今本《周易》卦序排列数学规律新探

今本《周易》六十四卦卦序是依据什么道理排列出来的,迄今仍然没有一个完美的解答。本文尝试把卦序问题作为一个数学问题去考虑,探讨卦序的制作者所依据的数学思想与技巧。《六十四卦错综图》是我们研究序卦最重要的参考图,并指出十对三明三阳卦在序卦排列中起着骨架作用．无论是十对三明三阳卦,还是围绕这十对卦左右的其它卦,其排列在序数配置、卦区划分和爻画布排等诸多方面都蕴含着丰富的数学内容,充分反映了序卦的制作者运用数学技巧的娴熟技艺和精妙构想。     

《序卦》卦序中的阴阳平衡互补与变通配四时思想

《周易》的基本思想是讲“生生之易”,而一切生命与变化归根到底来源于天地日月的运行与四时的变化,因而《周易》的核心思想在于阐述天地日月的运行与四时的变化以及人如何效法、因循天地日月的运行与四时变化而成德广业、开物成务。本文认为,《序卦》卦序正是以这一思想作为“易简”原则构造出来的一个象数体系,因而,《序卦》卦序体现了《周易》的核心思想,具有相当重要的地位,值得我们深入研究。而且,《序卦》卦序这种以一定思想作为“易简”原则构造出来的象数体系,是一种古老而又独特的形式化的体系,对于我们今天构造形式化的辩证逻辑体系具有重要的启发意义。     

《周易》卦序二题

卦序问题是《周易》象数学的主要问题之一。孔颖达明确提出《周易》经文六十四卦次序以“二二相耦,非覆即变”为基本原则。这一原则直接推动了《周易》上下经卦数不均问题和“观象系辞”问题的研究。上下经互变之卦的数量不均,是导致上下经总卦数不等的直接原因,而之所以如此安排又有其特殊之用意。诸卦“非覆即变”之象是作《易》者名卦和系辞的重要原则,因而较之于马王堆帛书《周易》卦序,传世本《周易》卦序应当是更为原始的卦序。《周易》经文卦序从整体架构到具体组合排布都有一定规则在其中。     

《周易·序卦传》爻象变化规律之试释

《周易·序卦传》爻象变化规律之试释刘蕙孙（一）《易》的卦序次第,古代《连山》、《归藏》、《周易》等三“易”文献无征,无可叙述,今言《易》序惟《周易》卦序及宋先天图卦序两种,先天图卦序完全是符号自然变化,简明易解,不论。《周易》卦序,则是两千年一个勘不...     

帛书《周易》卦序与宇宙论

帛书<周易>六十四卦卦序以上下卦相重,反映了卦的变化的思想,其上卦体现了"分阴分阳"的阴阳分类观念,其下卦则既体现了阴阳交错、阴阳相配的观念,又体现了正位的观念.更重要的是,帛<易>八卦序列与<大戴礼记·易本命>、<孔子家语·执辔>等典籍中所暗含的具有独特宇宙论意义的八卦序列具有相关性,由此我们提出一种设想,帛<易>八卦序列很可能反映的也是这种独特宇宙论思想.     

楚竹书《周易》中的特殊符号与卦序问题

濮茅左先生通过对战国楚竹书<周易>中出现的独特红、黑符号的分析,提出了竹书<周易>卦序是一种与今本、帛本等都不相同的另一种卦序.其分析虽然不无道理,可以作为竹书卦序的一种可能的方案,但其分析也有致命的弱点,就是他不能合理解释竹书中的红、黑符号在今本卦序中为什么具有如此强的规律性,甚至具有比其确立的所谓竹书卦序更有对称性.为此,我们通过分析认为,竹书卦序运用的很可能就是今本卦序,是运用今本卦序来表达宇宙天地、万物与人类的演化与发展阶段.如果这一分析成立,那么,我们将会进一步发现一种前所未见的在阴阳学说统摄下的包含"三段论""四段论"和"七段论"为一体的丰富、系统而又独特的事物发晨阶段论.     

《序卦》卦序中的“参伍”“错综”思想

今本《周易》六十四卦卦序即《序卦》卦序,是根据一定象数原则有规律地排列出来的,而这种象数原则又体现了当时人的宇宙观及《易》的基本精神。三才、五行及错综变化思想是古人宇宙观的基本内容之一,也是易学的基本内容之一,而在《序卦》卦序建构所运用的诸多象数原则中,就有"参伍"错综"原则。     

《周易》古经的解释原则兼释《离》、《兑》二卦

本文考察了<周易>古经的成书及流变过程,提出了解释<周易>古经应该遵循的五个基本原则.据此,笔者对<周易>古经中的<离>卦、<兑>卦作出了新的解释.作者认为,<离>卦以狼群袭击人类喻异族入侵.其中的"离"就是狼.狼很可能是异族入侵者的图腾,也是对该族人的称呼.笔者认为,<兑>卦反映了先秦比较常见的巫术之——"说"."说"是向神灵祈祷的一种巫术.从出土的占卜材料来看,占卜时若遇到有"忧"或有"祟",贞人往往建议人们进行"说"以除之.     

评孙利先生以幻方推演《周易》卦序的研究

<正>孙利先生自80年代中期开始探索各种卦序的来历问题,经过几十年的努力,他找到了一个以幻方推演诸种卦序的统一方法和途径。相比其他研究,孙利先生的方法条件设定最为简洁,且具有很强的可操作性,更突出的是,其也是目前唯一能够完整推演出《杂卦传》卦序和孟喜卦气卦序的方法。本期刊发的是他用幻方推演今本《周易》古经卦序的成果,其他成果将在日后陆续刊发。总体     

论《周易》古经卦序构造的数学原理——先天六十四卦到今本卦序的幻方推演

用先天六十四卦的序数构建一个八阶幻方,要求非覆即变的两卦必须在幻方中上下相邻,互补数亦尽可能上下相邻。然后采用迭代的方法给幻方中的各卦重新编号,奇数行的三十二卦按从右至左、自下而上的顺序依次编号1-32,偶数行的三十二卦按从左至右、自上而下的顺序依次编号33-64,从而使上下相邻的两卦既非覆即变又互为补数,即可得到一幅迭代图。取此迭代图中的六十四卦序号,遵循上下两卦非覆即变且互为补数的原则,构造新的幻方,然后采用相同的迭代规则又可以导出一幅迭代图。重复上述步骤,总共可以得到九个幻方和九幅相应的迭代图,之后便进入循环。其中,居中的第五个幻方按特定方式展开,即是按今本卦序排列的上经三十卦和下经三十四卦。笔者认为,这是目前所知的今本卦序最简单的构造原则,也应当是《周易》古经卦序的真实来源。     

From Freud to Gehrig to Rapaport to DiMaggio

Lacking the size, talent, and speed to play shortstop for the New York Yankees, I chose instead to become a psychologist/psychoanalyst. Yet, baseball and psychoanalysis share much in common. Each is played in the inner diamonds of one's mind, values the past and what is passing, and requires a strong work ethic. Both are timeless and involve an almost boring leisureliness between occasional moments of crisis. Then too, each calls for an attitude of consistency and patience and a responsibility to do one's best. From my parents and brother to my wife and son and his family, from my teachers and supervisors to my colleagues, and from Menninger to the Society for Personality Assessment (SPA), I feel deeply grateful for the partners and teammates I have and have had.     

From Biology to Consciousness to Morality

Abstract. Social animals are provisioned with prosocial orientations that operate to transcend self‐interest. Morality, as used here, describes human versions of such orientations. We explore the evolutionary antecedents of morality in the context of emergentism, giving considerable attention to the biological traits that undergird awareness and our emergent human forms of mind. We suggest that our moral frames of mind emerge from our primate prosocial capacities, transfigured and valenced by our symbolic languages, cultures, and religions.     

How Not to Apply to College

Samples of letters written by college students are excerpted to demonstrate the deterioration of students' writing skills. The relative unimportance many college students and graduates attach to the art of writing letters of inquiry is emphasized. A checklist is provided to assist students in preparing letters requesting information from colleges and universities.     

From object to image to object

Images are mental representations accommodated by grammatical structures. These structures order sensori-input of information as well as provide for articulated ways of expressing motor sequences associated with images. The psychological process of perception is reflected in the development of paradigmatic structures. The psychological process of action (behavior and its mental representations) is reflected in the development of syntagmatic structures. Forming and expressing imagery requires both paradigmatic and syntagmatic structuring. The former relates to logical issues of identity of objects and to the formation of concepts. The latter relates to the solution of psycho-logical questions of causality through articulation of grammatical roles in sentences. Two issues affecting the formation of a model to account for imagery are examined: (1) The tendency to explain imagery as a result of motor sequences and to utilize performance grammar. (2) The impact of ontogenesis on social processes affecting the logical and psycho-logical concerns facing the person at different stages of development. The grammar of imagery is seen as broader than one of performance. The epistemology of imagemaking does not reflect a linear ontogenetic development which precludes attention to problems of creating the logical structures of an object.     

Reply to Letter to the Editor

The current policy of the National Institute of Health designed to increase the participation of women and minorities is radically different from previous policies designed to protect minorities from abuses in research studies. The principal arguments to support this policy are twofold: 1) Increased representation of minorities and women in research would increase the generalizability of research data and allow for valid analyses of differences in subpopulations; and 2) being in a clinical research study is advantageous to participants regardless of the final research study results. It remains unclear whether minorities find these arguments compelling. Instead of telling minorities that participation in research is good for them, the research community should focus on understanding what minority communities want from clinical research and then tailoring the message to meet this need. Persuasive arguments to promote long-term increased representation of minorities in clinical research must come from within minority communities.