtag:blogger.com,1999:blog-1812431336777691886.post-21651150014498859442010-02-15T10:08:15.070-05:002010-02-15T10:08:15.070-05:00Yes yes. And there's ALWAYS something to disco...Yes yes. And there's ALWAYS something to discover!Holly Dunsworthhttps://www.blogger.com/profile/05260104967932801186noreply@blogger.comtag:blogger.com,1999:blog-1812431336777691886.post-57408526865003346122010-02-15T09:09:23.878-05:002010-02-15T09:09:23.878-05:00Paleontology is a great example, isn't it, Hol...Paleontology is a great example, isn't it, Holly? I imagine that paleontologists have to love the whole process of discovery -- whether or not they discover anything.Anne Buchananhttps://www.blogger.com/profile/09212151396672651221noreply@blogger.comtag:blogger.com,1999:blog-1812431336777691886.post-82725742358197073992010-02-15T08:40:13.585-05:002010-02-15T08:40:13.585-05:00Hear hear.Hear hear.Holly Dunsworthhttps://www.blogger.com/profile/05260104967932801186noreply@blogger.com