Humanistic Mathematics Network Journal最新文献

Humanistic Mathematics Network Journal Pub Date : 2002-06-01 DOI: 10.5642/HMNJ.200201.26.09

D. Joyner, P. Lejarraga

{"title":"Notes on Formal Constructivism","authors":"D. Joyner, P. Lejarraga","doi":"10.5642/HMNJ.200201.26.09","DOIUrl":"https://doi.org/10.5642/HMNJ.200201.26.09","url":null,"abstract":"Our aim is to sketch some ideas related to how we (as in, we two) think we (as in, we humans) think. \"That theory is useless. It isn't even wrong.\" Wolfgang Pauli. Our hope in this paper is to provide a theory, admittedly somewhat vague, of how we think about mathematics. We also hope our ideas do not cause the reader to be reminded of Pauli's quote above. These notes were motivated by the interesting book by Changeaux and Connes [CC]. REALISM VS CONSTRUCTIVISM Realism: Mathematical objects exist independently of experience (or \"physical reality\") which we process using our senses (smell, touch, sight, ... ) and interpret using our brain. For example, Descartes speaks of a triangle as an \"immutable and eternal\" figure whose existence is independent of the mind which imagines it. Similar statements are made regarding God by many religious experts. Constructivism: Mathematical objects exist solely in the mind as a certain electro-chemo-biological pattern of neurons, synapses, chemicals, ... in the brain. For an extreme example, Hume believed that ideas are merely copies of sense impressions. Examples: Alain Cannes (and probably most mathematicians) are realists. For example, the famous quote of Kronecker's, \"The integers are made by God, all else is made by man,\" indicates a realist point-of-view. On the other hand, the biologist Jean Pierre Changeux and philosopher David Hume are constructivists (though Hume is the more extreme). Poincare was possibly a constructivist in this sense (see [D], chapter 9). The realist position might be roughly summarized as 28 follows: The physical world is modeled as much as possible by mathematics. Mathematicians merely discover what is already in existence. The constructivist position might be summarized as follows: Models for the physical world are constructions of the mind (only) and all such mental constructs exist solely as electro-chemo-biological patterns of neurons, ... in the brain. To the question, \"Why is mathematics so well-suited to the description of physics?\", the constructivist might counter that physicists tend to examine reproducible phenomena which tend to have \"universal\" characteristics. Hence mathematics, which is also universal, is admirably suited for physical description. POINTS OF AGREEMENT • Mathematics provides a \"universal language\", i.e., a grammar and set of terms which can be understood by anyone (sufficiently trained), independently of their cultural background. • There is a \"physical world\" independent of our mind (which, however, we sense using our brain and sensory organs). • Mathematical objects can be represented as a certain electro-chemo-biological pattern of neurons, synapses, chemicals, ... in the brain. • A given mathematical construction can be represented as a program in a \"Turing machine\". (Using an over-simplification, these representations are modeled using neural networks, which are related to Turing machines [M].) FORMAL CONSTRUCTIVISM AssoRTED THOUGHTS OF OuR OwN •","PeriodicalId":176215,"journal":{"name":"Humanistic Mathematics Network Journal","volume":" 1226","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120826632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Letters and Comments, Issue 26, 2002 书信与评论，2002年第26期

Humanistic Mathematics Network Journal Pub Date : 2002-06-01 DOI: 10.5642/HMNJ.200201.26.24

D. Tahta

引用次数: 0

Teaching As Though Students Mattered: A Biography of Alvin White As Told to Sandra Keith 《学生至上的教学:阿尔文·怀特对桑德拉·基思的传记

Humanistic Mathematics Network Journal Pub Date : 2002-06-01 DOI: 10.5642/HMNJ.200201.26.22

A. White, Sandra Z. Keith

引用次数: 1

Pat's Prologues: Introductions to the First Two Airings of Math Medley, A Radio Talk Show. 帕特的开场白:介绍数学杂烩前两次播出，一个广播谈话节目。

Humanistic Mathematics Network Journal Pub Date : 2002-06-01 DOI: 10.5642/HMNJ.200201.26.08

P. C. Kenschaft

{"title":"Pat's Prologues: Introductions to the First Two Airings of Math Medley, A Radio Talk Show.","authors":"P. C. Kenschaft","doi":"10.5642/HMNJ.200201.26.08","DOIUrl":"https://doi.org/10.5642/HMNJ.200201.26.08","url":null,"abstract":"Humanistic Mathematics Network Journal #26 25 stone in Basle. Today, the double helix carries both a biological meaning as well as an intimation of human destiny. In my childhood, the circle persisted as a potent magic figure in the playtime doggerel \"Make a magic circle and sign it with a dot.\" The interested reader will find thousands of allusions to the phrase \"magic circle\" on the Web. Magic ellipses or rectangles are less frequent. The Buddhist mandalas which are objects of spiritual contemplation, embody highly stylized geometrical arrangements. The amulets and talismans that are worn on the body, placed on walls, displayed in cars; the ankhs, the crosses, the hexagrams, the outlined fish, the horseshoes, the triangular abracadabra arrangements and magical squares, the sigils (magical signs or images) of which whole dictionaries were compiled in the 17th century, the hex signs placed on house exteriors, all point to geometry in the service of religious or quasi-religious practice. There is a multitude of geometrical figures signs employed in kabbalistic practices, each associated with stars, planets, metals, stones, spirits, demons, and whose mode of production and use is specified rigorously. Wallis Budge, student of Near Eastern antiquities wrote: According to Cornelius Agrippa [physician and magician, 1486-1535], it is necessary to be careful when using a magical square as an amulet, that it is drawn when the sun or moon or the planet is exhibiting a benevolent aspect, for otherwise the amulet will bring misfortune and calamity upon the wearer instead of prosperity and happiness. Let semanticists and semioticists explain the relationship between our geometrical symbols and our psyches for it lies deeper than simple designation (e.g., crescent = Islam). The geometrical swastika, which over the millennia and cultures has carried different interpretations, is now held in abhorrence by most Americans. The memory of World War II is certainly at work here, but the geometry can go \"abstract\" and its meaning become detached from an original historic context. Why has Salvador Dali (1904-1989) in his large painting Corpus Hypercubus in the Metropolitan Museum in New York, placed a crucifixion against a representation of a four dimensional cube? Art historian Mar-tin Kemp has commented: Dali's painting does stand effectively for an age-old striving in art, theology, mathematics, and cosmology for access to those dimensions that lie beyond the visual and tactile scope of the finite spaces of up-and-down, left and right, and in-and-out that …","PeriodicalId":176215,"journal":{"name":"Humanistic Mathematics Network Journal","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117003916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

When Is a Math Problem Really "Real"? 什么时候数学问题才是真正“真实的”?

Humanistic Mathematics Network Journal Pub Date : 2002-06-01 DOI: 10.5642/HMNJ.200201.26.13

M. E. Goldberg

引用次数: 0

Magic in a Box 盒子里的魔法

Humanistic Mathematics Network Journal Pub Date : 2002-06-01 DOI: 10.5642/HMNJ.200201.26.17

Lacie Juris

引用次数: 0

Marcy's Dots: A Problem on National Test Revisited 马西的斑点:重新审视全国考试中的一个问题

Humanistic Mathematics Network Journal Pub Date : 2002-06-01 DOI: 10.5642/hmnj.200201.26.11

Patricia Baggett, A. Ehrenfeucht

引用次数: 0

Special Section: On the Publication of the 26th Issue of the Humanistic Mathematics Network Journal 专题:《人文数学网络学报》第26期出版

Humanistic Mathematics Network Journal Pub Date : 2002-06-01 DOI: 10.5642/HMNJ.200201.26.21

Sandra Z. Keith

引用次数: 0

Humanizing Mathematics: The Humanistic Impression in the Course for Mathematics Teaching. 数学人性化:数学教学过程中的人文印象。

Humanistic Mathematics Network Journal Pub Date : 2002-06-01 DOI: 10.5642/HMNJ.200201.26.06

A. Katsap

引用次数: 1

History of Mathematics, an Intuitive Approach 数学的历史，一个直观的方法

Humanistic Mathematics Network Journal Pub Date : 2002-06-01 DOI: 10.5642/HMNJ.200201.26.05

A. Garciadiego

{"title":"History of Mathematics, an Intuitive Approach","authors":"A. Garciadiego","doi":"10.5642/HMNJ.200201.26.05","DOIUrl":"https://doi.org/10.5642/HMNJ.200201.26.05","url":null,"abstract":"The main goal of this essay is to discuss, informally, an intuitive approach to the history of mathematics as an academic discipline. The initial point of departure includes the analysis of some traditional definitions of the concept of 'history' taken from standard dictionaries. This concise dissection attempts to suggest the complexity of the discipline. The term 'history' is familiar to almost everyone, and most people believe they know its meaning intuitively. The lay person sometimes thinks of history in terms of dates, names, places and of colorful anecdotes on interesting characters. History provides a record of where someone lived and what he did. In short, history is the repository of the past. But what exactly is the history of mathematics as an academic discipline? The events that took place yesterday are now part of history. Photographs are history: they reflect the way we once were. History is studied in elementary school, especially that of student's native countries. Teachers, who often seem old enough to have taken part in some of the historical events, teach-over and over again-anecdotes, names, places, dates, and so on. Historical movies, TV programs and books are popular. The media affects the way people understand history as a discipline. Unfortunately, sometimes the public's knowledge of important historical issues is derived from the popular media (especially movies), and not from professional sources. Thus, their understanding of these events can be distorted. Unlike the word mathematics, the term history is used on a daily basis by the news media. Some reporters may believe that history is actually being made when they type or read the news. On occasions, reporters and anchormen have trouble attempting to disassoci-ate themselves from the event they are reporting on. Of course, in most cases, the term history is misused by professional reporters. Often, for example, TV sports commentators discuss player's individual records while narrating a baseball game. These statistics include the player's batting average, number of times at bat in the game, number of stolen bases, etc. Sometimes, the commentators also narrates the player's background. They mention the college the player attended; where he played in the minor leagues, his previous professional teams and so on. The commentator may also discuss some of the player's qualities as a human being (e.g., generosity, sportsmanship). Then, the sportscaster may try to explain why the player was motivated to become a professional. After the commentator has finished …","PeriodicalId":176215,"journal":{"name":"Humanistic Mathematics Network Journal","volume":"108 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128689134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2