tag:blogger.com,1999:blog-4843467029909324968.comments2011-03-28T08:04:12.520+02:00Tolle et legeRafael Ignacio Purasnoreply@blogger.comBlogger5125tag:blogger.com,1999:blog-4843467029909324968.post-83486282284273186242011-03-28T04:38:09.720+02:002011-03-28T04:38:09.720+02:00The picture of the centennial bridge in panama is ...The picture of the centennial bridge in panama is wrongSofia Millannoreply@blogger.comtag:blogger.com,1999:blog-4843467029909324968.post-57966340140572699472010-11-30T06:29:54.528+01:002010-11-30T06:29:54.528+01:00As I read this paper I realized that I have had th...As I read this paper I realized that I have had the same feeling as Hamming about the "unreasonable effectiveness of mathematics" and asked the same question that he was asking in the paper, i.e., "Why is mathematics so unreasonably effective in the sciences?"<br /><br />I have almost completed the first draft of a proposal for developing and teaching a course or series of courses, entitled Research and Knowledge Generation. Interestingly, within this proposal one section deals with the question, "What is mathematical knowledge?" and within that section a subsection deals with Hamming's question, in slightly different words.<br /><br />The following is that subsection in first draft form.<br /><br />Sterling Portwood, csp@hawaii.rr.com<br /><br />Center for Interdisciplinary Science<br /><br /><br />9) Why does mathematics happen to be the language of science? Discuss.<br /><br />Actually this is not just a happenstance. In fact it is hard to imagine that it could be any other way. Mathematics is not a free-form language like English; it is a sequence of logically necessary, connected steps from beginning to end; ultimately a tautology. In fact a discourse in (i.e., a branch of) mathematics is a specific instance of the application of logic; it is a subset of logic which is still logic. Therefore mathematics is, in the final analysis, logic. <br /><br />Determining the value of an unknown in an algebraic equation is simple, but algebra is not absolutely required to attain the result. One could simply start from scratch and use logic alone, rather than the rules of algebra, and still obtain the answer, but with greater difficulty, and as the complexity of the problem increases, the difficulty of the solution using logic alone goes up exponentially. Hence mathematics does not yield a result which transcends logic; it is simply a short hand composed of rules of manipulation (previously derived from a foundational axiom set) which makes it comparatively easy to arrive at a logical implication or consequence. <br /><br />So, given an appropriate scientific theory, logic alone could eventually lead to an implication flowing from that scientific theory, but often with great difficulty. Hence, as indicated in Subsection 8 above, if the portion of science under consideration satisfies (i.e., is consistent with) the foundations (i.e., the primitives, the definitions, and the axioms) of the mathematical discourse, the logical connection between the beginning of a scientific calculation and the end (i.e., the prediction, the extension, the inference, etc.) of the mathematical manipulation is solid, like an ax handle can be swung at a tree with confidence that the ax head will follow. <br /><br />With these understandings, it should be clear and reasonable why mathematics is so "unreasonably" effective in the sciences.Sterling Portwoodhttp://causalstatistics.orgnoreply@blogger.comtag:blogger.com,1999:blog-4843467029909324968.post-34298758810788832612010-07-07T10:16:21.067+02:002010-07-07T10:16:21.067+02:00Muy interesante, aunque no comprendo del todo el ú...Muy interesante, aunque no comprendo del todo el último párrafo.Alejandrohttp://www.ingenierotraductor.comnoreply@blogger.comtag:blogger.com,1999:blog-4843467029909324968.post-90618991114992087392010-06-25T07:42:57.976+02:002010-06-25T07:42:57.976+02:00Pues me temo lo peor con la Sagrada Familia porque...Pues me temo lo peor con la Sagrada Familia porque las personas que dirigen España no son de lo más "cuidadosas" con lo religioso.eleuhttps://www.blogger.com/profile/05529942190835880316noreply@blogger.comtag:blogger.com,1999:blog-4843467029909324968.post-441530034701475352010-05-23T22:16:25.146+02:002010-05-23T22:16:25.146+02:00!Qué gran verdad decir que la oración no sólo nos ...!Qué gran verdad decir que la oración no sólo nos acerca a Dios sino que nos es imprescindible!<br /><br />En verdad, el católico que no hace uso frecuente de la oración se queda seco porque el agua viva de Dios no le llega.eleuhttps://www.blogger.com/profile/05529942190835880316noreply@blogger.com